A square has a perimeter of 44 yd. What is the length of each side?

1 meter = 100 cm

So a 800 cm roll can cover 8 meters

(800/100 = 8)

She has 5 rolls so 5 x 8 = 40 meters total.

Answer:

a) 11.51% probability that a random college woman has a height of 68 inches or​ more

b) This height is 70.135 inches.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

The normal distribution has two parameters, which are the mean and the standard deviation.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 65, \sigma = 2.5[/tex]

a. What is the probability that a random college woman has a height of 68 inches or​ more?

This is 1 subtracted by the pvalue of Z when X = 68. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{68 - 65}{2.5}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

1 - 0.8849 = 0.1151

11.51% probability that a random college woman has a height of 68 inches or​ more

b. To be in the Tall​ Club, a woman must have a height such that only​ 2% of women are taller. What is this​ height?

This weight is the 100-2 = 98th percentile, which is the value of X when Z has a pvalue of 0.98. So X when Z = 2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.054 = \frac{X - 65}{2.5}[/tex]

[tex]X - 65 = 2.054*2.5[/tex]

[tex]X = 70.135[/tex]

This height is 70.135 inches.

Answer: 4/10, simplified to 2/5

Step-by-step explanation:

1/10 plus 3/10 plus 2/10 is 6/10

10/10 minus 6/10 is 4/10

4/10 simplified (divide the numerator and the denominator by 2) is 2/5

Final answer:

Terry has covered 3/5 of the distance to home by running, walking, and skipping. Therefore, he still has 2/5 of the distance left to cover.

Explanation:

The question asks how much distance Terry still has to cover to reach home, given the fractions of the journey he has completed by running, walking, and skipping.

Terry ran 1/10 of the distance, walked 3/10 more, and skipped 2/10 more of the distance. To find the total distance covered, we add these fractions together:

To find the distance Terry still has to go, we subtract the fraction of the distance he has covered from the whole distance (1 or 5/5):

Therefore, Terry still has to cover 2/5 of the distance to reach home.

Final answer:

Equations B (−x = y) and D (6x −3y = 12) represent linear functions because they can be written in the standard linear form y = mx + b, where m and b are constants.

Explanation:

When determining if an equation represents a linear function, we look for the standard form y = mx + b, where m represents the slope and b represents the y-intercept. In this form, both m and b must be constants, and the equation should not have variables with exponents other than 1. Given the options:

A. y = x2 - This equation is not linear because of the exponent on x.

B. −x = y - This can be represented in linear form as y = −x (or y = −0x + 0), hence it is linear.

C. y = 14x2 + 4 - This equation is not linear due to the exponent on x.

D. 6x −3y = 12 - This can be rewritten in linear form as y = 2x - 4, making it a linear equation.

E. y = −2x2 + 1 - This is not linear for the same reason as options A and C.

The equations that represent linear functions from the given options are B and D.

Step-by-step explanation:

Three m minus eight n divided by thirteen

Answer:

27.19% probability that a female driver was involved in an accident

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

74,250 car accidents. Of those, in 20,187, the driver was a female.

Based on this, what is the probability that a female driver was involved in an accident?

p = 20187/74250 = 0.2719

27.19% probability that a female driver was involved in an accident

The probability that a female driver was involved in one of the car accidents in 2005 is approximately 27.2%.

To determine the probability that a female driver was involved in an accident, we use the following formula:

In this case, the number of favorable outcomes is the number of accidents involving a female driver (20,187), and the total number of outcomes is the total number of car accidents (74,250).

Therefore, the probability that a female driver was involved in an accident is approximately 27.2%.

Answer:

Positive increase of 200%

Step-by-step explanation:

Answer:

Step-by-step explanation:

percentage increase =increase /original *100

=750-250/250×100

=500/250×100

=200%

hope this helps

plzz mark me brainliest

Answer:

Neither

Step-by-step explanation:

In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.

For direct variation, [tex]y=kx[/tex] and for indirect variation, [tex]y=\frac{k}{x}[/tex] where k is a constant.

x  2    5   20  40

y  40  20  5     2

Here,

[tex]\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20[/tex]

So, this is neither a direct variation nor an indirect variation.

