Answer:
32901 gallons
Step-by-step explanation:
First, we find the volume of the cylindrical water tank when it is full.
The volume of a cylinder is given as:
V =
where r = radius and h = height of the cylinder
The diameter of the tank is 20 feet, hence, its radius is 10 feet.
Volume, V, is therefore:
V =
This is the volume of the tank, when it is full.
When it is 70% full, the volume will be:
1 cubic foot () is 7.48 gallons.
Therefore, the volume of the 70% full tank in gallons will be:
4398.23 * 7.48 = 32901.05 gallons ≅ 32901 gallons
The tank contains 32901 gallons of water.
Answer:
approximately 32,900 gallons
Step-by-step explanation:
volume water in tank
v = πr²h * .70
v = π * 10² * 20 * .70
v = 4,398.2297150257 ft³
1 ft³ = 7.48 gallons
gallons in tank
4,398.2297150257 * 7.48 = 32,898.7582683922
~ 32,900 gallons
What is the value of x in the triangle?
Round your final answer to the
nearest hundredth
Given:
In a right angle triangle,
Hypotenuse = 25 cm
Base = x
Angle between base and hypotenuse = 18 degrees.
To find:
The value of x.
Solution:
In a right angle triangle,
[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]
In the given right triangle,
[tex]\cos (18^\circ) =\dfrac{x}{25}[/tex]
[tex]\cos (18^\circ) \times 25=x[/tex]
[tex]0.9510565 \times 25=x[/tex]
[tex]23.7764125=x[/tex]
Round the answer to the nearest hundredth (two decimal).
[tex]x=23.78[/tex]
Therefore, the value of x is about 23.78 cm.
Can someone Help me?
The Answer: C I did this yesterday
Step-by-step explanation:
Ms. Lesure is going to buy lunch for Mr. Shows Interactions A class. How many whole pizzas would she need to buy (assume each pizza has 8 slices) assuming there are 10 boys and 8 girls and the boys will eat 2 slices each and the girls will eat 1.5 slices each?
Answer:
Ms. Lesure is going to need to buy 4 pizzas for Mr. Shows Interactions A class. The boys would eat 20 slices and the Girls in total will eat 12 slices. In total you'll need about 32 slices and 32 divided by 8 is 4.
Step-by-step explanation:
Determine the value of”k” when the lines y=k/3x+2 and y=1/4x+2 are perpendicular.
Answer:
k = -12
Step-by-step explanation:
When lines are perpendicular, their slopes are the opposite reciprocal of each other.
The opposite reciprocal of [tex]\frac{1}{4}[/tex] is -4
[tex]\frac{k}{3}=-4[/tex]
k = -12
The expression 6 x 2gives the surface area of a cube, and the expression x 3gives the volume of a cube, where x is the length of one side of the cube. Find the surface area and the volume of a cube with a side length of 2 meters
Answer Expert Verified
3.1/5
18
Surface of a cube=S(x)
S(x)=6x²
S(2 m)=6(2 m)²=6(4 m²)=24 m²
The surface of this cube is 24 m².
Volume of a cube=V(x)
V(x)=x³
V(2 m)=(2 m)³=8 m³
Answer:
18
Step-by-step explanation:
The figure shown is composed of a right rectangular prism attached to a right triangular
prism. The surface area of the figure is 130 cm?
What is the value of n, in centimeters?
n cm
4 cm
2 cm
Use the number pad to enter your answer in the box.
5 cm
cm
5 cm
4 cm
9514 1404 393
Answer:
n cm = 3 cm
Step-by-step explanation:
The total surface area is the sum of the base areas and the lateral area. The base areas are the sum of the areas of the rectangle and triangle that define the shape of the base.
The rectangle has dimensions 5 cm by n cm. The triangle is 5-2 = 3 cm high and 4 cm at the base. Then the front face area is ...
