Write 81 as a power in many ways as you can.

Answer:

integer

Step-by-step explanation:

the slope looks like it's 4/1 when simplified it's 4. (integer)

Answer:

The slope is the integer 4

Step-by-step explanation:

take the points (-2, -9) (-1, -5) and put them in the formula  y2 - y1 over x2 - x1 and you get m = 4

Answer:

6y

Step-by-step explanation:

uhhhh

The concept with the correct symbol or term is p-value< α. Option F

The p-value could be a degree of the quality of prove against the invalid theory. When the p-value is less than the foreordained importance level α (as a rule set at 0.05), it shows a measurably noteworthy result.

This implies that the observed data is impossible to have happened by chance alone in the event that the invalid theory is genuine.

However, rejecting the null hypothesis in favor of the alternative hypothesis is appropriate.

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Answer:

Triangle KLM

Step-by-step explanation:

Firstly, we need to write the coordinates of triangle NPQ

We have this as;

(-7,-6) for N

(-4,-3) for P

(-4,-6) for Q

Now, we are going to use the given translation formula;

(x + 8, y + 1)

N’ will be (-7+ 8, -6 + 1) = (1,-5)

P’ will be (-4+ 8, -3+1) = (4,-2)

Q’ will be (-4+ 8, -6+1) = (4,-5)

Now, we need to find the triangle with the exact given transformation coordinates calculated above;

We have the triangle as;

KLM

With K as (1,-5) ; L as (4,-2) and ; M as (4,-5)

The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission if each boat has a failure rate of 1 failure per 100 hoursis 99.5%. Hence, the correct option is (A).

To determine the probability of mission success, we'll need to calculate the probability of failure for each boat and then use the binomial probability formula.

Here are the steps:

1. Calculate the probability of failure for each boat during the 20-hour mission: Since each boat has a failure rate of 1 failure per 100 hours, the probability of failure for each boat in 20 hours is 20/100 = 1/5 or 0.2.

2. Calculate the probability of success for each boat: The probability of success for each boat is 1 - probability of failure = 1 - 0.2 = 0.8.

3. Use the binomial probability formula to find the probability of at least 11 boats operating successfully:
P(X ≥ 11) = 1 - P(X ≤ 10), where X is the number of successful boats.

4. Calculate P(X ≤ 10) using the binomial probability formula:

P(X ≤ 10) = ∑[C(16, k) × (0.8)^k × (0.2)^(16-k)], where k ranges from 0 to 10, and C(16, k) is the binomial coefficient or the number of ways to choose k successes from 16 boats.

5. Calculate 1 - P(X ≤ 10) to get the probability of mission success.

After performing the calculations, the probability of mission success is found to be approximately 99.5%, which corresponds to option A.

So, the probability of mission success, given that at least 11 of the 16 patrol boats must operate for the duration of the 20-hour mission and each boat has a failure rate of 1 failure per 100 hours, is approximately 99.5%.

Hence, option (A) is correct.

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volume : 7.5 cm²

\(\hookrightarrow \sf Length \ * Width \ * \ Height\)

\(\hookrightarrow \sf 2 \ * 1\dfrac{1}{4} \ * \ 3\)

\(\hookrightarrow \sf 2 \ * \dfrac{5}{4} \ * \ 3\)

\(\hookrightarrow \sf \dfrac{15}{2}\)

\(\hookrightarrow \sf 7.5 \ cm^2\)

Answer:

\(\sf volume=7 \frac12 \ cm^3\)

Step-by-step explanation:

Formula

volume of cuboid = length × width × height

Given dimensions of the ice cube:

Substituting the given values into the formula:

\(\sf \implies volume=2\times 1 \frac14 \times 3\)

Converting to improper fractions:

\(\sf \implies volume=\dfrac21\times \dfrac54 \times \dfrac31\)

                  \(\sf =\dfrac{ 2\times 5 \times 3}{1 \times 4 \times 1}\)

                  \(\sf =\dfrac{30}{4}\)

Dividing the numerator and denominator by the highest common factor:

\(\sf \implies volume=\dfrac{30 \div 2}{4 \div 2}\)

                  \(\sf =\dfrac{15}{2}\)

Converting the improper fraction into a mixed number:

\(\sf \implies volume=7 \frac12 \ cm^3\)

Answer:

To find a basis for the orthogonal complement of the subspace spanned by v1, v2, v3, and v4, we need to find a basis for the subspace of vectors in R^5 that are orthogonal to all four of these vectors.

