Length of the platform at the front of the room whose area is 3x² + 10x - 8 and width is (x+4) m is (3x - 2) m
Area of the rectangular platform = 3x² + 10x - 8
Width of the rectangular platform = x+4
Area = length × width
Length = area/width
Length = [tex]\frac{3x^{2} + 10x - 8}{x+4}[/tex]
By splitting the middle term we get
Length = [tex]\frac{3x^{2} + 12x -2x -8 }{x+4}[/tex]
By taking common we get
Length = [tex]\frac{3x(x+4) - 2(x+4)}{x+4}[/tex]
By taking x+4 common we get
Length = [tex]\frac{(3x-2)(x+4)}{x+4}[/tex]
Cutting the x+4 from denominator and numerator we get
Length = 3x-2
Length of the platform at the front of room is 3x-2
To know more about area click here :
https://brainly.com/question/27683633
#SPJ4
In Exercises 1-11, calculate all four second-order partial derivatives and check that fxy = fyx. Assume the variables are restricted to a domain on which the function is defined. 1. f(x,y) = (x + y)2 2. f(x,y) = (x + y) 3. f(x,y) = 3x"y + 5xy! 4. f(x,y) = 2xy 5. f(x,y) = (x + y)ey 6. f(, y) = xe 7. f(x, y) = sin(x/y) 8. f(x,y) = x2 + y2 9. f(x, y) = 5x®y2 - 7xy? + 9x² +11 10. f(x, y) = sin(x2 + y2) 11. f(x, y) = 3 sin 2x cos 5y
For each function, all four second-order partial derivatives are f(x,y) are (x + y)2, (x + y), 3x^2y + 5xy^2, 2xy, (x + y)e^y, xe^y, sin(x/y), x^2 + y^2, 5x^3y^2 - 7xy^3 + 9x^2 +11, sin(x^2 + y^2) and 3 sin(2x) cos(5y). It is proved that f x y is equals to f y x.
f(x,y) = (x + y)2
f x x = 2, f xy = 2, f yx = 2, f y y = 2
Since f x y = fy x, the mixed partial derivatives are equal.
f(x,y) = (x + y)
f x x = 0, f x y = 1, f y x = 1, f y y = 0
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = 3x^2y + 5xy^2
f x x = 6y, f x y = 6x + 10y, f y x = 6x + 10y, f y y = 10x
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = 2 x y
f x x = 0, f x y = 2, f y x = 2, f y y = 0
Since f x y = f y x, the mixed partial derivatives are equal.
f(x,y) = (x + y) * e^y
f x x = e^y, f x y = e^y + e^y, f y x = e^y + e^y, f y y = (x + 2y) * e^y
Since f x y = f y x, the mixed partial derivatives are equal.
f(x,y) = x * e^y
f x x = 0, f x y = e^y, fy x = e^y, f y y = x * e^y
Since fx y = fy x, the mixed partial derivatives are equal.
f(x, y) = sin(x/y)
f x x = -sin(x/y) / y^2, f x y = cos(x/y) / y^2, f y x = cos(x/y) / y^2, f y y = -x * cos(x/y) / y^4 - sin(x/y) / y^2
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = x^2 + y^2
f x x = 2, f x y = 0, f y x = 0, f y y = 2
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = 5x^2y^2 - 7xy + 9x^2 + 11
f x x = 10xy^2 + 18, f x y = 10x^2y - 7, f y x = 10x^2y - 7, fy y = 10x^2y^2
Since fx y = fy x, the mixed partial derivatives are equal.
f(x,y) = sin(x^2 + y^2)
fx x = 2xcos(x^2 + y^2), fx y = 2ycos(x^2 + y^2), fy x = 2ycos(x^2 + y^2), fy y = 2x * cos(x^2 + y^2)
Since fx y = fy x, the mixed partial derivatives are equal.
f(x,y) = 3sin(2x)cos(5y)
fx x = 0, fx y = -30sin(2x)sin(5y), fy x = -30sin(2x)sin(5y), fy y = 0
Since fx y = fy x, the mixed partial derivatives are equal.
To know more about partial derivatives:
https://brainly.com/question/31397807
#SPJ4
Lindsey wears a different outfit every day. Her outfit consists of one top, one bottom, and one scarf.
How many different outfits can Lindsey put together if she has 3 tops, 3 bottoms, and 3 scarves from which to choose? (hint: the
counting principle)
A)3 outfits
B )9 outfits
C)24 outfits
D )27 outfits
Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.
How to determine How many different outfits can Lindsey put togetherTo find the number of different outfits that Lindsey can put together, we need to use the counting principle, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.
In this case, there are 3 ways for Lindsey to choose a top, 3 ways to choose a bottom, and 3 ways to choose a scarf. To find the total number of outfits, we multiply these numbers together:
Total number of outfits = number of tops x number of bottoms x number of scarves
Total number of outfits = 3 x 3 x 3
Total number of outfits = 27
Therefore, Lindsey can put together 27 different outfits if she has 3 tops, 3 bottoms, and 3 scarves to choose from. The answer is (D) 27 outfits.
