A set of data points could be modeled by a decreasing linear function include the following: C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}.
What is a linear function?In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the set of data points, we can reasonably infer and logically deduce that it set C is decreasing as follows 50, 42, 33, 25, 16.
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3. let f be a differentiable function on an open interval i and assume that f has no local minima nor local maxima on i. prove that f is either increasing or decreasing on i.
Shown that if f has no local minima nor local maxima on i, then f is either increasing or decreasing on i.
Since f has no local minima nor local maxima on i, it means that for any point x in i, either f is increasing or decreasing in a small interval around x. In other words, either f'(x) > 0 or f'(x) < 0 for all x in i.
Now suppose there exist two points a and b in i such that a < b and f(a) < f(b). We want to show that f is increasing on i.
Consider the interval [a,b]. By the Mean Value Theorem, there exists a point c in (a,b) such that f'(c) = (f(b) - f(a))/(b - a). Since f(a) < f(b), we have (f(b) - f(a))/(b - a) > 0, which implies f'(c) > 0. Since f'(x) > 0 for all x in i, it follows that f is increasing on [a,c] and on [c,b]. Therefore, f is increasing on i.
A similar argument can be made if f(a) > f(b), which would imply that f is decreasing on i.
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A cement walkway is in the shape of a rectangular prism. The length is 10 feet, the width is three feet and the depth is 1.5 feet. How much cubic feet of cement will they need?
The volume of cement in cubic feet that will be needed is 45 cubic feet.
What is volume?Volume is the space occuppied by an object.
To calculate the volume of cement in cubic feet that will be needed, we use the formula below
Formula:
V = lwh....................... Equation 1Where:
V = Volume of the cement that is neededl = Length of the walkwayw = width of the walkwayh = depth of the walkwayFrom the question,
Given:
l = 10 feetw = 3 feeth = 1.5 feetSubstitute these values into equation 1
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If (arc)mEA=112* and m
If angle of arc EA is 112 degrees then value of arc IV is 36 degrees by outside angles theorem
Given that Arc EA measure is One hundred twelve degrees
By Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs
(112-x)/2=38
112-x=38×2
112-x=76
112-76=x
36 degrees = angle IV or x
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What is the equation, in slope-intercept form, of the line that passes through
(0, 5) and has a slope of -1? (6 points)
Oy=-x-5
Oy=x+5
Oy=-x+5
Oy=x-5
Answer:
C) y = - x + 5---------------------------
The given point (0, 5) represents the y-intercept and we have a slope of -1.
It translates as:
m = - 1, b = 5 in the slope-intercept equation of y = mx + bBy substituting we get equation:
y = - x + 5This is option C.
What is the meaning of a relative frequency of 0. 56
A relative frequency of 0.56 means that out of the total number of observations in a given sample or population, 56% of those observations belong to a particular category or have a certain characteristic.
In other words, it is the proportion or fraction of the observations that fall into that particular category or have that characteristic, relative to the total number of observations. For example, if we had a sample of 100 people and 56 of them had brown hair, then the relative frequency of brown hair would be 0.56 or 56%.
To calculate relative frequency, you divide the frequency of a specific event or category by the total number of observations. In this case, the specific event or category occurs 56% as often as the total events or categories observed.
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Is the following data an example of a linear function?
Answer:
Yes
Step-by-step explanation:
Yes, because its graph represents a straight line
A bracelet is now reduced to £420.this is 70% of the original price. what is the original price?
Answer:
.70p = £420, so p = £600
The original price of the bracelet is £600.
The original price of the bracelet was £600.
To find the original price of the bracelet, we need to use the information that the current price is 70% of the original price. We can use algebra to solve for the original price:
Let X be the original price of the bracelet.
70% of X is equal to £420.
We can write this as:
0.7X = £420
To solve for X, we can divide both sides of the equation by 0.7:
X = £420 ÷ 0.7
Evaluating the right-hand side gives us:
X = £600
Therefore, the original price of the bracelet was £600.
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The Greens bought a condo for $110,000 in 2005. If its value increases at 6% compounded annually, what will the value be in 2020?
