A town is mapped on a coordinate grid. The library is located at point (-3, 9) and the museum is located at
point (8, 2).
Where is the midpoint of the line segment whose endpoints are the library and the museum?
O (-5.5, 5.5)
O (-5.5, 3.5)
O (2.5, 3.5)
O (2.5, 5.5)

Answer:

  67.5 cm²

Step-by-step explanation:

The figure can be decomposed into figures whose area formulas you know.

As the attached figure shows, one way to decompose the figure is by extending the horizontal line. This divides the figure into an upper trapezoid and a lower rectangle.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

where b1 and b2 are the parallel bases, and h is the height.

The bases of the trapezoid in this figure are 6 and 3 cm, and the height is 5 cm. Its area is ...

  A = 1/2(6 cm +3 cm)(5 cm) = 22.5 cm²

The area of a rectangle is given by the formula ...

  A = LW

where L and W represent the length and width, respectively.

The dimensions of the rectangle in this figure are 15 cm long by 3 cm wide. Its area is ...

  A = (15 cm)(3 cm) = 45 cm²

The total area of the figure is the sum of the areas of the trapezoid and rectangle:

  A = (22.5 cm²) + (45 cm²) = 67.5 cm²

The are of the figure is 67.5 cm².

Using a linear function, the total charge from parking in the lot for 72 hours is of:

b. $146.

A linear function is modeled by:

y = mx + b

In which:

Both the basic fee, which is the y-intercept, and the hourly fee, which is the slope, are of $2, hence the cost of parking x hours is given by:

C(x) = 2x + 2

Hence the cost for parking 72 hours is:

C(72) = 2 x 72 + 2 = 2 x 73 = $146.

Which means that option b is correct.

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Samantha and Mia are 13 km apart from each other.

A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.

Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.

Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.

A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.

Hypotenuse of the triangle, which measures distance between the females

the Pythagorean theorem,

H² = P² + B²

H² = 7² + 11²

H² = 49 + 121

H = √170

H = 13.038

H = 13km

Between them, there is a 13 kilometer distance.

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Step-by-step explanation:

using gp formula

tn=ar^n-1

which our a which is the first term is = -3

our r which is t2/t1=-6

t8=(-3)(-6)^8-1

=(-3)(-6)^7

=(-3)(-279936)

=839808

The numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.

In the question, we are asked to simplify the numerical expression:

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3.

To simplify the expression, we will follow the BODMAS rule, where B means Brackets, O means Of, D means Divide, M means Multiplication, A means Addition, and S means Subtraction.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

= 2/3 ÷ 16 + (3/4 + 1/6) ÷ 1/3 {Solving 2⁴ = 16, before proceeding BODMAS}.

= 2/3 ÷ 16 + ((9+2)/12) ÷ 1/3 {Solving Brackets by taking LCM}

= 2/3 ÷ 16 + 11/12 ÷ 1/3 {Simplifying}

= 2/3 * 1/16 + 11/12 * 3/1 {Solving divisions by taking reciprocals}

= 1/24 + 11/4 {Multiplying}

= (1 + 66)/24 {Adding using LCM}

= 67/24 {Simplifying}.

Thus, the numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.

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The provided question is incomplete. The complete question is:

"Type the correct answer in the box. Use numerals instead of words. For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.

Simplify the numerical expression.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

The expression has a value equal to."

The end behavior of the given polynomial is that as x → -∞ or  x → ∞, then, f(x) → 5

We are given the polynomial;

f(x) = 5x/(x - 25)

Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get; f(x) = 5/(1 - (25/x))

Thus, applying limits we have;'

lim x → ±∞ [5/(1 - (25/x))]

From algebraic limit laws we know that;

If f(x) = k, then;

lim x → +∞ [f(x)] = k

Also, lim x → -∞ [f(x)] = k

Thus, applying limits at infinity to our polynomial gives;

lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5

This is because lim x → ∞ for 1/x is 0.

Thus, f(x) has horizontal asymptotes at y = 5

Thus, we conclude that the end behavior is that as x → -∞ or  x → ∞, then, f(x) → 5

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The value of the function w(5) is 53

The function is given as:

w(x) = 9x + 8

The expression w(5) implies that the value of x is 5

i.e. x = 5

Substitute the known values in the above equation

w(5) = 9 * 5 + 8

Evaluate the product

w(5) = 45 + 8

Evaluate the sum

w(5) = 53

Hence, the value of the function w(5) is 53

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The group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.

A sample that best represents a population under study is a sample that is a subset of the entire population, that is, research subjects that are drawn as samples should reflect the general characteristics of the entire population without leaving out any part of the population. Also, a good sample should enable a researcher make generalization.