We can use the Gram-Schmidt process to find an orthogonal basis for the subspace spanned by v1, v2, v3, and v4. Let's call this basis {u1, u2, u3, u4}. Then, any vector in the orthogonal complement of this subspace will be orthogonal to u1, u2, u3, and u4.

Using the Gram-Schmidt process, we can find an orthogonal basis for the subspace spanned by v1, v2, v3, and v4 as follows:

u1 = v1 = (1, 4, 5, 6, 9)

u2 = v2 - proj_u1(v2) = v2 - ((v2 · u1) / (u1 · u1))u1 = (3, -2, 1, 4, -1) - ((3 + 16 + 5 + 24 + 81) / (1 + 16 + 25 + 36 + 81))(1, 4, 5, 6, 9) = (-2, -10, -4, -10, -28)

u3 = v3 - proj_u1(v3) - proj_u2(v3) = v3 - ((v3 · u1) / (u1 · u1))u1 - ((v3 · u2) / (u2 · u2))u2 = (-1, 0, -1, -2, -1) - ((-1 + 0 - 5 - 12 - 9) / (1 + 16 + 25 + 36 + 81))(1, 4, 5, 6, 9) - ((-2 + 0 + 4 + 8 + 28) / (4 + 100 + 16 + 100 + 784))(-2, -10, -4, -10, -28) = (-11/5, -2/5, -6/5, 6/5, -9/5)

u4 = v4 - proj_u1(v4) - proj_u2(v4) - proj_u3(v4) = v4 - ((v4 · u1) / (u1 · u1))u1 - ((v4 · u2) / (u2 · u2))u2 - ((v4 · u3) / (u3 · u3))u3 = (2, 3, 5, 7, 8) - ((2 + 12 + 25 + 42 + 72) / (1 + 16 + 25 + 36 + 81))(1, 4, 5, 6, 9) - ((-6 - 12 - 4 - 40 + 28) / (4 + 100 + 16 + 100 + 784))(-2, -10, -4, -10, -28) - ((-22/5 - 6/5 + 6/5 - 42/5 + 18/5) / (121/25 + 4/25 + 36/25 + 36/25 + 81/25))(-11/5, -2/5, -6/5, 6/5, -9/

give thanks, your welcome <3

Step-by-step explanation:

Answer:

\(y=\frac{5}{3}x+8\)

Step-by-step explanation:

Remember, slope intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

To get the given equation into slope-intercept form, we would have to first solve for y in terms of x.

10x - 6y = -48

Subtract 10x from both sides.

-6y = -48 - 10x

Multiply both sides by -1.

6y = 10x + 48

Divide both sides by 6.

\(y=\frac{5}{3}x+8\)

And now, looking at the equation that we found and the equation for slope-intercept form, we can see that we have found the equation for 10x - 6y = -48 in slope-intercept form.

I hope you find my answer to be helpful. Happy studying.

The answer that describes the polygon RSTU is as follows:

A quadrilateral is a polygon with 4 sides. Therefore, let's use the properties to find the name of the shape  RSTU as follows:

The polygon has 4 sides therefore, it is a quadrilateral.

The quadrilateral has opposite side parallel to each other. The opposite sides are RS and TU.

A trapezoid is a quadrilateral with only one pair of opposite side parallel to each other.

Therefore, the shapes that defines the polygon are as follows:

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Integer represents the change in the height of the elevator, in meters, every second is 25200.

The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Given Data

The main elevator in the Willis Tower descends 420 meters in 60 seconds.

Distance = 420meters

Time = 60 seconds

Speed = distance (time)

Speed = 420(60)

Speed = 25200

Integer represents the change in the height of the elevator, in meters, every second is 25200.

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Formulating with the value of Sine and sides of a triangle we can find the distance between Pablo's head and the kite (perpendicularly above) to be 58.6 feet ( approximated to the nearest tenth).

It is given that Pablo is flying a kite with a string PK that is 129 feet long.

The string is inclined at an angle of elevation, O of 27 degrees.

Say, ∠POQ = 27°

From the diagram we can say that PK is the hypotenuse of an triangle formed namely POQ.

Say the distance between Pablo's head and the kite (perpendicularly above) be x (in feet).

We can find the value of x by application of sine as,

Sin Ф = Perpendicular / Hypotenuse

⇒ Sin 27° = x / 129

The value of Sin 27° is 0.454 ( approximated to 3 decimal places ).

