The circle below has center K, and its radius is 7 in. Given that m

We can identify key terms in word problems that can tell use what math symbols or operations to use:

There are other key terms that can help us, including:

We're given:

11 is more than twice x:

Less than 44:

Combine all of these to get the inequality:

11 + 2x < 44

The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)

Here, we need to construct a 99% confidence interval for population mean (μ) is given by

μ = x + Zα/2 * σ/√n   or    μ = x - Zα/2 * σ/√n

where, μ = population mean

x = sample mean

  = 3 inches

σ = population standard deviation

  = 0.3 inches

Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)

So, the upper limit would be,

μ = 3 + 1.645 * (0.3/√36)

μ = 3 + 1.646 * (0.3/6)

μ = 3.0823

And the lower limit would be,

μ = 3 - 1.645 * (0.3/√36)

μ = 3 - 1.646 * (0.3/6)

μ = 2.9177

Hence, the 99% confidence interval is (2.9177, 3.0823)

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The probability that is lower than 63 grams is 95%

Given that,

X~ Normal ( 67 grams, 5 grams ) , n = 5

=> E( x ) = 67 grams , Var( X ) =5 grams

* ~ Normal ( 67 grams , 1 grams )

We know that, if X~ Normal ( E ( x) = a . Val (x ) = b)

Then X~ Normal ( E(x) = a, √Var (x)/n = √b/n)

E(x) = a, Var (x)/ = √b/n

Probability that sample mean X , is blw 65 and 70 grams

P ( 65< X<70 ) =

= P(Z<1. 76 ) - P(Z≤-2.65)

Using standard normal table values represent area

left of the Z- score, we get

= 0.96080 - 0.00402

= 0 .95678

=0.9568

So,The probability that is lower than 63 grams is 95%

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The proof for the difference between the squares of any two consecutive integers is equal to the sum of these two integers is done.

Let x stand in for any integer.

The next integer (the one that comes after) should then be x+1.

The assertion calls for proof;

(x+1)² - x² = x+(x+1)

Address the left side;

= x² + x + x + 1² - x²

= 2x+1 (Left Hand Side Solution)

Now, work on the right side.

= x + (x + 1)

= 2x + 1

Since, the LHS=RHS (left hand side=right hand side) is obvious, subtracting the difference between two successive squared numbers equals adding the two integers.

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There will be 80 chairs and 10 tables to furnish a school cafeteria

What exactly is a two-variable linear equation?

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Detailed explanation:

There are 8 chairs around each table. 8×40$ =320$

Each table cost $200.

Each table and chair combination is

200 + 320= 520

The total amount the school may spend is $5,200.

So, 5200 minus 520 equals 10.

Therefore, there are ten sets of table and chairs.

There are thus 10 tables.

Eight plus ten chairs total 80.

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A y-intercept of the continuous function in the table is;  (0, –6)

The y-intercept of a function is defined as the point where the graph intersects the y-axis. This means the point where the x-value is zero.

Now, from the function table given, we can see the coordinates of the function are given as;

(-4, 10)

(-3, 0)

(-2, 0)

(-1, -4)

(0, -6)

(1, 0)

Now, from the coordinates above , we can see that the only coordinate that has the x-value as zero is the one (0, -6) and as such by definition, it is the y-intercept.

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She needs to add 4 liters of the 8% acid solution when a chemist wants to combine a 4% acid solution.

Given that,

A chemist wants to combine a 4% acid solution. She has 8 liters of 2% acid on hand and wants to mix with some 8% acid to get the needed 4% acid solution.

We have to find she needs to add how much of the 8% acid solution.

We know that,

Assuming she wants to use all 8 liters of the 2% acid, you can set up the solution as follows:

x = required liters of the 8% acid

(2%)(8) + (8%)x = (4%)(x + 8)

2(8) + 8x = 4(x + 8)

16+8x=4x+32

8x-4x=32-16

4x=16

x=16/4

x=4 liters

Therefore, she needs to add 4 liters of the 8% acid solution when a chemist wants to combine a 4% acid solution.

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The sample space is all the cards in the deck if an experiment involves choosing one card from a deck of playing cards.

