Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as
the other. If they meet 3 hours later, what is the speed (in mi/h) of the faster cyclist?
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist.
b. What is the speed of the faster cyclist?
mi/hr

We get that the birds and the dancers will clock out again in 30 minutes.

We are given that:

a cuckoo clock has birds that pop out of their nests every 6 minutes.

And the dancers that pop out every 15 minutes.

Now, they have popped out the same time. For this to happen again, we will find the LCM of 6 and 15.

6 = 2 × 3

15 = 3 × 5

LCM = 2 × 3 × 5

LCM = 3 × 10

LCM = 30

So, they will pop out again after 30 minutes.

Therefore, we get that the birds and the dancers will clock out again in 30 minutes.

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Answer: C=550+121m

Step-by-step explanation:

Answer:

3x+4x-1+x+2=73

8x+1=73

8x=73-1

8x=72

8x/8=72/8

x=9

Perimeter (p) of a triangle:

[tex]p = a + b + c[/tex]

P = 73 units

To find the value of x

[tex]73 = 3x + 4x - 1 + x + 2[/tex]

→[tex]73 = 8x + 1 \\ 73 - 1 = 8x[/tex]

→[tex]8x = 72[/tex]

→[tex] \frac{8x}{8} = \frac{72}{8} [/tex]

[tex]x = 9[/tex]

Answer:

use air math

Step-by-step explanation:

hope that helps

The number 67 and 113 are not the multiples of 3,6 and 7.

Multiples are the results of multiplying one whole number from another whole number.

Now, for the given question;

As, 67 and 113 are not completely divisible by 3. They are not multiple of 3.

67 and 113 are not entirely divisible by 6. So, they are also not the multiple of 6.

Now, 67 and 113 are also not entirely divisible by 7. Thus, they are also not the multiple of 7.

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The light's coverage area is given mathematically as i.e. Area=[tex]\pi d^{2}[/tex]

Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.

The revolving beam of light covers the whole space i.e entirely 360°

I.e. it forms a circle-like region

Area of circle = [tex]\pi r^{2}[/tex]{ where r is the radius of circle}

Let's assume the distance traveled by light as "d"

as it forms a circular region, it forms a circle of radius "d"

Mathematical connection i.e. area of the region

⇒area of circular region=[tex]\pi d^{2}[/tex] {where d is the radius of region}

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Answer: 8 kitkats

Step-by-step explanation:

40+24= 64

72-64=8

Answer:

Total candy bars to snickers = 72:40 or simplified 9:5

Ratio of kit kats to milky ways = 8:24 or simplified 1:3

Ratio for kit kats to total candy bars = 8:72 or simplified 1:9

Step-by-step explanation:

72 = 40 + 24 + x

x = 8

Answer:

Number of 12$ Shares? 25

Number of 14$ Shares? 57

Step-by-step explanation:

Let x = number of $12 shares.

Let y = number of $14 shares.

"Ivan has $1098 worth of $12 and $14 stock shares."
12x + 14y = 1098

The number of $14 shares is seven more than twice the number of $12 shares.

y = 2x + 7

We have a system of equations.

12x + 14y = 1098

y = 2x + 7

We can use the substitution method since the second equation is already solved for y. Substitute 2x + 7 for y in the first equation.

12x + 14(2x + 7) = 1098

12x + 28x + 98 = 1098

40x = 1000

x = 25

There are 25 $12 shares.

y = 2x + 7 = 2(25) + 7 = 57

There are 57 $14 shares.

Check:

25 × $12 + 57 × $1`4 = $300 + $798 = $1098

The total value is correct, so the answer is correct.

The total number of hours taken by farmer's son to plow the farm is 19 hours.

Time refers to the duration of any task or activity that occurs or continues.

Work is a process or set of tasks designed to achieve a specific result.

For, the given question;

Let F be the number of hours taken by farmer to finish the work.

Let S be the number of hours taken by farmer' son to finish the work.

The amount of work finished in 1 hour by farmer is 1/F = 1/11.

The amount of work finished in 1 hour by farmer's son is 1/S.

The amount of work finished by both in 1 hours is;

1/F + 1/S = 1/7

1/S = 1/7 - 1/F

1/S = 1/7 - 1/11

Simplifying the given term;

1/S = 4/77

or, S = 77/4 = 19.25 hours.

S = 19 hours (fraction reduced to lowest terms)

Thus, the time taken by the farmer's son to complete the plow of field is 19 hours.

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Answer: i=-1.75

Step-by-step explanation:

3i - 6 = 7i + 1

3i-3i-6=7i-3i+1

-6=4i+1

-6-1=4i+1-1

4i=-7

i=-7/4

i=-1.75

Answer:

(a)  [tex]\frac{620}{3195}[/tex]

(b) [tex]\frac{645}{3195}[/tex]

Step-by-step explanation:

Relative frequency of an event = Event Frequency/Total Frequency

In this case the event is the number of responses for each reason and the total frequency is the sum of all responses.

