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Complete the sentences about simplifying this expression.

A probability of 1/10000 means that only one person can get the Pick 4 lottery among 10000 pickers.

The term probability has to do with the chance that an event will occur or not. Usually probability is expressed as a fraction.

The meaning of the saying that the  probability of picking the winning 4-digit number in a Pick 4 lottery is 1/10000 is that only one person can get the Pick 4 lottery among 10000 pickers.

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2800\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\dotfill &12 \end{cases} \\\\\\ A=2800e^{0.055\cdot 12}\implies A=2800e^{0.66}\implies A\approx 5417.42[/tex]

To solve this problem, we have to calculate the volume of a hemisphere and the volume of a cylinder and add them together. The volume of the glass can be only be calculated when we find the volume of the hemisphere and the volume of the cylinder and then add then up together.

The volume of a hemisphere is given as

[tex]v = \frac{2}{3} * \pi * r^3[/tex]

Data

Let's substitute the values into the equation and solve.

[tex]v = \frac{2}{3} * \pi * r^3\\v = 56.556cm^3\\[/tex]

The formula of volume of a cylinder is

[tex]v = \pi r^2 h[/tex]

data given

Let's substitute the values into the equation and solve

[tex]v = \pi r^2 h\\v = 3.142 * 3^2 * 3\\v = 84.834cm^3[/tex]

Let's add both volumes together so we have the volume of the glass cup

[tex]56.556 + 84.834 = 141.39cm^3[/tex]

The volume of the glass can be only be calculated when we find the volume of the hemisphere and the volume of the cylinder and then add then up together.

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Answer:

10 cm

Step-by-step explanation:

Answer:

write an article for publication in the daily graphic on the topic every school must have a library

Answer:

  4.0%

Step-by-step explanation:

If we assume that potential impact sites are uniformly distributed over the area, the probability of interest is the ratio of the area of Connecticut to the area of the circle within 200 miles of Hartford.

__

The area of a circle with radius 200 miles is ...

  A = πr²

  A = π(200 mi)² = 40000π mi² ≈ 125,664 mi²

The area of a rectangle 100 miles by 50 miles is ...

  A = LW

  A = (100 mi)(50 mi) = 5000 mi²

The probability of interest is the ratio of these areas:

  p(impact in CT) = (5000 mi²)/(125664 mi²) ≈ 0.03979

The probability the meteor landed in Connecticut is about 4.0%.

Answer:

At 4:40, the minute hand is on the 8, and the hour hand is two-thirds of the way from the 4 to the 5

Answer:

[tex]\dfrac{d^2y}{dx^2} = 5e^{3x} \sin (2x)+12e^{3x} \cos (2x)[/tex]

Step-by-step explanation:

[tex]\large \boxed{\begin{minipage}{5 cm}\textsf{\underline{Product Rule}}\\\\$ \textsf{When } \:y=uv\\\\\dfrac{dy}{dx}=u\dfrac{dv}{dx}+v \dfrac{du}{dx}$\\\end{minipage}}[/tex]

Given:

[tex]y=e^{3x} \sin(2x)[/tex]

First Derivative

[tex]\textsf{let } u=e^{3x} \implies \dfrac{du}{dx}=3e^{3x}[/tex]

[tex]\textsf{let } v= \sin(2x) \implies \dfrac{dv}{dx}=2 \cos (2x)[/tex]

Using the Product Rule:

[tex]\begin{aligned}\dfrac{dy}{dx} & =e^{3x}\cdot 2 \cos (2x) + \sin (2x) \cdot 3e^{3x}\\& = 2e^{3x} \cos (2x) + 3e^{3x} \sin (2x)\\& = e^{3x}(2 \cos (2x) + 3 \sin (2x))\end{aligned}[/tex]

Second Derivative

[tex]\textsf{let } u=e^{3x} \implies \dfrac{du}{dx}=3e^{3x}[/tex]

[tex]\textsf{let } v= 2 \cos (2x)+3 \sin (2x) \implies \dfrac{dv}{dx}=-4 \sin (2x) +6 \cos (2x)[/tex]

Using the Product Rule:

[tex]\begin{aligned}\dfrac{d^2y}{dx^2} & =e^{3x}(-4 \sin (2x) +6 \cos (2x)) +3e^{3x} (2 \cos (2x)+3 \sin (2x))\\& = e^{3x}[-4 \sin (2x) +6 \cos (2x)+6 \cos (2x)+9 \sin (2x)]\\& = e^{3x}[5 \sin (2x) +12 \cos (2x)]\\& = 5e^{3x} \sin (2x)+12e^{3x} \cos (2x)\end{aligned}[/tex]

Answer:

[tex] \tt{ \frac{ {d}^{2} y}{d {x}^{2} } = 5 {e}^{3x} \sin(2x) + 12 {e}^{3x} \cos(2x)}[/tex]

Step-by-step explanation:

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[tex]y = {e}^{3x} \sin(2x) \\ { \sf{To \: find}} \: \frac{ {d}^{2}y }{d {x}^{2} } [/tex]

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[tex] \sf using \: \frac{d}{dx} uv = u \frac{d}{dx} v + v \frac{d}{dx} u \: formula[/tex]

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[tex] \bold{ \frac{dy}{dx} = {e}^{3x} \frac{d}{dx} \sin(2x) + \sin(2x) \frac{d}{dx} {e}^{3x} } \\ \\ \bold{ \frac{dy}{dx} = {e}^{3x} \cos(2x) \frac{d}{dx} 2x + \sin(2x) {e}^{3x} \frac{d}{dx} 3x}[/tex]

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[tex] \bold{ \frac{dy}{dx} = {e}^{3x} \times 2 \cos(2x) + \sin(3x) \times 3 {e}^{3x} }[/tex]

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[tex] \bold{ \frac{dy}{dx} = 2 {e}^{3x} \cos(2x) + 3 {e}^{3x} \sin(2x) }[/tex]

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⠀⠀● First solving 2e^3x cos(2x)

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[tex] \bold{ 2( {e}^{3x} \frac{d}{dx} \cos(2x) + \cos(2x) \frac{d}{dx} {e}^{3x}) }[/tex]

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[tex] \bold{2( {e}^{3x} - \sin(2x) \frac{d}{dx} 2x + \cos(2x) {e}^{3x} \frac{d}{dx} 3x)} \\ \\ \bold{ - 4 {e}^{3x} \sin(2x) + 6 {e}^{3x} \cos(2x) }[/tex]

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⠀⠀● Now solving 3e^3x sin(2x)

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[tex] \bold{ 3( {e}^{3x} \frac{d}{dx} \sin(2x) + \sin(2x) \frac{d}{dx} {e}^{3x} )}[/tex]

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[tex] \bold{ 3( {e}^{3x} \cos(2x) \frac{d}{dx} 2x + \sin(2x) {e}^{3x} \frac{d}{dx} 3x)} \\ \\ \bold{ 6 {e}^{3x} \cos(2x) + 9 {e}^{3x} \sin(2x) }[/tex]

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[tex] \bold{ \frac{ {d}^{2}y }{d {x}^{2} } = - 4 {e}^{3x} \sin(2x) + 6 {e}^{3x} \cos(2x) + 6 {e}^{3x} \cos(2x) + 9 {e}^{3x} \sin(2x) } \\ \\ \bold{ \frac{ {d}^{2} y}{d {x}^{2} } = 5 {e}^{3x} \sin(2x) + 12 {e}^{3x} \cos(2x) }[/tex]

A) Right Angle Triangle

B) 25 units²

C) (15 + 5√5) units

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Distance between C and A

[tex]\rightarrow \sf CA = \sqrt{(1 - (-1))^2 + (4 - (-7))^2} \ = \ 5\sqrt{5}[/tex]

Distance between C and T

[tex]\rightarrow \sf CT = \sqrt{(-1-5)^2+(-7-1)^2} \ = \ 10[/tex]

Distance between A and T

[tex]\rightarrow \sf AT = \sqrt{(1-5)^2 +(4-1)^2} \ = \ 5[/tex]

Part A:

When drawn on graph, we can identify it is a right angle triangle.

Or use Pythagoras Theorem:

10² + 5² = (5√5)²

125 = 125... Hence it is a right angle triangle confirmed.

Part B:

Area of triangle = ½ × base × height = ½ × 10 × 5 = 25 units²

Part C:

Total Sum or measure of all sides: 5 + 10 + 5√5 = 15 + 5√5 units

Answer: The function h because the graphs of f and h are symmetrical about the line y=x.

Answer:

x = 20

Step-by-step explanation:

63−3x=3

−3x=−60

x=20

Answer:

y=3

x=1

Step-by-step explanation:

1 by substitution method

2x+y=5 (1)

x+y=4 (2)

find x in eq 2

x=4-y

put the value in eq 1

2x+y=5

2(4-y)+y=5

8-2y+y=5

8-y=5

-y=5-8

-y=-3

y = 3

x=4-y

x=4-3

x=3

hope it helps you

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Answer:

The complete list of factors for 805 are 1, 5, 7, 23, 35, 115, 161, and 805.

Step-by-step explanation:

A factor pair is a combination of two factors which can be multiplied together to equal 805. In proper math terms, the number 805 is called the product and the two numbers that can be multiplied together to equal it are called the factors.

In order to work out the factor pairs of 805 we need to first get all of the factors of 805. Once you have the list of all those factors we can pair them together to list out all of the factor pairs.

The complete list of factors for 805 are 1, 5, 7, 23, 35, 115, 161, and 805.

Answer:

A) reflection over the x-axis

Step-by-step explanation:

Answer:

The arrangements of things following one after another in time

Answer:

18

Step-by-step explanation:

In 6 years, both other their ages will add up to 39. So 12 years back( 6 years for each of them), their combined age will be 27.

Now we have to find the age of Suma. We can find her brother age first.

We can use the equation 2x+x=27

In this equation, x is the age of Suma's brother. 2x + x = 3x.

3x = 27.

27 divided by 3 is 9 so Suma's brother is 9 years old. And since Suma is twice as old. Suma is 18 years old.

Answer:

Suma is 18 years old

Step-by-step explanation:

Let s = Suma's age

Let b = brother's age

Suma is twice as old as her brother:

⇒ s = 2b

In 6 years time, the sum of their ages will be 39 years:

⇒ (s + 6) + (b + 6) = 39

Substitute  s = 2b  into  (s + 6) + (b + 6) = 39  and solve for b:

⇒ (2b + 6) + (b + 6) = 39

⇒ 3b + 12 = 39

⇒ 3b = 27

⇒ b = 9

Substitute found value of b into  s = 2b  and solve for s:

⇒ s = 2(9)

⇒ s = 18

Therefore, Suma is 18 years old and her brother is 9 years old.

Answer:

A term is a single number or variable, in this case, the number 2.

The sum in this equation would be 4x + 2.

The product is the result of multiplication, in this equation, the result of 5(4x + 2).

The factors are the digits that are being multiplied, in this case, 5 & 4x + 2

The quotient is the result of a division, in this case, the result of (4x + 2) / 7y.

A coefficient is a number that is being multiplied by a variable, in this case, 4 & y.

Answer:

-2

2

Step-by-step explanation:

just use common sense. what does "local maximum" mean ?

it means a point, where the curve in the nearest neighborhood does not have a higher value. where the curve comes from smaller values, turns around and leaves with smaller values again.

(a) there is one point in this graph : at x = -2

(b) and that maximum value at that point is y = 2

Answer:

3 is the right answer because it is less than 4 and greater than 2

Answer:

The answer is 1230cm square

Answer:

Original price = t = $24

Expression = t + 0.05t

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New price = t + 0.05t = 24 + (0.05*24) = $25.20

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Have a nice day!!

Answer:

$25.20

Step-by-step explanation:

Original price = t = $ 24

New price = 1.05*24

                 = 25.20

Just multiply 1.05 by 24

Answer:

13?

Step-by-step explanation:

idrk best guess. 26 divided by 2= 13.   11-13 + 2

Answer:

angle A: 33.005

Angle B: 35.04

Angel C: 111.955

Step-by-step explanation:

look at attached image for more info

Hope it helps! Have a wonderful day

Answer:

y=3x+12

Step-by-step explanation:

Use this formula: y-y1=m(x-x1)
(y-Your y point=slope(x-Your x point)

Point= (-2, 6), Slope= 3

(Anything negative, you add. Anything positive, you subtract.)

Plug in your values: y-6=3(x+2)
distribute: y-6=3x+6
Add six to both sides of the equation:y-6(+6)=3x+6(+6)
We get our answer: y=3x+12
Hope this helps!! :)

The standard error is an estimate of the standard deviation of the sampling distribution. The value of the standard error of the mean is 387.970.

It is an estimate of the standard deviation of the sampling distribution. It measures the variability of a considered sample statistic.

Suppose that we're given that:

Population standard deviation = σ

Size of the sample we're working on = n

Then, the standard error can be calculated as:

[tex]SE = \dfrac{\sigma}{\sqrt{n}}[/tex]

where SE denotes the standard error.

The standard error of the mean can be written as,

SE = σ/√n

SE = 2,125/√30

SE = 387.970

Hence, the value of the standard error of the mean is 387.970.

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The probability that she picks a blue marble three times in a row is 1/125.

Given that

Samantha has a bag of 5 different colored marbles.

She randomly picks a marble from the bag, records the color, and returns it to the bag before picking another marble.

We have to determine

What is the probability that she picks a blue marble three times in a row?

According to the question

Samantha has a bag of 5 different colored marbles.

She randomly picks a marble from the bag, records the color, and returns it to the bag before picking another marble.

The probability of picking a bag one time is,

Number of bag pack at a time

Total number of bag

=1/5

The probability of picking a bag second time is,

Number of bag pack at a time Total number of bag

=1/5

The probability of picking a bag third time is,

Number of bag pack at a time

Total number of bag

=1/5

031%

Therefore,

The probability that she picks a blue marble three times in a row is,

= 1/5 X 1/5 X 1/5

1 /125

Hence, the probability that she picks a blue marble three times in a row is 1/125.

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Step-by-step explanation:

hope this helps

Answer:

39cm

Step-by-step explanation:

area of square = side^2 =169

side = 13cm

Perimeter of triangle = 3*side

=3 * 13 = 39cm

Answer:

52

Step-by-step explanation:

√169 =13

13*4= 52 because the perimeter of the square is equal to the perimeter of the triangle

Answer:

∠ e = 20°

Step-by-step explanation:

you should have also subtracted 2e from the 360

since UV is a straight line, the angles lying on it sum to 180° , that is

90° + e + 70° = 180°

e + 160° = 180° ( subtract 160° from both sides )

e = 20°