7. in a certain microwave oven on the high power setting, the time it takes a randomly chosen kernel popcorn to pop is normally distributed with a mean of 140 seconds and a standard deviation of 25 seconds. a) what is the probability that the time required to pop is greater than 120 seconds?

Use the formula shown:

6^2 + 2.5^ = c^2

36 + 6.25 = c^2

42.25 = c^2

Take the square root of both sides:

c = 13/2 as a fraction or 2.5495 as a decimal (round off as needed)

To find Cara's new balance, we first need to calculate the interest on her unpaid balance.

Interest = (unpaid balance) x (APR/12)
Interest = 5392.39 x (0.132/12)
Interest = 59.43

So Cara's interest for this period is $59.43.

Next, we need to add the interest and her new transaction to her unpaid balance to get her new balance.

New balance = unpaid balance + interest + new transaction
New balance = 5392.39 + 59.43 + 204
New balance = $5655.71

Therefore, the answer is Option C: $5655.71.
Cara's unpaid credit card balance is $5,392.39, and she made a new transaction of $204. To find her new balance, simply add the new transaction amount to her current balance:

$5,392.39 + $204 = $5,596.39

Her APR is 13.2%, but we don't have any information about how the interest is compounded or the time period, so we cannot calculate the interest. Therefore, her new balance is $5,596.39, which is not among the given options (A, B, C, or D).

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Explanation

We are to first find the inverse of the function:

To do so, we will follow the steps below:

Step 1:

Step2: Interchange x with y

Step 3: solve for y

Thus, the inverse of the function is

Part 2

Simplifying further

Also

Simplifying further

The survey aimed to understand how frequently families eat at home and the results provide an indication of the reported frequency of family meals in households with children under the age of 18. This information can be valuable for understanding the prevalence of family meals at home during the given time period.

According to a survey conducted by Harris Interactive, adults living with children under the age of 18 were surveyed to explore the frequency of family meals at home. The survey results, presented in the table, provide insights into this aspect. To summarize the findings, the table showcases the percentage of respondents who reported eating meals together at home either rarely, occasionally, often, or always. It is important to note that the data was collected by Harris Interactive and reported by USA Today on January 3, 2007.

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The solution to the given simultaneous equations are;

x = 5/3 and y = 7/3

We are given the two simultaneous equations as;

x + y = 4  

y = 2x -1

Rearranging the second equation to have all the variables on one side gives; 2x - y = 1

Thus, we have the equations;

x + y = 4   ------(1)

2x - y = 1    -----(2)

Add eq 1 to eq 2 to get;

3x = 5

divide both sides by 3 using division property of equality to get;

x = 5/3

Put 5/3 for x in eq 1 to get;

⁵/₃ + y = 4

y = 4 - ⁵/₃

y = ⁷/₃

Thus, those are the solutions to the simultaneous equations.

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The sum οf (5x³ − 4x² + 6) and (4x³ − 2x − 2) is 9x³ − 4x² − 2x + 4, written in standard fοrm.

Tο find the sum οf twο οr mοre pοlynοmials, we need tο cοmbine the like terms. This is dοne by adding the cοefficients οf the like terms while keeping the variable and its expοnent the same.

Tο find the sum οf (5x³ − 4x² + 6) and (4x³ − 2x − 2), we can simply add the like terms:

(5x³ − 4x² + 6) + (4x³ − 2x − 2) = 9x³ − 4x² − 2x + 4

Therefοre, the sum οf (5x³ − 4x² + 6) and (4x³ − 2x − 2) is 9x³ − 4x² − 2x + 4, written in standard fοrm.

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The exact length of the curve y = 7 + (1/5)cosh(5x) for 0 ≤ x ≤ 2 is approximately 8.826 units.

To find the exact length of the curve y = 7 + (1/5)cosh(5x) for 0 ≤ x ≤ 2, we need to use the arc length formula:

L = ∫[a,b] sqrt(1 + [f'(x)]^2) dx

where a = 0, b = 2, and f(x) = 7 + (1/5)cosh(5x).

First, we need to find f'(x):

f'(x) = (1/5)*sinh(5x)

Now we can substitute f'(x) and f(x) into the arc length formula:

L = ∫[0,2] sqrt(1 + [f'(x)]^2) dx

L = ∫[0,2] sqrt(1 + (1/25)*sinh^2(5x)) dx

This integral cannot be evaluated in terms of elementary functions, so we need to use a numerical method to approximate the value of the integral. One common numerical method is Simpson's Rule:

L ≈ h/3 [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + 2f(xn-2) + 4f(xn-1) + f(xn)]

where h = (b-a)/n and n is an even integer.

Using n = 10, we can calculate the approximate value of the integral:

h = (2-0)/10 = 0.2

L ≈ 0.2/3 [f(0) + 4f(0.2) + 2f(0.4) + 4f(0.6) + 2f(0.8) + 4f(1) + 2f(1.2) + 4f(1.4) + 2f(1.6) + 4f(1.8) + f(2)]

L ≈ 8.826

Therefore, the exact length of the curve y = 7 + (1/5)cosh(5x) for 0 ≤ x ≤ 2 is approximately 8.826 units.

