When Richard works out, he spends 12 minutes doing cardio and 18 minutes doing resistance training. Cooper's workout consists of 10 minutes of cardio and 16 minutes of resistance training. Who does a higher ratio of cardio to resistance training?

Final answer:

The expression for the number of miles traveled by the airplane is 150h.

Explanation:

The expression for the number of miles traveled by the airplane is 150h. This expression represents the distance covered by the airplane based on the number of hours, h, it has been traveling at a speed of 150 miles per hour.

The expression for the number of miles traveled is [tex]\[ \text{Distance} = 150h \][/tex].

To determine the number of miles an airplane travels given its speed and the duration of travel, we can use a basic formula from physics that relates distance, speed, and time. The formula is:

[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]

Here, the speed of the airplane is given as 150 miles per hour, and the time is represented by ( h ) hours.

Step 1.Identify the given values:

Speed ( v ) = 150 miles per hour

Time ( h ) = number of hours

Step 2. Apply the formula for distance:

Distance ( d ) = [tex]Speed (\( v \)) \(\times\) Time (\( h \))[/tex]

Step 3. Substitute the given values into the formula:

[tex]\( d = 150 \text{ miles per hour} \times h \text{ hours} \)[/tex]

[tex]\( d = 150h \)[/tex]

Thus, the expression for the number of miles traveled by the airplane, when it travels at 150 miles per hour for ( h ) hours, is:

[tex]\[ \text{Distance} = 150h \][/tex]

Answer:

13.74

Step-by-step explanation:

the top right angle is 90 (opposite angles in a quadrilateral add up to 180). use the sine rule. x = 47/sin 90 × sin 17

= 13.74

Answer:

x = 13.7

Step-by-step explanation:

The angle at the top of the triangle = 90° - 17° = 73°

The left side of the triangle is x ( opposite sides of a rectangle )

Using the cosine ratio in the right triangle

cos73° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{47}[/tex]

Multiply both sides by 47

47 × cos73° = x, hence

x ≈ 13.7

Answer: x^3+30x+75

             -----------------------------

                       15x

Step-by-step explanation:

5x/x^2+2x÷30x^2/x+2

1/15x^5+2x^3+5x^2

---------------------------

x^3

x^3+30x+75

-----------------------------

15x

[tex]\bf \cfrac{5x}{x^2+2x}\div \cfrac{30x^2}{x+2}\implies \cfrac{5x}{x^2+2x}\cdot \cfrac{x+2}{30x^2}\implies \cfrac{\begin{matrix} 5x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{x~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} x+2\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{\begin{matrix} 5x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\cdot 6x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{1}{6x^2}~\hfill[/tex]

Final answer:

To locate the person who moved from (0, 1) with a slope of -4, we need to know the specific horizontal distance they moved. Without this, we can only say they moved downward 4 units for every 1 unit they moved to the right.

Explanation:

The student's question involves determining the position of a person who has moved along a slope on a coordinate plane. Since the individual started at the point (0, 1) and moved to the right with a slope of -4, we can assume they are moving in the negative y-direction (downward), as the negative slope indicates a decrease in y for every increase in x. The specific horizontal distance isn't given, so we cannot provide an exact new coordinate without more information. However, if we had a specific horizontal distance the person moved, we could calculate the new position using the slope (-4), which means for every 1 unit moved horizontally to the right, the person would move 4 units down.

Answer:

Step-by-step explanation:

The cross section will have the same shape as the base of the pentagonal prism; the dimensions will be proportionally smaller.

Experimental studies compare B. Two or more treatments are compared in the study (possibly including "no treatment" and C. One or more treatment groups and a control group are included in the study.

Regarding the characteristics that experiments have but surveys do not, the options that apply are that two or more treatments are compared in the study (possibly including "no treatment and one or more treatment groups and a control group are included in the study. These characteristics are specific to experimental design. In an experiment, there is a deliberate manipulation of variables to test a hypothesis, often involving a treatment and a control group to establish causality.

Surveys, on the other hand, typically gather data at one point in time or over time without manipulating variables, as seen in longitudinal or cross-sectional surveys. The two methodologies are distinct in that experiments can provide causal conclusions due to their internal validity, while surveys, although helpful in understanding correlations and trends, cannot as readily establish causation.

