A student is solving the equation 3(x−12)=9x . Which describes a first step the student could use to solve the equation correctly? Responses The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 36 = 9 x . The student can distribute 3 on the left side of the equation, resulting in 3x−12=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 12 = 9 x . The student can divide both sides of the equation by 3 , resulting in x−12=6x . The student can divide both sides of the equation by 3 , resulting in x − − 12 = 6 x . The student can divide both sides of the equation by 3 , resulting in x−4=3x .

Based on both the median and mean values, it appears that Bus 14 typically has a faster travel time compared to Bus 18.

What is the median and mean?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.

Here,

Cοmparing the medians, we can see that Bus 14 has a higher median οf 14, while Bus 18 has a lower median οf 12. This suggests that Bus 14 may have a faster travel time οn average.

Hοwever, we alsο need tο cοnsider the means. Cοmparing the means, we can see that Bus 14 has a higher mean οf 14, while Bus 18 has a lower mean οf 12. This further supports the idea that Bus 14 may have a faster travel time οn average.

Hence, based on both the median and mean values, it appears that Bus 14 typically has a faster travel time compared to Bus 18.

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Answer:

The peak of the cylinder is about 9 yards.

Explanation:

From the above question,

They have given:

     A cylinder with a diameter of 8 yards has a volume of 452.16 yd³.

Here we need to find what is the height of the cylinder

Here,

       [tex]\pi = 3.14[/tex]. 44 yards 11 yards 8 yards 3 yards

To locate the radius of the cylinder, which is half of of the diameter.

        [tex]\text{radius = 8 yards} \div \text{2}[/tex]

        [tex]\text{radius} = 4 \ \text{yards}[/tex]

Then we can use the formulation for the quantity of a cylinder to locate the height:

       [tex]\text{volume} = \pi \times \text{radius} \times \text{height}[/tex]

       [tex]452.16 = 3.14 \times 4^2 \times\text{height}[/tex]

       [tex]452.16 = 50.24 \times \text{height}[/tex]

       [tex]\text{height} = 452.16 \div 50.24[/tex]

       [tex]\text{height} = 9 \ \text{yards}[/tex]

Therefore, the peak of the cylinder is about 9 yards.

Answer: 9 yards

The first person to answer was correct.

Step-by-step explanation:

I took the quiz so you don't have to! <3

1 yard = 3 feet

6 yards = 18 feet

Truck = 20 feet

Difference = 2 feet = 24 inches

England receives a total weighted score of [tex]1.9[/tex] , while Canada receives a score of [tex]1.6[/tex].

Instead of hiring an own accountant, a small business may choose to contract bookkeeping responsibilities to an accounting company in to cut expenses. Some companies find it advantageous to outsource HR department duties including payroll and medical coverage.

Outsourcing has several benefits, including better systems and service quality, access to the world's best workers, improved scheduling, avoiding personnel concerns, and many more.

a) Using the factor-rating method, we can calculate the total weighted score for each country as follows:

For England:

Total score [tex]= (2 * 0.1) + (3 * 0.6) + (1 * 0.2) + (1 * 0.1) = 1.9[/tex]

For Canada:

Total score [tex]= (3 * 0.1) + (1 * 0.6) + (3 * 0.2) + (2 * 0.1) = 1.6[/tex]

Therefore, based on the risk-avoidance criteria and weightings established by the executives, we would select Canada as the better choice.

b) If we double each of the weights used in part (a), the total weighted score for each country changes as follows:

For England:

Total score [tex]= (2 * 0.2) + (3 * 1.2) + (1 * 0.4) + (1 * 0.2) = 4.0[/tex]

For Canada:

Total score [tex]= (3 * 0.2) + (1 * 1.2) + (3 * 0.4) + (2 * 0.2) = 2.2[/tex]

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this is answer 44rrrrrrrrrrrrrrrrrrrrfrrrrrrrrrrr

Answer:

7/8, 1/5, 1/3, 5/9, 11/12, 2/5, 3/5, 3/20, 9/25, 3/7, 3/8, 4/9, 8/15, 4/5, 5/7, 1/8, 7/12, 21/25, 1/6, 3/14, 1/4, 8/27, 3/4, 2/3, 5/6, 2/15, 27/40, 9/10, 5/12

the secret message spells "YES"

Step-by-step explanation:

you cant divide any of the numbers above by the same number and not get a decimal.

Answer: The word is yes

Step-by-step explanation:

Shade in 7/8, 1/5, 2/5, 3/7, 8/15, 3/14, 3/4, 5/9, 3/8, 4/5, 1/4, 2/3, 1/3, 3/5, 5/7, 1/8, 5/6, 2/15, 11/12, 3/20, 9/25, 4/9, 7/12, 21/25, 1/6, 8/27, 9/10, 27/40, and 5/12.

The area of the shaded region is evaluated to be equal to the expression 24z² - 22z + 3

To get the area of the shaded region, we subtract the area of the small square from the area of the bigger square as follows:

area of bigger square = (5z - 2)(5z - 2)

area of bigger square = 25z² - 20z + 4

area of small square = (z + 1)(z + 1)

area of bigger square = z² + 2z + 1

area of the shaded region = 25z² - 20z + 4 - (z² + 2z + 1)

area of the shaded region = 25z² - 20z + 4 - z² - 2z - 1

area of the shaded region = 24z² - 22z + 3

Therefore, the area of the shaded region is evaluated to be equal to the expression 24z² - 22z + 3

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The cumulative relative frequency for flossing 3 times per week is 58.57%.

a. Let's complete the table.

We can calculate the missing relative frequency for 0 times flossing per week by dividing the frequency (4) by the total number of people (70).

Relative Frequency for 0 times flossing = 4/70 = 0.0571 (rounded to 4 decimal places)

For 6 times flossing per week, the frequency is missing.

We can calculate it by summing up the frequencies for all other days and subtracting that from the total number of people.

Missing frequency for 6 times flossing = 70 - (4 + 11 + 15 + 11 + 6 + 7 + 6) = 70 - 60 = 10

Now, let's calculate the cumulative frequency for 5 times flossing per week.

Cumulative Frequency for 5 times flossing = Cumulative Frequency for 4 times flossing + Frequency for 5 times flossing = 47 + 7 = 54

The completed table looks like this:

of times floss per week | Frequency | Relative Frequency | Cumulative Frequency

0 | 4 | 0.0571 | 4

1 | 11 | 0.1571 | 15

2 | 15 | 0.2143 | 30

3 | 11 | 0.1571 | 41

4 | 6 | 0.0857 | 47

5 | 7 | 0.1 | 54

6 | 10 | 0.1429 | 64

7 | 6 | 0.0857 | 70

b. The cumulative relative frequency for flossing 3 times per week is the cumulative frequency for 3 times flossing divided by the total number of people (70).

Cumulative Relative Frequency for 3 times flossing = Cumulative Frequency for 3 times flossing / Total number of people = 41 / 70 = 0.5857 (rounded to 4 decimal places)

The cumulative relative frequency for flossing 3 times per week is 58.57%.

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The factors of [tex]16x^2yz[/tex]  are [tex]4xyz, xz, and 12.[/tex]yz, xz, and 12.

The factors of the given expression 16x^2yz are:

[tex]4xyz:[/tex]This is a valid factor of  [tex]16x^2yz[/tex] because it contains all the variables x, y, and z, and the exponent of x is 1, the exponent of y is 1, and the exponent of z is 1. Additionally, it contains a numerical factor of 4.

[tex]2xy:[/tex]This is not a factor of 16x^2yz because it does not include the variable z, which is present in the given expression.

[tex]xz:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it does not include the variable y, which is present in the given expression.

[tex]12:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it is a numerical factor and does not contain any of the variables x, y, or z.

[tex]xyz:[/tex] This is not a factor of [tex]16x^2yz[/tex] because it does not contain any numerical factor. It only includes the variables x, y, and z without any exponents.

Therefore, the factors of [tex]16x^2yz[/tex]  are [tex]4xyz, xz, and 12.[/tex]

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Answer: 2 hours 40 minutes

Step-by-step explanation: 2/3 x 4 = 8/3 simplified to 2 2/3

2 hours and 2/3 of an hour = 2 hours 40 minutes

Answer:

C

Step-by-step explanation:

It can't be A since you can't have a negative inside a square root

It can't be B [tex]-\sqrt{x+2}[/tex] since it would always be negative and the graph starts positive then turns negative at x=4

C makes since since the graph looks sort of like an upside down [tex]\sqrt{x}[/tex] and has an intercept at y=2

It can't be D since after x=2 the inside of the square root would become negative and you can't have a negative inside of a square root

Answer:

Yes

Step-by-step explanation:

Angle RDE =angle TVA=28°

REV=TAV=42°

DRE=VTA=110°

THEREFORE TRIANGLE DER IS SIMILAR TO TRIANGLE ATV

Answer:

Y value is -128

Step-by-step explanation:

To find the y-value when x = -12, sub -12 for x in the equation.

y = -200 - 6(x)

y = -200 - 6(-12)

y = -200 + 72

y= -128

Answer:

Using the Pythagorean theorem, we know that in a right-angle triangle, we have:

a^2 + b^2 = c^2

where c is the hypotenuse.

From the given information, we have:

ab = 11 - x

a = x

b = 11

c = 11 (given)

We can use the given values to eliminate a or b from the Pythagorean theorem:

a^2 + (11 - x)^2 = 11^2

Expanding and simplifying, we get:

a^2 + 121 - 22x + x^2 = 121

a^2 + x^2 - 22x = 0

Substituting a = x into the above equation, we get:

x^2 + x^2 - 22x = 0

2x^2 - 22x = 0

2x(x - 11) = 0

So, either x = 0 or x - 11 = 0.

Since x cannot be zero (as it represents a length), we have x - 11 = 0.

Therefore, x = 11.

Hence, the value of x in its simplest form with a rational denominator is 11/1 or just 11.

Answer:

[tex]x=11\sqrt{2}[/tex]

Step-by-step explanation:

The given right triangle is an isosceles right triangle since its legs are equal in length (denoted by the tick marks).

Side x is the hypotenuse of the isosceles right triangle.

Given both legs are 11 units in length, we can use Pythagoras Theorem to calculate the length of the hypotenuse.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

As a and b are the legs, and c is the hypotenuse, substitute the following values into the formula and solve for x:

Therefore:

[tex]\implies 11^2+11^2=x^2[/tex]

[tex]\implies 121+121=x^2[/tex]

[tex]\implies 242=x^2[/tex]

[tex]\implies x^2=242[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{242}[/tex]

[tex]\implies x=\sqrt{242}[/tex]

To simplify the radical, rewrite it as a product of prime numbers:

[tex]\implies x=\sqrt{11^2 \cdot 2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

[tex]\implies x=\sqrt{11^2}{\sqrt{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies x=11\sqrt{2}[/tex]

Therefore, the length of side x in simplest radical form is 11√2.

Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.

The answer to this problem: 2

The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

We can start by using the trigonometric identities:

cos(-θ) = cos(θ)

tan(-θ) = -tan(θ)

csc(θ) = 1/sin(θ)

Substituting these identities into the original expression, we get:

cos(θ) * (-tan(θ)) * (1/sin(θ))

Simplifying this expression, we can cancel out the cos(θ) and the sin(θ) terms:

-1 * cos(θ) * (1/(cos(θ))) The cos(θ) term cancels out and we are left with -1. Therefore, the equivalent expression is -1.

In other words, the original expression simplifies to -1 for all values of θ where it is defined (i.e. θ ≠ (2n + 1)π/2, where n is an integer). This means that as θ varies, the value of the expression will always be -1 when it is defined. Trigonometric identities are mathematical equations that involve trigonometric functions and are true for every possible value of the variables involved. There are various types of trigonometric identities, including:

Pythagorean Identities:

[tex]sin^2a + cos^2a= 1\\tan^2a + 1 = sec^2a\\1 + cot^2a = csc^2a[/tex]

Angle Sum and Difference Identities:

sin(α±β) = sin α cos β ± cos α sin β

cos(α±β) = cos α cos β ∓ sin α sin β

tan(α±β) = (tan α ± tan β) / (1 ∓ tan α tan β)

Double Angle Identities:

sin 2θ = 2 sin θ cos θ

cos 2θ =[tex]cos^2[/tex]θ - [tex]sin^2[/tex]θ = 2 [tex]cos^2[/tex]θ - 1 = 1 - 2[tex]sin^2[/tex]θ

tan 2θ = (2 tan θ) / (1 - [tex]tan^2[/tex]θ)

Half Angle Identities:

sin (θ/2) = ± √[(1 - cos θ) / 2]

cos (θ/2) = ± √[(1 + cos θ) / 2]

tan (θ/2) = ± √[(1 - cos θ) / (1 + cos θ)]

Product-to-Sum Identities:

sin α sin β = (1/2) [cos (α-β) - cos (α+β)]

cos α cos β = (1/2) [cos (α-β) + cos (α+β)]

sin α cos β = (1/2) [sin (α+β) + sin (α-β)]

Sum-to-Product Identities:

sin α + sin β = 2 sin [(α+β)/2] cos [(α-β)/2]

sin α - sin β = 2 cos [(α+β)/2] sin [(α-β)/2]

cos α + cos β = 2 cos [(α+β)/2] cos [(α-β)/2]

cos α - cos β = -2 sin [(α+β)/2] sin [(α-β)/2]

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The two triangles have similar angles, thus the two triangles are similar using the AA criteria.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are identical, two triangles are said to be congruent. These are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.

For the triangle ABC using the sum of interior angles of triangle we have:

A + B + C = 180

65 + 70 + B = 180

135 + B = 180

B = 45

Now, for triangle DEF we have:

F = 45.

E = 180 - 115 = 65

Thus, D = 70

The two triangles have similar angles, thus the two triangles are similar using the AA criteria.

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Answer:

To find the average (also known as the arithmetic mean) of the data values, we need to divide the sum of the values by the number of values. We are given the sum of 12 data values, which is 942. So:

Average = Sum of values / Number of values

Average = 942 / 12

We can simplify this by dividing both the numerator and denominator by their greatest common factor, which is 6:

Average = (942 ÷ 6) / (12 ÷ 6)

Average = 157 / 2

Average = 78.5

Therefore, the average of the 12 data values is 78.5.

Step-by-step explanation:

Actually, the correct identity is: cot(x + y) = (cot x cot y - 1) / (cot x + cot y) This identity can be derived from the sum formulas for tangent and cotangent: tan(x + y) = (tan x + tan y) / (1 - tan x tan y) cot(x + y) = (cot x cot y - 1) / (cot x + cot y) We can start by substituting cot(x + y) with its equivalent expression: cot(x + y) = cot x cot y - 1 / (cot x + cot y) Multiplying both sides by (cot x + cot y), we get: cot(x + y) (cot x + cot y) = cot x cot y - 1 Expanding the left side, we get: cot x cot y + cot x cot

According to the given information, the mean age of 25 people in the cinema is 24, which means the total age of all 25 people is:

25 people * 24 years = 600 years

When the new person arrives, the total age becomes:

26 people * 25 years = 650 years

The difference between the two totals is the age of the new person:

650 years - 600 years = 50 years

Therefore, the age of the new person is 50 years old.

The two cylinders have the exact same volume given by:

V = pi*r²*h

The volume of a cylinder of radius r and height h is given by:

V = pi*r²*h

Where pi = 3.14

While the volume for a slanted cylinder, like the one in the image, is computed in the same way, as long as the height h is measured with a line normal from the bases (like in the image).

Now, notice that the first cylinder has a diameter of 2r and height h, so its radius is 2r/2 = r, and the volume is:

v = 3.14*r²*h

The second cylinder has a radius r and a height h, so its volume is

v = 3.14*r²*h

So yea, both cylinders have the same volume.

