Carly has just opened her own nail salon. Based on experience, she
knows that her daily profit, P, in dollars, can be modelled by the relation
P = - 15x2 + 240x - 640, where x is the number of clients per day.
How
many
clients should she book each day to maximize her profit?
F

Answer:

g(x) =1

x-1

it's either g(x) or f(x)

Answer:1.625=158

Step-by-step explanation:

Answer:

1.625=158

Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator

1.625=1.6251

Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000

1.6251×10001000=16251000

Find the Greatest Common Factor (GCF) of 1625 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 125,

1625÷1251000÷125=138

Simplify the improper fraction,

=158

In conclusion,

1.625=158

Answer:

a₄ = - 2

Step-by-step explanation:

to calculate a term in the sequence subtract 5 from the previous term

give first term a₁  = 13 , then

a₂ = a₁ - 5 = 13 - 5 = 8

a₃ = a₂ - 5 = 8 - 5 = 3

a₄ = a₃ - 5 = 3 - 5 = - 2

Answer:

68°

Step-by-step explanation:

arctan(x) = 5/2

Answer:

14.7

Step-by-step explanation:

The solution set of the given system of equations is {(4, 0), (2, 4)}.

The given system of equations is: y = x² – 6x + 8 and y = –x + 4

To solve the given system of equations, we need to solve both the equations simultaneously.

We can solve the equations by the following method:

First Equation:

y = x² – 6x + 8

Rewriting in vertex form, we get:

y = (x – 3)² – 1

This is a parabola that opens upward and its vertex is at (3, –1).

Second Equation:

y = –x + 4

This is a line that passes through (0, 4) and (4, 0).

Now, we can find the solution of the given system of equations by plotting the graph of both the equations on the same graph.

We can observe from the graph that the two graphs intersect at (4, 0) and (2, 4).

Therefore, the solution of the given system of equations is: x = 4, y = 0, x = 2, y = 4

So, the solution set of the given system of equations is {(4, 0), (2, 4)}.

Learn more about vertex form visit:

brainly.com/question/22649174

#SPJ11

Answer:

\(c=85\)

Step-by-step explanation:

\(c=180-a-b\) where \(a=62\) and \(b=33\)

Step 1.  Substitute a for 62 and b for 33

\(c=180-(62)-(33)\)

Step 2. Subtract \((180 - 62)\)

\(c=118-33\)

Step 3. Subtract (again)

\(c=85\)

so c = 85

The mean (µx) and standard deviation (σx) of a sample can be determined using the given parameters of the population mean (µ), population standard deviation (σ), and sample size (n).

In this case, since we are given the population mean (µ = 84), the mean of the sample (µx) will be the same as the population mean.

µx = 84 (same as the population mean)

σx = 18 / √36 = 3 (the population standard deviation divided by the square root of the sample size)

To determine the standard deviation of the sample (σx), we divide the population standard deviation (σ = 18) by the square root of the sample size (n = 36). This is based on the principle that the standard deviation of the sample is expected to be smaller than the standard deviation of the population, and it decreases as the sample size increases.

Therefore, in this scenario, the mean of the sample (µx) is 84, and the standard deviation of the sample (σx) is 3. These values represent the central tendency and variability of the sample data.

Learn more about sample size here:

brainly.com/question/30100088

#SPJ11

Answer:169.52

Step-by-step explanation:

=(26)(6.52)

Answer:

the answer is 3.(6.5)9 that's the answer to the equation

Answer:

-0.4

Step-by-step explanation:

its that one

The strongest correlation is -0.4.

Option C is correct.

Correlation is a statistical term that expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical tool for describing simple relationships without stating a cause and effect link.

When the result is closer to +1 (positive correlation) or -1 (negative correlation), the strongest correlation is considered (negative correlation).

A positive correlation coefficient means that the value of one variable is directly related to the value of another.

Here -0.4 is the closest value to 1.

So, the strongest correlation is -0.4.

Learn more about Correlation here:

https://brainly.com/question/28898177

#SPJ7

The length of the longest side is 27 units, in the isosceles trapezoid.

What is isosceles trapezoid?

A four-sided shape called a trapezoid has two parallel lines on each side (normally the top and bottom sides). A trapezoid that has equal-length non-parallel sides (the legs) is said to be isosceles. Considering everything mentioned before, we may start learning how to calculate an isosceles trapezoid's perimeter.

