Identify the fractions labeled with the letters a and b on the scale below

The choice in the solution set of the equation 4x = 30 is x = 7.5

The equation is given as:

4x = 30

Divide both sides of the equation by 4

4x/4 = 30/4

Evaluate the quotients

x = 7.5

Hence, the choice in the solution set of the equation 4x = 30 is x = 7.5

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The best intervals would be 41-45, 46-50, 51-55, 56-60, 61-65, and 69-70.

The best way to decide the appropriate interval would be to find the range of the numbers.

We have given a data set,

The minimum is the smallest value in the data set. The maximum is the largest value in the data set.

This would be 69-42=27.

If you need six intervals you would need to round 27 up to 30 to be able to divide it out evenly and include all of the data.

The best intervals would be 41-45, 46-50, 51-55, 56-60, 61-65, and 69-70.

This way you are one over and one under the highest and lowest values.

Therefore, The best intervals would be 41-45, 46-50, 51-55, 56-60, 61-65, and 69-70.

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Answer:

Hi,

Step-by-step explanation:

a)

[tex]if\ \dfrac{x}{2}-3\ > \ 0\ then\ |\dfrac{x}{2}-3|=\dfrac{x}{2}-3\\\\\dfrac{x}{2}-3 > 4\\\\\dfrac{x}{2} > 7\\\\x > 14\\[/tex]

b)

[tex]if\ \dfrac{x}{2}-3\ < \0 \ then\ |\dfrac{x}{2}-3|=-(\dfrac{x}{2}-3)=-\dfrac{x}{2}+3\\\\-\dfrac{x}{2}+3\ > \ 4\\\\-\dfrac{x}{2}\ > \ 4-3\\\\-\dfrac{x}{2}\ > \ 1\\\\\dfrac{x}{2}\ < \ -1\\\\x\ < \ -2\\[/tex]

[tex]S=\{x\in\mathbb{R}\ :\ |\dfrac{x}{2}-3|\ > \ 4\}=(-\infty,-2[\ \cup\ ]14,\infty)\\[/tex]

Trigonometric Formula's:

[tex]\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}[/tex]

[tex]\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }[/tex]

Given to verify the following:

[tex]\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a[/tex]

[tex]\texttt{\underline{rewrite the equation}:}[/tex]

[tex]\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )[/tex]

[tex]\texttt{\underline{apply distributive method}:}[/tex]

[tex]\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)[/tex]

[tex]\texttt{\underline{simplify the following}:}[/tex]

[tex]\rightarrow \sf 2cos^2 a + sin^2 a[/tex]

[tex]\texttt{\underline{rewrite the equation}:}[/tex]

[tex]\rightarrow \sf 2(1 - sin^2a ) + sin^2 a[/tex]

[tex]\texttt{\underline{distribute inside the parenthesis}:}[/tex]

[tex]\rightarrow \sf 2 - 2sin^2a + sin^2 a[/tex]

[tex]\texttt{\underline{simplify the following}} :[/tex]

[tex]\rightarrow \sf 2 - sin^2a[/tex]

Hence, verified the trigonometric identity.

Answer:

See below ~

Step-by-step explanation:

Identities used :

⇒ cos²a = 1 - sin²a

⇒ tan²a = sin²a / cos²a

============================================================

Solving :

⇒ (cos²a) (2 + tan² a)

⇒ 2cos²a + (cos²a)(tan²a)

⇒ 2(1 - sin²a) + sin²a

⇒ 2 - 2sin²a + sin²a

⇒ 2 - sin²a [∴ Proved √]

Answer:

Step-by-step explanation

Sorry but your answer is a fake question which I can't answer

Based on the number of children and tricycle wheels, the ratio of children to tricycle wheels is 10 : 18

Total wheels of tricycle = Number of tricycles × Number of wheels per tricycle

= 6 × 3

= 18 wheels

Ratio of children to tricycle wheels = 10 : 18

= 5 : 9

Therefore, the ratio of children to tricycle wheels is 10 : 18

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's find the volume of the given figure ~

[tex]\qquad \sf  \dashrightarrow \:Volume_{(cuboid)}= length \cdot width \cdot height [/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(cuboid)}= 4 \cdot x \cdot x [/tex]

[tex]\qquad \sf  \dashrightarrow \:Volume_{(cuboid)}= 4 {x}^{2} [/tex]

So, the correct choice is ~ C

Volume

Option C

Based on the cost of the contract and the probability to win it, the total expected value of the contract proposal is -$2500.

