When you rewrite an addition or subtraction problem using the Distributive Property, you have to ______ both values by a common factor, usually the GCF.

The values of x make the triangle a right triangle is 25

Given that

Legs = 15 and 20

For a right triangle, we have

x^2 = 15^2 + 20^2

So, we have

x^2 = 625

This gives

x = 25

In this case, the value of x would be less than 25 calculated above

In this case, the value of x would be greater than 25 calculated above

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The probability that exactly 3 of the 7 people selected at random have obtained their flu shot is approximately 0.315 or 31.5%.

This problem can be solved using the binomial distribution, which models the probability of getting a certain number of successes (in this case, people who received their flu shot) in a fixed number of trials (in this case, selecting 7 people at random) when each trial has the same probability of success (in this case, 60%).

The probability of getting exactly 3 people who received their flu shot is given by the formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the total number of trials (7), k is the number of successes (3), p is the probability of success (0.6), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Plugging in the values, we get:

P(X = 3) = (7 choose 3) * (0.6)^3 * (1-0.6)^(7-3)

= 35 * 0.216 * 0.4096

= 0.315

Therefore, the probability that exactly 3 of the 7 people selected at random have obtained their flu shot is approximately 0.315 or 31.5%.

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Answer:

Quadrant 3.

Step-by-step explanation:

Quardant 1: Postive x-coordinate and postive y-coordinate. (northeast)

Quardant 2: Negative x-coordinate and postive y-coordinate. (northwest)

Quardant 3: Negative x-coordinate and negative y-coordinate. (southwest) <=

Quardant 4: Postive x-coordinate and negative y-coordinate. (southeast)

Therefore, it is the third one

The squares may or may not fit in the classroom, depending on the dimensions

The number of cubes is given as

Cubes = 1000000

The area of a square is

Area = Length^2

In this case, the number of cubes is the area

So, we have

Length^2 = 1000000

Take the square root of both sides

Length = 1000

This means that the dimensions would be 1000 by 1000

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The height of the model is 5 inches

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

The ratio of the model to the original building is

1in : 10 feet.

converting 10feet to inches

10feet = 120inches since 1 feet is 12 inches.

Therefore the ratio will be;

1: 120

therefore if the building is 50 feet tall

50 feet = 50×12 = 600inches

the model height = 600/120 = 5 inches

therefore the height of the model is 5 inches

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Measure of angle ABC would be equal half measure arc of AB

angle ABC = 1/2 × 246

                  = 123

Answer: He was on stage for exactly 80 minutes

Step-by-step explanation: Because it can't be 72 because that would be 70% of the time just like 88.9 that's 88.9% of the time and 112.5 will be to much so the correct answer is C 80 minutes.

The points that represent this data are shown in the scatter plot attached below.

In this scenario, the age (in years) would be plotted on the x-axis (x-coordinate) of the scatter plot while the hair length (in inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the age (in years) and the hair length (in inches), a linear equation for the line of best fit is given by:

y = 0.0502x + 7.73

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After considering all the given data  we conclude that the upper estimate regarding t= 5 is 74.65 ft/sec, the lower estimate regarding t = 5 is 45.28 ft/sec, the upper estimate regarding t = 3 is 63.18 ft.

It is known that acceleration of the object is measured in ft/sec² and measured every second after the drop for 5 seconds. The acceleration decreases over time because of air resistance.

The upper estimate for the speed when t=5 is 32+19.41+11.77+7.14+4.33= 74.65 ft/sec.

The lower estimate for the speed when t=5 is 19.41+11.77+7.14+4.33+2.63=45.28 ft/sec.

The upper estimate for the distance fallen when t=3 is 32+19.41+11.77=63.18 ft.

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We can write the slope of the line mathematically as -

m = (y₂ - y₁)/(x₂ - x₁)

or

m = dy/dx

The general equation of a straight line is -

y = mx + c

Here,  {c} is the {y} - intercept & {m} is the slope of the line. It also denotes the unit rate. Unit rate is the rate at which the value of {y} changes per unit change in the value of {x}. We can write the slope of the line mathematically as -

m = (y₂ - y₁)/(x₂ - x₁)

or

m = dy/dx

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The requried table of values for P inversely proportional to t  has been shown below.

To complete the table of values for P inversely proportional to t, we need to use the formula for inverse proportion:

P = k/t

where k is the constant of proportionality. To find k, we can use any one of the given values of P and t. Let's use the first row of the table where P = 8 and t = 2:

8 = k/2

k = 16

Now we can use this value of k to find the corresponding values of P for the other values of t in the table:

t P

2 8

4 4

6 2.67

8 2

10 1.6

We can see that as t increases, P decreases, which is consistent with the behavior of inverse proportion.

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Answer:

(x−h)2+(y−k)2=r2

(x−0)^2+(y+5)^2=25

Step-by-step explanation:

Based on control groups, experiments indicate cause-and-effect relationships. While observational studies, great care must be taken in concluding cause and effect. Correct options are i and ii.

