5. 5. Write the first equation in polar form and the second one in Cartesian coordinates. a. x + y = 2 b. r= -4sino

Answer:

\(5 \sqrt{3} \)

Step-by-step explanation:

Frist find which perfect square goes into 75. In this case its 25 * 3. You then find out what is the square root of 25. Which is 5. you put that number outside the radical and the other number inside the radical. resulting in 5 square roots of 3.

Answer: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

5√3

Decimal Form:

8.66025403…

Hey there! I'm happy to help!

We want to get m all by itself on one side of the equation. To do this, we use inverse operations on both sides of the equation to cancel out variables on one side to isolate m.

am/c=n

We multiply both sides by c.

am=nc

We divide both sides by a.

m=(nc)/a

I hope that this helps! Have a wonderful day! :D

Answer:

Their weights are:

Dorris = 5 lbs

Borris = 7 lbs

Morris = 9 lbs

Step-by-step explanation:

Let the weights of the frogs be:

Dorris = d

Borris = b

Morris = m

given:

d + b = 12 - - - (1)

b + m = 16 - - - (2)

d + m = 14 - - - (3)

from (3)

d + m = 14

m = 14 - d - - - (4)

putting the value of m into equation 2:

b + m = 16

b + (14 - d) = 16

b - d + 14 = 16

b - d = 16 - 14

b - d = 2

b = 2 + d - - - - (5)

putting the value of 'b' in equation 5 into equation (1)

d + b = 12 - - - (1)

where: b = 2 + d - - -  (5)

∴ d + (2 + d ) = 12

d + d + 2 = 12

2d = 12 - 2

2d = 10

∴ d = 10 ÷ 2 = 5

d = 5

putting the value of 'd' into eqn (5)

b = 2 + d - - - - (5)

where d = 5

b = 2 + 5 = 7

b = 7 lbs

to find 'm', let us use eqn (3)

d + m = 14 - - - (3)

where d = 5

∴ 5 + m = 14

m = 14 - 5 = 9

m = 9 lbs

Therefore their weights are:

Dorris = 5 lbs

Borris = 7 lbs

Morris = 9 lbs

Prochlorperazine is a dopamine receptor antagonist that is commonly used as an antiemetic to treat nausea and vomiting caused by various conditions.

The prototype antiemetic is a medication called prochlorperazine. Prochlorperazine belongs to a class of drugs known as phenothiazines, which are known to have antiemetic properties. It is commonly used to treat nausea and vomiting caused by various conditions, including motion sickness, chemotherapy, and postoperative nausea and vomiting. While prochlorperazine is often considered the prototype antiemetic, there are many other medications that can also be effective in treating nausea and vomiting, including ondansetron, metoclopramide, and promethazine, among others. The choice of antiemetic medication will depend on the underlying cause of the nausea and vomiting, as well as other individual patient factors.

Prochlorperazine works by blocking dopamine receptors in the brain, which can help to reduce nausea and vomiting. It is available in several forms, including tablets, suppositories, and injections, and can be prescribed by a healthcare provider.

The prototype antiemetic is dopamine antagonist, which works by blocking dopamine receptors in the brain. This reduces the activity of the chemoreceptor trigger zone (CTZ), which in turn reduces the signals sent to the vomiting center in the medulla oblongata, ultimately resulting in decreased nausea and vomiting. The chemical equation for this interaction can be represented as:

Dopamine antagonist + Dopamine receptor → Blocked dopamine receptor

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Given statement "f the null hypothesis is correct, the probability of getting a sample mean greater than $189,500 is .0668" is true. Because, It's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.

The null hypothesis is a general statement that there is no significant effect or difference between the considered groups or variables.

In this case, the null hypothesis would be that the true mean valuation of homes is equal to or less than $189,500.
The probability of 0.0668, mentioned in the question, represents the likelihood of getting a sample mean greater than $189,500 if the null hypothesis is true.

In other words, it's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.

This probability (0.0668) is also known as the p-value.

The p-value helps to determine the significance of the results.

If the p-value is less than a predetermined significance level (usually 0.05), the null hypothesis is rejected in favor of the alternative hypothesis.
In this case, the p-value of 0.0668 is higher than the common significance level of 0.05.

