The difference in ages between a father and a son is 35. The sum is
their ages is 101. Find the ages of each man.

Part A:

This is correct because it has a set rate of 10 points per dollar.

$9 * 10 = $90

Part B:

This is correct because it has a set rate of 4 minutes per customer.

Hope this helps!

Answer:

Slope: 2/3

Step-by-step explanation:

Take the first point (2,1) as (x1, y1), and,

the second point (5,3) as (x2, y2).

Using the slope formula to calculate the slope:

m = \(\frac{y2-y1}{x2-x1}\)

= (3-1)/(5-2)

= 2/3

Hence, the slope is 2/3

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Answer:

surface area = 6a^2 = 6

hence are = 6 unit.sq

Answer:

(3.4/100)*115 = $3.91

Step-by-step explanation:

Divide by 100% and multiply by 115 (100%+15%)

Answer:

D

Step-by-step explanation:

They are similar and proportional

The firm should produce 3.5 units to maximize profit, but the maximum profit is -$300, indicating the firm is operating at a loss.

To find the units of production that maximize profit, we need to first find the profit function by subtracting the cost function from the revenue function:

Profit = Revenue - Cost = R - C = 1400x - (700 + 1200x) = 200x - 700

Now, to find the units of production that maximize profit, we need to find the value of x that maximizes the profit function. We can do this by taking the derivative of the profit function with respect to x and setting it equal to zero:

d(Profit)/dx = 200 - 0 = 0

Solving for x, we get:

x = 3.5

Therefore, the firm should produce 3.5 units to maximize its profit.

To find the maximum profit, we can substitute the value of x back into the profit function:

Profit = 200x - 700 = 200(3.5) - 700 = -300

So the maximum profit is -$300, which means the firm is operating at a loss. This suggests that the firm should re-evaluate its production costs and revenue strategies to try and reduce costs or increase revenue in order to achieve a positive profit.

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Answer:

x = 14

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Multiply -2 to both sides of the equation:

-2 * (-1/2x) = -2 * -7

x = -2 * -7

x = 14

Note that when you multiply two negative numbers, the answer will be positive.

14 is your answer for x.

~

Answer:

just flip it

Step-by-step explanation:

here to help!!

Step-by-step explanation:

by J Orloff · Cited by 3 — We have shown that a line or circle in x, y is transformed to a line or circle in u, v. This shows that inversion maps lines and circles to lines and circles

Answer:

it would be -3i and 3i  of and not half (half circle as factoring -9 would be -6 /2  =-3   = 3 sq rt f(x) -3 = x/2 where x stays 1     sqrt  of 1  * 3 -3 = 0 and here is a low line ascending curve see photo

Step-by-step explanation:

Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3) 2 = (+3) 2 = 9. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root  The 2nd root of 9, or 9 radical 2, or the square root of 9 is written as -3

Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.

The word "percent" simply refers to "per hundred," and the sign for percentage is %. By multiplying the total or whole number by 100, one percent (or 1%) is equal to one hundredth of the whole or whole. A percentage is calculated by multiplying the intended results by 100% and dividing the total number of outcomes. In a variety of contexts, percentages are often utilized. For instance, percentages are used to convey discounts in stores, bank interest rates, inflation rates, and various statistics in the media. The financial components of daily living may be understood by using percentages.

In this problem it is found that:

A total of 1260 + 650 + 180 = 2090 people were surveyed.

Of those, 1260 were completely satisfied.

Hence: P = (1260/2090) × 100%

P = 60.29%

60.29% of the people surveyed were completely satisfied with the car.

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Answer:

72 meters

Step-by-step explanation:

12 times 9 is 72

Answer:

243 m²

Step-by-step explanation:

Given the scale is 4 : 6 = 2 : 3 , then

scale of areas = 2² : 3² = 4 : 9

area of scale drawing = 12 × 9 = 108 cm²

let x be the actual area then using proportion

\(\frac{4}{108}\) = \(\frac{9}{x}\) ( cross- multiply )

4x = 972 ( divide both sides by 4 )

x = 243

Actual area = 243 m²

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Answer:

x= 105°

Step-by-step explanation:

one interior angle of a hexagon is=120°

one interior angle of an octagon is=135° 360-255= 105

The size of the angle between the two regular polygons, marked x, is: 105°.

Thus,

x° = 360 - sum of one interior angle of the regular octagon and hexagon.

One interior angle of octagon = [(8 - 2)180]/8 = 135°

One interior angle of hexagon= [(6 - 2)180]/6 = 120°

x° = 360° - 135° - 120°

x° = 105°

Therefore, the size of the angle between the two regular polygons, marked x, is: 105°.

