Use numerals instead of words. if necessary, use / for the fraction bar. if p − 1 is a factor of p4 + p2 p − k, the value of k is:____.

The probability is 0.0062. This is calculated using the normal approximation to the binomial distribution, with mean μ = 80 and σ = 9.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

1. Calculate the mean (μ): μ = 80

2. Calculate the standard deviation (σ): σ = 9

3. Calculate the z-score for 90 free throws: z = (90-80)/9 = 1

4. Calculate the probability using the z-score: P(x≥90) = 1 - P(x<90) = 1 - 0.8413 = 0.1587

5. Round the probability to four decimal places: P(x≥90) = 0.0062

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Answer:

Option C is the correct answer.

Step-by-step explanation:

There are two terms in business

So,

In this case, Philippines is doing exporting and Canada is doing Importing.

Thus, The answer is Philippines.

Answer:

702,653

Step-by-step explanation:

but the real total added up is 945,556

The event  the number is even and less than 12 covers the entire sample space of this experiment.

What is sample space?

In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.

Given:

A number is selected at random from the set {2, 4, 6, 8, 10}.

Let's examine each instance:

A. There are more than two.

When we get number 2, this does not apply to the situation. 2 is equal to 2 and not greater, therefore.

B. The number is not divisible by 5, whereas 10 and 5 are. As a result, the sample space is not completely covered.

C. It's an even number or less than 12.

Let's note that every number from "2, 4, 6, 8, 10" is less than 12, indicating that the event's even portion has no bearing. This encompasses the whole sample area.

D. Neither the number is prime nor is it a composite.

There cannot be a number that is neither prime nor composite because they are mutually exclusive terms in mathematics. No number of the set is covered by this event.

E. The number's square root is less than 3.

This excludes the number 10, whose square root is approximately 3,16, which is greater than 3.

Hence, the event  the number is even and less than 12 covers the entire sample space of this experiment.

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The statement which is best explained by the alternate exterior angles theorem is ∠1 ≅∠2.

What do you mean by angles?

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

We know that, alternate exterior angles theorem states that, when two parallel lines are cut by a transversal line, the resultant exterior angles are congruent.

∠1 and ∠2 are both alternate exterior angles.

Therefore, the correct answer for the following problem is ∠1 ≅∠2.

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Answer:

D

Step-by-step explanation:

The sum of the length of any 2 sides is greater than the length of any 3rd side

10+8 = 18, so D is not possible

The net worth of the surf shop is  $859,489

We know that a balance sheet is the summary of the assets and liabilities of the legal person.

The balance sheet appears thus:

Assets:                                       $

Building mortgage                109,850

Accounts receivable                10,760  

property value                         182,974

Long term investment             237,000

Owned inventory                       72,980      

cash                                         215,083

Savings account                      128,721

Equipment                                 30,971

Liabilities

Debt                                        35,988

Long term liability                 38,000

Small business loan              62,700

Difference in assets and liabilities = $859,489

Therefore, the net worth of the surf shop is $859,489

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Mathematical equations are essentially relationships. A line equation describes the relationship between x and y values found on a coordinate plane.

Firstly understand the values in the table. The numbers in a table are often the x and y values that are true for the line, which means the x and y values correspond to the coordinates of points on the line.

Then we need to determine the slope. We can do this by taking two points from the table and plugging them into formula.

Next we need to find the y-intercept. To do this, we need one point from the table to plug into our function.

Once you find the value of the slope, plug it into the the slope-intercept form of the line. The result is the function that describes the relationship in the given table of values.

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Answer:

-4

Step-by-step explanation:

Slope is represented by:

Rise/run

So, count up from a point on the line and count across to another point on the graph.

I started from -1, counted up 4 and counted 1 across to point (-1,3)

So your slope is 4/-1, which is the same as -4

The slope of a line from the given graph is -4. Therefore, option D is the correct answer.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

From the given graph,

Rise is (-5-(-1)=-4

Run is 1

So, Slope =Rise/Run

= -4/1

= -4

The slope from the graph is -4. Therefore, option D is the correct answer.

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Put all terms on one side of the equal sign, leaving zero on the other side.

Factor.

Set each factor equal to zero.

Solve each of these equations.

Check by inserting your answer in the original equation.

The test statistic under the null hypothesis of is when the sample mean is for a random sample of size 15 from a normal population with unknown variance. The given statement is true.