Statement i is a true statement. Experiments are designed to test causal relationships between variables by manipulating one variable while keeping all others constant, allowing researchers to establish cause-and-effect relationships with greater certainty.

The use of control groups allows researchers to isolate the effects of the independent variable from other potential confounding variables.

Statement ii is also a true statement. Observational studies are more prone to the influence of lurking variables that cannot be controlled for, which makes it more difficult to establish a cause-and-effect relationship between variables.

However, careful analysis and the use of statistical methods can help control for the influence of some lurking variables and provide evidence to support a causal relationship.

Statement iii is a false statement. While a complete census can provide comprehensive information about a population, it does not necessarily establish cause-and-effect relationships absolutely.

Causality is typically established through well-designed experiments or observational studies that carefully control for confounding variables, and it is rare for any single study to establish causal relationships with absolute certainty.

Instead, scientific evidence is accumulated over time through multiple studies that support the same conclusion, and even then, there is always some degree of uncertainty and potential for alternative explanations.

Correct options are i and ii.

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Answer:

[tex] {x}^{2} = {9}^{2} + {26}^{2} [/tex]

[tex] {x}^{2} = 81 + 676 = 757[/tex]

[tex]x = \sqrt{757} = 27.5[/tex]

So x = about 27.5

Answer:

The new value of the stock is 3 times the original value, which is $10,000 x 3 = $30,000.

The increase in value is $30,000 - $10,000 = $20,000.

The rate of return is the increase in value divided by the original investment, which is $20,000/$10,000 = 2 or 200%.

Therefore, the percent increase (rate of return) on Dana's investment is 200%.

Answer:

-249/28

Step-by-step explanation:

a) If the nth term of sequence 32,-8,2, aₙ = 3aₙ₋₂ - 2aₙ₋₃ and a₁ = 32.

b) If explicit formula is aₙ = -7+10(n-1), a₁ = -7 and aₙ = aₙ₋₁ + 10.

a) a₁ = 32 (the first term of the sequence is given)

aₙ = 3aₙ₋₂ - 2aₙ₋₃ (since the sequence is not arithmetic or geometric, we can use this formula to find the nth term)

So, using this formula, we get:

a₂ = 3(32) - 2(-8) = 104

a₃ = 3(-8) - 2(2) = -26

And so on.

b)

a₁ = -7 (the first term of the sequence is given by the explicit formula)

aₙ = aₙ₋₁ + 10 (since the difference between consecutive terms is 10, we can use this formula to find the nth term recursively)

So, using this formula, we get:

a₂ = a₁ + 10 = 3

a₃ = a₂ + 10 = 13

And so on.

In general, the recursive formula for a sequence gives us a way to generate each term of the sequence based on the previous terms, while the explicit formula gives us a way to calculate any term of the sequence directly.

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The transformations on their most likely corresponding equations are;

1. O'P' lies on x = 3; N'R' lies on x = 6.

Clockwise rotation of 180° about the origin and then a reflection over the x-axis2. O'P' lies on y = -3; N'P' lies on y = -6.

Reflection over the y-axis and then reflect over the  x-axis3.

P'R' lies on y = -2, and O'N' lies on y = -6.

Counterclockwise rotation of 90° about the origin  

To identify transformations, we have to be conversant with various rules of transformation. When we reflect over the x or y-axis, the signs of the coordinates for x or y are supposed to change to negative.

However, Any transformation that happens such that the coordinates of the equation are both positive means that the image is on the first quatrain of the graph, which is the right and upper side of the x-axis.

If the rectangle is at the second quatrain, and it is rotated 180° degrees, it means that it still maintains its upright position. and when it is reflected back through the x-axis, it still maintains its upright position.

If the rectangle is rotated 90° counterclockwise, it bends and therefore the coordinates change.

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There are 205,320 ways to select one person to be the president, one person to be the vice president, and a third person to be the treasurer from a group of 60 members.

The number of ways to select the president from the 60 members is 60, since any one of the 60 members can be chosen.

Once the president has been chosen, there are only 59 members left to choose from for the vice president. Therefore, there are 59 ways to select the vice president.

Similarly, after the president and vice president have been chosen, there are only 58 members left to choose from for the treasurer. Therefore, there are 58 ways to select the treasurer.

Using the multiplication principle of counting, the total number of ways to select one person to be the president, one person to be the vice president, and a third person to be the treasurer is

60 x 59 x 58 = 205,320

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Answer: 24

Step-by-step explanation:

For inequalities, you would solve for x like you would if it were an equal sign but keep the sign in middle.  The only thing that changes the sign is if you multiply or divide by a negative, then the sign flips(this is not so in this case.

[tex]\sqrt{x}[/tex]<5     square both sides to get rid of square root

x<5²

x<25   x is less than 25; it cannot be = to 25 so the largest integer it can be is 24

Answer:

To compare the purple paints that Madelyn and Arturo made, you need to find the ratio of red to blue in each mixture. You can do this by dividing the amount of red paint by the amount of blue paint.

