The figure below (above) shows a triangular prism that Tasha is using for a science experiment


What is the volume of Tasha’s prism?


A. 180cm3
B. 242cm3
C. 324cm3
D.360cm3




PLEASE HELP!!

Halving the height halves the volume, but halving the radius quarters it; their effects on volume differ.

It seems there might be a typo or a mistake in your reasoning. Let's reassess the situation:

Original cone:

- Radius, [tex]\( r = 2 \)[/tex]

- Height, [tex]\( h = 6 \)[/tex]

- Volume, [tex]\( V_1 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (2)^2 (6) = 8\pi \)[/tex] cubic units

Now, you're considering two scenarios:

1. If the height is changed to [tex]\( h = 3 \)[/tex]:

  - New volume, [tex]\( V_2 = \frac{1}{3} \pi (2)^2 (3) = 4\pi \)[/tex] cubic units

2. If the radius is changed to \( r = 1 \):

  - New volume, [tex]\( V_3 = \frac{1}{3} \pi (1)^2 (6) = 2\pi \)[/tex] cubic units

Now, let's analyze the effects:

- Changing the height from 6 to 3 reduces the volume by half (from [tex]\( 8\pi \)[/tex] to [tex]\( 4\pi \)[/tex]).

- Changing the radius from 2 to 1 reduces the volume by a factor of [tex]\( \frac{1}{4} \)[/tex] (from [tex]\( 8\pi \)[/tex] to [tex]\( 2\pi \))[/tex].

So, changing the height to half of its original value reduces the volume by half, while changing the radius to half of its original value does not reduce the volume by half but rather by a quarter. Therefore, the effects are not the same.

Convert the exponential equation to a logarithmic equation using the logarithm base

(

4

)

(

4

)

of the right side

(

16

)

(

16

)

equals the exponent

(

2

)

(

2

)

.

log

4

(

16

)

=

2

It’s a rational number.

Hope this helps!

Answer:

Rational

Step-by-step explanation:

Irrational numbers are numbers that are infinite and non- repeating numbers

irrational- pi, square root of 2, etc

rational- anything else.

rational- .333333..., 1/3,  2, 1, -5, .111..., .7171..., etc.

Answer:

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

[tex]3(2x-5)=5(x-4)+x\\\\(3)(2x)+(3)(-5)=(5)(x)+(5)(-4)+x\\\\6x-15=5x-20+x\qquad\text{combine like terms}\\\\6x-15=6x-20\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-15=-20\qquad\bold{FALSE}[/tex]

Answer:

[tex]f * g = 21x ^ 2 + 32x +12[/tex]

Domain: all real numbers [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

We have the functions [tex]f (x) = 3x + 2[/tex] and [tex]g (x) = 7x + 6[/tex]

We want to find f*g. Then we must multiply the function f by the function g.

Note that the function [tex]f (x) = 3x +2[/tex] is a linear function, therefore its domain is all real numbers. In the same way the function [tex]g (x) = 7x + 6[/tex] is also a linear function and its domain is all real numbers.

The multiplication of f * g will be

[tex]f * g = (3x + 2) (7x + 6)\\\\f * g = 21x ^ 2 + 18x + 14x +12\\\\f * g = 21x ^ 2 + 32x +12[/tex]

The function g(x) is a quadratic function and its domain is the intercept of the domain of f(x) with the domain of g(x), that is, all real numbers.

I would make a table and plug values(or just plug in x values) in to figure out the equation's graph:  (plug in values that will make it easy for you since you have a √)

f(x) = 3(√x)

x = 0

f(0) = 3(0) = 0       ------> (0 , 0)

x = 1

f(1) = 3(√1) = 3(1) = 3  ------> (1 , 3)

x = 4

f(4) = 3(√4) = 3(2) = 6   ------>    (4 , 6)

Now that you have found some points, find a graph/line that goes through these points

The answer for your question is d

Answer:

D)15+15+10+10+6+6

Step-by-step explanation:

the formula to find the SA of a rectangular prism is:

2(lw)+2(lh)+2(hw)

where

l=length

w=width

and

h=height

let's substitute the values,3,2,and 5 into the equation

2(5*3)+2(5*2)+2(3*2)=62

62 is the SA

from the options:

10+6=16

10+10+6+6=32

15+15+10+10+6=56

and

15+15+10+10+6+6=62

so option D is correct

Answer:

[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)[/tex]

Step-by-step explanation:

[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}[/tex]

Apply formula:

[tex]\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex] and

[tex]\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex]

We get:

[tex]=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}[/tex]

[tex]=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}[/tex]

[tex]=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}[/tex]

[tex]=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}[/tex]

[tex]=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}[/tex]

