Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles. What is the total running distance of the four runners?

Answer:

the relation is a function since one input provides us with only one output

outputs are the range since we know that range is the set of all possible outcomes

The value of the function f (g (5)) will be 10.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function are,

f(x) = 3x + 10 and g(x) = x - 2

Now,

Solve the function as;

f (g (5)) = f (5 - 2)

          = f (3)

          = 3 × 3 + 10

          = 9 + 10

          = 10

Thus, The value of the function f (g (5)) will be 10.

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Answer:  (a) 720°,  (b)  120°

Step-by-step explanation:

A hexagon is a polygon with six sides.

Formula for finding the interior angle of a polygon = ( 2n - 4 )complementary

                                                                                    = ( 2n - 4 ) 90

complimentary angle is 90°  or

                                                                                     = ( n - 2 )supplementary

supplementary angle is 180° . Now solving the question now since n = 6

we now put it in any of the formula above

       ( 2 x 6 - 4 ) x 90  =  ( 12 - 4 ) x 90

                                   =   8 x 90

                                   = 720°     or

     ( 6 - 2 ) x 180        =  4 x 180

                                  = 720°.

The second part of the question, each size of the interior angle

                                  = ⁷²⁰/₆

                                  = 120°

Answer:

5, -4, and -7

Step-by-step explanation:

5x² = 4x + 7

The standard form of a quadratic equation is

y = ax² + bx +c, where

a, b, and c are the coefficients.

If we convert your quadratic to the standard form, it becomes

5x² - 4x - 7 = 0

The coefficients are 5, -4, and -7.

Answer:

[tex]-2x-28[/tex]

Step-by-step explanation:

We can apply the distributive property then combine like terms for a simpler equation.

[tex]-4(x+6)+2(x-2)\\\\-4x-24+2x-4\\\\-2x-28[/tex]

Hope this helped!

Answer:

-2x -26

Step-by-step

Answer:

sinθ = -5/√61

secθ = √61/6

tanθ = -5/6

Step-by-step explanation:

From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Let us get the value of the radius 'r' first before calculating the trigonometry identities.

Using the Pythagoras theorem;

[tex]r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}[/tex]

Using SOH, CAH, TOA to get the trigonometry identities;

Given x = 6, y =5 and r = √61

[tex]sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\[/tex]

Since sin θ, is negative in the fourth quadrant, [tex]sin \theta = -5/\sqrt{61} \\[/tex]

[tex]cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\[/tex]

[tex]sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}[/tex]

For tanθ:

[tex]tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\[/tex]

Since tan θ, is negative in the fourth quadrant, [tex]tan \theta = -5/6[/tex]

 [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex],

[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]  

[tex]TAN\Theta=\frac{-5}{6}[/tex].

Given coordinate of point be (6, -5).

So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.

By Pythagorean theorem, we find that the hypotenuse

[tex]H=\sqrt{6^{2} +(-5)^{2} }[/tex]

[tex]H=\sqrt{61}[/tex]

We know from trigonometric ratios,

[tex]SIN\Theta=\frac{Perpendicular}{hypotenuse} \\[/tex]

[tex]SIN\Theta=\frac{5}{\sqrt{61} }[/tex]

Since [tex]SIN\Theta[/tex] is negative in 4th quadrant,

so,

[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex]

Similarly,

[tex]SEC\Theta=\frac{hypotenuse}{base}[/tex]

[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]

And,

[tex]TAN\Theta=\frac{perpendicular}{base}[/tex]

[tex]TAN\Theta=\frac{-5}{6}[/tex]

Hence,  [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex], [tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]  and [tex]TAN\Theta=\frac{-5}{6}[/tex].

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Answer:

The answer is 14 :)

Step-by-step explanation:

We have,

Find the measure of ∠ x ?

∠PQR + ∠RQS = ∠PQS

⇒ 76° + x = 90°

⇒ x = 90° - 76°

⇒ x = 14°

1 year = 52 weeks. 2 years would be 104 weeks.

$12 per week x 104 weeks = $1248 total.

1248 - 900 = $348

348 /900 = 0.3866 = 38.7%

The answer is B

Answer: 7 handshakes in all.

Step-by-step explanation:

If you and another person have one shake  and there are 14 total people in the cabin that means that there will be 7 handshakes  in all.

Answer:

Plato

Step-by-step explanation:

The line segment chosen is HI. Its image is H'I'. The slope of preimage HI is -1.25 and the slope of the image H'I' is -1.25.

The Scale Factor is used to scale shapes in different dimensions. We study different geometrical shapes in geometry, both two-dimensional and three-dimensional. The scale factor is a metric for comparing figures with similar appearances but differing scales or metrics.

The image of a transformation is the shape after the transformation. The preimage of a transformation is the shape before the transformation. The image is scale factor times preimage.

A line passing through the points (x₁, y₁) and (x₂, y₂) will have a slope

m = (y₂ - y₁)/(x₂ - x₁).

We are asked to select a line segment other than LK, which is not a vertical or horizontal line segment, for the scale factor n = 3.

