When 390 junior college students were surveyed,115 said that they have previously owned a motorcycle. Find a point estimate for p, the population proportion of students who have previously owned a motorcycle.

a. 0.705
b. 0.228
c. 0.295
d. 0.418

\(\underset{\leftarrow ~~ 6x+9 ~~ \to }{J\stackrel{20}{\rule[0.35em]{15em}{0.25pt}} K\stackrel{x + 9}{\rule[0.35em]{10em}{0.25pt}} L} \\\\\\ \stackrel{JL}{6x+9}~~ = ~~\stackrel{JK}{20}+(\stackrel{KL}{x+9})\implies 6x+9=29+x\implies 5x+9=29 \\\\\\ 5x=20\implies x=\cfrac{20}{5}\implies x=4\hspace{5em}\boxed{\underset{KL}{\stackrel{(4)~~ + ~~9}{13}}}\)

Answer: 24.2° SouthWest

Step-by-step explanation:

First step: DRAW A PICTURE of the vectors from head to tail (see image)

I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.

Perpendicular (x):

 cos 35° = adjacent/hypotenuse

  cos 35° = x/160

→ x = 160 cos 35°

Angle (θ):

sin θ = opposite/hypotenuse

sin θ = x/320

sin θ = 160 cos 35°/320

    θ = arcsin (160 cos 35°/320)

    θ = 24.2°

Direction is down (south) and left (west)

Reggie travels 300 km an hour

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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Answer:

42

Step-by-step explanation:

2,​4,6,10,​16,26,​___

The pattern is adding the previous two numbers to get the next number

2+4 = 6

4+6 = 10

6+10 = 16

10+16 = 26

16+26 =42

Answer:

p = 8

Step-by-step explanation:

Divide -5 to both sides

-5p = -40

5p = 40

p = 8

So p = 8

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Answer:

409

Step-by-step explanation:

Answer:

Step-by-step explanation:

17.4% of 8350 equals 1452.9 or 14529/10

Hope this helps! <3

A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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Answer:

The answer is "1.448 miles".

Step-by-step explanation:

X= The distance to both the nozzle clogged from of the starting point.

X \(\sim\) Uniform(0,2) miles.

They are simulating the random number Y=0.724, and the Y has both a distribution uniform(0,1). Therefore 2Y is distributed evenly (0.2). And They model the clogging of its nozzle at 2Y=1.448 miles

Answer:

8/12 and 10/12

Step-by-step explanation:

If the bottom changes the top changes also know as the numerator and denominator

Answer:

3/12=1/4

Step-by-step explanation:

2/3=8/12

5/12=5/12

8/12-5/12=3/12

Answer:

I want in English

Step-by-step explanation:

I don't know other languages than English

Using Factorization, The solution of the algebraic fraction is \(\frac{10}{p-4}\).

Due to the fact that they have polynomials on both sides of the equality sign, algebraic equations are also known as polynomials. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of algebraic equations.

Numbers are factored using formulas for factorization. Decomposing an entity into the result of another entity or factors that, when multiplied together, produce the original number is known as factorization. Simple factorization formulas are used in factorization procedures to simplify algebraic or quadratic equations. Instead of expanding parentheses, expressions are expressed as the sum of their constituent parts. Each equation may have factors that are algebraic expressions, variables, or .

\(\frac{p - 8}{8 p²-12p+32} \div \frac{1}{10}\)

first we factorize the denominator and using invert Endo to the other fraction.

\(\frac{p - 8}{8 p²-12p+32} \times \frac{10}{1}\\\frac{p - 8}{(p - 8)(p - 4)} \times 10\)

= \(\frac{10}{p-4}\)

Hence the simplified fraction is \(\frac{10}{p-4}\)

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Answer:

12.56

Step-by-step explanation:

First of all, pi = 3.14

Diameter=4

Radius=2

3.14×\(2^{2}\)

So,

3.14 × 4 =

12.56

Hope this helps!! (Hope I did this in time!!)

Answer:

B and D

Step-by-step explanation:

2+-14 = -12

-4+(- 8) = -12

because its a negative number it wont go up it will go down

Answer:

\(a) - 13 + - 1 = = - 13 - 1 = - 14 \\ b)2 + - 1 4 = 2 - 14 = - 12 \\ c) - 5 + 17 = 12 \\ d) - 4 + - 8 = - 12 \\ b \: and \: d \: represent \: - 12as \: answer \\ thankyou\)

Answer:

its false cause there is nothing isacly to answer to 18

Annual expenses need to be budgeted for monthly, therefore the statement is false.

A budget is vital for an individual to plan well. It's important for an individual to budget monthly for annual expenses. This will make it easier for the person to pay.

An annual expense can include house rent, paying for a car, etc. Therefore, it's important for one to plan ahead. Ta essential for one.to pay them on time too.

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Step-by-step explanation:

if I understand you correctly, then we have the 4 described cards. 3 of these 4 cards are face cards (Jack, Queen, King).

a probability is always desired cases over totally possible cases.

so, for the first pull we have a probability of

3/4 = 0.75

we have 4 total possibilities, and 3 of them are the desired outcome.

for the second pull we have then only 3 cards left (we did not replace the first pulled card). and because the first pulled card was in this scenario a face card, 2 out of these 3 cards are face cards.

so, the probability to pull a face card here is

2/3 = 0.66666...

when we combine these 2 events into one connected event (we are creating event 1 AND event 2), we multiply the probabilities, giving us

3/4 × 2/3 = 6/12 = 1/2 = 0.5

Answer:

8/12 and 9/12

Step-by-step explanation:

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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Answer:

Step-by-step explanation:

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

A) First day = x blocks

Second day = x + 2 blocks

Third day = x + 4 blocks

Fourth day = x + 4 blocks

Fifth day = x + 4 blocks

B) All possible values that Makaila could walk on the first day to reach her goal are; x ≥ 11.2

C) The fewest number of blocks she could walk on this day and still meet her goal is; 70 blocks

A) We are told that the first day, she walks x blocks

Thus;

Second day = x + 2 blocks

Third day = x + 4 blocks

Fourth day = x + 4 blocks

Fifth day = x + 4 blocks

B) Total blocks = x + x + 2 + x + 4 + x + 4 = 5x + 14

Makaila would like to walk at least 70 blocks over the next five days. Thus, the equation is;

5x + 14 ≥ 70

Subtract 14 from both sides of this equation to get:

5x ≥ 56

Divide both sides of this equation by 5 to get:

x ≥ 11.2

C) She must walk greater than or equal to 11.2 blocks the first day to reach her goal.

assume she walks exactly 11.2 blocks the first day.

then her total walking based on the formula would be:

first day 11.2

second day 13.2

third day 15.2

fourth day 15.2

fifth day 15.2

total walked is 11.2 + 13.2 + (3 * 15.2)

this equals 24.4 + 45.6 which equals 70.0

Any number of blocks over 11.2 on the first day will result in a total greater than 70 blocks.

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Answer:

Step-by-step explanation:

To solve the system of differential equations:

dx/dt = 3x - 18y ...(1)

dy/dt = 2x - 9y ...(2)

Step 1: Solve for x in equation (2):

2x = dy/dt + 9y

x = (1/2) (dy/dt + 9y)

Step 2: Substitute the expression for x from step 1 into equation (1):

dx/dt = 3x - 18y

dx/dt = 3[(1/2) (dy/dt + 9y)] - 18y

dx/dt = (3/2) dy/dt + (9/2) y - 18y

dx/dt = (3/2) dy/dt - (9/2) y

Step 3: Rewrite the equation from step 2 in terms of y and its derivative:

dx/dt + (9/2) y = (3/2) dy/dt

Step 4: Solve for y(t) using the integrating factor method:

Multiplying both sides by exp(9t/2), we get:

exp(9t/2) dx/dt + (9/2) exp(9t/2) y = (3/2) exp(9t/2) dy/dt

Applying the product rule on the left-hand side:

d/dt (exp(9t/2) x) = (3/2) d/dt (exp(9t/2) y)

Integrating both sides with respect to t:

exp(9t/2) x = (3/2) exp(9t/2) y + C

where C is the constant of integration.

Step 5: Solve for x(t) using the expression for y(t) from step 4:

x = (3/2) y + C exp(-9t/2)

where C is the constant of integration.

Therefore, the general solution to the system of differential equations is:

x = (3/2) y + C exp(-9t/2)

y = exp(9t/2) [(1/3) C1 + C2]

where C and C1, C2 are constants of integration.

Mei bought a magazine and some notepads for $46

A magazine cost $6

A notepad cost $5

Let n represents number of notepads bought

The expression to relate the sum of a magazine and "n" number of notepads bought is given below as,

Solving to find the value of n,

Hence, she bought 8 notepads

Answer:

X Y

10 7

8 5

6 3

Step-by-step explanation:

Not much to explain - just put a number 3 smaller than X into column Y

The required table for the given rule can be completed as follows:

X Y

10 7

8 5

6 3

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The rule is given in the question, as follows:

y is 3 less than x

For each value of x in the first column, the corresponding value of y in the second column can be calculated by subtracting 3 from x.

For example, if x is 10, then y is 3 less than x, which is 7 (10 - 3 = 7).

Similarly, if x is 8, then y is 5 (8 - 3 = 5), and if x is 6, then y is 3 (6 - 3 = 3).

The table for the given rule can be completed as follows:

X Y

10 7

8 5

6 3

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If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~