[tex]=\frac{\sin\left(x\right)}{\cos\left(x\right)}[/tex]

[tex]=\tan\left(x\right)[/tex]

Hence final answer is

[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)[/tex]

Answer:

60x + 18

Step-by-step explanation:

6 (9x + 3) + 6x

distribute

54x + 18 + 6x

combine like-terms

60x + 18

Answer:

Simplify

Step-by-step explanation:

6(9x+3)+6x

Distribute:

=(6)(9x)+(6)(3)+6x

=54x+18+6x

Combine Like Terms:

=54x+18+6x

=(54x+6x)+(18)

=60x+18

Each pencil box usually contains same amount of pencils. In given context  the number of pencils in five boxes is 10 pencils.

Suppose that its given that 'a' boxes contains 'b' items, then, assuming that each box contains 'x' items, then

[tex]x + x + ... + x \text{ (a times)} = b\\\\x \times a = b\\\\x = \dfrac{b}{a}[/tex]

Thus, there are 'b/a' items contained in each box.

Since there are six pencils in three boxes, let there are 'x' pencils in one box, then we have:

[tex]x + x + x = 6\\3 \times x = 6\\\\\text{Dividing both sides by 3}\\\\x = \dfrac{6}{3} = 2[/tex]

Thus, there are 2 pencils in each pencil box.

Thus, for 5 boxes, we get [tex]2 \times 5 = 10[/tex] pencils.

Thus,

In given context  the number of pencils in five boxes is 10 pencils.

Learn more about division here:

https://brainly.com/question/2689177

Final answer:

By using proportional reasoning, if three boxes contain 36 pencils, then five boxes would contain 60 pencils.

Explanation:

If thirty-six pencils are packed in three boxes, then there are twelve pencils per box because 36 divided by 3 equals 12.

To find out how many pencils are packed in five boxes, we multiply twelve pencils (the number of pencils per box) by five boxes.

Therefore, 12 pencils/box × 5 boxes = 60 pencils in five boxes.

This is a simple proportional reasoning problem, often encountered in mathematical exercises in school.

Answer:

d

Step-by-step explanation:

she has 16 quarters

1$=4 quarters

so 4$= 16 quarters

plus one more from the thirty cense

she could have 17 which is strange it’s not an option so go with B ig

10 questions = 40%

X question = 100%

40x = 1000

X = 25 questions

25 questions were on the test.

There are two ways to assess observational error: accuracy and precision. Precision measures how closely spaced or widely separated a set of measurements are from one another, whereas accuracy measures how near or far off a given set of measurements are from their true value.

Given

60% accurate means 40% inaccurate.

10 inaccurate answers means 40% inaccurate

10/40 x 100 = 25

To know more about accuracy refer to :

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These are the factors of 36:

1, 2, 3, 4, 6, 9, 12, 18, 36

1, 2, 3, 4, 6, 9, 12, 18, 36

1 x 36 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

2 x 18 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

3 x 12 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

4 x 9 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

6 x 6 = 36

Hope this helped!

Answer:

1, 2, 3, 4, 6, 9, 12, 18, 36

Step-by-step explanation:

I took test on edge 2021

Answer:6/36

Step-by-step explanation:

The probability of rolling a number less than 5 and even on a die is 1/2.

To find the probability of rolling a number less than 5 and even, we need to determine the number of outcomes that satisfy both conditions and divide it by the total number of possible outcomes.

There are three outcomes that satisfy both conditions: {2, 4, 6}. The total number of possible outcomes is six since a die has six sides.

Therefore, the probability of rolling a number less than 5 and even is 3/6, which simplifies to 1/2.

Answer:

To find the circumference of a circle you have to multiply Pi (3.14) with the diameter of the circle.

You need to find circumference of the circle first

Step-by-step explanation:

[tex]100xh=1,150\qquad\text{divide both sides by}\ 100x\neq0\\\\\dfrac{100xh}{100x}=\dfrac{1,150}{100x}\\\\\boxed{h=\dfrac{115}{x}}[/tex]

To solve the equation \( 1,150 = 100 \times x \times h \) for \( h \), you want to isolate \( h \) on one side of the equation. Follow these steps:
**Step 1: Understand the equation**
The equation is saying that 100 times the product of \( x \) and \( h \) is equal to 1,150.
**Step 2: Isolate \( h \)**
To solve for \( h \), you need to get \( h \) by itself on one side of the equation. Right now \( h \) is being multiplied by \( 100 \times x \). To undo this, you'll divide both sides of the equation by \( 100 \times x \).
**Step 3: Perform the division**
Divide both sides of the equation by \( 100 \times x \):
\[
\frac{1,150}{100 \times x} = \frac{100 \times x \times h}{100 \times x}
\]
**Step 4: Simplify both sides**
On the right-hand side, \( 100 \times x \) in the numerator and \( 100 \times x \) in the denominator cancel each other out:
\[
\frac{1,150}{100 \times x} = h
\]
**Step 5: Result**
You are left with \( h \) by itself on one side of the equation and \( \frac{1,150}{100 \times x} \) on the other:
\[
h = \frac{1,150}{100 \times x}
\]
Now \( h \) has been solved in terms of \( x \), and you can find the value of \( h \) if you know the value of \( x \) by simply substituting that value into this equation and performing the calculation.