So, we have to select a preimage( other than LK), and its image (3 times the preimage).

So we select the preimage as HI and its image as H'I', as the scale factor between them is n = 3, and HI is not a vertical or horizontal line segment.

Now, we calculate their slopes.

For the preimage HI (slope is m₁):

HI passes through the points (2, 0) and (0, 2.5). Substituting these values in the slope formula, we get

m₁ = (2.5-0)/(0-2) = -2.5/2 = -1.25.

For the image H'I' (slope is m₂):

HI passes through the points (6, 0) and (0, 7.5). Substituting these values in the slope formula, we get

m₂ = (7.5-0)/(0-6) = -7.5/6 = -1.25.

∴ The line segment chosen is HI. Its image is H'I'. The slope of preimage HI is -1.25 and the slope of the image H'I' is -1.25.

NOTE: The slopes of images and preimages are always the same as the image is just an enlarged or diminished form of the preimage.

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Answer:

9000000+20000+20+9

Step-by-step explanation:

Answer:

a. [tex]Total = 4P[/tex]

b. [tex]Gas = 2P[/tex]

c. [tex]2P - 5[/tex]

d. [tex]P = 20[/tex]

Step-by-step explanation:

Given

[tex]Amount\ received = P[/tex]

[tex]Number\ of\ days = 4[/tex]

[tex]Coffee = \$5[/tex]

[tex]Amount\ Left = \$35[/tex]

Calculating (a); the total amount earned;

[tex]Total = Amount * Days[/tex]

[tex]Total = 4 * P[/tex]

[tex]Total = 4P[/tex]

Calculating (b): Money Spent on Gas

From the question, we understand that 1/2 of his earnings is spent on gas;

Hence;

[tex]Gas = \frac{1}{2} * Total[/tex]

Substitute 4P for Total

[tex]Gas = \frac{1}{2} * 4P[/tex]

[tex]Gas = 2P[/tex]

Calculating (c): Expression for coffee

First, we need to calculate the amount left after buying Gas;

[tex]Amount = Total - Gas[/tex]

[tex]Amount = 4P - 2P[/tex]

[tex]Amount = 2P[/tex]

From this amount, he bough coffee of $5;

Hence; he's left with

[tex]2P - 5[/tex]

Calculating (d): Calculating his daily earnings

After (c) above, he has $35 left

So, we have

[tex]2P - 5 = 35[/tex]

Add 5 to both sides

[tex]2P - 5 + 5= 35 + 5[/tex]

[tex]2P = 40[/tex]

Divide through by 2

[tex]P = 20[/tex]

Hence, his daily earnings is $20

Answer:

The original number is -7.

Step-by-step explanation:

In this section, we are trying to figure out a mysterious number. Let's call this number y. To find the value of y, we need to create an equation. Our equation will be based on clues hidden in the text. So, what do we know?

- A number, aka y, is increased by 3. (y+3)

-That number is doubled. 'That number' refers to the answer of y+3. So, (y+3)x2.

-Finally, the end result is -8.

Great! Now we know our equation: 2(y+3)=-8. We need to figure out what y equals, so let's isolate the y term with some algebra.

2(y+3)=-8; Original formula

2y+6=-8; Distribute the (y+3)

2y=-14; Carry the 6 to the other side of the equation.

y=-7: Divide

Thus, our mysterious number is -7. Hope this helps:)))

This question is incomplete because the options are missing; here is the complete question:

Which expression is equivalent to (73) 5 • 74?

Select each correct answer:

73 • 5 + 4

73 + 5 + 4

73 + 5 • 74

73 • 5 • 74

The answer to this question is  73 • 5 • 74

Explanation:

The symbol • represents multiplication, this implies the numbers 5 and 74 should be multiplied when solving this operation. Moreover, if the expression is simplified the same symbol or a multiplication symbol should be used.

Moreover, the lack of a symbol between these numbers and 73 indicates multiplication. Indeed, in algebra and some fields of mathematics, the multiplication symbol is omitted, and two numbers standing side by side with no symbol indicate the multiplication. Thus, it is correct to place a multiplication symbol between 73 and the other numbers.

Answer:

y = 5x + 1

Step-by-step explanation:

Lines that are parallel to each other on a graph would have the same slope but different y-intercepts. When option A's equation is graphed along with the line given in the question, the lines appear to be parallel.  

Option A should be the correct answer.

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

Explanation:

Hello,

First of all, dividing by 0 is not defined we will take x different from 1/3 (because -1+3x= 0 <=> x = 1/3)

Then, dividing this polynomial by (-1+3x) means that you have to have Q(x), a polynomial of degree 1 and R a real number such that

[tex]\dfrac{9x^2-6x+2}{-1+3x}=Q(x)+\dfrac{R}{-1+3x}\\\\\text{We can multiply by (-1+3x)}\\\\9x^2-6x+2=(-1+3x)Q(x)+R[/tex]

Either you do the division and you can select the correct answer or you check the different answer to identify the correct one.

