A runner can run 3miles in 15 minutes. At this rate, how many miles can he run in 45minutes?

The probability that the red balls can be drawn before the green ball is drawn is 3/8.

The probability is the measure of the likelihood of an event to happen.

Given:

red balls= 3

white balls = 4

green balls = 1

So, Probability of red balls

=3/8

Probability of green balls

=1/7

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Answer:

  tan(α+β) ≈ -5.8688

Step-by-step explanation:

You can use the formula for the tangent of the sum of angles, or you can use a calculator to find the angles. The latter is much simpler.

  tan(α+β) = tan(arccos(0.871) +arccos(0.338))

  tan(α+β) ≈ -5.8688

Note that the two angles total slightly more than 90°, so the tangent of their sum is a large negative number.

The use of trig identities also requires a calculator, and many more steps.

The tangent of the angle can be found from the cosine using ...

  tan(x) = √((1/cos(x))² -1)

  tan(α) = √((1/0.871)² -1) ≈ √(1.1481056² -1) ≈ 0.56404479

  tan(β) = √((1/0.338)² -1) = √(2.9585799² -1) ≈ 2.7844559

And the tangent of the sum of angles is ...

  tan(α +β) = (tan(α) +tan(β))/(1 -tan(α)tan(β))

  tan(α+β) = ((0.56404479 +2.7844559)/(1 -(0.56404479)(2.7844559))

  tan(α+β) = 3.3485007/(1 -1.5705579)

  tan(α+β) ≈ -5.8688

__

Additional comment

The approximate angles are ...

  α ≈ 29.4249°

  β ≈ 70.2448°

Then α+β ≈ 99.6699°

The value of x will be -7. The expression is solved using the identity.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Given expression;

[tex]\rm log_2(\frac{1}{128}) = x[/tex]

The expression is solved using the identity as;

[tex]\rm log_e1 = x\\\ e^x=1[/tex]

Apply the identity;

[tex]\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7[/tex]

Hence the value of x will bed -7.

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Answer:

d.

Step-by-step explanation:

k gets 3^3

a gets 4^2

subtract 3^3-4^2=d.

Answer:

Step-by-step explanation:

1) [tex]FB \parallel CG[/tex], [tex]\angle BFE[/tex] and [tex]\angle C[/tex] are supplementary (given)

2) [tex]\angle ABF \cong \angle C[/tex] (corresponding angles theorem)

3) [tex]\angle BFE[/tex] and [tex]\angle ABF[/tex] are supplementary (supplements of congruent angles are congruent)

4) [tex]CA \parallel FE[/tex] (converse of the same-side interior angles theorem)

Answer:

  (c)  714.96 = 21.6(w +4.7)

Step-by-step explanation:

The area of the rectangular park will be the product of its length and width. This relation is used to write an equation to find the original width of the park.

Let w represent the original width of the park in meters. The new width is 4.7 meters more, so is represented by (w +4.7).

The length of the park is given as 21.6 meters. The area is given as 714.96 square meters.

The various dimensions of the park are related by the area formula:

  A = LW

  714.96 = 21.6(w +4.7)

Answer: The answer is C i took the k12 5.21 unit test

Step-by-step explanation:

Answer:

1.

p=M/V. by rearranging this formula you get

V=M/p

V=560kg/7kg/m³

=80m³ b/c kg canceled kg

2.

p=M/V

=352kg/220m³

=1.6kg/m³

1. The amount of money in the account after 10 years is 42,317.96 dollars.

2. it will take Pamela and Kevin 7.5 hours to complete the task together

Question(1)

Using compound interest formula,

[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 30,000

r = 3.5% = 0.035

t = 10

n = 1

Therefore,

[tex]A = 30000(1+\frac{0.035}{1} )^{1X10}[/tex]

A = $42,317.96

Question 2:

Pamela takes 12 hours to complete a task.

Kelvin takes 20 hours to complete same task.

The time it will take both of them can be computed as follows:

using rate principle,

let

x = time it will take both of them to do the work together.

[tex]\frac{1}{x}=\frac{1}{12} + \frac{1}{20}[/tex]

[tex]\frac{1}{x}=\frac{20+12}{240}[/tex]

[tex]\frac{1}{x}=\frac{32}{240}[/tex]

cross multiply

240 = 32x

x = 240 / 32

x = 7.5 hours

Therefore,  it will take Pamela and Kevin 7.5 hours to complete the task together

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Based on the type of transaction that Fantastic Catering completed, the types of accounting basis they are in will be:

                                        Cash Basis                               Accrual Basis

May 1                                    (2,700)                                          0

May 5                                    (240)                                            (240)

May 9                                   2,700                                          2,700

May 14                                  (2,400)                                             0

May 23                                     0                                                2,900

May 31                                     0                                                 (1,800)

May 31                                     0                                                 ( 900 )

May 31                                      0                                                ( 730)

The cash basis is used for when cash transactions have happened. There has to be cash changing hands for this to be recorded like the prepaid rent and the payment for kitchen equipment.

The accrual basis is used for all payments and revenue including both cash transactions and those that are recorded on account such as the banquet on May 23 and accrued salaries.

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Answer:

£1.44

Step-by-step explanation:

N1 = £0.12

N12 = 12 × N1 = 12 × £0.12 = £1.44

Using a system of equations, it is found that the average of sheep A and sheep D is of 191 pounds.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are the weights of the sheep, given by A, B, C and D.