Answer:

360 degree

Step-by-step explanation:

The sum of all the exterior angles is 360 for any polygon.

This can be proved for polygon with 20 sides also.

We know that sum of all the angles of polygon is given by formula = (2*n -4) *90

where n is the no. of sides of polygon

for 20 sides polygon sum of  sum of all the angles = (2*20 -4) * 90

= (40-4)*90 = 36*90 = 3240 degree

measure of each angle of polygon = sum of total angles of polygon/ no of sides of polygon = 3240/20 = 162

We also know that sum of interior and exterior angle of triangle is 180 degree, as interior and exterior angle  lies on straight line and they  are supplementary

so

162 + value of exterior angle = 180

=> value of exterior angle = 180 - 162 = 18

Value of one exterior angle is 18 degree

in 20 sided polygon there are 20 exterior angle

therefore, value of 20 exterior angle is 18*20 degree which is 360 degree.

__________________________________________________________

As a general point one can memorize than sum of all the exterior angle for a polygon with any number of side is 360.

Answer:

0.45 part of the banner is painted orange.

Step-by-step explanation:

Given that the area for green = 0.75

The area of orange on green is = 0.6

So the area of orange is = 0.75*0.6 = 0.45

Learn more: https://brainly.com/question/1594198

To find the part of the banner that is painted orange, we multiply the green area by 0.6 and divide by the total area of the banner.

To find the part of the banner that is painted orange, we need to calculate the orange area compared to the total area of the banner.

Let's say the total area of the banner is 100 square units. Using the steps above:

https://brainly.com/question/30659007

#SPJ3

Answer:

(-1/2,-9/2)

Step-by-step explanation:

that is the coordinates for the vertex of the function y=2xsqaured+2x-4

Answer:

2

Step-by-step explanation:

y-intercept is where x = 0, and that point is (0,2), so it's 2

Answer:

Step-by-step explanation:

first method is to try out all possible combinations and pick out the best one which has the minimum operations but that would be infeasible method if the no of matrices increases  

so the best method would be using the dynamic programming approach.

A1 = 100 x 50

A2 = 50 x 200

A3 = 200 x 50

A4 = 50 x 10

Table M can be filled using the following formula

Ai(m,n)

Aj(n,k)

M[i,j]=m*n*k

The matrix should be filled diagonally i.e., filled in this order

(1,1),(2,2)(3,3)(4,4)

(2,1)(3,2)(4,3)

(3,1)(4,2)

(4,1)

                 Table M[i, j]                                            

             1                      2                  3                    4

4    250000          200000        100000                0  

3      

750000        500000            0

2      1000000             0

1            

0

Table S can filled this way

Min(m[(Ai*Aj),(Ak)],m[(Ai)(Aj*Ak)])

The matrix which is divided to get the minimum calculation is selected.

Table S[i, j]

           1          2         3        

4

4          1           2         3

3          

1          2

2            1

1

After getting the S table the element which is present in (4,1) is key for dividing.

So the matrix multiplication chain will be (A1 (A2 * A3 * A4))

Now the element in (4,2) is 2 so it is the key for dividing the chain

So the matrix multiplication chain will be (A1 (A2 ( A3 * A4 )))

Min number of multiplications: 250000

Optimal multiplication order: (A1 (A2 ( A3 * A4 )))

to get these calculations perform automatically we can use java

code:

public class MatrixMult

{

public static int[][] m;

public static int[][] s;

public static void main(String[] args)

{

int[] p = getMatrixSizes(args);

int n = p.length-1;

if (n < 2 || n > 15)

{

System.out.println("Wrong input");

System.exit(0);

}

System.out.println("######Using a recursive non Dyn. Prog. method:");

int mm = RMC(p, 1, n);

System.out.println("Min number of multiplications: " + mm + "\n");

System.out.println("######Using bottom-top Dyn. Prog. method:");

MCO(p);

System.out.println("Table of m[i][j]:");

System.out.print("j\\i|");

for (int i=1; i<=n; i++)

System.out.printf("%5d ", i);

