A fair dice is rolled.
Work out the probability of getting a factor of 8.
Give your answer in its simplest form.

a) The area of Helen's circular garden is 314 m².

b) The estimation for the number of boxes of grass seed Helen needs, is 5 boxes.

c) B. The estimation we did in (b) is an underestimation.

The area of a circle is calculated by the formula,

A = πr² sq. units; r - radius

When we have the diameter, we can find the radius by

r = d/2 units

Given that Helen has a garden in the shape of a circle of diameter 20 m.

She is going to cover the garden with grass seed to make a lawn.

Grass seed is sold in boxes. Each box of grass seed will cover 58 m² of the garden.

a) The area of the circular garden is

A =  πr² = 3.14 × (d/2)²

⇒ A = 3.14 × (20/2)²

⇒ A = 3.14 × 100

∴ A = 314 m²

Thus, the area of Helen's garden is 314 m².

b) The number of boxes of grass seed to cover the area of 314 m² is

= area of the garden/area covered by each box of seeds

= 314 m²/58 m²

= 5.4179

So, on an estimation, there are 5 boxes of grass seed that Helen needs.

c) Here, in the above estimation, we rounded the decimal number 5.4179 to 5. Since the number is rounded to the nearest value (smallest value), the estimation is an underestimate.

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while statistics is a valuable tool for understanding and making decisions based on data, it is important to remember that mathematics cannot evaluate non-numerical priorities.

Therefore, correct answer will be:- a. Non-numerical priorities

Statistics is a field of mathematics that deals with collecting, analyzing, and interpreting data. It involves the use of mathematical techniques and methods to extract insights and make decisions based on data.

Non-numerical priorities refer to values, beliefs, and preferences that cannot be quantified or measured using numbers. For example, considerations such as morality, ethics, cultural norms, personal opinions, and emotions cannot be expressed or evaluated using mathematical models or statistical techniques.

When making decisions, it is often necessary to take into account these non-numerical priorities, in addition to the quantitative data and analysis.

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The maximum number of packages of hot dogs they can buy is 6.6 packages.

Amount of bill with father and son = $20

Cost of a bottle of lemonade = $3.50

Number of bottles of lemonade bought = 1

Cost of a package of hot dogs = $2.50

Number of packages of hotdogs bought = x

(Cost of a bottle of lemonade × Number of bottles of lemonade bought) + (Cost of a package of hot dogs × Number of packages of hotdogs bought) = Amount of bill with father and son

(3.50 × 1) + (2.50 × x) = 20

3.50 + 2.50x = 20

subtract 3.50 from both sides

2.50x = 20 - 3.50

2.50x = 16.50

divide both sides by 2.50

x = 16.50 / 2.50

x = 6.6 packages

Therefore, the father and son can buy a maximum of 6.6 packages of hotdogs.

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Answer:

The length is 15.71 feet.

Step-by-step explanation:

The probability that the sample average falls outside the 3-sigma control limits of the X-bar chart is 0.27%.

The 3-sigma control limits are calculated using the standard deviation of the process. If the process is in control, then 99.73% of the sample averages will fall within the 3-sigma control limits. The remaining 0.27% of the sample averages will fall outside the control limits.

In this case, the sample size is 4, which is smaller than the sample size of 9 that was used to construct the control chart. This means that the control limits for the sample of size 4 will be narrower than the control limits for the sample of size 9.

As a result, the probability that the sample average falls outside the control limits will be higher for the sample of size 4.

Specifically, the probability that the sample average falls outside the 3-sigma control limits for a sample of size 4 is 0.27%. This means that there is a 0.27% chance that the new employee will observe a sample average that falls outside the control limits, even if the process is in control.

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Answer:

9

Step-by-step explanation:

To remove (-6) from the brackets, two minuses (negatives) cancel each other out becoming a plus (positive).

Example:

3 - (-6) = 3 + 6 = 9

*tip: if you see "- (-" imagine it automatically become a +*

Answer:

\(y=8x-781\)

Here, \(x\) represents temperature and \(y\) denotes rate of chirping per minute.

Step-by-step explanation:

Let \(x\) represents temperature and \(y\) denotes rate of chirping per minute.

At \(106\)°F, a certain insect chirps at a rate of \(67\) times per minute.

Take \((x_1,y_1)=(106,67)\)

At \(108\)°F, they chirp \(83\) times per minute.