We have similar triangles so

[tex]\dfrac{4'6"}{18"} = \dfrac{x}{11'9"}[/tex]

[tex] x= \dfrac{ (12(11)+9 )(12(4)+6) }{18 } = 423 \textrm{ inches}[/tex]

Answer: 35' 3"

To find the height of a light pole given the shadow lengths of the pole and a woman of known height, we use a proportion. The height of the light pole is calculated to be 35.25 feet based on the given information.

The question asks how tall a light pole is if the pole's shadow is 11 feet 9 inches, and a woman who is 4 feet 6 inches tall casts a shadow that is 18 inches long. This is a problem of proportional relationships between the heights of objects and the lengths of their shadows. Using the fact that the ratio of the height of an object to the length of its shadow is the same for all objects at a given time, we can set up a proportion:

Height of woman / Length of woman's shadow = Height of light pole / Length of light pole's shadow

(4.5 feet) / (1.5 feet) = Height of light pole / (11.75 feet)

Now, we can solve for the height of the light pole:

Height of light pole = (11.75 feet) * (4.5 feet) / (1.5 feet)

Height of light pole = (11.75 * 4.5) / 1.5 = (52.875) / 1.5 = 35.25 feet

So, the height of the light pole is 35.25 feet.

A newspaper asking readers to complete a survey on their webpage is not conclusively biased or unbiased without knowing more about the survey's design and intention. Surveys can be a method to engage with and understand the readership better, but the potential for selection bias and the phrasing of questions could introduce bias. Whether the survey is biased or not depends on its execution and underlying methodological rigor.

The question "Is a newspaper asking readers to complete a brief survey on their webpage biased or unbiased" revolves around evaluating the intentions and methodology behind collecting reader satisfaction feedback. Given the nature of the survey is to collect feedback directly from readers on the newspaper webpage this can initially seem like a genuine effort to improve their service.

For evaluating the unbiased information based on research, it is crucial to consider the intent behind the survey and the potential for selection bias. It might inadvertently capture only the opinions of those willing to participate, or primarily those with strong opinions, positive or negative. Despite these considerations, the effort to engage with the readership directly can also be seen as a step towards transparency and improvement, indicating a potential to balance partiality with constructive feedback.

However, to ensure the process is unbiased, the newspaper would need to follow rigorous methodological standards, like random sampling, to ensure that the survey findings reflect the actual population of readers accurately. It's also essential to ensure that questions are phrased neutrally to avoid leading respondents towards a particular answer.

Answer:

D. <F = 65 degrees

Step-by-step explanation:

First off, we know that the measures of <F and the angle adjacent to it add to 90 degrees, as indicated by the right angle. They are complementary angles.

The complementary angle of <F has an intercepted arc of 50 degrees. Because the angle is on the opposite end of the circle, it is half of the measure of the arc. Therefore, it is 25 degrees.

Because this angle and <F sum to 90, just subtract 90-25 to find <F.

<F = 65 degrees

Answer:

F is equal to 65 (option D)

Answer:

Choice C.

Step-by-step explanation:

You already have two sides and two angles. Now you need the other two sides that include the angle. Choice C is correct.

Answer: C. [tex]\overline{SU}\cong\overline{JL}[/tex]

Step-by-step explanation:

In the given picture , we have two triangles ΔSTU and Δ JKL , in which we have

[tex]\overline{ST}\cong\overline{JK}[/tex]

[tex]\angle{S}\cong\angle{J}[/tex]

To prove ΔSTU is congruent to Δ JKL, we need [tex]\overline{SU}\cong\overline{JL}[/tex] such that [tex]\angle{S}\text{ and }\angle{J}[/tex] becomes congruent the included angles between pair of  congruent sides.

Hence, C is the right option.

Given the conditions: f(x) approaches 300 and g(x) approaches 0 (and is less than zero as x approaches 5), the limit as x approaches 5 of the quotient f(x)/g(x) is negative infinity.

Based on the given conditions: f(x) approaches 300 and g(x) approaches 0 as x approaches 5. Moreover, g(x) is less than zero, and therefore negative, as x approaches 5. When you divide f(x) by g(x), the sign of the outcome is determined by the signs of the numerator (f(x)) and the denominator (g(x)).

