Which statement about the order of operations is TRUE?

Complete all subtraction operations before addition.
Simplify operations within the innermost grouping symbols first.
Complete all division operations before multiplication.
Simplify exponents before operations in grouping symbols.

After solving, the height in feet of the sixth bounce is 1.892 feet.

In the given question, we ave to find the height, in feet, of the sixth bounce.

From the given question,

Height on the first bounce = 6.7

Subsequent bounce reaches a height of the previous bounce = 81%

Suppose the height is h.

So according to the question:

h(6) = height on the first bounce*(subsequent bounce reaches a height of the previous bounce)^6

h(6) = 6.7*(81%)^6

h(6) = 1.892 feet

So the height of sixth bounce is 1.892 feet.

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Answer:

$8

Step-by-step explanation:

The number of hours that the team trains per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:

c ≤ (3.50 × 4)

c ≤ 14

The cost will be at most $14.

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Answer: To find the height of the goalpost, we can use the information provided in the problem and the concept of similar triangles. Since Violet is looking down at the mirror, the line of sight from her eyes to the top of the goalpost forms a right angle with the ground. This right angle creates two similar triangles, one between her eyes, the ground, and the top of the goalpost, and the other one between the mirror on the ground, the goalpost, and a point on the ground that is the same distance from the mirror as the top of the goalpost is from Violet's eyes.

Since similar triangles have the same angle measures, we can set up the following proportion:

(distance from mirror to point on the ground) / (distance from mirror to top of goalpost) = (distance from Violet's eyes to ground) / (height of goalpost)

We can now use the information provided in the problem to solve for the height of the goalpost.

(6.65+4.25)/x = 1.75 / H

x = (6.65+4.25) * (1.75/H)

Where x is the distance from mirror to top of the goalpost.

Substitute the known values and solve for H

H = 1.75*(6.65+4.25) / x = 1.75*10.9 / x

We know that x = 4.25, so

H = 1.75*10.9 / 4.25 = 4.093 m

The height of the football goalp

Step-by-step explanation:

The value of x would be 32.

What are a congruent quadrilaterals?

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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By analyzing the figure, The value of x would be 32.

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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The factors of (x^3 +  y^3) are ( x +  y )(x^2 - x . y +  y^2).

In order to find the factors of  (x^3 +  y^3), you need to apply the sum of cubes formula:

(x^3 +  y^3) = ( x +  y )(x^2 - x . y +  y^2)

(x^3 +  y^3) = ( x +  y )(x^2 - x y +  y^2)

Therefore, in order to find the factor of the given expression, you just simply need to learn the sum of cubes formula.

Similarly, the difference of cubes formula is as follows:

(x^3 -  y^3) = ( x -  y )(x^2 + x y +  y^2)

Which gives factors of (x^3 -  y^3).

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Equation = P(1+r)^x, where P is the initial amount invested, r is the fixed interest rate, and x is the number of years.

It is important to note that the equation provided is the formula for compound interest. P is the initial principal, r is the annual interest rate, and x is the number of years the money is invested. The equation gives the total amount of money in the account after x years.

It should be also noted that the interest rate is given as a decimal and not a percentage.

For example, if the interest rate is 5%, then r = 0.05.

In order to use this equation, the value of P, r and x should be known

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The required value of x is 17 for the given equation 11 = x - 6.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

11 = x - 6

We can determine the value of x by adding 6 to both sides of the equation.

As per the question, we have

⇒ 11 = x - 6

⇒ 11 + 6 = x - 6 + 6

⇒ x = 11 + 6

Apply the addition operation, and we get

⇒ x = 17

Therefore, the required value of x is 17.

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The correct solutions for "x" after factorizing the cubic equation are:

x1 = -4

x2 = 0.5

x3 = 3

Cubic Equation:

A cubic polynomial in mathematics is a polynomial whose highest degree is three. A cubic equation is one that contains a cubic polynomial.

Either one real root or three real roots are present in every cubic equation. The cubic equation is written as ax^3+bx^2+cx+d=0.

Therefore, standard form of the cubic equation is: ax^3 + bx^2 + cx + d = 0

Given: 2x³ +x² -25x +12

On comparing with the standard form of the cubic equation, we get;

a=2

b=1

c=-25

d=12

After factorizing the cubic equation, we have three roots.

x1 = -4

x2 = 0.5

x3 = 3

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Answer:

when x=10 & y=6

10-6=4 so,

x=8

y=4

a) A simulation of the probability that a family with 4 children will have 2 boys and 2 girls can be done using coins. We can represent boys as heads (H) and girls as tails (T).

To simulate the birth of one child, we will flip a coin. If it comes up heads, it represents the birth of a boy, and if it comes up tails, it represents the birth of a girl. We will repeat this process four times to simulate the birth of four children.

We can use the simulation to estimate the probability of the family having 2 boys and 2 girls. We can do this by performing the simulation multiple times (e.g. 100, 1000 or more) and counting the number of times that the family has 2 boys and 2 girls.