Answer:
$264,000
Step-by-step explanation:
PV = $110,000
i = 6%
n = 15 years
Compound formula:
FV = PV (1 + i)^n
FV = 110,000 (1 + 0.06)^15
FV = 110,000 · 2.40(rounded) = $264,000
Shelby was in the next stall, and she needed 150 mL of a solution that was 30% glycerin. The two solutions available were 10% glycerin and 40% glycerin. How many milliliters of each should Shelby use?
Taking the data into consideration, Shelby should use 50 mL of the 10% glycerin solution and 100 mL of the 40% glycerin solution, as explained below.
How to find the amountsLet x be the amount of 10% glycerin solution and y be the amount of 40% glycerin solution that Shelby needs to use. We know that Shelby needs a total of 150 mL of the 30% glycerin solution, so we can write:
x + y = 150 (equation 1)
We also know that the concentration of glycerin in the 10% solution is 10%, and the concentration of glycerin in the 40% solution is 40%. So, the amount of glycerin in x mL of the 10% solution is 0.1x, and the amount of glycerin in y mL of the 40% solution is 0.4y. The total amount of glycerin in the 150 mL of 30% solution is 0.3(150) = 45 mL. So, we can write:
0.1x + 0.4y = 45 (equation 2)
We now have two equations with two variables. We can use substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.1, we get:
0.1x + 0.1y = 15 (equation 3)
Subtracting equation 3 from equation 2, we get:
0.3y = 30
y = 100
Substituting y = 100 into equation 1, we get:
x + 100 = 150
x = 50
Therefore, Shelby needs to use 50 mL of the 10% glycerin solution and 100 mL of the 40% glycerin solution.
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A sheet of dough has six identical circles cut from
it. Write an expression in factored form to represent the
approximate amount of dough that is remaining. Is
there enough dough for another circle
Approximate amount of dough that is remaining. Is (length - 2r)(width - 3r) - 6πr^2.
Without the size of the original sheet of dough or the size of the circles cut from it, it's not possible to give an exact expression. However, assuming that each circle has the same radius of 'r' and the original sheet of dough was a rectangle, we can write an expression in factored form for the remaining area of the dough:
Remaining area of dough = (Area of original rectangle) - 6(Area of circle)
= (length x width) - 6(πr^2)
= (length - 2r)(width - 3r) - 6πr^2
Whether there is enough dough for another circle would depend on the size of the circles and the original sheet of dough.
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thank you !!!!!!!! (Choose ALL answers that are correct)
Answer:
a and b
Step-by-step explanation:
Pleas help im stuck on this question and im too afraid to get it wrong
Step-by-step explanation:
g(x) is just f(x) shifted UP three units ...so
g(x) = f(x) +3
In 1680, Isaac Newton, scientist astronomen, and mathematician, used a comet visible from Earth to prove that some comers follow a parabolic path through space as they travell around the sun. This and other discoveries like it help scientists to predict past and future positions of comets.
Comets could be visible from Earth when they are most likely to fall down into earth
I Need help with a Math Problem (zoom in if you can’t see it) (if you can’t see it the problem is ( x degrees 49 degrees and 39 degrees) find the value of x
Answer:
Step-by-step explanation:
If there are 180 degrees in a triangle total and in this problem we know that one angle is 49 and the other is 39, we can assume that subtracting 39 and 49 from 180 will find x. In this case, x will be 92.
A grocery store’s earnings in dollars can be modeled by the equation y 5 0. 75x 2 0. 15x, where x represents the number of tomatoes that they sell. If they sell 200 tomatoes in one day, how much money do they earn?
The grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.
We need to find how much the grocery store earns when it sells 200 tomatoes in one day. When The grocery store’s earnings in dollars can be modeled by the equation,
y = 0.75x² + 0.15x
where,
x = number of tomatoes they sell = 200
To find the earnings we need to substitute x in the equation it can be given as,
y = 0.75x² + 0.15x
y = 0.75(200)² + 0.15(200)
y = $30,030
Therefore, the grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.
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please help i need this asap
All the value of angles are,
⇒ ∠a = 118°
⇒ ∠b = 62°
⇒ ∠q = 84°
⇒ ∠v = 84°
Given that;
Two parallel lines t₁ and t₂ are shown in image.
Here, we have;
Apply the definition of corresponding angles,
∠d = 180 - 62
∠d = 118°
Hence, By definition of vertically opposite angles,
⇒ ∠a = 118°
And,
∠b = 180 - 118°
∠b = 62°
Apply the definition of corresponding angles,
∠q = 180 - 96
∠q = 84°
Hence, By definition of vertically opposite angles,
⇒ ∠v = 84°
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50 POINTS ASAP Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of five eighths to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(5.8, −3), B′(1.6, −1.5), C′(−1.6, 3), D′(2.5, 3)
A′(−16, 24), B′(−8, 8), C′(16, −24), D′(16, 16)
A′(2.5, −3.75), B′(1.25, −1.25), C′(−2.5, 1.25), D′(−2.5, −2.5)
A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)
Answer:
A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)
Step-by-step explanation:
in the described situation you only need to multiply the coordinates by the scale factor (in our case the given 5/8)
A (-4, 6) turns into
A' (-4×5/8, 6×5/8) = A' (-2.4, 3.75)
and therefore we know already here that all the other answer options are wrong.
17. What number is not part of the solution set to the
inequality below?
w - 10 < 16
A. 11
B. 15
C. 26
D. 27
Answer:
Step-by-step explanation:
To find the solution set to the inequality w - 10 < 16, we can solve for w by adding 10 to both sides of the inequality:
w - 10 + 10 < 16 + 10 w < 26
This means that any number less than 26 is part of the solution set to the inequality. So, out of the given options, the number that is not part of the solution set is D. 27 because it is greater than 26.
In ABC, the bisector of A divides BC into segment BD with a length of
28 units and segment DC with a length of 24 units. If AB -31. 5 units, what
could be the length of AC ?
To find the length of AC in triangle ABC, we will use the Angle Bisector Theorem and the given information:
In triangle ABC, the bisector of angle A divides BC into segments BD and DC, with lengths of 28 units and 24 units, respectively. Given that AB has a length of 31.5 units, we want to determine the possible length of AC.
Step 1: Apply the Angle Bisector Theorem, which states that the ratio of the lengths of the sides is equal to the ratio of the lengths of the segments created by the angle bisector. In this case, we have:
AB / AC = BD / DC
Step 2: Plug in the known values:
31.5 / AC = 28 / 24
Step 3: Simplify the ratio on the right side:
31.5 / AC = 7 / 6
Step 4: Cross-multiply to solve for AC:
6 * 31.5 = 7 * AC
Step 5: Calculate the result:
189 = 7 * AC
Step 6: Divide both sides by 7 to find AC:
AC = 189 / 7
Step 7: Calculate the value of AC:
AC = 27 units
So, the length of AC in triangle ABC could be 27 units.
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In Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet. Find the
length of US to the nearest tenth of a foot
If in Angle STU, the measure of U=90°, the measure of S=31°, and TU = 77 feet, then the length of US to the nearest tenth of a foot is approximately 39.4 feet.
In angle STU, we have a right triangle with U=90°, S=31°, and TU=77 feet. To find the length of US, we can use the sine function:
sin(S) = opposite side (US) / hypotenuse (TU)
sin(31°) = US / 77 feet
To find the length of US, multiply both sides by 77 feet:
US = 77 feet * sin(31°)
US ≈ 39.4 feet
Therefore, the length of US to the nearest tenth of a foot is approximately 39.4 feet.
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Choose the description that correctly compares the locations of each pair of points on a coordinate plane.
a. (–2, 5) is
choose...
(–2, –1).
b. (1, 212) is
choose...
(4, 212).
c. (3, –6) is
choose...
(3, –3).
d. ( −212, 1) is
choose...
(–3, 1).
e. (312 , 12) is
choose...
( 12, 12).
f. (2, 5) is
choose...
(2, –5).
The point (–2, 5) is located above the point (–2, –1).
The point (1, 212) is located to the left of the point (4, 212).
The point (3, –6) is located below the point (3, –3).
The point (−212, 1) is located to the left of the point (–3, 1).
The point (312, 12) is located to the right of the point (12, 12).
The point (2, 5) is located above the point (2, –5).