The general formula to calculate the expected value is:

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The types of rotation are:

In this case:

 ⇒ it is reflection since the graph is inverted and each point is the same distance from the line of reflection

Answer: reflection

Hope that helps!

The dot product of the two matrices D and n is determine as (4, - 7).

The dot product of the two matrices is calculated as follows;

n = (-2, -1), and D = [-4   2]

                               [4    3]

D.n =  (-2, -1). [-4   2]  = (-2 x -4) + (-1 x 4) = 4

                     [4    3]  = (-2 x 2) + (-1 x 3) = -7

D.n = (4, - 7)

Thus, the dot product of the two matrices D and n is determine as (4, - 7).

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Answer:

.............30000.............

Here we must write and solve a linear equation to find the number of miles that Arun traveled in the taxi. We will find that Eva traveled 11 miles.

So we know that the taxi charges a fee of $4.10 and then a plus of $0.50 per mile.

So if you travel for m miles, the cost equation is:

C(m) = $4.10 + $0.50*m

Now, we know that for Eva the total fare (total cost) was $9.60, then we need to solve:

$9.60 = C(m) = $4.10 + $0.50*m

$9.60 = $4.10 + $0.50*m

$9.60 - $4.10 = $0.50*m

$5.50 = $0.50*m

$5.50/$0.50 = m = 11

This means that Arun traveled 11 miles in the taxi.

The Eva traveled 25 miles in the taxi.

It is required to find how many miles was the taxi ride.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

The taxi company charged a pick-up fee of $4 plus $4.25 per mile.

The total fare was $110.25.

The cost equation is:

C(m) = $4 + $4.25*m

Now, we know that for Eva the total fare (total cost) was $110.25, then we need to solve:

$110.25 = C(m) = $4 + $4.25*m

$110.25-$4=$4.25*m

$106.25=$4.25*m

m =25

Therefore, the Eva traveled 25 miles in the taxi.

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The figure has a rotational symmetry and the number of lines of symmetry is 3

The given figure is an equilateral triangle.

An equilateral triangle has 3 equal sides and 3 equal angles.

This means that it has a rotational symmetry and the number of lines of symmetry is 3.

The angle of rotational symmetry is calculated as:

Angle = 180/3

Evaluate

Angle = 60

Hence, the angle of rotational symmetry is 60

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Answer: A

Step-by-step explanation:

Since the triangles are congruent by HL, we know that there is a sequence of rigid motions.

By inspection, we know this sequence involves rotating triangle A 90 degrees clockwise and then translating it right.

Answer: Remeber 2+2=5 and

Step-by-step explanation: if yur on fire stop drop and roll do it and your awesome. Another thing is if someones taking forever drinking water when your behind them sing 123 can you hurry up please 456 imma hit you with a brick 789 imma spit this sick ryme

Using the least common multiple, it is found that you need to buy 3 packs of hot dogs and 2 packs of buns to have the exact same number of each.

First, we need to find the total number of each element, finding the least common multiple of the sizes of each package, that is, 8 and 12.

The lcm is found factoring them by prime factors, hence:

8 - 12|2

4 - 6|2

2 - 3|2

1 - 3|3

1 - 1

Hence, lcm(8,12) = 2³ x 3 = 24.

Then:

Which means that you need to buy 3 packs of hot dogs and 2 packs of buns to have the exact same number of each.

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Answer:

3km

Step-by-step explanation:

d = 2r so r = 1/2 * d = 1/2 * 6 = 3km

The volume of the triangular base prism is 120 centimetre cube.

volume of a triangular prism = BH

where

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 4 × 6 = 24 / 2 = 12 cm

Hence,

volume of a triangular prism = 12 × 10

volume of a triangular prism = 120cm²

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Answer:

  80 in²

Step-by-step explanation:

When side length and apothem of a regular polygon are given, the applicable area formula is ...

  A = 1/2Pa

where P is the perimeter of the polygon, and 'a' is its apothem.

__

The perimeter of a regular 8-sided polygon will be 8 times the side length, so the area is ...

