What is the area of a circle with a radius of 13 cm
?
(Use 3.14 for Pi.)

Answer:

40

Step-by-step explanation:

There are 6 sides. Four sides have 8 squares, 4 * 2, and the other 2 sides have 4, 2 * 2. 8 * 4 = 32, 4 * 2 = 8, 32 + 8 = 40

Answer:

it is (4,120)

hope this helps you

Answer:

Gary is now 24years

Step-by-step explanation:

let the age of Jan be x and that of Gary be x+15

in six years time they will be as follows

Jan =x+6

Gary=x+15+6=x+21

2(x+6)=x+21

2x+12=x+21

collect the like terms

2x-x=21-12

x=9

Gary =9+15=24years

Answer:

7/4 is larger than -4/7

Step-by-step explanation:

7/4 is greater than a whole. 4/4 = 1 whole and the fraction is 7/4. -4/7 is smaller than a whole and is a negative number.

Therefore 7/4 is bigger

Hope this helps!

Answer:

yes 7/4 is bigger than -4/7

Step-by-step explanation:

its bigger because its positive!

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Answer:

Step-by-step explanation:

a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.

The irrigation system is positioned 7.5 feet above the ground

__

b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...

  h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet

The spray reaches a maximum height of 32.5 feet at a horizontal distance of 5 feet from the sprinkler head.

__

c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.

The spray reaches the ground at about 10.7 feet away.

Answer:

7.5

32.5

5

maximum

10.7

Step-by-step explanation:

Answer:

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Linear pair of angles are supplementary (180°).

So,

(3q) + (15q + 18) = 180°.

Answer:

Sum = 19,662

Step-by-step explanation:

Given that this is a finite geometric series (meaning it stops at a specific term or in this case -24,576), we can use this formula:  

[tex]\frac{a(1-r^n)}{1-r}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.

Substituting for everything and simplifying gives us:

[tex]\frac{6(1-(-4)^7)}{1-(-4)} \\\\\frac{6(16385}{5}\\ \\\frac{98310}{5}\\ \\19662[/tex]

Step-by-step explanation:

t8 = a1 + (n - 1)*d

t8 = 17

17 = a1 + 7*d

t12 = 25

25 = a1 + 11d

17 = a1 + 7d Subtract

8 = 4d Divide by 4

8/4 = 4d/4

2 = d

17 = a1 + 7d

17 = a1 + 7*2

17 = a1 + 14 Subtract 14

3 = a1

Sum 20 terms

The 20 term = a1 + 19*2

The 20 term = 3 + 38

= 41

Sum = (a1 + a20) * 20 / 2

Sum = (3 + 41)* 20/2

Sum = 44 * 10

Sum = 440

Answer:

Step-by-step explanation:

4*(n +5) - 2*(5 + 7n) = -70

4*n + 4*5 + 5*(-2) + 7n*(-2) = -70

4n + 20 - 10 - 14n = -70

4n - 14n + 20 - 10 = -70

- 10n + 10 = -70

Subtract 10 from both sides

-10n = -70 - 10

-10n = -80

Divide both sides by (-10)

n = -80/-10

n = 8

Step-by-step explanation:

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If the slope of the line y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.

The general formula for calculating an equation of a line is expressed as:

[tex]y = mx + b[/tex] where:

m is the slope of the line

Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:

[tex]mx=1x\\[/tex]

Divide through by x

[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]

Hence the slope of the line y = x - 1 is 1.

According to the question, since we are told that the  slope of the line

y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

Learn more about the slope of a line here: https://brainly.com/question/16949303

Answer:

Step-by-step explanation:

Hello!

√32 × √24 =

= √768 =

= 16√3

Good luck! :)

Answer:

16×sqrt(3)

Step-by-step explanation:

what full square numbers are factors in the numbers under the square root that we can pull out ?

and then multiply the rest under the square root and possibly repeat one more time.

32 = 16×2

16 is a great square number.

in 24 we find 4 as the largest square factor.

so,

sqrt(32)×sqrt(24) = sqrt(16×2)×sqrt(4×6) =

= 4×sqrt(2)×2×sqrt(6) = 8×sqrt(2×6) = 8×sqrt(12) =

= 8×sqrt(4×3) = 8×2×sqrt(3) = 16×sqrt(3)

Answer:

n(B) = 1350

Step-by-step explanation:

Using Venn sets, we have that:

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

Three values are given in the exercise.