A = lw + 1/2bh
A = (5 cm)(n cm) +1/2(4 cm)(3 cm) = (6 +5n) cm²
The lateral area is the product of the perimeter of the base and the depth of the prism.
A = Ph
A = (5 cm + n cm + 2 cm + 5 cm + 4 cm + n cm)(4 cm) = (64 +8n) cm²
The total surface area is the sum of the areas of the two bases and the lateral area:
130 cm² = 2(6 +5n) cm² +(64 +8n) cm²
130 = 76 +18n . . . . . . divide by cm², collect terms
54 = 18n . . . . . . . . . subtract 76
3 = n . . . . . . . . . . divide by 3
The value of n in centimeters is 3 cm.
y+1=5(x-4) write a slope intercept form
Helppp
Answer:
y = 5x - 21
Step-by-step explanation:
[tex]y+1=5(x-4)\\y+1=5x-20\\y=5x-21[/tex]
Use the quadratic formula to solve the equation.
8x2−17x+7=0
Enter your answers, in simplified radical form, in the boxes.
x =
or x =
Answer:
just took the test
1st root= x1 =(17+√65)/16
2nd root =x2 =(17-√65)/16
What is Quadratic Equation?A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown and a, b , and c represent known numbers , where a should not be equal to 0.
D = b^2 - 4 * a *c
D = (-17)^2 - (4)(8)(7)
D= 65 >0
There will be two solutions exist in this condition
1st root : (-b+√D)/2a
=(-(-17)+√65)/2*8)
1st root= x1 = (17+√65)/16
2nd root : (-b-√D)/2a
= (-(-17)-√65)/2*8)
2nd root = x2 = (17-√65)/16
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In a survey, 15 high school students said they could drive and 15 said they could not. Out of 60 college students surveyed, 30 said they could drive. Micah concluded that knowing that a person is in college means they are more likely to drive. Is Micah’s conclusion correct? Explain.
Answer:
No.
Step-by-step explanation:
#1, the sample size is not indicative of a proper high school population, unless of all there is a small amount of students in the high school (or even only 30 students in it). On a individual basis, it can vary widely, and so data analysis such as this is not correct. The data size is skewed as well for the college, especially as college campuses typically house more students then usual. To only ask 60 college students also skew the data gotten. Another sample error may be locational error, in which the location of the schools may warrant the need for a driver license, or if it is not needed, as well as the distance of the student's house and/or where needed facilities are to accommodate a student's needs and desires.
If we were to set all these problems aside and focus more on the question, 15 high school students said they could drive, and 15 said they could not, which makes the sample size of 30 high school students in all. 15 say they can drive, therefore:
15/30 = 1/2, or there is a 50% chance of obtaining a student that can drive.
On the other hand, out of 60 college students surveyed, 30 said they can drive, therefore:
30/60 = 1/2, or there is a 50% chance of obtaining a student that can drive.
∴ Micah's prediction is incorrect in obtaining a college student that can drive more easily then obtaining one that can drive in a high school.
However, remember that too small of a data size can lead to a heavy skew, and it will not represent reality as well.
~
Answer:
Sample Response: No, Micah is not correct. Since there are equal numbers in the group that drive and the group that doesn’t drive, the relative frequency for each is 50%. Because the relative frequencies are the same, there is no association between the variables.
Step-by-step explanation:
Got this from Edg 2021
what is the scale factor from ABC to DEF?
Answer:
C
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{EF}{BC}[/tex] = [tex]\frac{11}{66}[/tex] = [tex]\frac{1}{6}[/tex] → C
factorize 3x(j-f) -4(f-j)
9514 1404 393
Answer:
(3x +4)(j -f)
Step-by-step explanation:
3x(j -f) -4(f -j) = 3x(j -f) +4(-f +j) . . . . distribute the minus sign in -4(f-j)
= 3x(j -f) +4(j -f)
= (3x +4)(j -f)
Question 1
Find the area of AJKD (Triangle JKD)
+y
F
4
2
A
0
B
6
с
8
D
10
2
4
12
А
12units2
B
15units
С
bunits2
D
14units
Answer:
6 units^2
Step-by-step explanation:
To solve this problem i use the net to find the area. Each square is a unit. there was 4 units and 4 halves. 4 halves combined, would be 2.