Given, the congruent nonparallel sides has length 13.

he height of the trapezoid is 12.

the extra length of the larger side will be 2*x, as it will be extra portion in both side.

So x² = 13²-12²

x² = 169-144 = 25

x = √25 = 5

So the lentgh of the larger side is 10 unit larger than smaller side.

The perimer of the isosceles trapezoid will be P = sum of all sides

P = 2*13 + L + L+10

⇒70 = 26+10 +2L

⇒2L = 70 - 36

⇒2L = 34

⇒L = 17

The length of the larger side will be 17+10 = 27 units.

Hence the length of the longest side is 27 units.

Learn more about isosceles trapezoid, by the following link.

https://brainly.com/question/27019271

#SPJ1

Answer:

function is a parabola, with a lowest point of -4

Step-by-step explanation:

g(x)=x^-4

g(-3)= -3^2-4 = 9-4 = 5

g(-2)= -2^2-4 = 4-4 = 0

g(-1)= -1^2-4 = 1-4 = -3

g(0)= 0^2-4 = 0-4 = -4

g(1)= 1^2-4 = 1-4 = -3

g(2)= 2^2-4 = 4-4 = 0

g(3)= 3^2-4 = 9-4 = 5

Answer:

1 × 10^(-5)

Step-by-step explanation:

The scientific notation of the given number is 1.0×10⁻⁵.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given number is 0.000010.

Here, scientific notation is

1.0×10⁻⁵

Therefore, the scientific notation of the given number is 1.0×10⁻⁵.

To learn more about the Scientific notation visit:

https://brainly.com/question/18073768.

#SPJ2

The proportion of people that separates the lowest 33% from the upper 67% is 0.27 and σp = 0.056.

What is proportion?

In mathematics, proportion is a statement that two ratios or fractions are equal. Proportions are often used to compare the sizes of different quantities, and they can be expressed using the symbol ":", as well as with the words "is to" or "equals".

To solve this problem, we need to use the normal distribution function in Excel.

First, we need to find the z-score that separates the lowest 33% from the upper 67%:

z = NORM.INV(0.67,0,1) ≈ 0.44

Next, we can use the formula for the standard error of the proportion:

SE = \(\sqrt{(p(1-p)/n)\)

where p is the proportion of clients who are on the right track for retirement savings. We can solve for p by trial and error, starting with a guess of 0.29:

SE = \(\sqrt{(0.29*0.71/80)\) ≈ 0.056

Now we can use the formula for the margin of error:

ME = z*SE ≈ 0.0246

Finally, we can find the confidence interval for p:

p ± ME

0.29 ± 0.0246

The lower bound of this interval is:

0.29 - 0.0246 ≈ 0.2654

Rounded to the nearest hundredth, the proportion of people that separates the lowest 33% from the upper 67% is 0.27.

Therefore, the solution is:

σp = 0.056

p = 0.27

To learn more about proportion visit:

https://brainly.com/question/1496357

#SPJ1

The pattern in y = x² exhibits a nonlinear increase in y as x increases, forming a U-shaped curve, while the pattern in y = 15 + x shows a linear increase in y as x increases at a constant rate.

The patterns in the equations y = x² and y = 15 + x differ in terms of the direction of change. In the equation y = x², the pattern shows an increase in y as x increases.

As x increases from negative to positive values, the corresponding y values also increase, forming a symmetric U-shaped curve. The rate of increase for y becomes steeper as x moves further away from zero.

On the other hand, in the equation y = 15 + x, the pattern shows a linear increase in y as x increases. As x increases, the corresponding y values increase in a straight line.

The rate of increase for y remains constant at one unit per increase in x. This linear pattern reflects a constant upward shift of the graph as x increases.

For such more questions on Nonlinear:

https://brainly.com/question/30294608

#SPJ11

Answer:

$150

Step-by-step explanation:

Well we know that 10% is going to equal 1/10 of 100%.

So now just multipy 15% times 10 to get the original price.

