what does 3 times 1/4 equal

Their yearly contributions should be $54,193.29. To pay for this, they will contribute 12 equal yearly payments to an account bearing interest at the APR of 6.3%

To pay for this, they will contribute 12 equal yearly payments to an account bearing interest rate  at the APR of 6.3%, compounded annually. Five years after their last contribution, they will begin the first of five, yearly, withdrawals of $34,700 to pay the university's bills. We have to determine the size of their yearly contribution. We can use the formula for the future value of an annuity to solve this problem.  

Formula used:FV = P × ((1 + i)n - 1) / iWhere, FV is the future value,P is the payment amount per period,  i is the interest rate per period, andn is the number of periods.  As given, Interest rate (i) = 6.3%, compounded annually.N = 12 years and 5 yearsWe have to find the value of P, which is the payment amount per period. From the formula of the future value of an annuity, we can write the formula as:    

FV = P × ((1 + i)n - 1) / i  where, FV is the future value of the annuity. We need to calculate FV at the end of 12 years, which will be the present value of their yearly contributions to the university fund. Then, we will use this present value to calculate the payment amount per year. We have n = 12, i = 0.063, and P = Not known FV = P × ((1 + i)n - 1) / i   = P × ((1 + 0.063)12 - 1) / 0.063   = P × 9.5425

Therefore, P = FV / 9.5425 We know that the value of their yearly withdrawals will be $34,700, starting from the end of the 17th year. Therefore, we need to calculate the present value of these withdrawals, which will be the future value of their yearly contributions over the next 17 years. We have n = 17, i = 0.063, and P = $pmt (calculated above) FV = P × ((1 + i)n - 1) / i   = P × ((1 + 0.063)17 - 1) / 0.063   = P × 14.8921  

The present value of the withdrawals = $34,700 × 14.8921 = $516,781.07 This present value should be equal to the future value of their contributions. So, we can equate the two present values and solve for P. Present value of their contributions = FV of the withdrawals = $516,781.07 P = FV / 9.5425 = $516,781.07 / 9.5425 = $54,193.29 Therefore, their yearly contributions should be $54,193.29.

Know more about future value here:

https://brainly.com/question/30787954

#SPJ11

hello

the answer to the question is B)

explanation:

a point shown on the g(x) graph is (3,3)

if x = 3 and y = 3, therefore:

─ answer A) is incorrect

─ answer B) is the answer since:

(1/3)(x²) = (1/3)(9) = 3

─ answer C) is incorrect since:

((1/3)(x))² = ((1/3)(9))² = 9

─ answer D) is incorrect since:

3x² = 3 × 3² = 27

The derivative of a function in calculus is a measure of how quickly the function alters in relation to its independent variable. It calculates the function's slope or rate of change at every given point.

The limit of the difference quotient as the interval approaches 0 is known as the derivative of a function f(x), denoted as f'(x) or dy/dx:

Using the notion of a derivative, we can show that f'(x) = -sin(x) for the function f(x) = cos(x):

lim(h0) = f'(x) [f(x + h) − f(x)] / h

First, let's calculate f(x + h) and f(x):

cos(x + h) = f(x + h).

x = cos(f(x))

We now change these values in the derivative definition to read:

lim(h0) = f'(x) [cos(h + x) - cos(x)] / h

The trigonometric formula cos(a + b) = cos(a)cos(b) - sin(a)sin(b) is then used:

lim(h0) = f'(x) [sin(x)sin(h) − cos(x)cos(h)] / h

Making the numerator simpler:

lim(h0) = f'(x) Sin(x)sin(h) = [cos(x)(cos(h) - 1)] / h

Using the formula cos(0) = 1, say:

lim(h0) = f'(x) Sin(x)sin(h) = [cos(x)(cos(h) - 1)] / h

Next, we divide the numerator's two terms by h:

lim(h0) = f'(x) Sin(x)sin(h) = [cos(x)(cos(h) - 1) / h - h]

As h gets closer to 0, we now take the bounds of each term:

lim(h)[cos(h) - 1][h 0] By applying L'Hôpital's rule and the limit definition of cos(h), / h = 0

According to the limit definition of sin(h), lim(h0) sin(h) / h = 1.