Given statement,

If an experiment is selecting a card from a deck of cards, then the sample space is,

For the given case,

The sample space in this case is " all the cards in the deck "

Therefore, If an experiment is selecting a card from a deck of cards, then the sample space is all the cards in the deck.

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The required number of associates is 2 and the number of partners is 4.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

daily rate charged to the client for each associate = $400

daily rate charged to the client for each partner = $900

According to question :

The law firm designated twice as many partners as associates , that means

P=2A                                 ---(1)

900*P +400A =4400       ---(2)

substitute the value of eqn (1) in (2).

900 *2A +400A = 4400

1800 A+400 A =4400

2200A =4400

A= 2

therefore P = 4.

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The probability that the drawn marble is green is 5/9.

What do you mean by an intersection in probability?

P(A∩B) denotes the probability of A and B occurring together, also known as the likelihood of A intersecting with B, or the likelihood of two occurrences occurring concurrently, or the probability of two events occurring simultaneously.

We define the intersection of two events as the set of all results that occur for any two events A and B. In other words, if both A and B happen, the intersection will happen. A and B are crossed when A∩B is used as a symbol.

Solution Explained:

Total number of white marbles = 6

Total number of black marbles = 2

Total number of green marbles = 10

Marbles in total = 6 + 2 + 10 = 18

A marble is drawn on random

Therefore, the probability of the marble being green P(G) = 10/18 = 5/9

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The midpoint of line PQ is (4,4).

What is the midpoint?

A location that is halfway between two other points is considered to be a line segment's midway. The distance between the midway and each endpoint is the same.

Midpoint formula:

{(x₁ + x₂)/2, (y₁ + y₂)/2}

Here, we have

Given points P(1,6) and Q(7,2)

Now we apply the midpoint formula and get

= {(x₁ + x₂)/2, (y₁ + y₂)/2}

= {(1 + 7)/2 , (6 + 2)/2}

= (8/2, 8/2)

= (4,4)

Hence, the midpoint of line PQ is (4,4)

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2,042,040 alternative ways are there to select the teams so that each project has the following number of employees: 6,3,8.

Given that,

Consider that you have 17 employees under your management and that you must organize three teams to work on various tasks. Assume that every employee will be part of a team and that they all possess the same credentials and abilities to ensure that everyone has an equal chance of being selected.

We have to find how many alternative ways are there to select the teams so that each project has the following number of employees: 6,3,8.

We know that,

Assume we have k groups to place the n interchangeable objects in, with n₁ + n₂ +... + nₐ = n objects in each group. The multinomial coefficient, or (n!) / [(n₁!) (n₂) ... (nₐ!)], measures the number of possible ways to accomplish something.

Since all of the employees in this situation have the same credentials and skills, we have n = 17 people and k = 3 groups to place them in.

Additionally, we have n₁ = 6, n₂ = 3, and n₃ = 8 (remember that 6 + 3 + 8 = 17).

The total number of teams that can be selected is therefore (17!) / [(6!) (3!) (8!)], which equals 2,042,040.

Therefore, 2,042,040 alternative ways are there to select the teams so that each project has the following number of employees: 6,3,8.

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Answer:The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

Step-by-step explanation:

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

The correct option d. All of the above are correct; for the sales of gasoline in local gasoline station.

According to the law of demand, for almost all things, demand decreases as price increases.

Because your neighbourhood gas station

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Slope intercept form of equation of a line is described by y - y1 = m(x - x1)

The are three kinds of equation of a line

a) point intercept form

b) slope point form

c) point point form

The formula y - y1 = m(x - x1) is usually described as the 'point-slope form' for the equation of a line.

where m represents the slope of the line and x1 and y1 is the point given through which the line passes.

It is useful when one point on a certain line and the slope of that certain line is known, then the equation of the line can be structured using this form.

Thus, the slope intercept form of equation of a line is described by y - y1 = m(x - x1)

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The Option b and e are correct they are the actual relationship between salary raises and performance rating is linear and  if the mean performance rating is 1.2, then the mean raise is $3800.

Given that,

The relationship between the magnitude of annual wage increases and the performance evaluations given to employees of a certain organization is described by a set of data. The least squares regression equation is y = 1400 + 2000x, where x is the performance rating and y is the raise amount (in dollars).

We have to find which of the following suppositions has to be accurate.