The probability can be calculated by dividing the number of successful outcomes (2 boys and 2 girls) by the total number of simulations.

b) A simulation of the probability that a basketball player will hit at least 75% of his shots within the groups can be done using coins. We can represent hitting a shot as heads (H) and missing a shot as tails (T). To simulate one shot, we will flip a coin. If it comes up heads, it represents hitting the shot, and if it comes up tails, it represents missing the shot. We will repeat this process four times to simulate the shooting of four shots.

To determine the probability of hitting at least 75% of the shots, we will perform the simulation multiple times (e.g. 100, 1000 or more) and count the number of times that the player hits at least 3 out of 4 shots.

The probability can be calculated by dividing the number of successful outcomes (3 or 4 shots hit) by the total number of simulations

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Answer:

13/15

For this question, you could type it into the calculator.

Hence, this question is too trivial, and your question might get deleted as a result. Since this is your first question, I will help you out but subsequently, do use a calculator to solve this kind of questions.

Step-by-step explanation:

4 1/3 can be converted to 13/3 as an improper fraction.

Next, evaluate 13/3 divided by 5

(13/3) / 5 = (13/3) x (1/5)

               = 13/15

Answer:

Step-by-step explanation:

There are a number of ways to do this.  I am going to take a little longer, but I am hoping that it will make sense to you.

4[tex]\frac{1}{3}[/tex] ÷ 5  

Another name for 1 is [tex]\frac{3}{3}[/tex]  I am going to rewrite 4[tex]\frac{1}{3}[/tex] knowing this.

[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{13}{3}[/tex]

Another way to write 5 is [tex]\frac{5}{1}[/tex].

I want both of my fraction to have the same denominator so I will multiple

[tex]\frac{5}{1}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{15}{3}[/tex]  I am now ready to divide by fractions

[tex]\frac{13}{3}[/tex] ÷ [tex]\frac{15}{3}[/tex]  Divide across

[tex]\frac{\frac{13}{15} }{\frac{3}{3} }[/tex] = [tex]\frac{\frac{13}{15} }{1}[/tex] = [tex]\frac{13}{15}[/tex]

A table of equivalent ratios for the number of treasure chests and hours that Hannah recovered is as follows:

Treasure chests      Hours

8                                  4

12                                 6

10                                 5

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 4/8

Constant of proportionality (k) = 0.5.

When hours y = 6, the number of treasure chests x is given by:

x = y/k

x = 6/0.5

x = 12.

When treasure chests x = 10, the number of hours y is given by:

y = kx

y = 0.5(10)

y = 5.

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Complete Question:

Hanna is recovering hundreds of treasure chests from an ancient shipwreck. She is able to recover 8 chests every 4 hours.

Complete the table using equivalent ratios. Select all the answers that will fill the table.

Answer:

The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.

Step-by-step explanation:

In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.

Answer:

independent variable = m

dependent variable = p

Step-by-step explanation:

The number of people they are able to serve depends on the number of meals they prepare.

when the input r, is 4, then the output g, is 13.

The function g = 25 - 3r gives the output g when the input r is given.

If we substitute r = 4 into the equation, we get:
g = 25 - 3×4
g = 25 - 12
g = 13

Therefore, when the input, r is 4, the output g, is 13.


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The approximate arc length rounded to the nearest hundredth, between each spoke is 54.9 mm.

Diameter = 559 mm, r = d/2 = 279.5 mm

Number of spokes = 32

π = 3.14

To solve this question, we have to use the formula of the length of an arc which is given as

L = θ/360 × 2πr

To calculate the angle between each spoke, let's divide 360 by 32

θ = 360/32

θ = 11.25°

Now we have the value of the angle, substitute it and solve for the length of the arc.

[tex]L_{arc}[/tex] = θ/360 × 2πr

= 11.25/360 × 2 × 3.14 × 279.5

= 54. 9 mm

Therefore the length of the arc is approximately 54.9 mm.

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 The value of h'(2) = 50.

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. In other word, it is a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

here we are given a function h(x)

here h(x) = - 5f(g(x)) ------(i)

and we are given the value of

g(2) =3   ;   f(2) = 1     ;     g'(2) = -2

f(3) = 4   ;    f'(3) = 5    ;    f'(2) = 6.

and we need to find the value of h'(2).

here f(x), g(x) and h(x) are the function of x and f'(x), g'(x) and h'(x) denotes the derivative of f(x), g(x) and h(x) respectively.

so we are given ,

h(x) = - 5f(g(x))

differentiating with respect to x both side

h'(x) = -5 f'(g(x).g'(x).

at x =2,

h'(2) = [tex]-5*f'(g(2))*g'(2)[/tex]

and we know  g(2) = 3 and g'(2) = -2.

so,

h'(2) = [tex]-5*f'(3)*-2[/tex]

h'(2) = [tex]-5*5*-2\\[/tex]       ( as f'(3) = 5 )

h'(2) = 50

so Option C is correct, the value of h'(2) = 50.

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The value of e (exponential) is approximately equal to 2.718281 which is rounded to 6 digits. The exponential constant frequently happens in mathematics every time the exponential functions are involved.

