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The width of the shower caddy is 8 inches.

What is Volume?

Volume is a measure of the total amount of material that an object contains. In mathematical terms, volume is calculated by multiplying the length, width, and height of an object.

We can use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.

We know that the volume of the caddy is 420 cubic inches, the length is 10.5 inches, and the height is 5 inches. Let's substitute these values into the formula and solve for the width:

420 = 10.5w × 5

Divide both sides by 52.5:

8 = w

Therefore, the width of the shower caddy is 8 inches.

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The only true statement is 2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4.

option A.

BODMAS is an acronym that stands for "Brackets, Orders, Division, Multiplication, Addition and Subtraction".

The rule of BODMAS states that when you have a mathematical expression that involves multiple arithmetic operations, you need to perform them in a certain order. You should start by evaluating anything inside brackets or parentheses first. Then, you should work out any exponents or square roots. After that, you should perform any division or multiplication from left to right, and finally, you should perform any addition or subtraction from left to right.

If we apply the rule of BODMAS to all the given options, we would notice that only option 1 is true.

2 x (4 + 2) - 6 = 14 ÷ (3.5 x 2 ) + 4

L.H.S ⇒ 2 x (6) - 6

= 12 - 6

= 6

R.H.S ⇒ 14 ÷ (3.5 x 2 ) + 4

= 14 ÷ (7) + 4

= 2 + 4

= 6

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The section for piano will have 60 degrees in the circle graph.

To find out how many degrees the section for piano will have in the circle graph, we first need to find the fraction of the circle that the piano represents.

The total degrees in a circle is 360 degrees. We can use the given fraction of piano (1/6) and multiply it by 360 degrees to find out the degrees of the section for piano.

Degrees for piano = (Fraction of piano) × 360

Degrees for piano = (1/6) × 360

Now, multiply the fraction by 360:

Degrees for piano = 60

So, the section for piano will have 60 degrees in the circle graph.

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→ 60° ( btw, ° means degrees )

— if a WHOLE circle is 360° and the piano is 1/6 of the circle, then all you have to do is multiply 1/6 by 360° which gives you 60 OR 60°

HEY- you look hungry, eat up !! →

Answer: about 169.65

Step-by-step explanation:

You do pi r squared multiplied by height over 3.

28.27 is the area of the circle and you multiply is by six because 18/3=6. 28.27x6 = about 169.65

Answer:

(2) {1/2,-2}

Step-by-step explanation:

2x² + 3x - 2 = 0

Delta = b² - 4ac

= 3² - 4 (2)(-2)

= 9 + 16

Delta = 25

[tex] \sqrt{25} = 5[/tex]

X= -3-5÷4 = -2

X'= -3+5÷4 = 2/4 = 1/2

S = { 1/2 ; -2 }

Answer:

Step-by-step explanation:

2x² + 3x - 2 = 0

2x² -x +4x - 2 = 0

(2x² -x) +(4x - 2) = 0

x(2x -1) +2(2x -1) = 0

(x +2)(2x-1) =0

(x +2) =0

x = -2

OR

(2x-1) =0

x = 1/2

ans: (2) (1/2, -2)

The measure of ∠JMK =52° and ∠KML = 38°.

Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove:  is a right angle.

Proof:

Statements  Reasons

1. m∠JMK = 52°                  Given

2. m∠KML = 38°                  Given

3. m∠JMK + m∠KML = m∠JML

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. 52° + 38° =m∠JML            Substitution property of equality

5. 90° = m∠JML                    Simplification

6. ∠JML is a right angle.      Definition of right angle

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Since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.

A triangle is a three-sided polygon that is one of the basic shapes in geometry. It is defined by three points that are connected by three line segments. Triangles have three angles, which add up to 180 degrees, and three sides, which add up to the sum of the lengths of the other two sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. Triangles come in a variety of forms, from the equilateral triangle, which has three sides of equal length, to the isosceles triangle, which has two sides of equal length, to the scalene triangle, which has three sides of different lengths.