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The total number of ways sandwiches and james makes are 1905.

Using the combination formula.

The number of ways in which 1 or 2 slices of bread is selected.

= 5C1 + 5C2

= 5 + 10

= 15

Now,

The number of ways to choose the ingredients:

= 2⁷ - 1

= 127 ways.

Number of ways sandwiches can james makes:

15 x 127 = 1905

Thus, the total number of ways sandwiches and james makes are 1905.

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Answer:

18

Step-by-step explanation:

6*3=18

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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The rate at which the distance is changing is calculated to be 14.42 miles per hour.

Consider the east direction to be denoted by x and the north direction to be denoted by y, therefore;

dx / dt = 12 mph

dy / dt = 8 mph
x is equal to 4 miles

Consider the distance between them to be s

Time taken by you to travel 4 miles = distance / speed

Time taken by you to travel 4 miles = 4/12 hour

Distance traveled by the friend in that time = speed × time

Distance traveled by the friend in that time = 8 × (4/12) = 2.67 miles

Now we use the Pythagorean theorem,

x^2 + y^2 + s^2 ...... (1)

Substitute, x = 4 miles and y = 2.67 miles

s^2 = 16 + 7.1289 = 23.1289

s = 4.81

Now differentiate equation 1 with respect to t as follows;

2x (dx/dt) + 2y (dy/dt) = 2s (ds/dt)

2(4) (12) + 2(2.67) (8) = 2 (4.81) (ds/dt)

96 + 42.72 = 9.62 (ds/dt)

138.72 = 9.62 (ds/dt)

ds/dt = 138.72/9.62 = 14.42 miles per hour

Thus the distance is changing at the rate of 14.42 miles per hour.

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Answer:

First we write y and its derivatives as power series:

y=∑n=0∞anxn⟹y′=∑n=1∞nanxn−1⟹y′′=∑n=2∞n(n−1)anxn−2

Next, plug into differential equation:

(x+2)y′′+xy′−y=0

(x+2)∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

x∑n=2∞n(n−1)anxn−2+2∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

Move constants inside of summations:

∑n=2∞x⋅n(n−1)anxn−2+∑n=2∞2⋅n(n−1)anxn−2+∑n=1∞x⋅nanxn−1−∑n=0∞anxn=0

∑n=2∞n(n−1)anxn−1+∑n=2∞2n(n−1)anxn−2+∑n=1∞nanxn−∑n=0∞anxn=0

Change limits so that the exponents for  x  are the same in each summation:

∑n=1∞(n+1)nan+1xn+∑n=0∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−∑n=0∞anxn=0

Pull out any terms from sums, so that each sum starts at same lower limit  (n=1)

∑n=1∞(n+1)nan+1xn+4a2+∑n=1∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−a0−∑n=1∞anxn=0

Combine all sums into a single sum:

4a2−a0+∑n=1∞(2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an)xn=0

Now we must set each coefficient, including constant term  =0 :

4a2−a0=0⟹4a2=a0

2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an=0

We would usually let  a0  and  a1  be arbitrary constants. Then all other constants can be expressed in terms of these two constants, giving us two linearly independent solutions. However, since  a0=4a2 , I’ll choose  a1  and  a2  as the two arbitrary constants. We can still express all other constants in terms of  a1  and/or  a2 .

an+2=−(n+1)nan+1+(n−1)an2(n+2)(n+1)

a3=−(2⋅1)a2+0a12(3⋅2)=−16a2=−13!a2

a4=−(3⋅2)a3+1a22(4⋅3)=0=04!a2

a5=−(4⋅3)a4+2a32(5⋅4)=15!a2

a6=−(5⋅4)a5+3a42(6⋅5)=−26!a2

We see a pattern emerging here:

an=(−1)(n+1)n−4n!a2

This can be proven by mathematical induction. In fact, this is true for all  n≥0 , except for  n=1 , since  a1  is an arbitrary constant independent of  a0  (and therefore independent of  a2 ).

Plugging back into original power series for  y , we get:

y=a0+a1x+a2x2+a3x3+a4x4+a5x5+⋯

y=4a2+a1x+a2x2−13!a2x3+04!a2x4+15!a2x5−⋯

y=a1x+a2(4+x2−13!x3+04!x4+15!x5−⋯)

Notice that the expression following constant  a2  is  =4+  a power series (starting at  n=2 ). However, if we had the appropriate  x -term, we would have a power series starting at  n=0 . Since the other independent solution is simply  y1=x,  then we can let  a1=c1−3c2,   a2=c2 , and we get:

y=(c1−3c2)x+c2(4+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(4−3x+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(−0−40!+0−31!x−2−42!x2+3−43!x3−4−44!x4+5−45!x5−⋯)

y=c1x+c2∑n=0∞(−1)n+1n−4n!xn

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Multiple regression analysis is applied when analyzing the relationship between one dependent variable and two or more independent variables. The goal is to determine the extent to which the independent variables predict the dependent variable.

