A red light flashes every 6 seconds.
A yellow light flashes every 4 seconds.
They both flash at the same time.
After how many seconds will they next both flash at the same time?

Answer:

x ≈ 46.7°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{OP}{NP}[/tex] = [tex]\frac{4}{5.5}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{4}{5.5}[/tex] ) ≈ 46.7° ( to the nearest tenth )

Answer:

The first student, with 20 measurements, will have the more precise interval due to the larger sample size.

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

[tex]M = z\frac{s}{\sqrt{n}}[/tex]

In which z is related to the confidence level, s to the standard deviation and n to the sample size.

The margin of error is inversely proportional to the square root of the sample size, which means that a larger sample will lead to a lower margin of error, that is, to a more precise interval.

In this question:

One student will use 5 measurements, other 20. The first student, with 20 measurements, will have the more precise interval due to the larger sample size.

Answer:

The answer is -0.71666666666 in decimal form.

In fraction form it is -43/60.

Step-by-step explanation:

Answer:

43.98

Step-by-step explanation:

The circumference of a circle with a radius of 7 units is approximately 43.98 units, which corresponds to option A.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

Given that the radius of the circle is 7 units, we can substitute this value into the formula:

To find the circumference of a circle, we can use the formula C = 2πr, where C represents the circumference and r represents the radius.

C = 2π(7) = 14π

Use the approximation π ≈ 3.14:

C ≈ 14(3.14) = 43.96

Rounding this value to the nearest hundredth, we get approximately 43.98 units.

Therefore, the circumference of a circle with a radius of 7 units is approximately 43.98 units.

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Answer:

2,000 cubic centimeters

Step-by-step explanation:

if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable

the equation that represents inverse proportion :

[tex]v = \frac{b}{p}[/tex]

where b = constant of proportionality

5000 = b / 200

b = 5000 x 200 = 1,000,000

v = 1,000,000 / 500

v = 2000

Answer:

C. -5

Step-by-step explanation:

If the two lines are parallel, they have the same slope. Therefore the slope of AB is -5.

Slope of line AB parallel to CD is -5

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.

Given,

AB is parallel to CD

Slope of CD m = -5

When two lines are parallel

their slopes are same

m' is slope of AB

then

m' = m

m' = -5

Slope of AB is -5.

Hence, -5 is slope of line AB.

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Answer:

12.16 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 5000=2500e^{0.0570t}[/tex]

[tex]\sf \implies \dfrac{5000}{2500}=\dfrac{2500e^{0.0570t}}{2500}[/tex]

[tex]\sf \implies 2=e^{0.0570t}[/tex]

Take natural logs of both sides:

[tex]\sf \implies \ln 2=\ln e^{0.0570t}[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\sf \implies \ln 2=0.0570t\ln e[/tex]

As ln e = 1:

[tex]\sf \implies \ln 2=0.0570t[/tex]

[tex]\sf \implies \dfrac{\ln 2}{0.0570}=\dfrac{0.0570t}{0.0570}[/tex]

[tex]\sf \implies t=\dfrac{ \ln 2}{0.0570}[/tex]

[tex]\implies \sf t=12.16047685...[/tex]

Therefore, the time required for the amount to double is 12.16 years (2 d.p.).

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Answer:

(25m^4n^1/12)(m^1n^1/12)

Step-by-step explanation:

Re-order terms to the left.  

(5*5m^4/3 * n^1/4) (m^1/3*2n^1/8)

Combine terms

(5*5m^4n^1/3/4)     2m^1n^1/3/3/8    

Multiply

(25m^4n^1/3/4)       2m^1n^1/3/3/8    

(25m^4n^1/3 * 4)    2m^1n^1/3/3*8    

(25m^4n^1/12).        2m^1n^1/3/24

cancel common terms in both num and denominator

Final - (25m^4n^1/12) (2m^1n^1/12).

Answer:

I'm not sure but I thing the answer is 10

Step-by-step explanation:

Answer: Upper right corner (northeast corner)

x-3y = 15

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

Explanation:

The y intercept always occurs when x = 0.

If we plug x = 0 into 2x+y = -10 (northwest corner), then we solve for y to get...

2x+y = -10

2(0)+y = -10

0+y = -10

y = -10

We see that the y intercept here is -10, but we want -5 instead. So we can rule this out.

In the northeast corner, plugging x = 0 leads to,

x-3y = 15

0-3y = 15

-3y = 15

y = 15/(-3)

y = -5

We get the correct y intercept we're after. So we can stop here.

