7
A number cube was rolled as part of an experiment. The results are displayed in the table below.
Number
Frequency
1 2
3
4 6 5
4
7
5 6
3 ¹5
What is the best explanation of how to find the experimental probability of rolling a 3?
O To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total
number of trials. Simplify if necessary.
O To find the experimental probability of rolling a three, write a ratio of the total number of trials to the frequency of the
number three. Simplify if necessary.
O To find the experimental probability of rolling a three, write a ratio of the number three to the total number of trials.
Simplify if necessary.
To find the experimental probability of rolling a three, write a ratio of the total number of trials to the number three.
Simplify if necessary.

The linear equation that passes through the two given points is

3y - 2x = 22

Remember that a linear equation that passes through the points (x₁, y₁) and (x₂, y₂) has a slope:

a = (y₂ - y₁)/(x₂ - x₁)

In this case the points are  (-5,4) and (10,14), then the slope is:

a = (14 - 4)/(10 + 5) = 10/15 = 2/3

Then the line is something like:

y = (2/3)*x + b

To find the value of b, you can replace the values of one of the points there.

14 = (2/3)*10 + b

14 - 20/3 = b

22/3 = b

Then the line is:

y = (2/3)*x + 22/3

3y = 2x + 22

3y - 2x = 22

That is the line that passes through the two points.

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Answer:

C

Step-by-step explanation:

using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{40}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{18}{40}[/tex] ) ≈ 27° ( to the nearest degree )

The Use of  python programming language to find the differentiation of y= e^2x sin2x/cos 4x. is given in the image attached.

This programming code given in the image is one that uses SymPy's symbolic mathematics abilities to create a function, calculates its derivative, and then utilizes the lambdify feature to generate NumPy functions that can be applied to evaluate the function and its derivative at particular locations.

Therefore, through the use of matplotlib, a variety of x values are generated and the function and its derivative are plotted.

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There are no sufficient evidence using hypothesis to conclude percentage of commercial truck drivers those who suffer from sleep apnea is different from population's percentage of 5.2%.

To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.2%,

Use a hypothesis test.

Let p be the true proportion of commercial truck drivers who suffer from sleep apnea.

The null hypothesis is that the proportion of commercial truck drivers who suffer from sleep apnea is equal to 5.2%, or p = 0.052.

The alternative hypothesis is that the proportion is not equal to 5.2%, or p ≠ 0.052.

Use a z-test for the proportion to test this hypothesis.

The test statistic is,

z = (p₁ - p) / √(p(1-p) / n)

where p₁ is the sample proportion, n is the sample size, and p is the hypothesized population proportion.

In this case, we have,

p₁ = 30/397

   = 0.0756

n = 397

p = 0.052

Plugging these values into the formula, we get,

z = (0.0756 - 0.052) / √(0.052(1-0.052) / 397)

 = 2.11

The critical value for a two-tailed test at a 0.02 level of significance is ±2.33.

Since our test statistic, 2.11, is less than the critical value of 2.33, we fail to reject the null hypothesis.

Therefore, as per hypothesis we do not have sufficient evidence to conclude percentage of commercial truck drivers who suffer from sleep apnea is different from population's percentage of 5.2%.

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The radian solutions of the equation are θ = 2.71 and θ = 0.43 radians

From the question, we have the following parameters that can be used in our computation:

-sin² (θ) - 2sin (θ) + 1 = 0

Divide through by -1

So, we have

sin² (θ) + 2sin(θ) - 1 = 0

Let y = sin(θ)

So, we have

y² + 2y - 1 = 0

When solved graphically, we have

y = 0.414 and -2.414

This means that

sin(θ) = 0.414 and sin(θ) = -2.414

Take the arcsin of both sides

θ = 2.71 and θ = 0.43

Hence, the angles are θ = 2.71 and θ = 0.43

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Approximately 17.95% of the people over the age of 55 prefer other sports and/or hate sports.

The number of people in the "55 and older" age group who prefer other sports or hate sports is 7.

Now we need to find the total number of people in the "55 and older" age group, which is 39.

To find the percentage, we'll use the following formula:

Percentage = (Number of people in the category / Total number of people in the age group) * 100

Percentage = (7 / 39) * 100

Percentage ≈ 17.95%

So, approximately 17.95% of the people over the age of 55 prefer other sports and/or hate sports.

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Answer:

1250 m²

Step-by-step explanation:

Area of rectangle = L x W

L = 50 meters

W = 25 meters

Let's solve

50 x 25 = 1250 m²

So, the area of the piece of land is 1250 m²

There are 57 green cards in the deck.

We are given the ratio of green cards to blue cards in a deck as 3 to 2, and there are 38 blue cards in the deck. Our goal is to find the number of green cards in the deck.

Step 1: Write the given ratio as a fraction.
Green cards / Blue cards = 3/2

Step 2: Use the information provided to create an equation.
Since we know there are 38 blue cards, we can write the equation as:
Green cards / 38 = 3/2

Step 3: Solve for the number of green cards.
To find the number of green cards, we can cross-multiply the equation:
Green cards = (3/2) × 38

Step 4: Calculate the result.
Green cards = (3 × 38) / 2
Green cards = 114 / 2
Green cards = 57

So, there are 57 green cards in the deck.

In summary, to find the number of green cards in the deck, we first expressed the given ratio as a fraction, then used the information provided to create an equation.

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The number of chairs that Mr. Carter can paint in 3 hours is (60/t) chairs and he would use (15/t) litres of paint to paint them.

We know that Mr. Carter can paint 20 chairs in t hours. Therefore, we can say that he can paint:

(20 chairs) / (t hours) = (20/t) chairs per hour

Using this rate, we can find the number of chairs that he can paint in 3 hours as:

(20/t chairs per hour) x (3 hours) = (60/t) chairs in 3 hours

Now we can use the information that Mr. Carter uses 3 litres of paint for every 12 chairs that he painted. This means he uses 1 litre of paint for every 4 chairs painted. Therefore, he would use:

(60/t) chairs / 4 chairs per litre = (15/t) litres of paint

So, in terms of t, the number of chairs that Mr. Carter can paint in 3 hours is (60/t) chairs and he would use (15/t) litres of paint to paint them.

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The function is a logarithmic function

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = { 2 , 5 , 8 , 11 , 14 }

Now , the values of x of the function are

x = { 2 , 6 , 18 , 54 , 162 }

Plotting the points on the graph , we get a logarithmic equation

Hence , the function is logarithmic

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Answer:

D: $1.75

Step-by-step explanation:

To calculate the expected value of the payout, we need to multiply each cash prize amount by the probability of winning that prize and then sum the results.

The probability of winning the $350 prize is 1/400, since there is only one $350 prize and 400 tickets sold. The probability of winning the $200 prize is 1/399, since there is only one $200 prize and one ticket has been removed from the pool of available tickets. Similarly, the probability of winning the $100 prize is 1/398 and the probability of winning the $50 prize is 1/397.

So, the expected value of the payout is:

(1/400) x $350 + (1/399) x $200 + (1/398) x $100 + (1/397) x $50 = $0.875 + $0.501 + $0.251 + $0.126 = $1.753

Therefore, the expected value of the payout is $1.75 (rounded to the nearest cent). So, the answer is D: $1.75.

Answer:

The value of the expected value of payout is $1.75.

What is expected value?

In probability theory, the idea of expected value denotes the typical result of a random event when the event is repeated a lot of times. It is determined by multiplying each potential result by its likelihood before adding together all of these numbers. The anticipated value can shed light on the possible risks and benefits associated with various options or scenarios, making it frequently used to estimate the long-term average of a random process or to make decisions under uncertainty.

To get the payout we need to determine the probability of winning each prize.

For first prize = 1/400

Second prize = 1/400.

Third prize = 1/400.

Fourth prize = 1/400.

The expected value is calculated as:

(1/400) * $350 + (1/400) * $200 + (1/400) * $100 + (1/400) * $50

= $0.875 + $0.50 + $0.25 + $0.125

= $1.75

Hence, the value of the expected value of payout is $1.75.

Step-by-step explanation:

The value of c is 12 for the given expression c = (2)(1) + (-1)(-1) + (3)(3)

To find the value of c, we need to perform the calculation

c = (2)(1) + (-1)(-1) + (3)(3)

Expanding the products, we get:

c = 2 + 1 + 9

Simplifying, we get:

c = 12

So the value of c is 12.

However, no information is given about d or any other values, so we cannot calculate the value of d or any other variables with the given information.

Overall, the calculation to find c is (2)(1) + (-1)(-1) + (3)(3) = 12.

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-- The given question is incomplete, the complete question is

"Find the value of c for the given expression c = (2)(1)+(-1)(-1)+(3)(3)" --

a) 18.80% probability that among 18 randomly observed individuals exactly 4 do not cover their mouth when sneezing

b) 10.4 probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing.

c) It would not be surprising if fewer than half covered their mouth when​ sneezing.

Using the formula,

P(X= x) = C( n, x)[tex]p^x q^{1-x[/tex]

Here n= 18, p= 0.267

a) P(X= 4)

= C( 18, 4) [tex]0.267^{18} 0.733^{14[/tex]

= 3060 x 4.755 x [tex]10^{-11[/tex] x 0.01292574681

= 188.073 x [tex]10^{-11[/tex]

b) The probability is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

P(X= 0) =0.0037

P(X= 1)= 0.0245

P(X= 2)= 0.0758

So, P(X < 3) = 0.0037 + 0.0245 + 0.0758 = 0.104

c) E(X) = np = 18 x 0.267 = 4.81.

and, standard deviation

= √18 (0.267)(0.733)

= 1.88

Thus, it would not be surprising if fewer than half covered their mouth when​ sneezing.

