The equation 7(2W + 3) = 14W + 20 has no solutions. Change one term in the original equation to create a new equation with infinitely many solutions.​

As per unitary method, it will take 9 years for the man to be three times as old as his son.

The unitary method is a mathematical technique that involves finding the value of a single unit, and then using that unit to find the value of a larger quantity.

First, let's define our variables:

Let the man's age be M

Let the son's age be S

According to the problem, we know that:

M = 42

S = 12

We want to find out how many years it will take for the man's age (M) to be three times his son's age (S). Let's call this number of years "y".

Using the unitary method, we can set up the following equation:

M + y = 3(S + y)

Here's what this equation means:

M + y represents the man's age after y years

S + y represents the son's age after y years

3(S + y) represents three times the son's age after y years

We can simplify this equation by distributing the 3:

M + y = 3S + 3y

Next, we can isolate the variable y (which represents the number of years we're trying to find) by moving all the other terms to the opposite side of the equation:

y - 3y = 3S - M

Simplifying this, we get:

-2y = 3S - M

Finally, we can solve for y by dividing both sides by -2:

y = (M - 3S) / -2

Plugging in the values we know, we get:

y = (42 - 3(12)) / -2

y = 9

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Complete Question:

A man's age is 42 years and his son's age is 12 years. After how many years will the man be thrice as old as his son?

The length of AC is √(4x⁴+ 16x³ + 76x² - 16x + 64). In order to find the unit length of AC you have to get more measurement and solve for x in the equation.

We can use the fact that the diagonal of a rectangle is the square root of the sum of the squares of its sides. If the sides of the rectangle are "a" and "b", then the length of the diagonal is given by: √(a² + b²)

Let's call the length of AC "d". Then, from the information given, we have: d = √((2x² + 4x - 6)² + (x² - x + 8)²)

Expanding and simplifying the squares, we get:

d = √(4x⁴ + 16x³ + 12x² + 64x² - 16x + 64)

d = √(4x⁴+ 16x³ + 76x² - 16x + 64)

So, the length of AC is √(4x⁴ + 16x³ + 76x² - 16x + 64).

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Answer:

1. not a function

Since x=5 produces y=9 and y=0, it can't be a function

2. it is a function because there is one value of y for every value of x

3. A circle is not a function. because it doesn't pass the vertical line test

4. I think is d but not sure has been a while since I have done these questions so sorry if I am wrong :)

Step-by-step explanation:

have a nice day and good luck

The volume of the sphere with a radius of 8.9 m is given as follows:

V = 2,951.5 m³.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

The radius for this problem has the measure given as follows:

r = 8.9m.

Hence, considering that π is rounded to 3.14, the volume of the sphere is obtained as follows:

V = 4 x 3.14 x (8.9)³ x 1/3

V = 2,951.5 m³.

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Answer:

68 people choose meat over pork

Step-by-step explanation:

subtract 17 from 85

Using the normal curve to estimate the following percentages. The answer that is closes to being correct is 39.4%. So, the correct answer is C.

Since the distribution is approximately normal, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages.

a. 10.6%: This corresponds to the area under the curve that is more than 2 standard deviations below the mean. Using the rule, we know that about 2.5% of the area under the curve is more than 2 standard deviations below the mean. So 10.6% is too high. The answer is not a.

b. 89.4%: This corresponds to the area under the curve that is less than one standard deviation above the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 89.4% is too high. The answer is not b.

c. 39.4%: This corresponds to the area under the curve that is within one standard deviation of the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 39.4% is the closest to being correct. The answer is c.

d. 78.8%: This corresponds to the area under the curve that is less than two standard deviations above the mean. Using the rule, we know that about 95% of the area under the curve is within two standard deviations of the mean. So 78.8% is too high. The answer is not d.

e. 68.27%: This corresponds to the area under the curve that is within one standard deviation of the mean. This is the same as c. So e is not the correct answer.

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Answer:

It would equal 2/5. First flip the 5/6 so then it would be 6/5. Then the 3 and 6 can cross cancel so it would equal to 2 in the numerator.

