Find the area enclosed in the graph of
x² + y² 16x + 32y.

Answer:

5/9

Step-by-step explanation:

f(x) = 5 * 3^x

Let x = -2

f(-2) = 5 * 3^-2

We know a^-b = 1/a^b

     = 5 * 1/3^2

    = 5/9

F(-2) means the value of x is -2

Replace x with -2 and solve:

3^-2 = 1/9

5 x 1/9 = 5/9

Answer: D.5/9

always do the PEMDAS it helped me a lot in school

Answer:

P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960

Answer:

slope = 3/4

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Basically you have to divide 3.14 by 452.16 (the formula for area of circle is pi times r squared) and that will get you 144. The square root of 144 is 12 :)

Given:

There is a 65% chance you will make a free throw.

To find:

The percent of the time you will miss.

Solution:

If p is the percent of success and q is the percent of failure, then

[tex]p+q=100\%[/tex]

[tex]q=100\%-p[/tex]         ...(i)

It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss.  It means we have to find the percent of failure.

Substituting p=65% in (i), we get

[tex]q=100\%-65\%[/tex]

[tex]q=35\%[/tex]

Therefore, there is a 35% chance you will miss the free throw.

Answer : Four sides (1, 2, 3, 4) are less than 5. The probability is 4 out of 6, or 2/3 or 0.6667.

The solution is, the correct answer is B. comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

We will consider all the sets of probabilities, the one with the highest probability is the right answer.

a) You roll an odd number and roll a 5: the probability is calculated thus:

1/6 * 3/6

=0.0833

b) You land on an odd number or you roll a 6: the probability is calculated thus:

3/6 +1/6

= 0.6667

c) You roll a six and roll a 4: the probability is calculated thus:

1/6 * 1/4

= 0.0417

d) You roll a 3 and roll an old number: the probability is calculated thus:

1/6 * 3/6

=0.0833

Now, comparing all the probabilities, the set of independent events with the highest probability is the event of You land on an odd number or you roll a 6.

Therefore the correct answer is B.

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Answer:

3 sqrt(3) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 30 = x/6

6 cos 30 = x

6 ( sqrt(3)/2) = x

3 sqrt(3) =x

Answer:

38.6 cm

Step-by-step explanation:

add all of the sides up to get your perimeter

Answer:

x=3

Step-by-step explanation:

The ratios need to be the same

AB             CB

---------- = ----------

AD             ED

3           x

-----  = ---------

3+9       12

3           x

-----  = ---------

12          12

X must equal 3

Answer:

The answer is "There are [tex]97.5\%[/tex] of the students pass in the test ".

Step-by-step explanation:

Since a normally distributed random variable, the practical rule states:

About 68% of the metrics are in the 1 default deviation

About 95% of metrics correspond to 2 standard deviations from the average.

About 3 standard deviations of the average represent 99.7% of the measurement.

We have the following in this problem:

Average of 78, the average 9 default.

 Calculating the percentage of students that passed the test.

[tex]Above 60\\\\60 = 78 - 2\times 9[/tex]

Therefore 60 is under the average for two standard deviations.

Its normality test is symmetric, so 50% of such observations are below mean and 50% below mean.

Everything was cleared of the 50 percent above.

Of the 50% below, 95% (within 2 known mean deviations) succeeded.

therefore

[tex]p=0.5+0.5 \times 0.95=0.975[/tex]

Answer:

b.,............................

Step-by-step explanation:

correct answer.

The equation which is rewritten of [tex]log_{7}[/tex] (343) = 3 will be 7³ = 343 which means the option (B) will be correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

By log property of  [tex]log_{a}[/tex] b = x ⇒ [tex]a^{x}[/tex] = b

So  [tex]log_{7}[/tex] (343) = 3 ⇒ 7³ = 343 will be the correct answer to the question.

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Answer:

37 hours.

Step-by-step explanation:

Since you need $416.25 start with that. Then divide by $11.25 to see how many hours you need to work. 416.25 divided by 11.25 is 37.

