Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot

The Integral \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

Given integral;

\(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt\)

By solving the above integral, we have;

⇒ \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt\)

By applying the sum rule,

⇒ \(\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\)

\(=\int \sec ^2\left(t\right)idt+\int \:t\left(t^2+1\right)^4jdt+\int \:t^6\ln \left(t\right)kdt\)

\(\int \sec ^2\left(t\right)idt=i\tan \left(t\right)\)

\(\int \:t\left(t^2+1\right)^4jdt = \frac{j\left(t^2+1\right)^5}{10}\)

\(\int \:t^6\ln \left(t\right)kdt = k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

⇒ \(i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

Therefore, the integral \(\int \sec ^2\left(t\right)i+t\left(t^2+1\right)^4j+t^6\ln \left(t\right)kdt = i\tan \left(t\right)+\frac{j\left(t^2+1\right)^5}{10}+k\left(\frac{1}{7}t^7\ln \left(t\right)-\frac{t^7}{49}\right)\)

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Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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Answer:

Step-by-step explanation:

150% is equivalent to 1.5 so the answer is:

1250 * 1.5

= 1875.

Answer:

1875

Step-by-step explanation:

Then 62.5% of the campers at the Wild Outdoors camp this morning will be horseback riding

To find the percentage of campers that will be horseback riding, we need to first add the ratio together to get the total number of parts. In this case, the ratio of horseback riding to canoeing is 5:3, so there are 5 + 3 = 8 parts in total.

To find the percentage of campers that will be horseback riding, we divide the number of parts for horseback riding by the total number of parts, then multiply by 100 to get the percentage.

So, 5 parts out of 8 parts are for horseback riding. This is equivalent to 5/8 or 0.625 as a decimal. To find the percentage, we multiply by 100, which gives us 62.5%.

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Since quadrilateral GHJK is a rectangle, then triangle GKJ will be a right triangle. And therefore, the angle GKJ will be a right angle, that is, 90°. Then, you have

Now, the triangle Sum Theorem says that the sum of the three interior angles in a triangle is always 180°, then you have

Therefore, the measure of angle 2 is 36°, given that the measure of angle 4 is 54°. And the correct answer is B. 36°.

Answer: 20

Step-by-step explanation:

Multiply 2.4*10-4

Calculate 24-4

the answer is (12x^10000)/5

Answer:

2 (4x - 1) + 6 = 8x + 4 = 4(2x+1)

Step-by-step explanation:

2 (4x - 1) + 6

= (2*4x + 2*-1) + 6

= 8x - 2 + 6

= 8x + 4

= 4/(2x+1)

Answer:

4(2x+1)

Step-by-step explanation:

First, factor it out:

2(4x-1+3)

Then calculate:

2(4x+2)

Factor out 2:

2 • 2(2x+1)

Then finally multiply:

4(2x+1)

Answer:

I think its C

Step-by-step explanation:

Answer:

The value is  \(E(X) = 4 \ days\)

Step-by-step explanation:

From the question we are told that

   The mean is  \(\mu = 36^oC\)

    The standard deviation \(\sigma = 3^oC\)

Generally the probability that in June , the midday  temperature is between  

39°C and 42°C is mathematically represented as

      \(P(39 < X < 42) = P(\frac{39 - 36}{3} < \frac{X - \mu }{\sigma} < (\frac{42 - 36}{3} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

      \(P(39 < X < 42) = P(1 < Z <2 )\)

=>   \(P(39 < X < 42) = P(Z < 2) - P( Z <1 )\)

From the z table  the area under the normal curve to the left corresponding to  1 and  2  is

     P(Z   < 2)  = 0.97725

and

    P(Z   < 1)  = 0.84134

    \(P(39 < X < 42) = 0.97725 - 0.84134\)

=>  \(P(39 < X < 42) = 0.13591\)

Generally number of days in June would you expect the midday temperature to be between 39°C and 42°C

      \(E(X) = n * P(39 < X 42 )\)

Here n is the number of days in June which is  n = 30

       \(E(X) = 30 * 0.13591\)

=>    \(E(X) = 4 \ days\)

Answer:

The coefficient of variation for the weight and age are 5.9% and 10.6%.

Step-by-step explanation:

The coefficient of variation (CV) is well defined as the ratio of the standard deviation to the mean. It exhibits the degree of variation in association to the mean of the population.

The formula to compute the coefficient of variation is:

\(CV=\frac{\sigma}{\mu}\times 100\%\)

Here σ = standard deviation and µ = mean.

Compute the mean and standard deviations of the two data set in Excel using the following functions.

Mean=AVERAGE()

Standard deviation=STDEV.S()

Consider the Excel sheet attached.

The mean and standard deviation of weight are:

Mean = 202, Standard deviation = 11.87

And the mean and standard deviation of weight are:

Mean = 25.88, Standard deviation = 2.75

Compute the coefficient of variation for the weight as follows:

\(CV_{weight}=\frac{\sigma}{\mu}\times 100\%\)

              \(=\frac{11.87}{202}\times 100\%\\\\=5.87624\\\\=5.9\%\)

Compute the coefficient of variation for the age as follows:

\(CV_{age}=\frac{\sigma}{\mu}\times 100\%\)

              \(=\frac{2.75}{25.88}\times 100\%\\\\=10.62597\\\\=10.6\%\)

Thus, the coefficient of variation for the weight and age are 5.9% and 10.6%.

