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Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 12.

Answer:

3 4/7 = 25/7

Step-by-step explanation:

multiply the whole number(3) by the denominator(7).

Then you have 21.

Add the product of the last 2 numbers to the numerator(4)

21 + 4 = 25

Note: (denominator x whole number) + numerator

We are required to convert 3 and 4/7 to an improper fraction.

The fraction 3 and 4/7 to an improper fraction is 25 / 7

Given:

3 4/7

= {7(3) + 4} / 7

= (21 + 4) / 7

= 25 / 7

Therefore, the fraction 3 and 4/7 to an improper fraction is 25 / 7

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Answer:

B is better option

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given:

Given that the rectangular prism with length l = 2..6 yards.

The width of the rectangular prism is 3.5 yards.

The height of the prism is h yards.

We need to determine the simplified expression for the surface area of the rectangular prism.

We also need to determine the surface area of the prism if the height is 4 yards.

Expression for the surface area of the prism:

The surface area of the rectangular prism can be determined using the formula,

[tex]SA=2(lw+wh+lh)[/tex]

Substituting l = 2.6, w = 3.5, h = h, we get;

[tex]SA=2[(2.6)(3.5)+(3.5)h+(2.6)h][/tex]

[tex]SA=2(9.1+3.5h+2.6h)[/tex]

[tex]SA=2(9.1+6.1 h)[/tex]

[tex]SA=18.2+12.2h[/tex]

Thus, the simplified expression for the surface area of the prism is [tex]SA=18.2+12.2h[/tex]

Surface area of the prism:

Now, we shall determine the surface area of the prism if the height is 4 yards.

Substituting the value h = 4 in the expression [tex]SA=18.2+12.2h[/tex], we have;

[tex]SA=18.2+12.2(4)[/tex]

[tex]SA=18.2+48.8[/tex]

[tex]SA=67 \ yd^2[/tex]

Thus, the surface area of the rectangular prism is 67 square yards.

Answer:

1/105 m³

Step-by-step explanation:

the volume of a rectangular prism = base area x height

1/3 x 1/5 x 1/7 = 1/105 m³

Answer:

1/105m^3

Step-by-step explanation:

I did the question and it was correct

Answer:

Both three and six are divisible by three. Therefore, this fraction could be simplified to one-half.

Step-by-step explanation:

Three divided by three is equal to one.

Answer: odd number:1/2

number less than six:5/6

Step-by-step explanation:

Answer:

The store sold 120 ounces fewer ounces of cashew than walnut.

The store sold 11.25 pounds of cashews and 18.75 pounds of walnuts.

To find out how many pounds of each type of nut were sold, we first need to multiply the number of cans sold by the weight of each can. This gives us the total weight in ounces. Then, we convert from ounces to pounds.

For the cashews: 30 cans * 6 ounces/can = 180 ounces. 180 ounces / 16 ounces/pound = 11.25 pounds of cashews.

For the walnuts: 30 cans * 10 ounces/can = 300 ounces. 300 ounces / 16 ounces/pound = 18.75 pounds of walnuts.

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To subtract the matrices [5 0 - 2] and [-1 3 8], subtract each corresponding element, resulting in the matrix [6 -3 -10].

The question asks for the result of the subtraction of two matrices: [5 0 - 2] minus [-1 3 8]. When we subtract matrices, we subtract the corresponding elements from each matrix. Therefore, this subtraction will result in a new matrix where each element is the subtraction of the corresponding elements from the given matrices.

To perform the subtraction, we subtract each element in the second matrix from the corresponding element in the first matrix:

So, the result of the matrix subtraction is [6 -3 -10].

Answer:

a function

Step-by-step explanation:

a function is where u plug something in and get another thing out. the entire function is dependent on another independent variable

It would actually depend on the way that you want your result. It can be in h, min, s

For example, in hours it would be 5.5h

in minutes, 330min

in seconds, 19800s

She should write 5.5 hours on her time card.

To write 5 hours and 30 minutes on her time card, she can simply write 5.5 hours. This is because 30 minutes is half of an hour, so it can be represented as 0.5 hours.

Answer:

The minimum score required for an A grade is 89.8.

Step-by-step explanation:

We are given that a psychology professor assigns letter grades on a test according to the following scheme. A : Top 7% of scores. B : Scores below the top 7% and above the bottom 64%. C : Scores below the top 36% and above the bottom 25%. D : Scores below the top 75% and above the bottom 6%. F : Bottom 6% of scores.

Scores on the test are normally distributed with a mean of 78.4 and a standard deviation of 7.6.

Let X = Scores on the test

SO, X ~ Normal([tex]\mu=78.4,\sigma^{2} =7.6^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

                              Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = mean time = 78.4

            [tex]\sigma[/tex] = standard deviation = 7.6

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, the minimum score required for an A grade so that it represents Top 7% of scores is given by;

      P(X [tex]\geq[/tex] x) = 0.07   {where x is the required minimum score

      P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{x-78.4}{7.6}[/tex] ) = 0.07

       P(Z [tex]\geq[/tex] [tex]\frac{x-78.4}{7.6}[/tex] ) = 0.07

So, the critical value of x in the z table which represents the top 7% of the area is given as 1.4996, that is;

                        [tex]\frac{x-78.4}{7.6} =1.4996[/tex]

                        [tex]{x-78.4}{} =1.4996\times 7.6[/tex]

                        [tex]x[/tex]  = 78.4 + 11.39696 = 89.8 or 90

Hence, the minimum score required for an A grade is 89.8.

Answer:

B. Information from the sample is typical of information in the population.

Step-by-step explanation:

In Statistical Research, a Bias refers to the tendency of a sample statistic to systematically overestimate or underestimate a population parameter.

(A)When portions of the population are excluded or underrepresented from the sample, it is a Sampling Bias.

(C)When those responding to a survey or poll differ systematically from the nonrespondents, it is referred to as Non-Response Bias.

(D)When certain groups in the population are systematically underrepresented in the sample, it is referred to as Selection Bias.

Therefore option B is not an example of a Bias.

Final answer:

The correct answer is "Information from the sample overemphasizes a particular stratum of the population."

Explanation:

Bias in research refers to systematic errors or deviations from the true population value. It can occur at various stages, including during sampling, data collection, analysis, and interpretation. The options provided describe different forms of bias commonly encountered in research:

1. Exclusion or underrepresentation of portions of the population from the sample is known as sampling bias. This can lead to results that do not accurately reflect the characteristics of the entire population.

2. Overemphasizing a particular stratum of the population is an example of selection bias. This occurs when certain groups within the population are disproportionately represented in the sample, leading to skewed or inaccurate results.

3. Differences between respondents and nonrespondents in a survey or poll can lead to nonresponse bias. This occurs when those who choose to respond to a survey differ systematically from those who do not respond, leading to results that may not be generalizable to the entire population.

4. Systematic underrepresentation of certain groups in the sample can also lead to bias. This is similar to sampling bias but specifically refers to the consistent exclusion or underrepresentation of certain demographic groups.

It is important to recognize and address bias in research to ensure the validity and reliability of the findings. Researchers can use various techniques such as random sampling, stratified sampling, and sensitivity analysis to mitigate bias and improve the quality of their research.

Answer:

x = theta = 0°

Step-by-step explanation:

Given the trigonometry function

Tan²x/2-2 cos x = 1

Tan²x-4cosx = 2 ... 1

From trigonometry identity

Sec²x = tan²x+1

tan²x = sec²x-1 ... 2

Substituting 2 into 1, we have:

sec²x-1 -4cosx = 2

Note that secx = 1/cosx

1/cos²x - 1 - 4cosx = 2

Let cosx. = P

1/P² - 1 - 4P = 2

1-P²-4P³ = 2P²

4P³+2P²+P²-1 = 0

4P³+3P² = 1

P²(4P+3) = 1

P² = 1 and 4P+3 = 1

P = ±1 and P = -3/4

Since cosx = P

If P = 1

Cosx = 1

x = arccos1

x = 0°

If x = -1

cosx = -1

x = arccos(-1)

x = 180°

Since our angle must be between 0 and 1 therefore x = 0°

Answer:

The student who did the German test scored 2 standard deviations above the mean and the student who did the French test scored 1.6 standard deviations above the mean. Relative to their classmates, the student who did the German test scored better due to the higher z-score.

Step-by-step explanation:

Z-score

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

German test

Mean was 66 and the standard deviation was 8, scored an 82.

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{82 - 66}{8}[/tex]

[tex]Z = 2[/tex]

French test:

Mean was 27 and the standard deviation was 5, scored a 35.

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 27}{5}[/tex]

[tex]Z = 1.6[/tex]

The student who did the German test scored 2 standard deviations above the mean and the student who did the French test scored 1.6 standard deviations above the mean. Relative to their classmates, the student who did the German test scored better due to the higher z-score.

Final answer:

The German test taker scored 2 standard deviations above the mean, while the French test taker scored 1.6 standard deviations above the mean. Thus, the German test taker scored comparatively higher relative to their peers.