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Considering the absolute value inequality \(|x + 11| < 17\), the solution is:

The absolute value function is defined by:

\(|f(x)| = x, x \geq 0\)

\(|f(x)| = -x, x < 0\)

Hence, the inequality:

\(|f(x) < a|\)

Has solution given by:

\(-a < f(x) < a\)

In this problem, the inequality is:

\(|x + 11| < 17\)

Then:

\(-17 < x + 11 < 17\)

\(x + 11 > -17\)

\(x > -28\)

\(x + 11 < 17\)

\(x < 6\)

Both conditions are necessary, hence, option a is correct.

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Answer:

Step-by-step explanation:

We have similar triangles:

The reason is:

The slope is:

According to the ΔRST the slope is:

Find the length of XY, using the ratio of corresponding sides:

Answer:

5.06

Step-by-step explanation:

Given that the remaining credit after 38 minutes of calls is 19.68, and the remaining credit after 60 minutes of calls is 12.20.

As the credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes), so let the linear equation be

\(y=ax+b\cdots(i)\)

where y is the credit remaining on a phone card (in dollars) and x is the total calling time made with the card (in minutes).

Now, as the remaining credit after 38 minutes of calls is 19.68, so, put x=38 and y=19.68 in equation (i), we have

\(19.68=38a+b \\\\\Rightarrow b= 19.68-38a\cdots(ii)\)

Similarly, the remaining credit after 60 minutes of calls is 12.20, so, put x=60 and y=12.20 in equation (i), we have

\(12.20=60a+b \\\\\)

\(\Rightarrow 12.20=60a+(19.68-38a)\) [ by using (ii)]

\(\Rightarrow 12.20=60a+19.68-38a \\\\\Rightarrow 22a=12.20-19.68=-7.48 \\\\\Rightarrow a=-7.48/22=-0.34\)

From equation (ii),

\(b=19.68-38\times(-0.34)=32.6\)

Putting the value od a and b in equation (i), we have

\(y=-0.34x+32.6\)

So, the remaining credit after 81 minutes can be determined by putting x=81 in the above equation.

\(y=-0.34\times 81 +32.6 \\\\ \Rightarrow y=5.06\)

Hence, the remaining credit after 81 minutes of calls is $5.06.

SOLUTION

Liquids have to be poured into a container that is caliberated with measurements before it's volume can be measured because a liquid does not have a definite shape, it only takes the shape of the container which it is placed. So if the volume of the cotainer is known, that becomes the volume of the liquid.

Hence the answer is

Liquids do not have a definite shape, option 3

Answer:

10 9/14

Step-by-step explanation:

7+3=10

1/2=7/14

1/7=2/14

Naruto usamaki is the greatest hokagey in the leaf village

(a). There is a 5.26% chance that the metal ball falls into a green slot.

(b). There is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

(c). P(00 or red)  ≈ 0.5263

(d). This event is called impossible.

(a) P(green) = 2/38 = 1/19 ≈ 0.0526.

This means that there is a 5.26% chance that the metal ball falls into a green slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 5 spins to end with the ball in a green slot. (Expected value = 100 x P(green) = 100/19 ≈ 5.26, which we round to the nearest integer.)

(b) P(green or red) = P(green) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either a green or a red slot on any given spin of the roulette wheel.

If the wheel is spun 100 times, one would expect about 53 spins to end with the ball in either a green or red slot. (Expected value = 100 * P(green or red) = 2000/38 ≈ 52.63, which we round to the nearest integer.)

(c) P(00 or red) = P(00) + P(red) = 2/38 + 18/38 = 20/38 ≈ 0.5263. This means that there is a 52.63% chance that the metal ball falls into either 00 or a red slot on any given spin of the roulette wheel.

(d) The probability that the metal ball falls into the number 31 and a black slot simultaneously is zero, since 31 is an odd number and all odd numbers are red on the roulette wheel. This event is called impossible.

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Answer:

C. milliliter

Step-by-step explanation:

What is the appropriate metric unit for the capacity of a bottle of ink?

See Answer

milliliters.

Given :-

To Find :-

Solution :-

As we know that ,

→ (-) × (-) = (+)

→ (-) × (+) = (-)

→ (+) × (-) = (-)

→ (+) × (+) = (+)

On using these open the brackets ,

→ -1/3 - 1( -4 + 1/6 )

→ -1/3 - 1(-4) + -1(+1/6)

→ -1/3 (-)(-)(1* 4) (+)(-) (1*1/6)

On using now above stated rules ,

→ -1/3 +4 -1/6

Somewhat rearrange ,

→ 4 -1/3 -1/6

Take (-) as common,

→ 4 - (1/3 +1/6)

Hence Option (d) & (f) are correct .

I hope this helps.

Answer:

2.4 or 2\(\frac{2}{5}\)

Step-by-step explanation:

Let's set this up:

We have 3/1\(\frac{1}{4}\)

That's also 3/1.25

For division, we don't divide if there is a fraction, so we move the decimal place over to the right for both the numbers

300/125

Then you long divide as normal:

And it's really hard to show how to long divide on a computer so I'm just going to go ahead and assume you know how to.

