Find the volume of the figure below. Round to the nearest tenth.
7 cm
7 cm
9 cm
20 cm
11 cm

Answer:

a)x - 4y -14 =0

5x - y - 13 =0

Step-by-step explanation:

Using substitution method to solve equation above gives:

x - 4y - 14 =0 ....eq1

5x - y -13 =0 ....eqn2

From eqn1, making x the subject formula:

x - 4y - 14 =0

x - 4y =14

x = 14+4y ...eqn3

From eqn2, substitute value of x and solve for y:

5(14+4y)-y-13 =0

70+20y-y-13 =0

70+19y-13 =0

70 - 13 = -19y

57 = -19y

divide both sides by -19

-57/19 = -19y/-19, then

y = -3

From eqn1:

x = 14 + 4y

substitute the value of y in the expression above

x = 14 + 4(-3)

x = 14 + (-12)

x = 14 - 12

x = 2

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80

Step-by-step explanation:

We are given that you have a sample of 40 14-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 14-year-old has a score on the emotion recognition scale of 11.80.

Assume that scores on the emotion recognition scale are normally distributed.

Let [tex]\mu[/tex] = true average score on the emotion recognition scale

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80

This a right-tailed test because the higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion.

We can evaluate this hypothesis using One-sample t-test statistics or One-sample z-test statistics depends on the information given in the question.

If the z-test statistic is used, then the critical region at 0.05 level of significance will be an area more than the critical value of 1.645.

And if the t-test statistic is used, then the critical region at 0.05 level of significance with 39 degrees of freedom will be an area more than the critical value of 1.685.

The null hypothesis should be considered as the [tex]H_0: \mu = 11.80[/tex]

The alternative hypothesis should be considered as the [tex]H_A: \mu > 11.80[/tex]

It is the right-tailed test.

Since The average 14-year-old has a score on the emotion recognition scale of 11.80.

So here the null hypothesis should be [tex]H_0: \mu = 11.80[/tex]

And, here it is the right-tailed test since there should be higher the score on the given scale, due to this it should strongly an emotion that represent for rightly identified. Also high scores represent the high difficults for recording the emotion.

Learn more about hypothesis here: https://brainly.com/question/18831983

Answer:

Step-by-step explanation:

Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;

m = −0.05x²+3.5x−49

when m= 9

9 = −0.05x²+3.5x−49

−0.05x²+3.5x−49 = 9

0.05x²-3.5x+49 = -9

Multiplying through by 100

5x²+350x−4900 = 900

Dividing through by 5;

x²+70x−980 = 180

x²+70x−980 - 180 = 0

x²+70x−1160 = 0

Using the general formula to get x;

a = 1, b = 70, c = -1160

x = -70±√70²-4(1)(-1160)/2

x = -70±√4900+4640)/2

x = -70±(√4900+4640)/2

x = -70±√9540/2

x =  -70±97.7/2

x = -70+97.7/2

x = 27.7/2

x = 13.85mph

x ≈ 14 mph

Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph

Answer:

$0.558

Step-by-step explanation:

The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:

Then our expected value can be calculated as:

[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]

Answer:

x < -( 8-2b) /a  a > 0

Step-by-step explanation:

−ax + 2b > 8

Subtract 2b from each side

−ax + 2b-2b > 8-2b

-ax > 8 -2b

Divide each side by -a, remembering to flip the inequality ( assuming a>0)

-ax/-a < ( 8-2b) /-a

x < -( 8-2b) /a  a > 0

Answer: [tex]x<\frac{-8+2b}{a}[/tex]

                  [tex]a>0[/tex]

Step-by-step explanation:

[tex]-ax+2b>8[/tex]

[tex]\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}[/tex]

[tex]-ax>8-2b[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]

[tex]\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)[/tex]

[tex]ax<-8+2b[/tex]

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

[tex]\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0[/tex]

[tex]x<\frac{-8+2b}{a};\quad \:a>0[/tex]

Answer:

50

Step-by-step explanation:

The ratio of marked fish to caught fish is 4:10, we need to solve for x in 20:x, since 4 * 5 = 20, 10 * 5 = x so x = 50 fish.

Answer:

5 1/7

Step-by-step explanation:

To find the mean, add up all the numbers and then divide by the number of numbers

(10+ 6+ 9+ 6+ 2+ 0+ 3)/7

The sum of all the numbers is 36 and there are 7 numbers

36/7 =

7 goes into 36  five times with 1 left over

5 1/7

Answer:

5.143

Step-by-step explanation:

Add them all up then divide by the amount of numbers there are.

Answer:

its a postulate

Step-by-step explanation:

The statement represents a geometric postulate.

A postulate is one of the basic concepts of geography, and indicates an assumption that is accepted as true in the given theory.  

In this way, the main characteristic of the postulate is its general acceptance by the spectrum that studies it, that is, by the totality or vast majority of the scientists who are dedicated to its analysis.

Learn more in https://brainly.com/question/17252827

You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:

[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]

We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].

We also need to have

[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]

Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means

[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]

Then

[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]

So we end up with

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

Answer:

Step-by-step explanation:

In the form ...

  y(t) = Asin(ωt +φ)

you have ...

The translation from ...

  y(t) = 2sin(4πt) +5cos(4πt)

is ...

  A = √(2² +5²) = √29 . . . . the amplitude

  ω = 4π . . . . the angular frequency in radians per second

  φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift

Then, ...

  y(t) = √29·sin(4πt +1.1903)

_____

Comment on the conversion

You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)

If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.

Answer:

[tex]Probability = \frac{1}{8}[/tex]

Step-by-step explanation:

Given

Box of Cards -- 1 -- 2 -- 3 -- 4 -- 5 -- Total

Black --------------1 ---1 ----1 ----1 ---1 ----5

Red ---------------- 1 ---1 ----1 ----0--- 0--- 3

Total --------------- 2 ---2 --2-----1 -----1 ---8

Required

Determine the probability of a card being black and being card 1

To solve this, we the the number of card 1 that is black

This is shown below

Box of Cards -- 1

Black --------------1

This implies that, 1 card is black and also card 1

Represent this with [tex]n(Black\ and\ 1)[/tex]

[tex]n(Black\ and\ 1) = 1[/tex]

Next, is to get the total number of cards

From the given parameters;

[tex]Total = 8[/tex]

The probability is calculated as follows

[tex]Probability = \frac{n(Black\ and\ 1)}{Total}[/tex]

[tex]Probability = \frac{1}{8}[/tex]

Answer:The answer is c

Step-by-step explanation:

Answer: The rule of complements is apprising us that, the person selected will.eithwr have a type B blood or will not have a type B blood

Step-by-step explanations:

Find explanations in the attachment

Answer:

There are 23 people in line at 6:00 A.M

Step-by-step explanation:

When you plug in h=1, we get 23 people

h corresponds with the time 6:00 am, as a result there are 23 people in line

The equation represents how many people will come as the hour increases.

23 represents the initial amount of people in line.

(got this from Khan academy too:))

Answer:

a equals 105°

Step-by-step explanation:

angles in a straight line add up to 180°

a+75=180

a=180-75

a=105°

Step-by-step explanation:

The general form of a sine wave is:

y = A sin(2π/T x − B) + C

where A is the amplitude,

T is the period,

B is the phase (horizontal shift),

and C is the midline (vertical shift).

f(x) = 2 sin(πx)

This is a sine wave with an amplitude of 2, a period of 2, a phase of 0, and a midline of y=0.

To graph, the wave is centered at y=0 and has zeros every half period (x = 0, 1, 2, 3, etc.).  Between the zeros, the wave is either a min or max (±2).

The domain of the function is (-∞, ∞).

The range of the function is [-2, 2].

Answer:

For

[tex]f(x) = 2\sin(\pi x)[/tex]  

the domain is the real numbers, Range = [-2,2]

Step-by-step explanation:

About the domain, you can take any number, remember that the domain are the "x" that you can plug in on your function, for this case, you can plug in any value and you will have no problem.

Think about it like this, if you have f(x)= 1/x  , you can't plug in x=0, but you can plug in all the other numbers, so the domain of that function would be all numbers except 0.

Therefore  for

[tex]f(x) = 2\sin(\pi x)[/tex]

the domain is the real numbers.

About the range, it is the "y" axis, which numbers can you reach on the "y" axis, if you graph the function you will see that it is between [-2,2]

Range = [-2,2]

check the image I attach.

Answer:

It will take Mrs Chandler 18 hours 45 minutes or 18.75 hours to catch up Mr Chandler

Step-by-step explanation:

What we want to know here is that at how many hours will they have traveled same distance.

Let the total time taken by Mrs Chandler to catch up be x hours

Since Mr Chandler left 2.5 hours earlier , then the total time taken by him would be x + 2.5 hours

Now, we know that distance = speed * time

Since it’s same distance covered;

For Mr Chandler, his distance is calculated as 75(x + 2.5)

For Mrs Chandler, her distance is calculated as 85x

We equate both since they are equal;

75(x + 2.5) = 85x

75x + 187.5 = 85x

85x -75x = 187.5

10x = 187.5

x = 18.75 hours or 18 hours 45 minutes

Answer:

15 pt

Step-by-step explanation:

to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15

Answer:

add up c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

For the rectangle ABCD

AB= DC= 11

BC= AD= 2

Point E lies halfway between AB and CD

The shaded are forms two triangles, I'll refer to the upper triangle as "Triangle one" and the lower triangle will be "triangle 2"

The area of a triangle is calculated as

[tex]a= \frac{bh}{2}[/tex]

b= base

h= height

Triangle 1

b₁= AB= 11

[tex]h_1= \frac{BC}{2}= \frac{2}{2}= 1[/tex]

[tex]a_1= \frac{b_1h_1}{2}= \frac{11*1}{2}= 5.5[/tex]

Triangle 2

b₂= DC= 11

[tex]h_2= \frac{BC}{2}= \frac{2}{2} = 1[/tex]

[tex]a_2= \frac{b_2h_2}{2}= \frac{11*1}{2}= 5.5[/tex]

Now you add the areas of both triangles to get the area of the shaded region:

a₁ + a₂= 5.5 + 5.5= 11

Since point E is halfway to all sides of the rectangle, even tough it doesn't see so, the shaded area is equal to half the area of the rectangle:

area= bh= DC*AD= 11*2= 22

area/2= 22/12= 11

I hope this helps!

Step-by-step explanation:

8.x×8-12=50

8x-12=50

9.1/2x>or=100

10.2 whole number5/9-x=31

Answer:

Step-by-step explanation:

The derivative of your function is ...

  y' = dy/dx = 2e^(2x) +6

At x=0, the value is ...

  y'(0) = 2e^0 +6 = 8

  dy = 8·dx

__

  Δy = y'(0)·Δx

  Δy = 8(.03)

  Δy = 0.24

Hey there! I'm happy to help!

PART A

There are 3 $1 bills, 1 $5 bill, and 1 $10 bill. This gives us 5 total bills.

First, we want to find the probability of winning $12. Well, to win, you have to draw the $10 bill. You only have room for two dollars beforehand to equal $12 dollars after pulling out the ten. So, this is the probability of drawing two one dollar bills and the the ten. Let's calculate this below.

[tex]\frac{3}{5} *\frac{1}{2} *\frac{1}{3} =\frac{1}{10}[/tex]

Where did I get these numbers from? Well 3 of the 5 bills are $1, so the first probability is 3/5. Then, if we draw one of the $1 bills, there are only 2 of those left and 4 total bills, so the probability is then one half. Finally, there would be only 3 left and you need to pick the $10 bill, which is a probability of 1/3.

The probability of winning $12 is 1/10 or 10%.

PART B

Now, we want to find the probability of picking every single bill before the ten. This means that we pick the three one dollar bills and the five dollar bill before the ten.

To pick the first $1 bill, our probability is 3/5, and then for the second it is 1/2. For the third, there are three total cards and 1 $1 bill, so the probability is 1/3. Then we have a 1/2 chance of picking the $5 bill over the $10 bill, giving us this solution.

[tex]\frac{3}{5} * \frac{1}{2} * \frac {1}{3} * \frac{1}{2}= \frac{1}{20}[/tex]

The probability of winning all bills in the urn is 1/20 or 5%.

PART C

For this event, we want to get any bill that isn't the $10 and then we want the $10 on the second one.

Since there are 4 bills that aren't the $10, our first probability is 4/5. Then, we only have 4 left, with 1 being the $10, so our second probability is 1/4.

[tex]\frac{4}{5}*\frac{1}{4}=\frac{1}{5}[/tex]

The probability of the game stopping at the second draw is 1/5 or 20%.

Have a wonderful day! :D

The probability of winning $12 will be 0.15.

The game stops after drawing$10 bill. There can also be 2 draws of $2 and $10 to make $12.

Therefore, the probability of winning $12 will be calculated thus:

= Probability of getting $2 × probability of getting $10

= 3/5 × 1/4

= 0.15

The probability of winning all balls in the urn will be:

= 4/5 × 3/4 × 2/3 × 1/2

= 0.2

Lastly, the probability of the game stopping at the second draw will be:

= First draw × Second draw

= 4/5 × 1/4

= 0.2

Learn more about probability on:

https://brainly.com/question/24756209

Answer:

0.2006

Step-by-step explanation:

The probability the first calculator is defective is 42/62.