⇒ 0.454 = x / 129

⇒ x = (0.454) ( 129)

⇒ x = 58.566

⇒ x = 58.6 ( approximated to the nearest tenth) in feet

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A z-statistic reports how many standard deviations an observed value is from the expected value, where the expected value is calculated using the population mean and standard deviation.

To calculate the z-statistic, use the following formula:

Where:

x = the observed value

μ = the population mean

σ = the population standard deviation

n = the sample size

The z-statistic tells us how many standard deviations an observed value is from the expected value, which is the population mean. A positive z-score indicates that the observed value is above the expected value, while a negative z-score indicates that the observed value is below the expected value. A z-score of 0 indicates that the observed value is equal to the expected value. By calculating the z-statistic, we can determine how unusual or significant an observed value is relative to the population.

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Complete Question:

a z-statistic reports how many sds an observed value is from the expected value, where the expected value is calculated using the___.

Answer:

4×1000000 6×100000 7×10000 2×1000

Step-by-step explanation:

Answer:

\(4.672 * 10^{6}\)

Step-by-step explanation:

move the orginial number 6 decimal points to the left to determine its scientific notation

4672000

467200.0

46720.00

4672.000

467.2000

46.72000

4.672000

The probability that the student will be a student who lives on campus is 0.24

In math the term probability is referred as the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

Here we have given that one full-time student who is a freshman or sophomore is selected at random.

Here we need to find the probability that the student will be a student who lives on campus.

Here we know that the probability that a student is a sophomore is calculated as,

=> P(S) = 19/42 = 0.45.

Whereas the probability that a student has a freshman is calculated as,

=>P(H)=25/42=0.6.

Then the probability that the student will be a student who lives on campus is calculated as,

=> P(H∩S)=P(S)+P(H)−P(S∪H)

Apply the values then simplify this one then we get,

=> 0.45+0.6−(42−8)/42=0.24

Complete Question:

Suppose that a certain college class contains 42 students and then if one full-time student who is a freshman or sophomore is selected at random, what is the probability that the student will be a student who lives on campus?

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Answer:

33

Step-by-step explanation:

Answer:

$56.00

Step-by-step explanation:

35+(60/100)

=21

35+21

=$56.00

Answer:

Step-by-step explanation:

3 times 10 =30

4 times 5=20

30+20=50 $

10+5 equals 15 pounds

10 pounds of chicken and 5 of pork

The induced magnetic field is proportional to the applied magnetic field B = (μ0σBo/4) sin(wt).

The Induced electric field can be found using Faraday's law:

∇ × E = -∂B/∂t

Since the magnetic field is only changing in magnitude and not direction, we can simplify this to:

E = -∂A/∂t

where A is the magnetic vector potential. The magnetic vector potential for a uniform magnetic field along the z-axis is given by:

A = (Bo/2w) cos(wt) (r^2 - z^2)

where r is the distance from the axis of the disk and z is the height above the center of the disk. Taking the time derivative of A gives us:

∂A/∂t = -(Bo/2) sin(wt) (r^2 - z^2)

So the induced electric field is:

E = (Bo/2) sin(wt) (r^2 - z^2)

The current density can be found using Ohm's law:

J = σE

So the current density is:

J = (σBo/2) sin(wt) (r^2 - z^2)

The current density will be greatest at the center of the disk, and will decrease as we move away from the center. At the edges of the disk, the current density will be zero.

The power dissipated per unit volume is given by:

J⋅E

Substituting the expressions for J and E gives:

J⋅E = (σBo^2/8) sin^2(wt) (r^2 - z^2)^2

c) The total power dissipated in the disk at time t is given by:

∫ J⋅E dV

Integrating over the volume of the disk (assuming it is a cylinder with height h and radius a), we get:

P = (πσBo^2a^2h/4) sin^2(wt)

The average power dissipated per cycle of the field is given by:

(1/T) ∫ P dt

where T = 2π/w is the period of the field. Integrating over one cycle of the field gives:

(πσBo^2a^2h/8)

To heat up the frying pan with 1000 watts of power at a frequency of 20 kHz, we need:

P = (πσBo^2a^2h/4) sin^2(wt) = 1000 watts

σ = 5.96×10^7 S/m (for copper)

Assuming the frying pan has a radius of 20 cm and a height of 5 cm, we have:

a = 10 cm

h = 5 cm

w = 2πf = 125.7 rad/s

Substituting the values and solving for Bo, we get:

Bo ≈ 2.23 T

This seems like a high magnetic field, and it may not be feasible to achieve with typical equipment.

