Let x be a binomial random variable with n = 15 and p= .5. Using the exact
binomial calculation and the normal approximation with the continuity
correction, find P(x>6).

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

\(75; 85; 95; 105\)

Step-by-step explanation:

Given

\(Angles: x, x + 10, x + 20, x + 30\)

Required

Find the angles

Angles in a \(quadrilateral \add\ up\ to\ 360\)

So:

\(x+ x + 10+ x + 20+ x + 30 = 360\)

Collect like terms

\(x+ x + x + x = 360 - 10 - 20 - 30\)

\(4x = 300\)

Solve for x

\(x = \frac{300}{4}\)

\(x = 75\)

So, the angles are:

\(x = 75\)

\(x +10= 75 + 10 = 85\)

\(x +20= 75 + 20 = 95\)

\(x +30= 75 + 30 = 105\)

Based on the information given the least possible total mass is 255kg.

Since the Five boys have a mass is 10kg. Hence the least possible total mass will be:

40 lies in 35≤x<45

50 lies in 45≤x<55

50 lies in 45≤x<55

60 lies in 55≤x<65

80 lies in 75≤x<85

Hence:

Total mass=35+45+45+55+75

Total mass=255 kg

Inconclusion the least possible total mass is 255kg.

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Answer:

0.7704 = 77.04% probability that he is through grading before the 11:00 P.M. TV news begins

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 p-value, we get the probability that the value of the measure is greater than X.

Distribution of n values from a normal distribution:

If we take n values from a normally distributed variable, the mean is \(\mu*n\), and the standard deviation is \(s = \sigma\sqrt{n}\)

There are 46 students in an elementary statistics class. For each student, the mean is of 5 min and a standard deviation of 4 min.

This means that

\(\mu = 46*5 = 230\)

\(s = 4\sqrt{46} = 27.13\)

(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

This is the probability that he finishes grading in 4 hours and 10 minutes, that is, 4*60 + 10 = 250 minutes, which is the pvalue of Z when X = 250.

\(Z = \frac{X - \mu}{\sigma}\)

In this distribution

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{250 - 230}{27.13}\)

\(Z = 0.74\)

\(Z = 0.74\) has a pvalue of 0.7704

0.7704 = 77.04% probability that he is through grading before the 11:00 P.M. TV news begins

The graph of the function is attached below.

The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.

Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.

We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.

In the given problem;

The graph of the function f(x) = 1 + x / x² - 1 is attached below;

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44.99-39.99=5.00

5.00÷.45=11.11 additional minutes i would round to 11 because you can't have a fraction of an additional minute.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

The expression 6 - 5 x 3 does not have the value 3.

6 - 5 x 3 = - 9

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

The math operation can be addition, subtraction, multiplication, or division.

We have,

-3( 4 - 5 )

= -3 x -1

[minus x minus = positive]

= 3

|-2| + 1 ( 3 - 2)

The modulus of any value is always positive.

= 2 + 1 x 1

= 2 + 1

= 3

-8 ÷ -4 + 1

Minus gets canceled after division.

= -8/-4 + 1

= 2 + 1

= 3

6 - 5. 3

= 6 - 15

= -9

Thus all the expressions have a value of 3 except the expression

6 - 5 x 3.

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Step-by-step explanation:

AC B D

AD B C

A BC D

A BD C

hope it's right

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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Solution :

         Direct          Indirect           Combination

1          17                  16.6                    25.2

2        18.5                22.2                    24

3        15.8                20.5                    21.5

4        18.2              18.3                       26.8

5        20.2             24.2                      27.5

6        16                   19.8                     25.8

7        13.3                21.2                      24.2

n         7                     7                           7

\($\bar X$\)        17                   20.4                      25

s         2.238            2.501                      2.002

\($\bar X_{avg}$\)   20.8              

Source               df           SS              MS                F          P-value

treatments        2        225.680     112.840      22.1593    0.000

error                  18        91.660       5.092

total                   20       317.340

The test hypothesis is :

\($H_0$\) : the basis for the judgement does not affects the quality of the judgment.

\($H_a$\) : the basis for the judgement affects the quality of the judgement.

Given a = 0.05, since the p-value is less than 0.05, so we reject \($H_0$\).

Therefore, the basis for the judgement affects the quality of the judgement.

Sample size of 2.78 is needed so that the confidence interval will have a margin of error of 0.064

The formula to calculate the margin of error for population proportion is given by :-

Error =z * √p * (1 - p) / √n

Given : The proportion of operations result in complications is 0.08:

Significance level : ∝=1-0.99=0.1

Critical value =  2.576    [By standard normal distribution table]

Margin of error : E= 0.064

Substitute all the value in the above formula, we get

0.064=2.576×√0.08(0.92)/n

0.16486=√0.0736/n

Squaring both sides , we get

0.027180138496=0.0736/n

n=0.0736÷0.027180138496

n=2.70785963

Hence, the required sample size = 2.78

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Answer:

Step-by-step explanation:

y - 8 = 3(x + 6)

y - 8 = 3x + 18

y = 3x + 10

answer is a

Answer:

\(m_{perpendicular}\) = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x + 6y = - 24 ( subtract x from both sides )

6y = - x - 24 ( divide through by 6 )

y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form

with slope m = - \(\frac{1}{6}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6

Answer:

Step-by-step explanation:

Its 4.51

A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

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Answer: d. percentage of observations on the vertical (y) axis, whereas a frequency histogram indicates counts.