We cannot reject the null hypothesis, meaning the probability of getting a sample mean greater than $189,500 is indeed 0.0668 if the null hypothesis is correct

Hence, the statement is true.
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1st

\(1 \sqrt{18} \)

2nd

\( 1\sqrt[1]{18} \)

3rd (Can't use the symbols this time)

1 1^sqrt18

1

4th

\( 1\sqrt[1]{18} \)

\( - \frac{1}{0} \)

5th

\( 1\sqrt[1]{18} \)

\( - \frac{1}{08} \)

6th

\( 1\sqrt[18]{18} \)

\( - \frac{1}{08} \)

7th

\(1 \sqrt[18]{18} \)

\( - \frac{1}{08} \)

8

8th

\(1 \sqrt[18]{18} \)

\( - \frac{1}{08} \)

\( \frac{8}{0} \)

Your done because there's no more digits to move down to divide therefore your answer is just 18. And there's 0 remainders. And that's how you do it long division.

Answer:

p=(-0.0125n) + 42.5

Step-by-step explanation:

Let p= price

n = number of shirts

m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

There are two points which are (1000, $30) and (3000, $5)

Our slope m = (p1-p2)/(n1-n2)

Filling in from our points m = (30-5)/(1000-3000)

m = 25/-2000

m = -0.0125

Since we have determined our slope, we can now find our equation

p-p1=m(n-n1)

p-30=(-0.0125)(n-1000)

p-30= (-0.0125n) + 12.5

p=(-0.0125n) + 42.5

Then, we can double check with the other point there:

p=(-0.0125n) + 42.5

5? (-0.0125x 3000) + 42.5

5= 5

Therefore,linear equation in the form p(n) is

p=(-0.0125n) + 42.5

Answer:

X = 3   Y = -3

Step-by-step explanation:

The arrow is on X = 3 and the other side of arrow is on Y = -3

Hope I helped

Answer:

12

Step-by-step explanation:

that is because 20 of 60 is 12

60X20/100=12

Answer:

C. Some input values are integers

Step-by-step explanation:

Answer:

313.5 feet cubed

Step-by-step explanation:

A = a+b /2 (h)

14+24/2(16.5)

38/2 (16.5)

= 313.5

The probability that the dart lands inside the triangle is \(\frac{1}{4}\).

we know that

Probability = \(\frac{Favourable outcomes}{total outcomes}\)

Probability = \(\frac{162}{648} = \frac{1}{4}\)

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Answer:

25%.

Step-by-step explanation:

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Answer:

3!

Step-by-step explanation:

Answer:

Y = -3x - 1

Step-by-step explanation:

Y= mx + b

M is the slope

Y is the y intercept

Answer:

the negative reciprocal is -17/20

Answer:

17/20

Step-by-step explanation:

i hope this helps u

Answer:

B. Intersecting

Step-by-step explanation:

If you were to extend the lines, they would cross eachother

The given lines are intersecting.

When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection.

As, from the figure we can see that the line p and q are not parallel to each other because the distance between them is not constant.

Now, the lines are not either skew or perpendicular.

If we extend the lines p and q then will meet at some point which is know as intersecting lines.

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The value of function at x = - 2 is, 4

The value of function at x = 0 is, 6

The value of function at x = 5 is, 11

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function is,

⇒ f (x) = x + 6

Now, Substitute x = -2 in above equation,

⇒ f (x) = x + 6

⇒ f (-2) = -2 + 6

⇒ f (-2) = 4

Substitute x = 0 in above equation,

⇒ f (x) = x + 6

⇒ f (0) = 0 + 6

⇒ f (0) = 6

Substitute x = 5 in above equation,

⇒ f (x) = x + 6

⇒ f (5) = 5 + 6

⇒ f (5) = 11

Thus, The value of function at x = - 2 is, 4

The value of function at x = 0 is, 6

The value of function at x = 5 is, 11

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x=3 , 8

remember the square of a binomyal

Step 1

given

we need to isolate x, so

a) rise each side to power 2

Step 2

solve the quadratic equation:

b) use the quadratic formula

so

i)let

ii) now, replace in the formula

therefore, the solutions are x= 3 and x= 8

so, the answer is

x=3 , 8

I hope this helps you

The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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Answer:

\( \purple {\bold {m\angle PTR=136\degree}} \)

\( \orange {\bold {m\angle PQR=68\degree}}\)

Step-by-step explanation:

PS and RS are tangents to the circle with center T at points P and R. (given)

TP and TR are radii of the given circle.