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Answer:

D) 48

Step-by-step explanation:

area = length x width x height

8 x 2 x 3

16 x 3 = 48

The solution to the possible values of θ for the trigonometric equation is given by θ = 0.96255... + 2πn and θ = 2π - 0.96255... + 2πn

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

4sec ( θ ) - 7 = 0

Adding 7 on both sides , we get

4sec ( θ ) = 7

Divide by 4 on both sides , we get

sec ( θ ) = 7/4

From the trigonometric relations , we get

sec θ = 1/cos θ

cos θ = 4/7

Taking inverse on both sides , we get

θ = 0.96255... + 2πn and θ = 2π - 0.96255... + 2πn

Hence , the solution to the equation is θ = 0.96255... + 2πn and θ = 2π - 0.96255... + 2πn

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the solution is [tex]x = \pi /3, 2\pi /3[/tex].

the equation's solutions in the range [0,21) are π/3 and 2π/3. Because it is already included in the solutions to the first equation.

A mathematical statement that declares two expressions to be equal is known as an equation. In most cases, it is made up of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division. The two expressions on either side of the equal symbol "=" are considered to be equivalent. Equations are used to explain how variables relate to one another and to solve issues by identifying the values of the variables that satisfy the equation. Equations are essentially instruments that allow us to communicate and work with mathematical ideas and concepts in a clear, accurate, and succinct way.

Setting each element to zero and figuring out x will allow us to solve the equation:

As much as

[tex]2 cos x + 1 = 0, 2 sin x - 3 = 0[/tex]

When we solve the first equation, we obtain:

[tex]2 sin x = \sqrt3\\sin x = \sqrt3/2[/tex]

In the range [0,21], there are two solutions to this equation: π/3 and 2π/3.

When we solve the second equation, we obtain:

[tex]2 cos x = -1\\cos x = -1/2[/tex]

There is just one answer to this equation in the range [0,21): 2π/3.

As a result, the equation's solutions in the range [0,21) are π/3 and 2π/3. Because it is already included in the solutions to the first equation, we have omitted the solution from the second equation, 2π/3 .

Thus, the solution is

[tex]x = \pi /3, 2\pi /3.[/tex]

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We can choose different fruits in 252 ways.

Given that, a smoothie shop offers 10 different kinds of fruit. we need to select 5 kinds of fruits, we need to find the in how many ways can we do so,

Using the concept of combination,

ⁿCₓ = n! / r!(n-r)!

Therefore,

¹⁰C₅ = 10! / 5!(10-5)!

¹⁰C₅ = 10! / 5!·5!

¹⁰C₅ = 10·9·8·7·6·5! / 5!·5!

¹⁰C₅ = 10·9·8·7·6 / 5!

¹⁰C₅ = 252

Hence, we can choose different fruits in 252 ways.

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The measure of angle x of the quadrilateral inscribed in a circle is x = 31°

Given data ,

Let the quadrilateral be ABCD inscribed in a circle

Now , the measure of angles of the quadrilateral are

Opposite angles are supplementary: A + C = 180° and B + D = 180°.

Adjacent angles are supplementary: A + B = 180°, B + C = 180°, C + D = 180°, and D + A = 180°

And , the sum of opposite angles is always equal to 180°

So , the measure of 118° + 2x° = 180°

On simplifying , we get

2x = 62

Divide by 2 on both sides , we get

x = 31

Hence , the angle is solved and x = 31

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Answer:

50° 54' 55"

Step-by-step explanation:

To convert decimal degrees to degrees, minutes, and seconds, we can use the following conversion factors:

1 degree = 60 minutes

1 minute = 60 seconds

To convert 350.9154° to degrees, minutes, and seconds, we can follow these steps:

Therefore, 350.9154° is equivalent to 350° 54' 55".

Answer:

Step-by-step explanation:

Correct option is C)

Let α be the common root,

⇒α

2

+bα+c=0.....(i) and α

2

+cα+b=0.....(ii)

(i)−(ii)⇒(b−c)α+(c−b)=0⇒α=1, since b



=c

Hence from (i) or (ii), b+c+1=0

Answer:

x2 bx 1*2

Step-by-step explanation:

The probability of tossing tails and rolling a multiple of 2 is 1/4.

Probability is measuring the likelihood of an event occurring, based on the available information.

According to the multiplication rule, the probability of two independent events happening together is equal to the product of their individual probabilities.

Here we have

A fair coin and a fair six-sided number cube

The probability of tossing tails with a fair coin is 1/2, and the probability of rolling a multiple of 2 on a fair six-sided number cube is 3/6.

