Answer:
The amount of water is [tex]30,240in^3[/tex]Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a rectangular prism in the form of a bathtub.
Given data
depth of bathtub= 24 in
width of bathtub= 24 in
length of bathtub= 60 in
the volume of water in the bathtub is a function of the depth of water in relation with the dimension of the bathtub.
the depth of water is 3 in below the the top
hence the depth of water (24 in- 3 in)= 21 in
the expression for the volume of water is given as
[tex]volume= length* width*depth\\volume= 60*24*21=30,240in^3[/tex]
From an upstairs window, I can see my neighbor's fence. The angle of depression is 7 degrees. If my window is 15 ft off the ground, how far is my neighbor's fence from my house? Round to the nearest whole number, do not include units. *
It’s not 17 or 1.8 I have tried and those are wrong
Answer: 122 ft
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Tan α = opposite side / adjacent side
Where α is the angle of depression, the opposite side is the height of the window above the ground, and the adjacent side (x) is the distance between the neighbor's fence and the house.
Replacing with the values given:
Tan 7 = 15/x
x = 15/tan 7
x = 122 ft
Feel free to ask for more if needed or if you did not understand something.
Natasha uses 2.5 feet of twine to tie campfire wood into bundles. The proportional relationship between the number of bundles, x, and the amount of twine, y, in feet she uses is shown in the graph. What does the point (3, 7.5) represent in a graph?
Answer:
She uses 7.5 feet of twine to make 3 bundles of wood.
express 1.875 in the form p/q
Answer:
If the answer asks for improper fraction it is [tex]\frac{15}{8}[/tex]
If it asks for simplest form it is [tex]1\frac{7}{8}[/tex]
Step-by-step explanation:
Rewrite the decimal number as a fraction with 1 in the denominator
[tex]1.875=\frac{1.875}{1}[/tex]
Multiply to remove 3 decimal places. Here, you multiply top and bottom by [tex]10^3=1000[/tex]
[tex]\frac{1.875}{1} *\frac{1000}{1000} =\frac{1875}{1000}[/tex]
Find the Greatest Common Factor (GCF) of 1875 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 125
[tex]\frac{1875/125}{1000/125} =\frac{15}{8}[/tex]
Simplify the improper fraction
[tex]=1\frac{7}{8}[/tex]
How do I find the value of x to the nearest degree?
Answer:
I don't know if it's too advanced for you but you could use the arctangent function.
[tex]tan (x)=\frac{15}{8}\\ x=tan^{-1}(\frac{15}{8} )\\x= 61.9275[/tex]
Find the distance of point U(2, 3) from point V(5, 7).
Answer:
5
Step-by-step explanation:
You can draw a point at (5,3) and call it point A.
Connect point A with V and U to get VA = 4 and UA = 3.
You get a right triangle and use pythagoream theroem. The answer is the root of 4^2 + 3^2 which equals to 5.
The answer is 5
lindsey completed a 30 point assignment. she eared 21 points what percent did she earn?
Answer:
Lindsey got 70% on this assignment.
Step-by-step explanation:
21 divided by 30 equals 0.7 which is 70% in percent form.
Answer:
She earned a seventy percent.
Step-by-step explanation:
You set the problem up like 21/30 = x/100.
Then, you cross multiply and you get 30x=2100.
From there, you divide each side by thirty and then you get x = 70.
And that brings you to 70 percent. Hope this helps!
Solve the equation.
r^4/7=16
Answer:
use the indices formula
Find the slope of the line that passes through the pair of points (10/17,2/17) and (9/17,13/18) a.-18/185 b. -185/18
Answer:
b) -185/18
Slope of the line [tex]m = \frac{-185}{18}[/tex]
Step-by-step explanation:
Explanation:-
Given two co-ordinates are
[tex](\frac{10}{17} , \frac{2}{17} ),(\frac{9}{17} , \frac{13}{18} )[/tex]
Slope of the line
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
[tex]m = \frac{13/18 - 2/17 }{9/17 - 10/17 }[/tex]
[tex]m = \frac{\frac{221-36}{18 X 17} }{\frac{-1}{17} }[/tex]
On simplification, we get
[tex]m = \frac{-185}{18}[/tex]
wiil mark bianleast
Which describes the translation?
7 units to the right and 2 units down
7 units to the right and 2 units up
2 units to the left and 7 units up
7 units to the left and 2 units down
Answer:
7 units to the right and 2 units up
Step-by-step explanation:
What’s the vertex of y=1/3(x+2)^2-5
Answer:
vertex is (2,-5)
Step-by-step explanation:
y = a(x – h)^2 + k
the vertex is (h,k) in the equation h =2 and k = -5
Please HELP!! will mark brainiest
Which correlation coefficient could represent the relationship in the scatterplot? A) 0.34 B) -.098 C) -1.43 D) 0.99
Answer:
B) -0.98
Step-by-step explanation:
Correlation coefficient is usually denoted with numbers ranging from 1 to -1. Automatically, this eliminates option C) as our possible answer, since -1.43 is outside the range.
The trend shown in the scatter plot describes a negative relationship because, as the values in the Y-axis decreases, the values at the X-axis increases. The possible correlation coefficient we are likely to get is one that is negative. This eliminates option A and option and option D is our possible correlation coefficient for the scatter plot given since both values are positive.
Option B) -0.98, best represents the correlation coefficient of the given scatter plot. Since the points on the scatter plot seem closely aligned on a straight line, a negative value if -0.98 is mostly the possible one to get.
Answer:
-0.98
Step-by-step explanation:
The measure of Angle 1 is 95 degrees. Which of the following is NOT a true
statement about the angles shown below?*
Answer:
The second choice. m < 4 = 85 degrees.
Step-by-step explanation:
m < 4 = 180 - m < 1
= 180 - 95
= 85 degrees.
The measure of angle 4 is 85 degrees.
How does an angle form?An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.
The point of their joint is called vertex of that angle.
Those two line segments forming it are called arms of that angle.
The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.
We are given that measure of Angle 1 is 95 degrees.
Therefore, we can see that angle 4 and Angle 1 makes linear pair so.
Angle 4 = 180 - Angle 1
= 180 - 95
= 85 degrees.
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A roll of gift-wrapping paper can cover 232.2 sq. in. Jimmy wants to wrap a soccer ball that he is giving as a gift. What is the maximum radius of the ball that Jimmy can wrap? Use 3.14 for π.
a. 3.8
b. 4.3
c. 9.2
d. 18.5
Answer:
Radius, r = 3.8 inch
Step-by-step explanation:
A roll of gift-wrapping paper can cover 232.2 sq. in. Jimmy wants to wrap a soccer ball that he is giving as a gift.
We need to find the maximum radius of the ball that Jimmy can wrap. The volume of a spherical shaped object is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
r = radius of the ball
[tex]r=(\dfrac{3V}{4\pi})^{1/3}\\\\r=(\dfrac{3\times 232.2}{4\times 3.14})^{1/3}\\\\r=3.8\ \text{inch}[/tex]
So, the maximum radius of the ball that Jimmy can wrap is 3.8 inches. Hence, this is the required solution.
The maximum radius of the ball that Jimmy can wrap is 3.8 inches.
Maximum radius of the ball
The maximum radius of the ball is calculated from volume of a sphere.
V = ⁴/₃πr³
where;
r is radius of the spherical ball232.2 = ⁴/₃πr³
3(232.2) = 4πr³
696.6 = 4πr³
r³ = 696.6/4π
r³ = 55.433
r = (55.433)^¹/₃
r = 3.8 in
Thus, the maximum radius of the ball that Jimmy can wrap is 3.8 inches.
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what is the y-intercept, maximum point and the x intercepts of f(x)= -x^2÷1 +4
Answer:
maximum point: (0, 4)
x-intercepts: (2, 0), (-2, 0)
y-intercepts: (0, 4)
How does the graph of f(x) = (x - 1)2 relate to the basic function f(x) = x??
a.
shift 1 unit to the left
shift 1 unit to the right
C.
d.
shift 1 unit up
shift 1 unit down
b.
Please select the best answer from the choices provided
Answer:
Shift 1 unit to the right, i.,e. option (c).
Step-by-step explanation:
Note: Both functions can not be represented by f(x) and square is missing in basic function.
The given basic function is
[tex]f(x)=x^2[/tex]
The given function is
[tex]g(x)=(x-1)^2[/tex]
So, the given function can be written in the form of basic form as
[tex]g(x)=f(x-1)[/tex] ...(1)
The translation is defined as
[tex]g(x)=f(x+a)2+b[/tex] .... (2)
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
[tex]a=-1,b=0[/tex]
Therefore, graph of f(x) shift 1 unit to the right to get graph of g(x).
Answer:
It C
Step-by-step explanation:
factor the expression. x^2+11x+28
Answer:(x+4)(x+7)
Step-by-step explanation:
The middle number is 11 and the last number is 28.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 11
Multiply together to get 28
Can you think of the two numbers?
Try 4 and 7:
4+7 = 11
4*7 = 28
Fill in the blanks in
(x+_)(x+_)
with 4 and 7 to get...
(x+4)(x+7)
If f(x) = 2(x)2 + 5 /(x+2)
Answer:
7.07
Step-by-step explanation:
f(x) = 2(x)^2 + 5 sqrt(x+2)
Let x= 0
f(x) = 2(0)^2 + 5 sqrt(0+2)
= 2*0 + 5 sqrt(2)
= 0 + 5 sqrt(2)
= 5 sqrt(2)
= 7.07106
To the nearest hundredth
= 7.07
The perimeter of the scalene triangle is 54.6 cm.
