i need help

Cerise waters her lawn with a sprinkler that sprays water in a circular pattern at a distance of 15 feet from the sprinkler. The sprinkler head rotates through an angle of 300°, as shown by the shaded area in the accompanying diagram.

What is the area of the lawn, to the nearest square foot, that receives water from this sprinkler?

Responses
a. 79 ft. 2
b. 94 ft.2
c. 707ft.2
d. 589 ft.2

Answer:

739 m²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Equation}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The given scenario can be modelled as an exponential equation.

Let y be the area the fire covers (in meters squared).

Let x by the time (in hours).

If the fire currently covers an area of 32 m² then the initial value, a, is 32.

If the area covered by the fire increases by 17% each hour, then the growth factor, b, is 1.17 (since an increase of 17% is 117% of the previous amount).

Therefore:

Substitute the values of a and b into the exponential formula:

[tex]y=32(1.17)^x[/tex]

To find the area that the first covers in 20 hours' time, simply substitute x=20 into the equation:

[tex]\implies y=32(1.17)^{20}[/tex]

[tex]\implies y=32(23.1055991...)[/tex]

[tex]\implies y=739.37917...[/tex]

Therefore, the area the fire will cover in 20 hours' time is 739 m²  (nearest 1 m²).

Miles has to spend $295.3375 on his new computer.

Sales tax is applied to the price after the discount is applied because discounts are typically provided directly by the retailer and lower both the sales price and the money the retailer receives.

So Original price of Computer  is $325.00

Discount with computer is 15% off.

15% of $325 is (325*15)/100 = $48.75.

Price of computer after discount = 325-48.75 =$276.25

Now sales tax will be applied on this price.

7% sales tax = 0.07

amount of sales tax = 276.25*0.07 = 19.3375

Price of Computer after sales tax   = 276+19.3375 = 295.3375.

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a)[tex]$z=\frac{40.5-40}{\frac{1.25}{\sqrt{10}}}=1.265$[/tex]

Now we can calculate the p value since we have a right tailed test the p values is given by:

[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]

And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .

b) [tex]$p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029$[/tex]

c) [tex]$\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$[/tex]

d) We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:

[tex]n=\frac{\left(z_\alpha+z_s\right)^2 \sigma^2}{(x-\mu)^2}[/tex]

The true mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:

[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]

e) For this case we can calculate a one sided confidence interval given by:

[tex]$\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)$[/tex]

And if we replace we got:

[tex]$40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152$[/tex]

And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]

And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.

What is null hypothesis?

In a scientific setting, a hypothesis (plural: hypotheses) is a testable claim about the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed.

Part a

We have the following data given:

n=10 represent the sample size

[tex]$\bar{x}=40.5$[/tex] represent the sample mean

[tex]$\sigma=1.25$[/tex]represent the population deviation.

We want to test the following hypothesis:

Null: [tex]$\mu \leq 40$[/tex]

Alternative: [tex]$\mu > 40$[/tex]

The significance level provided was [tex]$\alpha=0.05$[/tex]

The statistic for this case since we have the population deviation is given by:[tex]z=\frac{\bar{x}-\mu}{\frac{-\mu}{\sqrt{n}}}$[/tex]

If we replace the values given we got:

[tex]$z=\frac{40.5-40}{\frac{1.24}{\sqrt{10}}}=1.265$[/tex]

Now we can calculate the p value since we have a right tailed test the p values is given by:

[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]

And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .

Part b

The p value on this case is given by:

[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]

Part c

For this case the probability of type II error is defined as the probability of incorrectly retaining the null hypothesis and is defined like this:

[tex]\beta=P\left(Z < z_\alpha-\frac{(x-\mu) \sqrt{n}}{\sigma}\right)[/tex]

Where [tex]$z_\alpha=1.645$[/tex]represent the critical value for the test that accumulates 0.05 of the area on the right tail of the normal standard distribution.

The true mean on this case is assumed [tex]$\mu=42$[/tex], so then we can replace like this:

[tex]\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$$[/tex]

Part d

We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:

[tex]n=\frac{\left(z_\alpha+z_\beta\right)^2 \sigma^2}{(x-\mu)^2}[/tex]

The ture mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:

[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]

Part e

For this case we can calculate a one sided confidence interval given by:

[tex]\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)[/tex]

And if we replace we got:

[tex]40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152[/tex]

And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]

And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.

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The measure of ∠JKM is 145°.

The measure of an exterior angle of a triangle is bigger than either of the measures of the distant interior angles, according to the external angle theorem, Proposition 1.16 in Euclid's Elements.