As f(x) is positive and g(x) is negative, the quotient will be negative. Since f(x) is approaching a finite value and g(x) is approaching 0, the quotient f(x)/g(x) tends toward negative infinity as per the properties of limits.

Therefore, the value of lim x→5 f(x)/g(x) is negative infinity.

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The inscribed angle theorem tells you that both angles must have the same measure, so

[tex]2(3m+2)=4m+20[/tex]

[tex]6m+4=4m+20[/tex]

[tex]2m=16[/tex]

[tex]m=8[/tex]

But this isn't the final answer! You're supposed to find the angles' measures, which are [tex]2(3m+2)^\circ[/tex] and [tex](4m+20)^\circ[/tex] where [tex]m=8[/tex]. So the answer is [tex]2(3\cdot8+2)^\circ=\boxed{52^\circ}[/tex].

The inscribed angle is half that of the arc it comprises. The measure of both the angle is 52°.

we know that the inscribed angle is half that of the arc it comprises.

Here, the arc that the inscribed angles comprise is the same.

2(3m+2)° = (4m+20)°

by solving for m

6m + 4 = 4m + 20

6m - 4m = 20 - 4

2m = 16

m = 8

To find the measure of the angle

(4m+20)°= 4(8) + 20 = 52°

2(3m+2)° = 2(26) = 52

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Answer:

100π

Step-by-step explanation:

step 1

Find the circumference

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=10\ in[/tex]

substitute

[tex]C=2\pi (10)[/tex]

[tex]C=20\pi\ in[/tex]

step 2

we know that

An object moves along a circular path and makes 5 revolutions in 1 minute

Remember that

[tex]1\ rev=2\pi r[/tex] ----> circumference of the circle

therefore

[tex]5\ rev=5(20\pi)=100\pi\frac{in}{minute} [/tex]

Answer:

$1236.25

Step-by-step explanation:

We can convert the percentage to 0.075 to make it easier. Then, multiply 1150 by 1.075 to get 1236.25. We add the one because we need to include the initial $1150.

There are 252 ways to divide the 10 players into two teams of 5 without any restriction.

To determine the number of ways you can divide 10 players into two teams of 5 without any restriction,

Using the formula, C(n, k) = [tex]\frac{n!}{k!(n-k)!}[/tex]

By finding the number of ways to choose 5 players out of 10, which is the same as choosing the other 5 players who are not on the first team.

Where n = 10

k = 5

C(10, 5) = [tex]\frac{10!}{5!(10-5)!}[/tex]

C(10, 5) = [tex]\frac{10!}{5!(5)!}[/tex]

C(10, 5) = 10*9*8*7*6*5*4*3*2*1/5*4*3*2*1(5*4*3*2*1)

C(10, 5) = 30240/5*4*3*2*1

C(10, 5) = 252 ways

Therefore, there are 252 ways to divide the 10 players into two teams of 5 without any restriction.

Final answer:

To find the probability of drawing a four and then a five from a standard deck with replacement, multiply the probabilities of the independent events: (1/13) × (1/13) = 1/169.

Explanation:

The question involves calculating the probability of two independent events when drawing cards from a standard deck. The first event (A) is drawing a card that is a four, and the second event (B) is drawing a card that is a five. The probability of each of these events is calculated separately since the card is replaced after each draw, making the draws independent of each other.

The probability of drawing a four (P(A)) from a standard deck is 1/13, as there are four fours in a 52-card deck. Similarly, the probability of drawing a five (P(B)) is also 1/13. Since the events are independent, the combined probability is the product of the two probabilities: P(A) × P(B) = (1/13) × (1/13) = 1/169.

The exact value for the equation is true but I don't really think that's the question so anyways...

- 15.) The exact form for this equation is -13pi/3 and the decimal form -13.613...

- 16.) The exact form for this equation is 23pi/4 and the decimal form 18/064...

- 17.) The exact form is -7pi/2 as the decimal is -10.995...

- 18.) The exact is -29pi/6 and the decimal is -15.184...

We know any trig problem that asks for exact values probably has something to do with 30° or 45° and their multiples.  That's [tex]\pi/6[/tex] and [tex]\pi/4[/tex]; we're apparently doing radians in this one.