A scalene triangle where all sides are different lengths. The base of the triangle, labeled 3 a, is three times that of the shortest side, a. The other side is labeled b.
Which equation can be used to find the value of b if side a measures 8.7 cm?
8.7 plus b equals 54.6
17.4 plus b equals 54.6
26.1 plus b equals 54.6
34.8 plus b equals 54.6
Answer:
8.7 plus b equals 54.6
Step-by-step explanation:
4(8.7) + b = 54.6.
b = 19.8 cm.
The sum of the sides = the perimeter = 3a + a + b = 54.6.
Now a = 8.7, so:
3(8.7) + 8.7 + b = 54.6
4(8.7) + b = 54.6.
b = 54.6 - 4(8.7)
b = 19.8.
Answer: D.) 34.8 + b = 54.6
Step-by-step explanation: i hope this helps :)
use the data from the table to create a scatter plot. plot al the data points from the table.
Answer:
Place a point at
8,4
5,7
6,5
10,4
2,11
4,7
3,9
1,13
1,11
3,12
4,2
7,2
5,24
9,3
5,5
Step-by-step explanation:
Answer:
Put points on
8,4
5,7
6,5
10,4
2,11
4,7
3,9
1,13
1,11
3,12
4,2
7,2
5,24
9,3
5,5
Step-by-step explanation:
Simply
(3x^2 y^3/x^3)^3
The answer is 27y^9/x^3
if multiple choice the answer is 27x^6 y^9/x^9
Pictures so you can see
Answer:
[tex]=\frac{27y^9}{x^3}[/tex]
Step-by-step explanation:
[tex]\left(\frac{3x^2y^3}{x^3}\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}\\\left(\frac{3x^2y^3}{x^3}\right)^3=\frac{\left(3x^2y^3\right)^3}{\left(x^3\right)^3}\\=\frac{\left(3x^2y^3\right)^3}{\left(x^3\right)^3}\\\mathrm{Simplify}\:\left(3x^2y^3\right)^3:\quad 27x^6y^9\\=\frac{27x^6y^9}{\left(x^3\right)^3}\\\mathrm{Simplify}\:\left(x^3\right)^3:\quad x^9\\=\frac{27x^6y^9}{x^9}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}[/tex]
[tex]\frac{x^6}{x^9}=\frac{1}{x^{9-6}}\\\frac{x^6}{x^9}=\frac{1}{x^{9-6}}\\=\frac{27y^9}{x^{9-6}}\\\mathrm{Subtract\:the\:numbers:}\:9-6=3\\=\frac{27y^9}{x^3}[/tex]
The ratio of the number of A's in the class to B's in the class was 2:5. How many people got A's if there were 40 people who got B's?
Answer:
16 students got an A
Step-by-step explanation:
Set up an equation to compare the ratio to the scores:
[tex]\frac{2}{5} = \frac{x}{40}[/tex]
Cross multiply:
80 = 5x
Divide each side by 5:
x = 16
Now, check if [tex]\frac{16}{40} = \frac{2}{5}[/tex]
16/8 = 2
40/8 = 5
The ratios are the same! Therefore, 16 students got an A!
Hope this helps! Feel free to contact me if you have any questions :)
[tex]Total- no- of- students = 56\\A -students = Total- no- of- students - B-students\\A - students = 56 - 40\\A students = 16[/tex]Answer:
A Students = 16 students
Step-by-step explanation:
[tex]A :B\\2 :5\\ No- of -A -students =?\\No- of -B -students = 40\\2+5 =7\\\frac{5}{7} *x = 40\\\frac{5x}{7} =40\\Cross - multiply\\280 = 5x\\Divide-both-sides-of-the-equation -by 5\\\\\frac{280}{5} = \frac{5x}{5} \\x = 56[/tex]
Pls I Need Help!
Triangle E F G. Side E F is 6 meters, F G is 5 meters, E G is 7 meters. Triangle K L J. Side K L is 28 meters, L J is 24 meters, J K is 20 meters.
Given that these triangles are similar, which side corresponds to side GE?
Given that these triangles are similar, which side corresponds to side JK?
Answer: The first one is KL and the second one is most likely FG.
Answer:
1: KL
2: FG
Step-by-step explanation:
Just did it on Edge 2020-2021
Vector donated 1/5 of yesterday's sales plus an additional $125. He gave Azul $2,225 total. How much money did the store make in sales yesterday?
15. The set of ordered pairs represents a function.
{(1,3), (2, 9), (k, 12), (5,9), (8,0)}
Which of these could be the value of k?
A. 0
B. 1
C. 5
D. 8
Answer:
A. 0
Step-by-step explanation:
In a function, all x-coordinates must be different.
