which number line represents |x - 5| < 3?

The value of test statistics z=1.04

First, state the null and alternative hypotheses:

[tex]H_o=u_1=u_2\\H_a=u_1 > u_2[/tex]

Use z-statistics:

[tex]z=\frac{x_1-x_2}{y} ------(1)[/tex]

where x₁ and x₂ are the means and:

[tex]y=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }[/tex]

Calculating the value of test statistics:

[tex]y=\sqrt{\frac{(23.53)^2}{47}+\frac{(71.32)^2}{54} }[/tex]

[tex]y=\sqrt{\frac{533.6609}{47}+\frac{5086.542}{54} }[/tex]

[tex]y=\sqrt{11.780+7.460}[/tex]

[tex]y=\sqrt{19.24}[/tex]

y = 4.386

Now substitute the y value in equation (1)

[tex]z=\frac{75.57-71.32}{4.386}[/tex]

z = 1.04

The test statistics is z = 1.04

The decision rule for rejecting the null hypothesis is:  α≤ test statistics

Using the z-score table, it is possible to determine the p-value, which is:

value = 0.877

Comparing the p-value with the level of significance (α = 0.05):

0.877 > 0.05

Therefore, we fail to reject the null hypothesis.

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The given statement about Histogram that , " if median of a data set is larger than mean, then the histogram of data will likely have a longer right tail" is FALSE .

A histogram is a graph in which most of data falls to the right of graph's peak and is known as a right-skewed histogram. This type of histogram is  also known as a positively skewed histogram.

The relation between the mean , median and mode in a right-skewed histogram is denoted as : mean > median > mode .

A distribution is called skewed Right if, in histogram , the right tail (smaller values) is much longer than the left tail (larger values).

Therefore , For histogram to have longer right tail , the median should be less than the mean .

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The correct option is Option C - 85.274.94.

The face value of the 10-year term insurance policy on a 25-year-old Female given that the annual premium for the insurance policy of $384.59 is 85,274. 94.

Given:

Annual premium for the insurance policy = $384. 59

According to the chart at the conclusion of the answer, the amount paid per $1,000 of coverage for a female 25 year old for a 10 year policy is 4.51.

Face value = (1,000 x Annual premium) / Amount paid for 25 year old female for 10 year policy)

Face value = (1000 x 384.59) /4.51

Face Value = 384590 / 4.51

Face Value = 85274.94

Therefore the face value is 85274.94.

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The table is given by the image shown at the end of the answer.

The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.

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The number of students who do not buy lunch is 624 students - 420 students = 204 students.

The circle graph represents the proportion of students who buy lunch and those who don't. To find the number of students who don't buy lunch, we need to subtract the number of students who buy lunch from the total number of students.

Since 255° represents the proportion of students who buy lunch, we can use this to find the number of students who buy lunch. To do this, we divide the number of degrees by 360° and multiply by the total number of students, 624:

(255° / 360°) x 624 students = 420 students

Therefore, the number of students who do not buy lunch is 624 students - 420 students = 204 students.

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Answer:

7 hours

Step-by-step explanation:

So you know in the second to third row of boxes how a hour and a half later the car loses 3 gallons of gas let's says another hour and a half goes by and the car has 1 gallon of gas left so each 30 minutes the car lost gas so now that we have that 1 gallon of gas left 30 minutes went by and now we are out gas

The value of given expression 9x=4 equals to 4/9.

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.

Given expression ,

log 9x = log 4

log 9 + log x = log 4

log x = log 4 - log 9

log x = log 4 / 9

x = 4 /9.

Hence, The value of given expression 9x=4 equals to 4/9.

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It has a diameter of about 60,000 light-years (18,400 parsecs).

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The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.

The equations are given below.

2y = 180° - 126°

2y = 54°

y = 27°

2x + 1 = 180° - 85°

2x + 1 = 95°

2x = 94°

x = 47°

The value of the variables 'x' will be 47° and the value of the variables 'y' will be 27°, respectively.

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The complete question is attached below.

The given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.

(1) 0.4 is a rational number because it can be written as 4/10 which is a fraction with a denominator that is not zero.

(2) 0.21 is a rational number because it can be written as 21/100 which is a fraction with a denominator that is not zero.

(3) 0.14 is a rational number because it can be written as 14/100 which is a fraction with a denominator that is not zero.

(4) 0.124 is a rational number because it can be written as 124/1000 which is a fraction with a denominator that is not zero.

(5) -1.124 is a rational number because it can be written as -1124/1000 which is a fraction with a denominator that is not zero.

(6) 19.45 is a rational number because it can be written as 1945/100 which is a fraction with a denominator that is not zero.