Learn more about word problems at https://brainly.com/question/21405634
#SPJ1
Let f(x, y)= 1 + 3x² - cos(2y). Find all critical points and classify them as local maxima, local minima, saddle points, or none of these. critical points: (give your answers as a comma separated list of(x, y) coordinates. If your answer includes points that occur at a sequence of values, e.g., at every odd integer, or at any constant multiple of another value, use m for any non-zero even integer, n for any non-zero odd integer, add/or k for other arbitrary constants.) classifications: (give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points)
The critical points and their classifications are: (0, kπ/2), local minimum for all k.
To find the critical points of f(x, y), we need to find where the partial derivatives of f with respect to x and y are equal to zero:
∂f/∂x = 6x = 0
∂f/∂y = 2sin(2y) = 0
From the first equation, we get x = 0, and from the second equation, we get sin(2y) = 0, which has solutions y = kπ/2 for any integer k.
So the critical points are (0, kπ/2) for all integers k.
To classify these critical points, we need to use the second derivative test. The Hessian matrix of f is:
H = [6 0]
[0 -4sin(2y)]
At the critical point (0, kπ/2), the Hessian becomes:
H = [6 0]
[0 0]
The determinant of the Hessian is 0, so we can't use the second derivative test to classify the critical points. Instead, we need to look at the behavior of f in the neighborhood of each critical point.
For any k, we have:
f(0, kπ/2) = 1 + 3(0)² - cos(2kπ) = 2
So all the critical points have the same function value of 2.
To see whether each critical point is a maximum, minimum, or saddle point, we can look at the behavior of f along two perpendicular lines passing through each critical point.
Along the x-axis, we have y = kπ/2, so:
f(x, kπ/2) = 1 + 3x² - cos(2kπ) = 1 + 3x²
This is a parabola opening upwards, so each critical point (0, kπ/2) is a local minimum.
Along the y-axis, we have x = 0, so:
f(0, y) = 1 + 3(0)² - cos(2y) = 2 - cos(2y)
This is a periodic function with period π, and it oscillates between 1 and 3. So for each k, the critical point (0, kπ/2) is neither a maximum nor a minimum, but a saddle point.
For more such questions on Critical points.
https://brainly.com/question/18687565#
#SPJ11
REI sells a four person nylon tent shaped like a square pyramid. The slant height of the triangle is 6.5 feet and each side of the square base measures 8 feet. What is the minimum square footage of nylon used to make the tent?
The minimum square footage of nylon used to make the tent is 168 square feet.
How to determine the minimum square footage of nylon used to make the tent?To find the minimum square footage of nylon used to make the tent, we need to calculate the area of each of the four triangular faces and the area of the square base, and then add them up.
The area of each triangular face is given by the formula:
A = 1/2 × base × height
where the base is the side length of the square base (8 feet), and the height is the slant height of the pyramid (6.5 feet).
A = 1/2 × 8 × 6.5
A = 26
So each of the four triangular faces has an area of 26 square feet.
The area of the square base is given by the formula:
A = [tex]side length^{2}[/tex]
A = [tex]8^{2}[/tex]
A = 64
So the square base has an area of 64 square feet.
To find the minimum square footage of nylon used to make the tent, we can add up the areas of the four triangular faces and the square base:
4 × 26 + 64 = 104 + 64 = 168
Therefore, the minimum square footage of nylon used to make the tent is 168 square feet.
To know more about square
brainly.com/question/14198272
#SPJ1
describe the likelihood of the next elk caught being unmarked
The probability of the next elk caught being unmarked is 0.96 when the total number of elks is 5625 and the number of elks marked is 225.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Total number of elks = 5625
Number of elks marked = 225
We need to find the total number of elks not marked or unmarked we can find it by,
= 5625 - 225
= 5500
Therefore, the total number of elks unmarked is 5500.
We can determine determined the likelihood of the next elk caught being unmarked by using probability. The probability is given by:
P = 5500/5625
= 44 / 45
= 0.96
Therefore, The total number of elks unmarked is 0.96.
To learn more about probability:
https://brainly.com/question/30390037
#SPJ4
The complete question is,
Describe the likelihood of the next elk caught being unmarked.
PLEASE HELP WILL MARK BRANLIEST!!!
The child can make 120 different bracelets using one of each charm. To solve this problem, we need to use a combinatorial approach.
The number of different bracelets that the child can make depends on the number of charms that can be used for each bracelet & the order in which they are arranged. Since each charm can be used only once, we have to choose five charms out of the total of five available charms, which can be done in 5C5 ways.
We can think of this problem as a permutation problem. There are five distinct charms, and we need to choose five of them to make a bracelet. The order in which we choose the charms matters, as each order gives us a different bracelet. Therefore, we need to use the formula for permutations.