If you plugged x = 0 into the equation of the southwest corner, you'll get y =  5 which is fairly close but not quite what we want. The southeast corner equation leads to a y intercept of y = 5 as well.

Answer:

x - 3y = 15

Step-by-step explanation:

x - 3y = 15

-3y = -x + 15

y = 1/3x - 5

-5 is the y-intercept.

Answer:

A) 16

Step-by-step explanation:

∠PQR and ∠TQS are vertical, meaning they equal each other

set up your formula as

3x+18=66

3x=66-18

3x=48

x=48/3

x=16

✽✽✽✽

[tex]\frac{x\cdot \:3}{4\left(x+21\right)}=10.5[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}4\left(x+21\right)[/tex]

[tex]\frac{x\cdot \:3}{4\left(x+21\right)}\cdot \:4\left(x+21\right)=10.5\cdot \:4\left(x+21\right)[/tex]

[tex]3x=42\left(x+21\right)[/tex]

[tex]3x=42x+882[/tex]

[tex]\mathrm{Subtract\:}42x\mathrm{\:from\:both\:sides}[/tex]

[tex]3x-42x=42x+882-42x[/tex]

[tex]-39x=882[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-39[/tex]

[tex]\frac{-39x}{-39}=\frac{882}{-39}[/tex]

[tex]x=-\frac{294}{13}[/tex]

❅❅❅❅❅❅❅❅❅❅

Answer:

V=82944

Step-by-step explanation:

FORMULA (Im guessing u just wanted answer but if u want formula there u go.

V= 1/3(a^2h)

Answer:

[tex]576 ~cubic ~centimeters[/tex]

Step-by-step explanation:

[tex]B=144cm^2[/tex]

[tex]h=12cm[/tex]

[tex]V=1/3~B*h[/tex]

[tex]=1/3(144)(12)[/tex]

[tex]=576 cm[/tex]

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

hope it helps...

have a great day!!

Answer:

A cube is dilated by a factor of 3.5.

The volume of the resulting cube is _3.5³=42.875__ times the volume of the original cube.

Answer:

the volume of cube diladet

_______

Answer:

12 inches

Step-by-step explanation:

hope this helps

Answer:

720

Step-by-step explanation:

20 yards = 720 inches

The area of the base of the first sandbox is 64 square feet

Area is the measure of the amount of surface that a two-dimensional figure or shape covers. It is typically expressed in square units, such as square inches or square meters.

The area of a shape can be calculated by multiplying the length of its base by its height or by using specific area formulas for different shapes, such as the area of a circle or the area of a triangle.

The area of a square is given by the formula: A = s², where s is the length of one side of the square.

In this case, the sandbox has a square base with a side length of 8 feet. Therefore, the area of the base of the first sandbox is:

A = 8² = 64 square feet.

So, the area of the base of the first sandbox is 64 square feet

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Answer:

The true statements are :

A. A random variable is a numerical description of the outcome of a statistical experiment.

B. In most​ applications, discrete random variables represent counted​ data.

C. In most applications, continuous random variables represent measured data.

Step-by-step explanation:

It is true statement that,

A. A random variable is a numerical description of the outcome of a statistical experiment.

B. In most​ applications, discrete random variables represent counted​ data.

C. In most applications, continuous random variables represent measured data.

The false statement is -

D. The expected value of a discrete random variable is equal to the standard deviation of the random variable.

Reason -

The mean value, or expected value, of a discrete random variable X is given by the following equation:

μ = E(x) = ∑ x p(x)

And

The variance of a discrete random variable is given by the following formula:

σ²=∑ (x−μ)² P(x)

And

The square root of the variance, or, in other words, the square root of σ², is the standard deviation of a discrete random variable :

σ = √σ²

Answer:

[tex]\huge\boxed{Answer\hookrightarrow}[/tex]

[tex]30 + 30 - 20 \times 2 + 600 \\ = 60 - 40 + 600 \\ = 20 + 600 \\ = 620[/tex]

⎇ The correct answer is 620.