We know that,

[tex]\hat{y}[/tex]= 1400+2000x

Where,

[tex]\hat{y}[/tex] is predicted raise amount,

x is performance rate

Now,

If we compare the given equation with general form of simple linear regression equation i.e. y = a + b²

Option-B is correct.

Now,

For x=1.2 ,

[tex]\hat{y}[/tex] =1400+2000*1.2=3800

So, that option e) is also correct Option.

Therefore, The Option b and e are correct they are the actual relationship between salary raises and performance rating is linear and  if the mean performance rating is 1.2, then the mean raise is $3800.

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The eigenvector of matrix A4 is 4096.

The eigenvalue of the matrix A-1 is 1/8.

(A+4I) has an eigenvalue of 12.

40 is the eigenvalue of 5Av.

The collection of scalar values known as the eigenvalues of a matrix are connected to the set of linear equations that are most likely contained within the matrix equations.

The eigenvectors are also known as the characteristic roots.

If the matrix A's eigen vector v is linked to an eigen value.

Av then equals lamda v.

The fact that v is an eigen vector of A with the value eight is assumed.

hence, Av = 8v.

We must determine the eigenvalue of A4.

A4*v equals A3(8v) = 84*v equals 4096v.

As a result, the eigenvalue of A4 is 4096.

Suppose A has an eigenvalue of 8. The eigenvalue of A-1 is thus 1/8.

It is calculated that the eigenvalue of (A+4I) is (A +4In)v = Av + 4v = 8v + 4v =12v.

(A+4I) has an eigenvalue of 12.

The value of 5Av's eigenvalue is 5Av = 5*8v = 40v.

40 is the eigenvalue of 5Av.

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The value of x is 24

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

2/10 = 3/(x-9)

Do cross multiplication

2(x-9) = 10*3 = 30

2x-18=30

2x=30+18=48

x=48/2=24

So, the value of x is 24

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The area of a sector from the given figure is 50.24 square units.

From the given figure, radius of sector =8 units and the central angle =90°.

The area of a sector is the space inside the section of the circle created by two radii and an arc. It is a fraction of the area of the entire circle.

The formula to find the area of a sector = [tex]\frac{\theta}{360^o} \times\pi r^2[/tex].

Here, r=8 units and θ=90°

Using the area of a sector formula, we get

90°/360° ×3.14×8²

= 0.25×3.14×64

= 50.24 square units

Therefore, the area of a sector from the given figure is 50.24 square units.

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The leading coefficient of a polynomial is the coefficient of the leading term. In the above example 7+x−3x^2, the leading coefficient is −3.

A polynomial's leading coefficient is the coefficient of the leading term. In the preceding example, the leading coefficient is 3.

The leading coefficient of a polynomial is the coefficient of the leading term. In the preceding example, the leading coefficient is -3. (called that because the "standard notation" manner of writing polynomials has the terms organized from terms with high powers down to the constant term).

The term with the greatest power of x in a polynomial function is called the leading term. The leading coefficient is the leading term's coefficient.

The numbers written before the variable with the greatest exponent are known as leading coefficients. They, like regular coefficients, can be positive, negative, real, or imaginary, in addition to being whole numbers, fractions, or decimals. For example, the highest exponent in the equation  -7x^4 + 2x^3 - 11 is 4.

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According to the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

It is given to us that -

Amount of time a person experiences cold virus symptoms are normally distributed with

a mean of 7.5 days

and, a standard deviation of 1.5 days

We have to find out the proportion of cold sufferers that experience symptoms for more than 8 days.

Now, from the given information, we have

Mean = μ = 7.5

Standard deviation = σ = 1.5

and, X = 8

Now, the proportion of cold sufferers that experience symptoms for more than 8 days can be represented as -

P(X > 8)

= P{[(X-μ)/σ] > [(8-7.5)/1.5]}

=P(Z>0.33)

Looking at the z-score values, we find out that

P(Z>0.33) = 0.129 = 12.9%

Thus, from the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

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The  pair of triangles given in the option B are congruent by the SSS congruence postulate.

What is SSS  congruence postulate ?

A type of triangle congruence rule called Side-Side-Side (SSS) asserts that two triangles are congruent if their three sides are equal to their respective three sides of another triangle. When the dimensions of the matching sides and angles of two or more triangles match, the triangles are said to be congruent.

