State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Angles 1 and 7 are alternate exterior angles.

Answer:

-170 2/3

Step-by-step explanation:

Divide both sides by 3 to get p by itself

p = -512/3

Simplify

- 170 2/3

Answer:

p=−8

Step-by-step explanation:

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

[tex] \rightarrow \sf \: p {}^{3} =−512[/tex]

Step 1: Take cube root.

[tex] \sf p={(−512) }^{ ( \frac{1}{3} )}[/tex]

[tex] \sf \: p=−8[/tex]

Answer:

in 1 year Allan would save 120 dollars, this is because, 10x12=120

Step-by-step explanation:

to find out what he would save I 2 years just multiply 120 by 2, 120x2=240, and for 3 years multiply 120 by 3, and so on.

Answer:

Final Cost of 3 pounds: 7.25

Final cost of p pounds: 3.50p

Step-by-step explanation:

3.50p - 3.25 = ?

3.50(3) - 3.25 = ?

10.50 - 3.25 = $7.25

Write an expression of the cost to buy at least one pound of chicken.

3.50p

I hope this helps!

The inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is  x < 4

The given parameters are

Flat cost = $58

Rate = $3 per gigabyte

Budget = Under $70

The equation is represented as:

Total cost = Flat cost + Rate * Number of gigabyte

So, we have

y = 58 + 3x

The budget is under 70

So, we have

58 + 3x < 70

Subtract 58 from both sides

So, we have

3x < 12

Divide both sides by 3

So, we have

x < 4

Hence. the inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is  x < 4

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Answer:

Step-by-step explanation:

-24

Answer: The answer to this equation is 53.91

The other root of the given quadratic equation is a = ± 3/√2.

Given that, x=2 and x²+ax+12=0.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

Now, put x=2 in x²+ax+12=0 and find the value of a.

That is, 2²+2a+12=0

⇒4+12+2a=0

⇒16+2a=0

⇒2a=-16

⇒a=-8

So, the value of a is -8.

Put (0, 6) and (4, 6) in the function y=2x²+bx+c and find the value of b and c.

That is, 6=2(0)²+b(0)+c

⇒ c=6

6=2(4)²+b(4)+c

⇒ 6 = 32+4b+c

⇒ -26 = 4b + 6

⇒ 4b = -32

⇒ b = -8

So, the value of b is -8 and the value of c is 6.

Put x=a (root) in the equation 2x + x/a -9 = 0 and find the other root.

That is, 2a²+a/a -9 = 0

⇒ 2a² - 9 = 0

⇒ a²=9/2

⇒ a = ± 3/√2

Therefore, the other root of the given quadratic equation is a = ± 3/√2.

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45% of 315 = 141.75

When you are using a % number convert it into a decimal ( 45% would be 0.45 or 55% would be 0.55 ). After you convert it into a decimal you can multiply it by the number ( Here it would be 315 )

0.45 x 315 = 141.75

Answer:

141.75

Step-by-step explanation:

To do this question, first, we can write 45% as 45/100.

Now, we have to multiply.

45/100x315

=141.75

Hope that helped!

:D

Answer:

Infinite solutions, regardless of the value of n.

Step-by-step explanation:

[tex]5\left(n-2\right)=5n-10\\5\left(n-2\right)\\5n-5\cdot \:2\\5n-10\\5n-10=5n-10\\5n - 10+10=5n-10 + 10\\5n = 5n\\5n-5n=5n-5n\\0=0\\\mathrm{\:for\:n = \infty,-\infty}[/tex]

The wavelength of the waves on a string that is vibrating at 220 MHz is 2.20 m. These waves move at a 4840 rpm rate as they move up and down the string.

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm). According to the available data, the wavelength is more frequently expressed in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (VL), ultraviolet (UV), and gamma radiation ().

V=∧F

V=220×22

V=4840m/s

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Answer:

(b) Draw the image of

ΔDEF

∆DEF

Step-by-step explanation:

The equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]

Given,

m = [tex]\frac{-3}{4}[/tex]

The point = (8,-1)

The point-slope form of the line

[tex](y-y_{1} )=m(x-x_{1})[/tex]

Substitute the values in the equation

[tex](y-(-1))=-\frac{3}{4}(x-8)\\ y+1=-\frac{3}{4}(x-8)[/tex]

Hence, the equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]

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Answer:

3 1/2 ÷ 1 1/4

7/2 ÷ 5/4

7/2 · 4/5

28/10

2.8

Step-by-step explanation:

Answer: 660 miles

Step-by-step explanation:

66 miles * 10 hours/1 hour =

66*10/1=

66*10=660 miles

Using trigonometric functions, the value of 2 cos x is equals to √3.

One of the six mathematical functions used to express the side ratios of right triangles, the trigonometric function includes the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). The graphic shows these six trigonometric functions in respect to a right triangle.

Cos (π/6) = √3/2

So. f(x) = 2 cos x

⇒ f(x) = 2 cos(π/6)

⇒ f(x) = 2 × √3/2

f(x) = √3

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Answer: 81

Step-by-step explanation: The square root and the squared function cancel each other out

Answer$550.32

Step-by-step explanation: 7day = $320

commission = 8% of 2879

=230.32

 total earnings = 320 + 230.32

= 550.32

Answer:

x=−2+2y/5

Step-by-step explanation:

Add 2y to both sides of the equation.5x=−10+2y

Divide each term in 5x=−10+2y by 5 and simplify.