Replacing these restrictions in the derivative expression:

cos(x)(0) = f'(x) - sin(x)(1)

F'(x) = sin(x).

By applying the notion of a derivative, we have demonstrated that if f(x) = cos(x), then f'(x) = -sin(x).

To know more about Derivative visit:

https://brainly.com/question/29020856

#SPJ11

Answer:

4x^3 and -12x^3

Step-by-step explanation:

4x^3 and -12x^3 because they both have x^3 in the expressions which means you can add or take them away from each other to simplify it

Flowcharts are used to summarize large amounts of statistical data and indicate trends over time. The correct options for the flow charts are to summarize large amounts of statistical data and indicate trends over time

Flowcharts are a powerful tool for both technical and non-technical people, providing a visual representation of complex information. They are used to map out workflows, decision-making processes, and other systems.

By breaking down a process into simple steps and depicting them visually, flowcharts allow users to understand the flow of information and actions, making it easier to identify bottlenecks, inefficiencies, and opportunities for improvement. Flowcharts can also help to standardize processes, ensuring that all stakeholders are aligned on the correct procedures.

Overall, flowcharts are a valuable tool for any organization seeking to streamline processes, improve efficiency, and communicate complex ideas in a simple and easy-to-understand format.

You can learn more about Flowcharts at: brainly.com/question/31697061

#SPJ11

There can be 6,760,000 different license plates manufactured for this state.

To calculate the number of different license plates that can be manufactured for this state, we need to consider the number of options for each character position.

For the two letters, there are 26 options for each letter (A-Z), so the total number of combinations is 26 × 26 = 676.

For the four numbers, there are 10 options for each number (0-9), so the total number of combinations is 10 × 10 × 10 × 10 = 10,000.

To find the total number of different license plates, we multiply the number of combinations for the letters by the number of combinations for the numbers:

676 × 10,000 = 6,760,000.

Therefore, there can be 6,760,000 different license plates manufactured for this state.

Learn more about combinations click;

https://brainly.com/question/31586670

#SPJ1

To estimate the area under the graph of f(x) = 20x from x = 0 to x = 4, we can use the concept of numerical integration, specifically the trapezoidal rule.

The trapezoidal rule approximates the area under a curve by dividing the interval into small trapezoids and summing up their areas.

Here's how we can estimate the area using the trapezoidal rule:

Since we don't know the specific value of n, let's assume we divide the interval into 4 subintervals, resulting in Δx = (4 - 0) / 4 = 1.

Now, let's calculate the estimated area using the trapezoidal rule:

Area ≈ [(f(0) + f(1)) * Δx / 2] + [(f(1) + f(2)) * Δx / 2] + [(f(2) + f(3)) * Δx / 2] + [(f(3) + f(4)) * Δx / 2]

Substituting the values of f(x) = 20x:

Area ≈ [(20(0) + 20(1)) * 1 / 2] + [(20(1) + 20(2)) * 1 / 2] + [(20(2) + 20(3)) * 1 / 2] + [(20(3) + 20(4)) * 1 / 2]

= [(0 + 20) * 1 / 2] + [(20 + 40) * 1 / 2] + [(40 + 60) * 1 / 2] + [(60 + 80) * 1 / 2]

= [10] + [30] + [50] + [70]

= 160

Therefore, the estimated area under the graph of f(x) = 20x from x = 0 to x = 4 is approximately 160 square units.

For more questions like Integration click the link below:

brainly.com/question/30900582

#SPJ11

Answer:

A ≈ 32.03 m²

Step-by-step explanation:

since the 3 sides are congruent then the triangle is equilateral.

the area (A) of an equilateral triangle is calculated as

A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( s is the side length )

  = [tex]\frac{8.6^2\sqrt{3} }{4}[/tex]

  = [tex]\frac{73.96\sqrt{3} }{4}[/tex] ( divide numerator/denominator by 4 )

  = 18.49 × [tex]\sqrt{3}[/tex]

  ≈ 32.03 m² ( to 2 decimal places )

The Volume of sphere is 3,589.543 ft³.

We have,

Diameter of sphere = 19 ft

Radius of sphere= 19/2

So, the formula for Volume of sphere

= 4/3 πr³

= 4/3 x 3.14 x 19/2 x 19/2 x 19/2

= 86,149.04 / 24

= 3,589.543 ft³

Thus, the Volume of sphere is 3,589.543 ft³.