Find out the comparisons of the location of each pair of points?a. (–2, 5) is above (–2, –1). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (–2, 5) is located above the point (–2, –1).
b. (1, 212) is to the left of (4, 212). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (1, 212) is located to the left of the point (4, 212).
c. (3, –6) is below (3, –3). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate decreases as you move down on the coordinate plane, the point (3, –6) is located below the point (3, –3).
d. (−212, 1) is to the left of (–3, 1). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate decreases as you move to the left on the coordinate plane, the point (−212, 1) is located to the left of the point (–3, 1).
e. (312, 12) is to the right of (12, 12). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (312, 12) is located to the right of the point (12, 12).
f. (2, 5) is above (2, –5). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (2, 5) is located above the point (2, –5).
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Consider the geometric series 1 - x/3 - x^2/9 - x^3/27......
What is the common ratio of the series and for what values of x will the series converge? Determine the function f representing the sum of the series.
The function f representing the sum of the series for x in the interval (-3, 3). Hi! The given geometric series is 1 - x/3 - x^2/9 - x^3/27...
The common ratio of the series is obtained by dividing a term by its preceding term. Let's consider the first two terms:
(-x/3) / 1 = -x/3
Therefore, the common ratio (r) of the series is -x/3.
For a geometric series to converge, the absolute value of the common ratio must be less than 1, i.e., |r| < 1. In this case:
|-x/3| < 1
To find the values of x for which the series converges, we need to solve the inequality:
-1 < x/3 < 1
Multiplying all sides by 3, we get:
-3 < x < 3
So, the series converges for x in the interval (-3, 3).
Now, let's determine the function f representing the sum of the series. For a converging geometric series, the sum S can be calculated using the formula:
S = a / (1 - r)
where a is the first term and r is the common ratio. In this case, a = 1 and r = -x/3. Therefore:
f(x) = 1 / (1 - (-x/3))
f(x) = 1 / (1 + x/3)
This is the function f representing the sum of the series for x in the interval (-3, 3).
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Given the center, a vertex, and one focus, find an equation for the hyperbola:
center: (-5, 2); vertex (-10, 2); one focus (-5-√29,2).
The equation of the hyperbola is -(x + 5)²/71 + (y - 2)² = -71
How to calculate the valueWe can also find the distance between the center and the given focus, which is the distance between (-5, 2) and (-5 - √29, 2):
d = |-5 - (-5 - √29)| = √29
Substituting in the known values, we get:
c² = a² + b²
(√29)² = (10)² + b²
29 = 100 + b²
b² = -71
(x - h)²/a² - (y - k)²/b² = 1
where (h, k) is the center of the hyperbola.
Substituting in the known values, we get:
(x + 5)²/100 - (y - 2)²/-71 = 1
Multiplying both sides by -71, we get:
-(x + 5)²/71 + (y - 2)²/1 = -71/1
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Find the volume of a cylinder with a diameter of 28 meters and a height of 6 and one half meters. Approximate using pi equals 22 over 7.
28,028 cubic meters
4,004 cubic meters
1,274 cubic meters
572 cubic meters
The volume of the cylinder is 4004 cubic metres.
How to find the volume of a cylinder?The diameter of the cylinder is 28 metres and the height of the cylinder is 6.5 metres.
Therefore, the volume of the cylinder can be found as follows:
Hence,
volume of a cylinder = πr²h
where
r = radiush = heightTherefore,
volume of the cylinder = 22 / 7 × 14² × 6.5
volume of the cylinder = 22 / 7 × 196 × 6.5
volume of the cylinder = 28028 / 7
volume of the cylinder = 4004 cubic metres
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A student takes a measured volume of 3. 00 m hcl to prepare a 50. 0 ml sample of 1. 80 m hcl. What volume of 3. 00 m hcl did the student use to make the sample?.
The student used 30.0 mL of 3.00 M HCl to make the 50.0 mL sample of 1.80 M HCl.
To find the volume of 3.00 M HCl needed to make a 50.0 mL sample of 1.80 M HCl, we can use the equation:
M₁V₁ = M₂V₂
Where M₁ is the initial concentration, V₁ is the initial volume, M₂ is the final concentration, and V₂ is the final volume.