Answer with step-by-step explanation:

Ordered pairs that satisfy the given equation:

x  0  1  2  3  4

y  5  3  1  -1  -3

To find the x-intercept, we will substitute y = 0 and solve for x to get:

[tex]0 = -2x + 5[/tex]

[tex] -2x = -5[/tex]

[tex]x = 5/2[/tex]

x-intercept = (5/2, 0)

To find the y-intercept, we will substitute x = 0 and solve for x to get:

[tex]y = -2(0) + 5[/tex]

[tex]y = 5[/tex]

y-intercept = (0, 5)

Answer: option d.

Step-by-step explanation:

To create a table of five ordered pairs that satisfy the equation, you need to give values to the variable "x" and substitute these into the function to find the corresponding value of "y":

For [tex]x=-2[/tex]

[tex]y = -2(-2) + 5=9[/tex]

For [tex]x=-1[/tex]

[tex]y = -2(-1) + 5=7[/tex]

For [tex]x=0[/tex]

[tex]y = -2(0) + 5=5[/tex]

For [tex]x=1[/tex]

[tex]y = -2(1) + 5=3[/tex]

For [tex]x=2[/tex]

[tex]y = -2(2) + 5=1[/tex]

Then, you can make the table:

x   -2  -1  0  1  2

y   9  7  5  3  1

To find the  x-intercept, substitute [tex]y=0[/tex] into the function and solve for "x". Then:

[tex]0 = -2x + 5\\\\x=\frac{-5}{-2}\\\\x=\frac{5}2}[/tex]

This is: ([tex]\frac{5}{2}[/tex], 0)

To find the  y-intercept, substitute [tex]x=0[/tex] into the function and solve for "y". Then:

[tex]y= -2(0) + 5\\\\y=5[/tex]

This is: (0,5)

Answer:

C

Step-by-step explanation:

The degree of a polynomial is determined by the value of the largest exponent of a term in the expression.

The largest exponent is 4 from the term [tex]x^{4}[/tex]

Hence the degree of the polynomial is 4 → C

Answer:

C (4)

Step-by-step explanation:

Answer:

26 degrees.

Step-by-step explanation:

180 - 154 = 26

Answer:

Function for given situation is : [tex]V(t)=3000(0.70)^t[/tex]

Value of computer after 4 years = $720.3.

Step-by-step explanation:

Given that the value of a $3000 computer decreases about 30% each year. Now we need to write a function for the computers value V(t). then we need to find about how much will the computer be worth in 4 years.

It clearly says that value decreases so that means function represents decay.

For decay we use formula:

[tex]A=P(1-r)^t[/tex]

where P=initial value = $3000,

r= rate of decrease =30% = 0.30

t= number of years

A=V(t) = future value

so the required function is [tex]V(t)=3000(1-0.30)^t[/tex]

or [tex]V(t)=3000(0.70)^t[/tex]

Now plug t=4 years to get the value of computer after 4 years.

[tex]V(4)=3000(0.70)^4[/tex]

[tex]V(4)=720.3[/tex]

Hence final answer is $720.3.

Answer:

A = $3000(0.70)^t

Step-by-step explanation:

100% - 30% = 70%.  Thus, the common ratio in this exponential function is 0.70.

Use a formula with the form of the compound amount formula:

A = P(1 + r)^t, where r is the common ratio as a decimal fraction and t is the number of years.

Here, A = $3000(1 - 0.30)^t, or    A = $3000(0.70)^t

Answer:

  15 inches

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of its sides. A square has 4 sides, all the same length. We can either add up the side lengths, or we can recognize that multiplication of one side's length by 4 is a useful alternative.

  perimeter = 4 × (3 3/4 in)

  = (4×3 +4×3/4) in

  = 12 in + 3 in = 15 in

Answer: 12.20 feet.

Step-by-step explanation:

Observe in the figure attached that a right triangle is formed.

Then, you  need to remember the identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case you can identify that:

[tex]adjacent=10\\hypotenuse=x[/tex]

[tex]\alpha=35\°[/tex]

Then, to find the length of the wooden board (x), you need to substitute values and solve for x.