For a random sample of size 15 from a healthy population with known variation. the statistical measure under test for the null hypothesis.

Even when the population variance is known and the sample size is modest, the Z-test can be used.

The given statement is true.

Hypothesis :

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

Complete question:

True or False: For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H_o: u =  (i - uo)/n), when i is the sample mean.

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The equation that represents the array (rectangles and area) multiplication model that sows two grey shaded columns of length one ninth each and three rows with dots of width one fourth each is option a

a) The equation with fractions two ninths times three fourths is equal to six thirty sixths

[tex]\dfrac{2}{9} \times \dfrac{3}{4} = \dfrac{6}{36}[/tex]

An array representation of a multiplication is a rectangular visual order of positioning of rows and columns that indicates the terms of a multiplication equation.

Please find attached the area model to multiply the fractions

The terms of the equation represented by the model are indicated by the two columns of length one ninth each shaded grey and the three rows of width one fourth each covered with dots, such that the equation can be presented as follows;

[tex]\left(\dfrac{1}{9} +\dfrac{1}{9}\right) \times \left(\dfrac{1}{4} +\dfrac{1}{4} + \dfrac{1}{4} \right) = \dfrac{2}{9} \times \dfrac{3}{4} =\dfrac{6}{36}[/tex]

The equation that the model represents is therefore;

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Answer:

the component form of the resultant vector is (-2, -1).

Step-by-step explanation:

To find the component form of the resultant vector, we need to add the corresponding components of the two input vectors. In this case, the x-component of the resultant vector is equal to the x-component of vector b minus the x-component of vector u, and the y-component of the resultant vector is equal to the y-component of vector b minus the y-component of vector u.

We can therefore write the component form of the resultant vector as follows:

-u + b = (-u_x + b_x, -u_y + b_y) = (-5 + 3, -2 + 1) = (-2, -1)

therefore, the component form of the resultant vector is (-2, -1).

A total of 288 hours of exercise did by the end of the year.

What is distributive property?

Distributive Property is defined as the "distribute" of anything to divide it up or to give someone a piece of it.

Exercise in one month = 24 hours

Total exercise in a year = 24*12 = 288 hours

Hence, a total of 288 hours of exercise did by the end of the year.

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The factorised form of given function f(x) is (x + 2)(x +√3)(x-√3)

Describe a polynomial.

A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.

We have been given the polynomial function:

⇒ x³ + 2x² - 3x -6

Simplify the radical by breaking the radicand up into a product of known factors.

⇒ x³ + 2x² - 3x -6

Add and subtract the second term to the expression and factor by grouping.

⇒ x²(x + 2) - 3(x + 2)

⇒ (x + 2)(x² - 3)

⇒ (x + 2)(x +√3)(x-√3)

Therefore, the factorised form of given function f(x) is (x + 2)(x +√3)(x-√3).

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Answer:

B) on edge

Step-by-step explanation:

If we choose to use a diameter of 201 for the experiment, the strength will be 786.6596.

Given, the experiment in which weld diameter and shear strength (in pounds) were measured for five distinct spot welds on steel produced the data that is included.

The gathered information and the regression equation are shown below.

Strength = -941.6992 + 8.5988×Diameter

we have to calculate the predicted y-hat value for the diameter value of 201.

Now, we are given the regression equation with the strength and diameter as the variables.

now, when we put the diameter equal to 201, the strength will be

Strength = -941.6992 + 8.5988×Diameter

Diameter = 201

Strength = -941.6992 + 8.5988×201

Strength = -941.6992 + 1,728.3588

Strength = 786.6596

So, the value of the strength be 786.6596

Consequently, the strength value when the diameter is 201 be, 786.6596.

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Answer: 4/5

Message: If this was helpful let me know! :)

Answer:

PEmDas so -53Step-by-step explanation:

Answer:

-53

Step-by-step explanation:

-9 + (-44)

-9 - 44

- 53

The relationship (comparison) between the measures in the specified angles found using the angle–side triangle inequality shows the following inequalities between the angles

m∠QRW < m∠RWQ

7. m∠RTW < m∠TWR

m∠RST > m∠TRS

9. m∠RWQ  < m∠QRW

The angle–side triangle inequality indicates that in a triangles, the larger the angle of a triangle, the larger is the side opposite the angle.

Similarly, the larger the side length of a side of a triangle, the larger is the angle opposite the specified side.