2 + 4= 6.
How do the perimeters of the triangles compare? Original: height-18, slant-30, length-24 Scaled: height-6, slant-10, length-8 A) the scaled triangles perimeter is 3x's larger than the original triangles perimeter. B) the scaled triangles perimeter is 6x's smaller than the original triangles perimeter C) the scaled triangles perimeter is 1/9 the size of the original triangles perimeter D) the scaled triangles perimeter is 1/3 the size of the original triangles perimeter
Answer:
D) the scaled triangles perimeter is 1/3 the size of the original triangles perimeter
Step-by-step explanation:
Given
Original:
[tex]Height = 18, Slant = 30, Length =24[/tex]
Scaled:
[tex]Height =6, Slant=10, Length=8[/tex]
Looking at the dimension of both triangles, The relationship between the original and the scaled copy is:
[tex]Scaled = \frac{1}{3} * Original[/tex]
Hence, the perimeter is:
[tex]Perimeter (Scaled) = \frac{1}{3} * Perimeter (Original)[/tex]
15/25 = y/30. Solve for y.
15/25= y/30
y= 3/5×30
y= 3×6
y=18
THE ANSWER IS Y=18
Answer:
y = 6
Step-by-step explanation:
One way of doing this problem is to start by reducing the first fraction, 5/25, obtaining 1/5. Then
1 y
---- = -----
5 30
Through cross-multiplication, we get 5y = 30, or y = 6
Describe fully the transformation that maps shape a and b
Answer:
Rotate 90' clockwise Centre (-2, -2)
if you mean A onto B
help help help help help
Answer:
x = 4.4
Step-by-step explanation:
cos theta = adjacent side / hypotenuse
cos 24 = y/x
cos 24 = 4/x
x cos 24 = 4
x = 4/cos 24
x =4.378545114
Rounding to 1 decimal place
x = 4.4
Answer:
x=4.4cm
Step-by-step explanation:
We can use cosine to find x as we're given y (adjacent) and the angle. This is also a right triangle.
cos24=4/x
x=4/cos24
x=4.4
Mike graphed an exponential growth function that has a y-intercept of 5.
Which of the following functions did Mike graph?
a) y = 2^5x
b) y= 5(2^x)
c) y= 2^x +5
d) y= 2^x-5
Write an equation that passes through the points (3, 6) and (1,-1)
Answer:
y = 7/2x - 9/2
Step-by-step explanation:
y2 - y1 / x2 - x1
-1 - 6 / 1 - 3
-7 / -2
7/2
y = 7/2x + b
-1 = 7/2(1) + b
-1 = 7/2 + b
-9/2 = b
Help pls and thank uu
Answer:
f(- 4) = - 4
Step-by-step explanation:
f(- 4) with x = - 4 gives f(- 4) = - 4
The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario. Which graph represents this wage increase for x < 12?
The solution is Option C.
The graph which represents the inequality equation is
f ( x ) = { 0.50 , if x < 3
1 , if 3 ≤ x < 6
1.50 , if 6 ≤ x < 9
2.00 , if 9 ≤ x < 12 }
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of years be = x
Let the increment in wages be = y
Now , the equation will be
For the employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour
So , the inequality equation is x < 3 , f ( x ) = 0.50
Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00
So , the inequality equation is 3 ≤ x < 6 , f ( x ) = 1
Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour
So , the inequality equation is 6 ≤ x < 9 , f ( x ) = 1.50
Employees of at least nine years, but less than twelve years receive an increase of $2.00
So , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2
Therefore , the graph which represents the solution is Option C.