Answer

The total minutes that Jim spent last month = 1102 minutes

Explanation

Jim pays $75 per month for a cell phone plan, plus $0.30 per minute beyond the first 1000 minutes.

His bill was $105.60 last month. How many minutes did he use.

Let the number of minutes that Jim used that was above the first 1000 minutes be x.

Jim's total charge for using an extra x minutes above the first 1000 minutes will be = (75 + 0.30x) dollars.

This total charge was given as $105.60

75 + 0.30x = 105.60

Subtract 75 from both sides

75 + 0.30x - 75 = 105.60 - 75

0.30x = 30.6

Divide both sides by 0.30

(0.30x/0.30) = (30.6/0.30)

x = 102 minutes.

This means that Jim spent an extra 102 minutes above the first 1000 minutes.

So, the total minutes that Jim spent last month = 1000 + 102 = 1102 minutes.

Hope this Helps!!!

The value of X, given the matrices, can be found to be X = [ [ 4 ], [-1.5 ] ].

We are told that the value of X can be found to be :
2X + A = B

Solving this would give:
X = (B - A) / 2

We can then apply this to the matrices to give:
B - A = [ [ 11 - 3 ], [1 - 4 ] ]

B - A =  [[ 8 ],  [ -3 ] ]

X = [ [ 8 / 2 ], [ -3/2 ] ]

X = [ [ 4 ], [-1.5 ] ]

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Answer:

I hope option D is write

I hope you help

Answer:

B. 32°

Step-by-step explanation:

The reference angle for 212°

=212°-180°

=32°

Hope it is helpful to you

The standard deviation of the sample is approximately 9.15

To find the standard deviation of the sample, we first need to calculate the sample mean. The sample mean is the sum of all the data points divided by the total number of data points. In this case, we are given the frequency distribution of the costs per load of 34 dish-washing detergents.

To calculate the sample mean, we multiply each class midpoint by its corresponding frequency, sum up these products, and divide by the total number of data points (34 in this case).

The class midpoint for each class interval can be calculated by adding the lower class limit to the upper class limit and dividing by 2. For example, the class midpoint for the interval 20-28 is (20 + 28) / 2 = 24.

Using this information, we can calculate the sample mean:

(24 * 13 + 33 * 15 + 42 * 4 + 51 * 2) / 34 = 32.44

Next, we need to calculate the squared deviation of each data point from the sample mean. The squared deviation is obtained by subtracting the sample mean from each data point and squaring the result.

For each class interval, we can calculate the squared deviation by subtracting the class midpoint from the sample mean, squaring the result, and multiplying by the frequency.

The sum of these squared deviations is then divided by the total number of data points minus 1 (n-1) to obtain the variance.

Using the given data, the variance is calculated as follows:

((24 - 32.44)^2 * 13 + (33 - 32.44)^2 * 15 + (42 - 32.44)^2 * 4 + (51 - 32.44)^2 * 2) / (34 - 1) = 83.6

Finally, to find the standard deviation, we take the square root of the variance:

√(83.6) ≈ 9.15

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Answer:

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. ... After a dilation, the pre-image and image have the same shape but not the same size.

Answer:

I would say False

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. After a dilation, the preimage and image have the same shape but not the same size.

Hope this helps.

The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..

Based on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.

The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.

In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.

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Solution:

Note that a Poisson probability distribution would be a good choice for r = number of earthquakes in a given time interval. That is, because, the frequency of earthquakes is a rare occurrence. It is reasonable to assume the events are independent.

(a) Compute the probability of at least one major earthquake in the next 51 years. Round to the nearest hundredth, and use a calculator. (Use 4 decimal places.)

The average earthquake for the next 51 years is:

that is:

now, the probability of at least one major earthquake is given by the following equation:

to solve this equation, note that:

thus,

then, the correct answer is:

(b) Compute the probability of no major earthquakes in the next 51 years. Round to the nearest hundredth, and use a calculator. (Use 4 decimal places.)

The probability of no major earthquakes in the next 51 years is given by P(X=0).

P(X=0) is calculated in the above item which is:

so that, the correct answer is:



Answer:

This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.

Step-by-step explanation:

x < 3 or x > 5

This means, x is less than 3, but greater than 5.

Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.

Taking the left hand and right hand limits of the piecewise function into consideration, they are not equal and the limit of the function as it approaches -1 does not exist.

To determine the limit of the given function as it approaches -1, we can check the left-hand and right hand limits and see if they're equal.