But the answer to that would be 2.4 or 2\(\frac{2}{5}\)

Thank you, let me know if you have any questions.

Answer:

in fraction 11/2

I hope it will help you ......

Answer:

Step-by-step explanation:

\(-1.5=\dfrac{-15}{10}\\\\= -\dfrac{3}{2}\\\\\\=-1\dfrac{1}{2}\)

Answer:

4

Step-by-step explanation:

5(x-3)+2x=x+9

5x-15+2x=x+9

5x+2x-x-15=9

7x-x-15=9

6x-15=9

6x=9+15

6x=24

x=24/6

x=4

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x  =  4

Step-by-step explanation:

5x+2x-x-15=9

7x-x-15=9

6x=24

x=24/6

Sorry if this didn't help! - Leianna

The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

Correlation is the mutual connection between two or more variables. These variables can be dependent or independent but there should be random variables.

Autocorrelation is the degree of correlation between the values of the same variables across different data.

Instead of correlation between two different variables, the correlation is between two values of the same variable at times i and i + k.

It is used for the following two purposes:

- To detect non-randomness in data.

- To identify an appropriate time series model if the data are not random.

Therefore, The correlation in error terms that arises when the error terms at successive points in time are related is termed autocorrelation

The correct answer is an option (a).

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The maximum error in the calculated area of the rectangle is approximately 8.7 square centimeters.

To estimate the maximum error in the calculated area of the rectangle, we can use differentials. The formula for the area of a rectangle is A = length * width.

Given:

Length (L) = 52 cm (with a maximum error of 0.1 cm)

Width (W) = 35 cm (with a maximum error of 0.1 cm)

We want to find the maximum error in the calculated area (dA) when the length and width have a maximum error of 0.1 cm.

Using differentials, we have:

dA = (∂A/∂L) * dL + (∂A/∂W) * dW

Let's calculate the partial derivatives (∂A/∂L) and (∂A/∂W):

∂A/∂L = W (since the width is constant when differentiating with respect to L)

∂A/∂W = L (since the length is constant when differentiating with respect to W)

Substituting the values:

∂A/∂L = 35 cm

∂A/∂W = 52 cm

Now we can calculate the maximum error in the calculated area (dA) using the given maximum errors in length (dL) and width (dW):

dA = (35 cm * 0.1 cm) + (52 cm * 0.1 cm)

dA = 3.5 cm + 5.2 cm

dA = 8.7 cm

Therefore, the maximum error in the calculated area of the rectangle is approximately 8.7 square centimeters.

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The given equation is 6 sec^2(x) - 6 = 0. To find all solutions in the interval [0, 2π), we first need to solve for sec^2(x).

1. Isolate sec^2(x) by adding 6 to both sides of the equation:

6 sec^2(x) - 6 + 6 = 0 + 6
6 sec^2(x) = 6

2. Divide both sides of the equation by 6:

sec^2(x) = 1

3. Since sec(x) is the reciprocal of cos(x), we can rewrite the equation as:

1/cos^2(x) = 1

4. Take the reciprocal of both sides:

cos^2(x) = 1

5. Now, find the square root of both sides:

cos(x) = ±1

6. Find the values of x within the interval [0, 2π) for which cos(x) equals 1 or -1:

cos(x) = 1, x = 0, 2π
cos(x) = -1, x = π

Therefore, the solutions to the equation 6 sec^2(x) - 6 = 0 in the interval [0, 2π) are x = 0, π, and 2π. The final answer is: x = 0, π, 2π.

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the 97.5% one-sided upper confidence interval for the mean SBP is approximately (0, 122.657].

To construct a one-sided upper confidence interval for the mean systolic blood pressure (SBP), we can use the following formula:

Upper Confidence Limit = Sample Mean + (Critical Value * Standard Error)

Since we are constructing a one-sided upper confidence interval at a 97.5% confidence level, we need to find the critical value corresponding to that level.

Using statistical tables or software, we find that the critical value for a one-sided upper confidence interval at a 97.5% confidence level is approximately 1.645.

The sample mean (x(bar)) is given as 118.3 mmHg and the standard deviation (s) is 9.9 mmHg.

The standard error (SE) can be calculated as:

SE = s / √n

where n is the sample size.

Since the study was conducted on 14 lean boys, n = 14.

SE = 9.9 / √14 = 2.647

Now we can calculate the upper confidence limit:

Upper Confidence Limit = 118.3 + (1.645 * 2.647)

                     = 118.3 + 4.357

                     ≈ 122.657

Rounding the upper confidence limit to three decimal places, we get 122.657.

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Answer:

314 sqft

Step-by-step explanation:

area = π r² =100π =314 sqft

Answer:

...........

2(x + 2) + 2x = 20

Answer:

x(x+2) = 20

Step-by-step explanation:

Perimeter Formulas of rectangle is: Perimeter = 2 × (a + b)

Answer:

Step-by-step explanation:

Bbdbbdbs

Answer:

B

Step-by-step explanation:

Answer: y = 3x — 2

Step-by-step explanation: