A long-distance runner trains for 3 hours.
During the first part of the training, he
keeps a pace of 7 miles per hour (mph).
For the second part, he slows down to 5
mph. At the end of the run, he has
traveled a total of 19.5 miles. How long did
he spend at each speed?

The simplified value of (3/4)(-5/6)(-2/5) is 1/4.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

(3/4)(-5/6)(-2/5)

Now, multiplying the given fraction as

(3/4)(-5/6)(-2/5)

=(3 x (-5) x (-2))/ (4 x 6 x5)

=30/ 120

=3/12

=1/4

Hence, the simplified value is 1/4.

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The number of times the spinner lands on a shaded section are 8 times.

What is the probability?

Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true.

We have,

2 Shaded sections are on a spinner,

8 unshaded sections are on a spinner,

10 total sections are on a spinner,

Therefore,

The probability of the spinner to land on a shaded section:

P = 2 ÷ 10 = 1 ÷ 5

consider x, the number of times the spinner lands on a shaded section.

If the spinner were spun 40 times:

so,   \(\frac{x}{40} = \frac{1}{5}\)

By cross multiplying we get,

5x = 40

x = 8

Hence, the number of times the spinner lands on a shaded section are 8 times.

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If you spin the spinner 52 times, we expect the spinner to land on purple approximately 13 times in 52 spins.

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

Since there are 4 equal-sized sectors on the spinner, the probability of landing on purple on any given spin is 1/4.

To find the expected number of times the spinner will land on purple in 52 spins, we can multiply the probability of landing on purple by the total number of spins:

Expected number of times landing on purple = (Probability of landing on purple) x (Total number of spins)

Expected number of times landing on purple = (1/4) x (52)

Expected number of times landing on purple = 13

Therefore, we expect the spinner to land on purple approximately 13 times in 52 spins.

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Answer:

98% of  confidence interval for the true population

(0.6326 , 0.7674)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 250

She surveys 250 individuals and finds that 175 have taken a drug test for work.

sample proportion

                \(p = \frac{x}{n} = \frac{175}{250} =0.7\)

level of significance ∝ = 0.05

98% of  confidence interval for the true population is determined by

\((p^{-} - Z_{0.02} \sqrt{\frac{p(1-p)}{n} } ,p +Z_{0.02} \sqrt{\frac{p(1-p)}{n} } )\)

Z₀.₀₂ = 2.326

Step(ii):-

98% of  confidence interval for true population is determined by

\((0.7 - 2.326\sqrt{\frac{0.7(1-0.7)}{250} } ,0.7 + 2.326 \sqrt{\frac{0.7(1-0.7)}{250} } )\)

( 0.7 -  0.0674 , 0.7 + 0.0674)

(0.6326 , 0.7674)

Conclusion:-

98% of  confidence interval for the true population is determined by

(0.6326 , 0.7674)

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

Adjacent

\( \div \)

Opposite

Answer:

r= -0.1

Step-by-step explanation:

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

1/8

Step-by-step explanation:

(6m^-1n^0)^-3 =

= (6 × 1/3 × (-5)^0)^-3

= (6/3)^-3

= 2^-3

= 1/2^3

= 1/8

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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Answer:

1.08.

Step-by-step explanation:

Answer:

4x+7=3x+7

Step-by-step explanation:

-3(2x-5)=15-6x is infinite solution

top left is x=-3

top right is x=5 5x

Answer:

680

Step-by-step explanation:

Vito works at a clothing store. He earns a weekly salary of $500 plus 5% commission on sales. His sales last week totaled $3600. What was his total pay (salary and commission) last week?

therefore the answer is $680.

The vague pronoun "it" can be replaced by -

Option D: the spaceship

What is a pronoun?

An alternative to a noun is a pronoun. In order to avoid using the noun more than once in a paragraph or piece of writing, it replaces. Singular and plural pronouns can be used. The verb in the sentence should be utilised in keeping with the specific pronoun form that is being employed.