A sample that is a subset of a population and reflects the characteristics of the general population would not be biased.

Given the situation above, the population of the study are smart phone customers that use dat in the cell phone company. So, a sample that would better represent this general population would be customers that currently have a smart phone plan, since the average amount of data they use is what the cell pone company wants to ascertain.

Therefore, the group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.

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Answer:

Maximum/Minimum Value:  (0,−2)   is a local minima (1/8,8)  is a local maxima

Explanation: Use the derivative to find the maximum and minimum

Answer:

Period = ¹/₄

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

f(x) = A cos(B(x + C)) + D

where:

Given function:

[tex]y=-5 \cos (8 \pi x)+3[/tex]

Comparing the given function with the standard form:

[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]

Therefore, the period of the given function is ¹/₄.

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Based on the amount of money that Jerl had and then the amount that she put away, the possible values of the number of dollars in the original pile of money was ( 200, 440).

The amount that was above $200 that she found can be x which means that the greater side of the inequality is:

= 200 + x

She then gave away $80:

= 120 + x

She gave away 1/3 of the money so the amount left is:

= 2/3 x (120 + x)

The lesser side of the inequality:

(x + 2) - 200 = x

So then:

((120 + x) x 2) / 3 > x

240 + 2x > 3x

240 > x

x < 240

The interval that shows the possible values of the original pile of money is therefore:

( 200, 440)

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Step-by-step explanation:

it is a line, so that is 1 point, where it cuts the x-axis.

in general that means y = 0.

so,

0 = 4x - 3

4x = 3

x = 3/4

the point, where the line cuts the x-axis is

(3/4, 0)

Answer:

Using the usual notations and formulas,

Using the usual notations and formulas,mean, mu = 3550

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculate

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000

Using the usual notations and formulas,mean, mu = 3550standard deviation, sigma = 870Observed value, X = 3000We calculateZ= (X-mu)/sigma = (3000-3550)/870 = -0.6321839Probability of weight below 3000 lbs=P(X < 3000) = P(z < Z) = P(z < - 0.6321839) =0.2636334Answer:Probability that a car randomly selected is less than 3000=P(X < 3000) = 0.2636 (to 4 decimals)Probability that a car randomly selected is greater than 3000=1 - P(X < 3000) = 1 - 0.2636 (to 4 decimals) =0.7364 (to 4 decimals)

Y receives $30000 less than if the profit were divided in proportion to how much they invested.  

In a proportional tax system, everyone is compelled to pay the same amount of taxes as a percentage of their income.

Profit will Divide into 4 equal parts.

The total Profit for the month is  = $120,000

The party will receive a sum of = $30,000

This shows that Y also receive the same amount

Y = $30,000 (Profit received)

Now

If the Profits were divided in proportion to the investments made .

The proportion on investment made by Y.

The total investment made = $12000+$6000+$25000+$7000

                                            = $50000

Out of this the Amount invested by Y = $25000

The Proportional Profit of Y.

=  (25000/ 50000) x 120000                      

= $60,000

So Y receives 60000 - 30000

                       = 30000

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Answer: Option 2

Step-by-step explanation:

Let f(y)=x.

[tex]x=2y+3\\\\x-3=2y\\\\y=\frac{1}{2}x-\frac{3}{2}\\\\f^{-1}(x)=\frac{1}{2}x-\frac{3}{2}[/tex]

The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 2x + 3

Now,

We can find the inverse of function as;

⇒ f (x) = 2x + 3

Put y = f (x);

⇒ y = 2x + 3

Solve for x;

⇒ y - 3 = 2x

⇒ x = 1/2 (y - 3)

⇒ f ⁻¹(x) = 1/2 (x - 3)

Thus, The inverse of the function is,

⇒ f ⁻¹(x) = 1/2 (x - 3)

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The expected value or mean of binomial distribution is also increased by increasing the number of trials.

The standard deviation of binomial distribution is also increased by increasing the number of trials.

According to the question

There is binomial experiment.

The condition given in the question is 'if the number of trials is increased, what happens to the expected value and to the standard deviation'.

We all know,

In binomial distribution, The mean or expected value is given by np whereas the variance is given by np(1 - p) where (1 - p) taken as q is the probability of failure and p is the probability of success.

The standard deviation of binomial distribution is [tex]\sqrt{npq}[/tex].

From the expected value formula we can see that number number of trials is directly proportional to mean or expected value.

Thus we can say that

If the number of trials is increasing, then the expected value is also increasing.