The measure of angle ACD for the given circle is 67.5 degree.

A triangle is inside a circle when a circle encircles it, and each vertex of the triangle touches the circle.

When a circle encircles a triangle, the triangle lies outside the circle and the circle makes one point contact with each of the triangle's sides. The triangle's sides are perpendicular to the circle.

Given that,

The inscribed angle CDA = 1/2(arc AC).

arc AC = 90 degree.

Then:

∠ CDA = 90 / 2

∠ CDA = 45

Triangle ACD is isosceles, so:

∠ ACD + ∠ CAD + ∠ CDA = 180 degree

Here, ∠ ACD = ∠ CAD

∠ ACD + ∠ACD + ∠ CDA = 180 degree

∠ ACD = 180-45 / 2

∠ ACD   = 67.5 degree

Hence, the measure of angle ACD for the given circle is 67.5 degree.

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The correct question is:

Points A, B, C, and D lie on circle M. Line segment BD is a diameter.

Triangle A C D is inscribed within circle M. Point B is on the circle between points C and B. A line is drawn to connect points D and B. Lines are drawn from points C and A to point M to form a right triangle. Arcs C D and A D are congruent.

What is the measure of angle ACD?

45.0°

67.5°

112.5°

135.0°

After 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

Let's start by defining some variables:

We can then use this information to set up two equations that represent how much money each person has saved:

J = 20j + 8

M = 18m + 26

We want to know when J and M are equal, so we can set these equations equal to each other:

20j + 8 = 18m + 26

We can simplify this equation by subtracting 8 from both sides:

20j = 18m + 18

Then, we can divide both sides by 2 to simplify the equation further:

10j = 9m + 9

We want to find the smallest values of j and m that make this equation true. We can start by trying j = 1 and then incrementing j until we find a value that makes the right-hand side of the equation (9m + 9) divisible by 10. We can then solve for m and check that the left-hand side of the equation (10j) is equal to the same value.

If we try j = 1, we get:

10(1) = 9m + 9

Simplifying this equation gives us:

m = 1

So, if Jeremy tutors his cousin for 1 week and Mary babysits her sister for 1 week, they will both have the same amount of money saved. We can check this by plugging j = 1 and m = 1 into the original equations for J and M:

J = 20j + 8 = 20(1) + 8 = 28

M = 18m + 26 = 18(1) + 26 = 44

So, after 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

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Answer: As the ratio of newts and toads, 3:4

Step-by-step explanation:

The equivalent solution to the equation is (-1, -2)

Given the simultaneous equation below:

Y=2x+4

y=-x+1

Since both equations are y expressions, we will equate then to have;

2x+ 4 = -x + 1

2x + x = 1 - 4

3x = -3

x = -1

For the value of y;

y = -x + 1

y = -1-1

y =-2

Hence the solution to the system of equation is (-1, -2)

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The equation of the quadratic function is x² + x - 6

Note that functions are equations, laws or expressions showing the relationship between two variables.

These variables are;

From the information given, we have that;

x = 2 and  = -3 are the roots

Then,

(x -2)(x + 3)

expand the bracket, we get;

x² + 3x - 2x - 6

collect the like terms, we have;

x² + x - 6

Hence, the equation is x² + x - 6 = 0

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The probability of Shawna bowling a perfect game is 7.23%.

Assuming that Shawna's chance of getting a strike is independent on each roll (which may not be entirely accurate in real life), the probability of her getting a strike on any given roll is 0.75.

To calculate the probability of Shawna bowling a perfect game (i.e., getting a strike on all 12 rolls), we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, the probability of Shawna getting a strike on the first roll is 0.75. The probability of her getting a strike on the second roll, assuming she got a strike on the first roll, is also 0.75. Similarly, the probability of her getting a strike on the third roll, assuming she got strikes on the first two rolls, is also 0.75. We can continue this pattern for all 12 rolls.

Therefore, the probability of Shawna bowling a perfect game is:

0.75 x 0.75 x 0.75 x ... (12 times)

which is approximately equal to 0.0723, or about 7.23%.

