What is the arc length when θ =pi over 3 and the radius is 5 cm? (5 points) 5 pi over 3 cm 10 pi over 3 cm 16 pi over 3 cm pi over 3 cm

Answer:

The four answers in the attached figure

Step-by-step explanation:

Part 1) we have

[tex]x-99\leq-104[/tex]

Solve for x

Adds 99 both sides

[tex]x-99+99\leq-104+99[/tex]

[tex]x\leq-5[/tex]

The solution is the interval ----> (-∞, -5]

All real numbers less than or equal to -5

In a number line, the shaded area at  left of x=-5 (close circle)

Part 2) we have

[tex]x-51\leq-43[/tex]

Solve for x

Adds 51 both sides

[tex]x-51+51\leq-43+51[/tex]

[tex]x\leq 8[/tex]

The solution is the interval ----> (-∞, 8]

All real numbers less than or equal to 8

In a number line, the shaded area at  left of x=8 (close circle)

Part 3) we have

[tex]150+x\leq144[/tex]

Solve for x

Subtract  150 both sides

[tex]150+x-150\leq144-150[/tex]

[tex]x\leq -6[/tex]

The solution is the interval ----> (-∞, -6]

All real numbers less than or equal to -6

In a number line, the shaded area at  left of x=-6 (close circle)

Part 4) we have

[tex]75<69-x[/tex]

Solve for x

Subtract 69 both sides

[tex]75-69<69-x-69[/tex]

[tex]6<-x[/tex]

Multiply by -1 both sides

[tex]-6> x[/tex]

Rewrite

[tex]x < -6[/tex]

The solution is the interval ----> (-∞, -6)

All real numbers less than -6

In a number line, the shaded area at  left of x=-6 (open circle)

Juan needs to sell 18 fruit baskets and 2 pencils to achieve his goal.

The number of items = (total price for the items)/(each price of the required item)

Given that,

Price of a fruit basket = $16.50

Price of a pencil = $1.50

His goal is to achieve $300

So,

The number of fruit baskets required to sell by the Juan = 300.00/16.50

⇒ 18.18 (rounding off)

⇒ 18 fruit baskets

And

Then 2 more pencils are to be sold to achieve his goal.

Therefore, 18 fruit baskets need to be sold by Juan.

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Answer:

The first two terms are √2 and 6.

Step-by-step explanation:

a3^2+4=1604

a3=40

a2^2+4=40

a2=6

a1^2+4=6

a1=√2

The first two terms are approximately a1 ≈ 2.52 and a2 ≈ 6.33.

First Two Terms of the Sequence

To find the first two terms of the sequence defined recursively by the formula an = (an-1)2, given that a4 = 1604, we need to work backwards.

Step-by-Step Explanation:

Therefore, the first two terms of the sequence are approximately a1 ≈ 2.52 and a2 ≈ 6.33.

Answer:

Step-by-step explanation:

Without brackets, we are not exactly sure what is under the root sign. There are 3 choices.

sqrt(x) + 2 - 15 = - 3

sqrt(x + 2) - 15 = - 3

sqrt(x + 2 - 15) = - 3

I think the middle one is what you intend. If not leave a note.

sqrt(x + 2) - 15 = - 3                Add 15 to both sides.

sqrt(x + 2) - 15+15 = - 3+15     Combine

sqrt(x + 2) = 12                        Square both sides

x + 2 = 12^2                             Do the right

x + 2 = 144                               Subtract 2 from both sides.

x + 2-2 = 144-2

x = 142

Answer:

142

Step-by-step explanation:

Answer:

The ratio of their surface areas is 4:49

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

In this problem the scale factor is equal to the ratio 2:7

and

Remember that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore

In this problem the ratio of their surface areas is (2:7)^2 = 4:49

The ratio of their surface areas is,

⇒ 4 : 49

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

\

We know that;

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor.

In this problem the scale factor is equal to the ratio 2/7,

Hence, If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore,

In this problem the ratio of their surface areas is ,

⇒ (2 / 7)²

⇒ 4 / 49

⇒ 4 : 49

Thus, The ratio of their surface areas is,

⇒ 4 : 49

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Answer:

$1,466.23 Will be your answer mate !!!!!!

