Write the area for the figure below by using distributive property.

Answer:

The gravitational force acting on the 6-kg bowling ball at the top of the 120-meter tall building is approximately 58.64 Newtons.

Step-by-step explanation:

The equation for the linear function is  y=3x -5.

A linear function can be represented by a linear equation. The standard form for the linear equation is: y= mx+b , for example, y=10x+6.

The standard for the linear equation( y= mx+b), also it is known as the Slope-Intercept Form.

Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=10 and b=6.

The question gives some points of the linear function, see below.

x    y

1    -2

2   1

3   4

4  7

From the given data you can find the slope by solving the system linear equation.

For example, you can write a system linear equation from the points: (1,-2) and (4,7).

-2=m+b  (1)

7=4m+b    (2)

Multiplying equation 1 by -1, you have

2= -m -b     (1)

7= 4m+b    (2)

Summing the previous equation, you can find the slope (m):

9=3m

m= 9/3

m= 3

If m=3, from equation 2, you can find the coefficient b.

7 = 4m + b

7 = 4*3 +b

7=12 + b

b= 7-12

b= -5

Thus, the standard form for the linear equation represented by the given table is y=3x -5.

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The expression that shows John's score will be 2x + 9.

It is vital to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, Mai has a score of x while John has 9 more than twice mai's score.

The expression for this relationship will be:

= (2 × x) + 9

= 2x + 9

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Complete question

Mai has a score of x. John has 9 more than twice mai's score. Illustrate the expression for Johnsc score.

From the triangle KLM inside the circle, the value of KM is calculated. And, the value is 1.2079.

A triangle is a polygon made up of three vertices, three angles, and three sides. First, draw a circle with a midpoint represented by O. Then, draw a triangle KLM inside a circle. Now, construct the line segments KO, MO, and LO because they form the circle's radius.

Given that KL = LM. Since two sides of the triangle KLM is equal, it is an isosceles triangle. Also, ∠K=∠M=17°. The total angle of this triangle is 180°. Then, ∠L=180°-17°-17°=146°.

Half the angle L is 73°. Then, ∠KLO=∠MLO=73°.

Consider triangle KLO, this triangle is also isosceles because KO = LO. Then, ∠KLO=∠OKL=73°.

Now, ∠KOL is calculated as follows from the triangle KLO,

[tex]\begin{aligned}\angle KOL&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]

Similarly, consider triangle MLO, this triangle is also isosceles because LO=MO. Then, ∠MLO=∠OML=73°.

Now, ∠LOM is calculated as follows from the triangle MLO,

[tex]\begin{aligned}\angle LOM&=180^{\circ}-73^{\circ}-73^{\circ}\\&=34^{\circ}\end{aligned}[/tex]

Then,

[tex]\begin{aligned}\angle KOM&=\angle KOL+\angle LOM\\&=34^{\circ}+34^{\circ}\\&=68^{\circ}\end{aligned}[/tex]

Using, the cosine law of the triangle KOM, we get,

[tex]\begin{aligned}(KM)^2&=1.08^2+1.08^2-2(1.08)(1.08)\cos 68^{\circ}\\&=2.3328-2.3328(\cos 68^{\circ})\\&=2.3328(1-\cos 68^{\circ})\\&=2.3328(0.6254)\\&=1.4589\\KM&=\sqrt{1.4589}\\&=1.2079\end{aligned}[/tex]

Therefore, the required answer is 1.2079.

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Answer:

See below

Step-by-step explanation:

1/2 + 1/3 w = 1/6     subtract 1/2 from both sides of the equation

1/3 w = - 2/6           multiply both sides by 3

w = -1

Answer: x=10

Step-by-step explanation:

x is an unknown number trying to figure out what number equals 20? You subtract 10 from 20 to figure out x.

She needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

To determine how many times you need to go to the swimming pool to make the membership fee worth paying, you can use the following formula:

Number of visits = membership fee / (cost without the membership - cost with membership)

Plugging in the values, we get:

Number of visits = $50 / ($5 - $3.50)

The savings from the membership's lower entrance price will have surpassed the cost of the membership after 14 visits.

Hence, she needs to go to the swimming pool about 14 times for it to be worth paying the membership fee.

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The probability that a death will result from an accident is 0.105, or 10.5%.

Given:

In foggy conditions, 25% of accidents result in fatalities.

Rain-related accidents result in fatalities in 12.5% of cases.

In sunny weather, 5% of accidents result in fatalities.

