Question 1 of 5
Select the correct answer.
Consider functions f and g, where function g is a transformation of function f.



Which statement correctly describes a transformation on the graph of function f to arrive at the graph of function g?


The graph of function f is shifted 3 units to the right.

The midline of function f is shifted 3 units down.

The graph of function f is reflected over the x-axis.

The amplitude of function f is vertically stretched by a factor of 3.

Answer:

[tex]BD = 4[/tex]

[tex]BC =4\sqrt 3[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find BD and BC

Solving BD

Considering angle at D, we have:

[tex]\cos(D) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(60) = \frac{BD}{8}[/tex]

Solve for BD

[tex]BD = 8 * \cos(60)[/tex]

[tex]\cos(60) = 0.5[/tex] So:

[tex]BD = 8 * 0.5[/tex]

[tex]BD = 4[/tex]

To solve for BC, we make use of Pythagoras theorem

[tex]CD^2 = BC^2 + BD^2[/tex]

This gives

[tex]8^2 = BC^2 + 4^2[/tex]

[tex]64 = BC^2 + 16[/tex]

Collect like terms

[tex]BC^2 =64-16[/tex]

[tex]BC^2 =48[/tex]

Take square roots

[tex]BC =\sqrt{48[/tex]

Expand

[tex]BC =\sqrt{16*3[/tex]

Split

[tex]BC =\sqrt{16}*\sqrt 3[/tex]

[tex]BC =4\sqrt 3[/tex]

Answer:

By the Central Limit Theorem, the sampling distribution of the sample mean amount of money in a savings account is approximately normal with mean of 1,200 dollars and standard deviation of 284.6 dollars.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Average of 1,200 dollars and a standard deviation of 900 dollars.

This means that [tex]\mu = 1200, \sigma = 900[/tex]

Sample of 10.

This means that [tex]n = 10, s = \frac{900}{\sqrt{10}} = 284.6[/tex]

The sampling distribution of the sample mean amount of money in a savings account is

By the Central Limit Theorem, approximately normal with mean of 1,200 dollars and standard deviation of 284.6 dollars.

The sampling distribution of the sample mean amount of money in a savings account is mean of 1,200 and standard deviation of 284.6 dollars.

Since the distribution of the amount of money in savings accounts for Florida State students has an average of 1,200 dollars and a standard deviation of 900 dollars. And, a random sample of 10.

So here the mean should be $1,200

And, the standard deviation should be

[tex]= 900 \div \sqrt10[/tex]

= $284.6

learn more about mean here: https://brainly.com/question/9588526

Answer:

Option C.

Step-by-step explanation:

If we have two functions:

f(x) and g(x)

the product is given by:

(f*g)(x) = f(x)*g(x)

So, if here we have

f(x) = √(3*x)

g(x) = √(48*x)

And remembering that the square root is distributive, so:

√a*√b = √(a*b)

We can write:

(f*g)(x) = f(x)*g(x) = √(3*x)*√(48*x) = √(3*x*48*x)

          = √(3*48*x*x) = √(144*x^2) = √(144)*√(x^2)

And here we can use that:

12*12 = 144, then √144 = 12

and

x*x = x^2, then √x^2 = x

So:

√(144)*√(x^2) = 12*x

Then the correct option is C.

Answer:

#1. 150, #2. 650, #3. 2 PM to 4 PM #4. 8AM to 4PM (8 hours) #5. the frequency of weight in pounds #6. 22 cats

#7. 1 - 40 pounds #8. 11 - 20 pounds

Answer:

Solution given:

1.

diameter(d)=6mm

base(b)=8mm

height (h)=5mm

Area of figure=area of parallelogram +area of semi circle

2.

for triangle

base[b]=6ft

height(h)=9ft

for square

length[l]=9ft

Area of figure=area of square +area of triangle

Answer:

Step-by-step explanation:

All other things being equal (and there are a lot of other things) the 50 gram mass will show a larger temperature

increase than the 100 gram mass.

Why?

The formula is the same from both masses of water (50 grams and 100 grams)

The amount of heat added is the same. (Instead of using hot water, we'll a hot plate on a very low temperature but above what they are now.).