Step-by-step explanation:

The present value is calculated by discounting each of the cash flows to the present therefore if we assume no salvage value:  

PV = $100 / 1.08 + $100 / 1.08^2 + $100 / 1.08^3 + $200 / 1.08^4 + $300 / 1.08^5 + $600 / 1.08^6  

PV = $923.98  

Technically, as we have assumed there are no salvage value then in the future value will be zero. If you are asking how much remains in the investment. If you are asking how much the investment has yielded, keep in mind that the cash flows are not by definition reinvested so the time value of those cash flows can't be accounted for. If you do not account for the time value of those cash flows then the future value is just:  

$100 * 3 + $200 + $300 + $500 = $1,300  

However if you use the 8% per annum effective rate as a discount rate to take into consideration the time value of the money which is basically saying that you can reinvest the cash flows at 8% per annum effective then the future value would be:  

$100 * 1.08^5 + $100 * 1.08^4 + $100 * 1.08^3 + $200 * 1.08^2 + $300 * 1.08 + 500 = $1,466.23

you'll get your answer as : $1,466.23 !

Final answer:

The present value of the investment with varying cash flows and an 8% discount rate is $943.28. The future value, assuming reinvestment at an 8% interest rate until the end of Year 6, is $1,466.23.

Explanation:

To calculate the present value of the investment with varying cash flows and an 8% discount rate (interest rate), we discount each cash flow to its present value using the formula [tex]PV = FV / (1 + r)^t,[/tex]where PV is present value, FV is future value, r is the annual interest rate, and t is the number of years until the payment.

Year 1:  [tex]\$100 / (1 + 0.08)^1 = $92.59[/tex]

[tex]Year 2: \$100 / (1 + 0.08)^2 = $85.73 \\Year 3: \$100 / (1 + 0.08)^3 = $79.38 \\Year 4: \$200 / (1 + 0.08)^4 = $150.26 \\Year 5: \$300 / (1 + 0.08)^5 = $220.08 \\Year 6: \$500 / (1 + 0.08)^6 = $315.24 \\[/tex]

The sum of these values is the total present value of the investment, which equals $943.28.

For the future value, we grow each cash flow by the interest rate for the remaining period it would be invested until the end of Year 6, since payments are made at the end of each year.

[tex]Year 1: \$100 * (1 + 0.08)^5 = $146.93 \\Year 2: \$100 * (1 + 0.08)^4 = $136.05 \\Year 3: \$100 * (1 + 0.08)^3 = $125.97 \\Year 4: \$200 * (1 + 0.08)^2 = $233.28 \\Year 5: \$300 * (1 + 0.08)^1 = $324.00 \\[/tex]

Year 6: $500 = $500.00

By adding all future values, the total future value of the investment is $1,466.23.

Answer:

x= 42/5

alternative forms:

x=8 2/5

x=8.4

Step-by-step explanation:

Start with x-1/6x=7

Multiply both sides by 6 to get 6x-x=42

combine like terms (the Xs) to get 5x (6x-x is 5x)

5x=42

divide both sides by 5 to get x=42/5

Answer:

x = 42/5

Step-by-step explanation:

x -1/6x=7

Get a common denominator

6/6x - 1/6 x = 7

5/6x = 7

Multiply each side by 6/5 to isolate x

6/5 * 5/6x = 6/5*7

x = 42/5

Answer:

-0.89 < -0.51

B. Felipe's Restaurant has less value than Ming's Lodge.

Step-by-step explanation:

If you have a big debt you're going to have less money.

Answer:

Option The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above

the line

Step-by-step explanation:

we have

[tex]y>3x-8[/tex]

The solution of the inequality is the shaded area above the dashed line The equation of the dashed line is [tex]y=3x-8[/tex]

The slope of the dashed line is positive [tex]m=3[/tex]

The y-intercept of the dashed line is -8

see the attached figure to better understand the problem

Answer:

D is the correct answer

Step-by-step explanation:

Answer:

=

Step-by-step explanation:

9/10  vs 36/40

Multiply 9/10 by 4/4 so the denominators are equal

9/10*4/4 = 36/40

36/40 vs 36/40

They are equal

Answer:

The answer is (2,-2)

You just distribute the 2 into (1,1) and same with the -4 into (0,1) and add them together ‍

Step-by-step explanation:

ANSWER

[tex]\binom{2 }{ - 2}[/tex]

EXPLANATION

We were given the vector equation:

[tex]2 \binom{1}{1} ) - 4 \binom{0}{1} [/tex]

We perform the scalar multiplications first to get:

[tex]\binom{2 \times 1}{2 \times 1} ) - \binom{4 \times 0}{4 \times 1}[/tex]

Simplify the components of each vector

[tex]\binom{2 }{2} - \binom{0}{4}[/tex]

We subtract the corresponding components of the vector to get:

[tex]\binom{2 - 0}{2 - 4} [/tex]

This simplifies to

[tex]\binom{2 }{ - 2}[/tex]

Gradient is the slope of the line.