Take \((x_2,y_2)=(108,83)\)

Slope intercept form:

\(y-y_1=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)\)

\(y-67=(\frac{83-67}{108-106})(x-106)\\\\y-67=(\frac{83-67}{108-106})(x-106)\\\\y-67=(\frac{16}{2})(x-106)\\\\y-67=8(x-106)\\y-67=8x-848\\y=8x+67-848\\y=8x-781\)

Answer:

See below.

Step-by-step explanation:

\((5x^2y^3)^0\div(-2x^{-3}y^5)^{-2}\)

First, note that everything to the zeroth power is 1. Thus:

\(=1\div(-2x^{-3}y^5)^{-2}=\frac{1}{(-2x^{-3}y^5)^{-2}}\)

Distribute using Power of a Power property:

\(=\frac{1}{(-2)^{-2}(x^{-3})^{-2}(y^5)^{-2})}\)

Make the exponents positive by putting them to the numerator:

\(=\frac{(-2)^2(x^{-3})^2(y^5)^2}{1}\)

\(=\frac{4x^{-6}y^{10}}{1}\)

Make the exponent positive by this time putting it to the denominator:

\(=\frac{4y^{10}}{x^6}\)

Question:

During a walk-a-thon, Noah's time in hours was t, and distance in miles, d, are related by the equation \(\frac{1}{3}d = t\).  A graph of the equation includes points (12,4).

1. Identify the independent variable.

2. What does the point (12,4) represent in this situation?

3. What point would represent the time it took to walk \(7\frac{1}{2}\) miles?  

Answer:

(a) d

(b) He spent 4 hours to walk 12 miles

(c) \((7\frac{1}{2},2\frac{1}{2})\)

Step-by-step explanation:

Given

\(t = \frac{1}{3}d\)

Solving (a): The independent variable

The independent variable, in this problem is the distance walked. Because the distance walked stands alone, and it is when the distance is known, that the time spent is known.

Hence:

The independent variable is distance (d)

Solving (b): What (12, 4) represents

This implies that:

\(distance = 12\)

\(time\ spent = 4\)

So: He spent 4 hours to walk 12 miles

Solving (c): Point to represent the time to walk \(7\frac{1}{2}\) miles

This implies that:

\(d = 7\frac{1}{2}\)

Substitute \(d = 7\frac{1}{2}\) in \(t = \frac{1}{3}d\)

\(t = \frac{1}{3} * 7\frac{1}{2}\)

Express as improper fraction

\(t = \frac{1}{3} * \frac{15}{2}\)

\(t = \frac{5}{2}\)

Express as mixed number

\(t = 2\frac{1}{2}\)

So: The point is, \((7\frac{1}{2},2\frac{1}{2})\)

As, stx = tsx for every eigenvector x of t, and eigenvectors corresponding to distinct eigenvalues are linearly independent, we can conclude that st = ts.

To prove that st = ts, where v is finite-dimensional, t and s are linear operators on v, t has dim v distinct eigenvalues, and s has the same eigenvectors as t (not necessarily with the same eigenvalues), we can use the fact that eigenvectors corresponding to distinct eigenvalues are linearly independent.

Let's consider an eigenvector x of t with eigenvalue λ. We can write this as tx = λx. Now, since s has the same eigenvectors as t, we can write this as sx = λx.

Now, let's consider the product stx. Using the definitions of s and t, we have stx = s(λx) = λ(sx).

Since sx = λx, we can substitute this in the above equation to get stx = λ(λx) = λ²x.

On the other hand, let's consider the product tsx. Using the definitions of s and t, we have tsx = t(λx) = λ(tx).

Since tx = λx, we can substitute this in the above equation to get tsx = λ(λx) = λ²x.

Since stx = tsx for every eigenvector x of t, and eigenvectors corresponding to distinct eigenvalues are linearly independent, we can conclude that st = ts.

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Answer:

pls ask question in English

The degrees of freedom for the sample variance is equal to the number of data points in the sample minus 1, so for a sample of 27 people, the degrees of freedom would be 26.

The degrees of freedom for the sample variance is calculated by taking the number of data points in the sample and subtracting 1. In this case, the sample size is 27 people, so the number of degrees of freedom is 26. This is because we need to account for one degree of freedom in order to calculate the overall variance of the sample. The degrees of freedom is important in estimating the population variance because it helps to determine the size of the sample necessary to accurately estimate the population variance. By knowing the degrees of freedom, we can better understand the accuracy of our estimates and adjust our sample size accordingly.

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we can take the reflection over the line perpendicular to side BC passing through point A as the required transformation.

What is triangle?

A triangle is a closed two-dimensional figure with three straight sides and three angles.

1. To sketch the result of dilating triangle ABC using a scale factor of 2 and a center of A, we first draw a segment from point A to a point B' on the other side of side BC such that AB' = 2AC. Similarly, we draw a segment from point A to a point C' on the other side of side AB such that AC' = 2AB. Finally, we draw the triangle AB'C', which is the image of triangle ABC after dilation with a scale factor of 2 and center at point A.

Here is a sketch of triangle AB'C':

B'

 / \

/   \

A-----C'

2. To sketch the result of dilating triangle ABC using a scale factor of -2 and a center of A, we first draw a line through point A and perpendicular to side BC. Let the intersection of this line with BC be called D. Then, we draw a segment from point A to a point B" on the other side of line AD such that AB" = 2AD. Similarly, we draw a segment from point A to a point C" on the other side of line AD such that AC" = 2AD. Finally, we draw the triangle AB"C", which is the image of triangle ABC after dilation with a scale factor of -2 and center at point A.

3. To find a transformation that would take triangle AB'C' to AB"C", we first note that the dilation with a scale factor of -2 and center at point A is equivalent to a composition of a reflection over the line perpendicular to side BC passing through point A followed by a dilation with a scale factor of 2 and center at point A.

Therefore, we can take the reflection over the line perpendicular to side BC passing through point A as the required transformation.

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Answer:

ΔABC is congruent to ΔEDC by the Angle-Side-Angle congruency rule

Step-by-step explanation:

The

Statement                   \({}\)                                    Reason

∠FAB ≅ ∠GED                   \({}\)                             Given

C = Midpoint of \(\overline {AE}\)                     \({}\)                    Given

∠BAC and ∠FAB are supplementary             Angles on a straight line

∠DEC and ∠GED are supplementary             Angles on a straight line

∠BAC ≅ ∠DEC                     \({}\)                            Transitive property

\(\overline {AC}\) ≅ \(\overline {CE}\)                    \({}\)                                       Definition of midpoint

ΔABC ≅ ΔEDC                     \({}\)                             ASA congruency rule  

Where two angles and an included side of one triangle is congruent to the corresponding two angles and an included side of another triangle, both triangles are congruent.     \({}\)                              

Answer:

Option i) At least 64 of the numbers are greater than or equal to 35 must be true

Since the median is 35, we know that there are 63 numbers greater than 35 and 63 numbers smaller than 35. However, since there is an odd number of total numbers (127), the median itself must be included in one of these groups. Therefore, there are at least 64 numbers that are greater than or equal to 35.

The probability that a box weighs between 16.4 and 16.5 ounces is approximately 14.45% (rounded to 2 decimal places). To solve this problem, we need to use the z-score formula:
z = (x - μ) / σ
where x is the weight of the box, μ is the mean weight of all boxes, σ is the standard deviation of weights, and z is the number of standard deviations away from the mean.

In this case, we want to find the probability that a box weighs between 16.4 and 16.5 ounces. We can convert these weights to z-scores as follows:

z1 = (16.4 - 16.3) / 0.21 = 0.48
z2 = (16.5 - 16.3) / 0.21 = 0.95

Using a z-score table or calculator, we can find the area under the standard normal curve between these two z-scores:

P(0.48 ≤ z ≤ 0.95) = 0.1736

Therefore, the probability that a box weighs between 16.4 and 16.5 ounces is 0.17 or 17% (rounded to 2 decimal places).
Hi! To find the probability that a box weighs between 16.4 and 16.5 ounces, we can use the z-score formula and the standard normal table.

First, let's calculate the z-scores for 16.4 and 16.5 ounces using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 16.4 ounces:
z1 = (16.4 - 16.3) / 0.21 ≈ 0.48

For 16.5 ounces:
z2 = (16.5 - 16.3) / 0.21 ≈ 0.95

Now, use the standard normal table to find the area between these z-scores:
P(0.48 < z < 0.95) = P(z < 0.95) - P(z < 0.48) ≈ 0.8289 - 0.6844 = 0.1445

The probability that a box weighs between 16.4 and 16.5 ounces is approximately 14.45% (rounded to 2 decimal places).

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You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:

slope = (3 - 4) / (3 - x - x)

slope = -1 / (3 - 2x)

To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.

For example, if x = 1, the slope of the secant line PQ is:

slope = -1 / (3 - 2(1))

slope = -1 / (3 - 2)

slope = -1 / 1

slope = -1

Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

And so on, you can calculate the slope of the secant line for different values of x.

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The monthly rate for the given loan is 1.0118%.The annual rate for this loan is 12.1423%.

Given loan: $150,000

Payment per month: $1,770

Duration of loan: 10 years

Interest = ?

The formula for monthly payment is given by:

\(PV = pmt x (1 - (1 + r)^-n) / r\)

Where, PV is the present value, pmt is the payment per period, r is the interest rate per period and n is the total number of periods.Solving the above formula for r will give us the monthly rate for the loan.

r = 1.0118%The monthly rate for the given loan is 1.0118%.The annual rate can be calculated using the following formula:

Annual rate = \((1 + Monthly rate)^12 - 1\)

Annual rate = 12.1423%

The annual rate for this loan is 12.1423%.The effective annual rate can be calculated using the following formula:

Effective annual rate =\((1 + r/n)^n - 1\)

Where, r is the annual interest rate and n is the number of times interest is compounded per year.If interest is compounded monthly, then n = 12

Effective annual rate = (1 + 1.0118%/12)^12 - 1

Effective annual rate = 12.6801%

The effective annual rate for this loan is 12.6801%.

Total amount paid after 10 years = Monthly payment x Number of payments

Total amount paid after 10 years = $1,770 x 120

Total amount paid after 10 years = $212,400

The total amount paid after 10 years is $212,400.

The future value for this loan can be calculated using the following formula:

FV = PV x (1 + r)^n

Where, PV is the present value, r is the interest rate per period and n is the total number of periods.If the loan is paid off in 10 years, then n = 120 (12 payments per year x 10 years)

FV = $150,000 x (1 + 1.0118%)^120

FV = $259,554.50

The future value for this loan is $259,554.50.

Thus, the monthly rate for the loan is 1.0118%, the annual rate for this loan is 12.1423%, the effective annual rate for this loan is 12.6801%, the total amount paid after 10 years is $212,400 and the future value for this loan is $259,554.50.

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1. Null hypothesis: The mean age of purchasers and non-purchasers of toothpaste is the same. Alternative hypothesis: The mean age of purchasers and non-purchasers of toothpaste is significantly different.

2. The test statistic T can be calculated using the formula T = (X1 - X2) / (S1^2/n1 + S2^2/n2)^0.5, where X1 and X2 are the mean ages of purchasers and non-purchasers, S1 and S2 are the standard deviations of purchasers and non-purchasers, and n1 and n2 are the sample sizes. In this case, T = (37.21 - 30.7) / (6.612/50 + 8.35^2/50)^0.5 = 4.035.

3. The p-value can be calculated using a t-distribution with 98 degrees of freedom (since we have two samples of size 50 and therefore 98 degrees of freedom). Using Excel, the p-value is 0.0001.
4. The critical value can be found using a t-distribution with 98 degrees of freedom and a significance level of 0.01. Using Excel, the critical value is 2.364.

5. Since the calculated test statistic (T = 4.035) is greater than the critical value (2.364), we reject the null hypothesis and conclude that the mean age of purchasers and non-purchasers of toothpaste is significantly different at the 1% significance level.

6. Therefore, we can conclude that age is a significant factor in determining whether someone purchases toothpaste or not. Further research may be necessary to investigate other factors that may influence purchasing decisions. The attached Excel file includes all calculations and output.

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Answer:

Step-by-step explanation:

θ=l/r

where θ is central angle in degrees.

l=length of arc.

r=radius of circle.

6=14/r

6r=14

r=14/6=7/3 =2 1/3 inches.

The optimal measure of variability is the IQR, which equals 4. The proper measure of variability for the data is C.

The difference among the third and the first quartile is defined by the interquartile range. The entire series is divided into four equally sized pieces by the partitioned values referred to as quartiles. Three quartiles are present.

The spread of the middle 50% of the data, which is less susceptible to outliers than the range, is measured by the interquartile range (IQR), which is the best measure of variability for these data.

The IQR is calculated by deducting the third quartile (\(Q_3\)) from the first quartile (\(Q_1\)). We can see from the box plot that \(Q_1\) is roughly

17 and \(Q_3\) is roughly 21.

Therefore,

\(IQR=Q_3-Q_1\\\\IQR=21-17\\\\IQR=4\)

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The triangle is a right triangle, and the length of segment BD is 16.30

Start by calculating the length CD using the following Pythagoras theorem

\(CD = \sqrt{28.9^2 - 24.2^2}\)

Evaluate

\(CD = \sqrt{249.57}\)

Take the square of both sides

CD^2 = 249.57

The length BD using the following Pythagoras theorem

\(BD = \sqrt{CB^2 - CD^2}\)

So, we have:

\(BD = \sqrt{22.7^2 - 249.57}\)

Evaluate

\(BD = \sqrt{265.72}\)

Evaluate the square root

BD = 16.30

Hence, the length of segment BD is 16.30

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Answer:

area: 45 , perimeter: 2,025

Step-by-step explanation:

Answer:

Step-by-step explanation:

Parameters are measurable factors that can be used in an equation to calculate a result. The correct answer is E.

Parameters are measurable factors that can be used in an equation or model to calculate a result or make predictions. They are variables or values that can be adjusted or assigned specific values to influence the outcome of the equation or model.

In various fields, such as mathematics, physics, statistics, and computer science, parameters play a crucial role in describing relationships, making predictions, and solving problems.

In scientific and mathematical contexts, parameters are typically assigned specific values or ranges of values to represent the properties of a system or phenomenon under study. These values can be adjusted or modified to analyze different scenarios or conditions.

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Answer:

Swimming: We are able to swim because our density is just barely lower than the density of water.

Balloons: they are possible because we fill them with a low density substance/carbon dioxide.

Boating: Boats float because they are less dense than water.

Hot air balloons: they fly because we design them to have the same density as air.

Step-by-step explanation:

18p is the answer correct this

Answer:

the bottom one

Step-by-step explanation:

pls mark brainliest

Answer:

The second graph.

(a) The partial fraction decomposition of 2x² - 4(3x - 2)²(x + 3)(x² + 1) yields a general form consisting of multiple terms. The coefficients are not required for this problem.
(b) To find the partial fraction decomposition of x² + 6x + 10 / (x + 1)²(x + 2), we need to determine the coefficients. The decomposition involves expressing the rational function as a sum of simpler fractions with numerators of lower degrees than the denominator.


(a) The partial fraction decomposition of 2x² - 4(3x - 2)²(x + 3)(x² + 1) will have a general form with multiple terms. However, finding the coefficients is not necessary for this problem, so the specific expressions for each term are not provided.

(b) To find the partial fraction decomposition of x² + 6x + 10 / (x + 1)²(x + 2), we need to determine the coefficients. The decomposition involves expressing the rational function as a sum of simpler fractions with numerators of lower degrees than the denominator. We can start by factoring the denominator as (x + 1)²(x + 2). The decomposition will consist of terms with unknown coefficients over each factor of the denominator. In this case, the decomposition will have the form:

x² + 6x + 10 / (x + 1)²(x + 2) = A / (x + 1) + B / (x + 1)² + C / (x + 2),

where A, B, and C are the coefficients that need to be determined. By multiplying both sides of the equation by the denominator, we can find a common denominator and equate the numerators. The resulting equation will allow us to solve for the coefficients A, B, and C, which will complete the partial fraction decomposition.

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Answer: A) Yes, mold A is an exponential function that decreases faster than mold B, which is eventually an increasing quadratic function.

Step-by-step explanation:

To determine whether the number of spores in mold B will ever be larger than in mold A, we need to compare the growth patterns of the two functions. The function f(x) = 100(0.75)^(x-1) represents mold A, and it is an exponential function. Exponential functions decrease as the exponent increases. In this case, the base of the exponential function is 0.75, which is less than 1. Therefore, mold A is a decreasing exponential function. The function g(x) = 100(x-1)^2 represents mold B, and it is a quadratic function. Quadratic functions can have either a positive or negative leading coefficient. In this case, the coefficient is positive, and the function represents a parabola that opens upwards. Therefore, mold B is an increasing quadratic function. Since mold B is an increasing function and mold A is a decreasing function, there will be a point where the number of spores in mold B surpasses the number of spores in mold A. Thus, the correct answer is:

A) Yes, mold A is an exponential function that decreases faster than mold B, which is eventually an increasing quadratic function.