We'll leave it on until we see a rise in temperature  delta(t1) = 10 degrees

mc delta(t) = m1 * c * delta(t1)

m = 100

m1 = 50 grams.

c is going to be divided out

we'll solve for the ratio of delta(t) / delta(t1)

100 * delta(t) = 50 (delta(t1)

100 * delta(t) = 50*10

delta(t) = 50*10/100

delta(t) = 5 degrees.

Though this may look rather convoluted, the result is telling us is that delta(t1) for the 50 gram mass is twice as big as as for the 100 gram mass.

The 100 gram mass only rises 5 degrees.

The 50   gram mass rises 10 degrees.

Answer:

50 gram mass will show a larger temperature

increase than the 100 gram mass.

Step-by-step explanation:

50 gms water at 20 ⁰ C and 50 gms of water at 40⁰ C are mixed.  Since the masses of the liquid at different temperatures are same, the answer is very easy and simple :  average of 20⁰C and 40⁰C.  that is:  30⁰C.

Please Like

Answer:

[tex]180lb\ 12 oz - 79.3kg = 2.8kg[/tex]

Step-by-step explanation:

Given

[tex]180\ lb 12\ oz - 79.3kg[/tex]

Required

Solve

First, convert 180lb to kg

[tex]1lb \to 0.454kg[/tex]

[tex]180lb \to 180 *0.454kg[/tex]

[tex]180lb \to 81.7kg[/tex] -- to 1dp

Next, convert 12oz to kg

[tex]1oz \to 0.03kg[/tex]

[tex]12oz \to 12 * 0.03kg[/tex]

[tex]12oz \to 0.4kg[/tex] --- to 1 dp

So, the expression becomes:

[tex]180\ lb 12\ oz - 79.3kg[/tex]

[tex]81.7kg + 0.4kg - 79.3kg[/tex]

[tex]= 2.8kg[/tex]

Hence:

[tex]180lb\ 12 oz - 79.3kg = 2.8kg[/tex]

Answer:

Wat does that mean?

Step-by-step explanation:

Answer:

A) A(t)  =  4500*π  -  1600*t

B) A(4)  =  7730 in³

C) t  =  8,8 sec

Step-by-step explanation:

The volume of the sphere is:

d max  =  30   r max  =  15 in

V(s) =  (4/3)*π*r³      V(s)  =   (4/3)*π* (15)³

V(s) = 4500*π

A)  Amount of air needed to fill the ball A(t)

A(t)  = Total max. volume of the sphere - rate of flux of air * time

A(t)  =  4500*π  -  1600*t    in³

B) After 4 minutes

A(4)  =  4500*π  - 6400

A(4)  =  14130 - 6400

A(4)  =  7730 in³

C)  A(t)  =  4500*π  -  1600*t  

when  A(t) = 0   the ball got its maximum volume then:

4500*π -  1600*t  =  0

t  =   14130/1600

t  =  8,8 sec

Answer:

x= -11

Step-by-step explanation:

Answer:

Step-by-step explanation:3/5 of the pizza

Answer:

plug it into a calculator and you get 0.001

Step-by-step explanation:

50/50=1

then put in the decimal places to get 0.001

Answers:

Those are the costs for a whole small pizza.

==========================================================

Explanation:

Let

x and y are some dollar amount, so they cannot be negative numbers. It also doesn't make sense to have them be 0 either. So we'll make them positive.

2/3 of x is equal to 3.50 as the first sentence mentions. This forms the equation (2/3)*x = 3.50

Multiply both sides by the reciprocal of 2/3 to isolate x

(2/3)*x = 3.50

(3/2)*(2/3)*x = (3/2)*3.50

x = 5.25

Pizza Uno charges $5.25 for a whole small pizza.

----------------------------

Pizza Duo charges $4.20 for 3/4 of a small pizza, meaning the equation we need to solve is

(3/4)y = 4.20

We'll use the same idea as the last equation to get...

(3/4)y = 4.20

(4/3)*(3/4)y = (4/3)*4.20

y = 5.60

Pizza Duo charges $5.60 for a whole small pizza.

Pizza Uno is the better deal (assuming both pizzas taste the same or you don't have a preference for either). You would save $5.60 - $5.25 = $0.35 = 35 cents.