The formula for permutations is given by:
nPr = n! / (n-r)!
where n is the total number of objects, and r is the number of objects we want to choose.
For this problem, n = 5 (since there are five distinct charms), and r = 5 (since we want to choose all five charms).
Plugging these values into the formula, we get:
5P5 = 5! / (5-5)! = 5! / 0! = 5 x 4 x 3 x 2 x 1 / 1 = 120
Therefore, the child can make 120 different bracelets.
Alternatively, we can also think of this problem as a multiplication principle problem. There are five distinct charms, & we need to choose one charm out of five for the first position, one charm out of four for the second position, one charm out of three for the third position, one charm out of two for the fourth position, & one charm out of one for the fifth position.
Using the multiplication principle, we can multiply these numbers together to get the total number of different bracelets:
5 x 4 x 3 x 2 x 1 = 120
Therefore, the child can make 120 different bracelets using one of each charm.
To know more about combinatorial approach-
brainly.com/question/30589727
#SPJ1
In ΔUVW, the measure of ∠W=90°, UV = 4. 7 feet, and WU = 2. 2 feet. Find the measure of ∠U to the nearest degree
The measure of angle U in triangle UVW is approximately 28 degrees. This is found by using the inverse tangent function to solve for angle U given the lengths of two sides and the fact that angle W is a right angle.
To find the measure of ∠U in ΔUVW, we can use trigonometry. We know that sin(∠U) = opposite/hypotenuse, which is equal to UW/VW. Therefore, we can plug in the given values and solve for sin(∠U)
sin(∠U) = UW/VW = 2.2/4.7 = 0.4681
Next, we can use the inverse sine function (sin⁻¹) to find the measure of ∠U
∠U = sin⁻¹(0.4681) = 28.34 degrees (rounded to the nearest degree)
Therefore, the measure of ∠U in ΔUVW is approximately 28 degrees.
To know more about Triangle:
https://brainly.com/question/19976619
#SPJ4
If I wanted to draw Circles X and and wanted to make sure they were congruent to Circle A, what
would be required?
To ensure that Circles X are congruent to Circle A, you need to ensure that they have the same size and shape. In other words, the radii of Circle X should be equal to the radius of Circle A.
Here are the steps you can follow to draw congruent Circles X:
Use a compass to measure the radius of Circle A.
Without changing the radius setting on your compass, place the tip of the compass at the center of where you want to draw Circle X.
Draw Circle X using the compass, making sure that the radius is the same as the radius of Circle A.
Check that Circle X and Circle A have the same size and shape. You can do this by measuring their radii with a ruler or by comparing their circumference.
By following these steps, you can ensure that Circle X is congruent to Circle A.
Learn more about congruence at https://brainly.com/question/30020879
#SPJ11
In ΔVWX, w = 600 cm, mm∠V=26° and mm∠W=80°. Find the length of v, to the nearest 10th of a centimeter.
According to the given information in the question to find the length of side v in triangle VWX, we can use the Law of Sines. the length of side v is approximately [tex]281.8[/tex] cm.
What do mathematicians mean by centimetres?image for "define centimeters in high-level mathematics." A centimeter is a metric unit used to quantify small distances and the object's length. Cm is used to represent it in writing.
It can also be described as the measure of length in the current metric system, referred to as the International System of Units (SI). It is equal to one-hundredth of a meter.
which states that:
[tex]a/sin(A) = b/sin(B) = c/sin(C)[/tex]
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the opposite angles.
In this case, we know the length of side w (600 cm), and the measures of angles V and W.
To find the length of side v, we can use the Law of Sines with sides v and w and angle V:
[tex]v/sin(V) = w/sin(W)[/tex]
[tex]v/sin(26^\circ) = 600/sin(80^\circ)[/tex]
[tex]v = (600 \times sin(26^\circ))/sin(80^\circ)[/tex]
[tex]v \approx 281.8 cm[/tex] (rounded to the nearest 10th of a centimeter)
Therefore, the length of side v is approximately [tex]281.8 cm[/tex].
Learn more about centimetres here:
https://brainly.com/question/23366076
#SPJ1
Using the complex form, find the Fourier series of the function. (30%)
f(x) = 1, 2k -. 25 <= x <= 2k + ,25, k E Z
Answer:
The Fourier series of a periodic function f(x) with period 2L can be expressed as:
f(x) = a0/2 + Σ[n=1 to ∞] (ancos(nπx/L) + bnsin(nπx/L))
where
a0 = (1/L) ∫[-L,L] f(x) dx
an = (1/L) ∫[-L,L] f(x)*cos(nπx/L) dx
bn = (1/L) ∫[-L,L] f(x)*sin(nπx/L) dx
In this case, we have f(x) = 1 for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise. The period is 0.5, so L = 0.25.