To find the probability of both events happening, we multiply the probabilities:

P(tails and a multiple of 2) = P(tails) x P(multiple of 2)

P(tails and a multiple of 2) = (1/2) x (1/2)

P(tails and a multiple of 2) = 1/4

Therefore,

The probability of tossing tails and rolling a multiple of 2 is 1/4.

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Answer:

Step-by-step explanation:

Triangle UVW has vertices at U(−1, 0), V(−4, 1), W(−4, 4). Determine the vertices of image U′V′W′, if the preimage is rotated 90° counterclockwise.

U′(0, −1), V′(−1, −4), W′(−4, −4)

U′(0, −1), V′(1, −4), W′(4, −4)

U′(1, 0), V′(4, −1), W′(4, −4)

U′(−1, 0), V′(−4, 0), W′(4, −4)

The scale factor used in the dilation of the function f(x) to g(x) is 4

From the question, we have the following parameters that can be used in our computation:

The function f(x) dilated to get g(x)

Both functions pass through the origin

So, we have

Center = origin

Next, we have

The scale factor is calculated as

Scale factor  = g(x)/f(x)

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = 4/1

Evaluate

Scale factor = 4

Hence, the scale factor is 4

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There are 1.92 x 10²⁷ pennies weigh as much as the earth is,

We have to given that;

The Earth Weights 5.972 x 10²⁴ kilograms.

And, A penny weighs 3.1 x 10⁻³ kilograms.

Hence, Number of pennies weigh as much as the earth is,

⇒ 5.972 x 10²⁴ / 3.1 x 10⁻³

⇒ 1.92 x 10²⁷

Thus, There are 1.92 x 10²⁷ pennies weigh as much as the earth is,

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The experimental probability of selecting a black marble is 0.4, which is found by dividing the frequency of selecting a black marble (6) by the total number of marbles (15). The correct answer is C).

To determine the experimental probability of selecting a black marble, we need to divide the frequency of selecting a black marble by the total number of marbles.

The table shows that Michael has a bag of marbles with a total frequency of 4 + 6 + 5 = 15 marbles. The frequency of selecting a black marble is 6, so the experimental probability of selecting a black marble is:

6/15 = 0.4

Therefore, the answer is option (C), 0.40.

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The CPI for year 2 is 108. 78 and the rate of inflation from year 1 to year 2 is 8. 78 %.

The Consumer Price Index is a gauge of the mean fluctuation in costs of commodities and amenities that consumers procure across durations. It is measured by assessing the cost of a collection of provisions and utilities that symbolizes what an ordinary family acquires, then equating it to the price of the identical set during some antecedent period.

The CPI would be:

= Total cost of basket in year 2 / Total cost of basket in year 1

= ( (1. 65  x 3 bread ) + 3. 10 ) / ( ( 1.50 x 3 ) + 2. 90 )

= 108. 78

The inflation would then be :

= (CPI of year 2 - 100 base year CPI) x 100 %

= (108. 78 - 100) x 100 %

= 8. 78 %

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The mean is smaller for the houses owned by teachers, as we reject the null hypothesis to be assumed that the mean is similar for all the houses owned by teachers.

For this study, we should use t-test for a population mean because the population standard deviation is not known.

b. The null hypothesis and alternative hypotheses would be provided as:

H0: μ = 13 (the mean number of paintings for all teachers is 13)

H1: μ < 13 (the mean number of paintings for teachers is less than 13)

c. The test statistic is calculated as:

t = (X - μ) / (s / √n)

where:

X = sample mean,

μ = hypothesized population mean,

s = sample standard deviation, and

n = sample size.

Plugging in the values, we get:

t = (12.18 - 13) / (1.320 / √11) = -1.63

d.The p-value is the likelihood of seeing a t-value that is at least as extreme as -1.63, assuming that the null hypothesis is correct. The p-value is roughly 0.07, as determined using a t-table or a t-distribution calculator with 10 degrees of freedom (n-1).

The p-value above the significance level of 0.01, hence the null hypothesis cannot be rejected. We lack adequate data to draw the conclusion that the average number of artworks in homes owned by teachers is less than 13.  

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Complete question is:

The average house has 13 paintings on its walls. Is the mean smaller for houses owned by teachers? The data show the results of a survey of 11 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

12, 11, 11, 11, 11, 14, 11, 13, 14, 10, 14

What can be concluded at the α = 0.01 level of significance?

a. For this study, we should use t-test for a population mean.

b. The null and alternative hypotheses would be: H0: 13 H1: 13

c. The test statistic (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.)

d. The p-value =

Answer:

0.127 ft per min

Step-by-step explanation:

I used the ai app to verify my answer

Answer:

2

Step-by-step explanation:

This is because if you draw an imaginary line between them you can see that they can fold horizontally and vertically and thats it.