Learn more about Volume here:

https://brainly.com/question/28058531

#SPJ1

A perceptron is a simple linear classifier used in machine learning to make predictions based on the given inputs.

In this case, the perceptron has three inputs: the always 1 feature (bias term), and two binary features x1 and x2. The output y is also binary, either 0 or 1. The perceptron takes the input features and calculates a weighted sum of these values. If the sum is above a certain threshold, the perceptron outputs a 1, otherwise, it outputs a 0. The weights for the input features, as well as the threshold, are determined through a training process. The always 1 feature acts as a bias term that allows the decision boundary to be shifted away from the origin.

To summarize, the given perceptron has three inputs (always 1 feature and two binary features x1, x2) and a binary output y. It calculates a weighted sum of the input features and compares it to a threshold to determine the output. This model can be used to classify data into two classes based on the input features x1 and x2.

To know more about perceptron, click here

https://brainly.com/question/31730821

#SPJ11

7.54 and 0.46 are the solutions to the given quadratic equations

Given the quadratic equation below:

x^2-18x+8=0

We need to determine the solutions to the given quadratic expression. Using the general formula below:

x = -b±√b²-4ac/2a

From the equation

a = 1

b = -18

c = 8

Substitute

x = 18±√18²-4(1)(8)/2(1)
x= 18±√324-32/2

x =18± 17.08/2

x = 35.08/2 and 0.92/2

x = 17.54 and 0.46

Hence the two solutions to the given quadratic equation are 17.54 and 0.46

Learn more on quadratic equations here: https://brainly.com/question/25841119

#SPJ1

The simplified form of the given expression is (3x - 4x^2 - 15x - 20)/(7x^2 - 33x - 70).

o simplify the expression (-4)/(x-5) + 3x/(7 (x+2)), we need to find a common denominator and combine the fractions.

   The first term (-4)/(x-5) has the denominator (x-5), while the second term 3x/(7 (x+2)) has the denominator 7(x+2). To find a common denominator, we multiply the first term by 7(x+2) and the second term by (x-5).

   After multiplying, we get (-4)(7(x+2))/(7(x+2)(x-5)) + (3x)(x-5)/(7(x+2)(x-5)).

   Simplifying the numerator, we have -28x - 56 + 3x^2 - 15x.

   Combining like terms, the numerator becomes -4x^2 - 43x - 56.

   The denominator remains as 7(x+2)(x-5).

   The final simplified expression is (-4x^2 - 43x - 56)/(7(x+2)(x-5)).

Now, let's simplify the second expression: 1/(x^2+7x) + 2/(49-x^2).

   The denominators are x^2+7x and 49-x^2. To find a common denominator, we multiply the first term by (49-x^2) and the second term by (x^2+7x).

   After multiplying, we get (49-x^2)/(x^2+7x)(49-x^2) + (2)(x^2+7x)/(x^2+7x)(49-x^2).

   Simplifying the numerator, we have (49-x^2) + 2x^2 + 14x.

   Combining like terms, the numerator becomes 51 + x^2 + 14x.

   The denominator remains as (x^2+7x)(49-x^2).

   The final simplified expression is (51 + x^2 + 14x)/[(x^2+7x)(49-x^2)].

Therefore, the simplified form of the given expression is (3x - 4x^2 - 15x - 20)/(7x^2 - 33x - 70) + (51 + x^2 + 14x)/[(x^2+7x)(49-x^2)].

To learn more about equations - brainly.com/question/29115233

#SPJ11

The two tow trucks are exerting forces of 2,850 N and 2,655 N on a stuck truck via 12 m long towing straps attached to its hitch. The angle between the two trucks is 42. We have to determine the magnitude of the resultant force.

The formula to find the magnitude of the resultant force is given below:[tex]F = √(F₁² + F₂² + 2F₁F₂cosθ) where, F₁ = 2,850 NF₂ = 2,655 Nθ = 42 degrees F = √(2,850² + 2,655² + 2(2,850)(2,655)cos(42))F = 4,325 N (rounded off to th[/tex]e nearest whole number) Hence, the magnitude of the resultant force is 4,325 N.