System.out.print("\n---+");

for (int i=1; i<=6*n-1; i++)

System.out.print("-");

System.out.println();

for (int j=n; j>=1; j--)

{

System.out.print(" " + j + " |");

for (int i=1; i<=j; i++)

System.out.printf("%5d ", m[i][j]);

System.out.println();

}

System.out.println("Min number of multiplications: " + m[1][n] + "\n");

System.out.println("Table of s[i][j]:");

System.out.print("j\\i|");

for (int i=1; i<=n; i++)

System.out.printf("%2d ", i);

System.out.print("\n---+");

for (int i=1; i<=3*n-1; i++)

System.out.print("-");

System.out.println();

for (int j=n; j>=2; j--)

{

System.out.print(" " + j + " |");

for (int i=1; i<=j-1; i++)

System.out.printf("%2d ", s[i][j]);

System.out.println();

}

System.out.print("Optimal multiplication order: ");

MCM(s, 1, n);

System.out.println("\n");

System.out.println("######Using top-bottom Dyn. Prog. method:");

mm = MMC(p);

System.out.println("Min number of multiplications: " + mm);

}

public static int RMC(int[] p, int i, int j)

{

if (i == j) return(0);

int m_ij = Integer.MAX_VALUE;

for (int k=i; k<j; k++)

{

int q = RMC(p, i, k) + RMC(p, k+1, j) + p[i-1]*p[k]*p[j];

if (q < m_ij)

m_ij = q;

}

return(m_ij);

}

public static void MCO(int[] p)

{

int n = p.length-1;     // # of matrices in the product

m    =    new    int[n+1][n+1];        //    create    and    automatically initialize array m

s = new int[n+1][n+1];

for (int l=2; l<=n; l++)

{

for (int i=1; i<=n-l+1; i++)

{

int j=i+l-1;

m[i][j] = Integer.MAX_VALUE;

for (int k=i; k<=j-1; k++)

{

int q = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];

if (q < m[i][j])

{

m[i][j] = q;

s[i][j] = k;

}

}

}

}

}

public static void MCM(int[][] s, int i, int j)

{

if (i == j) System.out.print("A_" + i);

else

{

System.out.print("(");

MCM(s, i, s[i][j]);

MCM(s, s[i][j]+1, j);

System.out.print(")");

}

}

public static int MMC(int[] p)

{

int n = p.length-1;

m = new int[n+1][n+1];

for (int i=0; i<=n; i++)

for (int j=i; j<=n; j++)

m[i][j] = Integer.MAX_VALUE;

return(LC(p, 1, n));

}

public static int LC(int[] p, int i, int j)

{

if (m[i][j] < Integer.MAX_VALUE) return(m[i][j]);

if (i == j) m[i][j] = 0;

else

{

for (int k=i; k<j; k++)

{

int   q   =   LC(p,   i,   k)   +   LC(p,   k+1,   j)   +   p[i-1]*p[k]*p[j];

if (q < m[i][j])

m[i][j] = q;

}

}

return(m[i][j]);

}

public static int[] getMatrixSizes(String[] ss)

{

int k = ss.length;

if (k == 0)

{

System.out.println("No        matrix        dimensions        entered");

System.exit(0);

}

int[] p = new int[k];

for (int i=0; i<k; i++)

{

try

{

p[i] = Integer.parseInt(ss[i]);

if (p[i] <= 0)

{

System.out.println("Illegal input number " + k);

System.exit(0);

}

}

catch(NumberFormatException e)

{

System.out.println("Illegal input token " + ss[i]);

System.exit(0);

}

}

return(p);

}

}

output:

Answer:

Carlita's Speed or distance over time

Step-by-step explanation:

The rate of change of the data (her distance) is her speed.

Speed is the rate of change of distance, distance covered overtime.

Speed = distance/time

Unit = meter/seconds or miles per hour

Therefore, the rate of change for that data represent Carlita's Speed or distance over time

Answer:

The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

The absolute value of the subtraction of one of the bounds by the estimate [tex]\pi[/tex]

For this problem, we have that:

[tex]n = 240, \pi = \frac{96}{240} = 0.4[/tex]

97% confidence level

So [tex]\alpha = 0.03[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.03}{2} = 0.985[/tex], so [tex]Z = 2.17[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.3314[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.4686[/tex]

0.4686 - 0.4 = 0.0686

The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.

Final answer:

To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, the proportion p is calculated from the sample data and then substituted into the formula. The margin of error is also calculated using the formula.

Explanation:

To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, we can use the formula:

CI = p ± z*(√(p(1-p)/n))

Where:

First, we calculate the proportion p = 96/240 = 0.4

Next, we find the z-value using a standard normal distribution table. For a 97% confidence level, the z-value is approximately 1.88

Finally, substituting the values into the formula:

CI = 0.4 ± 1.88*(√((0.4*(1-0.4))/240))

Calculating the margin of error:

ME = z*(√(p(1-p)/n))

ME = 1.88*(√((0.4*(1-0.4))/240))

ME ≈ 0.036

Therefore, the 97% confidence interval for the percentage of all such companies that provide on-site health club facilities is approximately 0.364 to 0.436. The margin of error for this estimate is approximately ±0.036.

Answer:

from what I understand a 200% increase is tripling the number the increase is on

Answer:

(x-1)(x-42) or (x-1) x (x-42)              <-----(they're basically the same thing)

Step-by-step explanation:

1. x^2-43x+42  2. x^2-x-42x+42  3. x(x-1)-42x+42  4. x(x-1)-42(x-1)  5. (x-1)(x-42)

6. answer is (x-1)(x-42)

Answer:

The length of shadow of the woman is 14.375 ft.

Step-by-step explanation:

Here we are given that

Height of the woman = 5.75 ft

Height of the lamp post = 12 ft

Shadow of the lamp post = 30 ft

Let the angle of elevation of the light source be θ

By definition, in a right triangle, with respect to angle θ, we have;

tan(θ) = Opposite÷Adjacent

Therefore, tan(θ) = (Height of the lamp post)÷(Shadow of the lamp post)

and tan(θ) = 12 ft ÷ 30 ft = 0.4

θ = Actan(0.4) = tan⁻¹(0.4) = 21.8°

Since, angle of elevation of the light = Angle of depression of the light (alternate angles) = 21.8° we have

tan(θ) = (Height of the woman) ÷ (Length of shadow of the woman)

∴ Length of shadow of the woman = (Height of the woman) ÷ tan(θ)

Length of shadow of the woman = 5.75 ft ÷ tan(21.8) = 5.75 ft ÷ 0.4

Length of shadow of the woman = 5.75 ft ÷ 0.4 = 14.375 ft.

Answer:

99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.

True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.

Step-by-step explanation:

For this case we need to remember that the confidence interval for the true mean is given by this formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]

And for this case the 99.7 % confidence interval for the true mean is (12.64cm , 14.44cm) we analyze one by one the possible options in order to select one:

99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.

True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.

There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.

False the confidence interval can't be interpreted as a chance

There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm.

False the confidence interval can't be interpreted as a chance

If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.

False always the confidence interval contain the mean since is the middle value.

Final answer:

The correct interpretation of a 99.7% confidence interval for mean length of frog jumps is that if we repeat the sampling many times, 99.7% of the constructed confidence intervals would contain the true population mean. This emphasizes the methodology's reliability over repeated sampling rather than assuring specifics of individual outcomes.

Explanation:

The correct interpretation of a 99.7% confidence interval, like the one provided for the mean length of frog jumps (12.64 cm, 14.44 cm), is that if we were to repeat this sampling process many times, 99.7% of the confidence intervals we construct would contain the true population mean. The other statements provided misinterpret the concept of confidence intervals by implying a probability about individual measurements or the certainty of the mean falling within a specific interval, which is not accurate.

Confidence intervals are about the process of estimation rather than specifics about single outcomes. They provide a range in which we are certain to a specified level (in this case, 99.7%) that the true population mean lies, assuming the sampling and calculations are correct. The correct interpretation underscores the reliability of the methodology over repeated sampling rather than guaranteeing specifics of individual outcomes or the exact location of the population mean.