The induced magnetic field at the center of the pan can be found using the Biot-Savart law:

B = μ0∫ J(r')×(r-r')/|r-r'|^3 dV'

Assuming a uniform current density, we can simplify this to:

B = μ0Jπa^2/2

Substituting the expression for J gives:

B = (μ0σBo/4) sin(wt)

At the center of the pan (r=0, z=0), we have:

B = (μ0σBo/4) sin(wt)

The induced magnetic field is proportional to the applied magnetic field

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Answer:

B is correct

Step-by-step explanation:

adding the amount taken away and then subtracting it is the same as subtracting twice

Answer:

either b or c

Step-by-step explanation:

Answer:

15x+8=180-97 , solve for x and u shall get the answer

Answer:5

Step-by-step explanation:

Since 97 and the other angle together make a straight line, you can find the angle by doing 180-97 which is 83. Then you 15x+8=83. 15x=75. x=5.

Answer:

654 girls

Step-by-step explanation:

sum the parts of the ratio , 4 + 3 = 7 parts

divide total by 7 to find the value of one part of the ratio

1526 ÷ 7 = 218 ← value of 1 part of the ratio , then

number of girls = 3 × 218 = 654

The three-period moving average forecast for period 6 is 5215, rounded to the nearest whole number. This is calculated by averaging the last three periods of actual sales data, which are 5035, 4886, and 5724.

The three-period moving average forecast is a simple forecasting method that takes the average of the last three periods of actual sales data. This is a relatively easy method to calculate, and it can be a good starting point for forecasting future sales.

In this case, the three-period moving average forecast for period 6 is 5215. This is calculated by averaging the last three periods of actual sales data, which are 5035, 4886, and 5724. To calculate the average, we simply add these three numbers together and then divide by 3. This gives us a forecast of 5215.

It is important to note that this is just a forecast, and the actual sales for period 6 may be different. However, the three-period moving average forecast is a good starting point for estimating future sales.

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Answer:

702/9 is 78 your answer is 78

Step-by-step explanation:

27*13*2

Answer:

40, or if you need it unrounded 40.3

Step-by-step explanation:

The radius of the circle will be \(\sqrt{22}\).

In our question, we shall first extend QRS to the circle's point T.

According to the power of a point.

\(QP^{2}\)  =  QR*QT

\(6^{2}\)  =  3*QT

QT = 12

Since QR = 3, RT = 9.

Since RS = 3, ST = 6.

Draw OT and OR, creating a triangle(TSO) and triangle(RSO).

OT and OR are radii, Let the radius be r.

Use the Law of Cosines on these two triangles.

OT2  =  \(r^{2}\)  =  \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)

OR2  =  r2  =  \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)

Since these are equal:

\(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)  =  \(3^{2}\) + \(2^{2}\) - 2*3*2*cos(RSO)

40 - 24*cos(TSO)  =  13 - 12*cos(RSO)

Since angle(RSO) is supplementary to angle(TSO),  cos(RSO) = - cos(TSO)

40 - 24*cos(TSO)  =  13 + 12*cos(TSO)

27  =  36*cos(TSO)

0.75  =  cos(TSO)

Since  \(OT^{2}\)  =  \(r^{2}\)  =  \(6^{2}\) + \(2^{2}\) - 2*6*2*cos(TSO)

\(r^{2}\)  =  40 - 24*0.75  

\(r^{2}\)  =  22

r  =  \(\sqrt{22}\)

Hence the radius of the given circle will be \(\sqrt{22}\).

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Function 1, 2 and 3 are well-defined while function 4 is not well-defined.

A function f : A -> B is well-defined if f(a) is unique for all a in A. If a function is not well-defined, then it assigns different values to the same input, which violates the fundamental definition of a function. Here are the solutions to the given question:

1. f(x) = x/12

This function is well-defined since each input (x) is mapped to a unique output (x/12). Therefore, the function is well-defined.

2. g(x) = 1/(x - 3)

This function is well-defined since each input x is mapped to a unique output (1/(x-3)) that exists for all x ≠ 3. Therefore, the function is well-defined.

3. h(x) = 5/(1 + |x|)

This function is well-defined since each input x is mapped to a unique output (5/(1 + |x|)) that exists for all x. Therefore, the function is well-defined.

4. i(x) = √(-5)

This function is not well-defined because there is no real number whose square is negative. Therefore, the function is not well-defined.

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