Mr. Alfred's favorite number plus Mr. Coble's favorite number is 28. The difference between Mr. Alfred's number and twice Mr. Coble's number is 10. What is Mr. Coble's favorite number? *

Answer:

The answer is below

Step-by-step explanation:

Given that k(x) = -125x² +670x - 125, where x is the charge per cone and P = k(x) is the weekly profit

a) The maximum profit is at P'(x) = 0. Therefore we have to find the derivative of the profit equation and equate it to 0.

P'(x) = k'(x) = 0

k'(x) = -250x + 670 = 0

-250x + 670 = 0

250x = 670

x = $2.68

P = k(2.68) = -125(2.68²) + 670(2.68) - 125 = $772.8

Hence the maximum profit is $772.8 when the price of each ice cream cone is $2.68

b) At break even, the profit is 0. Hence P= k(x) = 0

-125x² + 670x - 125 = 0

x = 5.17 or x = 0.19

Therefore to break even, the price of the ice cream cone needs to be $0.19 or $5.17

c) g(x) = k(x - 2)

g(x) = -125(x - 2)² + 670 (x -2) - 125

Maximum profit is at g'(x) = 0

g'(x) = -250(x-2) + 670

-250(x-2) + 670 = 0

-250x + 500 + 670 = 0

250x = 1170

x = 4.68

g(4.68) = -125(4.68 - 2)² + 670(4.68 -2) - 125 = $772.8

Therefore function g has the same maximum value as function k

Answer:

f(8) = 0

Step-by-step explanation:

The definition of an x intercept is a point where the function is equal to zero.

The surface area of the right rectangular prism is given as follows:

358 m².

The surface area of a prism is obtained with the sum of the areas of each part of the prism.

The parts that compose the prism are given as follows:

The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.

Hence the surface area of the prism is calculated as follows:

S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².

(multiplication by two due to the two rectangles with each of the dimensions).

The prism is given by the image shown at the end of the answer.

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Answer:

a) 42

b) 42/120

Step-by-step explanation:

Oof, I was just about done with answering this question but I deleted it all by accident so I had to rewrite it.

Anyways, the first part of it is correct.

The second part of it is a bit harder. See, this is conditional probability, which uses the equation that I've attached below.

For Event A, you'll need the total boys / total students:

0.44166

For Event B, you'll need the total counters / total students:

0.83333

Now, plug these values into the equation. The weird U thingy is called "Union". It basically means "and".

P(A and B) / P(B)

P(0.44166 * 0.8333) / P(0.8333)

0.36803 / 0.8333

This is about 0.44165, or 53/120

\(x^{2} +5x-3=-4x-3\\x^{2} +5x+4x-3+3=0\\x^{2} +9x=0\\\\x(x+9)=0\\x=0 or x+9=0\\x= -9\)

I hope this helps.

Answer:

x = 0

or

x = (-9)

Step-by-step explanation:

\( {x}^{2} + 5x - 3 = - 4x - 3\)

transfer like terms to the same side of the equation

\( {x}^{2} + 5x + 4x = - 3 + 3\)

Add/subtract like terms

\( {x}^{2} + 9x = 0\)

Now we can factor terms

\( {x}^{2} = x \times x \: and \: 9x = 9 \times x\)

we can write them with their common divisor

x*(9+x) = 0 for this equation to be correct either x = 0 or (9+x) = 0

if x = 0 well then that's the first value of x

if (9+x) = 0 then x = -9 and this is the second value of x

Answer: 84, 35

Step-by-step explanation:

12*7=84

5*7=35

84-35=49

The two numbers are 35 and 84

Let the two numbers be x and y

If the ratio are in 12: 5, hence:

x/y = 12/5

5x = 12y

x = 12y/5

If their difference is 49, then;

x - y = 49 .................. 2

12y/5 - y = 49

7y/5 = 39

7y = 49 * 5

y = 7 * 5

y = 35

Recall that x - y = 49

x = 49 + y

x = 49 + 35

x = 84

Hence the two numbers are 35 and 84

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The number of packs of mini cupcakes ordered by Mary are 15 approximately if she has $200 to spend and the cost of each pack is $12.75 and shipping cost is $14.50.

Total amount, Mary can spend = $200

Cost of one pack = $12.75

Total shipping cost = $14.50

Amount remaining after shipping cost = $200 - $14.50 = $185.50

Total packs Mary can order = $185.50/$12.75 = 14.54

Hence, Mary can order approximately 15 packs of mini cupcakes.

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Answer:

I think 3+×37p I think it the answer

Answer:

d 70%

Step-by-step explanation:

30 students in class

21 students with 5+ vowels

21/30 x 100 = 70%

Answer:

500° celsius = 932.0° fahrenheit....

Answer:

932 fahrenheit

Step-by-step explanation:

500 celsius to fahrenheit is 932 fahrenheit    

Answer:

Wayne west would have $5,015 in six months

Step-by-step explanation:

The formula for exponential regression model is y = αβˣ

Where y is amount of money in 1000 dollars

           x is time in months

We are given that α = 4.2 and  β = 1.03 and x = 6 months

Therefore, based on this model, y = αβˣ, the amount he would have in 6 months, y = \(4.2*(1.03) ^{6}\)

y = 5.015 × 1000 = $ 5,015

Answer:

25?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given: MN ≅ MA

          ME ≅ MR

Prove: ∠E ≅ ∠R

From the given diagram,

YN ≅ YA

EY ≅ RY

<EMA = <RMN (right angle property)

EA = EY + YA (addition property of a line)

NR = YN + RY (addition property of a line)

EA ≅ NR (congruent property)

ΔEMA ≅ ΔRMN (Side-Side-Side, SSS, congruence property)

<MNR ≅ MAE (angle property of congruent triangles)

Therefore,

<E ≅ <R (angle property of congruent triangles)

Answer:

When it is in parentheses.

Step-by-step explanation:

In PEMDAS, first is always parentheses, no matter what operation.

If it is subtraction, do that first.

hope this helped!

Answer:

the 3rd one

Step-by-step explanation:

this is only true when it is in perenthisis because when you do PEDMAS you go in that order. P (perenthisis) beng first. so TECHNECLY perenthisis is first, but the first actual MATH PROBLEM being done is subtraction.

Answer:

  (c)  (-∞, -2] ∪ (-1, ∞)

Step-by-step explanation:

You want the range of the piecewise function shown in the graph.

The range is the vertical extent of the graph, the set of possible output values of the function.

This graph shows a gap between y = -2 and y = -1. The value y = -2 is included in the range, but the value y = -1 is not. (That's what the open circle means.)

Hence, the range is ...

  (-∞, -2] ∪ (-1, ∞)

We can find the linear equation by using the given graph, the equation is:

y = 4.8*x + 24

On the graph we can see the best fit line, remember that a linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is at y = 24, then:

y = m*x + 24

Now, notice that when x = 5, the value of y is 48, replacing these values we get:

48 = m*5 + 24

48 -24 = m*5

24/5 = m

4.8*m

The linear equation is:

y = 4.8*x + 24

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Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

Answer: A) JL ≈ HF

SSS means you need to know all three sides are congruent

The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.

A statistic called the standard deviation describes how much variation or dispersion there is in a set of statistics .In contrast to a high standard deviation, which shows that the values are spread out, a low standard deviation suggests that the values tend to be close to the mean of the collection. out over a wider range.

Here,

In this instance, the standard deviation is 11 and the mean is 175. Assume that x1 is the heaviest weight at which the bags fall into the lower 5% and x2 is the lightest weight at which they fall into the upper 4.5%. 5% of the time, and 4.5% of the time, the likelihood is below x1 and above x2. The raisin bags should fall below x1 and above x2 if they need to be repackaged. The points x1 and x2 are illustrated in the image below.

