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The number of toys sold per month can be modeled by f(x) = 2x^4^ + x^3^ + 6x + 5, where x represents the number of months since June. Let g(x) = f(x) + 7. Which of the following gives the rule for g and the correct explanation of the meaning of the transformation in terms of monthly toy sales?

The original price of the shirt was $6.25

In this question, we have been given Archie bought a shirt on sale that was 20% less than the original price. The original price was $5 more than the sale price.

We need to find the original price.

Let the original price of the shirt be x and the sale price of the shirt is y

20x/100 = y

x/5 = y

x = 5y

Now the second equation that we get is

x = y + 5

5y - y = 5

4y = 5

y = 5/4

Now putting the value of y in the first equation we get

x = 5y

 = 5 (5/4)

 = 25/4

 = 6 1/4

 = $6.25

Then we can say that the original price of the shirt was $6.25

Therefore, the original price of the shirt was $6.25

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Answer:

Step-by-step explanation:

Substitute given values

Answer:

Given that x - y = 5 and xy = -6/1/2,

Step-by-step explanation:

the value of x² + y².

=(x-y)²+2xy=5²+2×[-6 1/2]=25-13=12 is your answer

Answer:

C = 7.72 ~ 7.7

Step-by-step explanation:

So when you solve this equetion you must 1st find x then c

we can find x by using cos(60)

cos(60) = x/14

x = cos(60) × 14

x = 1/2 ×14

x = 7

so after we find x we are going to solve c by using cos (25)

cos (25) = X/C = 7/c

cos(25) × C = 7

C = 7/cos (25)

C = 7.72 ~ 7.7

so the solution is 7.7

19/403 of the people on the plane are crew

The given parameters are:

Population = 403

Passengers = 384

The number of crew is calculated using:

Crew = 403 - 384

Evaluate

Crew = 19

The fraction of crew is then calculated using:

Fraction = Crew/Population

This gives

Fraction = 19/403

Hence, 19/403 of the people on the plane are crew

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Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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The ordered pair is the best approximation of the exact solution is (0.6, 1.9). The correct option is c.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

y = -2x + 3

y = 5x - 1

Equate the right sides of both equations:

-2x + 3 = 5x - 1,

-2x - 5x = -1 -3,

x = 4/7

then

y = -2 x 4/7 + 3 = 8/7 + 3 = 3x7-8 /7 = 13/7 = 1 x 5/7

4/7 = 0.6 and 1 x 5/7 is equal to the ordered pair (0.6, 1.9).

Therefore, the correct option is c, (0.6, 1.9).

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The question is incomplete. The full question is given below:

Which ordered pair is the best approximation of the exact solution?

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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The researcher who has 80 participants for a study that involves four experimental conditions and who assigns participants to conditions using matched random assignment will form 20 matched clusters or blocks before assigning participants to conditions.

Matched Random Assignment is the process of grouping participants based on their similarities (matching variables) before randomly assigning them to different treatment groups (experimental conditions) to ensure that the groups are similar in all aspects except for the independent variable. This helps to control for extraneous variables that might affect the outcome of the study.

The number of matched clusters or blocks formed in matched random assignment is equal to the number of treatment groups (experimental conditions).

Since the researcher has four experimental conditions, she will form four matched clusters or blocks before assigning participants to conditions.

Therefore, the number of matched clusters or blocks that she will form before assigning participants to conditions is:

4 experimental conditions x 5 matched participants per block= 20 matched clusters or blocks.

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The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Answer:

Translation

Step-by-step explanation:

As you can see, the flag does not rotate. A translation describes an object being moved without changing its orientation. The flag is moved down.

The appropriate interpretation for the slope of the data given is that height of water in the pool increases at the rate 2 inches/minute.

Given table:

Time             height

2                     8

4                     12

6                     16

8                     20

10                   24

slope of line is equal to 2

slope of line is also called rate of change.

Negative slope indicates a decrease in one variable as the other increases.

Positive slope indicates both x and y increases.

Therefore height of water increases 2 inches/minute

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Option three \(\rm log3+log(x+4)\) is the equivalent to the logarithm expression \(\rm log3(x+4)\)

It is given that logarithm expression is  \(\rm log3(x+4)\)

It is required to simplify the above equation.