For instance, for the first answer, let's estimate

[tex](-1+3x)(3x-3)+\dfrac{-1+3x}{3x-1}\\\\=-3x+3+9x^2-9x+1\\\\=9x^2-12x+4[/tex]

and this is not equal to our initial polynomial, so this is not the correct answer.

Second Answer.

[tex](-1+3x)(3x-1)+\dfrac{-1+3x}{3x-1}\\\\=-3x+1+9x^2-3x+1\\\\=9x^2-6x+2[/tex]

And this is our initial polynomial. So this is the [tex]\large \boxed{\sf \bf \text{correct answer}}[/tex]

Thank you.

PS: in this example, you can even notice the following (so it makes the division trivial)

[tex](3x-1)^x=9x^2-6x+1 \\\\\text{So}\\\\9x^2-6x+2= (3x-1)^2+1\\\\\text{And, then.}\\\\\dfrac{9x^2-6x+2}{-1+3x}=3x-1+\dfrac{1}{3x-1}[/tex]

Answer:

thus, the ratios 8 : 16 and 6 : 12 are equal

Step-by-step explanation:

8 : 16 and 6: 12

8 : 16 = 1/2

6: 12= 1/2

Thus, the ratios 8 : 16 and 6 : 12 are equal

Answer:

x-3= 4

x= 4+3

Answer: x= 7

Answer:

x=7

Step-by-step explanation:

x-3=4

Adding 4on both sides

x-3+3=4+3

x=7

Hope it will help you :)

Answer:

73.437= 74 437/1000

Step-by-step explanation:

73.437 to fraction.

Let's acknowledge the presence of a decimal and how many digit we have after the decimal point.

Actually, the numbers after the decimal point will determine the amount of 10s to be divided with.

What I'm saying is this

73.437= 74 437/1000

In this case, 437 is a prime number

So

73.437= 74 437/1000

Full question attached

Answer explanation attached

Answer:

bottom right histogram fits the distribution

Step-by-step explanation:

we have chosen the bottom right histogram from the options as this fits the distribution best. It can be observed that probability for each outcome from 1(left from the table) increases till 6(right from the table)

Answer: I'll explore two options here. Your question wasn't entirely clear. If you meant a regular 2 step equation, this would be your answer:

-104(3+1)

-104(4)

   416

However, if you meant -104/(3+1) this would be your answer:

-104 ÷ (3+1)

(3+1) = 4

-104 ÷ 4 = -26

Hope this helped!

Answer:

B

Step-by-step explanation:

Answer:

(a) How many are there to select 2 pairs of gloves?

10 ways

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

130 ways

Step-by-step explanation:

We solve the above questions using Combination

Combination = C(n, r) = nCr

= n!/n! ×(n - r)!

(a) How many are there to select 2 pairs of gloves?

We have 5 pairs of gloves. Therefore, the number of ways to select 2 gloves =5C2

= 5!/2! × (5 - 2)!

= 5!/2! × 3!

= 5 × 4 × 3 × 2 × 1/(2 × 1) × (3 × 2 × 1)!

= 10 ways.

(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)

We are told to select 4 gloves out of the 10 gloves = 10C4

We have 5 pairs, we need to make sure that two out of the selected 4 make a pair = 5 × 2⁴

= 80

Hence,

10C4 - 5C4

= [10!/4! × (10 - 4)!] - 80

= 210 - 80

= 130 ways

Answer:

4917

Step-by-step explanation:

Given sequence:

This is AP with common difference of 1, the first term of 42 and the last term of 107

Number of terms:

Sum of the terms:

Answer is: 4917

Answer:

Step-by-step explanation:

B:  Above par.  Stock has gained a bit of value since it was purchased.

Answer:

[tex]a = \frac{1}{15}[/tex]

Step-by-step explanation:

Hey there!

To solve the given we'll use keep change flip.

[tex]\frac{1}{5} / 3 = a\\\\\frac{1}{5} *\frac{1}{3} = a\\\\\frac{1}{15} = a[/tex]

Hope this helps :)

Answer:

2 hours.

Step-by-step explanation:

From the question given,

Wade can do the work alone in 6 hours.

Rhonda can do the same work in 3 hours.

Next, we shall determine how much work is done by Wade and Rhonda in 1 hour each. This is illustrated below:

If Wade can do the work alone in 6 hours.

Then Wade can do 1/6 of the work in 1 hour.

If Rhonda can do the same work in 3 hours.

Then Rhonda can do 1/3 of the work in 1 hour.

Next, we shall determine the work done by Wade and Rhonda when they work together. This is illustrated below:

Wade's 1 hour work = 1/6

Rhonda's 1 hour work = 1/3

Therefore, work done by Wade and Rhonda together in 1 hour = 1/6 + 1/3 = 3/6 = 1/2

Since they completed 1/2 of the work in 1 hour, it means they will complete the work in 2 hours.

Answer:

b

Step-by-step explanation:

The y- intercept is the point on the y- axis where the graph crosses.

On the y- axis the x- coordinate is always zero.

From the table when x = 0 , y = 3, thus

(0, 3 ) is the y- intercept → b