  A = 1/2(8×4 in)(5 in) = 80 in²

The true statement about the equations include:

The equation given is h(t) = t² - 14t + 40. We'll factorize to get the value of t. This will be:

= t² - 14t + 40

= t² - 10t - 4t + 40

= t(t - 10) - 4(t - 10)

(t - 10) = 0.

t = 0 + 10

t = 10

In this case, the swimmer dives to a depth of 14 feet and then comes back up 10 seconds after the timer was started.

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Answer:

The swimmer comes back up 10 seconds after the timer was started.

The swimmer dives into the water 4 seconds after the timer was started.

Step-by-step explanation:

The guy above me ruined my test score, thanks.
Best of luck to all who find this
These are the correct answers

The probability of a chance event is a number between 0 and 1 that expresses the likelihood that an event would occur.

As a general rule in probability, we have:

The above represents the range of a valid probability (both inclusive).

This also represents the likelihood that an event would occur

Hence, the words that complete the blank are likelihood and would.

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Answer:

  133 miles

Step-by-step explanation:

The limited budget gives rise to an inequality that can be solved for the maximum number of miles.

__

The rental cost for m miles will be the sum of the fixed charges and the product of the mileage charge and the number of miles.

  cost = 19.95 +0.15m

We want this to be no greater than 40, so we have the inequality ...

  40 ≥ 19.95 +0.15m

This two-step inequality can be solved in the usual way:

  20.05 ≥ 0.15m . . . . . step 1, subtract 19.95 from both sides

  133.667 ≥ m . . . . . . . step 2, divide by the coefficient of the variable

The maximum whole number of miles Gabrielle can drive is 133.

A point that is exterior to an angle is found on the acute side of the angle which is true.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

We know that the sum of the exterior angle and interior angle is equal to 180 degrees.

"If one of the exterior angles is an acute angle, then the corresponding interior angle is an obtuse angle."

A point that is exterior to an angle is found on the acute side of the angle which is true.

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Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to factor out the GCF in the expression

[tex]\star~\star\mathrm{6x^3+3x}~\star~\star[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So let's divide.

But first. we should work out the GCF.

Both terms have 3x in common, so we divide both terms by 3x:

[tex]\mathrm{6x^3+3x}[/tex]

[tex]\mathrm{3x(2x^2+1)}[/tex]

To ensure that we've factored correctly, we can always use the distributive property, distribute 3x and see whether or not we end up with [tex]\mathtt{6x^3+3x}[/tex].

So the answer is

[tex]\mathrm{3x(2x^2+1)}[/tex]

Notice I put parentheses around 2x²+1. This indicates that 3x is multiplied times both 2x² and 1.

Hope it helps you out! :D

Ask in comments if any queries arise.

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Answer:

36+ Miles

Step-by-step explanation:

One in being 18 miles, and two cities that are inches apart. So 2 or more inches. Would make it anywhere from 36 or more miles.

Answer:

6.25cm²

Step-by-step explanation:

Hello!

The formula for the area of a triangle is [tex]A = \frac12 b*h[/tex]

The area of the triangle is 6.25 cm²

Using the discriminant of a quadratic equation, if the graph is translated shifted up 4 units, the graph will have no x-intercepts.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The discriminant is:

[tex]\Delta = b^2 - 4ac[/tex]

The solutions are as follows:

In this problem, the function is given by:

f(x) = (x + 5)² - 3.

In standard form:

f(x) = x² + 10x + 22.

We want to find coefficient k for which the function has [tex]\Delta < 0[/tex], then:

f(x) = x² + 10x + 22 + k.

The coefficients are a = 1, b = 10, c = 22 + k, hence:

[tex]\Delta < 0[/tex]

10² - 4(22 + k) < 0

100 - 88 - 4k < 0

4k > 12

k > 3.

Hence, with k = 4, the function is shifted up 4 units, and the graph will have no x-intercepts.

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The percent change if a city that used to produce 2050 kilowatt hours has reduced their consumption to 1125 kilowatt hours is 45.122% decrease.

Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.

we know,

% change = (final- initial) / initial * 100

=(1125-2050)/1125 *100

=45.122%

Hence, percentage change be 45.122% decrease.

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Answer:

405

Step-by-step explanation:

It tells in the table.