What is the vertex of the graph of y+2x+3 = -(x+2)^2 + 1?
A. (-3,-33)
B. (-3,3)
C. (3,-24)
D. (3,21)

Brad Hamilton's weekly salary as an accounting clerk is $625.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Brad Hamilton's annual salary as an accounting clerk is $32,500

So number of weeks in an year = 52

So, Brad Hamilton's weekly salary as an accounting clerk

                                  = Brad Hamilton's annual salary / number of weeks

⇒ Brad Hamilton's weekly salary = $32,500/52

⇒ Brad Hamilton's weekly salary = $625

Thus, Brad Hamilton's weekly salary as an accounting clerk is $625.

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The expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.

An expression 4x24 is given.

We have to write it using distributive property.

What is the distributive property of multiplication ?

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

As per the question ;

Expression is 4x24.

Let's rewrite it in form of distributive property ;

4 × 24

= 4 × ( 20 + 4 )

So ,

It is now in form A ( B + C ) , where ; A = 4 , B = 20 and C = 4

⇒ 4 × ( 20 + 4 )

= 80 + 16

= 96

Thus , the expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.

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The expression 2^4 \u00b7 2^{-7} simplifies to 2^{-3}, which is the same as 1/2^3 or 1/8.

The expression 2^4 \u00b7 2^{-7} can be simplified using the properties of exponents, specifically the law that states when multiplying expressions with the same base, you add the exponents. Here, we are multiplying 2 raised to the power of 4 with 2 raised to the power of -7. Therefore, we add the exponents 4 and -7 together to get 2^{4-7} = 2^{-3}.

To simplify further, remember that a negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Hence, 2^{-3} = 1/2^3 = 1/8. Therefore, 2^4 \u00b7 2^{-7} simplifies to 1/8.

Segments and lines can be named using the letters that represent the points on them, such as AB or line AB.

In geometry, segments and lines are fundamental elements. A line is an infinite set of points extending in opposite directions, while a segment is a finite portion of a line with two distinct endpoints. These concepts are essential for understanding geometric shapes, angles, and spatial relationships in mathematics.

In mathematics, the name of a segment and the name of a line can be written differently by using the letters that represent the points on the segment or the line. For example, a segment between points A and B can be written as AB, while a line passing through points A and B can be written as line AB or simply AB. It is important to note that in both cases, the order of the points does not matter, as AB is the same as BA.

The type of bias in the questionnaire is question wording bias or survey question bias, influenced by the way the question is phrased to imply evolution being synonymous with promoting science, potentially leading respondents to answer in line with what they perceive to be the socially desirable response.

The type of bias present in the questionnaire regarding teaching only evolution in schools is an example of question wording bias or survey question bias. When the interviewer asks respondents if they favor promoting science by teaching only evolution, the question implies that evolution is synonymous with science and that alternative perspectives are not scientific. This phrasing can lead respondents to answer in a manner that aligns with what they perceive as the socially desirable response, rather than their true beliefs, which can also be similar to the concept of social desirability bias.

Additionally, using the phrase promoting science might influence the respondents' answers because it frames the question in a way that one answer appears more 'pro-science' than the other, potentially leading to an inflated percentage of respondents in favor of teaching only evolution in schools. This kind of bias prevents the collection of accurate data regarding the population's true stance on the issue being surveyed.

Given expression is:

By substituting the value of "g" in the given expression, we get

→ [tex]4g-12[/tex]

→ [tex]4(5) -12[/tex]

→ [tex]20-12[/tex]

→ [tex]8[/tex]

Thus the above answer is correct.

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Answer:

$43888.75

Step-by-step explanation:

We have been given that in 2010 the federal debt (in millions) was $13,561,623 and the population of the U.S. was 309 million.

[tex]\text{The federal debt per capita}=\frac{\text{Total debt}}{\text{Total population}}[/tex]

[tex]\text{The federal debt per capita}=\frac{\$13,561,623}{309}[/tex]

[tex]\text{The federal debt per capita}=\$43888.74757[/tex]

[tex]\text{The federal debt per capita}\approx \$43888.75[/tex]

Therefore, the federal debt per capita in 2010 was $43888.75.

Answer:

18, 20 cent and 36, 10 cent

Step-by-step explanation:

The inverse of y = 5 x² + 10 is , y = √ ( ( x / 5 ) - 2 )

What is an Inverse Function?

An inverse function is a function that undoes the action of the another function. To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

                                                   f⁻¹ ( x ) = y

Given data ,

y = 5 x² + 10

Now interchange the variable x and y , we get

x = 5 y² + 10

Subtract 10 from both sides , we get

x - 10 = 5 y²

Divide by 5 on both sides ,

( x / 5 ) - 2 = y²

Therefore , y = √ ( ( x / 5 ) - 2 )

Hence , the inverse f⁻¹ ( x ) = y = √ ( ( x / 5 ) - 2 )

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The formula for expense is given as:

E = V q + F

where, E = expense, V = variable cost, F = fixed cost

Therefore the equation should be:

E = 8.8 q + 14.50

So the answer is “False”

In this exercise we will use the knowledge of finance to calculate the total value of the purchase, we have:

Letter D

First, let's organize the information given in the statement as:

Taking the percentage over the total amount, we find:

[tex]6.6\% \ of \ 329.94\ is\ \$21.78\\Total= \$351.72[/tex]

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We are given a total size of 24 2/3 feet of wrapping paper. Convert this into fraction of denominator 6:

total paper = 24 2/3 = 74/3 = 148/6 feet

Subtract 5/6 foot:

remaining paper = 148/6 – 5/6 = 143/6 feet

Divide by 11:

each piece = (143/6) ft / 11 = 143/66  ft = 2.17 ft

Given

John had a roll containing of wrapping paper  

[tex]=24\tfrac{2}{3}[/tex]

First, he must cut off 5/6 foot because it was torn.

He wants to divide it into 11 pieces.

To proof

As given in question

John had a roll containing of wrapping paper

[tex]=24\tfrac{2}{3}[/tex]

[tex]=\frac{74}{3}[/tex]    ( solving the mixed fraction form)

 First, though, he must cut off 5/6 foot

than we get

[tex]= \frac{74}{3} - \frac{5}{6}[/tex]

Taking the L.C.M of 3 and 6 is 6

[tex]=\frac{148-5}{6}[/tex]

[tex]=\frac{143}{6}[/tex]

=23.83 feet (approx)

He wants to divide it into 11 piece

length of the each piece

[tex]=\frac{23.83}{11}[/tex]

length of the each pieces be 2.16 feet ( approx)

Hence proved

4 x 6 = 24 square feet

24/12 = 2

 so 1 person for every 2 square feet

1 mile - 5280 feet

4 x 5280 = 21120

21120 x 15 = 316800 square feet

316800/2 = 158,400 people