The correct answer is: Segment BF = 9. This can be proved true using the given theorem, since segment DE is parallel to segment BC and segment EF is parallel to AB. Therefore, since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.

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The equation y - 4 = -2(x - 1) in slope-intercept form include the following: C. y = -2x - 2.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

By making the variable "y" the subject of formula, we have the following:

y - 4 = -2(x - 1)

y = -2x + 2 - 4

y = -2x - 2

Therefore, the slope (m) is equal to -2.

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Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex]

It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.

The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.

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If a sample of 100 Americans is taken that same week, then the probability that "sample-proportion" has between a 42% and a 47% approval rating is 0.7693 or 76.93%.

To calculate the probability that the sample-proportion falls between 42% and 47% for a sample of 100 Americans, we use the standard normal distribution.

The Sample size (n) is = 100,

The Sample proportion (p) = 46% or 0.46,

The "Standard-deviation" (σ) = √(p×(1-p)/n) = √(0.46×(1-0.46)/100) ≈ 0.0497,

We now calculate the "z-scores" corresponding to the lower and upper bounds of the desired range,

We know that, the value of "z" is (x - μ)/σ,

where x = desired proportion, μ = mean proportion, and σ = standard deviation,

So, The probability that the sample proportion has between a 42% and a 47% "approval-rating", is written as :

⇒ P(0.42 < x < 0.47) = P[(0.42 - 0.46)/0.0497 < z < (0.47 - 0.46)/0.0497],

⇒ P(0.42 < x < 0.47) = P[-0.807 < z < 2.015],

⇒ P(0.42 < x < 0.47) = 0.9783 - 0.209,

⇒ P(0.42 < x < 0.47) = 0.7693,

Therefore, the required probability is 0.7693 or 76.93%.

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It will take John approximately 17 months to pay off the balance.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

Assuming that John does not use the credit card for any other purchases and that the credit card company uses a simple interest calculation method, we can use the following steps to calculate the number of months it will take John to pay off the balance:

Calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:

Monthly interest rate = 19% / 12 = 0.01583

Calculate the monthly finance charge by multiplying the outstanding balance by the monthly interest rate:

Monthly finance charge = $2000 x 0.01583 = $31.66

Subtract the monthly payment from the monthly finance charge to get the amount that will be applied to the outstanding balance:

Payment applied to balance = $150 - $31.66 = $118.34

Divide the outstanding balance by the payment applied to balance to get the number of months it will take to pay off the balance:

Number of months to pay off balance = $2000 / $118.34 = 16.9

(rounded up to the nearest whole number)

Therefore, it will take John approximately 17 months to pay off the balance.

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A(n) "spanned" volume is similar to a primary partition, but in fact, is not a primary partition.

A spanned volume is similar to a primary partition, but in fact, is not a primary partition. In a spanned volume, you can combine free space from multiple disks to create a larger logical storage unit, while a primary partition is a segment of a hard disk drive that the operating system recognizes as a separate logical storage unit. A volume can span multiple partitions depending on how it is configured, or it can encompass a single partition. Different operating systems have different ways of configuring and managing volumes.

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The complete table is:

x (weeks since 5 years ago)         y (in $)

260                                                 150.01

259                                                 150.06

256                                                 149.42

234                                                 142.03

208                                                 152.79

104                                                   97.65

0                                                       70.43

The coordinates are given by (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).

The X axis suggests the weeks since 5 years ago and Y axis suggests the closing price at each time.

Number of weeks in a year is 52 weeks.  