First, we can find the value of a0:
a0 = (1/0.5) ∫[-0.25,0.25] 1 dx = 1
Next, we can find the values of an and bn:
an = (1/0.5) ∫[-0.25,0.25] 1*cos(nπx/0.25) dx = 0
bn = (1/0.5) ∫[-0.25,0.25] 1*sin(nπx/0.25) dx
Since the integrand is odd, we have:
bn = (2/0.5) ∫[0,0.25] 1*sin(nπx/0.25) dx
Using the substitution u = nπx/0.25, du/dx = nπ/0.25, dx = 0.25du/(nπ), we get:
bn = (4/nπ) ∫[0,nπ/4] sin(u) du = (4/nπ) (1 - cos(nπ/4))
Therefore, the Fourier series of f(x) can be written as:
f(x) = 1/2 + Σ[n=1 to ∞] [(4/nπ) (1 - cos(nπ/4))] * sin(nπx/0.25)
for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise.
Find an equation of the plane with the given characteristics.
The plane passes through (0, 0, 0), (6, 0, 3), and (-3, -1, 5).
To find the equation of the plane, we first need to find two vectors that lie on the plane. We can do this by taking the differences between the three given points:
$\vec{v_1} = \begin{pmatrix}6 \\ 0 \\ 3\end{pmatrix} - \begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix} = \begin{pmatrix}6 \\ 0 \\ 3\end{pmatrix}$
$\vec{v_2} = \begin{pmatrix}-3 \\ -1 \\ 5\end{pmatrix} - \begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix} = \begin{pmatrix}-3 \\ -1 \\ 5\end{pmatrix}$
Now we can find the normal vector to the plane by taking the cross product of these two vectors:
$\vec{n} = \vec{v_1} \times \vec{v_2} = \begin{pmatrix}6 \\ 0 \\ 3\end{pmatrix} \times \begin{pmatrix}-3 \\ -1 \\ 5\end{pmatrix} = \begin{pmatrix}3 \\ -27 \\ 6\end{pmatrix}$
Next, we can use the point-normal form of the equation of a plane:
$(\vec{r} - \vec{a}) \cdot \vec{n} = 0$
where $\vec{a}$ is a point on the plane and $\vec{n}$ is the normal vector.
We can choose any of the three given points as $\vec{a}$. Let's use $(0, 0, 0)$:
$(\begin{pmatrix}x \\ y \\ z\end{pmatrix} - \begin{pmatrix}0 \\ 0 \\ 0\end{pmatrix}) \cdot \begin{pmatrix}3 \\ -27 \\ 6\end{pmatrix} = 0$
Simplifying, we get:
$3x - 27y + 6z = 0$
This is the equation of the plane.
To find the equation of the plane passing through points (0, 0, 0), (6, 0, 3), and (-3, -1, 5), first find two vectors in the plane and then compute their cross product to obtain the normal vector of the plane. Finally, use the normal vector and a point on the plane to find the equation of the plane.
Vectors in the plane:
V1 = (6, 0, 3) - (0, 0, 0) = (6, 0, 3)
V2 = (-3, -1, 5) - (0, 0, 0) = (-3, -1, 5)
Cross product (normal vector N):
N = V1 x V2 = (0*(-5) - 3*(-1), 3*(-5) - 6*5, 6*(-1) - 0*(-3))
N = (3, -15, -6)
Equation of the plane using the normal vector and a point on the plane (0, 0, 0):
3x - 15y - 6z = 0
So, the equation of the plane is 3x - 15y - 6z = 0.
Learn more about matrix here: brainly.com/question/29132693
#SPJ11
Stephen has a counter that is orange on one side and brown on the other. The counter is shown below: A circular counter is shown. The top surface of the counter is shaded in a lighter shade of gray and Orange is written across this section. The bottom section of the counter is shaded in darker shade of gray and Brown is written across it. Stephen flips this counter 24 times. What is the probability that the 25th flip will result in the counter landing on orange side up? fraction 24 over 25 fraction 1 over 24 fraction 1 over 4 fraction 1 over 2
The probability that the 25th flip will result in the counter landing on orange side up is fraction 1 over 2. The correct answer is D.
The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, Stephen has flipped the counter 24 times and he wants to know the probability of getting an orange side up on the 25th flip.
Since the counter has two sides - orange and brown, the probability of landing on the orange side is 1/2 or 0.5.
Each flip of the counter is independent of the others, so the previous flips do not affect the outcome of the 25th flip. Therefore, the probability of the 25th flip landing on the orange side up is still 1/2 or 0.5. The correct answer is D.
Learn more about probability at https://brainly.com/question/9870709
#SPJ11
Which statement is true about the streets? Select all that apply. A. First Street intersects with Second Street and Third Street. B. Second Street is perpendicular to Third Street. C. First Street and Third Street are parallel. D. Second Street and Third Street are parallel. E. First Street is perpendicular to Second Street and Third Street. 6 /
The correct options are: A and D
Streets 2 and 3 are parallel and Street 1 is intersecting it
What is a Parallel Line and Intersections?Parallel lines are two or more straight lines that continue indefinitely without ever crossing each other, despite their extended lengths. They have an equal inclination and remain the same distance apart at all times. Consequently, intersections will never occur between them.