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

\(\rm a^b=c\\\rm log_ac=b\)

We have logarithm expression:

\(\rm log3(x+4)\)

We know the log property that we can split a logarithm into two logarithms if it contains the product of two numbers ie.

\(\rm logxy=logx+logy\)

By using this property we get:

\(\rm =log3(x+4)\\\rm = log3+log(x+4)\)

Because 3 and (x+4) are two different numbers, not (x+4).

Thus, option three \(\rm log3+log(x+4)\) is the equivalent to the logarithm expression \(\rm log3(x+4)\)

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Answer:

Step-by-step explanation:

optin three is the answer i have took the test                                                     (Which expression is equivalent to log3(x + 4)?

log3 – log(x + 4)

log12 + logx

log3 + log(x + 4)

StartFraction log 3 Over log (x + 4) EndFraction)

Answer:

x=7

Step-by-step explanation:

5-2 is 3

21 divided by 3 is 7

therefore 7 is x

Answer: 5x = 5 times 5. 2x = 2 times 2

AKA 25-4=21

After answering the presented question, we can conclude that function Therefore, \(So (f+g)(z) = -z + 23.\)

Mathematicians research numbers and their variants, equations or related structures, structures and their locations, and prospective locations for these things. The noun "function" describes the connection that exists among a set of inputs, each of which has a corresponding output. A function is an input-output connection where each input results in a single, separate output. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On functions, one-to-one skills, multiple capabilities, in skills, and on functions are the four major types of accessible functions.  

To find (f+g)(z),

\(f(z) = 7z + z + 1 = 8z + 1\\g(z) = 22 - 9z\)

Therefore,

\((f+g)(z) = f(z) + g(z) = (8z + 1) + (22 - 9z) = -z + 23\)

\(So (f+g)(z) = -z + 23.\)

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Answer:

The error is in Step 1. They translated from logarithmic to exponential form incorrectly.

The student should have used 4 as the base and 3 as the exponent. This would result in 64, not 81, on the right side of the equation.

The correct answer is x = 38.

Step-by-step explanation:

Answer:

The error is in Step 1. They translated from logarithmic to exponential form incorrectly.

The student should have used 4 as the base and 3 as the exponent. This would result in 64, not 81, on the right side of the equation.

The correct answer is x = 38.

Step-by-step explanation:

Step-by-step explanation:

Answer: Graph D

Step-by-step explanation:

The slope is 2

x goes after the slope in graph functions

The line goes through 3 on the y-axis so that’s where + 3 comes in.

2x + 3

Answer:

\(y=-3x+5\)

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

\(y= -3x -5\)

With the given line, we can identify clearly that -3 is in the place of m, making it the slope. Because parallel lines have the same slopes, the slope of the line we're currently solving for would also be -3. Plug this into \(y=mx+b\):

\(y=-3x+b\)

2) Determine the y-intercept (b)

\(y=-3x+b\)

Plug in the given point (1,2) and isolate b

\(2=-3(1)+b\\2=-3+b\)

Add 3 to both sides

\(2+3=-3+b+3\\5=b\)

Therefore, the y-intercept of the line is 5. Plug this back into \(y=-3x+b\):

\(y=-3x+5\)

I hope this helps!

Answer:

9 ft

Step-by-step explanation:

Hope this helps!

Have a great day!

Answer:

(4,2.5)

.................................

\(\(\sin \theta \cdot \sec \theta = \tan \theta\)\) is an identity, as the left side simplifies to the right side.

To establish the identity\(\(\sin \theta \cdot \sec \theta = \tan \theta\)\), we can rewrite the left side in terms of sine and cosine and then simplify:

We know that\(\(\sec \theta = \frac{1}{\cos \theta}\).\)

So, the left side becomes:

\(\[\sin \theta \cdot \sec \theta = \sin \theta \cdot \frac{1}{\cos \theta}\]\)

Now, let's simplify this expression by multiplying the numerator and denominator by \(\cos \theta\):

\(\[\sin \theta \cdot \frac{1}{\cos \theta} = \frac{\sin \theta}{\cos \theta} = \tan \theta\]\)

Therefore, we have shown that \(\sin \theta \cdot \sec \theta = \tan \theta\) is an identity, as the left side simplifies to the right side.