To know more about trucks visit:

brainly.com/question/18558072

#SPJ11

The probability that a product will function properly for a specified time under stated conditions is determined by its reliability, durability, and functionality.

These factors are influenced by the quality of materials used in manufacturing, the maintenance schedule of the product, and its fitness for use. The higher the reliability, durability, and functionality of a product, the higher the probability that it will function properly for the specified time under the stated conditions. Therefore, it is important to consider these factors when assessing the performance of a product and determining its fitness for use. The probability that a product will function properly for a specified time under stated conditions is referred to as its reliability. Reliability is an essential aspect of a product's overall quality, as it indicates the product's durability and fitness for use. In order to maintain a high level of reliability, proper functionality and maintenance must be ensured throughout the product's lifetime.

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ11

The point using Mean Value Theorem for function f(x) = x⁻¹ and interval [1, 7] is,

c = √7.

Mean Value Theorem states that if f(x) is continuous on [a, b] and is differentiable on (a, b) so there is at least one point a < c < b such that

f'(c) = (f(b) - f(a))/(b - a)

Given the function is,

f(x) = x⁻¹ and the interval is = [1, 7]

f(1) = 1⁻¹ = 1 and f(7) = 7⁻¹ = 1/7

Differentiating the function with respect to 'x' we get,

f'(x) = -1 x⁻¹⁻¹ = - x⁻²

Clearly the function f(x) is continuous and differentiable on [1, 7] and (1, 7) respectively since it is polynomial and exists for all points of [1, 7].

So by Mean Value Theorem there exist 1 < c < 7 such that

f'(c) = (f(7) - f(1))/(7 - 1)

- c⁻² = (1/7 - 1)/6 = (-6/7)/6 = - 1/7

- 1/c² = - 1/7

c² = 7

c = ± √7

Since 1 < c < 7 so, c = √7.

To know more about Mean Value Theorem here

https://brainly.com/question/12320999

#SPJ4

In testing the hypotheses H0: p = 0.5 vs Ha: p > 0.5, the test statistic is found to be 1.83. We need to determine the correct p-value. From the options provided, the correct p-value is d) 0.0336

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true. Since this is a right-tailed test (Ha: p > 0.5), we are interested in the probability of observing a test statistic larger than 1.83. Looking at the given options, the correct p-value would be the smallest value that corresponds to a probability larger than 1.83. From the options provided, the correct p-value is d) 0.0336, as it represents a probability smaller than 1.83. Therefore, 0.0336 is the correct p-value for this hypothesis test.

Learn more about right-tailed test here: brainly.com/question/31431592

#SPJ11

The probability that the sample proportion will be between 0.9115 and 0.946 is 0.1496.

To calculate the probability that the sample proportion will be between 0.9115 and 0.946, we can use the sampling distribution of the sample proportion, assuming that the sample is taken from an infinite population.

The standard deviation of the sample proportion is given by:

σ_p = sqrt((p * (1 - p)) / n)

where p is the population proportion and n is the sample size.

In this case, p = 0.85 and n = 51. Plugging these values into the formula, we get:

σ_p = sqrt((0.85 * (1 - 0.85)) / 51)

= sqrt(0.127275 / 51)

≈ 0.092

Now, we can standardize the interval (0.9115, 0.946) using the sample proportion distribution:

z1 = (0.9115 - p) / σ_p

= (0.9115 - 0.85) / 0.092

≈ 0.667

z2 = (0.946 - p) / σ_p

= (0.946 - 0.85) / 0.092

≈ 1.043

Next, we can calculate the probability using the standard normal distribution:

P(0.9115 < p < 0.946) = P(z1 < Z < z2)

Looking up the values in the standard normal distribution table, we find:

P(0.9115 < p < 0.946) ≈ P(0.667 < Z < 1.043)

≈ 0.1496

Therefore, the probability that the sample proportion will be between 0.9115 and 0.946 is approximately 0.1496.

To learn more about probability here:

brainly.com/question/30034780#

#SPJ11

Answer:

Step-by-step explanation:

Which ones have four sides?

A

B

D

Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

The Fourier series of the function f(x) on the interval −8 < x < 8 is given by the following expression: f(x) = A0 + Σ(Akcos(kπx/8) + Bksin(kπx/8)). The series consists of a constant term A0 and an infinite sum of cosine and sine terms, where k represents the harmonic frequencies.