On the contrary, if non-parallel lines exist, they intersect to create one point, famously known as the 'point of intersection'. This specific point supplies the solution to the system of equations formed by the two lines.
Hence, we can see from the given image that Streets 2 and 3 are parallel and Street 1 is intersecting it
Read more about parallel lines here:
https://brainly.com/question/16742265
#SPJ1
A parallelogram has an area of
25. 2
c
m
2
25. 2 cm
2
and a height of
4
c
m
4 cm. Use paper to write an equation that relates the height, base, and area of the parallelogram. Solve the equation to find the length of the base then what is the length of the base? (Can someone help me out please)
If the parallelogram has an area of 25.2 cm² and the height is 4 cm, the length of the base is 6.3 cm.
To start, we know that the area of a parallelogram is given by the formula:
A = bh
where A is the area, b is the length of the base, and h is the height. We also know that the area of the parallelogram in this case is 25.2 cm² and the height is 4 cm.
Substituting these values into the formula, we get:
25.2 = b(4)
To solve for b, we can divide both sides by 4:
b = 25.2/4
b = 6.3
So the length of the base is 6.3 cm.
More on parallelogram: https://brainly.com/question/17092823
#SPJ11
If p = (-4,7), find:
ry-axis (p)
([?], []).
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
We have,
To find the reflection of a point P in the y-axis, negate the x-coordinate of the point while keeping the y-coordinate unchanged.
Given that P = (-4, 7),
The reflection of P in the y-axis, denoted as [tex]R_{y-axis}(P),[/tex] can be found by negating the x-coordinate:
[tex]R_{y-axis}(P) = (4, 7)[/tex]
Thus,
The reflection of the point P = (-4, 7) in the y-axis is (4, 7).
Learn more about reflections here:
https://brainly.com/question/12463306
#SPJ12
The complete question:
If p = (-4, 7)
R_{y-axis} (P) = ?
A lake is to be stocked with smallmouth and largemouth bass. Let represent the number of smallmouth bass and let represent the number of largemouth bass. The weight of each fish is dependent on the population densities. After a six-month period, the weight of a single smallmouth bass is given by and the weight of a single largemouth bass is given by Assuming that no fish die during the six-month period, how many smallmouth and largemouth bass should be stocked in the lake so that the total weight of bass in the lake is a maximum
To maximize the total weight of bass in the lake, we should stock 3000 smallmouth bass and 4666.67 largemouth bass
To maximize the total weight of bass in the lake, we need to find the optimal values of and that will maximize the total weight of the fish.
Let's start by writing an expression for the total weight of the fish in the lake:
Total weight = (weight of a single smallmouth bass) × (number of smallmouth bass) + (weight of a single largemouth bass) × (number of largemouth bass)
Substituting the given expressions for the weight of a single smallmouth bass and largemouth bass, we get:
Total weight = (0.5 + 0.1) × × + (1.2 + 0.2) ×
Simplifying this expression, we get:
Total weight = (0.6) × × + (1.4) ×
To find the optimal values of and that maximize the total weight, we can take the partial derivatives of this expression with respect to and and set them equal to zero:
[tex]∂ \frac{(Total weight)}{∂} = 0.6-0.0002=0[/tex]
[tex]∂ \frac{(Total weight)}{∂} = 1.4-0.0003=0[/tex]
Solving these equations simultaneously, we get:
= 3000
= 4666.67
Therefore, to maximize the total weight of bass in the lake, we should stock 3000 smallmouth bass and 4666.67 largemouth bass.
To know more about "Partial derivatives" refer here:
https://brainly.com/question/31397807#
#SPJ11
Is y = 12 a solution to the inequality below?
0 < y− 12
A publisher reports that 30% of their readers own a laptop. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 130 found that 20% of the readers owned a laptop. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is approximately -2.49
To find the value of the test statistic for the marketing executive's claim that the percentage of laptop owners is different from the reported 30%, we will use the following formula for a proportion hypothesis test:
[tex]Test Statistic (Z) =\frac{ (Sample Proportion - Hypothesized Proportion)}{Standard Error}[/tex]
Here are the given values:
- Hypothesized proportion (p) = 0.30
- Sample size (n) = 130
- Sample proportion (p-hat) = 0.20
First, we need to calculate the standard error (SE) using this formula:
[tex]SE+\frac{\sqrt{p(1-p)} }{n}[/tex]
[tex]SE+\frac{\sqrt{0.30(1-0.30)} }{130}[/tex]
[tex]SE=\sqrt{\frac{0.21}{130} }[/tex]
[tex]SE=\sqrt{0.0016153846}[/tex]
[tex]SE = 0.04019[/tex]
Now, we can calculate the test statistic (Z) using the given formula:
[tex]Z=\frac{ (0.20 - 0.30)}{0.04019}[/tex]
[tex]Z=\frac{-0.10}{ 0.04019}[/tex]
[tex]Z = -2.49[/tex]
So, the value of the test statistic is approximately -2.49, rounded to two decimal places.