(7) -2.35 is a rational number because it can be written as -235/100 which is a fraction with a denominator that is not zero.

In conclusion, all the given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.

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The length of the diagonals of the rhombus is 3.5cm.

A rhombus's diagonals are always perpendicular to one another and always the same length. It contains four right angles, hence an acute angle of 840 is an obtuse angle. We are aware that in a rhombus, the diagonal is the hypotenuse of a right triangle, and the other two sides make up each half of the side.

Consequently, we can use the Pythagorean theorem to determine the diagonal's length:

c = √(a² + b²)

where an is the rhombus's half-length side and b is the other half, and c is the length of the diagonal. So we have:

a = (5cm) / 2 = 2.5cm

b = (5cm) / 2 = 2.5cm

c = √(2.5² + 2.5²) = √(6.25 + 6.25) = √12.5 = 3.5cm

Therefore, the length of the diagonals of the rhombus is 3.5cm.

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Elizabeth would travel a distance of [tex]11\frac{2}{5}[/tex] miles.

The distance between Elizabeth's house and Carson's house = Sum of (the distance between Elizabeth's house and the Library + the distance between the library and Millo's house + the distance between Millo's House and Carson's House). That is:

Total Miles = [tex]6\frac{1}{2}[/tex] + [tex]2\frac{2}{5}[/tex] + [tex]2\frac{1}{2}[/tex]

To calculate the total miles, we need to transform the mixed numbers into fractions. We can do that as:

[tex]6\frac{1}{2}[/tex] = [(6 × 2) + (1)]/2 = 13/2

[tex]2\frac{2}{5}[/tex] = [(2 × 5) + (2)]/5 = 12/5

[tex]2\frac{1}{2}[/tex] = [(2 × 2) + (1)]/2 = 5/2

So, the distance from Elizabeth's house to Carson's House has 57/5 miles, and it is calculated as:

13/2 + 12/5 + 5/2 = 57/5

Then, convert 57/5 into a mixed number, and we get:

57/5 = [tex]11\frac{2}{5}[/tex]

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Answer:

30 ft

Step-by-step explanation:

h/(40 + 8) = 5/8

h = 30

The calculator short hand notations are;

a) -4E3

b) -3E4

c) 3E4

d) 4E3

We have to note that the calculator short hand notation has to do with the manner in which the calculator would show an exponential function when we are solving the mathematical problem using the calculator.

It is common to see that the calculator would display the letter E to stand in for the mathematical figure * 10^n. The letter that is depicted by n would then be written at the right hand side of the letter E.

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A fraction can be converted to a decimal number by dividing the numerator—the piece at the top of the fraction—by the denominator, which can be done with a calculator. A decimal number that represents the value of the fraction is the answer.

The geometry and location of the primary source of radiation directly affect the ratio of flux between direct and reflected radiation, known as the "reflection fraction."

Flip is the mathematical term for reflection. An image of the shape reflected in a mirror. A line, called the line of reflection, is where an image will reflect. When one figure "reflect[s]" another, that phrase is used.

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The value of B in the table will be D. 90

The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.

The ratios between the two variables should be considered in order to determine whether a relationship is proportional. The relationship is proportional if the ratio remains constant. The relationship is not proportional if the ratio changes.

In this case, the relationship between part and whole is 7:10.

Therefore, the value of B will be:

= 10 / 7 × 63

= 10 × 9

= 90

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Answer: I believe the answer is 12

The diagonal V2 of the square will be √2 feet.

What are squares?

A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.

The most important properties of a square are listed below:

Area of square=(side)²

Perimeter of square=4*side

Now,

as side=1 foot

By applying Pythagorean theorem,

Diagonal²=side²+side²

therefore,

V2²=1²+1²

=2

V2= √2 feet

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An inequality which shows the constraint on the amount of flour John has to make pies and cobblers is: B. 3x + 3y ≤ 16

In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:

Since a pie uses 4 cups of apples and 3 cups of flour while a cobbler uses 2 cups of apples and 3 cups of flour, the constraint on the amount of flour is given by:

3x + 3y ≤ 16

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Answer:

3rd one

Step-by-step explanation:

Answer:

3rd one

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

AB and TB are perpendicular because the tangent and radius are perpendicular. So you have a right triangle. Triangle ABT is a right triangle.

Also, TB is a radius of the circle, but so is TC. They are the same length.

Use Pythagorean Theorem to solve this problem.

AB^2 + TB^2 = AT^2

see image.

Answer: x>17/2

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

7<2x−10

Step 2: Flip the equation.

2x−10>7

Step 3: Add 10 to both sides.

2x−10+10>7+10

2x>17

Step 4: Divide both sides by 2.