Using a computer to randomly generate 12 numbers from 1 to 4 and treating 1, 2, or 3 as a strike is a reasonable way to simulate the situation and estimate the probability of Shawna bowling a perfect game. By repeating this process many times, we can get a better idea of the distribution of possible outcomes and the likelihood of different results.

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The value of x in the coordinates (-12,1) and (x,7), having a slope of 1/8 is 36.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given that;

Point 1 (-12,1)

Point 2 (x,7)

Slope m = 1/8

Plug the values into the slope formula and solve for x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

1/8 = ( 7 - 1 )/( x - (-12) )

1/8 = ( 6 )/( x + 12)

Cross multiply

( x + 12) = 6 × 8

x + 12 = 48

x + 12 - 12 = 48 - 12

x = 36

Therefore, the value of x is 36.

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Answer: 8.8 moles

Step-by-step explanation:

Fun Fun! Chemistry :)

So, 5.3 x [tex]10^{24}[/tex] atoms can be converted to moles by dividing by Avogadros number, (6.02 x 10^23). This is because Avogadros number of atoms form one mole.

So the answer is about 8.8 moles of Kr

Answer: 54

Step-by-step explanation:

The expressions that show the number of students for each activity are;

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.

A set is a mathematical model for a collection of various things.

We are given;

Total number of students in the middle school = z

A) From the given table, we can deduce that;

B; Now, the expression to show the students that like either drama or dance is;

(1/7)z + 26 + (1/7)z + 22

>> (2/7)z + 48

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A middle school with z students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

Plan B will save you money for a 1-day rental if you drive more than 166.67 miles.

To determine the range of miles for which Plan B will save money over Plan A for a 1-day rental, we need to set up an equation that compares the total cost of each plan.

For Plan A, the cost is given by:

Cost(A) = 30 + 0.12x

where x is the number of miles driven.

For Plan B, the cost is given by:

Cost(B) = 50

since there is no additional charge for mileage.

To determine the range of miles for which Plan B is cheaper than Plan A, we need to find the value of x for which:

Cost(B) < Cost(A)

Substituting the expressions for the costs of each plan, we get:

50 < 30 + 0.12x

Simplifying this inequality, we get:

0.12x > 20

x > 20 / 0.12

x > 166.67

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If the height of seven and three fourths yards and a base of 20 yards, then the area of the right triangle is 77.5 square yards.

To calculate the area of a right triangle, we can use the formula:

Area = (base * height) / 2

where the base is one of the sides of the triangle, and the height is the perpendicular distance from that side to the opposite vertex.

In this case, the height of the right triangle is 7 and 3/4 yards, and the base is 20 yards. Plugging these values into the formula, we get:

Area = (20 * 7.75) / 2 = 155 / 2 = 77.5 square yards

In summary, to calculate the area of a right triangle, we can use the formula that relates the base and height to the area. In this case, we needed to use the given values of the height and base of the right triangle to compute the area in square yards.

The resulting area represents the amount of surface inside the triangle and is useful in many applications, such as geometry, physics, and engineering.

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The correct option regarding when Chicago first exceeded Phoenix in the percentage of calls answers within 10 seconds is given as follows:

C. Between September and October.

The output of the graph represents the percentage of calls answered within 10 seconds.

Chicago and Phoenix are represented as follows:

At the beginning of September, the red line was above the green line, but at the beginning of October, the green line was above the red line, hence the correct option is given by option C.

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Answer:

why and why not why .I have no idea wish I did

Probability 8 2/ 7 3=1.123 that the team lost a game if it played at lincoln park.

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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Answer: Is only definable if you can show the table but according to a valid explanation it would be most likely 41

Step-by-step explanation:

Lets say Bob has 17 strawberry, 19 Cola, and 4 blueberry, we can infer there is an equal amount of gumballs of each flavor in the machine; Before bob bought any gumballs there were 180 and if there were only 3 flavors we would divide 180 by 3 and get 60. That means each flavor has 60 of its own flavor and if we take 19 from the 60 cola flavored we can get 41.