Log mention to a logarithm to the base 10. Ln mentions a logarithm to the base e. This is also known as a common logarithm. This is also known as a natural logarithm.

The first common log is represented as log 10 (x) The second natural log is represented as log e (x) The exponent form of the common logarithm is 10 x =y.

An exponential function is a function in which a number or data is raised to the power of another number or a variable.

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Answer:

  9 cm

Step-by-step explanation:

You want the radius of the sphere that has a surface area of 324π cm².

The area of a sphere is given by the formula ...

  A = 4πr²

Filling in the given values, we can solve for r:

  324π = 4πr²

  81 = r² . . . . . . . . . divide by 4π

  9 = r . . . . . . . . . . . take the square root

The radius of the sphere is 9 cm.

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Answer:

See picture below

Step-by-step explanation:

By counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.

A high number of a certain number is estimated to be the closest whole number or significant number.

When estimating, the use of decimal points aids in separating the fractional portion from the entire figure.

For instance, we have a total of three integers after the decimal point if we want to calculate the product of 4.23 and 2.1.

     4.23

×         2.1

  4  2  3

________

8  4  6    

8  8  8  3  

Therefore, we shall move the decimal point three places, working our way from the back to the front.

The result of 4.23 and 2.1 is 8.883 then.

We can therefore say that we completely understand how estimating helps you accurately set the decimal point in a product.

Therefore, by counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.

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Correct question:

How does estimation help you place the decimal Point in a product correctly?

There are 90 ways to arrange 6 beads of distinct colors in a 2*3 grid if reflections and rotations are considered the same.

In order to reach this result, we may use Burnside's Lemma, which states that the average number of arrangements of a symmetric object's symmetric parts, is taken throughout the set of all possible symmetry operations of the object.

You may fix one element and position the rest around it because of the rotation. You now have a total of 90 configurations available.

Thus, If reflections and rotations are treated equally, there are 90 ways to arrange 6 beads of different colors on a 2*3 grid.

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The ladder touches the building at 4.53 meters right angle triangle vertical distance from the ground.

The triangle that has one 90 degrees angle is called right-angled triangle. The Pythagorean theorem is applicable for right-angled triangle.

What is the height of the point where the ladder touches the building A ladder leans up against a building at an angle of 65 degrees with the ground. the length of ladder = 5 meters

we understand that the ladder, building and ground together formed a right-angled triangle. The right angle is in between the building and ground. The length of ladder acts as a hypotenuse of this triangle. If we consider the angle 65 degrees,

then sin 65° = opposite side length / hypotenuse here, opposite side length = the required length we need to determine sin 65° × hypotenuse = opposite side opposite side = 0.9063 × 5 =4.53 meters

the ladder touches the build at 4.53 meters vertical distance from the ground.

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The total cost for your fun day out is $23.82.

In mathematics →

Given is that you decided to go snowboarding for the day and you have to figure out your budget. Tickets are $75.00 per day and there is a 5% convenience charge when you order your ticket. You also have to pay for a bus ticket that is $12 for the day. You mom gives you a 15% off coupon that applies to the lift ticket only.

Assume that the total cost for your fun day out is ${x}. Then, we can write the equation as -

{x} = 15% of (75 + {5% of 75}) + 12

{x} = 15% of (75 + {5/100 x 75}) + 12

{x} = 15% of (75 + {1/20 x 75}) + 12

{x} = (15/100) x (75 + 75/20) + 12

{x} = (3/20 x 78.75) + 12

{x} = 11.82 + 12

{x} = 23.82

Therefore, the total cost for your fun day out is $23.82.

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Answer:

5

Step-by-step explanation:

0-6x will be -6x if we divide that six then we will get -30/-6 since minus gets cancelled we will be left with 5

Answer:

d ≈ 7.07 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )

d = [tex]\sqrt{((1-(-6))^2+(7-8)^2}[/tex]

  = [tex]\sqrt{(1+6)^2+(-1)^2}[/tex]

  = [tex]\sqrt{7^2+1}[/tex]

  = [tex]\sqrt{49+1}[/tex]

  = [tex]\sqrt{50}[/tex]

  ≈ 7.07 units ( to 2 decimal places )

The range and the IQR of the weights are 3.3 pounds and 0.95 pounds respectivly.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.

The term "standard deviation" (or "[tex]\sigma[/tex]") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

a) the range is the difference between the highest and lowest value:

range =7.5-4.15 =3.3 pounds

the IQR is the difference between the third and first quartile

IQR= Q₃ -Q₁ =6.55 - 5.6 = 0.95 Pounds

b) Skewed because the mean and median are not the same value.

c) All values will be multiplied by 16

Mean: 96 ounce

Standard deviation: 10.4 ounce

Quartiles: 89.6 ounce and 104.8 ounce

Median:99.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

d) The mean,quartiles and median increase by 30,the result remain unchanged:

Mean: 126 ounce

Standard deviation: 10.4 ounce

Quartiles: 119.6 ounce and 134.8 ounce

Median:129.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

e)  The median, quartiles and IQR might not changed,because they are unaffected by an outlier.

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