Match each number on the left with the correct description of the number on the right.
Answer options on the right may be used more than once.
-10
This is an integer.
This is a rational number, but not an integer.
This is an irrational number.
√5
-5.6
31/
π

The value of x is 56 and the value if the unknown angle is 106°

Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. The law of angle on a straight line states that the sum of angle on a straight line is 180°

This means that (2x-6)°+74= 180

(2x-6)°= 180-74

(2x-6)° = 106

add 6 to both sides

2x= 106+6

2x= 112

x= 112/2

x= 56

therefore the unknown angle = 2(56)-6 = 112-6= 106°

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The values of the expression (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

The given parameters that will help us to calculate the values are

r(x) = x+5

s(x) = 4x +2

(1)  r*s(x) will be

(x+5)(4x+2)

Opening the brackets we have

4x²+2x+20x+10

= 4x²+22x+10

(2) (r-5)(x)

Putting the values of r and s

(x+5)- (4x+2)

Open the brackets to have

x+5-4x-2

Collecting like terms to get

-3x+3

(3) (r+s)(x)

By substitution we have

x+5+4x+2

⇒5x +7

In conclusion the values of the expressions are (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

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MP = 16 ,, where NP = 13

therefore : MP - NP = MN <=> MN = 16 - 13 <=> MN = 3

MP = 16 ,, where MO = 9

therefore : MP - MO = OP <=> 16 - 9 = MO <=> MO = 7

MO = 7 & MN = 3

therefore : MO - MN = NO <=> NO = 7 - 3 <=> NO = 4

5.8525 grams out of 25 grams of xenon will be left after 11 days.

The amount of time needed for an isotope's radioactivity to decrease to 50% of its initial value.

The given data is

T1/2=5.25 days.

No=25g

T=11 days

We'll have to find the disintegration constant first.

The formula for finding it is

T½ = In2 / λ

T½ = half-life

λ = disintegration constant

λ = In2 / T½

λ = 0.693 / 5.25

λ = 0.132

In(N / No) = -λt

where,

N = final mass of the radioactive sample

No = initial mass of the sample

λ = disintegration constant

t = time for the radioactive decay

In(N/No) = -λt

N / No = e^-λt

N = No(e^-λt)

N = 25 × e^-(0.132 × 11)

N=5.8525 g.

Therefore 5.8525 grams of Xe-133 will be left after 11 days.

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The area of the rectangle, in square meters, is 7.56 meters².

Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.

Given;

a rectangle has a length of 42 centimeters,

and a width of 18 centimeters.

To find the area of the rectangle:

We multiply the length of the rectangle by the width of the rectangle.

Use formula,

The area of the rectangle = length x width

Substitute the value of length and width

The area of the rectangle = 42 x 18

The area of the rectangle = 756 cm².

To change centimeter to meter:

We have the rate of change,

1 centimeter = 0.01 meter

756 centimeters = 0.01 x 756 meters

756 centimeters = 7.56 meters

Therefore, the area of the rectangle = 7.56 meters².

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Tamia will need 166 feet of fabric

Given that:

Tamia wants each curtain to be 24 inches long

At the fabric store, fabric is sold by the foot

Tamia's curtain company wants to make 83 curtains

1 curtain = 24 inches

83 curtains = 24×83 = 1992 inches

To convert inches to feet multiply by 1/12:

1992 inches =  1992 × 1/12 feet = 166 feet

Thus, she will need 166 feet

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Jane must therefore deposit her savings in the four rivers bank.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the data provided in the question,

Rate, r = 12%

After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:

[tex]A = P(1+\frac{r}{100} )^n[/tex]

For compounded quarterly,

n = 5 × 4

n = 20

A = 40000(1 + 12/(4 × 100))²⁰

A = 72244.44     (i)

If Jane placed her savings with the Four Rivers, then,

A = 40000(1 + 14/(2 × 100))¹⁰

A = 40000 × 1.9671

A = 78686.054  (ii)

Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.

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The valid conclusion is  A. We can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

The confidence interval used by the student researcher refers to the probability that the university's population parameter (average amount that students spent on sporting events last year) will fall between $217 and $677 for 90% of the time.

Thus, the interval measurement gives the researcher some degree of certainty that the calculated sample mean falls within the population mean most of the time.

