Ancient slingshots were made form straps of leather that cradled a rock until it was released. One would spin the slingshot
in a circle, and the initial path of the released rock would be a straight line tangent to the circle at the point of release.
The rock will travel the greatest distance if it is release when the angle between the normal to the path and the horizontal
is -450. The center of the circular path is the origin and the radius of the circle measure 1.25 feet.
Write and equation of the initial path of the rock in standard form.

Answer:

A=πr^2

22/7×6×6

=113 1/7

[tex]cdb = 8 \\ x = 4 \\ by \: pythagoras \: theorem \\ 8 {}^{2} = 4 {}^{2} + x{}^{2} \\ 64 = 16 + x {}^{2} \\ 64 - 16 = x {}^{2} \\ 48 = x{}^{2} \\ \sqrt{48 } = x\\ angle \: b = 60 \\ angle \: of \: equilateral \: triangle \: equal \: 60[/tex]

Answer:

A = 23.2 mm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 8 and h = 5.8 , then

A = 0.5 × 8 × 5.8 = 4 × 5.8 = 23.2 mm²

Answer:

Step-by-step explanation:

We can calculate probability by looking at the outcomes of an experiment or by reasoning What is the theoretical probability that a fair coin lands on heads? Choose 1 answer:  Random numbers for experimental probability. This means that if we roll a die 60 times we can expect each of the six faces to come up.

Hope this helps.

Please give me brainliest if it is correct

Answer:

Part A

The 95% confidence interval is approximately 12.66 ≤  [tex]m_R[/tex] - [tex]m_D[/tex] ≤ 13.34

Part B

We are 95% confident that the true difference in the mean amount of waste per dollar stated by the two categories of adults is larger than zero and it is approximately between 12.66 and 13.34

Step-by-step explanation:

Part A

The given parameters are;

The mean amount adults that consider themselves Republican say is wasted for every dollar, [tex]m_R[/tex] = 54 cents

The standard deviation of the statistics, s₁ = 2.9 cents

The number of respondents in the group, n₁ = 513

The mean amount adults that consider themselves Democrats say is wasted for every dollar,   [tex]m_D[/tex]  = 41 cents

The standard deviation of the statistics, s₂ = 2.6 cents

The number of respondents in the group, n₂ = 513

The F-test, F = s₁²/s₂² = 2.9²/2.6² = 1.244

The critical-t, t* = 1.962

F ≤ t*, therefore, we pool the data

[tex]s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]

[tex]s_p =\sqrt{\dfrac{\left ( 513-1 \right )\cdot 2.9^{2} +\left ( 513-1 \right )\cdot 2.6^{2}}{513+513-2}} = \sqrt{7.585}[/tex]

The 95% confidence interval is given by the following formula;

[tex]\left (m_R- m_D \right )\pm t^* \cdot s_p \cdot\sqrt{\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}}}[/tex]

The test statistic, is given as follows;

[tex]t = \dfrac{m_R - m_D}{s_p \times\sqrt{ \dfrac{1}{n_1} + \dfrac{1}{n_2}} }[/tex]

Therefore;

[tex]t = \dfrac{54 - 41}{\sqrt{7.585} \times\sqrt{ \dfrac{1}{513} + \dfrac{1}{513}} } \approx 75.598[/tex]

Given that the test statistic, t = 75.598 > The critical-t, t* = 1.962, we reject the null hypothesis, therefore, there is significant statistical evidence to suggest that there is a difference in the mean stated by the two sets

[tex]s_p =\sqrt{\dfrac{\left ( 513-1 \right )\cdot 2.9^{2} +\left ( 513-1 \right )\cdot 2.6^{2}}{513+513-2}} = \sqrt{7.585}[/tex]

[tex]C. I. = \left (54- 41 \right )\pm 1.962 \times \sqrt{7.585} \times \sqrt{\dfrac{1}{513}+\dfrac{1}{513}}[/tex]

The 95% confidence interval, C.I. ≈ 12.66 ≤  [tex]m_R[/tex] - [tex]m_D[/tex] ≤ 13.34

Part B

From the 95% confidence interval, we are 95% confident that the true difference in the mean amount adult who consider themselves Republicans say politicians waste and the true difference in the mean amount adult who consider themselves Democrats say politicians waste is between 12.66 and 13.34

Given that there is no '0' in the range of values in the 95% confidence for the difference in mean from the two groups,  difference in the mean amount of waste per dollar observed by the two categories of adults.

Answer:

Height = 4 ft

Step-by-step explanation:

Base are : 84.3 ft square

Volume : 337.2 square cuboid

Answer:

616 square feet

Step-by-step explanation:

Lateral surface area of a cylinder can be determined by;

Lateral surface area = 2[tex]\pi[/tex]rh

where: r is its radius, and h is its height.

Given in the question that the height of the cylinder is 14 feet and of radius 2 feet, then;

Lateral surface area = 2[tex]\pi[/tex]rh

                         = 2 x [tex]\frac{22}{7}[/tex] x 2 x 14

                         = 2 x 22 x 2 x 7

                         = 616

Lateral surface area = 616 square feet

Thus, the lateral surface area of the cylinder is 616 square feet.

Answer:

7

Step-by-step explanation;

Rewriting our equation with parts separated:

4+1/7+2+6/7

Solving the whole number parts:

4+2=6

Solving the fraction parts:

1/7+6/7=7/7 (7/7 is a whole number) But first before simplifing, reduce the fraction, 7/7=1/1. Then 1/1=1.

Combining the whole and fraction parts:

(Solving the whole number parts - 6)

(Solving fraction parts - 1)

Answer:

y = -3x + 4

Step-by-step explanation:

x   y

0  4

1    1

2  -2

Going down 3 for every increase of x by 1, when x = 0, y = 4

Answer:

Each shirt costed 9 dollars.

Step-by-step explanation:

35+10=45 (initial price)

45/5=9 dollars per shirt

Answer:

the answer to the question is 8

Answer:

7x + 2y = 9

Step-by-step explanation:

standard form is always written as:

Ax + By = C

Answer:

Box A

Step-by-step explanation:

Answer:

B is the correct answer

Answer:

D.

Step-by-step explanation:

7×3 = 21.

t × t = t².

y = y.

21t²y.

hope it helps. :)

Answer:

17 lies between 16 and 25. So√17 lies between √16 and √25. The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.

Answer:

The answer is 16,25

Answer:

You need to give the answer in ratio

Its really easy

Answer:

92

Step-by-step explanation:

plug -4 into the function

3(-4)²-10(-4)+4

48+40+4

92

Answer:

92

Step-by-step explanation:

f(-4)=3(-4)^2-10(-4)+4

=3(16)-10(-4)+4

=48+40+4

=92

Answer:  $4467.25

Step-by-step explanation:

Exponential decay problem. 8000(0.89)^5.  

100-11 = 89

89/100= 0.89, that is how we got the decimal.

Then, solve.

0.89 * 0.89 * 0.89 * 0.89 * 0.89 = 0.5584059449

0.5584059449 * 8000 = 4467.2475592

Round the decimal part to the nearest hundredth, which is $4467.25.

The y-intercept of the line shown is -4.

Answer: (b)-175 ft

Step-by-step explanation:

In [tex]\triangle ABC\ \text{and}\ \triangle CDE[/tex]

[tex]\angle ACB=\angle ECD\quad [\text{vertically opposite angles}]\\\angle ABC=\angle CDE\quad [\text{Each angle is }90^{\circ}]\\\therefore \triangle ABC \sim\ \triangle CDE\quad [\text{by AA similarity criteria}][/tex]

(ii)for similar triangles, we can write

[tex]\Rightarrow \dfrac{100}{d}=\dfrac{4x}{7x}\\\\\Rightarrow d=100\times \dfrac{7}{4}=175\ ft[/tex]

Answer:

25 is the answer.

Step-by-step explanation:

Answer:

25 because 7 squared plus 24 squared is 625 then you find the square root which is 25.

Step-by-step explanation:

[tex]x: 77 = 7 : 11 \\x = \frac{77 \times 7}{11} = \\ = 49[/tex]

From the given equivalent ratio the value of x is the number 49.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The given equivalent ratios are x:77=7:11

"Two or more ratios that reflect the same relation or comparison of numbers are known as equivalent ratios," according to the definition of the equivalent ratio. The idea of corresponding fractions is comparable. The term "proportion" also refers to the equivalence of two ratios.

Here, x/77 = 7/11

Multiply both the numerator and denominator of the ratio 7/11 by 7, we get 49/77

Now, x/77 = 49/77

So, x=49

Therefore, the value of x is 49.

To learn more about the ratio visit:

brainly.com/question/13419413.

#SPJ2

Answer:

umm actually x is equal to 15 cause

5 (15) + 11 = 86 try solving it hope it helps

cause all you had to do is find the value of X

thank me later if it's right, kk?

Answer:

-60

Step-by-step explanation:

Well just follow the equation from left to right

Add it all up.

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Answer: 4583.33$

Explanation:

55000 / 12

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

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Answer:

Experimental study

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

Answer:

[tex]22.21\ \text{mph}[/tex]

[tex]22.2\ \text{mph}[/tex]

Step-by-step explanation:

[tex]\dfrac{da}{dt}=13\ \text{mph}[/tex]

[tex]\dfrac{db}{dt}=18\ \text{mph}[/tex]

[tex]\dfrac{dc}{dt}[/tex] = Rate at which the distance between the two people is changing

At 25 minutes

[tex]a=13\times \dfrac{25}{60}=5.417\ \text{miles}[/tex]

[tex]b=18\times \dfrac{25}{60}=7.5\ \text{miles}[/tex]

[tex]c=\sqrt{5.417^2+7.5^2}\\\Rightarrow c=9.25\ \text{miles}[/tex]

Distance between the two people is

[tex]c^2=a^2+b^2[/tex]

Differentiating with respect to time we get

[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{5.417\times 13+7.5\times 18}{9.25}\\\Rightarrow \dfrac{dc}{dt}=22.21\ \text{mph}[/tex]

Distance between the two people is changing at a rate of [tex]22.21\ \text{mph}[/tex].

At 35 minutes

[tex]a=13\times \dfrac{35}{60}=7.583\ \text{miles}[/tex]

[tex]b=18\times \dfrac{35}{60}=10.5\ \text{miles}[/tex]

[tex]c=\sqrt{7.583^2+10.5^2}\\\Rightarrow c=12.95\ \text{miles}[/tex]

Distance between the two people is

[tex]c^2=a^2+b^2[/tex]

Differentiating with respect to time we get

[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{7.583\times 13+10.5\times 18}{12.95}\\\Rightarrow \dfrac{dc}{dt}=22.2\ \text{mph}[/tex]

Distance between the two people is changing at a rate of [tex]22.2\ \text{mph}[/tex].