Therefore, you get:

[tex]cos(35\°)=\frac{10}{x}\\\\(x)(cos(35\°))=10\\\\x=\frac{10}{cos(35\°)}\\\\x=12.20[/tex]

The length of the wooden board is: 12.20 feet.

Answer:

4

Step-by-step explanation:

How many selfies did Tania take? (my first answer would be too many, but that's probably not the answer you're looking for :-) )

We know that each cousin appear 2 or 3 times overall.

If she would have taken each cousin exactly 2 times, that would be 16 cousins/photos

If she would have taken each cousin exactly 3 times, that would be 24 cousins/photos

We know there's exactly 5 cousins per photo...

so we have to find a multiple of 5 cousins/photos that is between 16 and 24.

The only possibility is 20 cousins/photos.  20 / 5 = 4 photos.

Final answer:

Tania took 4 selfies with her cousins. Each cousin appeared in exactly 2 selfies, with some appearing a third time to account for 16 total cousin appearances divided by 5 cousins per selfie.

Explanation:

The problem presented is a combinatorial puzzle involving selfies and cousins. Since each cousin is in either 2 or 3 pictures, we can try to minimize the number of pictures by assuming each cousin is in exactly 2 pictures first. If there are 8 cousins and 5 cousins per picture, then by multiplying 8 by 2 (every cousin appears exactly 2 times), we get 16 cousin appearances in total.

Since each selfie has 5 cousins, we divide the total cousin appearances by the number of cousins per picture: 16 / 5, which results in 3.2. However, since it's not possible to have a fraction of a picture, we need at least 4 selfies to cover all appearances. Yet, this leaves us 4 extra appearances (because 4 pictures would mean 20 cousin appearances in total).

These 4 extra appearances account for the fact that some cousins appear 3 times instead of just 2. Therefore, Tania must have taken 4 selfies with her cousins to cover the 16 cousin appearances with some cousins appearing an additional third time.

Check the picture below.

recall that range is the interval over the y-axis for the graph of the function.

The range of the function shown is [4, ∝]

To learn more about range of the function, refer to

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Answer: the meaning of data is pretty simple

Step-by-step explanation: data is something you record or write down after you do a experiment. after you jot it down you can show your work to other scientests to show what you know. I hope this helps!

The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

Let's look at an example.

6, 8, 9, 14, 23

To find the mean of the data set shown above,

start by adding the numbers.

Adding the numbers, we get 60.

60 will be divided by the number of numbers in the set, which is 5.

So, 60 divided by 5 is 12.

So the mean of this data set is 12.

Answer:

640

Step-by-step explanation:

Expanding the binomial :

r⁵ - 40r⁴ + 640r³ - 5120r² + 20480r - 32768

The coefficient of r³ is 640

Answer:

Step-by-step explanation:

Apply binomial theorem to expand (a+b)^n where a = r, b = -8 n n = 5

the r^3 term is (5!/(2!*(5-2)!)*r^3*(-8)^(5-3)

=(5*4*3*2*1/1*2*1*2*3)*r^3*(-8)^2

=640*r^3

So the coefficient is 640.

One is rational and one is exponential.

Answer:

Step-by-step explanation:

the relationship between the graphs of y=2^x and y=2^-x is : symmetry by y-axis

Let's open up parenthesis:

20x+15-2x

Then simplify.

18x+15

...Which is A.

Hope I helped!

~Mshcmindy

Answer:

The correct answer is option A. 18x + 15

Step-by-step explanation:

It is given an expression in variable x,

5(4x + 3) - 2x

To simplify the given expression

5(4x + 3) - 2x = (5 * 4x) + (5 * 3) - 2x   (open the bracket)

  = 20x + 15 - 2x

  = 20x - 2x + 15

  = 18x + 15

Therefore the correct answer is 18x + 15

The correct option is option A.  18x + 15

The first graph the X is 45° because it right angle is 90 degrees Larry give us 55 degrees so 55 subtract the equals 45

The second graph has a degree of 113 because 180 subtracted by 67 is 113 because they straight angle has 180.

The first one is 45

The second one is 113

Answer:

17. x= 35

19. a= 113

Step-by-step explanation:

17.   55+x=90

90-55= 35

19. 180= 67+a

180-67=113

Answer:

a = -3

b = -2

c = 6

Step-by-step explanation:

The quadratic formula states that for an equation of the form:

[tex]ax^{2} + bx + c = 0[/tex]

The solution to that equation is:

[tex]\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]

In this case we have:

0=-3x^2-2x+6

Where:

a = -3

b = -2

c = 6