When it is pulled tight, a 30-foot rope used to hold a boat near a dock forms a 32° angle with the level of the water. The rope is connected to the boat at water level. What is the height of the dock to the nearest tenth of a foot?

Answer:

y = 4x - 25

Step-by-step explanation:

y = 4x + b

-1 = 4(6) + b

-1 = 24 + b

-25 = b

Answer:

68.8

Step-by-step explanation:

rounding to one decimal place is the same as rounding to the nearest tenth (see attached for reference).

In this case, 68.8 is already expressed as a number with one decimal place. No further manipulation is needed.

Brenna would take 20 min to cut the same wood into sixths.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let x be the rate at which Brenna cuts the wood in a single piece,
So, She can cut a log into thirds in 10 min.
x = 3/10

x = 0.3 cuts per minute for single wood,

Now,
time took to cut the same wood into 6 pieces
= 6 / x
= 6 / 0.3
= 20 min

Thus, Brenna would take 20 min to cut the same wood into sixths.

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Answer:

3/20

Step-by-step explanation:

-

Answer:

0.15

Step-by-step explanation:

Last term of `(a-2b)⁴` using the binomial `r`th term formula, we will use the formula `(nCr)*(a^n)*(b^r)` where `n` is the power of the binomial `(a-2b)` which is `4`. Also, `r` is the last term of `(a-2b)⁴` which is `4` and `n-r` is equal to the first term of `(a-2b)⁴` which is `0`.

So, substituting the values into the formula, we get;

(nCr)*(a^n)*(b^r)

= `(4C4)*(a^4)*(b^0)`

= `(1)*((a^4)*(1))`

= `a^4`

Therefore, the last term of `(a-2b)⁴` is `a^4`.

The long answer is;To find the last term of `(a-2b)⁴` using the binomial `r`th term formula, we will use the formula `(nCr)*(a^n)*(b^r)` where `n` is the power of the binomial `(a-2b)` which is `4`.

Also, `r` is the last term of `(a-2b)⁴` which is `4` and `n-r` is equal to the first term of `(a-2b)⁴` which is `0`.

The formula for the `r`th term of the binomial expansion

(a+b)^n` is `(nCr)*(a^(n-r))*(b^r)`.

This means that if the binomial expansion is `(a-2b)^4`, then the last term would be

`(4C4)*(a^(4-4))*(2b)^4`.

Simplifying `(4C4)` gives `1`, and `2^4` gives `16`.

Therefore, the last term of `(a-2b)^4` is `a^4`.

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The charge on the K+ ion is 1.6 × 10⁻¹⁹ C. This can be calculated using the force and electric field strength, which are related to the mass and acceleration of the ion.

The mass and acceleration of a K+ ion are given as 6.5 × 10⁻²³ kg and 1.7 × 10⁶ m/s², respectively.

To calculate the charge on the K+ ion, we need to use the formula:

F = ma

Where F is the force, m is the mass, and a is the acceleration.

We can rearrange the formula to solve for the force:

F = ma

F = (6.5 × 10⁻²³ kg) × (1.7 × 10⁶ m/s²)

F = 1.105 × 10⁻¹⁶ N

Next, we can use another formula to calculate the charge on the K+ ion:

F = qE

Where F is the force, q is the charge, and E is the electric field strength. We can rearrange the formula to solve for the charge:

q = F/E

We are given the acceleration of the K+ ion, which we can use to find the electric field strength:

E = a/q

We can substitute the value of acceleration a = 1.7 × 10⁶ m/s² and solve for the electric field strength:

E = a/q

q = a/E

Mass of K+ ion m = 6.5 × 10⁻²³ kg

Acceleration a = 1.7 × 10⁶ m/s²

Charge on K+ ion q = 1.6 × 10⁻¹⁹ C

The charge on the K+ ion is 1.6 × 10⁻¹⁹ C. This can be calculated using the force and electric field strength, which are related to the mass and acceleration of the ion.