To find : The probability that a death will result from an accidents

The likelihood that a death will ensue from an accident

5% of 60%(sunny) (sunny)

25% of 20%(foggy) (foggy)

12.5% of 20%(rainy) (rainy)

Probability = 0.05 x 0.6 x 0.25 x 0.125 x 0.22

Chance is 0.105

Chance is 10.5%.

There is a 10.5% chance that a fatal accident may occur.

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keeping in mind that since a year is 12 months, then 4 months is really 4/12 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 20\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ 20 = (1000)(\frac{r}{100})(\frac{1}{3})\implies 20=\cfrac{1000r}{300} \implies 6000=1000r \\\\\\ \cfrac{6000}{1000}=r\implies \stackrel{\%}{6}=r[/tex]

The system of equations are:

15 + x = y

13 + 2x = y

The weight of the package is 2 pounds.

The delivery cost for both services is 17$.

Here is a system of equations you can use to represent the cost of the two courier services:

First courier: 15 + x = y

Second courier: 13 + 2x = y

Where x is the weight of the package in pounds and y is the total cost of delivery.

We know that the two courier services are equivalent in terms of cost, so we can set the two equations equal to each other:

15 + x = 13 + 2x

then we can subtract 15 from both sides

x = 13 + 2x -15

x = -2 + 2x

then we can subtract x from both sides

-x = -2

then we can divide both sides by -1

x = 2

The package weighs 2 pounds, and the delivery cost for both services is 15 + 2 = 17$.

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The standard deviation of the household income will be increased by $5,000.

The standard deviation is a measure of variation from the mean that takes spread, dispersion, and spread into account. The standard deviation reveals a "typical" divergence from the mean. It is a popular measure of variability since it retains the original units of measurement from the data set.

standard deviation is increased by 5x/100 = 0.05x

Change in standard deviation = $5000

There is little variety when data points are near to the mean, and there is a lot of variation when they are far from the mean. How much the data differ from the mean is determined by the standard deviation. Standard deviation, which is based on all data, is the most often used metric for measuring dispersion. As a result, the standard deviation's value can be affected by even a slight change in one number.

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Answer:

Step-by-step explanation:

X =90

The probability that tails will turn up and that he will choose a red card is 1/6.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The probability of choosing a tail is 0.5.

The probability of choosing ref card is 1/3.

Therefore, the probability will be:

= 1/2 × 1/3

= 1/6

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The resultant answer of the given equation 7 – 5p + 3q is 23.

A math formula is a formula that uses the equal sign to represent the equivalence of two expressions.

The meanings of the word equation and its cognates in various languages can vary slightly.

For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

by inserting the provided values, we must determine the value of the given equation.

The result is obtained by changing the values of p and q in the above equation.

Thus, if p = 1 and q = 7.

So, we get the equation: 7 – 5p + 3q

Calculate as follows:

7 – 5(1) + 3(7)

7 – 5 + 21

28 – 5

23

Therefore, the resultant answer of the given equation 7 – 5p + 3q is 23.

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Correct question:

Evaluate 7-5{p}+3q7−5p+3q7, minus, 5, p, plus, 3, q when p=1p=1p, equals, 1 and q=7q=7q, equal, 7.

Answer: 12/48 = 25%

Step-by-step explanation: If the unit rate that characterizes my juice reflects its concentration, then there are 36 + 12 = 48 ounces of matter in total. The orange juice mix that we add is 12 ounces of mix, therefore the concentration is 12/48 = 25%.

Answer:

x=1, y=4

Step-by-step explanation:

5x+y=9

10x-7y=-18

(Multiply top equation by -2)

-10x-2y=-18

10x-7y=-18

(Add)

-9y=-36

(Divide -36 by -9)

y=4

(Substitute y(4) into the top equation)

5x+4=9

(Subtract 4)

5x=5

(Divide 5)

x=1

Answer: x=1 , y=4

Step-by-step explanation:

5x+y =9          y=9-5x

10x - 7y = -18

10x-7(9-5x)=-18                   y=9-5x

10x-63+35x=-18                  y=9-5(1)

45x-63=-18                          y=4

45x=-18+63

45x=45

x=1

The value of 0.6 is greater than the value of 0.39 because; C 0.6 is greater than 0.39 because 6 tenths is greater than 9 hundredths.

When we are talking about decimals, the left hand side before the decimal are referred to as whole numbers while the first digit after the decimal represents the tenths place, the next digit after the tenths place  represents the hundredths place, the next digit after the hundredths place represents the thousandths place and so on.

Now, we are given two decimals 0.6 and 0.39.