Use two points of the graphed line to find the slope, which is the change in Y over the change in x.

I'll use the points (4,0) and (6,8)

Slope = (8-0) / 6/4) = 8/2 = 4

The gradient is 4

Answer:

10/60 as a decimal is:

0.166666667

Step-by-step explanation:

To get 10/60 converted to decimal, you simply divide 10 by 60.

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Answer:

0.166666666666667

Step-by-step explanation:

Answer:

a = 16

First exclude any restricted values of y.

6/y = 9/24 , y is not equal 0

Simplify the right side of the equation using 3.

6y = 3/8

Cross multiply.

6 x 8 = 3

3 x y = 3y

6 x 8 = 3y

48 = 3y

Switch the sides of the equation.

3y = 48

Divide both sides by 3.

3y/3 = y

48/3 = 16

Answer:

my bad if im wrong but im pretty sure its b

Step-by-step explanation:

Answer:

The 99.7% confidence interval for the mean here is

[tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].

Step-by-step explanation:

The data in this question comes from random samples. In other words, the true population data are not known. Assume that both the sample average and the sample stdev are unbiased estimates for the population mean and stdev.  

The sample size 196 is sufficient large, such that the central limit theorem will apply. By the central limit theorem, the distribution of the mean (as well as the sum) of a sufficiently large samples resembles normal distributions. However, since stdev is only an estimate, the confidence interval can only be found using the Student's t-distribution.

What is the confidence interval for the mean of a random variable that follows the t-distribution?

[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex],

where

What is not given is

Start by determining the degree of freedom [tex]df[/tex] of [tex]t[/tex]. The degree of freedom for a one-variable estimate is usually equal to [tex]n -1[/tex] (that is: sample size minus one.) For this question, [tex]n = 196[/tex] so [tex]df = 196 - 1 = 195[/tex].

If [tex]T[/tex] represent a random variable that follows the [tex]t_{195}[/tex]-distribution, the value of t shall ensure that

[tex]P(-t \le T \le t) = \text{Confidence Interval} = 0.997[/tex].

The t-distribution is symmetric. As a result,

[tex]\displaystyle P(T > t) = 0.997 + \frac{1}{2}\times (1 - 0.997) = 0.9985[/tex].

Find the value of [tex]t[/tex] either with a t-distribution table or with technology. Keep in mind that for this question, [tex]df = n - 1 = 195[/tex].

[tex]t \approx 3.00549[/tex].

Apply the formula for the confidence interval:

[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex].

Lower bound:

[tex]\displaystyle \bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 - 3.00549\times \frac{3.5}{\sqrt{196}}\approx 11.2[/tex].

Upper bound:

[tex]\displaystyle \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 + 3.00549\times \frac{3.5}{\sqrt{196}}\approx 12.8[/tex].

In other words, the 99.7% confidence interval for the actual concentration is [tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].

Answer:

C. (3, 2)

Step-by-step explanation:

(3, 2) is the solutions to the inequality y ≤ 2x − 4 shaded region.

Answer:

Option D is correct.

Step-by-step explanation:

The first value is 1/32

if we multiply 1/32 with 2 i.e 1/32*2 we get 1/16

So, next value is 1/16

if we multiply 1/16 with 2 i.e 1/16 * 2 we get 1/8

So, next value is 1/8

if we multiply 1/8 with 2 i.e 1/8 * 2 we get 1/4

So, next value is 1/4

if we multiply 1/4 with 2 i.e. 1/4 *2 we get 1/2

so, next value is 1/2

if we multiply 1/2 with 2 i.e 1/2 * 2 we get 1

So, Option D multiply the previous value by 2 is correct.

