Sean made four bags of candy and 16 minutes if he continues at the same rate how long will it take them to make five bags of candy

Answer: \(8 \sin x +7(\dfrac{\sin^3x}{3})+C\)

Step-by-step explanation:

Consider \(\int \cos(x) (8+7 \sin^2(x)) \, dx\)

Substitute  t= sinx

then dt = cos x dx

\(\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C\)

\([\int x^ndx=\dfrac{x^{n+1}}{n+1}+C]\)

\(=8 \sin x +7(\dfrac{\sin^3x}{3})+C\)

Hence, \(\int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C\)

Answer:

H0 :

a. mu is greater than or equal to $108.50

Ha:

c. mu is less than or equal to $108.50

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence

In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.

The prove of the trig identity gives sin²θ + cos²θ = 1.

The proof of the trig identity is determined as follows;

Let's consider a right triangle with one acute angle θ.

Let the hypotenuse have length 1

Let the length of the adjacent side = cosθ

then, the opposite side length = sinθ

Apply Pythagorean theorem, to determine the hypotenuse side;

(sinθ)² + (cosθ)² = 1²

sin²θ + cos²θ = 1

Thus, we have proved the identity.

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Answer:

A

Step-by-step explanation:

JUst answered same question

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Study finds that Africa’s population increased by over 1 billion, from 228.7 million in 1950 to 1.341 billion in 2020: 431 million in Eastern Africa; 404 million in Western Africa; 247.5 million in Northern Africa; 193.5 million in Middle Africa; and 64.5 million in Southern Africa.

Exponential Decay APPLICATION The half-life of strontium-90 is 28 years, meaning that after 28 years a given amount of the substance will have decayed to half the original amount. Application In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Use the exponential growth model in which t is the number of years after 2000, to find the exponential growth function that models the data. The model isApplication continued:- By which year will Africa’s population reach 2,000 million. Use the exponential growth function model: to find how long it will take to reach a population of 2,000 million.

Nigeria is forecast to become the world’s third-biggest country – after India and China – with 405 million people. The main reason for these demographic trends is Africa’s high fertility rate compared with other regions


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Answer:

120,000 ft^3

Step-by-step explanation:

step 1: 20ft times 150ft is 3000ft.

step 2: 3000ft times 40ft^3 is 120,000ft^3

Answer:

since y=4

from one of the equations

6x+4y=46

substitute y=4 In the equation

6x+4(4)=46

6x+16=46

6x=46-16

6x=30

divide both sides by the co efficient of'x'

6x/6=30/6

x=5

Answer:

yes

Step-by-step explanation:

y + 4 = 12

Subtract 4 on both sides,

y + 4 - 4 = 12 - 4

y = 8

Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Like usual, we can solve this question using an equation. Let’s assume that John’s age is x, and his sister’s age is y.

x = 2y

To figure out John’s age, we need to know his sister’s age. He’s 2 times older than his sister.

x + y = 27

The sum of their ages is 27, and we can substitute the value of x here to figure out y.

2y + y = 27

We can now simplify this, and get y by itself.

3y = 27

Now, we can divide by 3 to get the y by itself.

y = 9

We now know that John’s sister is 9.

Now, using our original equation, we can substitute in the value of y.

x = 2(9)

We can simplify this.

x = 18

John’s age is 18!

Hope this helps.

Step-by-step explanation:

the full question please

Answer:

The length of the hypotenuse is 100.

Step-by-step explanation:

To find the length of the hypotenuse, we use the following formula:

c=\(\sqrt{a^2+b^2}\)

c=\(\sqrt{28^2+96^2}\)

c=\(\sqrt{10,000}\)

c=100

Therefore, the length of the hypotenuse is 100.

During halftime of a basketball game, a slingshot launches T-shirts at the crowd.

What is the maximum height?

Generally, To find the time it takes the T-shirt to reach its maximum height, we need to find the time when the height of the T-shirt stops increasing and starts decreasing. At this point, the velocity of the T-shirt will be 0, since it is not moving up or down.