The probability the second calculator is defective is 41/61.

The probability the third calculator is defective is 40/60.

The probability the fourth calculator is defective is 39/59.

The probability all four calculators are defective:

(42/62) (41/61) (40/60) (39/59) = 0.2006

Answer:

x = 0

Step-by-step explanation:

-7(5-3x)=-35

Divide by -7

-7/-7(5-3x)=-35/-7

5 -3x = 5

Subtract 5 from each side

5-3x-5 = 5-5

-3x=0

Divide by -3

x=0

Answer: x = 0

Step-by-step explanation: Start by distributing the -7 through the parenthses on the left side of the equation.

-7(5) is -35 and -7(-3x) is 21x.

So we have -35 + 21x = -35.

Next, isolate the x term by adding 35 to both sides.

When we do this, we get 21x = 0.

Now divide both sides by 21 and x = 0.

Answer:

U = 17 1/7

T = 51 3/7

S = 61 3/7

Step-by-step explanation:

Given

T+S+U=130\

T=3(U)

S= T+10 we have to find value of u

First step:

find S and T in terms of U

T is given

T = 3U

S = T +10 , using T = 3U

S = 3U+10

Using the above value in T+S+U=130

3U + 3U+10 + U = 130

=> 7U = 130-10 = 120

=> U = 120/7 = 17 1/7

T = 3U = 3*120/7 = 360/7 = 51 3/7

S = T+10 = 360/7 + 10 = (360+70)/7 = 430/7 = 61 3/7

Thus,

U = 17 1/7

T = 51 3/7

S = 61 3/7

Answer: Local Max = (-1, 0)

              Local Min = (1, -8)

Step-by-step explanation:

f(x) = (x + 1)² (x - 3)

Step 1: Find the zeros

(x + 1)² = 0 --> x = -1   (multiplicity of 2)

(x - 3) = 0  -->  x = 3

Step 2: Find the Vertices

x = -1 --> (multiplicity is even which means this is a vertex)

The midpoint between x = -1 and x = 3 is x = 1

Step 3:  Find the Local Max and Local Min

Use the x-value above to find the y-values

f(-1) = 0        because it is a zero

f(1) = (1 + 1)² (1 - 3)

    =    2²(-2)

    =    4(-2)

    =      -8

Conclusion:

(-1, 0) is the Local Max     bigger y-value

(1, -8) is the Local Min      smaller y-value

Answer:

f ( x ) = ( x – 3) 2 – 4; the minimum value is –4

Step-by-step explanation:

Given the function f ( x ) = x 2 – 6 x + 5, write an equivalent form of the function that reveals the minimum or maximum value of the function and state the minimum or maximum value.

f ( x ) = ( x – 3) 2 – 4; the minimum value is –4

( This The correct question to answer?) can't deleted..

Step-by-step explanation:

Hi there!!!

The answer is option A.

reason look in picture.

if you want to solve it just cross multiply it,

[tex]60x = 240000 \times 100[/tex]

or,

[tex]x = 24000000 \div 60[/tex]

and the answer would be 400000.

Hope it helps...

Answer:

2m - 9

Step-by-step explanation:

To simplify this, we need to combine like terms. m + m = 2m and -4 - 5 = -9 so the simplified version would be 2m - 9.

Answer:

8.2

Step-by-step explanation:

When you calculate it by 100, there are two zeros, so you move two decimals to the right.

This makes 8.2, and 8.2 will be the answer.

Another example could be... 0.082✖️10.

In this case, there is 1 zero, so you move the decimal to the right once, making it 0.82.

Hope this helps!!!

Answer:

8.2

Step-by-step explanation:

When you calculate it by 100, there are two zeros, so you move two decimals to the right.

so you will get 8.2

hope it helps you

Answer:

a. $849.45

Step-by-step explanation:

In the above question, we are given the following information

Coupon rate = 10%

Face value = 1000

Maturity = n = 20 years

t = number of periods = compounded semi annually = 2

Percent yield = 12% = 0.12

Bond Value formula =

C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)

C = coupon rate × face value = 10% × 1000 = 100

Bond value:

= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2

= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40

= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)

= 50 × 15.046296872 + 97.222187709

= $849.45

Bond value = $849.45