[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]
1. Why is line AC congruent to line CB in the diagram below?
Answer:
They are both identical triangles with the same angles and lenght which means they are congruent and so their hypotenuses lines AC and CB are also congruent.
Step-by-step explanation:
Hope this helps
Answer:
they are congruent because they are on a perpendicular line
If the original quantity is 8 and the new quantity is 4, what is the percent increase?
The percent increase is 50%.
What is percentage increase?The percentage increase in a quantity is the rate of difference in the old and new value to the old value, express in percentage.
i.e percentage increase = (old value - new value)/ old value
If the new quantity were be have decreased, then the percentage decrease can also be determined.
Considering the given question, the percentage increase can be determined by;
old quantity = 8
new quantity = 4
So that,
percentage increase = (old value - new value)/ old value
= (8 - 4)/ 8 *100%
= 4/ 8 * 100%
percentage increase = 50%
The percent increase is 50%.
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Solve the system of equations.
x + y + z = 9
-2x + y + 2z = 3
x - 4y - z = 2
Answer:
(4,-1,6)
Step-by-step explanation:
x=4
y=-1
z=6
A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.
Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective than B.
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that B is more effective than A.
No, because a difference in mean rating of 1.5 or less occurred 167 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
answer is D
The conclusion on if there is convincing evidence that the one detergent is better than the other is; Option D: No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
What is the conclusion of the sample research?We are told that, 25 pieces are randomly assigned to be cleaned with detergent A, while the remaining 25 pieces are cleaned with detergent B.
Therefore, we can say that the sample size for both detergent A and detergent B is same. We can also say that the sample is distributed randomly which means that the sample is unbiased (fair).
We are also told that the mean rating for detergent B is found to be significantly less than the mean rating for detergent A. Since we know that the mean is the average of a set of given numbers, then we can conclude that there is No evidence that the one detergent is better than the other because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
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What are the potential solutions to the equation below? 1ln(x+3)=0
A. x = -3 and x = -4
B. x = -2 and x = -4
C. x = 2 and x = -3
D. x = 2 and x = 4
The potential solutions to the equation are x = -2 and x = -4
What is logarithm ?A logarithm is the power to which a number must be raised in order to get some other number .
The given expression is ln(x + 3) = 0
It can be rewritten as
[tex]ln _e (x + 3) = 0[/tex]
[Since base of a natural logarithm is considered as e]
[tex]e^0 = (x + 3)[/tex]
Since in a logarithmic function if log b with base e = c
Then we further solve the expression to get the possible roots.
x + 3 = 1
x = 1-3
x = -2
Therefore, the potential solutions are x = -2 and x = -4
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1. Calculate the volume of the following figure.
H=2cm
W = 2cm
L = 5cm
Answer: It should be 2 x 2 x 5 = 20cm
Step-by-step explanation: Formula- volume = length x width x height
I hope this helps:)
Answer:It would be..
Step-by-step explanation:
5 x 2 = 10, And then we multply the with the 10. 10 x 2 = 20,
The Answer is 20.
The coordinates of a triangle are: R(-4,4) S(-2,-2) T(2, 3) Brian determined A RST was a scalene triangle, but he wanted to the find the lengths of the three sides. Complete the table to determine the three side lengths of ARST. 37 38 140 141 length of RS length of ST length of TR
The length of the sides RS, ST and TR are √72, √41 and √37 in the scalene triangle RST.
The distance between any two points A(a,b) and B(c,d) in the plane is given by,
AB = √((c-a)²+(d-b)²)
Here, it is given that the points of the triangle are R(-4,4) S(-2,-2) T(2, 3).
The triangle is scalene so length of every side is different.
Now, Using the above formula,
RS = √((2+4)²+(-2-4)²)
RS = √(36+36)
RS = √72
ST = √((2+2)²+(3+2)²)
ST = √(16+25)
ST = √41
TR = √((2+4)²+(3-4)²)
TR = √(36+1)
TR = √37
So, Brian is correct, the triangle is a scalene triangle.
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What is another way of expressing 96?
A. 2^5 × 3
B. 2³ × 3
C. 2×2×2×2×3
D.9 × 6
Answer:
A) 2⁵*3
Step-by-step explanation:
96
2*48
2*2*24
2*2*2*12
2*2*2*2*6
2*2*2*2*2*3
2⁵*3
Therefore, A is the correct answer.
Find the value of x. Round to the nearest tenth.
x
15.3
37°
help me asap
Answer:
x ≈ 25.4
Step-by-step explanation:
Using the sine ratio in the right triangle
sin37° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15.3}{x}[/tex] ( multiply both sides by x )
x × sin37° = 15.3 ( divide both sides by sin37° )
x = [tex]\frac{15.3}{sin37}[/tex] ≈ 25.4 ( to the nearest tenth )
Can you solve Pythagorean theorem with only C?
