find the slope of the line tangent to the polar curve at the given point. r= 3 sin theta (3/2, pi/6)

Answer:

A clockwise rotation of 90° about the origin

Answer:

the perimeter is 25 miles

Answer:

30 mi

Step-by-step explanation:

This is a right triangle, so the Pythagorean Theorem applies:

13^2 + x^2 = 12^2, or

x^2 = 25 and x = 5.

The perimeter is the sum of the dimensions of this triangle:  

12 mi + 5 mi + 13 mi = 30 mi

If this claim is true then one percent of response times take at least \(38.077\) minutes.

In the given question,

A fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes.

We have to assuming that the claim is true and finding that one percent of response times take at least how many minutes.

From the question,

Mean \(\mu=22\) minutes

Standard deviation \(\sigma=6.9\) minutes.

Since the given percentage is \(1\%\) and percentage means division of \(100\) so we can write \(1\%=1/100=0.01\)

So the one percent of response times take at least how many minutes is

\(P(x\geq a)=0.01\)

\(P(x\geq \frac{a-\mu}{\sigma})=0.01\)

As we know the all values. SO putting the values in the formula

\(P(x\geq \frac{a-22}{6.9})=0.01\dots\dots\)Equation 1

From the z table

\(P(z\geq 2.33)=0.01\dots\dots\)Equation 2

Now from Equation 1 and Equation 2

\(\frac{a-22}{6.9}=2.33\)

Multiply by \(6.9\) on both side

\(\frac{a-22}{6.9}\times6.9=2.33\times6.9\)

Simplifying

\(a-22=2.33\times6.9\)

\(a-22=16.077\)

Add \(22\) on both side

\(a-22+22=16.077+22\)

\(a=38.077\)

Hence, if this claim is true then one percent of response times take at least \(38.077\) minutes.

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Answer: X= -8

Step-by-step explanation:

Rearrange your terms:

5-X=13

-x+5+13

Subtract 5 from both sides

Simplify those = -X = 8

Dive both sides by same factor, -1

Simplify again

Solution= X= -8

Answer:

There is no x intercept

Step-by-step explanation:

Answer:

no x intercept

Step-by-step explanation:

it is parallel with the x axis. They will never touch

The length of line AX is 3p/4q.

The length of side AY is  9p²/4q + 3p/4.

The length of line AX is calculated as follows;

From the given figure, we can apply the principle of congruent sides of the parallellogram.

AD/DC = CX/AX

8q/6p = 1/AX

AX = 6p/8q

AX = 3p/4q

The length of side AY is calculated by applying the following formula as shown below.

Apply similar principle of congruent sides;

AX/CX = AY/CY

3p/4q / 1 = AY/(3p + q)

AY = 3p/4q(3p + q)

AY = 9p²/4q + 3p/4

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Answer:

Gradient: 5

y-intercept: (0, 15)

Step-by-step explanation:

The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.

Answer:

157/270

Step-by-step explanation:

Answer:

10.8

10.8

33.9

Step-by-step explanation:

Answer:

the ratio is 1/2

Step-by-step explanation:

because each number is times 2

Answer:

0.5   or    1/2

Step-by-step explanation:

plz mark as brainliest

since every inch, is 2 gallons

Answer:

(2x+3) (2x+3) so A

Step-by-step explanation:

Hope this helps have a great day:)

Answer:

Step-by-step explanation:

poop

Answer:

140, 60

Step-by-step explanation:

15x+5 + < CDB =180 line form an 180 angle

180-80-6x-6 = < CDB sum of angles in a triangle is 180

substitute < CDB from second to first

15x+5+180 -80-6x-6 =180

combine like terms

9x -81 =0

x=81/9=9

so angle YDC = 15*9+5 = 140 degrees

and angle DBC = 6*9+6= 60 degrees

Answer:

x = 14

BE = 6

Step-by-step explanation:

to find 'x':  BG = 1/2[(x-9) + (3x-13)]

BG = 4x-22 / 2

BG = 3x-25

3x-25 / 1 = 4x-22 / 2

cross-multiply:

4x-22 = 2(3x-25)

4x-22 = 6x-50

-2x = -28

x = 14

to find 'BE':  CB = BE

2x+4 = 7x-1

-5x = -5

x = 1

BE = 7(1) - 1

BE = 6

Answer:

B) 5

Step-by-step explanation:

They have a total of 4+8+3+5 = 20 bracelets

There is 4 girls

20/4 = 5

Answer:

C

Step-by-step explanation:

Let d = the distance from camp

d < 1.8 + 2.6 = 6.4    

d > 2.8

so 2.8 < d < 6.4,  therefore d could be 5.3

Answer:

I got a, so sorry if I'm wrong. math isnt my strongest subject. if I am right please mark brainliest

If d represents how many dozens of eggs were ordered, then the expression that represents the number of eggs that were ordered is 12d. Therefore, if we order d dozen of eggs, we will have 12 * d eggs.

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Answer: A cylindrical water storage tank has an inside base radius of 7m and depth of 11 m. ... Let the depth of the tank be h metres.