Answer:

Step-by-step explanation:

since it is a cuboid use this formula

volume of a cuboid=l*w*h

=2*8*3

Answer:

C) [tex]c=\sqrt{a^{2} +b^{2} }[/tex]

Step-by-step explanation:

The Pythagorean Theorem states that for a right triangle, the relationship between its three sides is [tex]a^{2} +b^{2} =c^{2}[/tex] where [tex]a[/tex] and [tex]b[/tex] are side lengths and [tex]c[/tex] is the length of the hypotenuse. This means that the length of the hypotenuse is [tex]c=\sqrt{a^{2} +b^{2} }[/tex] by taking the square root of both sides to solve for [tex]c[/tex], making option C correct.

Answer:

-0.625 = X

Step-by-step explanation:

Distributive Property

Answer:

x = 1/8

Step-by-step explanation:

3x + 8 + 5x = 3 to the second power

8x + 8 = 9

x = 1/8

9514 1404 393

Answer:

   625 square feet

Step-by-step explanation:

The greatest area of a polygon with a given perimeter is that of a regular polygon. A regular rectangle is one that has all sides the same length -- a square. The side length of a square with 100 ft perimeter is 25 ft. The area of a square with such a side length is

  A = (25 ft)² = 625 ft²

The maximum possible area is 625 ft².

__

In the attached, x is the length of one side. The area versus side length is plotted. The maximum is seen to be 625 ft² for a side length of 25 ft.

Answer:

112

Step-by-step explanation:

14.96-6 = 8.96, divide 8.96 by 0.08 and it comes out to 112 which would be how much minutes in total Lamar used.

0.08 being cents per minute

8.96 being the total amount used after the initial $6 monthly fee

Answer:

Step-by-step explanation:

Let's simplify step-by-step.

(k+1)(x2)−8kx+3k+5

Distribute:

=(k)(x2)+(1)(x2)+−8kx+3k+5

=kx2+x2+−8kx+3k+5

Answer:

=kx2−8kx+x2+3k+5

Answer:

         2x        -7

2x      4x²      -14x

-1       -2x        +7

Step-by-step explanation:

4x²-16x+7 factors as

(2x-7)(2x-1)

So the grid would be:

         2x        -7

2x      4x²      -14x

-1       -2x        +7

Answer:

D

Step-by-step explanation:

1/2 ×4 =2

Answer:

I think that these are only the smallest sum of money that can be purchased

9514 1404 393

Answer:

  xy ≈ 2.3

Step-by-step explanation:

Logarithms can be used to find x and y.

  3^x = 4

  x·log(3) = log(4)

  x = log(4)/log(3)

__

 4^y = 12

  y = log(12)/log(4)

__

Then xy is ...

  xy = log(4)/log(3) × log(12)/log(4) = log(12)/log(3)

  xy ≈ 1.079/0.477

  xy ≈ 2.26

Answer:

1) 2/1

2) 13/1

Step-by-step explanation:

Answer:

The answer to this question is x=2

Answer: To answer these and related questions, we can create a model using a linear function. ... When modeling scenarios with linear functions and solving problems ... A town's population has been growing linearly. ... Assume this trend continues. ... Identify the year in which the population will reach 15,000.

Step-by-step explanation: Done :P

The transformation of f(x) to g(x) is f(x) is shifted down 2 units to g(x).

The correct option is (A)

Transformations of functions mean transforming the function from one form to another. Transformation of functions is a unique way of changing the formula of a function minimally and playing around with the graph.

The given function f(x)= sin x

In the graph there is vertical shift from f(x) to g(x)

We know, the vertical shift depends on the value of k

When k>0, the vertical shift is described as

If we closely look at the graph the vertical distance in negative y-axis,

the distance between line f(x) and g(x) is from 0 to -2.

So, there is shifting of -2 units means there is downward shifting.

i.e., k=2

Hence, f(x) is shifted down 2 units to g(x).

Learn more about transformation of function here:

https://brainly.com/question/10377001

#SPJ2

Answer:

10xyz + 20xy - 15x

Step-by-step explanation:

5 x ( 2yz + 4 y - 3)

using the Distributive property multiply the each term by 5x

5x × 2yz + 5x × 4y - 5x × -3

calculate the product

10xyz + 20xy - 15x

Answer:

10xyz+20xy-15

Step-by-step explanation:

Answer:

number 2 is your answer for your problem