Answer:

25% probability you will roll a prime number and spin a prime number

Step-by-step explanation:

If we have two events, A and B, and they are independent, we have that:

[tex]P(A \cap B) = P(A) \times P(B)[/tex]

In this question:

Event A: Rolling a prime number.

Event B: Spinning a prime number.

Both the cube and the spinner have four values, ranging from one to four.

2 and 3 are prime values, that is, 2 of those values. Then

[tex]P(A) = P(B) = \frac{2}{4} = \frac{1}{2}[/tex]

What is the probability you will roll a prime number and spin a prime number

The cube and the spinner are independent of each other. So

[tex]P(A \cap B) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25[/tex]

25% probability you will roll a prime number and spin a prime number

Answer:

= 1/4

Step-by-step explanation:

In a  cube , we have  numbers labeled 1 - 6

the prime numbers we have is 2 , 3 and 5

The probability of selecting a prime number is

[tex]=\frac{3}{6} \\\\=\frac{1}{2}[/tex]

Now this means the probability of rolling a prime number here is 1/2

Now we calculate the probability of spinning a prime number

Prime numbers here are just 2 and 3

The probability of spinning a prime number is thus 2/4 = 1/2

Thus, the probability of rolling a prime number and spinning a prime number also becomes; 1/2 * 1/2

= 1/4

Answer: = ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 65.3

Standard deviation r = 5.2

Number of samples n = 36

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

65.3 +/-1.645(5.2/√36)

65.3 +/-1.645(0.86667)

65.3+/- 1.4257

65.3+/- 1.4

= ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Answer:

Yessirrr you are!!!

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

let a be the other number

so one number is [tex]\frac{2}{3}a - 3[/tex]

a + [tex]\frac{2}{3}a - 3[/tex] = 17

[tex]\frac{5}{3}a - 3 = 17[/tex]

[tex]\frac{5}{3}a[/tex] = 17 + 3 = 20

a = 20 x [tex]\frac{3}{5}[/tex] = 12

[tex]\frac{2}{3}(12) - 3[/tex] = 5

Answer:

its the 1st answer on edg

Step-by-step explanation:

I just took it

The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube

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

The volume of the cube = h unit * h unit * h unit = h³ unit³

Volume of each pyramid = (1/6) * h³ = (1/3) * base² * height

(1/6) * h³ = (1/3) * base² * height

(1/3) * h² * (1/2)h = (1/3) * base² * height

The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube.

Find out more on equation at: https://brainly.com/question/2972832

Answer:    x= 2/3

Step-by-step explanation:     For f(x) = g(x) we should equate the two functions to get the value of x.

f(x) = g(x)

−3x + 4 =  2

-3x + 4 - 4 = 2 - 4

-3x = -2

Dividing by -3 on both sides;

(-3x)/-3 = (-2)/-3

 x = 2/3

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

If f(x)=g(x), should be :  -3x+4= 2

-3x + 4 = 2

-3x = -2

x= -2/-3

x = [tex]\frac{2}{3}[/tex]

Hope this helps ^-^

Answer:

- The number of t-shirts he needs to print to obtain maximum profit = 2.79 (in thousand), that is, 2790 t-shirts.

- The maximum profit for this number of shirts is then = 12.208761 (in thousand dollars) = $12209

Step-by-step explanation:

Complete Question

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

The profit function is given as

p(x) = -x³ + 4x² + x

The maximum profit will be obtained by investigating the maximum value of the profit function

At the maximum value of the function,

(dp/dx) = 0 and (d²p/dx²) < 0

p(x) = -x³ + 4x² + x

(dp/dx) = -3x² + 8x + 1

at maximum point

(dp/dx) = -3x² + 8x + 1 = 0

Solving the quadratic equation

x = -0.12 or 2.79

(d²p/dx²) = -6x + 8

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0 (not a maximum point)

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0 (this corresponds to a maximum point!)

So, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousand).

So, the maximum profits that corresponds to this number of t-shirts is obtained from the profit function.

p(x) = -x³ + 4x² + x

p(x) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.717639 + 31.1364 + 2.79

p(x) = 12.208761 (in thousand dollars) = $12209 to the mearest whole number.