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The equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d

Let d be the total length of Alicia's trip in miles. According to the problem, the distance she drove to visit her grandparents is 4/5 of the total distance, so we can write:

260 = (4/5)d

To find the total distance d, we can solve this equation for d. First, we can multiply both sides by 5/4 to isolate d:

260 x 5/4 = (4/5)d x 5/4

325 = d

Therefore, the equation we can use to find d, the total length of Alicia's trip in miles, is: 260 = (4/5)d and the distance is d = 325

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Answer:

  a) congruent

  b) not congruent

  c) congruent

Step-by-step explanation:

You want to know which sets of isosceles triangles are congruent.

An isosceles triangle has two congruent sides and two congruent angles. If those sides and angles match corresponding sides and angles in another isosceles triangle, then the triangles will be congruent.

Unless the triangle is equilateral, the two congruent base angles will have different measures than the angle between the congruent sides. Once any of the angle measures is known, the others are determined—provided that we also know which angle it is that is known.

The congruent side measures are the same, and the apex angle is the same. This triangle pair is congruent.

The base angle of one triangle is the same measure as the apex angle of the other. (Neither is 60°.) These triangles cannot be congruent.

The congruent side measures are the same, and the base angles are the same. This triangle pair is congruent.

Answer:

$1,033.13.

Step-by-step explanation:

To find the selling price of the diamond ring, we need to add the markup amount to the original cost.

Markup amount = 175% of $375.50

= 1.75 x $375.50

= $657.63

Selling price = Original cost + Markup amount

= $375.50 + $657.63

= $1,033.13

Therefore, the selling price of the diamond ring will be $1,033.13.

Answer:

$1031.63

Step-by-step explanation:

Mark-up refers to the amount or percentage added to the cost price of a product to determine its selling price. It represents the increase in price that a business applies to cover its expenses, generate profit, and account for other factors like overhead costs, operating expenses, and desired profit margin.

To calculate the selling price of the diamond ring, we need to add the mark-up amount to the cost price and round the result to the nearest cent.

To find the mark-up amount, multiply the cost price by the mark-up percentage:

[tex]\begin{aligned}\textsf{Mark-up amount}&=\textsf{Cost price} \times \textsf{Mark-up percentage}\\\\&=\$375.50 \times 175\%\\\\&=\$375.50 \times \dfrac{175}{100}\\\\&=\$375.50 \times 1.75\\\\&=\$657.125\end{aligned}[/tex]

Therefore, the ring will be marked-up by $657.125.

To find the selling price, add the mark-up amount to the cost price:

[tex]\begin{aligned}\textsf{Selling price}&=\textsf{Cost price} + \textsf{Mark-up amount}\\\\&=\$375.50 +\$657.125\\\\&=\$375.50 +\$657.125\\\\&=\$1032.625\end{aligned}[/tex]

Finally, round the selling price to the nearest cent:

[tex]\large\boxed{\textsf{Selling Price} = \$1031.63}[/tex]

Therefore, the selling price of the diamond ring will be $1031.63, rounded to the nearest cent.

The z-score of a student who scores 97 is 2.83. In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.

It is used to indicate how many standard deviations a certain value is from the mean. It is calculated by subtracting the mean from the observed value and then dividing the result by the standard deviation.

This is calculated by subtracting the mean (80) from the student’s score (97) and dividing the result by the standard deviation (6).

97- 80/6

= 2.83

The z-score of 2.83 indicates that the student is in the top 1% of performers. This is because the z-score of 2.83 is greater than the z-score of 1.96, which is the z-score that is associated with the 1% percentile.

A z-score of 1.96 means that it is higher than 1% of the scores.

In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.

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The height h, on the other hand, denotes the slant height for oblique cylinders, which is the distance between the two circular bases on a straight line.

Two identical parallel spherical bases and a curving surface connecting the bases make up the three-dimensional geometric object known as a cylinder. It can be compared to a prism with rounded bases.

A line connecting the centres of the circle bases is the axis of a cylinder. The possibility that the axis is straight to the bases determines whether a cylinder is right or oblique.

Diagonal cylinders have bases that aren't perpendicular to the axis while right cylinders have bases that are perpendicular to the axis.

given

Both right and oblique cylinders can be calculated using the surface area of a cylinder formula, A = 2r2 + 2rh.

The height h, on the other hand, denotes the slant height for oblique cylinders, which is the distance between the two circular bases on a straight line.

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