Because the parallel postulate is not required for its proof, this is a fundamental conclusion in absolute geometry. Three of a triangle's corners are its vertices.

Two angles are produced by a triangle's sides (line segments) meeting at its apex (four angles if you consider the sides of the triangle to be lines instead of line segments). An interior angle of the triangle is the only one of these angles that has the third side of the triangle inside of it.

Here it is given that, ∠JLK= 70°

                                 ∠LJK = x°

(2x-5)°= 70°+x°

now applying exterior angle theorem,

x=75°

substitute 75 for x in 2x-5 to find m∠JKM.

=2x-5

=2×75-5

=145°

Hence, The measure of ∠JKM is 145°

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Answer:

Where you see the colors overlap is the answer.

Step-by-step explanation:

Desmos is a free graphing calculator.

The total volume of all 10 holes and pipes is about 24.135 cubic feet.

Generally, To calculate the volume of the holes, you can use the formula for the volume of a cylinder:

Volume = π * radius^2 * height

In this case, the radius of the hole is 0.5 feet (since the hole is 1 foot across and the diameter of the pipe is 3 inches, which is 0.25 feet), and the height is 3 feet. Plugging these values into the formula, we get:

Volume = π * 0.5^2 * 3 = 0.785 * 3 = 2.355 cubic feet

So each hole has a volume of about 2.355 cubic feet. To find the total volume of all 10 holes, you can simply multiply this number by 10:

Total volume = 2.355 * 10 = 23.55 cubic feet

This is the volume of the holes themselves, not including the volume of the pipes. To find the volume of the pipes, you can use the same formula, but with the radius of the pipe (which is 1.5 inches, or 0.125 feet) and the length of the pipe (which is 3 feet).

Volume = π * 0.125^2 * 3 = 0.0195 * 3 = 0.0585 cubic feet

So the volume of one pipe is about 0.0585 cubic feet. To find the total volume of all 10 pipes, you can multiply this number by 10:

Total volume = 0.0585 * 10 = 0.585 cubic feet

23.55 + 0.585 = 24.135 cubic feet.

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CQ not found

Answer: Thus, sqrt 18 < 23/5

Step-by-step explanation:

23/5=4.6

4.6x4.6=21.16

18<21.16

A line that goes through (0, 0) and (3.6, 14.4).

Wewant a description of the line that describes the same proportional relationship as the points given in the table:

(x, y) = (3.6, 14.4), (12.2, 48.8), (2.1, 8.4)

The graph of the relation will be a straight line through points with (x, y) values from the table. A graph of a proportional relation also goes through the point (0, 0).

Of the points listed in the answer choices, only (3.6, 14.4) and (12.2, 48.8) are ones that are given in the table. This eliminates all of the answer choices except the correct one:

A line that goes through (0, 0) and (3.6, 14.4).

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Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].

What is the slope of line?

The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.

Here given thaat the line that has a slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex].

Then,

[tex]y=mx+c\\\\y=\frac{x}{5}+c\\\\x=0,y=0\\\\0=0+c\\\\c=0[/tex]

Thus,

[tex]y=\frac{x}{5}+c\\\\c=0[/tex]

Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].

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The American adults who believes in alien as per given 95% of confidence interval and the given sample surveyed is in the range of

( 0.657 , 0.783 ).

As given in the question,

Number of American adults surveyed (sample size) 'n' = 200

Percentage of people who believes in aliens 'p'= 72%

                                                                               = 0.72

Percentage  of people who don't believes in aliens ' 1 - p'  = 1 - 72%

                                                                                                 = 28%

                                                                                                 = 0.28

95% Confidence interval that represents percent of people believes in aliens

Z - score of 95% confidence interval = ± 1.96

Margin of error = (z-score)√p ( 1- p) /n

                          = ( 1.96)√(0.72 × 0.28)/ 200

                          = 1.96 ( 0.032)

                          = 0.06272

                          = 0.063

Lower limit = p - Margin of error

                  = 0.72 - 0.063

                  = 0.657

Upper limit =  p + Margin of error

                  = 0.72 + 0.063

                  = 0.783

Therefore, for the given 95% confidence interval and sample size the Americans who believes in alien are in range of ( 0.657 , 0.783 ).

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They will pay You $5368709.12 on the 30th day

What does the term "compound interest" mean?

Compound interest is when you receive interest on both your interest income and your savings.

You start with a one cent.

You have $0.01 x 2 the following day.

You have $0.01 x 2 x 2 the following day.

and so forth

You will have $0.01 x 2^n-1 on day n.