Answer:

a=5.1

Step-by-step explanation:

Isolate the variable by dividing each side by the factors that don't contain the variable. Hope this helps! :)

The value of a, if The expression 2.4x − 3.9y − 1.2x + ay is equivalent to 1.2x + 1.2 y is 5.1.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Given:

2.4x−3.9y−1.2x+ay is equivalent to 1.2x+1.2y,

2.4x − 3.9y − 1.2x + ay = 1.2x + 1.2y

Simplify the above expression as shown below,

2.4x − 1.2x + ay - 3.9y = 1.2x + 1.2y

1.2x + y(a - 3.9) = 1.2x + 1.2y

As the expression is equivalent, compare the expression as shown below,

a - 3.9 = 1.2

a = 1.2 + 3.9

a = 5.1

Thus, the value of a is 5.1.

To know more about the expression:

https://brainly.com/question/13947055

#SPJ2

Answer:

$25(h) + $130

Step-by-step explanation:

Answer:

\( \sf 130 + 25h = TA \)

\(Solving Steps : - \)

Question :-Anna works as a painter. She charges S130 for paint supplies and $25 for each hour, h, she works. Which expression represents the total amount of money Anna charges?

Given :- To find the expression represents the total amount of money Anna charges?

She earns $ \sf 130 \:for\: paint\: supplies\: and\: $25 per hour

Therefore, will add $130 to $25 and add a variable letter 'h'

⇒ $130 + $25(h)

⇒ $130 + $25h = TA

Expression = \( 130 + 25h = TA \)

~Done~

Have a wonderful and fruitfull day :-)

Answer:

19 11/16

Step-by-step explanation:

5 1/4 x 3 3/4

Area = width x length

For a larger input size of 320,000 elements, it will take 240 ms to sort each half and 24 ms to merge the sorted halves, resulting in a total time of 264 ms.

The given information describes the time required for sorting and merging operations on two different input sizes. For 80,000 elements, it takes 18 ms to sort each half, resulting in a total of 36 ms for sorting. Merging the two sorted halves with 80,000 numbers in each takes 40 - 18 = 22 ms.

When the input size is doubled to 320,000 elements, the sorting time for each half increases to 240 ms, as it scales linearly with the input size. The merging time, however, remains constant at 4 ms since the size of the sorted halves being merged is the same.

Thus, the total time for sorting and merging 320,000 elements is the sum of the sorting time (240 ms) and the merging time (4 ms), resulting in a total of 264 ms.

Therefore, based on the given information, the total time required for sorting and merging 320,000 elements is 264 ms.

Learn more about total time here:

https://brainly.com/question/951637

#SPJ11

Answer:

when y=1 then x=0.5

Step-by-step explanation:

The graph is provided.

The equation y=4x-1 can be graphed by first graphing the -1 which is the y-intercept in the y=mx+b form. 4=m that is our slope. you can find the lines second point by moving 4 up and 1 to the right. rise/run =4/1. So when you move 4 up and 1 right you get another point on the line (1,3).

You can find out x=0.5 when y=1 by just tracing your finger over the graph and the point when y equals 1 the line intercepts x=0.5. Another screenshot is given.

I hope this helps!

Answer:

Second option

Step-by-step explanation:

They have two congruent pairs of sides and one congruent pair of angles.

The triangles B can be proven congruent by the SAS theorem

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

From the Option B) , we get

Let the first triangle be ΔABC

Let the second triangle be ΔBDE

Now , the measure of side AB = measure of side BD

And , the measure of side AC = measure of side BE

And , the measure of ∠ABC = measure of ∠DBE

Therefore , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Hence , the triangles are congruent by SAS theorem

To learn more about congruent triangles click :

https://brainly.com/question/26131452

#SPJ5

The value of the expression Z² + Q² is 4321

The radius of the chocolate spheres is given as:

r = 2

The maximum number of chocolates that can fit in a spherical capsule is calculated as:

Max = R³/r³

Where:

R represents the radius of the sphere.

For the spherical capsule whose radius is 8 inches, we have:

Z = 8³/2³

Evaluate

Z = 64

For the spherical capsule whose radius is 5 inches, we have:

Q = 5³/2³

Evaluate

Q = 15.625

Remove decimal

Q = 15

So, we have:

Z² + Q² = 64² + 15²

Evaluate the exponent

Z² + Q² = 4096 + 225

Evaluate the sum

Z² + Q² = 4321

Hence, the value of Z² + Q² is 4321

Read more about volumes at:

https://brainly.com/question/1972490

#SPJ1

a. To test the null hypothesis that there's no difference in handedness between men and women, we should use the Chi-Square-test for Independence.