Sheep A and sheep B have an average weight of 150 pounds, hence:

[tex]\frac{A + B}{2} = 150[/tex]

A + B = 300 -> B = 300 - A

Sheep B and sheep C have an average weight of 127 pounds, hence:

B + C = 254

300 - A + C = 254

C - A = -46.

A - C = 46.

C = A - 46.

Sheep C and sheep D have an average weight of 168 pounds, hence:

C + D = 336

A - 46 + D = 336.

A + D = 382.

The average weight of sheep A and sheep D in pounds is:

[tex]\frac{A + D}{2} = \frac{382}{2} = 191[/tex]

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Answer:

it shrink

if the number outside the absolute value is greater than 1 it shrinks

if the numerous is smaller than 1 it stretches

remember the saying about the parent function if you run less than 1 mile you are wider than the parent

if you run more than a mile here the number is 7 so it's skinner yhan the

Step-by-step explanation:

The time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

The time taken by the boat upstream will be calculated as:-

( B + W ) Td = D

( 12 + 3 ) Td = 32

( 15 ) Td = 32

Td = 32 / 15 = 2.1 hours

The time taken by the boat downstream will be calculated as:-

( B - W ) Tu = D

( 12 - 3 ) Tu = 32

9 Tu = 32

Tu = 32 / 9 = 3.56 hours.

Therefore the time taken by the boat to travel 32 miles downstream is 2.1 hours and for upstream 3.56 hours.

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The value of x in 4096^x = 8 is 0.25

The equation is given as:

4096^x = 8

Express 4096 as 8^4

8^(4x) = 8

Cancel the common base

4x = 1

Divide by 4

x = 0.25

Hence, the value of x in 4096^x = 8 is 0.25

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A bond purchased at a premium, it will have a yield to maturity and current yield that is lower than its coupon rate.

This is usually above its face value which may be as a result of the interest rate being higher than the current market interest rates.

When a bond is traded at a premium, the yield to maturity and current yield will be lower than its coupon rate.

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Answer:

55 Wide and 75 Long works.

Step-by-step explanation:

Since the Perimeter of the original is likely 80 + 80 +50 + 50 = 260 since it it a rectangular lot, 55 + 75 + 55 + 75 = 260 as well, meaning no change in perimeter. Now when we look at the area 80 x 50 = 4000, but

55 x 75 = 4125, leading to a larger plot

Answer:

Step-by-step explanation:

1y + 12 = 6 (1y + 1)

1y + 12= 6y + 6

12 - 6 = 6y - 1y

6 = 5y

y = 6/5

y = 1.2

I don't what you meant by rounding to 2 decimal points so my answer is

Answer:

  1/216

Step-by-step explanation:

The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.

If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.

The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...

  (1/6)³ = 1/216

The volume of the filled portion of the cup is 1/216 of the volume of the cup.

Answer: The truck is carrying 55 large boxes and 60 small boxes

Step-by-step explanation:

Let x represent the number of large boxes

Therefore,

The number of small boxes = 115 - x

[tex]\therefore[/tex] According to the question

60x + 25(105 -x) = 4550

60x + 2625 - 25x = 4550

35x = 4550 - 2625

35x = 1925

x = 55

Number of large boxes = x = 55

Number of small boxes = 115 - 55 = 60

The regression equation is (d) log(y) = 0.064x + 1.706

The table of values is given as:

x   2   3   4   5   6

y   73  77  85  101  133

Calculate the logarithm of the y values.

So, we have:

x          2   3   4   5   6

log(y)   1.86  1.89  1.93  2  2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

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Answer: A

Step-by-step explanation:

By the exterior angle theorem,

[tex]x+y=138\\\\\implies y=138-x[/tex]

Answer:

n=16

Step-by-step explanation:

The statement that cannot be true is that g cannot be parallel to h (g ║h)

On the plane ,

line b is parallel to line f.

Therefore,

b ║ f

line f is parallel to line g,

Therefore,

f ║ g

line h is perpendicular to line b.

h ⊥ b

Therefore,

Since line h is perpendicular b, line b is perpendicular to h.

b can be parallel to g on the plane.

g cannot be parallel to h because h is perpendicular to b.

h can be perpendicular to f because b is parallel to f.

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Answer:

$0.29 and if you want to round it up then it is going to be $0.30

Step-by-step explanation:

You are asking what 1 pack of gum costs. We already know that 6 packs of gum costs $1.74 and we need to find the unit rate which is basically what one pack of gum costs so in order to do that we need to [tex]\frac{1.74}{6}[/tex] which is 0.29 and that is the cost of 1 pack of gum. Hope that helps and also can you please mark me as brainlist. Thank you

Using it's concept, the range of function g is given by:

B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]

The range of a function is the set that contains all possible output values for the function. In a graph, it is the values of y.

In this graph, y assumes all values except y = -3 and y = -4, hence the range is given by:

B. [tex]\{y|y \in \mathbb{R}, y \neq -4, -3\}[/tex]

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The true statement is (a) it is a function

For a relation to be a function, the following must be true:

Each x value must be paired with exactly one y value

From the table of values, all x values have exactly one y value

This means that the relation is a function

Hence, the true statement is (a) it is a function

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The correct option regarding whether the relation is a function is:

It is a function.

A relation represents a function if each input X is mapped to only one output Y.

In this problem, this statement is true(input 3 is mapped to output 10 twice, same output so ok), hence it is a function.

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The domain of the function g(x) is x >= 5

The complete question is added as an attachment

From the graph, we have the smallest value of x to be 5.

And the value of x increases to the right

This means that:

x >= 5

Hence, the domain of the function g(x) is x >= 5

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