# ꧁❣ RainbowSalt2²2² ࿐

Answer:

[tex]620[/tex]

Step-by-step explanation:

[tex]30+30−20 \times 2+600[/tex]

[tex]30+30−40+600[/tex]

[tex]60 - 40 + 600[/tex]

[tex]20 + 600[/tex]

[tex]620[/tex]

Answer:

x = 1.289

Step-by-step explanation:

11^x = 22

Take the log of both sides

xlog11 = log22

Divide both sides by log11

x = log22 / log11

Use calculator

x = 1.289

Answer:

Difference= $25.28

Step-by-step explanation:

Giving the following information:

She took $48.95 with her to spend. She spent $23.57 at one store.

To calculate the money she has left, we need to use the following formula:

Difference= total amount of money - money spent

Difference= 48.95 - 23.57

Difference= $25.28

Step-by-step explanation:

4x+17=23

4x=23-17

4x=6

x=6/4

Answer:

720

Step-by-step explanation:

This is a permutation of 10 choose 3

10 !             10!

-----   =    ------------   = 10*9*8  = 720

(10-3)!            7!

Answer:

4.62 KG

Step-by-step explanation:

1000 grams = 1kg

3kg = 3000g

4 kg = 4000g

1.5 = 1500g

left over potatoes = 3000 - 1500 = 1500 g or 1.5kg

left over onions = 4000 - 880 = 3120 = 3.12kg

total kilos not used = 1.5 + 3.12 = 4.62

|a|-|b| is equal to a+b both equal to -3.Option K is correct.

It is the numerical order in which the smallest number appears first, followed by the next number, and finally, the largest number appears last.

If  a > 0,b < 0

Let a =3 and b = -6

|a|-|b|= |3|-|-6|= - 3

Check all the options;

F)|a-b|=|3-(-6)| = 9

G)|a-b|=|3+(-6)|=|3-6|=|-3|=3

H)|3|+|-6|=|3+6| = 9

J)a-b=3-(-6)=3+6 =9

K)a+b=3+(-6) = -3

|a|-|b| is equal to a+b both equal to -3.

Hence option K is correct.

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Answer:

Step-by-step explanation:

(256)-3/4

=256*-3/4

=-768/4

=-192

Answer: j=8

Step-by-step explanation: first, add 5 to both sides. You now have 9j = 72. Then divide each side by 9. You now have j=8

Given:

The data set is:

25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24

To find:

The box plot for the given data set.

Solution:

We have,

25, 36, 21, 30, 20, 32, 38, 19, 36, 31, 26, 33, 27, 18, 24

Arrange the data in ascending order.

18, 19, 20, 21, 24, 25, 26, 27, 30, 31, 32, 33, 36, 36, 38

Divide the data in two equal parts.

(18, 19, 20, 21, 24, 25, 26), 27, (30, 31, 32, 33, 36, 36, 38)

Divide each parenthesis in two equal parts.

(18, 19, 20), 21, (24, 25, 26), 27, (30, 31, 32), 33, (36, 36, 38)

Now, the five number summary of the given data set is:

Minimum value = 18

First quartile = 21

Median = 27

Third quartile = 33

Maximum value = 38

Therefore, the required box plot for the given data set is shown below.

Answer:

It's 46

Step-by-step explanation:

Because 90-44 it's 46

Answer:

Step-by-step explanation:

option c is correct

if u change the divide sign into multiplication then always do its reciprocal.

Answer:

[tex]\frac{3x^3z^5}{5y}[/tex] ( [tex]\frac{20y^3}{x^2z^6}[/tex])

Step-by-step explanation:

When given the following equation,

[tex]\frac{3x^3z^5}{5y}[/tex] ÷ [tex]\frac{x^2z^6}{20y^3}[/tex]

The first step is to convert the equation into a form that can be solved, in essence dividing any number by a fraction is the same as multiplying that number by the reciprocal of the fraction. The reciprocal of a fraction is when one switches the position of the numerator and denominator, the numerator is the number on top of the fraction, and the denominator is the number underneath the fraction.

[tex]\frac{3x^3z^5}{5y}[/tex] ÷ [tex]\frac{x^2z^6}{20y^3}[/tex]

[tex]\frac{3x^3z^5}{5y}[/tex] * [tex]\frac{20y^3}{x^2z^6}[/tex]

Simplify, reduce the numbers that are found in common between the numerator and denominator,

[tex]\frac{3x^3z^5}{5y}[/tex] * [tex]\frac{20y^3}{x^2z^6}[/tex]

[tex]\frac{3x^3z^5*20y^3}{5y*x^2z^6}\\\\=\frac{3x*4y^2}{z}\\\\=\frac{12y^2x}{z}[/tex]