The profit from a business is
described by the function
P(x) = -5x² + 30x + 8, where x
is the number of items made,
in thousands, and P(x) is the
profit in dollars. How many
items will maximize the profit?

Step-by-step explanation:

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Answer:

Ernest is wrong, because the sandwich can be made in 6 different ways (lunch > sandwich: white bread > cheese, pickles, mayonnaise ; wheat bread > cheese, pickles, mayonnaise) and the lunch can be made in 8 different ways.

Answer:

x = z - m + y

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z = m+x-y}[/tex]

To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.

[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]

Therefore, the answer to this question is x = z - m + y

Please let me know if you have any questions regarding my answer or explanation!

Kellie's original number given the analogy and corresponding equation is 13

let

(x × 2) × 3 = x + 65

2x × 3 = 65 + x

6x = 65 + x

6x - x = 65

5x = 65

x = 65/5

x = 13

check:

6x = 65 + x

6(13) = 65 + 13

78 = 78

Therefore, the unknown number, x is 13

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Vowels = {a, e, i, o, u}

There are 5 vowels out of 26 letters in the English alphabet. This leaves 26-5 = 21 consonants.

The theoretical probability of getting a consonant is 21/26 = 0.8077 = 80.77% approximately

Wayne found the empirical probability of a consonant as 60% which is quite a distance away from the 80.77% mentioned. The discrepancy is likely because vowels are tended to be used quite often in many words.

Words that are composed of consonants only are quite rare, but they do happen. Example: "fly" is a word with only consonants. I'm considering y to be a consonant.

Answer:

just solve normally as if theres no x,

1. 26x

2. -7x

Step-by-step explanation:

the perimeter is

2×length + 2×width = 86

length = 3×width

now we use the second equation as variable identity in the first equation :

2×3×width + 2×width = 86

6×width + 2×width = 86

8×width = 86

width = 86/8 = 43/4 = 10.75 cm

length = 3×width = 3×10.75 = 32.25 cm

Work Shown:

5x-6 = 44

5x-6+6 = 44+6 ... see note 1

5x = 50

5x/5 = 50/5 ... see note 2

x = 10

Answer:

Step-by-step explanation:

The transformation of a function may involve any change. The graph of g(x) is the graph of f(x) shifted 4 units to the right.

The transformation of a function may involve any change.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units, y=f(x+c) (same output, but c units earlier)

Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

As per the transformation of the function, if the function g(x) = f(x-4), then the graph of g(x) will be 4 units in the right of f(x).

Hence, the graph of g(x) is the graph of f(x) shifted 4 units to the right.

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Answer:

Step-by-step explanation:

Explanation

On a 6 sided die, there are three even numbers (2,4,6)

That's 1/2 the number on the die.

So getting 6 even numbers is

P(6) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.00781

Where did that extra 1/2 come from? Well one of the numbers thrown was an odd number, and it has to be counted.

P(7) = the same answer.                            0.00781

Total                                                           0.0156

Answer:

15 units

Step-by-step explanation:

15.0

Answer:

No solution

Step-by-step explanation:

[tex]3(5x - 4) < 15x \\ 15x - 12 < 15x \\ 15x - 15x < 12 \\ 0 < 12[/tex]

Answer:

4(9^0+48(2)^-3) I think it's like this

[tex]~~~~~~~~\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac 1{R_2}\\\\\\\implies \dfrac 1{R_2} = \dfrac{1}{R } - \dfrac 1{R_1}\\\\\\\implies \dfrac 1{R_2} = \dfrac{R_1 -R}{RR_1}\\\\\\\implies R_2 = \dfrac{RR_1}{R_1-R}\\\\\\\text{When}~ R= 24~ \Omega ~ \text{and}~ R_1 = 30~ \Omega,\\\\R_2 = \dfrac{24 \times 30}{30-24}~\Omega\\\\\\~~~~~=\dfrac{720}{6}~ \Omega\\\\\\~~~~= 120~ \Omega[/tex]

Answer:

21 rounds

Step-by-step explanation:

[tex]1[/tex] [tex]round = 0.4km[/tex]

[tex]Total[/tex] [tex]distance = 8.4km[/tex]

[tex]8.4/0.4[/tex]

[tex]=21[/tex]

The number of rounds he makes, if he runs a total of 8.4 km distance.

[tex]\large\boxed{R=\frac{Total \: distance}{Distance \: covered \: in \: 1 \: round}}[/tex]

So, we'll have to divide the total distance covered by distance covered in 1 round.