All sides are congruent to each other. I, II, and III symbols are present.

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Over the past forty years, there has been a sharp rise in the quantity and variety of interest groups. .

In general, federal courts handle cases involving federal law, while state courts hear cases involving state law. Because most crimes are violations of local or state law, state courts typically hear criminal cases.

The 94 District Courts (trial courts), 13 Courts of Appeals (intermediate appellate courts), and the United States Supreme Court are the three main categories of federal courts within the federal system (the court of final review).

The three main causes of this surge are the "New Politics" movement, the increase of the role of government, and grassroots conservative action. Federal jurisdiction over a wide variety of public policy problems was expanded throughout the 1960s and 1970s, and there was a matching rise in the number of interest organizations that could exert pressure on elected officials

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8/5 mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice.

It is given that a mini fruit juice box contains 4 fluid ounces of juice, we need to find how many mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice.

What is 1 quart?

A unit of the US customary system used in liquid measure, equal to 2 pints or 32 ounces

4 divided by 2 1/2

4 divided by 5/2

4 × 2/5

8/5

Therefore, 8/5 mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice.

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A 98% confidence interval for Americans' average daily eating and drinking time is (64.172, 82.228)

Given data,

How long do Americans spend drinking or eating? Let's say that, for a representative sample of 101 Americans, the daily average for eating or drinking is 73.2 minutes, with a straightforward standard deviation of 39 minutes. Create and analyze a 98% confidence interval for Americans' average daily eating and drinking time.

Let,

c = 98% = 0.98

n = 101

Mean μ = 73.2

Standard Deviation σ = 39

Now,

To analyze a 98% confidence interval for Americans' average daily eating and drinking time, we have;

CI = μ ± Z * σ/√n

CI = 73.2 ± 2.326 * 39/√101

    = 73.2 ± 9.028

    = 64.172, 82.228

Hence, the average daily calorie intake for Americans is within a 98% confidence zone (64.172, 82.228).

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5  is unit digit in the product  .

What do Units digits mean?

unit digit of (365 x 659 x 771 )

unit digit of ( 5× 9 × 1  )

unit digit of ( 45)

5  is unit digit in the product  .

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The Empirical Rule given helps in determining Let x = the time it takes an NFL running back to run the 40-yard dash and that P(x < 4.23) is =95%.

In Football, every play is made from both yardage benefit or yardage loss that is a calculation of a poor or advantageous number. With every byskip or run that the offense attempts, you need to upload the yardage that they made collectively to apprehend wherein they've superior to at the field.

Here we have that,

NFL= 40 yard run

x = the time it takes an NFL running back

[tex]mu=4.59 \\sigma= 0.12[/tex]

Using Empirical rule,

[tex](A)P(X)P(4.35 < x > = P( -2 < Z > = P\\\\(Zthe usage of empirical rule=95%/2 + 95%/2=47.5%+47.5%=95 %[/tex]\

Thus the P(x < 4.23) = 95%.

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Answer: 1.72

Step-by-step explanation:

18.92 ÷ 11 can be rewritten as: [tex]\frac{18.92}{11}[/tex].

Use long division to find the answer, as shown below:

Prime multiples are numbers that add to make a prime. The sum of the factors 1 and 7 is 7. Consequently, 1 and 7 are the prime multiples of 7.

In the given question we have to explian about the prime multiple.

The numbers that result from multiplying the original number by any whole number are the multiples of that number. Prime multiples are hence numbers that add to make a prime. The sum of the factors 1 and 7 is 7. Consequently, 1 and 7 are the prime multiples of 7.

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The number line which represents the solution set for the inequality is

x ≤ -5.

What is number line?

In elementary mathematics, a number line may be a image of a graduated line that is visual illustration of the important numbers. each purpose of variety|variety} line is assumed to correspond to a true number, and each real to a degree.

Main body:

[Given]=

-4(x + 3) ≤ -2 - 2x

Using the distributive property of multiplication on LHS

-4x-12 ≤ -2 - 2x

By transposing the terms with variables on one side and the constant on the other side

- 4x + 2x ≤ –2 + 12

By further calculation

- 2x ≤ 10

Divide both sides by -2

x ≤ -5

Therefore, x ≤ -5 represents the solution set.

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