At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6 (doughnuts)2 , respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P ? 1.5(3.6) 1.5(3.6) A 1.53.6−−−√ 1.53.6 B 1.5(3.6)−−−−−−√ 1.5(3.6) C 1.5(2.6) 1.5(2.6) D 1.52.6−−−√ 1.52.6 E

Answer: -16

Step-by-step explanation:

The distance away from zero is 16 and -16 is negative + do u do rsm

The value of a, b and c are found as 6, 10 and 2 respectively.

Values for exponents, commonly referred to as powers, indicate how many often to multiply a quantity by itself.

The given expression is;

\(4x^{8} y^{c} = \frac{24x^{b}y^{-3} }{ax^{2} y^{-5} }\)

Solving expression using the law of indices.

\(x^{8} y^{c} = \frac{6x^{b-2}y^{-3+5} }{a}\)

\(ax^{8} y^{c} = {6x^{b-2}y^{2} }\)

Comparing powers of both sides:

a = 6

8 = b-2 : b = 10

c = 2

Thus, the value of  a, b and c are found as 6, 10 and 2 respectively.

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Answer:

x = 3

Step-by-step explanation:

Answer:

5.3x - 3.8y - 1.5

Answer:

(3.1x+2.2x)+(−2.4y+1.4y)+(1.9+3.4)

Step-by-step explanation:

I just did this problem :>

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:

the distance around the school track would be x

Step-by-step explanation:

you would have to divide 0.25 by 5.1 is 20.4

Answer:

The answer is 30%

Step-by-step explanation:

I believe this should work for an explanation :) Have fun!

By using a 3-simple rule, we will see that 30% of the science club is on the Spanish club.

First, we know that there are 18 girls and 12 boys in the science club, then there are 12 + 18 = 30 students on the science club, this will be the 100%.

30 = 100%.

And there are 4 girls and 5 boys in the Spanish club, then there are 4 + 5 = 9 students on the Spanish club, let's say that this number represents a percentage X.

9 = X

Then we have the equations:

30 = 100%

9 = X

To find the value of X, we can take the quotient of these two equations:

9/30 = X/100%

Solving for X, we get:

(9/30)*100% = X = 30%

Then we can conclude that 30% of the science club is in the Spanish club.

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Answer:

By using the formula of;

A² + B² = C²

Where A and B could be either of the 2 legs and C always have to be the hypotenuse of the right triangle. Hypotenuse is the longest leg of the triangle is the leg that's opposite to the right angle of the right triangle.

Hope this helps! I have attached a diagram for u to help you understand:

The missing values are

<UTQ = 41 degree

x= 1

<UQT = 47 degree

We have a parallelogram QRST.

We know that the opposite sides of the parallelogram is equal and parallel then

QR || ST

QT || SR

Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)

<UTQ = 41

Similarly, <UQT = <SRQ = 47

Now, RU = UT

2x + 1= 3

2x = 2

x= 1

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The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer: It’s 12 dogs

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. x=1

2.x=  -2

3. x=13

4. x= -17

5. x= -41

Answer:

look at the image :)

Step-by-step explanation:

Answer:

what is your problem?    

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

18Πin3

Step-by-step explanation:

Answer:

500,000

Step-by-step explanation:

2 · 10^15 = 2,000,000,000,000,000

4 · 10^9 = 4,000,000,000

2,000,000,000,000,000 divided by 4,000,000,000 = 500,000

Tip: When you're multiplying 10 to the power of any number, you can just add that amount of zeros to 1.

Example: 10^7

Answer: 10,000,000

There are seven zeros.

Hope I helped :)

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Answer:

Both plans cost the same when 50 texts are sent

Step-by-step explanation:

Both the plans cost the same amount $22.5 when 50 texts are sent:

\(20+0.05*50 = 10+0.25*50\)✔️

Have a nice day! :)

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Answer:

d

Step-by-step explanation:

multiply by 2 then subtract 1

2(25)-1=49

2(49)-1=97

2(97)-1=193

Answer: 9.46 grams

Step-by-step explanation:

Given: Number of muffins made in one batch = 1 dozen =12 ]

[ as 1 dozen = 12]

Also, in one batch the quantity of sugar = \(\dfrac14\) pound

As there are 454 grams of sugar in a pound.

So,  in one batch the quantity of sugar = \(\dfrac14\times454=113.5\ grams\)

i.e. in 12 muffins , there is 113.5 grams of sugar.

Then, in one muffin the quantity of sugar = (113.5 grams) ÷ 12

≈9.46 grams

Hence, there are 9.46 grams of sugar in 1 muffin.

24 days

1) Consider that Bob reads at a regular pace. So, we can write out a pair of ratios. Note that if Bob reads half of a 200 pages book so he does 100 pages in 4 days

2) So writing out a pair of ratios we have:

Now, we can cross multiply them:

Answer:

The equation of the line is 2x - 3y = 9

Step-by-step explanation:

Given:

Write the equation of a line that is parallel to the line 2x - 3y = 5 and passes through the point (3, -1)

Solve:

- The line is parallel to the line 2x - 3y = 5

⇒ the slope of the line = the slope of the line 2x - 3y = 5

- Rearrange the terms of the equation to be in the form

⇒  y = mx + c to find the slope of it

2x - 3y = 5 → subtract 2x from both sides

-3y = 5 - 2x ⇒ divide two sides by -3

y = 5/-3 - 2x/-3 ⇒ y = 2/3 x - 5/3

The slope of the line is 2/3

Given that: The line passes through point (3, -1)

Lets use the rule to find the equation of the line:

y - (-1)/x - 3 = 2/3

y + 1/x - 3 = 2/3 ⇒ by using cross multiplication

3(y + 1) = 2(x - 3) ⇒ open the brackets

3y + 3 = 2x -6 ⇒ put x and y on one side

2x - 3y = 3 + 6

2x - 3y = 9

The equation of the line is 2x - 3y = 9

~Kavinsky

Answer:

B. x is less than or equal to 5

Step-by-step explanation:

The dot is on 5 and is also a solid dot which means it is less than or equal to or greater than or equal to

In this case it is less than or equal to because the line goes to the left

Hope this helped!

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Answer: 4.5 looks the most reasonable to me.

Step-by-step explanation: