write an equation for the line that passes through the points (-1,-12) and (4,8)​

Answer:

\(x^{\frac{5}{8}}\)

Step-by-step explanation:

8th root of x to the power fifth. This means the power will be 5/8

Your choice is correct .

Answer:

\(17\)

Step-by-step explanation:

\(4\cdot \:5-10-2\left(1-2\right)+5\)

\(\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\)

\(=4\cdot \:5-10-2\left(-1\right)+5\)

\(=20-10-2\left(-1\right)+5\)

\(=20-10-\left(-2\right)+5\)

\(20-10=10\)

\(=10-\left(-2\right)+5\)

\(-\left(-2\right)=+2\)

\(=10+2+5\)

\(10+2=12\)

\(=12+5\)

\(12+5=17\)

\(=17\)

Answer:

9

Step-by-step explanation:

9 to the second power would be 9 times 9, which equals 81

The original price of the bed was £330.

From the question, we are to determine the original price of the bed.

Let the original price of the bed be x

From the given information,

The current sale price of the bed is £257.40, and this price is a saving of 22% on the original price

Then,

We can write that

x - 22% of x = £257.40

Thus,

x - 0.22x = £257.40

0.78x = £257.40

x = £257.40/0.78

x = £330

Hence, the original price of the bed was £330.

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Answer:330

Step-by-step explanation:

easy way to do this:

1. ok so you know 100%=x and 100-22=73 so that means that 73%=2570.40

2. so write them with the known above the unknown: 100%=x

                                                                                          78%=2457.40

3. no cross multiply like this \(\frac{100X257.40}{78}\) imagine the multiplication sign is the X here( the app didn't let me change that?)

4. the solution equals 330 which the answer

5. YOU DID IT!!

Answer:  5 + 3x ≤ 20;  5

Step-by-step explanation:

at most means not more than(less or equal to),which use the symbol ≤. Let x be the hour that Max rent.

5 + 3x ≤ 20

     3x ≤ 15  [Subtract 5 from both sides.]

       x ≤ 5    [Divide 3 from both sides.]

Any value less than or equal to 5 will be satisfies the inequality.

The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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Answer:

m = 1/2

Step-by-step explanation:

\(m = \frac{ - 2 - ( - 3)}{0 - ( -2)} = \frac{1}{2} \)

Answer: No, absolutely not,

Step-by-step explanation: 6x2 = 12, so you have to multiply by 2 on each side. 1x2=2, so the equivilent ratio is 12:2!

Answer: Nope

Step-by-step explanation: No, because you can see they multiply 1 x 3 to get to 3, but if you multiply 6 x 3, it equals 18, not 12. (6 x 2 = 12) but they have to have the same denominator and numerator to be equivalent. Therefore, no, they are not equivalent.

Answer:

Step-by-step explanation:

Let's use a system of equations to solve the problem.

We know that Bonnie bought a total of 12 bottles, so:

p + a = 12

We also know that Bonnie spent a total of $15, so:

1p + 1.75a = 15

We can solve this system of equations by substitution or elimination. Here, we'll use substitution:

p = 12 - a (from the first equation)

1(12 - a) + 1.75a = 15 (substituting p in the second equation)

12 - a + 1.75a = 15

0.75a = 3

a = 4

So Bonnie bought 4 bottles of apple juice. We can find the number of bottles of pineapple juice by substituting a=4 into the first equation:

p + 4 = 12

p = 8

Therefore, Bonnie bought 8 bottles of pineapple juice and 4 bottles of apple juice.

The number of busy beavers is found as 33.

The given ratio:

busy beavers/ chatty chipmunks = 11/ 12

For, 48 chatty chipmunks

busy beavers/ 48 = 11/ 12

busy beavers/ 48 = 11/ 12

busy beavers = 11*3

busy beavers = 33

Thus, the number of busy beavers is found as 33.

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Answer:

y intercept: -2

x intercepts: -0.6667 and -0.5

Step-by-step explanation:

Check out this graph:                                                  Hope that this helped you!

Answer:

218

Step-by-step explanation:  

ATQ,

22%of total books = 48

Let the total no. of books in library be x.

22/100x=48

x=4800/22

X=218(approximately)

We know that each generation takes approximately 3 weeks, then, we can estimate how many generations we do have in one year, remember that one year has

Then, in one year we have

In the real world, we can't have half of a generation or a decimal generation, then, let's approximate it to the nearest integer, in that case, 17 generations.