Explanation:

To compare the scores of the two high school students who took equivalent language tests in German and French, we need to calculate the z-scores for each. The z-score is a measure that describes how far an individual test score is from the mean of the respective test, in terms of standard deviations. Let's calculate:

For the German test:

ZGerman = (Score - Mean) / Standard Deviation

ZGerman = (82 - 66) / 8

ZGerman = 16 / 8

ZGerman = 2.0

For the French test:

ZFrench = (Score - Mean) / Standard Deviation

ZFrench = (35 - 27) / 5

ZFrench = 8 / 5

ZFrench = 1.6

Comparing these z-scores, the student who took the German test scored higher relative to their peers (2 standard deviations above the mean) compared to the student who took the French test (1.6 standard deviations above the mean).

According to the American Red Cross, 9.2% of all Connecticut residents have Type B blood. If 18 Connecticut residents are taken at random, the standard deviation of the binomial distribution is about 1.214.

The question is asking for the standard deviation of a binomial distribution. To calculate the standard deviation for a binomial distribution, the formula used is √npq, where n is the number of trials, p is the probability of success, and q is the probability of failure (1 - p).

In this case, we have n equals to 18 (number of Connecticut residents randomly sampled), p equals to 0.092 (since 9.2% have Type B blood), and then, by subtraction, q equals to 0.908.

Therefore, the standard deviation would be √18*0.092*0.908, which is about 1.214 when evaluated.

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The standard deviation of the random variable X is approximately 0.067.

The standard deviation of the random variable X can be calculated using the formula:

Standard Deviation (SD) = sqrt(p(1-p)/n)

Given that p is the probability of success (9.2% or 0.092) and n is the sample size (18), we can substitute these values into the formula to find:

SD = sqrt(0.092(1-0.092)/18) = 0.067

Therefore, the standard deviation of the random variable X is approximately 0.067.

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The standard matrix of the transformation T, resulting from a composition of the reflection through the vertical x2-axis and the reflection through the line x2 = x1, is: [ 0 -1 ] [ 1 0 ].

Find the standard matrix of the transformation T.

To do this, we can break the transformation T down into two simpler transformations:

Reflection through the vertical x2-axis: This transformation negates the x1 coordinate of each point while leaving the x2 coordinate unchanged. The standard matrix for this transformation is:

[ -1   0 ]

[  0   1 ]

Reflection through the line x2 = x1: This transformation swaps the x1 and x2 coordinates of each point. The standard matrix for this transformation is:

[ 0   1 ]

[ 1   0 ]

Since we are performing these transformations one after the other, we need to multiply the matrices together. The order of multiplication matters here, because matrix multiplication is not commutative. So, the standard matrix for the combined transformation T is:

[ 0   1 ]   [ -1   0 ]   =   [ 0 -1 ]

[ 1   0 ]   [  0   1 ]     [ 1  0 ]

Therefore, the standard matrix of the transformation T is:

[ 0 -1 ]

[ 1  0 ]

Complete question:

Assume that T is a linear transformation. Find the standard matrix of T.

​T:

set of real numbers R squaredℝ2right arrow→set of real numbers R squaredℝ2

first reflects points through the

vertical x 2 dash axisvertical x2-axis

and then reflects points through the

line x 2 equals x 1line x2=x1

The standard matrix of the linear transformation reflects points through the vertical axis and the line[tex]\(x_2 = x_1\) is \([-1\ 1\ 0\ 0]\).[/tex]

To find the standard matrix of the linear transformation  T , we need to determine the images of the standard basis vectors [tex]\( \mathbf{e}_1 \) and \( \mathbf{e}_2 \)[/tex] under  T .

First, let's understand the transformation described:

1. Reflection through the vertical [tex]\( x_2 \)[/tex]axis:

  This transformation replaces each point [tex]\( (x_1, x_2) \) with \( (-x_1, x_2) \).[/tex]

2. Reflection through the line [tex]\( x_2 = x_1 \):[/tex]

  This transformation replaces each point [tex]\( (x_1, x_2) \) with \( (x_2, x_1) \).[/tex]

To find the images of the standard basis vectors under  T :

- [tex]\( T(\mathbf{e}_1) \) is obtained by reflecting \( \mathbf{e}_1 = (1, 0) \) through the \( x_2 \) axis, resulting in \( (-1, 0) \).[/tex]

- [tex]\( T(\mathbf{e}_2) \) is obtained by reflecting \( \mathbf{e}_2 = (0, 1) \) through the line \( x_2 = x_1 \), resulting in \( (1, 0) \).[/tex]

Now, we can construct the standard matrix of  T  using the images of the standard basis vectors:

[tex]\[ [T] = \begin{bmatrix} -1 & 1 \\ 0 & 0 \end{bmatrix} \][/tex]

This matrix represents the transformation  T  as described.

The Complete Question:

Assume that T is a linear transformation. Find the standard matrix of T.