Answer:

[tex](a)\ \frac{dP}{dt} = kP + r[/tex]

[tex](b)\ \frac{dP}{dt} = kP - r[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = kP[/tex]

Solving (a): Differential equation for immigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP + r[/tex]

Solving (b): Differential equation for emigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP - r[/tex]

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

Answer:

82991 employees

Step-by-step explanation:

One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that

28300 = 34.1%

If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get

829.912 = 1%

Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get

100% = 82991

9514 1404 393

Answer:

  220

Step-by-step explanation:

When the relationship is proportional, there are several ways you can find missing values. One of them is to recognize the distance for 4 hours will be double the distance for 2 hours.

  2 hours : 110 miles

  4 hours : 2×110 miles = 220 miles

Answer:

The Hong Kong dollar equivalent of K70 is HK $ 94.71.

Step-by-step explanation:

Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:

1,353 x 70 = X

94.71 = X

Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.

9514 1404 393

Answer:

  ΔGHF ~ ΔMLF by AA theorem

Step-by-step explanation:

Answer:

256

Step-by-step explanation:

How to find subsets = 2 raise the power n.

N=number of elements in a set.

=2raise the power 8 which is 256.

Answer:

4x-5=4x-5

Step-by-step explanation:

9514 1404 393

Answer:

  0

Step-by-step explanation:

Force AC resolves to 2 N in the AB direction and 2 N in the BC direction. Directions AB and CD are opposite, as are directions BC and DA. So, the sum of forces in the AB direction is ...

  AB -CD +part of AC = 1 -3 +2 = 0

The sum of forces in the BC direction is ...

  BC -DA +part of AC = 2 -4 +2 = 0

The resultant of these 5 forces is 0. There is no net force in any direction.

Answer:

8

Step-by-step explanation:

To determine the common difference, take the second term and subtract the first term

11-3 = 8

Check with the other terms in the sequence

19-11= 8

27-19 = 8

35-27=8

The common difference is 8

Answer:

C. 8

Step-by-step explanation:

There is a common difference between them and that’s 8.

3 + 8 = 11

11 + 8 = 19

19 + 8 = 27

27 + 8 = 35

Answer:

the answer is B

Step-by-step explanation:

[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]

write -8 form of 2 on up and complete other steps

Answer:

x = 74.2

Step-by-step explanation:

Recall: SOH CAH TOA

Reference angle (θ) = 70°

Angle opposite reference angle = x

Adjacent side = 28

Since we have Adjacent side and opposite side, we would apply the trigonometric ratio, TOA:

Tan θ = Opp/Adj

Substitute

Tan 70 = x/27

27*Tan 70 = x

x = 74.2 (nearest tenth)

Answer:

quadratic trinomial

Step-by-step explanation:

3x(x − 3) + (2x + 6)(-x − 3)

Distribute

3x^2 -9x  + (2x + 6)(-x − 3)

FOIL

3x^2 -9x   + -2x^2 -6x -6x -18

Combine like terms

x^2-21x-18

This has 3 terms so it is a trinomial

The highest power of x is 2 so it is quadratic

9514 1404 393

Answer:

Step-by-step explanation:

Eliminating parentheses, we get ...

  = (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)

  = 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)

  = 3x² -9x -2x² -6x -6x -18

  = x²(3 -2) +x(-9-6-6) -18

  = x² -21x -18

The highest power is 2, so this is a quadratic.

There are 3 terms, so this is a trinomial.

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]

In this case, we have

x(t) = exp(t ) + exp(-t )   ==>   dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t   ==>   dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]

[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]

The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.

[tex]e^2 -\dfrac{1}{e^2 }[/tex]

It is the reverse of differentiation.

The parametric equations are given below.

[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]

Then the arc length of the curve will be given as

[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]

Then

[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]

More about the integration link is given below.

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Answer:

We first find the volume of water without the stone.

V1 = 10 *(π * 52) = 250 π , where π = 3.14

The volume of water and stone is given by

V2 = 13.2 *(π * 52) = 330 π

The volume of the stone is given by

V2 - v1 = 330 π - 250 π = 80 π

= 251.1 cm3

Answer:

y=17

Step-by-step explanation:

y-7=10

transpose 7

y=10+7

y=17