The velocity of the T-shirt at any time t can be found by taking the derivative of the equation for height:

v(t) = dh/dt = -32t + 72

Setting the velocity to 0 and solving for t, we get:

0 = -32t + 72 32t = 72 t = 72/32 t = 9/4

So it takes the T-shirt 9/4 seconds, or approximately 2.25 seconds, to reach its maximum height.

To find the maximum height, we plug this value back into the equation for height:

h(t) = -16(9/4)^2 + 72(9/4) + 4 h(t) = -81 + 162 + 4 h(t) = 77

The maximum height of the T-shirt is 77 feet.

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In a case whereby baseball game receives 3 raffle tickets and a $2 certificate for the team store. A group of people receives 39 raffle tickets the amount of money in certificates the group receive is  $26.

If one baseball game receives 3 raffle tickets and a $2 certificate for the team store, then we can say that each raffle ticket is worth 2/3 dollars ($2 divided by 3 tickets).

So, for 39 raffle tickets, the group would receive (39 x 2/3) = $26

Therefore, the amount of money in certificates the group receive is  $26

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The given parallel lines have a transversal which passes through them.

Hence from the property of parallel lines we found the values of x and y as 16 and 10 respectively.

Given that two parallel lines are intersected by a transversal, pair of angles are created, such as:

angles that are vertically opposing and equal.

the related angle pairs that are equivalent.

the equal pairs of opposite exterior angles.

the opposite interior angle pairs that are equal.

From the diagram we have the alternate exterior angles which are equal.

Therefore, alternate angle 1 = (8x-14)°

and alternate exterior angle 2 = (5x+34)°

now equate them,

(8x-14)° =  (5x+34)°

8x-14=5x+34

8x-5x=34+14

3x=48

x=48/3

x=16

now substitute x value in angle 1:

8(16)-14

= 114°

therefore angle 1 = 180°-114°

= 66°

Hence (5y+16)° = 66

5y = 66-16

5y = 50

y = 50/5

y = 10

Therefore we get the values of x and y as 16 and 10 respectively.

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Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer:

1 1/6

Step-by-step explanation:

1 is nothing but 6/6

So then  you would have 6/6+1/6

then you would do 6+1=7

And keep denominator same

So you have 7/6

Which is the same 1 1/6

Because 6 goes one time into 7/6

But you still have 1/6 left

Answer:

\( \hookrightarrow \: { \rm{x = 3y {z}^{2} }} \\ \\ { \rm{y = \frac{x}{3 {z}^{2} } }}\)

The expression of x = 3yz² for y in terms of x and z is x/(3z²).

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

The constraint of expression is represented as = or <, >.

Given the expression,

x = 3yz²

Divide both sides by 3

x/3 = yz²

Divide both sides by z²

x/(3z²) = y

y = x/(3z²)

Hence "The expression of x = 3yz² for y in terms of x and z is x/(3z²)".

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Answer:

(x+5) metres

Step-by-step explanation:

correct question

The rectangle below has an area of x^2+8x+15 square meters and a width of x+3 meters. What expression represents the length of the rectangle?

Area of the rectangle = Length * width

Factorize the area

A(x) =  x^2+8x+15

A(x) = x^2+3x+5x+15

A(x) = x(x+3) + 5(x+3)

A(x) = (x+3)(x+5)

Since the width is x+3, the length of the rectangle will be (x+5) metres

Answer:

Hello,

Answer B

Step-by-step explanation:

Since A=15*20+B and B<15

The max for B is 14

==> 300+14=314

Answer:

I think x is 38 but it depend on how to solve it

the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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Answer:

18

Step-by-step explanation:

the width is 9 meters on two of the sides so 54-18=36 for the two lengths. The length of one side is 18 (36/2)

check answer : length + length + width + width = perimeter

                             18.    +.  18.     + 9.       +.   9.    =54.

Answer:

arc sr

Step-by-step explanation:

i can't see the options for the question so lol

im gonna say its sr arc

Answer:

The slope is undefined because there is no change in x, making it a vertical line

Step-by-step explanation: