a circular spinner is divided into 10 sectors of equal area: 2 red sectors, 3 blue, 4 yellow, and 1 green. find p(blue) on a single spin.

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

More can be learned about equivalent expressions at https://brainly.com/question/15775046

#SPJ1

Answer:

W = 4

Step-by-step explanation:

4/6 = 6/9

2/3 = 2/3  

Answer:

D) 56

Step-by-step explanation:

\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)

Answer:

14.4913767

Step-by-step explanation:

The bell-shaped curve, also known as a Gaussian curve or a symmetrical distribution , showcases a central peak with data symmetrically distributed around it .

Revered for its iconic shape, the bell curve enchants the discerning observer with its symmetrical countenance, reminiscent of a resonant chime.

This majestic distribution unveils its true essence through its discernible apex, a testament to central tendency , where the mean, median, and mode converge, bestowing upon it an air of distinction .

The rough sketch of the curve having the bell shape is shown attached to the question.

Find out more on bell curves at https://brainly.com/question/3441134

#SPJ1

Answer:

304.51.

Step-by-step explanation:

Your question is kind of confusing but I think your question is 8.23 x 37. The answer to that is 304.51.

The dimensions of the box packing the 36 basketballs are 88.5 inches (length) × 88.5 inches (width) × 118 inches (height).

To determine the dimensions of the box, we need to consider the arrangement of the basketballs and their diameter.

Given that there are 36 basketballs in a 3 × 3 × 4 formation, this means there are 3 basketballs stacked in the length, 3 basketballs stacked in the width, and 4 basketballs stacked in the height within the box.

Let's consider the length first.

Since there are 3 basketballs stacked in the length, and each basketball has a diameter of 29.5 inches, the length of the box can be calculated as:

Length = 3 × 29.5 inches = 88.5 inches

Next, let's consider the width.

Similarly, since there are 3 basketballs stacked in the width, the width of the box is:

Width = 3 × 29.5 inches = 88.5 inches.

Finally, let's consider the height.

With 4 basketballs stacked in the height, the height of the box is:

Height = 4 × 29.5 inches = 118 inches

For similar question on dimensions.

https://brainly.com/question/7582047  

#SPJ8

Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

CosФ=24/25

Sin Ф=7/25 CoseceФ=25/7

TanФ=7/24 cotФ=24/7

SecФ=25/24

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

For similar question on population sample.

https://brainly.com/question/27859177  

#SPJ8

The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

The correct answer is D.

The function f(x) has some specific characteristics as shown in the graph.

The graph of f(x) has five intercepts, as can be seen from the graph.

The intercepts of f(x) can be determined by observing where the graph of f(x) crosses the x-axis.

The function f(x) intercepts the x-axis at five different points: -6 only, -2, -1, 1, and 3 only.

At these points, f(x) = 0.
Furthermore, the graph of f(x) is increasing from -∞ to -6, then decreasing from -6 to -2.

The graph of f(x) then increases from -2 to -1, decreases from -1 to 1, increases from 1 to 3, and finally decreases from 3 to +∞.

Hence, we can deduce that the graph of f(x) has a local maximum point at x = -6, a local minimum point at x = -2, and another local minimum point at x = 3.
We can also conclude that f(x) is an odd function, meaning that f(-x) = -f(x).

This can be deduced from the symmetry of the graph about the origin.

Finally, we can see from the graph that the function f(x) is continuous everywhere except at x = -2 and x = 3.

At these points, f(x) is not defined.
The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

For such more questions on intercepts

https://brainly.com/question/24212383

#SPJ8

Answer:

288.62

Step-by-step explanation:

Answer:

the numbers would be 5 and 7.

Step-by-step explanation:

"the difference of two numbers is 2."

"their sum is 12."

since the difference of 7 and 5 is 2 and the sum of 7 and 5 is 12, 5 and 7 are the numbers that fulfill the statement.

i hope this helps! have a lovely rest of your day <3

Answer:

The answer is below

Step-by-step explanation:

The cost price (manufacturing price) of an article is Rs.50.

Retailer 1 marks his price 10% above cost, hence the selling price for retailer 1 is:

Selling price for retailer 1 = 10% of Rs.50 + Rs.50 = (0.1 * Rs.50) + Rs.50 = Rs.55

Retailer 2 sets a profit of 20% on his returns, hence the selling price for retailer 2 is:

Selling price for retailer 2 = 20% of Rs.50 + Rs.50 = (0.2 * Rs.50) + Rs.50 = Rs.60

The difference  between the retailers selling prices = Rs.60 - Rs.50 = Rs.10

The retailer with the highest price sells for Rs.60 and the difference between the retailers selling prices is Rs.10. For the profit to be equal, the percentage discount is:

Discount = (Rs.10 / Rs.60) * 100% = 16.67%

The image of vertex C under the given similarity transformation is (4, 2).

To apply the given similarity transformation, we need to perform two transformations: a rotation of 90 degrees counterclockwise about the origin (denoted by R) and a dilation by a factor of 2 (denoted by D2). We perform the transformations in order: first the rotation, then the dilation.

The image of a point (x, y) after a rotation of 90 degrees counterclockwise about the origin is (-y, x).

Thus, the image of C after the rotation is:

C' = (-(-2), 1) = (2, 1)

To find the image of C' after the dilation by a factor of 2, we multiply each coordinate by 2:

C" = (22, 21) = (4, 2)

Therefore, the image of vertex C under the given similarity transformation is (4, 2).