​T: set of real numbers R squaredℝ2right arrow→set of real numbers R squaredℝ2

first reflects points through the

vertical x 2 dash axisvertical x2-axis

and then reflects points through the

line x 2 equals x 1line x2=x1

Answer:

between 120 and 153 mph in race A between 125 and 145 mph in race B

Step-by-step explanation:

i got it right on my test

Answer:

its

C.between 120 and 153 mph in race A; between 125 and 145 mph in race B

Step-by-step explanation:

Answer:

0.15

Step-by-step explanation:

Answer:

Timmy is 18 and Tommy is 5.

Step-by-step explanation:

Step-by-step explanation:

So you have to find out tha ages which add up to 23 so if Tommy is 9 years old and when we add 5

So Timmy age = 9 + 5 = 14

Now if we add 14 and 9 the answer is 23

It means Timmy is 14 years old and Tommy is 9 years old

To solve the equation 2 sin(2θ) = 1, find the angles θ where sin(2θ) equals 1/2. The solutions for θ are π/12 + kπ, where k is any integer.

To solve the equation 2 sin(2θ) = 1, we can divide both sides of the equation by 2 to get sin(2θ) = 1/2. Since the range of sin function is -1 to 1, we need to find the angles θ where sin(2θ) equals 1/2.

Using the inverse sine function, we can find the principal value of 2θ which is π/6 radians. This gives us one solution for θ: π/12.

Since sin function is periodic with period of 2π, we can find additional solutions by adding integer multiples of π to the principal value. Therefore, the solutions for θ are π/12 + kπ, where k is any integer.

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Answer:

The point estimate for p is 0.5637.

Step-by-step explanation:

Point estimate for the proportion of all judges who are introverts.

We have a big sample.

So the proportion of the sample proportion of introverted judges can be used as the estimation of the population proportion.

In the sample:

502 judges

283 introverts.

So

p = 283/502 = 0.5637

The point estimate for p is 0.5637.

The point estimate for the proportion of judges who are introverts, denoted by p, is found by dividing the number of introverts (283) by the total number of judges in the sample (502), which gives a point estimate of 0.5637 when rounded to four decimal places.

To estimate the proportion of judges who are introverts, we use the given data from the random sample. The point estimate for p, representing the proportion of all judges who are introverts, can be calculated by dividing the number of introverts in the sample by the total number of judges in the sample. The formula for the point estimate p' is:

p' = X / n

where:

Using the given data:

p' = 283 / 502

Calculating this gives us a point estimate for p' of 0.5637 after rounding to four decimal places.

This result represents the estimated proportion of the population of judges who are introverts based on the sample.

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Step-by-step explanation:

The formula is subtracting by 20 you can count it so the next - 70

Answer:

10-20(n-1)

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Since Lupe is 3 times as many as Frances

39 ÷ 3= 13

Answer:

13

Step-by-step explanation:

Make an equation. Let x represent the bags that Frances sold. Since Lupe sold 3 times the popcorn Frances did, use multiplication.

[tex]39=3x[/tex]

Solve for x to find the amount Frances sold:

Divide both sides by 3:

[tex]\frac{39}{3}=\frac{3x}{3} \\\\13=x[/tex]

[tex]x=13[/tex]

Frances sold 13 bags.

The equation -9x - 3y^2 = 6 does not represent a function of x because each x-value has two possible y-values.

In order to determine if an equation represents a function of x, we need to check if each value of x produces a unique y-value. This means that for any x-value, there cannot be more than one y-value.

When we rearrange the given equation, we can solve for y in terms of x: y = sqrt((-9x - 6)/3). Since the square root of a positive number always has two possible values (positive and negative), we have two possible y-values for each x-value. Therefore, the given equation does not represent a function of x.

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Answer:

[tex] \bigg(\frac{2}{5} \bigg)^{4} [/tex]

Step-by-step explanation:

[tex] \frac{2}{5} \times \frac{2}{5} \times \frac{2}{5} \times \frac{2}{5} = \bigg(\frac{2}{5} \bigg)^{4} \\ [/tex]

Answer:

17 adult tickets

23 children's tickets

Step-by-step explanation:

Adult tickets 17x7=119

Child tickets 23x5=115                     23 is 6 more than 17.

119+115=234

Answer:

  $28

Step-by-step explanation:

The markup was 0.40×$20 = $8, so the new price is ...

 $20 +8 = $28

Answer:

31.2

Step-by-step explanation:

Because you only round up if the number next to the 1st decimal place is greater than 5, you just drop the 4 and keep 31.2.

you just drop the 4 and keep 31.2.

Answer:x=-15

Step-by-step explanation:You want to isolate x so u would subtract 7 from one side and subtract 7 from the other side

X+7=-8

X=-15