Total Responses = 583 + 620 + 187 + 163 + 558 + 645 + 439 = 3195

(a) What is the relative frequency for the reason "study hard"?
= Number of responses for "study hard" / 3195

= 620/3195

==> [tex]\frac{620}{3195}[/tex]   Answer to (a)

(b) What is the relative frequency for the reason "have a goal in mind"?

= Number of responses for the reason "have a goal in mind"/3195

= 645/3195

==> [tex]\frac{645}{3195}[/tex]   Answer to (b)

I think it is OK to leave it as it is without reducing the fraction any further

Answer:

this question is wrong .................

Answer:

39÷(5+(4×5÷2) )

39÷(5+(20÷2) )

39÷(5+10)

39÷15

2.6

In the above question the |x| represents the absolute value. |x - 1| < 5  is equivalent to -5 < x - 1 < 5.

Algebra usually requires us to be careful about not just size of a value but also its sign. -10 is different than the 10. 3+7  yields a different result than the 3+(-7) . But there are circumstances in which sign doesn’t matter, in mathematics and in real life. Have you ever stumbled stepping on or off the moving walkway? It doesn’t really matter if you’re moving faster or slower than ground surface—it’s the magnitude of difference that makes you lose your balance. Or think of taking long hike—your feet will get just as the sore whether you go to north or south. Direction doesn’t matter, only the distance.

In mathematics, there’s a concept for dealing with the situations where size matters more than sign. It’s called the absolute value. Absolute value of a number is it's value regardless of its sign.

Given,

|x - 1| < 5

|x| this represents absolute value. It is the distance of x from 0, so value of x can be both positive and negative.

⇒ |x - 1| < 5 can be (x - 1) < 5 and -(x - 1) < 5

⇒ -(x - 1) < 5

⇒ (x - 1) < -5

So equivalent of |x - 1| < 5 is -5 < x - 1 < 5

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Answer:

Its C

which is –5 < x – 1 < 5

The inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths

The numbers are given as:

125%, 0.47, and three and two fifths

Rewrite properly as:

125%, 0.47, and 3.4

Express the percentage as decimal

1.25, 0.47, and 3.4

Reorder the numbers in ascending order

0.47, 1.25 and 3.4

Rewrite as

0.47, 125% and three and two fifths

Include the less than inequality symbol

0.47 < 125% < three and two fifths

Hence, the inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths

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The probability that voter also plans to vote “yes” on issue Q is found to be 0.4.

The following equation is used to determine the probability of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes

Probability(Event) = x/n

Eight voters intend to vote "yes" on both issues.

So, the favourable outcome becomes = 8.

Twenty voters intend to vote "yes" on issue P.

Thus, the total outcome = 20.

This is denoted by 8 /20 = 0.4.

Therefore, the likelihood that a voter will vote "yes" on issue Q is found to be 0.4.

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Answer: 10

Step-by-step explanation: First you decide that each container can fill 3/4 of a cup. You have 8 cups so you need to divide 8 by 3/4 which will give you the answer of 10.666 repeating so the answer is you can only fill up 10 containers.

The missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is -33/4.

Let the missing ccordinate of the ordered pair be m.

According to the given question.

We have an equation 6x - 4y = 9.

Here, we have given a ordered pair (-4, ?) which satisfy the given equation 6x - 4y = 9.

Therefore, the missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is given by

6x - 4y = 9

⇒ 6(-4) - 4(m) = 9

⇒ -24 - 4m = 9

⇒ -4m = 9 + 24

⇒ -4m = 33

⇒ m = -33/4

Hence, the missing coordinate of the ordered pair (-4, m) for the equation 6x - 4y = 9 is -33/4.

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The perimeter of the given rectangle is a 3.31 meter.

According to the statement

We have to find that the perimeter of rectangle.

So, For this purpose, we know that the

Perimeter is the distance around the edge of a shape.

From the given information:

The length of the tabletop is 1.83 meters and the width is 0.74 meter.

Then the formula to find the perimeter is a

P =l +2w

Here substitute the values then

P =l +2w

P = 1.83 +2*0.74

Now add the terms to get a perimeter of the rectangle.

Then

P = 1.83 +1.48

P = 3.31.

So, The perimeter of the given rectangle is a 3.31 meter.

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Answer:

don't know that i'm looking for that to

Answer:

4n

Step-by-step explanation:

Answer:

-x^2-2xy-3x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function:

[tex]y=\sqrt{x-2}[/tex]

The domain is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, the domain of the given function is restricted.