We see clearly that 0.6 has a greater tenths digit than the hundredths digit in 0.39. This is seen as;

0.6 = 6/10 while 0.39 = 39/100

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There are 720 ways that personnel director for a corporation fills the positions

It is the ordered arrangement of members belonging to a set with no repeats.

To solve this problem the formula and the permutation procedure we must use is:

nPr = n! / (n-r)!

Where:

Information about the problem:

Applying the permutation formula we have:

nPr = n! / (n-r)!

10P3 = 10! / (10-3)!

10P3 = 10! / 7!

10P3 = 10*9*8*7! / 7!

10P3 = 10*9*8

10P3= 720

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The correct answer is Non-existent. If the Earth's spin axis were perpendicular to the Earth's orbital plane, the seasons and seasonal variation would be greatly reduced or eliminated.

This is because the tilt of the Earth's axis (currently at 23.5 degrees) causes the change in the amount of sunlight received at different latitudes during the year, leading to the seasons we experience.

After all, it causes our seasons in the first place. If the Earth's axis were vertical to its orbital airplane, there would be no seasons. Still, there would be minor variations in temperatures and rush throughout each time as Earth moves slightly closer and further down from the sun If the earth and ringed in an upright position around the sun.

If the Earth's spin axis were perpendicular to the ecliptic plane, the Northern and Southern hemispheres would receive roughly the same amount of sunlight throughout the year, and there would be little temperature variation, thus leading to little or no seasonal changes.

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The right response is Nonexistent. Seasons and seasonal fluctuation would be significantly diminished or completely gone if the Earth's spin axis were parallel to its orbital plane.

This is so that the seasons we experience may be attributed to the tilt of the Earth's axis, which is now 23.5 degrees, which affects the quantity of sunlight received at various latitudes throughout the year.

After all, it is the primary cause of our seasons. Seasons wouldn't exist if the Earth's axis were vertical to its orbital plane. If the earth were circled in an upright position around the sun, there would still be modest fluctuations in temperature and rush throughout each period as Earth travels a little closer to and further away from the sun.

The Northern and Southern hemispheres would get nearly the same amount of sunshine throughout the year, and there would be no temperature difference, which would result in little to no seasonal variations if the Earth's spin axis were perpendicular to the ecliptic plane.

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The frequency table has been created in the attachment

Given that 56 respondents did not belong to any clubs, we know that the number of 7th graders who belong to zero clubs is 56.

Given that twice as many 7th graders belonged to one club as no clubs, we can set up the equation:

x = 2 * 56

Given that 10 fewer 7th graders belonged to more than one club than no clubs, we can set up the equation:

y = 56 - 10

Given that twice as many 8th graders belonged to one club as more than one club, we can set up the equation:

z = 2*w

Now we have the following system of equations:

x = 2 * 56

y = 56 - 10

z = 2*w

x+z = 150

y+w = 150

By solving the above system of equations we get:

x = 112

y = 46

z = 112

w = 56

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The equation of the line in slope intercept form is y = -2.65x + 25.

The x-intercept means when the gift card has a balance of zero dollars.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore. let's find the slope of the line using (2, 19.7) and (4, 14.4).

Hence,

m = slope = 14.4 - 19.7 / 4 - 2

m = - 5.3 / 2

m = - 2.65

Therefore, let's find the y-intercept using (2, 19.7).

y = -2.65x + b

19.7 = -2.65(2) + b

b = 19.7 + 5.3

b = 25

Therefore, the equation of the line is y = -2.65x + 25.

The x-intercept is the value of x when y = 0.

Hence,

0 = -2.65x + 25

-25 = -2.65x

x = -25 / -2.65

x = 9.4

The x-intercept means the gift card has zero balance. At this point the medium cup of coffee is 9.4 .

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You can "find algebraically" if a function is even, odd, or neither by taking it, substituting -x for x, simplifying it, and then comparing the results to what you had initially.

The function is even if it is exactly the same as what you started with (that is, if f(-x) = f (x), with all the signs remaining the same. The function is odd if it is exactly the opposite of what you started with (that is, if f(-x) = -f(x), with all the signs switched.

The function is neither even nor odd if the outcome is neither exactly the same nor exactly the opposite (that is, neither having all the same words but with all the signs reversed).

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The transformation represented by the figure is (c) translation

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

The figure

On the figure, we have the following

A figure and its translated image

When a shape is translated to form another, then the transformation is a translation

Hence, the transformation is translation

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The linear equation parallel to y=(2/3)x+1 that passes through (3, 0) is:

y = (2/3)*x - 2

A general linear equation can be written in the slope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Particularly, two linear equations are parallel only if both equations have the same slope and different y-intercepts.