Answer:

AC = 16 cm

Step-by-step explanation:

given a tangent and a secant from an external point to the circle, then

the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant, that is

AB × AC = AD²

4x = 8² = 64 ( divide both sides by 4 )

x = AC = 16 cm

Answer:

16 cm

Step-by-step explanation:

tan/sec Theorem

a² = b(b+c)

8² = 4(4+c)

64 = 16 + 4c

48 = 4c

12 = c

12 + 4 = 16 cm

The number of many different outfits Sophia has to choose from should be 16.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given: Sophia is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.

She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.

So here the number of distinct outfits should be like

= 2 × 4 × 2

= 16

Hence, the number of many different outfits Sophia has to choose from should be 16.

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Answer:16

Step-by-step explanation:Total outcomes

=

Total outcomes=

2‾

pants

×

2‾

t-shirts

×

4‾

shoes

pants

2

​

​

×

t-shirts

2

​

​

×

shoes

4

​

​

Fundamental counting principle

=

=

16

The point (7,84) represents a precise location on a graph or coordinate plane.

A coordinate is a set of values that specifies the position or location of a point in a geometric space.

The point (7,84) represents a specific location on a graph or coordinate plane. The first number, 7, represents the point's position on the x-axis, which is a horizontal line that runs left to right. The second number, 84, represents the point's position on the y-axis, which is a vertical line that runs up and down. Together, the two numbers give us a precise location for the point.

In this situation, we don't have enough context to know what the point (7,84) represents. It could be the location of a city on a map, the amount of rainfall in inches on a specific day, or the price of a stock at a particular time. However, regardless of the situation, the point (7,84) is simply a specific location in a two-dimensional space that has been identified using coordinates.

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Complete Question:

What does the point (7,84) represent in the graph?​ And define the explanation for each value.

Using the unitary method, we find that the store created approximately 37 bags with 15 random cards in each bag.

This problem can be solved using the unitary method. It is given that the

number of Anniversary cards is 163,

number of Birthday cards is 258,

number of Get Well cards is 98

and the number of Thank you cards is 47

So, the total number of cards will be equal to the sum of all these cards, that is,

163+258+98+47

= 566 cards

To create bags of 15 random cards, we have to divide the total number of cards by 15  which gives,

566/15 = 37.734

Thereby, we can say that the store created approximately 37 bags with 15 random cards in each bag.

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The initial investment cost using the equity method would be:

Investment account balance + Phillips' share of retained earnings = Initial investment cost = $54,000 + $10,400 = $64,400

Fair Value Method:

The cumulative increase in fair value over the three years would be:

$2,000 + $2,000 + $2,000 = $6,000

Therefore, the initial investment cost would be:  

$54,000 - $6,000 = $48,000

Equity Method:

By the equity method, Phillips would have recorded its share of Jones Bag's earnings each year, as well as its share of dividends received. Phillips' share of Jones Bag's earnings and dividends would be based on its 40% ownership interest.

Phillips' share of Jones Bag's earnings and dividends would be as following:

Year Earnings Dividends

20X1 $3,200 $6,000

20X2 $4,800 $4,000

20X3 $8,000 $4,000

$40,000 - $14,000 = $26,000

Phillips' share of retained earnings would be 40% of $26,000, or $10,400.

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The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.

What is equation of straight line ?

Equation of straight line can be as follows, y = mx +b

where m is a slope of line.

Given,

To find , The cost, C, in dollars for advertising on a social networking website is proportional to the number n] of clicks on the advertisement.

When a business is charged $108.50 for 310 clicks on its advertisements.

The cost, C, and number of clicks, n, are related by the equation

C = k * n, where k is the constant of proportionality.

From the given information, we know that C = $108.50 when n = 310. We can use this information to find the value of k:

$108.50 = k * 310

Solving for k:

k = $108.50 / 310

k = $0.35

So, the equation for the relationship between cost and clicks is:

C = $0.35 * n

Therefore, The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.

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