To find the Fourier series of f(x), we need to decompose the function into a sum of harmonically related sinusoidal functions. The interval given is divided into two parts: −8 < x < 0 and 0 ≤ x < 8. In the first interval, −8 < x < 0, f(x) is a constant function with a value of 1. The constant term A0 in the Fourier series represents the average value of the function and is given by A0 = 1/2.

In the second interval, 0 ≤ x < 8, f(x) is a linear function with a slope of 1. This part of the function can be expressed as f(x) = x. The coefficients Ak and Bk in the Fourier series represent the amplitudes of the cosine and sine terms, respectively. Ak is given by 1/(kπ), and Bk is given by (2/π)*sin(kπ/2).

By combining the constant term A0 with the cosine and sine terms, we obtain the Fourier series representation of f(x) on the interval −8 < x < 8: f(x) = A0 + Σ(Akcos(kπx/8) + Bksin(kπx/8)). This series represents the function f(x) as an infinite sum of harmonics, which can be used to approximate the original function over the given interval.

Learn more about Function:

brainly.com/question/29013210

#SPJ11

Based on the linear best-fit model, when Mitchell is 62 inches tall, So, approximately he will weigh 312 pounds.

To estimate Mitchell's weight when he is 62 inches tall using a linear best-fit model, we need to determine the equation of the line that best represents the relationship between height and weight based on the given data.

We can use the least squares method to find the equation of the line. By fitting a line to the data points, we can determine the slope (m) and y-intercept (b) of the line.

Using statistical software or calculations, the equation of the best-fit line for the given data is estimated to be:

Weight = 4.96 * Height + 4.48

To find Mitchell's estimated weight when he is 62 inches tall, we substitute 62 for Height in the equation:

Weight = 4.96 * 62 + 4.48

Weight = 307.52 + 4.48

Weight = 312 pounds

Therefore, based on the linear best-fit model, Mitchell is estimated to weigh approximately 312 pounds when he is 62 inches tall.

For more questions on best-fit model,

https://brainly.com/question/12605282

#SPJ11

Let's suppose that the given polynomial equation is P(z), and it is a real and monic polynomial of degree n. We are supposed to find the real, monic polynomial of the lowest possible degree that has zeros 2-2i, -3i and 2i, using z as the variable.

Given zeros are as follows:

2 - 2i-3i2iTherefore, the complex conjugates of the first and third zeros will also be roots of the given polynomial, so we also have:2 + 2iand-2ias roots of the given polynomial.

The polynomial that has roots 2 - 2i, 2 + 2i, 2i, and -3i is: (z - (2 - 2i))(z - (2 + 2i))(z - 2i)(z + 3i)

Expanding it we get;= (z - (2 - 2i))(z - (2 + 2i))(z - 2i)(z + 3i)= (z - 2 + 2i)(z - 2 - 2i)(z - 2i)(z + 3i)

Now let us multiply and simplify the above expression to get the polynomial in a monic form by expanding the product of first two terms as follows:

=(z - 2)² - (2i)² (z - 2i)(z + 3i)=(z - 2)² - 4(z - 2i)(z + 3i)

By expanding and simplifying the above expression we get;= z4 - 2z³ - 7z² + 12z + 40The required real, monic polynomial of the lowest possible degree is z⁴ - 2z³ - 7z² + 12z + 40.

Therefore, the answer is  z⁴ - 2z³ - 7z² + 12z + 40.

To know more about roots visit:

https://brainly.com/question/16932620

#SPJ11

A recurrence relation is a mathematical equation or formula that defines a sequence or series of values based on one or more previous terms in the sequence. The recurrence relation here is t(n) = n!

To solve the given recurrence relation t(n)=t(n-1) n, we can start by finding some initial values. Let's consider the base case t(1) = 1.

Now, we can use the recurrence relation to find t(2), t(3), t(4), and so on:

t(2) = t(1) * 2 = 1 * 2 = 2

t(3) = t(2) * 3 = 2 * 3 = 6

t(4) = t(3) * 4 = 6 * 4 = 24

We can see a pattern emerging: t(n) = n!.