Based on the angle-side triangle inequality, we get;

∠QRW is the angle opposite to the side of length 45 units, and ∠RWQ is the angle opposite the side of length 47 units.

Therefore; m∠QRW < m∠RWQ

7. In triangle ΔRTW, ∠RTW is the angle opposite to the side of length 34 units, and ∠TWR is the angle opposite the side of length 35 units.

Therefore; m∠RTW < m∠TWR

In triangle ΔRST, ∠RST is the angle opposite to the side of length 35 units, and ∠TRS is the angle opposite the side of length 22 units.

Therefore; m∠RST > m∠TRS

9. In triangle ΔQRW, ∠RWQ is the angle opposite to the 47 unit long side and ∠QRW⇔ is the angle opposite the side of length 45 units.

Therefore; m∠RWQ > m∠QRW

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The required scale factor is 2/3 for the given figures.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

As we know scale factor is the ratio of sides in the original image and the image after transformation.

The side length of CD = 15 units

The side length of GH = 10 units

The scale factor = length of GH / length of CD

The scale factor = 10/15

The scale factor = 2/3

Therefore, the required scale factor is 2/3 for the given figures.

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Answer:

1 1/4

Step-by-step explanation:

Divide 125 by 100, which gets you 1.25 (also known as 1 1/4)

Henry walked 1.25 miles each day to and from school.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that,

Henry walks to and from school each day.

Distance travelled by Henry in 100 days = 125 miles

In order to find the distance travelled by Henry in 1 day to and from school, divide the total distance by 100.

Distance travelled in 1 day = 125 / 100 = 1.25 miles

Hence the distance Henry walk to and from school is 1.25 miles.

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Answer: (8,8)

Step-by-step explanation: because, you just need to do the math

The equation of line is y = ( 3/4 )x + 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( 8 , 8 )

Let the second point be Q = Q ( 4 , 5 )

Now , the slope of the line between the two points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 8 ) / ( 4 - 8 )

Slope m = -3/-4

Slope m = 3/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 3/4 ( x - 8 )

On simplifying the equation , we get

y - 8 = ( 3/4 )x - 6

Adding 8 on both sides of the equation , we get

y = ( 3/4 )x + 2

Therefore , the value of A is y = ( 3/4 )x + 2

Hence , the equation of line is y = ( 3/4 )x + 2

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The control limits help to separate common and special causes from each other.

Control lines are the horizontal lines drawn on the control chart. A control chart has several components. It has two control limits. They are represented by dashed lines. The lower one is called the lower control limit (LCL) and the upper one is called the upper control limit (UCL).

The control limits help us mark the highest (by UCL) and lowest (by LCL) error that is bearable. All those errors that occur between UCL and LCL are common errors/variations while the errors that occur above UCL or below LCL are the products with assignable causes variations.

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The Bus can hold 59 students and van can hold 18 students.

The freshman class rented and filled 1 van and 6 buses with 372 students. This can be illustrated as:

v + 6b = 372 .... i

The sophomore class rented and filled 4 vans and 12 buses with 780 students. This can be illustrated as:

4v + 12b = 780 ... ii

where v = van.

b = bus

v + 6b = 372

4v + 12b = 780

Reduce equation ii by 2. The new equations will be:

v + 6b = 372

2v + 6b = 390

Subtract

v = 18

The van can hold 18 students

Since v + 6b = 372

This will be:

18 + 6b = 372

6b = 354

b = 59.

Bus can hold 59 students.

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Answer:

D) no solution

Step-by-step explanation:

since 4+2= 6 but there no solution s because 8+? might not equal the same number as 4+2

Answer:

In Jewish tradition, Abraham is called Avraham Avinu (אברהם אבינו), "our father Abraham," signifying that he is both the biological progenitor of the Jews and the father of Judaism, the first Jew.

Step-by-step explanation:

The owner of a sandwich shop surveyed her customers on how often they came in as she also added the quantity this means that she had created marketing demand schedule.

The call for agenda indicates the variety of products customers will purchase at a given fee. An instance of this will be film ticketseconomics, a marketplace call for agenda is a tabulation of the amount of an awesome that each one customers in a marketplace will buy at a given fee. At any given fee, the corresponding cost at the call for agenda is the sum of all customers' portions demanded at that fee.

Demand schedules may be used to are expecting the quantity of cloth important primarily based totally at the fee of a product. If the call for agenda predicts that the amount demanded rises because the fee decreases, the enterprise may also want extra elements to provide extra products.

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