Hence ,we can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

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Answer:

write your question in a proper way

There are 19 members from 00 to 18 who do not equal 18.

There are 19 members from 19 to 37 who do not equal 18.

There are 3 members in the age range of 38 to 40, not 2.

Given info,

Explain what is wrong with each of the following simulation designs.

⇒ A roulette wheel has 38 colored slots - 18 red, 18 black members green. To simulate one spin of the wheel, let members 00 to 18 represent red, 19 to 37 represent members and 38 to 40 represent green.

The mistake is;

→ There are 19 member from 00 to 18 which is not 18.

→ There are 19 member from 19 to 37 which is not 18.

→ There are 3 member from 38 to 40 which is not 2.

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There are two points, 4 units from the origin and 2 units from the line x = -1.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given point is at a distance of 4 units from origin,

that is √x² + y² = 4

x² + y²= 16 is the equation of the locus of the point.

The given point is also 2 units from the line x =-1

that is √(x+1)² + y² = 2

(x+1)² + y²= 4 is the equation of the locus of the point.

Subtracting the second given equation from the first one,

we get x² - (x+1)² = 12

simplifying, x = 11/2

So the common coordinate point for these 2 points which is 11/2.

Substituting this value to the first equation,

(11/2)²+ y² = 16

Simplifying, y = ±(i√57)/2.

There are 2 points whose coordinates are;

( i√57/2 , 11/2 ) and ( -i√57/2 , 11/2 ).

Therefore there are two points, 4 units from the origin and 2 units from the line x = -1.

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Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

Item a:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 11 - 1 = 10 df and t = 1.91, hence it is of 0.0426.

The p-value is of 0.0426, which is less than 0.05, thus the null hypothesis is rejected.

Item b:

We have a left-tailed test, as it is being tested if the mean is less than a value.

The p-value is found using a t-distribution calculator, with 17 - 1 = 16 df and t = -3.45, hence it is of 0.0016.

The p-value is of 0.0016, which is less than 0.05, thus the null hypothesis is rejected.

Item c:

We have a two-tailed test, as it is being tested if the mean is different than a value.

The p-value is found using a t-distribution calculator, with 7 - 1 = 6 df and t = 0.83, hence it is of 0.4383.

The p-value is of 0.4383, which is more than 0.05, thus the null hypothesis is not rejected.

Item d:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 28 - 1 = 27 df and t = 1.91, hence it is of 0.0195.

The p-value is of 0.0195, which is less than 0.05, thus the null hypothesis is rejected.

Therefore, in an independent random sample is selected from an approximately normal population with an unknown standard deviation. Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

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We are given the following data set:

10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20

Standard deviation = 8.043

Confidence level = 1 - Significance Level = 1 - 99.74% = 4.56% = 0.0456

Answer:

4.358

Step-by-step explanation:

sqrt(19) = 4.358

The approximate distance from the playground to the road along the other path is 1.3 miles.

A town park has two paths leading to the playground. One path is 2 miles from the road and the other path makes a right angle with the road. The two paths intersect at an angle of  50 degrees.

The approximate distance from the playground to the road along the other path can be calculated as follows;

using trigonometric ratios,

cos 50° = adjacent / hypotenuse

let

x =  distance from the playground to the road along the other path

Hence,

cos 50 = x / 2

cross multiply

x = 2 cos 50°

x = 2 × 0.64278760968

x = 1.28557521937

x = 1.3 miles.

Therefore,

distance form play ground to the road = 1.3 miles.

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Physical changes are those that occur when a substance's physical properties, such as appearance, texture, color, etc.

Given that,

We have to find what term is used to name a change in the physical properties of a substance which is usually reversible.

We know that,

When only the physical characteristics of a material—such as its size, shape, color, condition, or appearance—alter, this is referred to as a physical change in the substance. Its chemical makeup is unaltered. a few instances of physical change water and sugar being dissolved. wax melting.

Physical changes are those that occur when a substance's physical characteristics, such as appearance, texture, color, odor, melting and boiling temperatures, density, solubility, polarity, etc., change.

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After solving the equation the jet is descending vertically at 12 mph.