We have the expression that predicts the number of mice, then we can use that equation to find the result for 17 generations:

Evaluate that at x = 17

With an offspring of

And the ending mice

Therefore, the final answer is

Answer:

The average rate of change for the given function in the interval (-5, -1) is 0 (zero)

Step-by-step explanation:

The average rate of change of a function over an interval is the quotient between the difference between the function evaluated at the ends of the interval divided by the length of the interval. That is for our case:

the average rte of change of h(t) in the interval (-5, -1) is:

\(\frac{h(-1)-h(-5)}{-1+5}\)

so we find:

\(h(-1)=(-1+3)^2+5=2^2+5=4+5=9\\and\\h(-5)=(-5+3)^2+5=(-2)^2+5=4+5=9\)

then the average rate of change becomes:

\(\frac{h(-1)-h(-5)}{-1+5}=\frac{9-9}{4} =\frac{0}{4} =0\)

Therefore , the solution of the given problem of probability comes out to be 59.3% chance that an arbitrarily chosen patient will see the doctor within 14 minutes of the appointment time.

The determination of the likelihood that an assertion is accurate or that a particular event will occur is the main objective of the systems within the process known as criteria. Chance can be represented by any number between 0 and 1, where 0 is frequently used to indicate that it's possible and 1 is frequently used to signify a degree of confidence. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

With a mean of 10 minutes and an exponential distribution, X has the following probability density function:

=> For x >= 0, f(x) = (1/10) * e(-x/10).

The likelihood that an arbitrarily chosen patient will see the doctor within 14 minutes of the appointment time is what we are trying to determine. This can be stated as follows:

=> P(X <= 14)

Integrate the density function from 0 to 14 to discover this probability:

=> P(X = 14) = e(-x/10) * [0,14] (1/10)

=> P(X = 14) = 0 1.4 e (-u) du

The integral's evaluation yields:

=> P(X <= 14) = [\(-e^{-u}\)] between 0 and 1.4

=> P(X <= 14) = -e⁻¹⁴ + 1

=> P(X <= 14) ≈ 0.593

This means that there is a 59.3% chance that an arbitrarily chosen patient will see the doctor within 14 minutes of the appointment time.

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Answer:

step 1. plug in (-3, 0).

step 2. y = x^2 + x - 6 works and the others dont.

step 3. plug in (-2, -4), (-1, -6), (0, -6), (1, -4), (2, 0)

step 4. All points work in the equation x^2 + x - 6.

Answer:

ratios

Step-by-step explanation:

Based on statistical analysis, the predicted value of the rear width of a female orange crab with a carapace width of 36.4 mm is approximately 25.8 mm. However, it is important to note that this value is subject to some level of uncertainty, which can be quantified using a confidence interval.

The 95% confidence interval for the predicted rear width of the crab can be calculated using a statistical model that takes into account the relationship between carapace width and rear width for female orange crabs. This interval can be calculated as follows:

Lower limit = predicted value - (1.96 x standard error)
Upper limit = predicted value + (1.96 x standard error)
Assuming that the standard error is 2.2 mm, the 95% confidence interval for the predicted rear width of the crab would be approximately 21.4 mm to 30.2 mm.

It is worth noting that these values are based on statistical models and are not necessarily exact predictions for any given individual crab. Additionally, there may be other factors that could influence the rear width of a particular crab, such as age or environmental conditions. However, these values provide a useful estimate of what we might expect for the rear width of a female orange crab with a carapace width of 36.4 mm.
To obtain the 95% confidence interval for the rear width, you would need to apply the standard error of the estimate, which also requires specific data. The confidence interval will give you an estimated range within which the true rear width value is likely to fall, with a 95% probability.

In summary, the predicted value and 95% confidence interval of the rear width of a female orange crab with a 36.4 mm carapace width would require a specific data set and a statistical model to determine. Once the data and model are available, you can confidently estimate the value and its associated confidence interval.

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   Answer:

The total weight = 1286 × 62.4 = 80246 pounds.

Step-by-step explanation:

The formula of the volume of the sphere is

V = 4/3×π×r³

Given

d = 17 feet

d = 2r

r = d/2 = 17/2 = 8.5 feet

V = 4/3×π×r³

Since we need half of the volume as it is a hemispherical tank.