The other is n(B), which we have to find. So

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

[tex]2290 = 1300 + n(B) - 360[/tex]

[tex]940 + n(B) = 2290[/tex]

[tex]n(B) = 2290 - 940 = 1350[/tex]

So

n(B) = 1350

Answer:

the number of flight lines needed is approximately 72

Step-by-step explanation:

Given the data in the question;

Aerial photography is to be taken of a tract of land that is 8 x 8 mi²

L × B = 8 x 8 mi²

Flying height H = 4000 ft = ( 4000 × 12 )inches = 48000 in

focal length f = 6 in

[tex]l[/tex] × b = 9 × 9 in²

side overlap = 30% = 0.3

meaning remaining side overlap = 100% - 30% = 70% = 0.7

{ not end to end overlap }

we take 100% { remaining overlap }

[tex]l[/tex]' = 9 × 100% = 9 in

b' = 9 × 70% = 6.3 in

Now the scale will be;

Scale = f/H

we substitute

Scale = 6 in /  48000 in = 1 / 8000

so our scale is; 1 : 8000

⇒ 1 in = 8000 in

⇒ 1 in = (8000 / 63360)mi

⇒ 1 in = 0.126 mi

so since

L × B = 8 x 8 mi²

[tex]l[/tex]' = ( 9 × 0.126 mi ) = 1.134 mi

b' = ( 6.3 × 0.126 mi ) = 0.7938 mi

Now we get the flight lines;

N = ( L × B ) / ( [tex]l[/tex]' × b' )

we substitute

N = ( 8 mi × 8 mi ) / ( 1.134 mi × 0.7938 mi )

N = 64 / 0.9001692

N = 71.0977 ≈ 72

Therefore, the number of flight lines needed is approximately 72

Answer:

[tex](a)\ Area = 13.0695[/tex]

[tex](b)\ Area = 26.139[/tex]

Step-by-step explanation:

Given

The attached image

Solving (a): The area (one side up)

This is calculated as:

Area= Area of semicircle + Area of rectangle

So, we have:

[tex]Area = \pi r^2 + l *w[/tex]

Where:

[tex]l,w =2,3[/tex] --- the rectangle dimension

[tex]d = 3[/tex] --- the diameter of the semicircle

So, we have:

[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]

[tex]Area = \pi * 2.25 + 6[/tex]

[tex]Area = 2.25\pi + 6[/tex]

[tex]Area = 2.25*3.142 + 6[/tex]

[tex]Area = 13.0695[/tex]

Solving (b): Area when both leaves are up.

Simply multiply the area in (a) by 2

[tex]Area = 2 * 13.0695[/tex]

[tex]Area = 26.139[/tex]

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is [tex]\frac{dx}{dt}[/tex] when y = 6 and [tex]\frac{dy}{dt}=-2[/tex].

The equation for Pythagorean's Theorem is

[tex]x^2+y^2=c^2[/tex] where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:

[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and divide everything by 2 to simplify:

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Looking at that equation, it looks like we need a value for x, y, [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex].

Since we are looking for [tex]\frac{dx}{dt}[/tex], that can be our only unknown and everything else has to have a value. So what do we know?

If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:

[tex]x^2+6^2=10^2[/tex] and

[tex]x^2+36=100[/tex] and

[tex]x^2=64[/tex] so

x = 8.

NOW we can fill in the derivative and solve for [tex]\frac{dx}{dt}[/tex].

Remember the derivative is

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so

[tex]8\frac{dx}{dt}+6(-2)=0[/tex] and

[tex]8\frac{dx}{dt}-12=0[/tex] and

[tex]8\frac{dx}{dt}=12[/tex] so

[tex]\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec[/tex]

Answer:

the total number of participants required is 90

Step-by-step explanation:

Given the data in the question;

Factor A has three levels

Factor B has three levels

sample size n; ten participants

we have two Way ANOVA involving Factor A and Factor B.

Now,

{ Total # Participants Required } = { #Levels factor A } × { #Levels factor B } × { Sample size of each level }

we substitute

{ Total # Participants Required } = 3 × 3 × 10

{ Total # Participants Required } = 9 × 10

{ Total # Participants Required } = 90

Therefore, the total number of participants required is 90

Hello,

[tex]\widehat{A}=180^o-24.4^o-103.6^o=52^o\\\\\dfrac{sin(24.4^o)}{37.3} =\dfrac{sin(103.6^o)}{c} \\\\\\c=87.760246\approx{87.8}\\\\\\\dfrac{sin(52^o)}{a} =\dfrac{sin(24.4^o)}{37.3} \\\\\\a=71.1510189...\approx{71.2}\\[/tex]

Answer:

(b)

Step-by-step explanation:

Given

[tex]8x + 3y = 24[/tex]

Required

The graph

First, make y the subject

[tex]3y = 24 - 8x[/tex]

Divide through by 3

[tex]y = 8 - \frac{8}{3}x[/tex]

Let x = 3

[tex]y = 8 - \frac{8}{3}*3 = 8 - 8 = 0[/tex]

Let x = 6

[tex]y = 8 - \frac{8}{3}*6 = 8 - 16 = -8[/tex]

So, we plot the graph through

[tex](3,0)[/tex] and [tex](6,-8)[/tex]

See attachment for graph

Answer:

0.9936 = 99.36% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

Step-by-step explanation:

For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Assume that there is a 8​% rate of disk drive failure in a year.

So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]

Two disks are used:

This means that [tex]n = 2[/tex]

What is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive?

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]

0.9936 = 99.36% probability that during a​ year, you can avoid catastrophe with at least one working​ drive

Answer:

The cutoff time be for concert setup should be of 51.4 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Average time it takes their sound tech to set up for a show is 56.1 minutes, with a standard deviation of 6.4 minutes.

This means that [tex]\mu = 56.1, \sigma = 6.4[/tex]

If the band manager decides to include only the fastest 23% of sound techs on the tour, what should the cutoff time be for concert setup?

The cutoff time would be the 23rd percentile of times, which is X when Z has a p-value of 0.23, so X when Z = -0.74.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.74 = \frac{X - 56.1}{6.4}[/tex]

[tex]X - 56.1 = -0.74*6.4[/tex]

[tex]X = 51.4[/tex]

The cutoff time be for concert setup should be of 51.4 minutes.

Answer:

4, 8, 16, 32, ...

Step-by-step explanation:

8 / 4 = 2

16 / 8 = 2

32 / 16 = 2

Common ratio is 2

So, The sequence 4, 8, 16, 32, …. is geometric.

Answer:

option D

Step-by-step explanation:

[tex]sin^2 ( \frac{3\pi}{2}) + cos^2(\frac{3\pi}{2}) = 1\\\\( -1)^2 + 0^2 = 1[/tex]

Explanation:

[tex]sin x = cos( \frac{\pi}{2} - x)\\\\sin(\frac{3\pi}{2}) = cos ( \frac{\pi}{2} - \frac{3\pi}{2})\\[/tex]

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

Therefore ,

               [tex]sin^2( \frac{3\pi}{2}) = ( - 1)^2[/tex]

Answer:

5 * 2 + 3(4 + 2) - 4(5 * 2)

= 10 + 3(6) - 4(10)

= 10 + 18 - 40

= 28 - 40

= -12

Answer:

yes your answer is right

Answer:

Yes it's Perfectly correct

Answer:

for each dress she used 6/3 of material

=2

then for a curtain =2x4=8 materials

Answer:

CI  95 %  =  (  28.92  ;  41.08 )

Step-by-step explanation:

Sample Information:

sample size    n  =  30

sample mean  =  35 %

sample standard deviation   s = 17

To construct a CI  95 %

significance level is    α  = 5 %   α = 0.05      α/2  =  0.025

z critical for α/2 from z- table is :   z (c) = 1.96

CI  95 %  =  (  x  ±  z(c) * s/√n )

CI  95 %  =  (  35 ± 1.96 * 17/√30 )

CI  95 %  =  (  35 ±  6.08 )

CI  95 %  =  (  28.92  ;  41.08 )

Answer:

He remained with 25 goats.

Step-by-step explanation:

35 - 10 = 25

Hope this helps.

Answer:

He remained with 25 goats

Step-by-step explanation:

35 - 10 = 25

[tex]option(c) \: cylinder[/tex]

Step-by-step explanation:

You can see that in the figure, this is rectangle. Here, ABCD is rotated around the vertical line through A and D. So, you will get Cylinder shape as you rotate it.

Answer: 130 liters

Step-by-step explanation:

1 hectoliter = 100 liters

1.3 hectoliters = 1.3 · 100 = 130 liters