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Answer:

\(y=x+4\)

Hope This Helps! :) Please give Brainliest!

Refer to attachment below;

Answer:

The solution of 12x>9(2x-3)-15 is x>7.

Answer: y=5/4x+13

Step-by-step explanation:

Slope-intercept form:

y= mx+b

Where x and y are the points, m is the slope, and b is the y-intercept.

Plug in the points to find the y-intercept.

-5= 5/4(-8)+b

Solve.

-5= 2.25(-8)+b

Combine like terms.

-5=-18+b

Add 18 on both sides.

13= b

Now you have the y-intercept. Plug in every point except the x and y, because you wouldn't be able to graph it if you had just numbers. (not that you have to; that is just the correct form)

y=5/4x+13

(a) Isla's trading cards are 125% of Lily's trading cards.

(b) Lily's trading cards are 80% of Isla's trading cards.

Given that,

There are 225 trading cards and Lily has 180 trading cards.

To calculate the percentage of Isla's trading cards compared to Lily's,

We can use this formula:

⇒ Isla's trading cards / Lily's trading cards x 100%

Plugging in the values we get:

⇒ (225 / 180) x 100% = 125%

Therefore,

Isla's trading cards are 125% of Lily's trading cards.

b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:

⇒ Lily's trading cards / Isla's trading cards x 100%

Plugging in the values we get:

(180 / 225) x 100% = 80%

Therefore,

Lily's trading cards are 80% of Isla's trading cards.

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Answer:

x=-1 or 5 or 2

Step-by-step explanation:

x³-6x²+3x+10=0

(x+1)(x-5)(x-2)=0

x+1=0 ⇒ x=-1

x-5=0 ⇒x=5

x-2=0 ⇒ x=2

Answer:

To find the unit price of bananas, we need to divide the total price by the number of bananas.

Unit price = Total price / Number of bananas

In this case, the total price is $3.20 and the number of bananas is 4.

Unit price = $3.20 / 4

Unit price = $0.80

So the unit price of bananas in this grocery store is $0.80 per banana.

Answer:

3

Step-by-step explanation:

3

Answer:

4

Step-by-step explanation:

7.185629 x 102985 =   740,012.002565 which has 4 zeros

Answer:

m=−37

Step-by-step explanation:

34 = -3 + -1m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add 'm' to each side of the equation.

34 + m = -3 + -1m + m

Combine like terms: -1m + m = 0

34 + m = -3 + 0

34 + m = -3

Add '-34' to each side of the equation.

34 + -34 + m = -3 + -34

Combine like terms: 34 + -34 = 0

0 + m = -3 + -34

m = -3 + -34

Combine like terms: -3 + -34 = -37

m = -37

Answer:

Sample Response:

The negative sign outside the parentheses represents –1. Distribute the –1 to everything inside the parenthesis. Use the addition property of equality first to add 3 to both sides. Then use the division property of equality to divide both sides by -1.

The number of subjects who experienced only one effect is between 75 and 100.

Let A, B, and C be the events that a subject experiences sweaty palms, vomiting, and dizziness, respectively. We are given

P(A) = 0.4

P(B) = 0.3

P(C) = 0.75

P(A ∪ B ∪ C) = 1 (since all subjects experienced at least one effect)

P(A ∩ B) = P(A ∩ C) = P(B ∩ C) = 0.35 (since 35% experienced exactly two effects)

We want to find P(exactly one effect). We can use the principle of inclusion-exclusion

P(exactly one effect) = P(A) + P(B) + P(C) - 2P(A ∩ B) - 2P(A ∩ C) - 2P(B ∩ C) + 3P(A ∩ B ∩ C)

Note that we subtract 2 times the probabilities of the intersections of two events because we counted them twice (once in each of the three terms we added) and we add 3 times the probability of the intersection of all three events because we subtracted it three times in the previous terms.