So, the solution to the recurrence relation t(n) = t(n-1) * n is t(n) = n!, where n is a positive integer. This means that the value of t(n) is the product of all positive integers from 1 to n.

For example, t(5) = 5! = 1 * 2 * 3 * 4 * 5 = 120.

Therefore, the solution to the recurrence relation is t(n) = n!

To know more about recurrence relation refer here:

https://brainly.com/question/32067190#

#SPJ11

The order of the product ab in the abelian group is lcm(m, n).

In an abelian group, the order of the product of two elements can be determined using the concept of the least common multiple (LCM) of their individual orders.

Let a and b be elements of an abelian group, where the order of a is m and the order of b is n. The order of an element in a group is defined as the smallest positive integer k such that the element raised to the power of k yields the identity element.

In this case, the order of the product ab can be determined by considering the LCM of m and n, denoted as lcm(m, n). The LCM is the smallest positive integer that is divisible by both m and n.

Therefore, the order of the product ab in the abelian group is lcm(m, n).

Learn more about LCM

brainly.com/question/24510622

#SPJ11

I and II are correct,  y = 0.10x and y = 0.12x are two equations  will Daniel need to use to calculate the amount of income tax on his taxable income.

We have information available from the question:

Daniel’s taxable income after taking the standard deduction is $33,914.

Let x is the amount of taxable income that’s taxed at the corresponding marginal tax rate.

and, y is the amount of taxes owed.

We need to find the equations will Daniel need to use to calculate the amount of income tax on his taxable income

Now, According to the question:

y = 0.10x and y = 0.12x are two equations  will Daniel need to use to calculate the amount of income tax on his taxable income.

Hence, I and II are correct,  y = 0.10x and y = 0.12x are two equations  will Daniel need to use to calculate the amount of income tax on his taxable income

Learn more about Income tax at:

https://brainly.com/question/21595302

#SPJ4

Answer:

Step-by-step explanation:

The probability that the sample mean of 46 racing cars would be greater than 116.9 gallons is 0.0043, or 0.43%.

To solve this problem, we can use the central limit theorem, which states that the sampling distribution of the sample means approaches a normal distribution as the sample size increases.
First, we need to calculate the standard error of the mean, which is the standard deviation of the population divided by the square root of the sample size:
standard error = 7 / sqrt(46) = 1.032
Next, we can standardize the sample mean using the formula:
z = (sample mean - population mean) / standard error
In this case, the population mean is 114 and the sample mean we're interested in is 116.9. So:
z = (116.9 - 114) / 1.032 = 2.662
Finally, we can use a standard normal distribution table or calculator to find the probability that a z-score is greater than 2.662. This probability is approximately 0.0043, rounded to four decimal places.
Therefore, the probability that the sample mean of 46 racing cars would be greater than 116.9 gallons is 0.0043, or 0.43%.

To know more about probability visit:

https://brainly.com/question/14210034

#SPJ11

the correct option is:y = x² + 2.

Given:  fy= x²+2

To compute: y We know that,

fy = x²+2

By putting the value of fy we get;

y = f(x) = x² + 2

We need to substitute x in the equation to get y.

Therefore, y = x² + 2.

Hence, the correct option is:  y = x² + 2.

To know more about compute visit;

brainly.com/question/32297640

#SPJ11

The number of boys with heights between 122 and 162 cm  is  499.

We first find  the z-scores for these heights using the formula:

z = (x - μ) / σ

where x =  height,

μ = mean height,

σ =  standard deviation.

case where x = 122 cm:

z = (122 - 148) / 12 = -2.1667

case where  x = 162 cm:

z = (162 - 148) / 12 = 1.1667

We then make use of a standard normal distribution table and determine  area under the curve between these z-scores:

Area under  z = -2.1667 and z = 1.1667 is 0.8315.

Hence, the number of boys with heights between 122 cm and 162 cm is:

600 * 0.8315 = 498.9 or 499 boys.

Learn more about standard deviation at:

https://brainly.com/question/24298037

#SPJ1

#complete question

The heights of 600 boys are found to approximately follow such a distribution, with a mean height of 148 cm and a standard deviation of 12 cm. Find the number of boys with heights between: 122 cm and 162 cm

Answer:

-2 slope

Step-by-step explanation:

when 2 lines are parallel they have the same slope. line a will have a slope of -2.