To know more about "Standard error" refer here:
https://brainly.com/question/30667112#
#SPJ11
The ratio of m angle wxz to m angle zxy is 11:25. what is m angle zxy
The measure of angle zxy is 125 degrees.
To solve the problem, we can use the fact that the sum of the measures of two adjacent angles is 180 degrees. Let's call the measure of angle zxy "x".
We know that the ratio of m angle wxz to m angle zxy is 11:25, which means that:
m angle wxz : m angle zxy = 11 : 25
We can write this as an equation:
m angle wxz / m angle zxy = 11/25
We also know that the two angles are adjacent, so their measures add up to 180 degrees:
m angle wxz + m angle zxy = 180
Now we can use these two equations to solve for x:
m angle wxz / x = 11/25
m angle wxz = (11/25)x
Substituting this into the second equation:
(11/25)x + x = 180
(36/25)x = 180
x = (25/36) * 180
x = 125
Therefore, the measure of angle zxy is 125 degrees.
Learn more about adjacent angles,
https://brainly.com/question/28394984
#SPJ11
Kaylee is working two summer jobs, making $10 per hour babysitting and $9 per
hour walking dogs. Kaylee must earn a minimum of $170 this week. Write an
inequality that would represent the possible values for the number of hours
babysitting, b, and the number of hours walking dogs, d, that Kaylee can work in a
given week.
The inequality that represents the possible values for the number of hours babysitting, b, and the number of hours walking dogs, d, that Kaylee can work in a given week is: 10b + 9d ≥ 170
To understand why this is the correct inequality, we can start by using algebra to represent Kaylee's total earnings for a given week as a function of the number of hours she spends babysitting, b, and the number of hours she spends walking dogs, d. We can use the following equation:
Total earnings = 10b + 9d
We know that Kaylee must earn a minimum of $170 in a given week. We can use this information to create an inequality by setting the total earnings equal to or greater than $170:
10b + 9d ≥ 170
This inequality tells us that Kaylee must earn at least $170 in total, and that the amount she earns from babysitting, 10b, plus the amount she earns from walking dogs, 9d, must be greater than or equal to $170. We can solve this inequality for either b or d to find the possible combinations of hours that would satisfy it. For example, if we solve for b, we get:
b ≥ (170 - 9d)/10
This inequality tells us that the number of hours spent babysitting must be greater than or equal to the expression (170 - 9d)/10, which is a function of the number of hours spent walking dogs, d. Similarly, if we solve for d, we get:
d ≥ (170 - 10b)/9
This inequality tells us that the number of hours spent walking dogs must be greater than or equal to the expression (170 - 10b)/9, which is a function of the number of hours spent babysitting, b. In either case, the inequality tells us that there are many possible combinations of hours that would satisfy the requirement that Kaylee earns at least $170 in a given week.
To learn more about inequality here
https://brainly.com/question/30228778
#SPJ4
Your team arrived to the scene at 9:30 am and found the temperature of the body at 85 degrees. The team
continued to help collect evidence and noted that the thermostat was set at 72 degrees. After collecting
evidence for one hour, your team checked the body temperature again and found it to now be at 83. 3
degrees
Your team must figure out what time the murder took place.
The murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.
Assuming that the body follows Newton's law of cooling, we can use the formula:
T(t) = Tm + (Ta - Tm) * e^(-kt),
where T(t) is the body temperature at time t, Tm is the temperature of the surrounding medium (in this case, the room), Ta is the initial temperature of the body, and k is a constant that depends on the properties of the body and the surrounding medium.
We can use the information given to find k:
At t = 0 (when the murder took place), T(0) = Ta = unknown
At t = 0.5 hours (30 minutes after the murder), T(0.5) = 85 degrees
At t = 1.5 hours (90 minutes after the murder), T(1.5) = 83.3 degrees
Using the formula above, we can write two equations:
85 = Ta + (72 - Ta) * e^(-0.5k)
83.3 = Ta + (72 - Ta) * e^(-1.5k)
Solving for Ta in the first equation, we get:
Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5k)
Substituting this expression for Ta into the second equation, we get:
83.3 = (72 + 13 / e^(-0.5k)) + (72 - (72 + 13 / e^(-0.5k))) * e^(-1.5k)
Simplifying and solving for e^(-0.5k), we get:
e^(-0.5k) = 0.979
the natural logarithm of both sides, we get:
-0.5k = ln(0.979)
Solving for k, we get:
k = -2 * ln(0.979) / 1 = 0.0427
Now we can use the formula again to find Ta:
Ta = 72 + (85 - 72) / e^(-0.5k) = 72 + 13 / e^(-0.5*0.0427) = 78.1 degrees
So the initial temperature of the body was 78.1 degrees.