Answer:

2x - (x/2) >12

Step-by-step explanation:

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Answer:

a = 5, b=1

Step-by-step explanation:

We can rewrite a whole number as a fraction by putting it over 1

5/1 = 5

a = 5, b=1

5/1 is a rational number since it can be written in the form a/b

Answer:

[(-15, 21), (-6, 12).(-1, 7)}

Step-by-step explanation:

we have

x+y=6

Find the values of y for XE (-15, -6, -1)

so

For x=-15

-15+y=6 --->y=21

therefore

a solution is the point (-15,21)

For x=-6

-6+y=6 --->y=12

therefore

a solution is the point (-6,12)

For x=-1

-1+y=6 --->y=7

therefore

a solution is the point (-1,7)

The set of ordered pairs that are solutions is

[(-15, 21), (-6, 12).(-1, 7)}

Final answer:

The correct set of ordered pairs, which are the solutions to the equation x + y = 6 given x in {-15, -6, -1}, is {(-15, 21), (-6, 12), (-1, 7)}.

Explanation:

To determine which set of ordered pairs are solutions to the given equation x + y = 6, we need to plug the x-values into the equation and solve for y.

The correct set of ordered pairs is therefore {(-15, 21), (-6, 12), (-1, 7)}.

The origin O appears rotated by 180° about ’( -2,0), (-4,0), (-5,2) , ’(-1,2).

Coordinate geometry (or analytic geometry) is described as the examination of geometry and the use of coordinate factors. using coordinate geometry.

Coordinate using the horizontal and vertical distances from the two reference axes. generally represented by way of (x,y) the x-price and y-cost.

Coordinate geometry is used to control and regulate air visitors. The coordinates of the flight are used to describe the plane's modern location. despite the fact that a plane actions a tiny distance (up, down, forward, or backward), the machine updates the coordinates of flight for each small change in its role.

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Answer:

D

Step-by-step explanation:

There are infinitely many possible parallelograms.  The angles are fixed at 50° and 130°, and two parallel sides are fixed at 10 cm, but the other two sides can have any length (except 10 cm).

Working and answer in the photo above. Hope this helps

The answer is going to be 19.

Answer:

C. 19

Step-by-step explanation:

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

[tex]|-7|=7[/tex]

[tex]3|4|=3*4=12[/tex]

Add.

[tex]7+12=19[/tex]

[tex]19[/tex], is the correct answer.

Answer:

y = 1/4 x - 1.

Step-by-step explanation:

The slope (from the 2 given points) =  (0 - -1) / (4 - 0) = 1/4.

The y-intercept is at y = -1, so the equation is:

y = 1/4 x - 1.

Answer:

12

Step-by-step explanation:

Volume of cylinder is pi*r^2*h    (this is equal to 540pi in this case)

So we have 540pi=pi*r^2*h  

this means that 540=r^2*h   (I just divided both sides by pi since both sides were being multiplied by pi)

The height,h, is 15 so plug in 540=r^2*15

Divide both sides by 15 giving 540/15=r^2

So r^2=36

So r=6

The diameter,d, is twice the radius, r.

So d=2(6)=12

Answer:

b. 12

Step-by-step explanation:

The volume of a cylinder is

[tex]\pi {r}^{2} h[/tex]

Let us compose an equality and solve for the radius.

540pi = pi × r^2 × 15.

Divide both sides of the equation by 15pi.

r^2 = 36

r = +/- 6.

Length cannot be negative, so r = 6.

diameter = 2 × r. In this case,

d = 2 × 6 = 12.

The diameter is 12 ft.

Answer:

3

Step-by-step explanation:

Range is the largest number minus the smallest number

4-1 = 3

The range is 3

Answer:

3

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set.

Sort your data from lowest to highest. You get

1, 2, 3, 4, 4, 4, 4, 4

Highest value = 4

Lowest value = 1

           Range = 3  chocolate chips

For this case we have the following equation:

[tex]81x = x ^ 2[/tex]

Rewriting we have:

[tex]x ^ 2-81x = 0[/tex]

We take common factor "x" from both terms:

[tex]x (x-81) = 0[/tex]

It is observed that equality is fulfilled when x = 0 and when x = 81

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = 81[/tex]

Answer:

[tex]x_ {1} = 0\\x_ {2} = 81[/tex]

Answer:

15% of 38= 5.7

Round up to 6

Answer: b) $6

Step-by-step explanation:

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