Then a line parallel to:

y = (2/3)*x + 1

Is of the form:

y = (2/3)*x + b

And we want this line to pass through the point (3, 0), replacing these values we will get:

0 = (2/3)*3 + b

0 = 2 + b

-2 = b

Then the linear equation is:

y = (2/3)*x - 2

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A geometric sequence begins with 72, 36, 18, 9, is Of(n) is 72(2)+1.

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Answer:

f(n) = 72(0.5)n−1

Step-by-step explanation:

Got right.

A list that shows the possible outcomes of one day one method of travel:

Monday, bus,

Monday, subway,

Monday, taxi,

Tuesday, bus,

Tuesday, subway,

Tuesday, taxi

The correct answer is an option (B)

Let A represents the set of days.

A = {Monday, Tuesday}

And set B represents the method of transportaion/travel.

B = {bus, subway,  taxi }

To find the list of possible outcomes of one day one method of travel we find the product of set A and set B.

We know that for non-empty sets A and B the Cartesian Product is given by AxB = {(a,b) | a ∈ A and b ∈ B}.

It is a set of all ordered pairs (a, b)

For above sets A and B,

A × B = {(Monday, bus), (Monday, subway), (Monday, taxi), (Tuesday, bus), (Tuesday, subway), (Tuesday, taxi)}

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Find the complete question below.

The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

A line is known as a perpendicular bisector when it divides a specified line segment in half, by creating a 90° angle at the intersection.

The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler.

On both sides of the line segment being divided, it forms a 90° angle.

Here we have

On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). It's midpoint M. The coordinates of M (3, 2).  

Slope from A(-1,-1) and B(7,5)  

=> [ 5 + 1]/[7 + 1 ] = 6/8 = 3/4

When we draw a perpendicular bisector of AB on the grid. It will pass through the point (0, 6)  

The slope of the perpendicular bisector i.e from (0, 6) to (3, 2)  

=> [2 - 6]/[3 - 0] = - 4/3

Let the equation of the bisector is y = mx + c

=> y = (-4/3)x + c

=> 3y = - 4x + 3c           [ ∵ Slope = -4/3 ]

As we know the bisector will pass through (3, 2)

=> 3(2) = -4(3) + 3c

=> 3c = 12 + 6

=> 3c = 18

Hence, the required equation of the line is 3y = - 4x + 18  

Therefore,

The slope of the line AB and the perpendicular bisector are reciprocal to each other and the equation of the line is 3y + - 4x = 18.  

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The statement that best describes Annie’s attitude toward her upcoming assignment in this excerpt is "she is studious and eager to share her knowledge"

Annie is all about maintaining optimism and hope throughout life's journey, no matter the circumstances.

The young orphan Annie has led a difficult life in the cruel matriarch Miss Agatha Hannigan's anything-but-cheerful orphanage. With a shattered necklace, she stealthily leaves her orphanage and goes in search of her parents, who she hopes would adopt her.

She may be the offspring of a Marleyan and an Eldian liaison, and her parents abandoned her when she was a baby. But after being transported to the Internment Zone, a guy took her up and started to train her as a warrior so that he could live better in Marley.

Therefore, Annie is studious and eager to share her knowledge.

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We would need to add 8 more sets of 3 candies to 23 candies in order to have the same amount as Casey.

To find this, we can divide the total amount of candy Johnny has (23) by the amount of candy Casey has (3) and round up to the nearest whole number:

(23) / (3) = 7.666...

Since we can't have a fraction of a set of candies, we must round up to the nearest whole number, which is 8.

So, to have the same amount of candy as Casey, we would need to add 8 more sets of 3 candies to Johnny's 23 candies.

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After inspecting the graph, when x=0  y is 6 so the constant is +6 which is Positive

What is polynomial function ?

A polynomial characteristic is a function that includes handiest non-bad integer powers or simplest tremendous integer exponents of a variable in an equation like the quadratic equation, cubic equation, and so forth. for example, 2x+5 is a polynomial that has exponent same to one.

Given ,

The graph is a polynomial function.

This is an odd degree polynomial since end behavior is +infinitely when x is positive and -infinity when x is negative

For an even degree polynomial en behavior will be positive regardless of the sign as a negative number raised to an even power is always positive

The leading coefficient is positive other wise the function would be flipped around the x axis

Inspect the graph. when x=0  y is 6 so the constant is +6 which is Positive

Hence , After inspecting the graph, when x=0  y is 6 so the constant is +6 which is Positive

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