The Chi-Square-test for Independence is used to determine if there is a relationship between two categorical variables. In this case, we want to compare handedness between men and women, which are two categorical variables.

The null hypothesis assumes that there is no association between the two variables, meaning the proportions of handedness are the same for men and women.

b. The expected frequencies for each category can be calculated by multiplying the row totals and column totals and dividing by the grand total.

Table of Expected Frequencies

Right   Left   Ambidextrous

Male    125.71   10.34   5.95

Female  431.29   35.66   20.52

c. The chi-square statistic is the sum of the squared differences between the observed and expected frequencies divided by the expected frequencies for each category.

The chi-square statistic is the sum of the following terms (rounded to 2 decimal places):

0.69 + 1.07 + 6.84 + 3.22 + 0.53 + 3.07 = 15.42

d. The chi-square statistic is 15.42.

e. The degrees of freedom can be calculated using the formula (number of rows - 1) * (number of columns - 1).

In this case, the degrees of freedom = (2 - 1) * (3 - 1) = 2.

f. The range of the p-value depends on the degrees of freedom. In this case, with 2 degrees of freedom, the range is 5% ≤ p-value < 10%.

g. Based on the p-value range, we cannot reject the null hypothesis. The different distribution of handedness in our survey data is very likely to be due to chance and does not reflect a real difference in the population in general.

To learn more about null hypothesis click here

brainly.com/question/19263925

#SPJ11

Answer:

Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula,

Answer:

the answer is b

Step-by-step explanation:

78. I got it correct. Hope you could give me Brainliest! Anyway, Based on the given conditions, formulate: 65÷56 Divide a fraction by multiplying its reciprocal:65×65Cross out the common factor:13×6

Calculate the product or quotient:78. Therefore, getting 78.

Answer:

Based on the information provided, the correct choice is:

fail to reject it

Here are the key points:

• The mean depression score for the sample of 20 4th graders was 4.4.

• The counselor tested the null hypothesis that these 4th graders were less depressed than the general 4th grader population.

• The t score calculated was 2.8.

To reject the null hypothesis and conclude the sample differs from the population, we would need a high enough t score. But the t score of 2.8 is not conclusively high enough here.

Some additional considerations:

• The general 4th grader population mean is 5, so the sample mean of 4.4 is a bit lower, but not drastically. This suggests the sample may not differ hugely from the population.

• There is no information on the variation or standard deviation for either the sample or population. Without this, we can't determine if a t score of 2.8 actually signifies a statistically significant difference.

• The sample size of 20 is decent but not very large. Larger sample sizes provide more conclusive results.

• No p-value is given, making it hard to judge if the t score of 2.8 is high enough to reject the null hypothesis. By convention, p<0.05 is often used but we don't have the p-value here.

So overall, there is not enough definitive evidence provided to conclusively reject the null hypothesis. The t score of 2.8 alone is probably not high enough, given the considerations around sample size, variation, and lack of a p-value. More data and analysis would be needed to make a firm decision either way.

Therefore, the correct choice is: "fail to reject it". There is not enough information given in this question and results to conclusively reject the null hypothesis.

Step-by-step explanation:

The real numbers can be classified as either rational or irrational numbers.

1. Rational Numbers:
Rational numbers can be expressed as the ratio (or fraction) of two integers. They can be written in the form p/q, where p and q are integers and q is not equal to zero. Rational numbers can be positive, negative, or zero. Some examples of rational numbers include 1/2, -3/4, and 5.

2. Irrational Numbers:
Irrational numbers cannot be expressed as the ratio of two integers. They are non-repeating and non-terminating decimals. Irrational numbers can be positive or negative. Some examples of irrational numbers include √2, π (pi), and e (Euler's number).

It is important to note that the set of real numbers contains both rational and irrational numbers. Every rational number is a real number, but not every real number is a rational number. This means that there are real numbers that cannot be expressed as a fraction.

In summary, the classification of real numbers as rational or irrational depends on whether they can be expressed as a ratio of integers (rational) or not (irrational). The set of real numbers contains both rational and irrational numbers, providing a comprehensive representation of all possible values on the number line.

Know more about Irrational Numbers here:

https://brainly.com/question/29194459

#SPJ11