We are given M₁ = 3.00 M, M₂ = 1.80 M, and V₂ = 50.0 mL. We can rearrange the equation to solve for V₁:
V₁ = (M₂V₂) / M₁
V₁ = (1.80 M * 50.0 mL) / 3.00 M
V₁ = 30.0 mL
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What is the volume of the prism, measured in cubic inches
Answer:
360 cubes
Step-by-step explanation:
A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch?
Answer:
To make 3 gallons of punch, you need 2 cups of cranberry juice.
We can set up a proportion to find out how much cranberry juice is needed for 1 gallon of punch:
2 cups / 3 gallons = x cups / 1 gallon
To solve for x, we can cross-multiply:
2 cups * 1 gallon = 3 gallons * x cups
2 cups = 3x
x = 2/3 cup
Therefore, you would need 2/3 cup of cranberry juice to make 1 gallon of punch using this recipe.
Sushi corporation bought a machine at the beginning of the year at a cost of $39,000. the estimated useful life was five years and the residual value was $4,000. required: complete a depreciation schedule for the straight-line method. prepare the journal entry to record year 2 depreciation.
Entry debits the Depreciation Expense account for $7,000 and credits the Accumulated Depreciation account for the same amount, reflecting the decrease in the value of the machine over time.
To calculate deprecation using the straight- line system, we need to abate the residual value from the original cost of the machine and also divide the result by the estimated useful life. Using the given values, we have
Cost of machine = $ 39,000
Residual value = $ 4,000
Depreciable cost = $ 35,000($ 39,000-$ 4,000)
Estimated useful life = 5 times
To calculate the periodic deprecation expenditure, we divide the depreciable cost by the estimated useful life
Periodic deprecation expenditure = $ 7,000($ 35,000 ÷ 5)
Depreciation Expense $7,000
Accumulated Depreciation $7,000
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The journal entry is as given in figure:
Let f(x) = 2 sqrt(x)/8x^2 + 3x – 9
Evaluate f’(x) at x = 4.
The derivative of the function f(x) = 2 \sqrt(x) / (8x² + 3x - 9) evaluated at x = 4.
To find f'(x), we need to differentiate the given function f(x) using the power rule and the chain rule of differentiation.
First, we can rewrite the function f(x) as:
f(x) = 2x^{1/2} / (8x² + 3x - 9)
Next, we can differentiate f(x) with respect to x:
f'(x) = d/dx [2x^{1/2} / (8x² + 3x - 9)]
Using the quotient rule of differentiation, we have:
f'(x) = [ (8x² + 3x - 9) d/dx [2x^{1/2}] - 2x^{1/2} d/dx [8x² + 3x - 9] ] / (8x² + 3x - 9)²
Applying the power rule of differentiation, we have:
f'(x) = [ (8x² + 3x - 9)(1/2) - 2x{1/2}(16x + 3) ] / (8x² + 3x - 9)²
Now we can evaluate f'(x) at x = 4 by substituting x = 4 into the expression for f'(x):
f'(4) = [ (8(4)² + 3(4) - 9)(1/2) - 2(4)^(1/2)(16(4) + 3) ] / (8(4)² + 3(4) - 9)²
f'(4) = [ (128 + 12 - 9)(1/2) - 2(4)^(1/2)(67) ] / (128 + 12 - 9)^2
f'(4) = [ 131^(1/2) - 2(4)^(1/2)(67) ] / 12167
Therefore, f'(4) = [ 131^(1/2) - 134(2)^(1/2) ] / 12167.
This is the value of the derivative of f(x) at x = 4.
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Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
The students will make a line plot of the data. They will use only one fraction in their scale. They must be able to plot all of the data above a label. Which should this fraction be?
Step-by-step explanation:
To determine the appropriate fraction for the line plot, we need to find the greatest common factor (GCF) of all the pencil lengths, and then express each length as an equivalent fraction with the GCF as the denominator.
The GCF of the pencil lengths is 1. Therefore, we can simply express each pencil length as an equivalent fraction with 1 as the denominator:
3/1, 7/1, 8/1, 5/1, 1/1, 4/1, 6/1, 8/1, 4/1, 2/1, 5/1
Now, we can see that the smallest unit increment we can use on the line plot is 1/8. This is because 1/8 is the smallest fraction that can represent all of the pencil lengths above the label (5/8, which is equivalent to 10/16).
Therefore, the students should use 1/8 as the fraction for the line plot.