2x/2 > 17/2

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Let's solve your inequality step-by-step.

−10+17<2x−10

Step 1: Simplify both sides of the inequality.

7<2x−10

Step 2: Flip the equation.

2x−10>7

Step 3: Add 10 to both sides.

2x−10+10>7+10

2x>17

Step 4: Divide both sides by 2.

[tex]\frac{2x}{2} > \frac{17}{2} \\\\ x > \frac{17}{2}[/tex]

Hope this helped :0

The probability that at least one person received $20 is 0.3

In math the term called probability is defined as a number that reflects the chance or likelihood that a particular event will occur.

Here we know that two people are picked at random from a group of 50 and given $10 each.

Here we have also know that three people are picked from the same group - one or more people could have been picked both times - and given $10 each.

Then the probability is calculated based on the binomial distribution is written as,

=> P = (50 3) 10³ (1 - 10) ⁵⁻³

When we simplify this one then we get the value of p as 0.3.

Then the following values are calculated through it,

μ = 15

σ = 3.24

σ² = 10.5

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Following are the different types of angles:

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The unit circle's sixteen unique angles, each indicated at the terminal point and measured in radians. These angles are frequently used as a parameter in trigonometric functions like the sine or cosine.

In the 1 figure,

∠1 and ∠2 are same - side interior angles

In the 2 figure,

∠1 and ∠2 are Alternate interior angles

In the 3 figure,

∠1 and ∠2 are corresponding angles

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The exact value of csc A is  (√89) /5

Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.

Since cot ⁡A = 8 /5  and that angle A is in Quadrant I.

tan A = 5/8       (Remember: tan = 1/cot and tan = opposite/adjacent)

opposite = 5 and adjacent = 8

hypotenuse = √(5² + 8²) = √89

sin A = 5/(√89)    (sin = opposite/hypotenuse)

csc A = (√89) /5     (csc = 1/sin)

Thus, the exact value of csc A is  (√89)/5

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The shortest possible height of the vase would be 45.650 centimeters.

Rounding to the nearest tenth of a centimeter, the height of a vase is 45.7 centimeters. The vase's height can be as short as possible. Include three digits in your response.

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The way that algebra can help in the creation of a histogram is that it helps organize and analyze the data in the histogram.

Algebra can be used to determine the range of values in the data set, and to create bins or intervals for the histogram. Algebra can be used to calculate the frequency of data points in each bin. This is important for creating the histogram, as it will determine the height of each bar.

Algebra can also be used to calculate the mean, median, mode, and standard deviation of the data set, which can provide a summary of the distribution of the data.

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Full question is:

Creating a historgram algebra. How does algebra help in creating a histogram ?

Answer:

70-14g

Step-by-step explanation:

-20g+70+6g = 70-14g

As number is rounded off to 30,000, the correct option is A i.e, it is closer to 30,000 than 29,000.

We look at the last three digits and round to the closest thousand. If these digits total 500 or more, the thousands digit is rounded up; if they total less than 500, the thousands digit is rounded down while remaining the same.

For example, to solve this question we have to check whether 16796 is closer to 16000 or 17000 in the counting. In this case, 16796 is closer to 16000, hence 17000 is the round figure of 16796.

In this problem, as the number is said to be rounded off to the nearest thousand is 30,000, this means that, the number is closer to 30,000 than 29,000.

The question is incomplete. The picture of number line is missing. It is placed in the attachment below.

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Answer: x = -7

Step-by-step explanation: Subtract 23 from both sides. 4x + 23 - 23 = x + 2 - 23, than simplify and subtract x from both sides

Two hidden cards out of five numbered cards with 8 as mode and 6 as mean of five numbers is equal to 8 and 1.

Total number of numbered cards is equal to 5

Number of hidden cards are two.

Let us consider two hidden cards be 'a' and 'b'.

Mode of the five numbered cards is 8

Three numbers are 4 , 9 , a, b, 8.

Mode represents the number with higher frequency.

4, 9, 8 only one time as 8 is the mode one of the number should be equal to 8.

let b = 8

Mean of five numbers is 6

Mean = ( Sum of all the numbers ) / total numbers

⇒ 6 = ( 4 + 9 + a + 8 + 8 ) / 5

⇒ 30 = 29 + a

⇒ a = 30 -29

⇒ a = 1

Therefore, two hidden numbers for the given mode and mean is equal to 8 and 1.

The above question is incomplete , the compete question is:

Basil has five numbered cards.

Two of the numbers are hidden. 4 9 ? ? 8

The mode of the five numbers is 8.

The mean of the five numbers is 6

c) Work out the two hidden numbers.

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