Note: In the process, we used the fact that \(\tan \theta = \frac{\sin \theta}{\cos \theta}\), which is a known trigonometric identity.

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Answer:  about 15

Step-by-step explanation:

Answer:

15 is the answer

Step-by-step explanation:

The length of the rectangular base is 9in

It is important to note that the formula for determining the volume of a pyramid with rectangular base is expressed as;

Volume = lwh/3

Where;

Given the value of the volume, width an height of the pyramid as 168, 7 and 8, we substitute the values, we have;

168 = l × 7 × 8/ 3

cross multiply

l × 7 × 8 = 168(3)

Find the product

56l = 504

To determine the length, divide both sides by 56, we get;

l = 504/ 56

l = 9In

Hence, the value is 9in

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Answer:

Mean score for the class B is 66.66

Step-by-step explanation:

Mean : It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list.

Mean = sum of all numbers/ total numbers

Given,

mean score of class A = 34.

mean score of both the classes = 55

mean score of class a = sum of marks/total strength of class

                              34   = sum of marks/10

                             340 = sum of marks of class A

similarly,  Mean score of both classes

= ( sum of marks of class A and class B)/(total students in both classes)

= (340 + sum of marks of class B)/ 28  

55 =  (340 + sum of marks of class B)/ 28  

55 × 28 =  (340 + sum of marks of class B)

1540 - 340 = sum of marks of students of class B    

     1200    =  sum of marks of students of class B  

now to find Mean score of class B

sum of marks of students of class B / total students in class B

1200/18 = 66.66 answer  

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Answer:  x=3

sorry i dont have anywork but i know its correct :)

I believe it is 312, hope this helps, sorry if it doesn't!:)

Answer:

4 to 2

Step-by-step explanation:

Answer:

The ration is 2 : 1

Step-by-step explanation:

Out of 6 members, there are:

4 girls

2 guys

Ratio of girls to boys:

girls : boys

4 : 2

Simplify by dividing.

4 ÷ 2 : 2 ÷ 2

2 : 1

The value assigned to variable y in the given expression "x = 0; y = (x > 0) ? 10 : -10;" is -10.

In the given expression "x = 0; y = (x > 0) ? 10 : -10;", the variables x and y are being assigned values based on a conditional statement.

First, the value of x is assigned as 0.

The conditional statement (x > 0) checks whether the value of x is greater than 0. In this case, since x is equal to 0, the condition evaluates to false.

The ternary operator ? : is used to specify different values for y based on the outcome of the conditional statement. If the condition is true, the value assigned to y would be 10. On the other hand, if the condition is false, the value assigned to y would be -10.

In this case, since the condition (x > 0) is false, the value assigned to y is -10, as indicated after the colon :.

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Asymptotic distribution of x(n-x)/n(n-1) is 0.

Let's discuss it further below.

To find the asymptotic distribution of x(n-x)/n(n-1), we will follow these steps:

1. Rewrite the expression as a ratio of two variables: X = x/n and Y = (n-x)/n.
2. Rewrite the expression in terms of X and Y: Z = X * Y / ((X + Y) * (X + Y - 1)).
3. Find the limit of Z as n approaches infinity, which represents the asymptotic distribution.

Let's proceed with these steps:

1. Rewrite the expression as a ratio of two variables:
  X = x/n and Y = (n-x)/n

2. Rewrite the expression in terms of X and Y:
  Z = X * Y / ((X + Y) * (X + Y - 1))

3. Find the limit of Z as n approaches infinity:
  Since X = x/n and Y = (n-x)/n, as n approaches infinity, both X and Y will approach 0. Therefore, the limit of Z as n approaches infinity is 0.

In conclusion, the asymptotic distribution of x(n-x)/n(n-1) is 0.

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Answer:

$100

Step-by-step explanation:

20/10= 2, from here multiply 50 by 2, you get 100

can i get brainliest please?

Answer:

3/7

Step-by-step explanation:

12/28=3*4/4*7=3/7