Divide each term in 5x=−10+2y by 55x5=−105+2y5Simplify the left side

. Cancel the common factor of 5

Cancel the common factor.5x5=−105+2y5Divide x by1.x=−105+y5

Simplify the right side.

Divide

−10 by 5

Answer:

x = 85

Step-by-step explanation:

the exterior angles of a polygon sum to 360°

note the exterior angle at P = 180° - 90° = 90°

sum the 4 exterior angles and equate to 360

x + 72 + 113 + 90 = 360

x + 275 = 360 ( subtract 275 from both sides )

x = 85

The eighth term of the given geometric sequence is: 0.00183.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: -30, 7.5, -1.875, ....

Here, [tex]\frac{7.5}{-30}=\frac{-1.875}{7.5}=-0.25[/tex]

That is, the given geometric sequence has a₁ = -30 and r = -0.25

The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, [tex]a_8=(-30)(-0.25)^7[/tex] ≈ 0.00183

Hence, The eighth term of the given geometric sequence is: 0.00183.

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Answer:

14x cannot be simplified any further.

Answer:

No, 14x can not be further simplified.

Step-by-step explanation:

I hope this helps.

The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 467) and (10, 647)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (647 - 467)/(10 - 2)

Evaluate

Rate = 22.5

This means that the rate of change is $22.5

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 22.5

So, we have

y = 22.5(x - x1) + y1

Using one of the points, we have

y = 22.5(x - 6) + 467

Set x = 0

So, we have

y = 22.5(0 - 6) + 467

Evaluate

y = 332

Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

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Answer:

1470 in³, 716 in²

Step-by-step explanation:

The figure is a cylinder, and it's volume can be found using the following formula:

Volume of cylinder

= area of circle base ×height

= πr²h

Identify the value of r and h:

From the diagram, the radius (r) is 6 in. while the height (h) is 13 in.

Using the formula,

volume of cylinder

= π(6²)(13)

= 468π

= 1470 in³ (3 s.f.)

The surface area of a cylinder is the total area of all its faces, i.e. the sum of the area of its two circular bases and its curved surface area.

Formula

Surface area of cylinder

= 2πr² +2πrh

Surface area of cylinder

= 2(π)(6²) +2(π)(6)(13)

= 72π +156π

= 228π

= 716 in² (3 s.f.)

Additional:

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Answer:

one way to name the symbol is our and another way to name the symbol is rco

Only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.

We have a set of mixed numbers.

We have to identify which set of mixed numbers has a difference less than 1.

A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers. Any mixed fraction can be converted into normal fraction using the formula -

[tex]X\frac{Y}{Z} =\frac{Z\times X+Y}{Z}[/tex]

According to the question -

Let us solve them one by one (for difference to be less than 1, the denominator should be less than numerator) -

Hence, only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.

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The 25th percentile of the data is represented by the 0 to 1 hour range.

48 speakers, or around 25% of the total of 192 speakers, are present.

According to the graph, 60 presenters gave presentations that lasted between 0 and 1 hours.

This means that 48 is between0 and1.

A score that compares a certain score to the scores of the other group members is known as a percentile. It shows the percentage of scores that a particular score outperformed.

A person's performance is gauged by using the percentile calculation to compare it to others. A student's test score is compared to that of other applicants using the percentile approach.

Therefore, the 0 to 1 hour period contains the data's 25th percentile.

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The term "length" is used to describe an object's size or the separation between two points. Lindsey must buy 4 feet of the board for the ramp itself.

The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.

Distance exists estimated in length. The length contain the dimension of distance in the International System of Quantities. The majority of measurement systems select a base unit for length from which all other units exists derived. The meter serves as the foundational unit of length in the International System of Units.

A rectangle, for instance, has length and width as its dimensions.

1/x = 15°

x = 1/sin 15°

simplifying the above equation, we get

x = 3.9ft

x ≈ 4 ft

Therefore, the value of x ≈ 4 ft.

Lindsey must buy 4 feet of the board for the ramp itself.

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The 100–meter backstroke swimming times of the 8 swimmers during the semifinal and the finals of the Olympic games gives;

First part;

The center of the semifinal round is approximately 57.3625

The variability in the semifinal round is 0.0998

Second part;

The center of the final round is approximately 57.0125

The variability in the final round is 0.3336

The times of the swimmers in the semifinal round are;

56.7, 57.2, 57.3, 57.3, 57.4, 57.5, 57.7, 57.8

The central value is given by the mean of the data, is found as follows;

(56.7+57.2+57.3+57.3+57.4+57.5+57.7+57.8)/8 = 57.3625

The variability is given by the standard deviation which is found by the formula;

[tex] \sigma = \sqrt{ \frac{ x_{i} - \mu}{n} } [/tex]

Where;

[tex]x _{i} = the \: ith \: value[/tex]

[tex] \mu = the \: mean[/tex]

The standard deviation found using the given values above and an online tool is presented as follows;

[tex] \sigma = \sqrt{ \frac{ x_{i} - 57.3625}{8} \approx 0.316 } [/tex]

Second part;

In the final, we have the following values from the dot plot;

56, 56.6, 56.6, 57, 57.1, 57.2, 57.7, 57.9

From the above values, using an online calculator, the center, which is taken as the mean is 57.0125

The variance for the final, [tex] \sigma^2 [/tex] ≈ 0.3336

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