\( \therefore PS\perp TP\: \&\: RS\perp TR\)

(radius is perpendicular to the tangent)

\( \therefore m\angle TPQ= m\angle TRS =90\degree \)

In quadrilateral SPTR

\( m\angle TPQ+ m\angle TRS+m\angle PSR +m\angle PTR=360\degree \)

\( 90\degree+ 90\degree+44\degree +m\angle PTR=360\degree \)

\( 224\degree +m\angle PTR=360\degree \)

\( m\angle PTR=360\degree - 224\degree\)

\( \purple {\bold {m\angle PTR=136\degree}} \)

By inscribed angle theorem:

\( m\angle PQR=\frac{1}{2} \times m\angle PTR\)

\( m\angle PQR=\frac{1}{2} \times 136\degree\)

\( \orange {\bold {m\angle PQR=68\degree}}\)

Answer:

286.333

Step-by-step explanation:

Find it doing long division...

Answer:

x=1

Step-by-step explanation:

3x=4-1

3x=3

x=1

A standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

The probability is calculated by dividing the total number of outcomes by the total number of events.

Odds and probability are two different concepts.

Divide the probability of an event occurring by the probability that it won't happen to calculate chances.

The four main types of probability that mathematicians study are axiomatic, classical, empirical, and subjective.

So, the probability that a standard normal random variable will occur with a probability ranging from 0.3 to 3.2 must therefore be calculated.

First, a mean and standard deviation are introduced for a standard normal random variable.

The probability that a standard normal random variable will fall between 0.3 and 3.2 needs to be calculated.

Therefore, it should be more likely that:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using the usual value of z:

P(0.3<z<3.2)=0.9993−0.6179

Justify by saying:

P(0.3<z<3.2)=0.3814

Therefore, a standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

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Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.

A relationship between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. Different inequalities are employed to contrast values of all sizes. By changing the two sides until only the variables are left, one can solve many straightforward inequalities. But a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.

given

the inequality for x 1/3 x - 3 -1 5/6 must first be resolved.

2 plus 3 on both sides

Simply multiply both sides of 1/3x by 3x31/2,

and then graph x31/2 on a number line.

Turn left and continue past the finish line after starting at 3.5 on the number line. Simply plot x=3 1/2 on a number line.

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By applying the binomial distribution formula, it can be concluded that the probability that the sample contains exactly two defective parts is 0.015.

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

C(n,r) = n! / (r! (n-r)!) where

n = number of samples

r = number of selected samples

The binomial distribution formula is used to find the probability of the specific outcome in a discrete distribution.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\) where:

C = combination value

p = probability of success on a single trial

q = probability of failure on a single trial

The probability of defective parts, p = 2% = 0.02

If q is the probability of parts with no defects, then:

q =  1 - 0.02

  = 0.98

We also have n = 10 and r = 2

Using the binomial distribution formula, we can calculate the probability that the sample contains exactly two defective parts.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\)

       = C(10,2) * \(0.02^{2}\) * \(0.98^{10-2}\)

       = 10! / (2! 8!) * 0.0004 *

       = 45 * 0.0004 * 0.85076302258

       = 0.0153137344

       ≈ 0.015

Thus, the probability that the sample contains exactly two defective parts is 0.015.

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The set S is a vector space.

To determine if S is a vector space, we need to check if it satisfies the ten properties of a vector space.

1. The zero vector exists: In this case, the zero vector would be the function y(x) = 0, which satisfies the differential equation y'' + 2y' - y = 0, since the derivative of the zero function is also zero.

2. Closure under addition: If f(x) and g(x) are both functions satisfying the differential equation y'' + 2y' - y = sin(x), then their sum h(x) = f(x) + g(x) also satisfies the same differential equation. This can be verified by taking the second derivative of h(x), multiplying by 2, and subtracting h(x) to check if it equals sin(x).

3. Closure under scalar multiplication: If f(x) is a function satisfying the differential equation y'' + 2y' - y = sin(x), and c is a scalar, then the function g(x) = c * f(x) also satisfies the same differential equation. This can be verified by taking the second derivative of g(x), multiplying by 2, and subtracting g(x) to check if it equals sin(x).

4. Associativity of addition: (f(x) + g(x)) + h(x) = f(x) + (g(x) + h(x))

5. Commutativity of addition: f(x) + g(x) = g(x) + f(x)

6. Additive identity: There exists a function 0(x) such that f(x) + 0(x) = f(x) for all functions f(x) satisfying the differential equation.

7. Additive inverse: For every function f(x) satisfying the differential equation, there exists a function -f(x) such that f(x) + (-f(x)) = 0(x).

8. Distributivity of scalar multiplication over vector addition: c * (f(x) + g(x)) = c * f(x) + c * g(x)

9. Distributivity of scalar multiplication over scalar addition: (c + d) * f(x) = c * f(x) + d * f(x)

10. Scalar multiplication identity: 1 * f(x) = f(x)

By verifying that all these properties hold, we can conclude that the set S is indeed a vector space.

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