From the standard deviation of binomial distribution we can see that if the number of trials increasing then the standard deviation also increasing because standard deviation is directly proportional to number of trials.

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The order of magnitude for total attended for a high school football team is 3

The given parameters are:

Average number of fan = 1000

Number of home games = 5

The total number of fans in the 5 games is:

Total number of fans = Average number of fan * Number of home games

Substitute known values in the above equation

Total number of fans = 1000 * 5

Express 1000 as 10^3

Total number of fans = 10^3 * 5

Rewrite the equation as:

Total number of fans = 5 * 10^3

The power of 10 represents the order of magnitude

Since the power of 10 is 3, the order of magnitude is 3

Hence, the order of magnitude for total attended for a high school football team that averages 1,000 fans for each of its 5 home games is 3

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The sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

For given question,

We have been given a sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex]

We need to determine whether the sequence converges or diverges.

From given sequence we have, [tex]a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}[/tex]

We use Ratio Test.

According to Ratio Test, [tex]r=\frac{a_{n+1}}{a_n}[/tex], where sequence converges if and only if |r| < 1.

Consider,

[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty[/tex]

Since [tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex] is not defined, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

Therefore, the sequence [tex]a_n=\frac{n^2}{n^3+5n}[/tex] diverges.

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Answer:

x=3

y = -2

Step-by-step explanation:

2x+5y = -4

y = x-5

We want to use substitution

In the first equation, every time we see y, substitute x-5

2x + 5( x-5) = -4

Distribute

2x + 5x -25 = -4

Combine like terms

7x -25 = -4

Add 25 to each side

7x -25+25 = -5+25

7x = 21

Divide each side by 7

7x/7 = 21/7

x=3

Now we can find y

y = x-5

y = 3-5

y = -2

The answer is x = 3, y = -2 or (3, -2).

We are given that :

Let us substitute the 2nd equation's value of y in the 1st equation.

Now, substitute for x in the 2nd equation.

The 90% confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

Given,

[tex]N_{1}[/tex] = 731

[tex]N_{2}[/tex] = 644

[tex]P_{1}[/tex] = 0.33

[tex]P_{2}[/tex] = 0.28

z score for 90% confidence interval = 1.645

Here, the confidence interval formula :

( [tex]P_{1} -P_{2}[/tex]) ± z [tex]\sqrt{\frac{P_{1}(1-P_{1}) }{N_{1} }+ \frac{P_{2}(1-P_{2}) }{N_{2} } }[/tex]

Substituting the values, we get

    (0.33 - 0.28) ± 1.645 [tex]\sqrt{\frac{0.33(1-0.33)}{731}+\frac{0.28(1-0.28)}{644} }[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0003024624+0.0003130435}[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0006155059}[/tex]

=    0.05 ± 1.645 × 0.0248093914

=    0. 05 ± 0.0408114489

Confidence interval:

- 0.05 - 0.0408114489 = - 0.0908114489 ≈ - 0.0908

- 0.05 + 0.0408114489 = - 0.0091885511 ≈ - 0.0092

The confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

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The area of the barn quilt is 3 sq.ft.

The amount of sugar needed to make 1/2 of a batch of cookies is 1/5 of a cup.

Number of boys are practicing hitting the ball = 4

Number of bags of lemons used by Rachel on Tuesday = 1[tex]\frac{3}{4}[/tex]

1. A painted barn blanket needed to be 1 1/3 feet by 2 1/4 feet in size.

Area of the barn quilt = 1 1/3*2 1/4

                                  = 4/3*9/4

                                  = 3 sq. ft.

2. The recipe for Mrs. Smith's oatmeal cookies asks for 2/5 cups of sugar.

Sugar needed for making 1/2 of a batch of cookies = 1/2*2/5

                                                                                 = 1/5 of a cup

3. Six boys are practicing baseball throwing, catching, and hitting in the park. Two thirds of those six youngsters are practicing hitting.

Number of boys practicing hitting the ball = 6*2/3 = 4

4. At the park's lemonade kiosk, Rachel works. She used 1 and 2/5 bags of lemons on Monday. She used 1 and 1/4 times as many lemons on Tuesday as she did on Monday.

Number of bags of lemon used on Tuesday = 7/5*5/4

                                                                     = 7/4

                                                                     = 1 and 3/4 bags

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Answer: Friday

Step-by-step explanation:

Answer:

J

Step-by-step explanation:

Answer:

Domain is 1 and 7 and range is -5and -4

Step-by-step explanation:

because domain is a first group element and range is a second element of a set