The Pythagorean theorem can be solved using a C programme, therefore yes. The Pythagorean theorem states that the hypotenuse's square length of a right triangle equals the sum of the squares of its other two sides. The slope is the side that faces the right angle.
Therefore, given the lengths of the two shorter sides (a and b), the length of the hypotenuse can be calculated using the formula: c = sqrt(a^2 + b^2).
Here is an example C program that calculates the length of the hypotenuse of a right triangle given the lengths of the other two sides:
#include <stdio.h>
#include <math.h>
Above command is for library
int main() {
double a, b, c;
Above command to initiate the variable.
printf("enter the first side's length.: ");
scanf("%lf", &a);
To enter the value in program
printf("enter the second side's length.: ");
scanf("%lf", &b);
Enter the value and print the value
c = sqrt(a*a + b*b);
Arithmetic command
print("The hypotenuse's length is: %lf\n", c); return 0;}
Print the value and return the program value to zero.
This program prompts the user to enter the lengths of the two shorter sides of the triangle, calculates the hypotenuse length using the Pythagorean theorem, and then prints the result.
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18,54, 162, ...
Find the 8th term.
Answer:
a₈ = 39366
Step-by-step explanation:
The terms have a common ratio between consecutive terms
r = 54 ÷ 18 = 162 ÷ 54 = 3
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 18 and r = 3 , then
a₈ = 18 × [tex]3^{7}[/tex] = 18 × 2187 = 39366
How do you tell if a log graph is growth or decay?
To tell if a log graph is a growth or decaying, look at the slope of the line. If the slope is positive, then it is growth; if the slope is negative, then it is decay.
A positive slope indicates that the value is increasing over time, while a negative slope indicates that the value is decreasing over time. To find the slope, take two points on the line and calculate the change in the y-value divided by the change in the x-value.
If the answer is positive, the graph is growth; if the answer is negative, the graph is decay. Additionally, you can look at the y-intercept of the graph, which is the value where the line meets the y-axis. If the y-intercept is positive, the graph is growth; if the y-intercept is negative, the graph is decay.
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PLEASE HELP YOU WILL GET BRAINLIEST!
Answer:
supplementary, complementary, acute 45, supplementary, x=10
Step-by-step explanation:
A rectangular piece of land is 1/4 miles long and a 1/2 mile wide what is the area of the piece of land in square miles
Answer:
1/8 square miles
Step-by-step explanation:
1/4 times 1/2 = 1/8
Which is equivalent to the ratio 35 : 100?
Answer: 7:20
Step-by-step explanation:
It seems like there are no options to choose from, but if that is one of the options, here's how:
You can simplify ratios by finding if there is a common multiple.
For 35 and 100, there is a common multiple of 5, so you can divide both sides by 5 to simplify the equation.
That leaves us with 7:20. Since one is a prime number, we can't simplify this further.
Answer:
The ratio equivalent to 35:100 is 7:20
Step-by-step explanation:
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is the Ratio?
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Given ratio,
= 35 / 100
= 5× 7 / 20 × 5
= 7 / 20
Lynn is a zoo kepper at matlock zoo.her hourly rate is $6.85.she earns $328.80 every week.how many hours does she works in a week?
Answer:
48 hours
Step-by-step explanation:
Answer:
48 hours
Step-by-step explanation:
328.80 a week, and a 6.85 hourly rate.
To find hours worked:
$328.80 (total earned) / $6.85 (earned hourly) = 48 hours
Please HURRY!!!
Which of the following must be true
need help with these 4
Thus, It is possible to visually assess whether a limit exists as x approaches a by looking at the function f (x) and g (x) graphs, which are 1 and 5 when x is very close to x=a.
How would you define limit?In mathematics, a limit is the value that a function, a sequence, or an index approaches as an input or an index gets closer to a particular value. Limits are essential to the study of calculus and mathematical analysis since they are used to define continuity, derivatives, and integrals.
Here,
From the function f (x) and g graphs shown here ( x)
1) lim f (x) plus lim g ( x )
= -1 + 2 = 1
2) f (-1) + lim g ( x)
= 3 + 2
= 5
Therefore , the solution of the given problem of limit comes out be 5.
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On a day, a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. This tend continues each day. Write an equation modeling the views, v, as a function of time. What would be the day when more than 20,000 people will see the video
Answer:
Day 13
Step-by-step explanation:
The question can be represented with a geometric sequence
Where,
a = 5
Common ratio , r = 2
v(t) = a * r^(t - 1)
v(t) = 5 * 2^(t-1)
20,000 = 5 * 2^(t-1)
Divide both sides by 5
20,000 / 5 = 5 * 2^(t-1) / 5
4,000 = 2^(t-1)
2^12 = 2^(t-1)
12 = t - 1
12 + 1 = t
t = 13 days
What would be the day when more than 20,000 people will see the video
Check:
v(t) = 5 * 2^(t-1)
= 5 * 2^(13-1)
= 5 * 2^12
= 5 * 4,096
= 20,480
Therefore,
The day when more than 20,000 people will see the video is day 13
The rectangular floor of a classroom is 26 feet in length and 36 feet in width. A scale drawing of the floor has a length of 13 inches. What is the perimeter, in inches, of the floor in the scale drawing?