Multiple regression analysis is a statistical technique used to explore and quantify the relationship between a dependent variable and multiple independent variables. It allows researchers to examine how changes in one or more independent variables impact the dependent variable, while controlling for the effects of other variables. By estimating the coefficients for each independent variable, the analysis provides insights into the strength, direction, and significance of their relationships with the dependent variable. This method is commonly employed in various fields, such as economics, social sciences, and business, to understand complex relationships and make predictions based on the interplay of multiple factors.

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Answer:

Huh

Step-by-step explanation:

Answer:

9711.5

Step-by-step explanation:

-8x + 44 > 60

-8x > 60 - 44

-8x > 16 / : (-8)

x < -2

-4x + 50 < 58

-4x < 58 - 50

-4x < 8 / : (-4)

x > -2

Using proportions, it is found that the parents must buy 114 yards of material in order to outfit all 24 members of the band.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the amounts needed for each member are given by:

Hence 2.25 + 2.5 = 4.75 yards of material.

For the 24 members, the total amount is:

24 x 4.75 = 114.

114 yards of material in order to outfit all 24 members of the band.

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Complete Question

The area of grandiose rectangular painting is 56 in.² the width of the painting is 7 inches what is the diagonal of the painting

Answer:

The diagonal of the rectangular painting is  \(z = 10.63 \ m\)

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image

From the question we are told that  

    The area is \(A = 56 \ in^2\)

    The width of the painting is \(w = 7 \ in\)

Generally the area of the rectangle is mathematically represented as

          \(A = l * w\)

where \(l\) the length which is mathematically evaluated as

          \(l = \frac{A}{w}\)

substituting value  

         \(l = \frac{56}{7}\)

          \(l = 8 \ in\)

According Pythagoras theorem

     \(z ^ 2 = l^2 +w^2\)

Where z is the diagonal of the rectangular painting

  Now substituting values

      \(z = \sqrt{7^2 + 8^2}\)

      \(z = 10.63 \ m\)

Answer:

The area would be 80

Step-by-step explanation:

Firstly we need the scale factor

At 2 to 5, the scale factor is 5/2 = 1 to 2.5

Mathematically, we have the area of a triangle as:

1/2 * b * h

So, if the other side is x ;

we have that :

1/2 * x * 2 = 8

2x = 16

x = 8

The bigger other side will be;

2.5 * 8 = 20

So the area of the second will be;

1/2 * 20 * 8 = 80

Answer:

110

Step-by-step explanation:

219 divided by 2 equals 109.5, so you basically just round to the nearest whole number. You should get 110, thus, your answer. Of course, you could just leave it as 109.5, but if you want it estimated, or simplified, the information above should help.

Hope this helps!

Answer:

10 secs

Hope this helped, if not, don’t hate.

The given argument is invalid. It says that if one person has more gray hair in their beard than another person, then they have a higher percentage of gray hair in their beard.

The argument is invalid because it is possible for one person to have a higher percentage of gray hair in their beard but a lower number of gray hairs in total.One possible counterexample by model is:Suppose Plato has 200 hairs in his beard and 50 of them are gray. So, 1/4 of his hairs are gray. Now, let's suppose Aristotle has 400 hairs in his beard, and 300 of them are gray. So, 3/4 of his hairs are gray. Even though Plato has fewer gray hairs than Aristotle, his percentage of gray hairs is more significant (1/4) than Aristotle's (3/4).

Therefore, the given argument is invalid since Aristotle's beard contains more gray hairs in quantity, but Plato has a higher percentage of gray hair in his beard.

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The standard deviation of the height distribution is approximately 6 inches (since 6 is half of 12), which corresponds to option (C).

The distribution of the heights of students in a large class is roughly Normal, with an average height of 68 inches, and approximately 95% of the heights are between 62 and 74 inches.

The height distribution is approximately Normal, we can use the empirical rule, which states that approximately 95% of the data falls within 2 standard deviations of the mean, to estimate the standard deviation.

The range of heights within which approximately 95% of the students fall is from 62 to 74 inches.

This range is 12 inches wide, and it corresponds to 2 standard deviations from the mean.

Thus, we have:

2 standard deviations = range of 95% of the data = 74 - 62 = 12 inches

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