General rules off the top of my head: Coterminal angles (gotten by adding or subtracting multiples of 2π) have the same values for their trig functions , cosine is even, sine is odd, cosine negate supplementary angles, sine of supplementary angles is unchanged, and the cosine of an angle is the sine of the complementary angle.

15

[tex]\cos (- \frac{13\pi}{3}) = \cos( 13\pi/3-6(2\pi)) =\cos(\pi/3) = \frac 1 2[/tex]

16

[tex] \csc(\frac{23 \pi}{4}) = \dfrac{1}{\sin (23\pi/4 - 3(8\pi/4))} = \dfrac{1}{\sin(-\pi/4)}= \dfrac{1}{- 1 /\sqrt{2}} = - \sqrt{2}[/tex]

17

[tex]\sec(-\frac {7 \pi}{2}) = \dfrac{1}{\cos(-7\pi/2+ (4/2)(2\pi) )}= \dfrac{1}{\cos(\pi/2)} = \dfrac 1 0[/tex]

That one is undefined

18

[tex]\cot(-\frac{29\pi}{6}) = \cot(-29\pi/6 + (18/6) (2 \pi)) = \cot(7\pi/6) \\= \tan(\pi/2 - 7\pi/6) = \tan(-4\pi/6)= \tan(-2\pi/3 + \pi) = \tan(\pi/3)= \sqrt{3}[/tex]

Whoever created this math homework problem needs a lesson in writing and typesetting math.  Let's list the errors:

Exact -- capitalized

each equation -- there are no equations

0 to 2 pi for theta -- do they want us to find the values or find the thetas but not evaluate the trig function?

theta is spelled out, not typeset

trig functions shouldn't be typeset in italics

sec -(7 pi/2)  is a typo

Sometimes there's a space after the problem number sometimes there isn't

This is awful.  Demand more of your teachers and online exercises!

[tex]\bf 7~~,~~\stackrel{7+6}{13}~~,~~\stackrel{13+6}{19}~~,~~\stackrel{19+6}{25}\qquad \impliedby \qquad \textit{common difference "d" is 6}[/tex]

we know all it's doing is adding 6 over again to each term to get the next one, so then

[tex]\bf \stackrel{\textit{Recursive Formula}}{\stackrel{\textit{nth term}}{f(n)}~~=~~\stackrel{\textit{the term before it}}{f(n-1)}~~~~\stackrel{\textit{plus 6}}{+~~~~6}}[/tex]

now for the explicit one

[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=7\\ d=6 \end{cases} \\\\\\ a_n=7+(n-1)6\implies a_n=7+6n-6\implies \stackrel{\textit{Explicit Formula}}{\stackrel{f(n)}{a_n}=6n+1} \\\\\\ therefore\qquad \qquad f(10)=6(10)+1\implies f(10)=61[/tex]

Answer:

every point will be 4 tons lower than it was

Step-by-step explanation:

26 is 4 less than 30, so the new function g(x) is ...

g(x) = f(x) -4

It is shifted down 4 units (tons) from the original function.

ANSWER

[tex]y = \sin(x) [/tex]

EXPLANATION

The trigonometric function that is zero at integral values is the sine function.

That is;

[tex]y = \sin(x) [/tex]

has x-intercepts at

[tex] n\pi[/tex]

where n is an integer.

In other words, the solution to the equation:

[tex] \sin(x) = 0[/tex]

is

[tex]x = n\pi[/tex]

where n is an integer.

Answer:

y=sin x

y=tan x

these are correct....

ANSWER

2nd and 3rd quadrant.

EXPLANATION

The given trigonometric equation is:

[tex] \sec(x) = - 2[/tex]

The secant ratio is negative in the second and third quadrant.

But it is positive in the first and fourth quadrants.

The given secant ratio is negative.

This implies that , the solution to given equation lies in the second and third quadrant.

Answer:

19

Step-by-step explanation:

to find the range, you have to subtract the smaller number from the biggest number

In this case it would be 45-26

45-26=19

range=19

Answer:-9+2I

Step-by-step explanation: MUTIPLYING THE SECOND BRACKET BY THE NEGATIVE SIGN.

