What percentage of the data values falls between the values pf 3 and 24 in the data set shown? 0 5 10 15 20 25 O 25% O 50% O 75% O 100%

To solve it for "a" is to isolate "a' in one side, by doing some algebraic operations.

U =ak -b

1) Let's rewrite it

-b+ak=u

2) Add b to both sides

-b +b +ak = u +b

ak = u+b

3) Divide both sides by k

4) Finally, we have it for 'a':

We can calculate the interest as the difference between the future and the present value of the investment:

The present value is $4780.

The annual interest rate is r=1.25/100=0.0125.

The number of years is 8, so n=8.

We can calculate the future value as:

Then, we can calculate the interest as:

Answer: D. $499.44

there are 2 possible triangles that can arranged one being the 8 the longest side, and another one being the 5 and 8 the sides of the triangle

use the pythagorean theorem to solve.

for the black triangle.

for the green triangle.

r-9<-25 is equal to solution: [tex]$\quad R < -16$[/tex], Interval Notation: [tex]$\quad(-\infty,-16)$[/tex]. The graph is shown in attachement.

R-9<-25

Add 9 to both sides

R-9+9<-25+9

Simplify

R<-16

A graph is simply an orderly representation of data. It aids us in comprehending the info. The numerical information gathered through observation is referred to as data.

Data is derived from the Latin term Datum, which meaning "anything supplied."

Data is collected continuously through observation when a research question is formulated. It is then organized, summarized, categorised, and graphically shown.

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Given

Find

Equivalent expression

Explanation

Here , we use laws of exponents

so ,

Final Answer

Therefore , the correct option is C

If we have two similar triangles, that ratio of the corresponding sides are all the same. This means that:

Substituting the lengths, we get:

ANSWER

2/27

EXPLANATION

There are a total of 9 marbles in the bowl. The probability of drawing a red marble is,

Then you draw another marble, but you put the first back in the bowl, so the total number of marbles is the same. The probability of drawing a yellow marble is,

The probability of drawing a red marble and a yellow marble is,

Original mean = 64

standand deviation = 13

Let the value of of the originalmean be X. If after 6 points have been added to every score in a sample, the mean is found to be M = 70, then;

X + 6 = 70

Subtract 6 from both sides

X + 6 - 6 = 70 - 6

X = 70 - 6

X = 64

Hence the mean of the original sample will be 64.

The standard deviation of the data will remain unchanged since the distance from the mean will remain the same no matter the change in mean. Therefore the standard deviation of the sample will be 13.

Translations

One point located at (x,y), translated to the point (h,k) has been applied the rule:

T(x,y) -> (h,k)

And the translation changed the coordinates by ( h-x, k-y).

The point (4,-9) is mapped to (9,-14). The change is:

(9 - 4, -14 - (-9 ) = (5 , -5)

The rule of translation is:

T(x,y) -> (x + 5 , y -5)

If we translated the point (-9,-8) under the same rule:

T(-9,-8) -> (-9 + 5 , -8 -5)

T(-9,-8) -> ( -4 , -13)

The image of the point (-9,-8) is ( -4 , -13)

Given the following vector:

The magnitude of the vector will be as follows:

So, the answer will be option 2) ||v|| = √15

B. 18

Explanation

The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number

it is given by.

so, we can find the dot product by multiplying the corresponding values in each vector and adding them together

Step 1

get the dot product

let

then

therefore, the answer is

B. 18

I hope this helps you

Answer:

Question:

Determine whether each sequence is arithmetic. If so, identify the common difference. -34, -28, -22, -16

The numbers are given below as

Concept:

Define an arithmetic sequence

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The general form of an arithmetic sequence is given below as

To check if they have a common difference, we will use the formulas below

Hence,

Since the sequence has a common difference,

It is therefore an ARITHMETIC SEQUENCE

Their common difference is

• The length of one side of the garage originally is approximately 14.9 ft

• The length of one side of the garage now​ is approximately 18.3 ft

Old garage = 222 sq. ft

New garage has 50% more floor space.

50% of 222 = 111

Therefore, the new garage is (222 + 111) sq. ft = 333 sq. ft

Since the garage is square,

one side of the old garage is:

One side of the new garage is:

We are asked to express 0.004 in scientific notation

The number 0.004 has the decimal point at the start, so we move this decimal point to the right until there is only one non-zero digit is left (4 in this case) and then count the number of times we moved.

In this case, we moved 3 times so the exponent (power) is -3

The sign of exponent is negative when we move to the right (like in this case)

The sign of exponent is positive when we move to the left.

Given expression is

We can expand the given expression as follows.

Multiplying 7 and 7, we get

Multiplying 49 and 7, we get

Hence 7^3 is 343.

We multiply the number twice by itself to find the cube of 7.

This strategy is easy and basic to find the cube of the number.

We can find the volume of the box by multiplying the length, width and heigth.

We can write this as:

The base layer is 24 cm^3 (24 cubes of 1 cm^3) because its the volume of width 4 cm and length 6 cm, with a height of 1 cm (the height of the cube).

If we multiply the number of cubes, 24 of 1 cm^3, by the real height, that is 5 times 1 cm, we get: 24 cm^3 * 5 = 120 cm^3.

Answer: the box has a volume of 120 cm^3

Answer:

Here are the numbers:

1) 25.578

2) 6,001.01

In this expression, we have the same value on the left side is equal to the same amount on the right side.