Substituting the given probabilities, we get

P(exactly one effect) = 0.4 + 0.3 + 0.75 - 2(0.35) - 2(0.35) - 2(0.35) + 3P(A ∩ B ∩ C)

P(exactly one effect) = 0.2 + 0.15 + 0.45 + 0.45 - 1.05 + 3P(A ∩ B ∩ C)

P(exactly one effect) = 0.2 + 0.6 - 1.05 + 3P(A ∩ B ∩ C)

P(exactly one effect) = -0.25 + 3P(A ∩ B ∩ C)

We know that the probability of any event is between 0 and 1, so the probability of exactly one effect must also be between 0 and 1. Therefore, we can write

0 ≤ P(exactly one effect) ≤ 1

0 ≤ -0.25 + 3P(A ∩ B ∩ C) ≤ 1

0.25/3 ≤ P(A ∩ B ∩ C) ≤ 1/3

Thus, the probability of exactly one effect is between 0.0833 (which is 0.25/3) and 0.3333 (which is 1/3). We don't know exactly what it is, but we can say that the number of subjects who experienced exactly one effect is between 25% and 33.33% of the total number of subjects (which is 300). Therefore, the number of subjects who experienced only one effect is between 75 and 100.

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Residual Plot A indicates that the linear model is not appropriate because the fanned pattern shows that the model's predicting power decreases as the values of the explanatory variable increases. Residual Plot B indicates that the linear model is appropriate because the scattered residuals suggest a linear relationship.

Residual Plot A shows a fanned pattern which indicates that the linear model is not appropriate. This means that the model's predicting power decreases as the values of the explanatory variable increases. This suggests that the relationship between the dependent and independent variables is not linear and a different model may be necessary. Residual Plot B, on the other hand, shows a scattered pattern which suggests that the linear model is appropriate. The scattered pattern indicates that the data points are randomly distributed, which is a sign of a linear relationship. This indicates that the linear model is an appropriate fit for the data.

the complete question is :

Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

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In 3.5 seconds the tire covered a distance of 2927.74 inches.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A wheel is 18 inches in diameter and the wheel turns at a constant rate of 14.8 rev/sec.

So, the radius is (18/2) = 9 inches.

Therefore the distance around the circle is 2π(9) inches.

= 6.52 inches.

So, In per second, the tire covers a distance of (6.52×14.8) inches.

= 836.50 inches.

Therefore in 3.5 seconds, the tire covers a distance of (836.5×3.5) inches.

= 2927.74 inches.

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Answer:

9

Step-by-step explanation:

I need to write 20 characters

Answer:

i believe its 5/10 or 1/2

Step-by-step explanation:

73² - 27² = 5329 - 729

= 4600

your welcome. Mark Me Brainliest

Answer:

Add 12+18= 30

Well the largest group could be in 6's.

They all can be split up to 6 groups, so each group will have 5 kids in it.

9. In the provided prism of volume 80 cm³, the value of w is 2 cm.

10. The value of y in the cylinder, rounded to the nearest hundred, is

1100 ft.

9. The prism stands 8 centimetres tall, with a base width of w and a length of 5 cm. As a result, the base region is B = lw = 5w.

Substituting the given values, we get:

V = Bh

80 = 5w × 8

80 = 40w

Dividing both sides by 40, we get:

w = 2

10. Volume is the quantity of space covered by a three-dimensional object. This is the amount of three-dimensional space enclosed by a closed surface or boundary. 

Volume is usually measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

Formula of volume of a cylinder is:

\(V = \pi r^2h\)

In this case, we are given that the radius is 9.3 ft and the volume is 3000 cubic ft. So we can put these numbers into the equation and find the height.

\(3000=\pi(9.3)^2\ h\)

Simplifying:

3000 = 271.71h

Dividing both sides by 271.71:

h = 11.04

Rounding to the nearest hundred, we get:

y = 1100 ft

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The test that will allow you to analyze the differences in blood pressure between groups, after adjusting for age is the one way ANOVA test.