Most recent time suggests, x = 52*5 = 260

when x = 260, then y = 150.01

7 days ago that is 1 weeks ago, x = 260 -1 = 259

The value of y then = $ 150.06

1 months ago that is 4 weeks ago, x = 260 - 4 = 256

The closing price then is, y = 149.42

6 months ago, x = 260 - 52/2 = 260 - 26 = 234

The closing price then is, y = 142.03

1 year ago that is 52 years ago, x = 260 - 52 = 208

The closing price was then, y = 152.79

3 years ago, x = 260 - 52*3 = 260 - 156 = 104

The closing price was then, y = 97.65

5 years ago, x = 260 - 52*5 = 260 - 260 = 0

The closing price was then, y = 70.43.

Then the coordinates are (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).

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Step-by-step explanation:

hope this will help you Thanks

Answer:

Add 1 1/4 x 1 1/4

Step-by-step explanation:

To calculate this probability, we need to use the cumulative binomial probability formula:

P(X ≤ k) = Σ(i=0 to k) (n choose i) p^i (1-p)^(n-i)

Where:
- X is the number of heads obtained
- k is the number of heads we want to calculate the probability for (in this case, the same number of heads obtained)
- n is the total number of coin flips (10 in this case)
- p is the probability of getting heads on a single flip (0.5 for a fair coin)
- (n choose i) is the binomial coefficient, which represents the number of ways to choose i heads out of n flips

For this problem, we want to calculate P(X ≤ 10), since we're interested in the probability of obtaining as many heads as we did or less. Plugging in the values, we get:

P(X ≤ 10) = Σ(i=0 to 10) (10 choose i) 0.5^i 0.5^(10-i)
          = (10 choose 0) 0.5^0 0.5^10 + (10 choose 1) 0.5^1 0.5^9 + ... + (10 choose 10) 0.5^10 0.5^0
          = 0.00098 + 0.00977 + 0.04395 + 0.11719 + 0.20508 + 0.24609 + 0.20508 + 0.11719 + 0.04395 + 0.00977 + 0.00098
          = 0.9453

Therefore, the probability of obtaining as many heads as we did or less when flipping a fair coin 10 times is 0.9453.

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The Number of atoms ≈ 5.119 x 10^24 atoms

The Mass ≈ 248.0 g

Mass ≈ 248.0 g

To find the number of atoms, we use Avogadro's number, which is 6.022 x 10^23 atoms/mole.

Number of atoms = (8.500 moles) * (6.022 x 10^23 atoms/mole)

Number of atoms ≈ 5.119 x 10^24 atoms

To find the mass, we need the molar mass of oxygen, which is 16.00 g/mole.

Mass = (15.50 moles) * (16.00 g/mole)

Mass ≈ 248.0 g

Determine the number of moles of helium in 1.953 x 10^8 g of helium.

To find the number of moles, we need the molar mass of helium, which is 4.00 g/mole.

Number of moles = (1.953 x 10^8 g) / (4.00 g/mole)

Number of moles ≈ 4.883 x 10^7 moles

Calculate the number of atoms in 147.82 g of sulfur.

To find the number of atoms, we first need to find the number of moles of sulfur, and then use Avogadro's number. The molar mass of sulfur is 32.07 g/mole.

Number of moles = (147.82 g) / (32.07 g/mole)

Number of moles ≈ 4.609 moles

Number of atoms = (4.609 moles) * (6.022 x 10^23 atoms/mole)

Number of atoms ≈ 2.772 x 10^24 atoms

Determine the molar mass of Co.

The molar mass of cobalt (Co) is 58.93 g/mole.

Determine the formula mass of Ca3(PO4)2.

To find the formula mass, we need to add up the molar masses of all the elements in the compound.

Ca3(PO4)2 contains 3 calcium (Ca) atoms, 2 phosphorus (P) atoms, and 8 oxygen (O) atoms.

Molar mass of Ca = 40.08 g/mole

Molar mass of P = 30.97 g/mole

Molar mass of O = 16.00 g/mole

Formula mass = (3 * 40.08) + (2 * 30.97) + (8 * 16.00)

Formula mass = 120.24 + 61.94 + 128.00

Formula mass ≈ 310.18 g/mole

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The justifications for 2 and 3 are;

Addition property of equality and

Multiplication property of equality

1. x/2 - 9 = -4 given

Add 9 to both sides

2. x/2 = -13 (Addition property of equality)

cross product

3.x = -26 (Multiplication property of equality)

Therefore, x/2 - 9 = -4 where x Is -26 is justified by addition and multiplication property of equality.