The given function already shows 1, 2, 5, and 8 as x-coordinates, so you must choose a number other than those.
Answer: 0
The correct option will be Option A : the value of k will be 0.
What is a function?The function is a relation between two sets where one set is called the domain and another set is the codomain which is one one or many one relations.
If the x or input values are different then the relation will become a function.
So we can say if the x values are repeated and their corresponding y or output values are the same, then also the relation becomes a function.
If the x values are repeated and their corresponding y or output values are different, then the relation will not become a function.
Given the ordered pairs are {(1,3), (2, 9), (k, 12), (5,9), (8,0)
As we know the x value is repeated and the y value is different then the relation will not be a function.
So here in the given ordered pair, there is no any second 12. So k value should not be equal to 1,2,5,8 otherwise it will not be a function.
By checking all the options
0 is not present in x value of the given ordered pair.
Therefore the correct option will be Option A : the value of k will be 0.
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If h(x) = x-7 and g(x) = x2, which expression is equivalent to (gº h)(5)?
Answer: [tex]g(5) *h(5) = (5-7)(5^2)= (25)(-2) = -50[/tex] Im assuming that g(x) is x^2, since you were incapable of writing the exponent sign
Step-by-step explanation:
[tex](g*h)(x)=g(x)*h(x)[/tex]
So this means the functions should be multipled and both evaluated at x = 5
The value of the composition of functions ( g o f ) ( 5 ) = 4
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as h ( x )
Now , the value of h ( x ) is
h ( x ) = x - 7
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = x²
Now , the composition of function ( g o f ) ( 5 ) is given by
The value of f ( 5 ) = 5 - 7 = -2
Now , the value of g ( -2 ) is
g ( -2 ) = ( -2 )²
g ( -2 ) = 4
Hence , the composition of function is solved and the value is given by A = ( g o f ) ( 5 ) = 4
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Every summer Kendra plants a vegetable garden in her yard last year she planted six rows of tomatoes eight rows of peppers Kendra wants to keep the same ratio this year but she only plants to plant three roasted tomatoes how many rows of peppers well Kendra plant this year
Answer: Ratio's 3:5
Step-by-step explanation:
Ratio of last year 6:8 Now this year since she wants to only plant 3 rows of tomatoes there would be five rows of tomatoes cuz ur taking away three rows form each typa veggie so the new ratio is now 3:5
((Hope it Helps))
IVE BEEN STUCK ON THIS QUESTION CAN I PLEASE GET SOME HELP I WOUDL APPRECIATE IT THANK YOU
Answer:
B. 3x² -17
Step-by-step explanation:
f(x)= 3x+1
g(x)= x² -6
(f °g)(x) =f(g(x)) so plug in in f for variable x²-6
(f °g)(x) = 3(x² -6) +1 =3x² -18 +1 = 3x² -17
the pair of figures is similar. find x. round to the nearest tenth if necessary.
A: 34cm
B: 29.6cm
C: 9.8cm
D: 21.9cm
Answer:
B
Step-by-step explanation:
Alaine has 1 gallon of paint. She is going to pour it into
paint tray that measures 10 inches wide, 12 inches long, and 5 cm deep.
(1 gallon = 231 in?, 1 inch = 2.54 cm)
Which of the following scenarios will happen?
The paint will not fill the tray by 369 cm
The paint will not fill the tray by 5.22 in
The paint will fill the tray exactly
The paint will overfill the tray by 5.22 in?
Answer:
First, solve for the volume of the tray by the equation V = L x W x H. Convert first all the dimensions to inches. The operation gives an answer of volume equal to 236.22 in³. Converting the amount of paint available to in³. This gives an answer of 231 in³. Hence, the answer is letter B.
Step-by-step explanation:
What is the measure of arc AB? A) 60° B) 75° C) 125° D) 150°
Answer:
150
Step-by-step explanation:
The arc would be the same as the angle that is in it's center because this is a circle.
The measure of arc AB is equal to the 150 degree, as central angle is equal to the intercepted arc. Option D is the correct option.
What is the central angle of the arc?The central angle is the angle which is subtended by the arc of the circle at the center point of that circle. The formula which is used to calculate the central angle of the arc is given below.
[tex]\theta=\dfrac{s}{r}[/tex]
Here, (r) is the radius of the circle, (θ) is the central angle and (s) is the arc length.
In the given circle, suppose the center of it is O. The central angle AOB given as,
[tex]\angle AOB=150^o[/tex]
The central angle is equal to the intercepted arc of the angle. Thus,
[tex]\text {arc } AB=\angle AOB\\\text {arc } AB=150^o[/tex]
Thus, the measure of arc AB is equal to the 150 degree as central angle is equal to the intercepted arc. Option D is the correct option.
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