[tex]x-2\geq 0 \implies x\geq 2[/tex]

Therefore, the domain of the given function is [2, ∞).

The range is the set of all possible output values (y-values).

As the square root of a negative number cannot be taken, the range of the given function is restricted.  

Therefore, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Therefore, the function is continuous on its domain [2, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}[/tex]

Therefore, there are no stationary points.

As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}[/tex]

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: [2, ∞)

Range: [0, ∞)

Continuity: Function is continuous on its domain [2, ∞).

Minimum point at (2, 0).

Increasing function: (2, ∞)

Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.

Answer:

Answer is (-10,7) and inequality form: -10<c<7

Step-by-step explanation:

First factor the equation.

(c+7)(c-10)

Then find out which intervals make (c+7)(c-10)<0.

Answer: 26

Step-by-step explanation:

17 + 2 × 9 ÷ 3 + 4 × 6 ÷ 8=

17 + (2 × 9 ÷ 3) + (4 × 6 ÷ 8)=    ==> multiplication and division come before addition

17 + (18 ÷ 3) + (24 ÷ 8)=

17 + 6 + 3=

23+3=26

The new ratio of ownership once the business was owned by only Andrea and Lindsay is 8 : 7

The ratio is given as:

Andrea : Dina : Lindsay = 7 : 9 : 14

The partnership worth is given as

Worth = $1,800,000

The amount received by Dina is:

Dina = Dina Ratio/Total Ratio * Worth

So, we have

Dina = 9/(7 + 9 + 14) * 1800000

Evaluate

Dina = 540000

Hence, Andrea pays Dina $540,000 for her share of the partnership

Initially, we have:

Andrea : Dina : Lindsay = 7 : 9 : 14

So, the new ratio is

Andrea : Lindsay = (7 + 9) : 14

Evaluate

Andrea : Lindsay = 16 : 14

As a percentage, we have

Andrea = 16/(16 + 14) * 100%

This gives

Andrea = 53.33%

Hence, Andrea owns 53.33% of the business after she bought out Dina

In (b), we have:

Andrea : Lindsay = 16 : 14

Simplify

Andrea : Lindsay = 8 : 7

Hence, the new ratio of ownership once the business was owned by only Andrea and Lindsay is 8 : 7

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Betsy needs to  invest $32,000 in the B-rated bonds paying 13% interest and $28,000 in the certificate of deposit paying 3% interest.

Interest is calculated by multiplying the rate with the principal.

Let x = the amount Betsy will invest in the B-rated bonds paying 13% per annum. The remaining amount, $60,000-x , she will invest in the certificate of deposit paying 3% per annum.

We can express the earnings on these two investments, after converting the percentages to their decimal equivalents, as: 0.13x+0.03(60000-x) and this is to earn a total of $5,000

Now we can write the necessary equation to solve for x.

or, 0.13x+0.03(60000-x) = 5000

or, 0.13x+1800-0.03x = 5000

or, 0.1x+1800 = 5000

or, 0.1x = 3200

or, x = 32000

So Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and the remainder ($60,000-$32,000 = $28,000) in the certificate of deposit paying 3% interest to obtain $5,000 in interest per annum.

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The number of weeks that it takes to empty the lake is; 350/11 weeks

We are told that Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.

Let w = number of weeks required to empty the lake

let the completed job = 1 (an empty lake)

Thus;

w/14 - w/25 = 1

Multiply through by 350 to get;

25w - 14w = 350

11w = 350

w = 350/11 weeks

Thus, the number of weeks that it takes to empty the lake is; 350/11 weeks

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The real number whose sum and product are both 12 area 1.101 and 11.899

Let first number be  " x "

Let other number be " 12 - x "

According to the question the product of two numbers is 12 which is given by         x(12 - x) = 12

                        12x - x² = 12

                         x²- 12x + 12 = 0

Using quadratic formula , we get

Put a = 1 , b = -12 , c = 12 in equation (1) , we get

                      [tex]\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)} }{2(1)} \\\\\frac{12\pm\sqrt{144-48} }{2} \\\\\frac{12\pm\sqrt{96} }{2} \\\\\frac{12\pm9.79 }{2} \\\\[/tex]

Two numbers are 12 + 9.79 / 2 = 1.10 and 12 - 9.79/2 = 10.89

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The probability that all of them are rose bouquets is 0.143.

It should be noted that this question is about probability without replacement.

The probability of picking a rise bouquet is 5/7. It should be noted that each value decreases since Ariel is selecting 4 bouquets.

The probability that all of them are rose bouquets will be:

= 5/7 × 4/6 × 3/5 × 2/4

= 5/7 × 2/3 × 3/5 × 1/2

= 30/210

= 1/7

= 0.143

The probability is 0.143.

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