To find the time of death, we can use the formula again and solve for t when T(t) = 78.1:
78.1 = 72 + (Ta - 72) * e^(-0.0427t)
Substituting Ta = 85 (the initial temperature of the body) and solving for t, we get:
t = -ln((85 - 72) / (78.1 - 72)) / 0.0427 = 1.17 hours
Therefore, the murder took place approximately 1.17 hours before the team arrived, which is 8:13 am.
To know more about collect evidences refer here:
https://brainly.com/question/28767044
#SPJ11
Use cylindrical coordinates Find the volume of the solid that is enclosed by the cone z = x 2 + y 2 and the sphere x 2 + y 2 + z 2 = 2
The volume of the solid is (7π - 8√2)/12 cubic units.
To find the volume of the solid enclosed by the cone and sphere in cylindrical coordinates, we first need to express the equations of the cone and sphere in cylindrical coordinates.
Cylindrical coordinates are expressed as (ρ, θ, z), where ρ is the distance from the origin to a point in the xy-plane, θ is the angle between the x-axis and a line connecting the origin to the point in the xy-plane, and z is the height above the xy-plane.
The cone z = x^2 + y^2 can be expressed in cylindrical coordinates as ρ^2 = z, and the sphere x^2 + y^2 + z^2 = 2 can be expressed as ρ^2 + z^2 = 2.
To find the limits of integration for ρ, θ, and z, we need to visualize the solid. The cone intersects the sphere at a circle in the xy-plane with radius 1. We can integrate over this circle by setting ρ = 1 and integrating over θ from 0 to 2π.
The limits of integration for z are from the cone to the sphere. At ρ = 1, the cone and sphere intersect at z = 1, so we integrate z from 0 to 1.
Therefore, the volume of the solid enclosed by the cone and sphere in cylindrical coordinates is
V = ∫∫∫ ρ dz dρ dθ, where the limits of integration are
0 ≤ θ ≤ 2π
0 ≤ ρ ≤ 1
0 ≤ z ≤ ρ^2 for ρ^2 ≤ 1, and 0 ≤ z ≤ √(2 - ρ^2) for ρ^2 > 1.
Integrating over z, we get
V = ∫∫ ρ(ρ^2) dρ dθ for ρ^2 ≤ 1, and
V = ∫∫ ρ(√(2 - ρ^2))^2 dρ dθ for ρ^2 > 1.
Evaluating the integrals, we get
V = ∫0^1 ∫0^2π ρ^3 dθ dρ = π/4
and
V = ∫1^√2 ∫0^2π ρ(2 - ρ^2) dθ dρ = π/3 - 2√2/3
Therefore, the total volume of the solid enclosed by the cone and sphere in cylindrical coordinates is
V = π/4 + π/3 - 2√2/3
= (7π - 8√2)/12 cubic units
Learn more about volume here
brainly.com/question/17056637
#SPJ4
The given question is incomplete, the complete question is:
Use cylindrical coordinates Find the volume of the solid that is enclosed by the cone z = x^2 + y^2 and the sphere x^2 + y^2 + z^2 = 2
Loudness of sound. The loudness L of a sound of intensity I is defined as 1 L = 10 log 1/1o' where lo is the minimum intensity detectable by the human ear and L is the loudness measured in decibels
Yes, the loudness L of a sound of intensity I is defined as:
L = 10 log(I/Io)
where Lo is the minimum intensity detectable by the human ear (also known as the threshold of hearing) and L is the loudness measured in decibels (dB).
In this equation, the intensity I is typically measured in watts per square meter (W/m^2), and Io is equal to 1 x 10^-12 W/m^2.
The logarithmic scale used in this equation means that each increase of 10 decibels represents a tenfold increase in sound intensity. For example, a sound that is 50 dB louder than another sound has an intensity that is 10 times greater.
To know more about Loudness of sound:
https://brainly.com/question/21094511
#SPJ4
Ribbon is sold at $7 for 3 metres at the factory and $2.50 per metre at the store. How much money is saved when 15 metres of ribbon is bought at the factory rather than at the store?
The cost of 15 meters of ribbon at the factory is:
15 meters / 3 meters per $7 = 5 times $7 = $35
The cost of 15 meters of ribbon at the store is:
15 meters x $2.50 per meter = $37.50
Therefore, the amount saved by buying 15 meters of ribbon at the factory rather than at the store is:
$37.50 - $35 = $2.50
WILL MARK YOU BRAINLIEST QUESTION IN THE PHOTO
The measure of arc DF is given as follows:
mDF = 58º.
How to obtain the arc measure?We have two secants in this problem, and point E is the intersection of the two secants, hence the angle measure of 52º is half the difference between the angle measure of the largest arc of 162º by the angle measure of the smallest arc.
Then the measure of arc DF is obtained as follows:
52 = 0.5(162 - mDF)
52 = 81 - 0.5mDF
0.5mDF = 29
mDF = 58º.