Hope this Helps!!!

Keegan should print around 2,000 shirts to maximize his profits, resulting in approximately $12,000 in earnings

To find the number of t-shirts Keegan should print to maximize his profits, we need to find the critical points of the profit function p(x) = -x^3 + 4x^2 + x.

Taking the derivative, we get p'(x) = -3x^2 + 8x + 1. Setting this equal to zero and solving for x gives:

0 = -3x^2 + 8x + 1

Using the quadratic formula, we find two potential values for x: x ≈ 2.37 and x ≈ -0.12. Since x must be a positive value representing the number of shirts, we discard the negative root.

Next, we need to determine whether this value of x corresponds to a maximum or minimum. We can do this by examining the second derivative, p''(x) = -6x + 8. Since p''(2.37) > 0, we conclude that x ≈ 2.37 corresponds to a local minimum.

However, since we're dealing with a cubic function, we need to consider behavior as x approaches infinity. As x gets very large, the -x^3 term dominates, making the function tend toward negative infinity. This means there is no global maximum, but rather a local maximum.

To find the approximate number of shirts Keegan should print, we take the nearest whole number, which is 2. The maximum profit can be found by plugging this value back into the profit function:

p(2) ≈ -2^3 + 4(2)^2 + 2 ≈ 12 (in thousands).

So, Keegan should print around 2,000 shirts to maximize his profits, which will be approximately $12,000 (rounded to the nearest whole dollar).

Complete question:

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

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Answer:

The minimum sample size required to create the specified confidence interval is 1804.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Minimum sample size for a margin of error of 0.06:

This sample size is n.

n is found when [tex]M = 0.06, \sigma = 1.3[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.06 = 1.96*\frac{1.3}{\sqrt{n}}[/tex]

[tex]0.06\sqrt{n} = 1.96*1.3[/tex]

[tex]\sqrt{n} = \frac{1.96*1.3}{0.06}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*1.3}{0.06})^{2}[/tex]

[tex]n = 1803.41[/tex]

Rounding up to the next integer

The minimum sample size required to create the specified confidence interval is 1804.

Answer:

40

Step-by-step explanation:

3x^2 + 8x = 2

3x^2 + 8x - 2 = 0

D = b^2+4ac

D = 8^2+4(3)(-2)

D = 64+(-24)

D = 64-24

D = 40

Answer:

(B) all numbers less than 7

Step-by-step explanation:

Given the inequality:

x<7

It means that:

Therefore, x<7 consists of all numbers less than 7.

Answer:

B

Step-by-step explanation:

Answer:

The length of rectangular photo frame is 15 cm and the breadth is 8 cm.

Step-by-step explanation:

The question is:

The diagonal of a rectangular photo frame is 2 cm more than the longest side. If the perimeter is 46 cm, how long are the sides of the frame?

Solution:

Let the length of the rectangular photo frame be denoted by x and breadth by y.

It is provided that the diagonal is 2 cm more than the length.

That is:

d = x + 2

The perimeter is 46 cm.

That is:

46 = 2 (x + y)

⇒ x + y = 23

⇒ x = 23 - y

The triangle form by the length, breadth and the diagonal of the rectangle is a right angled triangle, with the diagonal as the hypotenuse, length as perpendicular and breadth as the base.

So, according to the Pythagoras theorem,

d² = x² + y²

(x + 2)² = x² + y²

x² + 4x + 4 = y²

4x + 4 = y²

4 (23 - y) + 4 = y²

92 - 4y + 4 = y²

y² + 4y - 96= 0

Factorize the expression by splitting the middle term as follows:

y² + 4y - 96= 0

y² + 12y - 8y - 96= 0

y (y + 12) - 8 (y + 12) = 0

(y + 12)(y - 8) = 0

Either y = -12 or y = 8.

Since y represents the breadth of a rectangle, it cannot be negative.

Thus, the breadth of rectangular photo frame is 8 cm.

Compute the length as follows:

x = 23 - y

  = 23 - 8

  = 15

Thus, the length of rectangular photo frame is 15 cm.