HURRYYY I NEED HELP AGAIN!
Answer: 62 inches
Step-by-step explanation:
26÷13 =2
so 2 is the scale factor
so 36÷2= 18
18+18+13+13=62
I HOPE THAT HELPED
What is the Vertex of the graph?
options:
(1,1)
(-1,1)
(0,1)
(1,0)
Answer:
(-1, 1)Step-by-step explanation:
First coordinate of a point we read from X-axis and the second coordinate of a point we read from Y-axis
which values from the set (2,4,6,8,10) make the inequality n + 5 > 10 true ?
Answer: Values; 6,8,10
Step-by-step explanation:
❌ 2 + 5 > 10
❌ 4 + 5 > 10
✔️ 6 + 5 > 10
✔️ 8 + 5 > 10
✔️ 10 + 5 > 10
(I need the answer as FAST as possible so if anybody could help that would be greatly appreciated)
Katie has 3/4 of a yard of rope which she needs to divide into pieces, each 1/8 of a yard long. how many pieces will she have left?
Answers:
1/6
7
1/8
6
Answer:
not really understanding this question, but I think 6.
Step-by-step explanation:
3/4=6/8
Rewrite in simplest terms: 4 (d+9) -8 (-3d-3)
Answer:
28d + 60
Step-by-step explanation:
4d + 36 + 24d + 24
28d + 60
First I used distributive property to expand. Then I rewrote my answer into simplest form possible. As we know that two negatives equal postive which is what I did to get the correct answer.
the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³
The value of the length will be 17920cm.
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Since the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³.
The value of the length will be:
= 7 / (7 +5+2) × 35840
= 7/14 × 35840
= 17920cm
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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³. Find the value of the length
find the total surface area of this triangular prism
The surface area of the triangular prism is 156cm² when the triangle sides are 8cm and 15 cm rectangle sides are 17cm and 2 cm.
Given that,
We have to find the total surface area of the triangular prism in the given picture.
We know that,
First, we need to calculate the area of the triangle
a = area of triangle
a = 1/2 ×15 cm × 8 cm
a = 60 cm²
Now,
We must determine the three rectangles' areas.
a₁ = 2cm × 17cm
a₁ = 34cm²
a₂ = 2cm × 15cm
a₂ = 30cm²
a₃ = 2cm ×8cm
a₃ = 16cm²
Now, we must multiply the triangle by two and sum all the estimated areas.
a₁ + a₂ + a₃ + 2a =60cm² + 34cm² + 30cm² + 2 × 16cm² = 156cm²
Therefore, The surface area of the triangular prism is 156cm² when the triangle sides are 8cm and 15 cm rectangle sides are 17cm and 2 cm.
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What are the dimensions of a rectangle with an area of 96 square centimeters and a perimeter of 40 centimeters?
2. Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the weekend he worked for a total of 14 hours and made a total of $192. How many hours did he work for each job?
Max mowed the lawns for 6 hours and tutored students for 8 hours.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is that Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the weekend he worked for a total of 14 hours and made a total of $192.
We can write the system of equations as -
x + y = 14
12x + 15y = 192
Refer to the graph attached. On solving the equation graphically, we get-
x = 6, y = 8
Therefore, Max mowed the lawns for 6 hours and tutored students for 8 hours.
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Which of the following three equations represent the same line? 12(t) (2,2,4) +t(2,4,6) O A. 1(),12() and Ia(t O B. 11(t) and 12(t) . 12(t) and la(t) D. 1(t) and 1(t) E. none Submit
1(t) = 12(t) (2,2,4) +t(2,4,6) and Ia(t) = 12(t) (2,2,4) +t(2,4,6) represents the same line, as they are both equivalent to 12(t)(2,2,4) + t(2,4,6). So Option A is correct.
The equation of a line in 3-dimensional space can be represented in the form "r(t) = a + tb" where "r(t)" is a vector that represents any point on the line, "a" is a vector that represents a point on the line, and "b" is a vector that represents the direction of the line.
The given equations are:
1(t) = 12(t) (2,2,4) +t(2,4,6)
Ia(t) = 12(t) (2,2,4) +t(2,4,6)
As we can see that both equations are identical to equation 12(t) (2,2,4) +t(2,4,6) thus these three equations represent the same line.
The other given options B, C, and D are not equivalent to each other or to the original equation, thus they do not represent the same line.
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