Step-by-step explanation:

Answer:

the radius is 10 m apprx

Step-by-step explanation:

height of the cylinder = \(\pi r^{2} h\) = 4082 \(m^3\)

then \(r^{2}= \frac{4082}{13\pi } = 99.9493\)

r= \(\sqrt{99.9493}\) =10.0 m

A paired-test can be used to check if the two blood pressure taken from 2 groups,one group having normal blood pressure another having white coat hypertension differ or not.

A paired t-test is used to determine whether two sample means are equal or not. White coat hypertension occurs when a person's blood pressure rises when they are in a medical setting.

To assess whether the two blood pressure measurements differ, a paired t-test should be used. The paired t-test is used to compare two dependent samples that are connected in some manner. A random sample of 50 patients should be taken to see if the two blood pressures differ. Here are the steps for conducting a paired t-test:

- State the null and alternative hypotheses.
- Calculate the difference between the two groups of data.
- Calculate the sample mean, sample standard deviation, and sample size.
- Use the t-distribution to determine the critical value.
- Compute the test statistic.
- Determine the p-value.
- Make a decision.

It is worth noting that in order to use the paired t-test, the data must be normally distributed. Additionally, this test can be performed on a one-tailed or two-tailed basis, depending on the hypothesis test. F-distribution is not used in a paired t-test.

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Answer:

Step-by-step explanation:

i just put the numbers in X

for example

g(x) = 5 - 2(0)

g(x)= 5- 2(2)

g(x)= 5-2 (8)

Hope this helps!! :)

good luck you got this

The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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2/5 of an hour long will they take to mow the lawn together.

Additive identity is the value when added to a number, results in the original number. When we add 0 to any real number, we get the same real number. For example, 5 + 0 = 5. Therefore, 0 is the additive identity of any real number.

This is easy to do when you realize the the speed of mowing is additive. This is if John mows at 1 lawn / (2/3) hour and George mows at 1 lawn /  1hour, the total speed of mowing is:

1 / (2/3) + 1 = 3/2 + 1 = 5/2

=> 5/2 of lawn per hour

Now, the time is calculated as the amount of lawn divided by the speed:

1 lawn / (5/2 lawn/hour) = 2/5 hour

2/5 of an hour.

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The given question is incomplete, complete question is;

If Jorge can mow the lawn in 2/3 of an hour and George can mow the lawn in 1 hour, how long will they take to mow the lawn together? 2/5 of an hour 3/5 of an hour 3/4 of an hour

Answer:

Answer: \(12\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

20 is one third of a number:   (1/3)X = 20

                                                            X = 60

But then I can't interpret ". . . the result is the double of the number."

This may or may not mean 2*(60) = 120

Answer:

x=(2×4)-(4×2)

Step-by-step explanation:

The difference will be a number so we call it x. Subtract is represented as - in an expression. Thus the answer x=(2×4)-(4×2)

The pharmacist is left with 2100 ml(milliliter) of cough syrup.

According to the question,

Pharmacists have 3.6 L(liter) of cough syrup.

1 L = 1000 ml (Given)

Therefore, 3.6 L = 3.6 x 1000

                           = 3600 ml

It’s given in the question that the pharmacist fills a 1500 ml bottle with cough syrup.

To find the quantity of cough syrup left with the pharmacist, we will subtract the quantity of bottle from the total quantity of cough syrup.

Cough syrup left with her after filling the bottle = 3600 – 1500

                                                                              = 2100 ml

Hence, she is left with 2100 ml of cough syrup after filling up a bottle of 1500 ml quantity.

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a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Answer:

Step-by-step explanation:

Sandra, Deacon, and Breanna read a total of 5 + 6 + 7 = 18 books. Since one book was read by all three children, we need to subtract it once from the total. Therefore, they read 18 - 1 = 17 different books.

Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes, leaving 8 - 2 = 6 test tubes for the other two experiments. Since the two experiments required the same number of test tubes, each one required 6/2 = 3 test tubes.

It is unclear what the question is asking. Please provide more information or a specific question.

Branson and his sister Beatrice combined their allowance of $7 each to buy a movie for $12. They spent a total of 7 x 2 = $14 on the movie. Therefore, they had 14 - 12 = $2 left to buy fruit salad. They bought 2 containers of fruit salad for $1 each, leaving them with $0. They split the containers evenly between them, so each of them got 2/2 = 1 container of fruit salad.

Before Cam broke his right arm, he could type 9 words per minute on his phone. After he broke his arm, he could only type 6 words per minute. The difference between the number of words he could type in 5 minutes before and after he broke his arm is 5 x (9 - 6) = 5 x 3 = 15 words.

Gisselle saved $6 every week for 8 weeks, so she saved a total of 6 x 8 = $48. She found a used bicycle for $50, so she did not have exactly enough for the bicycle. She was $50 - $48 = $2 short.

Answer:

43°

Step-by-step explanation:

-the interior angle of a triangle always adds up to 180°

- angles that form a straight line always adds up to 180°

- the angle at 75° has the angle of 105° to add up to 180°

- the triangle needs a full degree of 180, but only affs up to 137° (105° + 32°) so you have to subtract the 137° from the total amount you need(180°) which gives you the answer of 43°

Answer:

Step-by-step explanation:

it cant be 73° then it would look about the same size as 75°

and it cant be 15° cause it would look smaller than 32°.

so in my Opinion it looks like it would be 43°.

sorry if its wrong

Answer:

therefore the summ of integers from 1 to 50 is 1275