Step-by-step explanation:

A frequency histogram is a graph showing the frequency for the occurrence of an outcome in a data set. A frequency histogram is used to organize data thereby making the data easy to comprehend.

A frequency histogram is a graph that shows how the number of times a particular thing happens, and this is shown in percentages.

Fir an histogram, the horizontal axis is a number line that contains classes of uniform length while the frequency or count is represented on the vertical axis.

The difference between a frequency histogram and a relative frequency histogram is that the relative frequency histogram indicates percentage of observations on the vertical (y) axis, whereas a frequency histogram indicates counts.

Therefore, option d is correct.

D) percentage of observations on the vertical \((y)\) axis, whereas a frequency histogram indicates counts.

A frequency histogram is a graph that depicts the frequency with which an outcome occurs in a data set. A frequency histogram is used to organize data and make it easier to understand.

A frequency histogram is a graph that depicts the number of times a given thing occurs in percentages.

The horizontal axis of a histogram is a number line that contains classes of uniform length, while the vertical axis represents the frequency or count.

A frequency histogram differs from a relative frequency histogram in that the relative frequency histogram shows percentages of observations on the vertical \((y)\) axis, whereas a frequency histogram shows counts.

Option D) is correct.

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The interval of systolic blood pressure that represents the middle 95% of males is [94, 126].

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

According to the empirical rule (also known as the 68-95-99.7 rule), for a normal distribution, approximately 68% of the observations fall within one standard deviation of the mean, approximately 95% of the observations fall within two standard deviations of the mean, and approximately 99.7% of the observations fall within three standard deviations of the mean.

In this case, we want to find the interval that contains the middle 95% of observations. Since the distribution is normal, we know that approximately 95% of the observations will be within two standard deviations of the mean. Therefore, we need to find the values that are two standard deviations away from the mean in both directions.

Using the formula for z-scores, we can find the z-score corresponding to the upper and lower endpoints of this interval:

z_lower = (x_lower - mu) / sigma = (x_lower - 110) / 8 = -2

z_upper = (x_upper - mu) / sigma = (x_upper - 110) / 8 = 2

Solving for x_lower and x_upper, we get:

x_lower = mu + z_lower * sigma = 110 + (-2) * 8 = 94

x_upper = mu + z_upper * sigma = 110 + 2 * 8 = 126

Therefore, the interval of systolic blood pressure that represents the middle 95% of males is [94, 126].

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Answer:

B) (-∞,∞)

Step-by-step explanation:

The domain is the x-values, so it’s all real numbers in this graph.  

I would use interval notation and choose B) (-∞,∞)

The range is the y-values, so it’s (2,-1), if that’s the next question.

Answer:

x = -2

Step-by-step explanation:

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

Answer:

x= 65

Step-by-step explanation:

x= 360- (130+75+90)

x= 360- 295

x= 65 degrees

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

The solutions of the equation of the graph is -4 and 2.

An placement of values to the uncertainties that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root. An equation's solution set is the collection of all possible solutions.

We know that the solution of the equation is determined using the graph by obtaining the point of intersection of the equation.

In the given graph the point of intersection of the two equations are at x = -4 and x = 2.

Hence, the solutions of the equation of the graph is -4 and 2.

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The complete question is:

The value of the variables in the right triangle are as follows;

A right triangle is a triangle that has one of its angles as 90 degrees.

The side of a right triangle can be found by using trigonometric ratios.

Therefore, let's find the variable length of the right triangle as follows;

sin 30 = opposite / hypotenuse

sin 30 = v / 3√2

1 / 2 = v / 3√2

cross multiply

3√2 = 2v

divide both sides by 2

v = 3√2 / 2

Let's find the variable w.

cos 30 = adjacent  / hypotenuse

cos 30 = w  / 3√2

√3 / 2 = w  / 3√2

cross multiply

√3 × 3√2 = 2w

3√6 = 2w

divide both sides by 2

w = 3√6 / 2

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The number of revolutions made by the wheel is 5.24 ≅ 5.  

One complete revolution is equal to 360 degrees, so to find the number of complete revolutions the wheel has made, we can divide the total number of degrees rotated by 360.    

Here we have

A wheel rotated by 1888°  

As we know One complete revolution is equal to 360 degrees

Hence, the angle can be rotated by the wheel in 1 rotate = 360°  

Let the wheel make 'x' revolution to make 1888°  

=> 360(x) = 1888

=> x = 1888/360

=> x = 5.24

Therefore,

The number of revolutions made by the wheel is 5.24 ≅ 5.    

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Answer:

7.5

0

5

1

3.67

Step-by-step explanation:

absolute value (the ||) means negative numbers become positive

it does not change values that are already positive

abs of 7.5 is 7.5

abs of 0 is 0

abs of -5 is 5

abs of -1 is 1

abs of -3.67 is 3.67

The expression simplified can be written as:

16m +  8

Here we want to simplify the following expression:

(8m + 4) + (8m + 4)

To simplify, we start by removing the parenthesis:

8m + 4 + 8m + 4

Now we can change the order of the terms so we get:

8m + 8m + 4 + 4

Now we can group the like terms to get:

(8m + 8m) + (4 + 4)

And simplify this to get:

16m +  8

That is the simplified expression.

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Answer:

46

Step-by-step explanation:

thats the answer