For Madelyn, the ratio of red to blue is:

10 / 3 = 3.33

For Arturo, the ratio of red to blue is:

4 / 1 = 4

Since Arturo has a higher ratio of red to blue, his purple paint will be redder than Madelyn’s.

Answer:

  x = 52°

Step-by-step explanation:

Given various inscribed angles in a circle, you want the measure of central angle x.

The inscribed angle theorem tells you an arc is double the measure of the inscribed angle it subtends:

  arc JKM = 2·80° = 160°

  arc JNL = 2·126° = 252°

The sum of arcs around a circle is 360°. This tells you ...

  arc JKL = 360° -252° = 108°

An arc has a measure equal to the sum of its parts, so ...

  arc JKM = arc LM +arc JKL

  160° = x + 108°

  x = 52° . . . . . . . . . . subtract 108°

The average number of people per km2​ is 0.0487

From the question, we have the following parameters that can be used in our computation:

Population = 7300000

Total land surface = 1.5 x 10 ^ 8 km squared kilometers

So, we have

Average number of people = Population/Total land surface

Substitute the known values in the above equation, so, we have the following representation

Average number of people = 7300000/(1.5 x 10 ^ 8)

Evaluate

Average number of people = 0.0487

Hence, the average number of people = 0.0487

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Answer:

3-(-5)

Step-by-step explanation:

The distance between these two points is 8. And this is the only answer that acheives this sum.

Answer:

|-5 - 3|

|3 -(-5)|

Step-by-step explanation:

Option 1 is the correct answer.

Let's look at our constraint for the y value:

[tex]0\leq y\leq 3[/tex]. Remember that these are greater/lesser than or equal to symbols.

You can tell which way they're facing by what direction they open up in.
In this case, the first opens towards y, and the second opens towards 3.
This means that y is greater than or equal to 0, but lesser than or equal to 3.

This means that y, the vertical axis, can go from anywhere to 0 to 3.
Let's look at the constraint for the x value:

It's [tex]x\geq 0[/tex]. The sign is facing towards x, which means that x is greater than or equal to 0.

This means x (the horizontal axis) can range from 0 to positive infinity.

The y axis will not go above 3, and will not go below 0.
The x axis will not go below 0.

The only graph that satisfies these conditions is Option 1.

The y value does not go past 3, and does not go under 0.

The x value does not go to the left of 0, but goes on forever to the right.

The null hypothesis implied that cars 20 years or older do not pass safety inspection ≤  30%.

The alternative hypothesis implied that cars 20 years or older do not pass safety inspection >  30%

The local county officials are testing a hypothesis about the proportion of cars 20 years.

And older that do not pass their annual safety inspection at the service station.

The null hypothesis and alternative hypothesis can be stated as follows,

Null hypothesis,

The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station ≤  30%.

Alternative hypothesis,

The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station > 30%.

The null hypothesis assumes that the service station is not allowing cars with known violations to pass the safety inspection.

And that the rejection rate of 30% is consistent .

With the true rate of cars 20 years and older that do not pass their annual safety inspection at the service station.

The alternative hypothesis suggests that the service station is allowing cars with known violations to pass the safety inspection.

And that the rejection rate is lower than the true rate of cars 20 years .

And older that do not pass their annual safety inspection at the service station.

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Based on the mentioned informations and provided values, the price of a square tablecloth with 3.5 m² sides and a cost of €7.25 per square meter is €88.81.

Calculate the price of a square tablecloth with 3.5 m² sides and the square meter of the cost €7.25

The area of the square tablecloth is:

Area = side x side = 3.5 m x 3.5 m = 12.25 m²

To calculate the price of the tablecloth, we need to multiply the area by the cost per square meter:

Price = Area x Cost per square meter

     = 12.25 m² x €7.25/m²

     = €88.81

Therefore, the price of a square tablecloth with 3.5 m² sides and a cost of €7.25 per square meter is €88.81.

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The complete question is :

Calculate the price of a square tablecloth with 3.5 m² sides if the per square meter cost of the cloth is €7.25.

Thus, the probability that the team wins nine games out of 10 is approximately 0.2365, or about 23.65%.

To solve this problem, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:
- P(X = k) is the probability of getting exactly k successes
- n is the total number of trials (games played)
- k is the number of successes (games won)
- p is the probability of success in one trial (winning a game)
- (n choose k) is the binomial coefficient, which can be calculated as n! / (k! * (n - k)!)

In this case, n = 10, p = 0.73, and k = 9. So we have:

P(X = 9) = (10 choose 9) * 0.73^9 * (1 - 0.73)^(10 - 9)
P(X = 9) = 10 * 0.73^9 * 0.27^1
P(X = 9) = 0.2365

Therefore, the probability that the team wins nine games out of 10 is approximately 0.2365, or about 23.65%.

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Answer:

c and d are worth 24 if c4.285 and d 3.75 multiply c and d and divide 24