The Pythagorean Theorem is a mathematical statement that states that in a right triangle the sum of the squares of the lengths of the two sides that make up the right angle are equal to the square of the length of the hypotenuse. This theorem is named after the ancient Greek mathematician, Pythagoras. It can be expressed as the equation: a2 + b2 = c2, where 'a' and 'b' are the lengths of the two sides adjacent to the right angle and 'c' is the length of the hypotenuse. The Pythagorean Theorem is a fundamental tool used in geometry and trigonometry, and it is used to calculate the lengths of the sides of a right triangle. It can also be used to calculate the distances between two points or to calculate the area of a triangle.

The jet is descending at 12 mph. This can be calculated by using the Pythagorean Theorem. Since the jet is approaching the oil depot horizontally at 738 mph and descending diagonally at a constant speed of 750 mph, we can use the Pythagorean Theorem to calculate the vertical component of the jet's descent.
750^2 = 738^2 + x^2
x = √(750^2 - 738^2)
x = 12 mph
Therefore, the jet is descending vertically at 12 mph.

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The algebraic equation representing cost can be given as C= 85n+1500.

What is an equation in one variable and power one?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers and x is a variable. This equation has only one solution which can be found by separating the constant and variable terms in the equation.

We are given that A banquet hall charges $1500 to rent the hall and $85 per guest that attends.

Let the number of guests be n

Hence, The equation can be given as

C = 85n+1500

Where C is the cost, n is the number of guests attending.

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There are 364 positive variables and 5984 non - negative integers.

An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). [1] A negative number is the additive reciprocal of the corresponding positive number. [2] In mathematics languages, sets of integers are often represented by a bold Z or blackboard bold . The integers form the smallest group and smallest ring containing the natural numbers. In algebraic number theory, integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers.

Let us take each xi = a₁+1

x₁+x₂+x₃+x₄ = 35

∴a₁+a₂+a₃+a₄ = 31 ,where each ai is non-negative.

Now using the stars and bars method the answer is -

([tex]\left \{ {{31 + 4 - 1} \atop {4 - 1}} \right.[/tex]  = [tex]\left \{ {{34} \atop {3}} \right.[/tex]}

               = [tex]\frac{34!}{3! * (34 - 3)!}[/tex]

               = 5984

A particular solution of this equation corresponds to the placement of 3 addition signs in the 14 spaces between successive ones in a row of 15 ones.

Since, a particular solution of the equation corresponds to the placement of k−1 addition signs in the n−1 spaces between successive ones in a row of n ones, the number of solutions of the equation x₁ + x₂ + x₃ +⋯+xₐ=n in the positive integers is

[tex]\left \{ {{n - 1} \atop {k - 1}} \right.[/tex]}

For instance, placing an addition sign in the fourth, seventh, and twelfth spaces gives

                         1111+111+11111+111

which corresponds to the solution x₁ = 4, x₂ = 3, x₃ = 5, x₄ = 3.

Hence, the number of such solutions is the number of ways we can select which three of the 14 spaces between successive ones in a row of 15 ones will be filled with addition signs, which is

                                    [tex]\left \{ {{14} \atop {3}} \right.[/tex]}

                             = [tex]\frac{14!}{3! * (14 - 3)!}[/tex]

                             = 364

Therefore, there are 364 positive variables and 5984 non - negative integers.

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The statement that characterizes the outcome of the game is option d;

All of the above are correct.

Given,

The statements;-

a. Both Firm A and Firm B have a dominant strategy to advertise.

b. There is a Nash equilibrium when both firms advertise.

c. Although both firms collectively would earn higher profits by maintaining the agreement not to advertise, self-interest will cause each firm to break the agreement.

d. All of the above are correct

We have to find the correct statement that characterize the outcome of this game.

Here,

All the statement will characterize the outcome of this game. So correct answer is option d, All of the above are correct

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The inequality that describes the problem is C. 8x ≤ 16

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Kamari's Sweet Treats, cookies are packaged in boxes of 8 and the most a box can cost is $16. This will be:

8x ≤ 16

The correct option is C.

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Gracie shay must add $11,873 to buy that new hammer with its initial investment.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the given information in the question,

The price of hammer =$28,000

The annual rate of interest = 6%

Total number of years = 5

Principal investment = $12,000

The equation for annual compound interest, with the principal amount included, is :

A = [tex]P(1+\frac{r}{n} )^(^n^t^)[/tex]

Substitute all the values from above in the equation,

A = 12,000(1+0.06/2)⁽²⁾⁽⁵⁾

A = 12,000 × 1.03¹⁰

A = $16127

After five years, Gracie won't be able to be the hammer and will have to pay more money:

28000 - 16127 = $11,873.