The sentence is "Did you see it in the sky last night?".

"The spaceship" is the most appropriate option to replace the ambiguous pronoun reference in this statement.

Did you see it in the sky last night? is a vague question because "it" could refer to a variety of sky-observed objects.

The language becomes clearer and more precise by swapping "it" for "the spaceship," referring specifically to a particular item observed in the sky.

Therefore, the spaceship is the correct choice.

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The if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

What is the Converse Statement?

That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.

We have given the statement:

Vertical angles are equal in measure.

A). Rewrite the statement as an if-then statement.

If angles are vertical angles then their measure is equal.

B). Write the converse of the implication

If the measure of angles is equal then they are vertical angles.

Hence, the if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

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If the value of x is 10. Then the measure of angle ∠COB will be 56°.

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.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

Given that A, O, and B lie on a straight line segment.

Then they make a linear angle that is 180 degrees.

Then we have

     ∠AOC + ∠COD + ∠DOB = 180

(3x + 94) + (x + 30) + (2x - 4) = 180

                               6x + 120 = 180

                                         6x = 60

                                           x = 10

Then the measure of angle ∠COB will be

∠COB = ∠COD + ∠DOB

∠COB = (x + 30) + (2x - 4)

∠COB = (10 + 30) + (20 - 4)

∠COB = 40 + 16

∠COB = 56°

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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The cost in 2008 based on the information is $70000.

It should be noted that percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

In this case, the cost in 2009 was $84000. This was 20% higher than the cost on 2008. The cost in 2008 will be x.

x + 0.2x = 84000

1.2x = 84000

Divide

x = 84000/1.2

x = 70000

The cost is $70000

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Answer:

7/30

Step-by-step explanation:

i think you are talking about 0.2333333...

=0.2+0.03+0.003+0.0003+0.00003+...

=0.2+x

x=0.03+0.003+0.0003+0.00003+...

a1=0.03

r=(0.003)/(0.03)=(0.003)/0.030)=3/30=1/10=0.1

x=a1/(1-r)=0.03/(1-0.1)=.03/0.90=3/90=1/30

so 0.233333....=0.2+1/30=2/10+1/30=6/30+1/30=7/30

9514 1404 393

Answer:

  x = 12

Step-by-step explanation:

Angle U is supplementary to the arc intercepted by the tangents.

  5x +10 = 180 -110

  5x = 60 . . . . . . subtract 10 and simplify

  x = 12 . . . . . . . . divide by 5

Answer: one hundred and five over three

Step-by-step explanation:

Answer: 57 i did the test

Step-by-step explanation:

Answer:

stan stray kids periodt

Answer:

so how you would wNt to go about this is we dont know tge ages so youd use variables

Answer:

Khalil is 7 years old. Angela is 2 years old.

Step-by-step explanation:

I hope this helps

Answer:

37/42 or 0.88

Step-by-step explanation:

\(( \frac{1}{6} + \frac{3}{7} ) + \frac{2}{7} \\ ( \frac{1}{6} + \frac{3}{7} ) = \frac{25}{42} \\ \)

\(\frac{25}{42} + \frac{2}{7} = \frac{37}{42} \\ \\ answer = \frac{37}{42} \)

Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Given:

Two sides of a triangle are 9 and 5.

To find:

The range of possible measures for the third side.

Solution:

In a triangle, the sum of smaller sides must be greater than the largest side.

Let x be the measure of third side.

Case 1: When x is the largest side, then

\(9+5>x\)

\(14>x\)            ...(i)

Case 2: When 9 is the largest side, then

\(x+5>9\)

\(x>9-5\)

\(x>4\)            ...(ii)

Using (i) and (ii), we get

\(4<x<14\)

Therefore, the range of possible measures for the third side is \(4<x<14\).

Answer:

B. (-12,-3,4,6)

Step-by-step explanation:

The above question is asking the domain

Answer:

C. 1/1,000

Step-by-step explanation:

yes or no ?