This means that on the 30th day, you have $0.01 x 2^29 = $5 368 709.12.

That is compound interest at work! It equates to daily payments of 100% interest. It immediately soars to inconceivable heights with even a penny as your initial investment!

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0.2620 is the probability of getting two red marbles.

Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

a jar contains 10 blue marbles and 11 red marbles.

So, there total 21 marbles are present.

Now among 21 marbles, 11 are red marble. So, odds of a red on the first are 11/21

Next, there are 20 marbles are present and 10 are red. So odds of a red on the second is 10/20.

For, probability both are red, just multiply

= (11/21) x (10/20)

= 0.2620.

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Answer: $146,410

Step-by-step explanation:

Answer: x= 18

Step-by-step explanation:

9 divided by 6 = 1.5

That is the rate change

So take 12 times 1.5 = 18

x= 18

If you can please give me a Brainliest, thank you!

Answer:

18

Step-by-step explanation:

See attached worksheet.

A scaled figure will have dirrent dimensions, but with the same proportions.  The ratio of the two sides in Figure A is 2/1 (Side/Top).  That same ratio will apply to Figure B.  So we could write:

                    x/9 = 2

                    x = 18

Answer:

4

Step-by-step explanation:

5x + 2 = 2x + 14

or, 5x - 2x = 14 - 2

or, 3x = 12

or, x = 12/3

.

. . x = 4

Answer:

[tex]\huge\boxed{\sf 3x -4}[/tex]

Step-by-step explanation:

Add both equations.

= 2x + 1 + x - 5

Combine like terms

= 2x + x + 1 - 5

[tex]\rule[225]{225}{2}[/tex]

Answer:

f(x) + g(x) = 3x - 4

Step-by-step explanation:

The problem is,

→ f(x) + g(x)

Let's solve the problem,

→ f(x) + g(x)

→ (2x + 1) + (x - 5)

→ 2x + 1 + x - 5

→ (2x + x) + (1 - 5)

→ 3x +(-4)

→ 3x - 4

Hence, answer is 3x - 4.

Answer:

a.  11

Step-by-step explanation:

Mona wants to buy pens each pens costs 3.50 she can only buy 3 pens with the money she has which of these could be the money she has:

a.  11

b. 10

c. 14

d. 9

3.5 * 3 = 10.5 cost

She has 11.

Number of ways can a person travels from A to C via B = 24 ways

How it can be calculated that a person can travel in no. of ways?

To calculate the likelihood of an event occurring, we will apply the equation number of favourable outcomes divided by total number of outcomes. We sometimes need to apply a permutation to calculate the overall number of outcomes. A permutation is a method for calculating the number of events that occur when order is important.

Given,

Connection of roads from a = 6

Connection of roads from a = 4

Number of roads from a to b =6

Number of roads from b to c =4

Number of ways can a person travels from a to c via b

= 6*4

= 24 ways

The number of ways a person can go from A to C via B is 24.

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Answer:

0.07407407

Step-by-step explanation:

divide 2 by 27

Answer:

0.0740

Step-by-step explanation:

just divide 2 by 27

The polygons (quadrilaterals) are similar by the congruency of three interior angles and the equal ratios (5 : 4) of  a pair of adjacent sides. The correct option is therefore

B. Yes; PQSN ~ AGKD, scale factor; 5 : 4

Similar polygons are polygons that have the same interior angle, and proportional dimensions.

The specified parameters indicate that we have;

Polygon PQSN and AGKD are quadrilaterals

Length of sides of polygon PQSN

Length of side PQ = 10, QS = 7.5, SN = 15, NP = 15

Length of sides of polygon AGKD

AG = 12, GK = 12, KD = 8, DA = 6

The measure of the angles are;

∠K ≅∠S

∠S ≅ ∠A

∠N = ∠G = 90°

The angle sum property of a quadrilateral indicates that the measure of the fourth angle of both quadrilateral are congruent

The ratio of two adjacent sides of the quadrilaterals are;

7.5/6 and 10/8

7.5/6 = 1.25

10/8 = 1.25

Therefore;

[tex]\dfrac{7.5}{6} =\dfrac{10}{8} =1.25[/tex]

The ratio of two adjacent sides of the quadrilaterals PQSN and AGKD are therefore the same.

The three interior angles of quadrilateral PQSN are congruent to three interior angles of quadrilateral AGKD, and the ratio of two adjacent sides from each quadrilateral are the same, therefore,  quadrilaterals are PQSN is similar to quadrilateral AGKD

The scale factor of dilation from quadrilateral PQSN to AGKD is 7.5 : 6 = 15 : 12 = 5 : 4

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If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.

There are four primary categories of probability: classical, empirical, subjective, and axiomatic. Since possibility and probability are equivalent, you may define probability as the likelihood that a specific event will occur.

given

A fair coin is repeatedly flipped until it comes up heads.

The coin is impartial.

On the third try, we need to calculate the likelihood of the first landing being on heads.

We are aware that each flip of a fair coin is independent of the others, and that each effort results in P(H) = P(T) = 0.5.

Required probability is the likelihood that the third attempt's first landing will be on heads.

= Chance of (I two trials result in tail and third result in head)

=P(I head) P(II head) P(III tail) (since each trial is independent)

= ( 1 /2 ) (1/2)(1/2) = (1/8 )

If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.

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Answer:

400000

Step-by-step explanation:

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The solution to the inequality expression -2n - 5 ≥ 1 or 5n + 7 > 2 is -1 > n ≥ -3

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

-2n-5≥1 or 5n + 7 > 2

So, we have

-2n - 5 ≥ 1 or 5n + 7 > 2

Evaluate the like terms

So, we have the following representation

-2n ≥ 6 or 5n > -5

Divide both sides by the coefficient of n

This gives

n ≤ -3 or n > -1

Combine the expression

-1 > n ≥ -3

Hence. the solution is -1 > n ≥ -3

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3/10 will be the proportion of those integers that are multiples of 15. Then, C is the best choice.

Mathematical branch known as algebra deals with symbols and arithmetic operations on them. These symbols are referred to as variables because they lack fixed values. We frequently observe certain values that change in our day-to-day problems. However, there is a continuing need to depict these shifting values. These values are frequently represented in algebra by symbols, which are known as variables, such as x, y, z, p, or q.

Take into account all positive numbers that are multiples of 10 and have a value lower than or equal to 200.

Let x be the quantity of positive integers that are multiples of 10. The equation then becomes

10x ≤ 200

The value of the x will then be.

x ≤ 20

Below is a list of the numbers.

Set = 20 {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200}

The set that can be divided by 15 is

Set = 6 {30, 6,0 90, 120, 150, 180}

So, the percentage of those integers that are multiples of 15 will be

⇒ 6 / 20

⇒ 3/10

3/10 will be the proportion of those integers that are multiples of 15. Then, C is the best choice.

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Answer:

Should be B

Step-by-step explanation:

Answer:

The transformations applied to the parent function k(x)=x| to obtain f(x)= -1/2|x+3/-1 are reflection in the y-axis, vertical stretching by a factor of 1/2, and a horizontal shift of 3 units to the right.

Step-by-step explanation:

To obtain f(x) from k(x), we first reflect k(x) in the y-axis, which changes the sign of the function and flips it over the x-axis. This gives us -k(x). Next, we vertically stretch the graph of -k(x) by a factor of 1/2. This makes the graph of -k(x) taller and narrower. Finally, we shift the graph of -k(x) 3 units to the right. This moves the entire graph 3 units to the right on the x-axis. The resulting function is f(x)=-1/2|x+3/-1.To understand why these transformations were applied, it's helpful to consider the effect of each transformation on the graph of k(x)=x|. Reflecting in the y-axis flips the graph over the x-axis and changes the sign of the function, so it becomes -k(x). Vertical stretching by a factor of 1/2 makes the graph of -k(x) taller and narrower. Finally, shifting the graph of -k(x) 3 units to the right moves the entire graph 3 units to the right on the x-axis. This results in the graph of f(x)=-1/2|x+3/-1.

Answer:

(Assuming it is k(x) = |x| and f(x) = -1/2|x+3| -1

Scale vertically by a factor of -1/2

Shift left 3

Shift down 1

Step-by-step explanation:

The -1/2 is multiplied by everything, so it scales the graph vertically by -1/2. The -1 is again, everything(as opposed to just modifying the x), so it shifts the graph down by 1.

The + 3 is a little more confusing. Basically, x would have to be x-3(which is shifting the graph left) in order to retain the same x-value(to make the equation true) for the same value. This is the same for y, but we usually isolate y so it doesn't come up as often. If we add 1 to both sides, we get [tex]f(x) + 1= -1/2|x+3|[/tex], and for the same reasoning the graph would shift down 1 even though it is f(x) + 1, because for the same x-value the y-value would need to be 1 less to make the equation to hold true.

Feel free to message me/comment on this answer if you would like more clarification/why it is "backwards" or anything else about my answer.

I hope this helps!