Learn more about Transformation here:

https://brainly.com/question/13801312

#SPJ1

Answer:

\( y'' =12x^2 -72=0\)

And solving we got:

\( x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}\)

We can find the sings of the second derivate on the following intervals:

\( (-\infty<x< -\sqrt{6}) , y'' = +\) Concave up

\(x=-\sqrt{6}, y =-180\) inflection point

\( (-\sqrt{6} <x< \sqrt{6}), y'' =-\) Concave down

\(x=\sqrt{6}, y=-180\) inflection point

\( (\sqrt{6}<x< \infty) , y'' = +\) Concave up

Step-by-step explanation:

For this case we have the following function:

\( y= x^4 -36x^2\)

We can find the first derivate and we got:

\( y' = 4x^3 -72x\)

In order to find the concavity we can find the second derivate and we got:

\( y'' = 12x^2 -72\)

We can set up this derivate equal to 0 and we got:

\( y'' =12x^2 -72=0\)

And solving we got:

\( x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}\)

We can find the sings of the second derivate on the following intervals:

\( (-\infty<x< -\sqrt{6}) , y'' = +\) Concave up

\(x=-\sqrt{6}, y =-180\) inflection point

\( (-\sqrt{6} <x< \sqrt{6}), y'' =-\) Concave down

\(x=\sqrt{6}, y=-180\) inflection point

\( (\sqrt{6}<x< \infty) , y'' = +\) Concave up

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

Learn more on the variance of a set of data here: https://brainly.com/question/30701163

#SPJ1

a. The monthly contribution from a friend's company is $120 minus 0.5, or $60.

b. The total monthly contribution to the fund is $180.

The computation of FV in Excel is shown in the attachment below:

Using the current number as a starting point, subtract the prior value to determine the growth rate. To calculate the growth rate in percentage terms, divide the difference by the previous amount and multiply the result by 100. Growth Rate equals (Ending Value - Beginning Value) - 1. The year-over-year (YoY) growth rate of a business, for instance, would be 20% if its revenue increased from $100 million in 2020 to $120 million in 2021.

GDP, turnover, wages, etc., all have growth rates that reflect how much they have changed over time (month, quarter, year). Percentages are a pretty common way to communicate it.

20 years is the age.

20 times 12 periods equals 240.

3% growth rate

The computation of FV in Excel is shown in the attachment below:

So, FV= $7,223,115.77

To know more about growth rate, visit:

https://brainly.com/question/11743945

#SPJ1

The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:

\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)

Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:

\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)

APR = (1.0100333³ - 1) x 4

APR = 0.04033 x 4

APR = 0.16132 or 16.132%

Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To know more about APR follow

https://brainly.com/question/2772156

#SPJ9

Answer:

Step-by-step explanation:

x + y = 102000

y = 102000 - x

x(0.10) + y(0.14) = 11320

x(0.10) + (102000 - x)(0.14) = 11320

0.10x + 14280 - 0.14x = 11320

0.04x = 2960

x = $74000 in the 10% account

102000 - 74000 = $28000 in the 14% account

b) to limit the risk to the overall investment plan

The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

If you want to learn more about speed:

https://brainly.com/question/4931057

#SPJ1

Hello there I hope you are having a great day :) You Question A plumber can complete a job in 2 hours. If an apprentice helps, it takes only 1 1/3 hours. How long would it take the apprentice working alone?

(1 1/3) / 2 + (1 1/2) / a = 1

(4/3)a + (4/3)2 = 2a              multiply both sides by 2a

(4/3)2 = (2/3)a                      subtract (4/3)a from both sides

8/3 = 2a/3                            simplify

8 = 2a

4 = a

Hopefully that help you :)

Answer:

30 feet

Step-by-step explanation:

We can use ratios to answer this question:

8 foot shadow: 20 feet high

Therefore if we multiply both sides by 1.5

12 foot shadow: 30 feet high

Check the picture below.

Answer:

  61.03°

Step-by-step explanation:

You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.

The law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...

  c² = a² +b² -2ab·cos(C)

Solving for angle C, we have ...

  cos(C) = (a² +b² -c²)/(2ab)

  C = arccos((a² +b² -c²)/(2ab))

In this triangle, that means ...

  C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)

  C ≈ 61.03°

The angle of interest is about 61.03°.

__

Additional comment

We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)

<95141404393>

The system of linear equations has no solution

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.

In this problem, we have two equations which are;

x = 10 + 6y ...eq(i)

x - 6y = 5 ...eq(ii)

From eq(i)

x = 10 + 6y;

We can substitute this into eq(ii)

10 + 6y - 6y = 5

10 +0 = 5

Since y is already canceled out, we don't have solution to this equations.

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

Answer:

  -43/102

Step-by-step explanation:

You want the value of the given expression involving radicals and logs.

The relevant rules of logarithms and radicals are ...

  \(\log_b{(b^a)}=a\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\)

The given expression can be simplified as follows.

  \(\dfrac{\log_3{\sqrt{243\sqrt{81\sqrt[3]{3}}}}}{\log_2{\sqrt[4]{64}}+\log{10^{-10}}}=\dfrac{\log_3{(3^5\cdot(3^4\cdot3^{\frac{1}{3}})^{\frac{1}{2}})^{\frac{1}{2}}}}{\log_2{2^{\frac{6}{4}}}+(-10)}\\\\\\=\dfrac{\log_3{3^{(5+13/6)(1/2)}}}{3/2-10}=\dfrac{43/12}{-17/2}=-\dfrac{2\cdot43}{12\cdot17}=\boxed{-\dfrac{43}{102}}\)

A suitable calculator can give you the same result.

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

For more questions on Function .

https://brainly.com/question/11624077

#SPJ8

Answer:

200.96 cm^2

Step-by-step explanation:

πr^2 is the formula for the area of a circle

π*8^2

64π

substitute pi with 3.14

64 * 3.14 = 200.96

200.96

mark brainliest please!