One-way analysis of variance is a statistical approach that can be used to determine if the means of two samples are substantially different or not. One-way ANOVA ("analysis of variance") examines the means of two or more independent groups to see if there is statistical evidence that the related population means differ significantly.

One-way ANOVA is commonly employed when there is a single independent variable, or factor, and the purpose is to determine whether fluctuations or various amounts of that factor have a measurable effect on a dependent variable. This van be used to illustrate the relationship.

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The present value of the payments is smaller than the amount of the loan, so you will not be able to pay off the loan.

The present value of the payments refers to the current value of the future payments, considering the time value of money. In this case, the payments are made over a period of 8 months, and each payment is listed. To determine if the payments will be enough to pay off the credit card, we need to calculate the present value of these payments and compare it to the initial loan amount of $5,000.

Since the interest rate on the credit card is 1.5% per month, we need to discount each payment back to its present value. By discounting the payments, we can see the equivalent value of these payments in today's dollars. If the present value of the payments is equal to or greater than $5,000, it would be enough to pay off the loan. However, if the present value is smaller than $5,000, it means the payments will not be sufficient to pay off the loan.

In this case, without specific information about the discount rate used to calculate the present value, we cannot make an exact determination. However, based on the given information, which states that the present value of the payments is smaller than the amount of the loan, it suggests that the payments will not be enough to pay off the credit card debt.

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To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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a. The first step we take to solve the radical equation is adding x to both sides.

b. The next step is to square both sides.

c. Solving the equation for x yields x = 0 or x = 16

d. Checking the solution, shows that it is correct.

A radical equation is an equation that contains a root.

Given the radical equation \(4x^{\frac{1}{2} } - x = 0\). To sove this, we proceed as follows.

a. The first step we take to solve the equation is adding x to both sides.

So, we have that

\(4x^{\frac{1}{2} } - x = 0\)

\(4x^{\frac{1}{2} } - x + x= 0 + x\\4x^{\frac{1}{2} } - 0= x\\4x^{\frac{1}{2} } = x\)

b. The next step is to square both sides. So, we have that

\(4x^{\frac{1}{2} } = x\\(4x^{\frac{1}{2} } )^{2} = x^{2} \\16x = x^{2}\)

c. The next step is to subtract 16x from both sides. So, we have that

16x = x²

16x - 16x = x² - 16x

0 = x² - 16x

x² - 16x = 0

Factorizing to solve for x, we have that

x² - 16x = 0

x(x - 16) = 0

x =0 or x - 16 = 0

x = 0 or x = 16

Solving the equation for x yields x = 0 or x = 16

d. Next, we check the solution.

So, when x = 0

\(4x^{\frac{1}{2} } - x = 0\\4(0)^{\frac{1}{2} } - 0 = 0\\4(0) - 0 = 0\\0 - 0 = 0\\0 = 0\)

When x = 16

\(4x^{\frac{1}{2} } - x = 0\\4(16)^{\frac{1}{2} } - 16 = 0\\4(4) - 16 = 0\\16 - 16 = 0\\0 = 0\)

Checking the solution, we see that it is correct.

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Answer:

Step-by-step explanation:

lets say that event A will not occur is lets suppose =x

so A will not occur will be = 5x

probability of A = 5x / (5x + x)

A= 5x/ 6x

A= 5/6 Ans

Answer:

B.

Fran's account balance > Zach's account balance

Step-by-step explanation:

Its speed is closest to 414m/s

given that

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in metres (m), centimetres (cm), or millimetres (mm) (mm). The wavelength is more frequently described in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (UV), and gamma radiation ().

Frequency, which is defined as the quantity of wave cycles per second, and wavelength have an inverse relationship. The wavelength of the signal decreases with increasing signal frequency.

a wave has a wavelength = 25.4cm

a frequency = 1.63khz

now, we need to find speed of the wave

speed = wavelength × frequency

speed = 25.4 × 16.3

           = 414m/s

speed = 414m/s

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