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8

x = 6

9

x=7

10

x= 15

see explanation in image

because you know that m and n are parralell you can use the vertical angle theorem as well as the fact that lines in a straight angle add to 180

if you have any questions just comment

Answer: Translation T = (x + 8, y + 4)

Step-by-step explanation:

The x coordinate moved to the right by 8 and the y coordinate moved up by 4.

Missing part of the equation is 6.0 × [tex]10^{-8}[/tex] [tex]m^{3}[/tex].

It is given that students sets up the equation (0.060 [tex]cm^{3}[/tex])(_) = (_) [tex]m^{3}[/tex].

i.e. we have units of [tex]cm^{3}[/tex] and wants units of [tex]m^{3}[/tex] .

We know that 100 cm = 1 meter

i.e. 100cm/1 meter

⇒  [tex](100cm/1 meter)^{3}[/tex] = 1 × [tex]10^{6} cm^{3}/m^{3}[/tex]

⇒1/(1 × [tex]10^{6} cm^{3}/ m^{3}[/tex]) = (1 × [tex]10^{-6} m^{3}/cm^{3}[/tex])

We can use this new conversation factor to convert volume from [tex]cm^{3}[/tex] to [tex]m^{3}[/tex].

(0.060 [tex]cm^{3}[/tex])(1 × [tex]10^{-6} m^{3}/cm^{3}[/tex]) = (_) [tex]m^{3}[/tex]

(0.060 [tex]cm^{3}[/tex])(1 × [tex]10^{6} cm^{3}/m^{3}[/tex]) = 6.0 × [tex]10^{-8} m^{3}[/tex].

This is the required equation.

If we want to convert measurement,

to convert a smaller unit to a larger init, divide it by the number of smaller units which are needed to make larger unit. To convert from a larger unit to a smaller one, multiply. To convert from a smaller unit to a larger one, divide.

A conversation factor is a number used to change one set of units to another, by multiplying or dividing.

Given question is incomplete.

a student sets up the following equation to convert a measurement. (the stands for a number the student is going to calculate.) fill in the missing part of this equation  (0.060 [tex]cm^{3}[/tex])(_) = (_) [tex]m^{3}[/tex].

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The polygon shown in the figure is trapezoid and the value if x is  .

What is trapezoid?

A trapezoid may be a polygonal shape that has just one try of parallel sides. These parallel sides also are referred to as parallel bases of trapezoid. the opposite 2 sides of trapezoids area unit non-parallel and referred to as legs of trapezoids

Main body:

by using the property of trapezoid ,

1/2(sum of both bases) = mid-line passing through trapezoid

according to question:

x = 1/2(x-8+2x-12)

x = 1/2(3x -20)

2x = 3x - 20

x = 20

Hence value of x is 20.

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No, least-squares fitting of a regression line doesn't only applies when there is one dependent variable and one independent variable.

A least-squares regression line, which minimizes the vertical distance between the data points and the regression line, is the line that best fits a linear relationship between two variables when the data indicates such a relationship.

The most used modeling technique is without a doubt linear least squares regression. It is what most people mean when they claim they fitted a model to their data using "regression," "linear regression," or "least squares."

The independent variable in a cause-and-effect relationship is the cause, while the dependent variable is the effect. A technique for predicting the value of a dependent variable Y based on the value of an independent variable X is known as least squares linear regression. That's why least-squares fitting of a regression line doesn't only applies when there is one dependent variable and one independent variable.

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Answer:

A) 40

B) 5

C) 55

D) 35

Step-by-step explanation:

The formula is:

[tex]\frac{(F - 32)5}{9}[/tex]

F is the temperature in Fahrenheit.

A)

[tex]\frac{(104-32)5}{9}[/tex]

40

B)

[tex]\frac{(41-32)5}{9}[/tex]

5

C)

[tex]\frac{(131-32)5}{9}[/tex]

55

D)

[tex]\frac{(95-32)5}{9}[/tex]

35