The Left-hand limit;

When x approaches -1 from the left, x < -1 and we consider the first part of the piecewise function f(x);

\(f(x) = (x+1)^3 + 2\)

Putting the value of -1 in this expression;

\(\lim_{\to x^-^1^- } (x+1)^3+2 = (0)^3+2=2\)

Right-hand limit:

When x approaches -1 from the right x ≥ -1, we can take the second part of the piecewise function into consideration

\(f(x) = e^x - 1\)

Putting the value of -1 in this expression;

\(\lim_{x \to \geq -1^+} e^(-1) - 1 =\frac{1}{e - 1}\)

Since the left-hand limit is 2 and the right-hand limit is 1/e - 1, they are not equal.

Therefore, the limit of f(x) as x approaches -1 does not exist.

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Answer:

12

Step-by-step explanation:

you have 72 and 6

72 divided by 6 equals 12.

12 x 6 = 72

12 = x

The runners can finish in 362880 possible results

What is Permutation?

Permutation is the different number of arrangements that can be formed by taking r things from the n available things.

The formula  n! = 1 × 2 × 3 × 4 × .......× n.

To get the order the runners could possibly finish,

= 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 326880

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Answer:

(-1,-2)

Step-by-step explanation:

Since the park is at (4,-2), going to the left 5 units will put us at x = -1

Since the school is at (-1,2) going down 4 units will put us at y = -2

(-1,-2)

Answer:

10 twenty cent pieces and 6 fifty cent pieces for 16 coins and 5 euros.

Step-by-step explanation:

If no accessories are sold, $3 will be paid out. In the event that accessories are sold, the compensation is $2.00 plus $1.00 plus 1.5 percent of their worth.

Based on the information given, the KPI payouts are:

$1.00 for each Prepaid Ring-out Only

$2.00 for each Prepaid Activation

1.5% of the value of each Accessories sale

$1.00 for each Equipment Protection sale

We need to know the values of the prepaid activation and equipment protection in order to compute the payment for activating a prepaid device with equipment protection. Assume that the equipment protection is worth $Y and the prepaid activation is worth $X.

The following would be the total payment for activating a prepaid device with equipment protection:

Payout = $2.00 (for activation) + $1.00 (for equipment protection) + 1.5% (of the value of accessories sold)

If no accessories are sold, the payout would be:

Payout = $2.00 + $1.00

= $3.00

If accessories worth $Z are also sold, the payout would be:

Payout = $2.00 + $1.00 + 1.5% of $Z

= $2.00 + $1.00 + 0.015Z

So the payout for activating a prepaid device with equipment protection depends on the value of the accessories sold.

Therefore,  If no accessories are sold, the payout is $3.00. If accessories are sold, the payout is $2.00 + $1.00 + 1.5% of the value of the accessories sold.

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a.) Exact result: 10.9375. Approximate: 11 quarts of heavy cream.

b.) Exact result: 65.625. Approximate: 66 eggs.

c.) Exact result: 43.75. Approximate: 44 lemons.

If 400 guest will consume 1.75 pastries, then the total of pastries is:

\(400*1.75=700\)

If one quarter of the pastries will have 2 ounces of lemon filling, then the amount of pastries that will ahve this filling is:

\(700*\frac{1}{4}= 175\)

If 175 will have 2 ounces of lemon filling, then the ounces of lemon filling needed is:

\(175*2=350\)

Then, the mass, in pounds, of lemon filling needed is:

\(350/16=21.875\)

To find the quarts of heavy cream needed, set up a rule of 3 like this:

2 pounds of filling ------------ 1 quart of heavy cream

21.875 pounds of filling ----- x

\(x= \frac{21.875*1}{2} =10.9375\)

The amount of quarts of heavy cream needed is, approximately, 11.

Do the same rule of 3 as in question 1, except that now we substitute the ingredient and que quantity:

2 pounds of filling ------------ 6 eggs

21.875 pounds of filling ----- x

\(x= \frac{21.875*6}{2} =65.625\)

The amount of eggs needed is, approximately, 66.

First, let's find out how many cups of lemon juice are needed through a rule of 3.

2 pounds of filling ------------ 1 cup of lemon juice

21.875 pounds of filling ----- x

\(x= \frac{21.875*1}{2} =10.9375\)

Now, convert the cups to ounces.

10.9375 cups * 8= 87.5 ounces.

Set up another rule of 3 to determine the number of lemons.

2 ounces ------------ 1 lemon

87.5 ounces ----- x

\(x= \frac{87.5*1}{2} =43.75\)

The amount of lemons needed is, approximately, 44.

Answer:

Answer is A $172.25

Step-by-step explanation:

Step 1: Our output value is 575.50.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$575.50=100\%$.

Step 4: Similarly, $x=30\%$.

Step 5: This results in a pair of simple equations

$575.50=100\%(1)$.

$x=30\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{575.50}{x}=\frac{100\%}{30\%}$

Step 7: Again, the reciprocal of both sides gives

$\frac{x}{575.50}=\frac{30}{100}$

$\Rightarrow x=172.65$

Therefore, $30\%$ of $575.50$ is $172.65$

Answer:

The total that will be saved at a 30% discount is $172.65

Explanation:

Since, the marked up price of the item will be $575.50,

and the discount percentage is 30%,

Therefore, $ 172.65 will be saved.

Answer: 12°

Hope this helps!