Hence , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2
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Pls help right now for 30 points
Use the edges of the triangles to determine which ones are closest together for the smallest of furthest apart for the largest.
1. Smallest = b
Largest = c
2. Smallest = f
Largest = g
. A study was conducted to evaluate the relationship between artificial sweeteners and bladder cancer. 3,000 cases and 3,000 controls were enrolled in the study. Among the cases, 1293 had used artificial sweeteners in the past, while 1707 had never used artificial sweeteners. Of the controls, 855 had used sweeteners and 2145 had not. a. What is the exposure and what is the disease
Answer:
Exposed group has 2 times the odds of bladder cancer than not exposed group based on our odds ratio.
The disease is bladder cancer.
Explanation:
Calculate odds for exposed group =
1293 with bladder cancer had used artificial sweeteners in the past/
855 without bladder cancer had used sweeteners= 1.51
Calculate odds for not exposed group=
1707 with bladder cancer had never used artificial sweeteners/ 2145 without bladder cancer had never used artificial sweeteners=0.795
Odds ratio=odds for exposed group/odds for not exposed group
= 1.51/0.795
= 1.899
Therefore exposed group has two times the odds of bladder cancer than not exposed group.
Which of the following is the equation of the line in slope-intercept form that has a slope of -2 and
passes through the coordinate (4, 1)?
A) y = –2x - 7
B) y -1 = -2(x - 4)
C) y = -2x + 9
D) y = -2x
Answer:
c). y = -2x + 9
Step-by-step explanation:
y = -2x + b
1 = -2(4) + b
1 = -8 + b
9 = b
A hula hoop is 113 inches around. What is its diameter to the nearest inch?
HURRY PLEASE
Answer:
35.97
Step-by-step explanation:
113 divided by pie (3.14)
The ratio of boys to girls in a class is 5:4. There are 36 Students in the class.How many students are girls
Answer:
16
Step-by-step explanation:
let boys equal to 5x
and girls equal to 4x
so 4x+5x=36
X=4
so boys are 5*4
boys are 20
and girls are 16
so boys are 4 more than girls
Answer:
16 girls
Step-by-step explanation:
boys : girls : total
5 4 5+4 = 9
take the total number of people and divide by 9
36/9 = 4
Each number should be multiplied by 4
boys : girls : total
5*4 4*4 9*4
20 16 36
There are 16 girls
The refractive index of benzene with respect to air is 1.5 and that of ruby with respect to air is 1.71. What will be the refractive index of benzene with respect to ruby?
Answer:
With respect to air, the refractive indices of water and benzene are 1.33 and 1.50 respectively
PLZ HELP ANY GUESS WOULD HELP
Answer:
1st onne I believe I couldd be wrong but thats what I got
Step-by-step explanation:
Write the equation of the line passing through the points (-4,6) and (-6,4).
Answer:
y=x +10
Step-by-step explanation:
answer is in photo above
Answer:
y = 1x + 10
Step-by-step explanation:
y2 - y1 / x2 - x1
4 - 6 / -6 - (-4)
-2 / -2
= 1
y = 1x + b
4 = 1(-6) + b
4 = -6 + b
10 = b
Given m || n, find the value of x and y
X = 21
Y = 30
X:
(3x - 15) + (6x + 6) = 180 -- combine like terms
9x - 9 = 180 -- add 9 to both sides
9x = 189
x = 21
Y:
Plug x into 3x-15
3(21) - 15 = y + 18
63 - 15 = y + 18
48 = y + 18 -- subtract 18 from both sides
y = 30
Given a circle with a center at (-3.1) and a radius of 4, is the point (1,-2) inside,
outside or on? Show all work for your proof.
Answer:
Step-by-step explanation:
distance between center and (1,-2) is
[tex]d=\sqrt{(1-(-3))^2+(-2-1)^2} \\=\sqrt{16+9} \\=5>4\\[/tex]
distance of the point from the center>radius of circle.
So it lies outside the circle.