Let's substitute according to the formula.

[tex]R= \frac{8.4}{0.4}[/tex]

= 21 rounds

Hence, the number of rounds he makes, if he runs a total of 8.4 km distance is 21

Answer:

This graph does not represent a function.

Step-by-step explanation:

The vertical line test describes how, in order to be a function, there must be only one output for every input. Remember, the input of a function is the "x" value and the output is the "y" value.

Because of the circular nature, this graph does not represent a function. As you can see, there are "x" values which could correspond with mutliple "y" values. For example, when x = 2, there are two "y" values:  y = -1 and y = -5.

Answer:

39 and 65

Step-by-step explanation:

the ratio of the two numbers is 3 : 5

sum the parts of the ratio, 3 + 5 = 8 parts

divide the sum by 8 to find the value of one part of the ratio

104 ÷ 8 = 13 ← value of 1 part of the ratio , then

3 parts = 3 × 13 = 39

5 parts = 5 × 13 = 65

the two numbers are 39 and 65

Answer:

Answer: A. The contrapositive of the statement will be :

Step-by-step explanation:

The contrapositive of an if-then statement "p then q' is given by :

"If not q then not p".

The given statement is

Then the contrapositive of the statement will be :

Hence, A is the right option.

The answer is A , for determining range look at Y-axis only from down to up .For this question we can also say

range: [1,7] , if both ends of the line are arrows it means the line goes from negative infinity to positive infinity (which means range is all real numbers) , but if the point is include just like this graph the points will be also include in range , but if the points are an empty circle the points won't be include for writing range

hope it helps

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Refer to the attachment

Answer:

Use given values of h and j, and find the value of k:

The equation is now:

Find the value of g when h is 2 and j is 3:

Correct choice is D

Answer:

D. 144

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?

A.

2.8 pounds of apples and 4.8 pounds of grapes

B.

3.3 pounds of apples and 1.3 pounds of grapes

C.

3.8 pounds of apples and 1.8 pounds of grapes

D.

4.5 pounds of apples and 2.5 pounds of grapes

The vertex form of all expressions is given below.

We have given that the expressions

We have to write the function in vertex form.

The vertex form of a quadratic function is given by f (x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Therefore the first equation

[tex]f(x)=(x-1)^2-7[/tex]

it can be written as

[tex]f(x)=1(x-1)^2+(-7)[/tex]

The second equation can be written as

[tex]f(x) = (x+1)^2 -7[/tex]

vertex for is,

[tex]f(x)=1(x-(-1))^2+(-7)[/tex]

The third equation is,

[tex]f(x) = (x -1)^2 - 5[/tex]

Vertex form is,

[tex]f(x)=1(x-1)^2+(-5)[/tex]

Forth equation is,

[tex]f(x) = (x +1)^2 +(- 5)[/tex]

Vertex form is,

[tex]f(x) =1 (x -(-1))^2 +(- 5)[/tex]

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An absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean is; |x – 515| ≤ 114

A) We are told that;

Mean score = 515

Standard deviation = 114

We are now given that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. Thus, the absolute value inequality is;

|x – 515| ≤ 114

B) The range of scores to within ±2 standard deviations of the mean is;

Range = 515 ± 2(114)

Range = 287 to 743

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Answer:

(- 5, 4 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

G (4, - 5 ) → G' (- 5, 4 )

The coordinates of the image of vertex G are (-5, 4)

When reflecting a figure in a line or in a point, the image is congruent to the pre image. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.

here, we have,

Let us revise some cases of reflection

If the point (x, y) reflected across the x-axis , then its image is (x, -y)

If the point (x, y) reflected across the y-axis , then its image is (-x, y)

If the point (x, y) reflected across the line y = x , then its image is (y, x)

If the point (x, y) reflected across the line y = -x , then its image is (-y, -x)

From the given figure

∵ The line of the reflection is y = x

→ That means we will switch the coordinates of the point to find its image

∵ The coordinates of vertex G are (4, -5)

∴ The x-coordinate = 4 and the y-coordinate = -5

→ Switch the two coordinates

∴ The coordinates of its image G' are (-5, 4)

∴ The coordinates of the image of vertex G are (-5, 4)

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Answer:

7

Step-by-step explanation:

[tex]\dfrac 13(15+6)\\\\\\=\dfrac{21}3\\\\\\=7[/tex]