So, let's start operating it to simplify it

6(_+x) -8(-3+8x)=30-58x

6(_+x)+24-64x=30-58x

6( ) +6x +24 -64x =30 -58x

6( ) -58x+24=30-58x

6( )-58x +58x=30-24

6( ) =14 DIviding both sides by six

( ) =7/3

Testing:

6(7/3 +x) -8(-3+8x)=30-58x

14+6x +24 -64x =30-58x

38

We have the following:

Therefore, the answer is real numbers

The given function's f(t) = (t - 4)(t + 1)(t - 7), f-intercept is f(t) = 28 and the t-intercepts are t = - 1, 4, 7.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the y-axis of the coordinate system in analytic geometry using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Therefore, x = 0 is satisfied at these sites. The x-intercept and y-intercept are the points where a line crosses each axis.

An intercept is a location where an axis and a graph intersect. The x-intercept is the name given to this particular one.

Put t = 0 in the function f(t) = (t - 4)(t + 1)(t - 7)

f(t)= (0-4)(0+1)(0-7)

f(t) = (-4)(1)(-7)

f(t) = 28

So, the f-intercept is (0,28)

Put f(t) = 0 to find t- intercepts

0 = (t-4)(t+1)(t-7)

So, t - 4 = 0

t = 4

For t + 1 = 0

t = -1

For (t - 7) = 0

t = 7

So, the t intercepts are t = -1, 4, 7.

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The given equation for the area of a cylinder is:

S = 2πr² + 2лrh

Subtract 2πr² from both sides

S - 2πr² = 2πr² - 2πr² + 2лrh

S - 2πr² = 2лrh

Divide both sides 2лr

An equilateral triangle is a triangle that has the same length on all its three sides. Therefore, we can say that:

Since the triangle is folded in half, then we can say that:

From this, we can solve "x" using the Pythagorean Theorem.

where "c" = hypotenuse and "a" and "b" can be either of the remaining sides.

Therefore, the height of our equilateral triangle is 7√3. This is found in the third option.

The value of the width in the rectangle is 8cm.

Based on the information, let the width be represented as w.

Let the width be represented as 5 × w = 5w

Perimeter = 96cm

Perimeter of a rectangle = 2(length + width)

Perimeter = 2(5w + w)

96 = 12w

Divide

w = 96/12

w = 8

The value of the width is 8cm.

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n(U) = 20

n(G) = 12

n(P) = 7

Let x represent students that play both instruments

n(PuG) = x

A. Venn diagram

B. What is the probability that a randomly selected student will play guitar and piano?

Firstly solve for x

12-x + x + 7-x + 4 = 20

23-x = 20

-x = 20 - 23

-x = -3

x = 3

Number of students that play guitar and piano = x = 3

Total students = 20

Probability that a randomly selected student will play guitar and piano = 3/20

C. What is the probability that a randomly selected student will play one of these two instruments?

D. What is the probability that a randomly selected student will not play the piano?

Students who do not play piano are students that play guitar only and students who do not play any instrument

students that play guitar only = 12 -x = 12 -3 = 9 students

students who do not play any instrument = 4

Probability that a randomly selected student will not play the piano =

Let's begin by listing out the information given to us:

Both triangles have Line BD equal

Line AB equals Line CD

Angle A equals Angle C

Hence, Triangle ABD is congruent to Triangle CDB

Given:

Required:

We need to find the median.

Explanation:

Recall that the vertical line that split the box in two is the median.

The vertical line that split the box in two is the median at 24 minutes.

The median is 24.

Final answer:

The median is 24.

Answer: 100 %

Explanation:

The first step is to rearrange the numbes in ascending order. It becomes

56, 57, 57, 57, 58, 62, 88, 92

The next step is to calculate the population μ, mean.

μ = sum of terms/number of terms

From the information given

n = number of terms = 8

μ = (56 + 57 + 57 + 57 + 58 + 62 + 88 + 92)/8 = 65.875

μ = 65.875

The formula for calculating the population standard deviation, σ is

σ = √[Σ(x - μ)^2]/n

Σ(x - μ)^2/n = [(56 - 65.875)^2 + (57 - 65.875)^2 + (57 - 65.875)^2 + (57 - 65.875)^2 + (58 - 65.875)^2 + (62 - 65.875)^2 + (88 - 65.875)^2 + (92 - 65.875)^2)]/8 = 197.859375

σ = √197.859375

σ = 14.1

2 population standard deviations to the left of the mean = 65.875 - 2(14.1) = 37.675

2 population standard deviations to the rig tof the mean = 685875 -+2(14.1) == 94.075

Number of terms between 37.675 and 94.075 = 8

Thus,

the percentage of data within 2 population standard deviations of the mean

= 8/8 x 100 = 100%

Given:

x = 9 and y = 6

Use the equation:

y = kx

Where y varies directly as x

K is the constant of proportionality.

Let's find the value of k:

k = ⅔

An equation to describe the direct variation is:

ANSWER:

The method use by both students are correct. Hence the right answer to the question is OPTION D

Considering Box A,

Total number of pens = 3 + 5 = 8 pens

Probability of picking a purple (P) and black (B) pen is given below as,

Considering Box B,

Total number of pens = 15 + 5 = 20 pens

Probability of picking a purple and black pen is given below as,

For event 1, probability of choosing a red (R) pen from Box B is zero because there is no red pen in the Box.

Event 1 P(R) = 0

For event 2, probability of choosing a purple or black pen from Box A is,

Event 2 P(P or B) = 1

For event 3, probability of choosing a purple pen from Box A is,

Event 3 (P) = 3/8

For event 4, probability of choosing a black pen from Box B is given below as,

Event 4 P(B) = 1/4

Arranging each events from the least likely to the most likely is in the order below

Answer deduced above.