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The probability that it is raining and the flight is delayed is equal to the probability of it raining multiplied by the probability of the flight being delayed.

Therefore, the probability that it is raining and the flight is delayed is 0.07 * 0.16 = 0.0112. Rounded to the nearest thousandth, this is 0.011.

Let's use the variable x to represent the list price of the car.

The total cost your cousin paid for the car is the list price plus a 7% sales tax on the list price, plus $450 in additional fees.

We can write this as an equation:

Total cost = List price + 0.07(List price) + 450

We know that the total cost your cousin paid was $12,755, so we can substitute that into the equation:

12,755 = x + 0.07x + 450

Simplifying the right side:

12,755 = 1.07x + 450

Subtracting 450 from both sides:

12,305 = 1.07x

Dividing both sides by 1.07:

x = 11,500

Therefore, the list price of the car your cousin bought was $11,500.

The list price of the car your cousin bought was $11,500.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's start by setting up an equation to represent the total cost of the car:

Total cost = List price + 7% of List price + $450

We know that the total cost is $12,755, so we can substitute that in:

$12,755 = List price + 0.07(List price) + $450

Simplifying this equation, we get:

$12,755 = 1.07(List price) + $450

Subtracting $450 from both sides, we get:

$12,305 = 1.07(List price)

Dividing both sides by 1.07, we get:

List price = $11,500

Therefore,

The list price of the car your cousin bought was $11,500.

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If a hypothesis test rejects the null hypothesis in the context of the claim made by the textbook company, it means that the observed proportion of students who read the book is statistically significantly greater than 55%, suggesting that their book may indeed be more engaging.

If a hypothesis test is performed that rejects the null hypothesis, it means that the observed results are unlikely to have occurred by chance if the null hypothesis were true. In the context of the claim made by the textbook company, the null hypothesis would be that the proportion of students who read the book is equal to or less than 55%.

If the hypothesis test rejects the null hypothesis at a certain level of significance (such as α = 0.05), it means that the observed proportion of students who read the book is statistically significantly greater than 55% at that level of significance.

However, it is important to note that statistical significance does not necessarily imply practical significance. Even if the hypothesis test rejects the null hypothesis, the difference between the observed proportion and 55% may be small, and the practical significance of the result may be limited.

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Answer: I’m pretty sure it’s B

Step-by-step explanation:

The slope of the regression line is 0.922. Option C is correct.

The coefficient of determination (R-squared) is defined as the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a linear regression model. It can be calculated as the square of the correlation coefficient (r) between the dependent and independent variables.

If we assume a simple linear regression model with a single independent variable (x) and a single dependent variable (y), the slope of the regression line (b) can be calculated as:

b = r * (Sy / Sx)

where r is the correlation coefficient between x and y, Sy is the standard deviation of y, and Sx is the standard deviation of x.

If the coefficient of determination is 0.85, then the correlation coefficient is the square root of 0.85, which is approximately 0.922. Assuming the standard deviations of x and y are known, we could use the formula above to calculate the slope of the regression line as:

b = 0.922 * (Sy / Sx)
Therefore, 0.922, could be the slope of the regression line in this case, if the assumptions of a simple linear regression model with known standard deviations are met. Option C is correct.

The complete question is

The coefficient of determination resulting from a particular regression analysis was 0.85. What was the slope of the regression line?

a. 0.85

b. -0.85

c. 0.922

d. There is insufficient information to answer the question.

e. None of the above

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Answer:

x<-1/5

Step-by-step explanation:

Imma assume the _ is a - soo

3x-1<-2x

5x<-1

x<-1/5