1 x 0.045 x 0.05 = 0.905 is the probability between x1 and x2. Below is a picture of the normal distribution curve for raisins bag weights.

To calculate x1 and x2, locate x1 first. To the left of x1, there is a 0.05 probability. To find x1, use Excel. 1. Start Excel. Toggle a cell that is empty. Press ENTER after typing =NORM.INV(0.05,175,11).

The answer is 157, rounded to the nearest whole number. Thus, x1≈157. To compute x2, use the formula 0.05+0.905=0.955 for the probability to the left of x2. To determine x2, use Excel. Start Excel. Toggle a cell that is empty. Enter the command =NORM.INV(0.955,175,11).

The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.

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The exponential equation to model this scenario is given  by y = 200(0.85)ˣ

An equation is an expression that shows the relationship between two or more numbers and variables.

A linear inequality has the form of a linear equation, showing the non equal comparison between numbers and variables.

The linear inequality y ≤ (1/3)x - 5 passes through the point (0, -5) and (15, 0)

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\(\text{Given that,}\\\\\cot A = -\dfrac{9}{\sqrt{40}}\\\\\\\implies \tan A = -\dfrac{\sqrt{40}}9\\\\\\\implies \tan^2 A = \dfrac{40}{81}\\\\\\\implies \sec^2 A -1 = \dfrac{40}{81}\\\\\implies \sec^2 A = 1 + \dfrac{40}{81}\\\\\implies \sec^2 A = \dfrac{121}{81}\\\\\implies \sec A = \pm \sqrt{\dfrac{121}{81}}= \pm\dfrac{11}{9}\\\\\\\text{Since the angle A is in quadrant II, the value of sec A will be negative.}\\\\\\\text{Hence,}~ \sec A=-\dfrac{11}{9}\)

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Slope can be conceptualized as rise over run.

To get rise, you can see the difference between the two 'y' coordinates. In this case, it's 0 (-5 and -5). At this point, since the numerator of our \(\frac{rise}{run}\) fraction is 0, you know it's just gonna be 0 no matter the value of the run.

Answer: 26 pounds

Step-by-step explanation:

Let +a+ = pounds of coffee A used

Let +b+ = pounds of coffee B used

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

(1) +4.1a+%2B+5.8b+=+709.8+

(2) +b+=+4a+

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

(1) +41a+%2B+58b+=+7098+

Substitute (2) into (1)

(1) +41a+%2B+58%2A4a+=+7098+

(1) +41a+%2B+232a+=+7098+

(1) +273a+=+7098+

(1) +a+=+26+

26 pounds of coffee A were used

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

check:

(2) +b+=+4a+

(2) +b+=+4%2A26+

(2) +b+=+104+

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

(1) +41a+%2B+58b+=+7098+

(1) +41%2A26+%2B+58%2A104+=+7098+

(1) +1066+%2B+6032+=+7098+

(1) +7098+=+7098+

The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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The graph of y = 2x shows the correct way to plot ratios of Williams books to Jan’s books as ordered pairs.

Hence option A is the correct option for this problem.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For every 1 book Willam reads, Jan reads 2, hence the constant for this problem is given as follows:

k = 2/1 = 2.

Thus the equation is:

y = 2x.

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The number written on the board will be negative 27. This can be solved by using the concept of algebra.

Algebra is the study of mathematical symbols, while logic is the manipulation of those symbols.

Let x be the number.

There is a number written on the board. One student increased the number by 23. Then the first number will be

⇒ x + 23

But another student decreased the same number by 1. Then the second number will be

⇒ x - 1

The first student's result was 7 times greater than the result of the second student.

7 first number = second number

or, 7(x + 23) = x - 1

or, 7x + 161 = x - 1

or, 6x = - 162

or, x = - 27

The number written on the board will be negative 27.

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