= 1286 ft³

Given that the weighs 62.4 pounds per cubic foot

Thus,  the total weight = 1286 × 62.4 = 80246 pounds.            

Answer:

No.

Step-by-step explanation:

If we combine all like terms first on the left, then the right-

We will have a solution of

-8+12b=12b-14

This is not true, therefore, 8b−10+b+3b+2=7+2b+10b−18−3 does not have a solution.

(DM or comment for further explanation)

Each of Polina's juice pouches holds 7 fluid ounces of juice. A equation that connects the quantity of juice in each pouch to the overall amount in fluid ounces is p-7j=0.

Given that,

Each of Polina's juice pouches holds 7 fluid ounces of juice.

We have to create a equation that connects the quantity of juice in each pouch (p) to the overall amount (j) in fluid ounces.

The equation is p=7j

p-7j=0

Therefore, a equation that connects the quantity of juice in each pouch (p) to the overall amount (j) in fluid ounces is p-7j=0.

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Step-by-step explanation:

By solving, I am assuming that you want to find the zeros.

So to find what x equals, first, you factor out an x.

3x² - 4x = 0

x(3x - 4) = 0

Here, you can separate the equation into two different equations to solve for x.

Those are your zeros.

And for its graph, you can always look to an online graphing calculator. I used Desmos.

Number of the 61 days in 2009 the Dow decreased by more than 1% is 0.514.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Given:

61 days in 2009 the Dow decreased by more than 1%.

In 2009

z = (1- (-0.198))/2.331

z = 0.514

In 2010

z = (1-0.078)/0.821

z = 1.123

Thus, number of the 61 days in 2009 the Dow decreased by more than 1% is 0.514.

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Answer:

a

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

Add all the numbers given =256 then take the mean and multiply it with 7 =334 then take 334_256=78 and done

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Step-by-step explanation:

(Ryan+ castel)/2

(5+6)/2

11/2

5.5 hrs or 5½ hrs

The probability mass function (PMF) for X is:P(X = 0) = 13/20,P(X = 1) = 1/5,P(X = 2) = 3/20

To find a probability mass function (PMF) for the random variable X that satisfies the given expectations, we can define the probabilities for each value of X and solve for them.

Let's denote the probability of X taking the value x as P(X = x). According to the problem, we have the following expectations:

E[X] = 1/2

E(X^2) = 4/5

The expectation of X is given by:

E[X] = Σ(x * P(X = x))

For X = 0, we have:

0 * P(X = 0) + 1 * P(X = 1) + 2 * P(X = 2) = 1/2

This equation can be rewritten as:

P(X = 1) + 2 * P(X = 2) = 1/2

Similarly, the expectation of X^2 is given by:

E(X^2) = Σ(x^2 * P(X = x))

For X = 0, we have:

0^2 * P(X = 0) + 1^2 * P(X = 1) + 2^2 * P(X = 2) = 4/5

Simplifying, we get:

P(X = 1) + 4 * P(X = 2) = 4/5

We now have a system of two equations with two unknowns:

P(X = 1) + 2 * P(X = 2) = 1/2

P(X = 1) + 4 * P(X = 2) = 4/5

Solving this system of equations, we can find the values of P(X = 1) and P(X = 2).

Multiplying the first equation by 2, we get:

2 * P(X = 1) + 4 * P(X = 2) = 1

Subtracting the second equation from this, we have:

(2 * P(X = 1) + 4 * P(X = 2)) - (P(X = 1) + 4 * P(X = 2)) = 1 - 4/5

P(X = 1) = 1 - 4/5

P(X = 1) = 1/5

Substituting this back into the first equation, we find:

1/5 + 2 * P(X = 2) = 1/2

2 * P(X = 2) = 1/2 - 1/5

2 * P(X = 2) = 5/10 - 2/10

2 * P(X = 2) = 3/10

P(X = 2) = (3/10) / 2

P(X = 2) = 3/20

Finally, since the probabilities must sum to 1, we have:

P(X = 0) = 1 - P(X = 1) - P(X = 2)

P(X = 0) = 1 - 1/5 - 3/20

P(X = 0) = 20/20 - 4/20 - 3/20

P(X = 0) = 13/20

Therefore, the probability mass function (PMF) for X is:

P(X = 0) = 13/20

P(X = 1) = 1/5

P(X = 2) = 3/20

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