More can be learned about angle measures at brainly.com/question/30820033
#SPJ1
1. explain what a positive and negative number means in this situation.
2. what is the total inventory on sunday?
3. how many paper towels do you think were used on thursday? explain how you know
Positive numbers indicate an increase in the number of cups, while negative numbers indicate a decrease. By using addition, the total inventory on Sunday is 2,893 cups. The number of cups used on Thursday is 2,127.
In this situation, a positive number means that the coffee shop received a delivery of cups, while a negative number means that they used or lost cups.
Assuming that the starting amount of coffee cups is 0, the total inventory on Sunday would be the sum of all the cups received and used until Sunday, which is
2,000 + (-125) + (-127) + 1,719 + (-356) + 782 + 0 = 2,893 cups
To estimate how many cups were used on Thursday, we can subtract the previous balance (2,000 cups) from the balance after Thursday's transaction (-127 cups) and get
-127 - 2,000 = -2,127 cups
Since the number is negative, it means that 2,127 cups were used on Thursday.
To know more about addition:
https://brainly.com/question/26495320
#SPJ4
--The given question is incomplete, the complete question is given
" Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time.
Monday:+2,000
Tuesday:-125
Wednesday:-127
Thursday:+1,719
Friday:-356
Saturday:782
Sunday:0
Explain what a positive and negative number means in this situation.
Assume the starting amount of coffee cups is 0. 2. what is the total inventory on sunday?
How many cups do you think were used on Thursday? Explain how you know."--
Find a formula for the slope of the graph of fat the point (x, f(x)). Then use it to find the slope at the two given points.
a. The formula for the slope at (x, f(x)) is f'(x) = -2x
b. The slope at (0, 8) is 0
c. the slope at (-1, 7) is 2
What is the slope of a graph?The slope of a graph is the gradient of the graph.
Given the graph f(x) = 8 - x² to find the formula for the slope of the graph, we proceeed as follow.
a. To find the formula for the slope of the graph, we know thta the slope of the graph is the derivative of the graph. So, taking the derivative of the graph, we have that
f(x) = 8 - x²
df(x)/dx = d(8 - x²)/dx
= d8/dx - dx²/dx
= 0 - 2x
= -2x
So, the formula for the slope at (x, f(x) is f'(x) = -2x
b. To find the slope at (0, 8), substituting x = 0 into the equation for the slope, we have that
f'(x) = -2x
f'(0) = -2(0)
= 0
So, the slope at (0, 8) is 0
c. To find the slope at (-1, 7), substituting x = -1 into the equation for the slope, we have that
f'(x) = -2x
f'(0) = -2(-1)
= 2
So, the slope at (-1, 7) is 2
Learn more about slope of a graph here:
https://brainly.com/question/28143793
#SPJ1
Sam cut a plank of wood into 4 pieces. He makes one cut at a time and each cut takes equally as long. He completes this task in 12 minutes. How long will it take him to cut another identical plank into only 3 pieces, working at the same pace?
Therefore, it will take Sam 8 minutes to cut another identical plank into only 3 pieces, working at the same pace.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equals sign (=). The LHS and RHS can be made up of variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the relationship between the LHS and the RHS. Equations are fundamental to many areas of mathematics, science, engineering, and everyday life.
Here,
If Sam cuts a plank of wood into 4 pieces, then he needs to make 3 cuts. Since each cut takes equally as long, he spends 12/3 = 4 minutes per cut.
To cut another identical plank of wood into 3 pieces, he needs to make 2 cuts. Since he spends 4 minutes per cut, it will take him 2 * 4 = 8 minutes to complete this task.
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
tomas earns 0.5% commision on the sale price of a new car. On wednesday, he sells a new car for $24,500. How much commison does tomas earn on this sale
Tomas earns a commission of $122.50 on the sale of the new car.
Tomas earns a 0.5% commission on the sale price of a new car. On Wednesday, he sells a new car for $24,500. To determine the commission Tomas earns, we need to multiply the sale price by the commission rate. The commission rate is given as 0.5%, which can be expressed as a decimal by dividing by 100. So, 0.5% is equal to 0.005 as a decimal.
Now, we can calculate Tomas's commission by multiplying the sale price by the commission rate. In this case, we multiply $24,500 by 0.005:
$24,500 x 0.005 = $122.50
To know more about commission, refer to the link below:
https://brainly.com/question/29636558#
#SPJ11
at a local farmers market a farmer pays $10 to rent a stall and $7 for every hour he stays there. if he pays $45 on saturday how many hours did he stay at the market
Answer: The answer is 5.
Step-by-step explanation:
You first set up the equation
10 + 7x = 45
You must put x because you don't know the number of hours he stays
You then subtract 10 from both sides of the numbers 10 and 45
That'll get you 7x = 35
To find out what x is you divide both sides by 7
7x divided by 7 is x
35 divided by 7 is 5
X = 5