(-3-3I)(-6+5I)

COLLECTING LIKE TERMS

(-3-6)(-3I+5I)

=-9+2I

Answer:

The difference is:

[tex]-9+2i[/tex]

Step-by-step explanation:

We have the subtraction of two complex numbers.

[tex](-3-3i)-(6-5i)[/tex]

To solve the operation, the product of:

[tex]-(6-5i)[/tex]

[tex]-6 +5i[/tex]

Now add the two expressions. Add real numbers with real numbers and complexes with complex numbers

[tex]-3-3i-6 +5i[/tex]

[tex]-3-6 +5i-3i[/tex]

[tex]-9+2i[/tex]

The difference is:

[tex]-9+2i[/tex]

She should expect 250 green marbles.

She has a 25 out of 40 chance of selecting a green marble each time since she is putting it back in the bag each time. 25/40 reduces to 5/8. Multiply 5/8 by 400 and you get 2000/8. Reduce the fraction to 250/1 or 250.

I know that the answer is A, however I can not answer the rest

Answer: $11,250

1850 + (4/100)x = 1850 + 0.04x.

1850 + 0.04x > 2300

0.04x > 2300 - 1850

0.04x > 450

x > 450 / 0.04

x > $11,250

Answer

x> 11,250

yyyyyyyyyyyyyyyyyeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answer:

(x, y) = (-20, 7), (-5, -2), (0, 3), (15, -4), (30, 5)

Step-by-step explanation:

You want 1/5x to match the x-value in the given table. To make that happen, multiply the given x by 5.

Example: when (1/5x) = -4, f(1/5x) = 7, so x = -4·5 = -20 for y = 7.

The transformation f(1/5x) is a horizontal expansion by a factor of 5, so each point of f(x) is now 5 times farther from the y-axis than it was.

The completed table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] is as follows:

x

−4

−1

0

3

6

​y

3

−2

3

7

5

To complete the table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\),[/tex] we need to substitute the given \(x\) values into the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] and calculate the corresponding \(y\) values.

The function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex]implies that we are scaling the input \(x\) by a factor of 5. This means the \(x\) values in the original table need to be multiplied by 5 to find the corresponding values for the new function. Let's calculate the values step by step:

1. For [tex]\(x = -4\):[/tex]

  [tex]\[y = f\left(\frac{1}{5}(-4)\right) = f(-0.8)\][/tex]

  Looking at the original table, when [tex]\(x = -0.8\), \(y = 3\).[/tex]

2. For [tex]\(x = -1\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(-1)\right) = f(-0.2)\][/tex]

  When [tex]\(x = -0.2\), \(y = -2\).[/tex]

3. For [tex]\(x = 0\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(0)\right) = f(0)\][/tex]

  When [tex]\(x = 0\), \(y = 3\).[/tex]

4. For [tex]\(x = 3\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(3)\right) = f(0.6)\][/tex]

  When [tex]\(x = 0.6\), \(y = 7\).[/tex]

5. For [tex]\(x = 6\):[/tex]

[tex]\[y = f\left(\frac{1}{5}(6)\right) = f(1.2)\][/tex]

  When [tex]\(x = 1.2\), \(y = 5\).[/tex]

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Explanation of experimental and theoretical probability of rolling a 3 on a six-sided number cube.

The experimental probability of rolling a 3:

Simulate 35 rolls of a six-sided number cube to get results.

Count the number of times a 3 is rolled and calculate the experimental probability by dividing the number of 3s rolled by 35.

The theoretical probability of rolling a 3:

Theoretical probability = Number of favorable outcomes / Total number of outcomes = 1/6 (since there is 1 favorable outcome out of 6 possible outcomes).

Differences between theoretical and experimental probabilities:

Theoretical probability is based on calculations and assumptions, while experimental probability is based on actual observations. Discrepancies between the two can occur due to sample size, random variations, or errors in the simulation.

Answer:

38.2 miles

Step-by-step explanation:

343.8 miles divided by 9 gallons equals 32.2 miles per gallon.

Answer:

  (n+2)(n+1)

Step-by-step explanation:

Write out the numerator and cancel common factors:

  (n+2)!/n! = (n+2)(n+1)n!/n! = (n+2)(n+1)

_____

You might be expected to multiply it out:

  = n·n +2·n +n·1 +2·1

  = n² +3n +2