Mai picked a mystery number that is less than 30. she says she can show 3 different rectangles on this grid whose area is the same as her mystery number
what could be Mai's mystery number?

Answer:

1. [tex]\frac{6}{11}[/tex] × [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{22}[/tex]

2. [tex]4\frac{1}{3}[/tex] × [tex]\frac{9}{14}[/tex] = [tex]\frac{13}{3}[/tex] × [tex]\frac{9}{14}[/tex]

               = [tex]\frac{39}{14}[/tex]

               = [tex]2\frac{11}{14}[/tex]

3. [tex]3\frac{3}{6}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{21}{6}[/tex] × [tex]\frac{2}{3}[/tex]

             = [tex]\frac{7}{3}[/tex]

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

4. [tex]\frac{6}{15}[/tex] ÷ [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{15}[/tex] × [tex]\frac{5}{2}[/tex]

            = 1

5. [tex]1\frac{4}{5}[/tex] ÷ [tex]\frac{3}{25}[/tex] = [tex]\frac{9}{5}[/tex] × [tex]\frac{25}{3}[/tex]

               = [tex]\frac{45}{3}[/tex]

               = 15

The actual number of respondents who rated themselves as above average drivers is 852 and we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.5007.

Given that, 84% of the sample of 1014 adults rated themselves as above average drivers.

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

Now,

84% of 1014

= 0.84×1014

= 851.76

≈ 852

Thus, the actual number of respondents who rated themselves as above average drivers is 852.

At the null hypothesis, we test if the proportion is 4/5 =0.8, that is

[tex]H_0:p=0.8[/tex]

At the alternative hypothesis, we test if the proportion is greater than 80%, that is:

[tex]H_0:p\ge0.8[/tex]

The test statistic is given by

[tex]z=\frac{\bar{p}-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

In which:

[tex]$\bar{p}$[/tex] is the sample proportion.

p is the proportion tested.

n is the size of the sample.

In this problem, the parameters are [tex]$\bar{p}$[/tex]=0.84, p=0.8 and n=1014

Thus, the value of the test statistic is

[tex]z=\frac{0.84-0.8}{\sqrt{\frac{0.8(1-0.8)}{1014} } }[/tex]

= 0.04/0.0125

z=3.2

0.4993

So, 1-0.4993=0.5007

Therefore, the actual number of respondents who rated themselves as above average drivers is 852 and we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.5007.

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Answer:

Too hard for me

The required range of the function y = x² + 2x - 3 for domain r -2 ≤ x ≤ 4 is given as -2 ≤ y ≤ 21.

Range, it is the set of values that come out to an outcome for a certain mathematical operation.

Here,
y =  x² + 2x - 3
For the domain -2 ≤ x ≤ 4,
x = -2             ;     x = 4
y = 4 - 4 - 3   : y = 16 + 8 - 3
y = -3             ; y = 21

Thus, the required range of the function y = x² + 2x - 3 for domain r -2 ≤ x ≤ 4 is given as -2 ≤ y ≤ 21.

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Given the fact the ball rolls down the slope, the gravitational force is the force caused the ball to move downhill.

In the test, when the ball is placed on the slope and slightly disturbed then ball will roll down the slope with increasing speed. This increasing speed of ball is due to the component of weight of ball which is along the inclined plane.

As shown in the attached, the component of weight perpendicular to inclined plane is used to counterbalance the normal force while other component of weight parallel to the inclined plane is accelerating the ball down the plane. Therefore, the Option D is correct.

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The volume of a conic wrap would be 209.44 cubic inches.

What is the volume of the cone?

The volume of a cone defines the cone's space or capacity. Cones are three-dimensional geometric shapes with a circular base that tapers from a flat base to a point known as the apex or vertex. A cone is made up of a series of line segments, half-lines, or lines that connect a common point, the apex, to all the points on a base in a plane that does not contain the apex.

      Volume of the cone = 1/3 ×πr²h

Given data:

Height of the conic wrap(h) = 8 inches.

Diameter of the conic wrap = 10 inches.

So radius(r) = 10/2 = 5 inches.

Now by using the formula for finding out the volume of the conic wrap, we get

            V = 1/3 × πr²h

               = 1/3 × 3.14 × (5)² × 8

            V = 209.44 cubic inches.

Hence, the volume of a conic wrap would be 209.44 cubic inches.

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The annual interest rate needed to accumulate $ 21.02 in simple interest from a $400.00 principal over 0.416667 years (5 months) is 12.612%.

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Here,

Simple interest paid=421.02-400

=$21.02

For ease of calculation, convert 5 months to 12 months per year, which equals 0.416667 years.

In order to convert r's decimal value to a percentage, we must solve our equation:

r = 21.02 / (40080.416667) = 0.1261199

R = 0.1261199 * 100 = 12.612%/year

For a $400.00 principal to earn $ 21.02 in simple interest over 0.416667 years (5 months), an annual interest rate of 12.612% is required.

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Answer:

Step-by-step explanation:

daddy

Answer:

b/2 min

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

x³ + 3x² ← factor out x² from each term

= x²(x + 3)

210 is the smallest number with exactly four different prime factors.

Prime factors:

In math, the  natural number, other than 1, whose only factors are 1 and itself. And the first few prime numbers are actually 2, 3, 5, 7, 11, and so on.

Given,

The smallest number with exactly three different prime factors is 30.

The prime factors of 30 are 2, 3 and 5.

Here we need to find the smallest number with exactly four different prime factors.

While we looking into the given question we have identified that the first three smallest prime factors are,

=> 2, 3 and 5

Now, we have to identify the fourth prime factor,

According to the definition of the prime factors, we have identified that the fourth prime factor is 7.

So, the number is calculated as,

=> 2 x 3 x 5 x 7

=> 210.

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The maximum height of the baseball will be 19.64 m

What are Equations of Motion?

The three equations of motions are :

Velocity-Time relation

v = u + at

Position-Time relation

S = ut + ( 1/2 ) at²

Position-Velocity relation.

v² - u² = 2aS

where v = final velocity

u = initial velocity

t = time

S = displacement

a = acceleration

Given data ,

Initial velocity u = 19.62 m/s

t = 2.01 s

a = -9.8 m/s² ( acceleration due to gravity )

To find maximum height of the baseball S , first we calculate the final velocity v

When the ball reaches the maximum height , the final velocity v will be 0

So v = 0

And , from the third equation of motion , we can find the maximum height of the baseball as

Position-Velocity relation.

v² - u² = 2aS

Substituting the value of v , u and a in the above equation , we get

0 - ( 19.62 )² = 2 x ( -9.8 ) x S

- 384.9444 = -19.6 x S

Dividing by ( -19.6 ) on both sides , we get

S = 19.64 m

Hence , the maximum height of the baseball will be 19.64 m

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Answer: sin(E) = 0.6

Step-by-step explanation:

10² = DF² + 8² ( Pythagoras theorem)

100 = DF² + 64

DF² = 36

DF = 6

sin(E) = opposite side/ Hypotenuse

          = DF/EF

          = 6/10 = 3/5 = 0.6

Number of ounces in a juice box is an example of quantitative.

What is Quantity?

A property called quantity or amount can take the form of a plurality or magnitude, which shows both discontinuity and continuity. Comparing quantities can be done by using phrases like "greater," "less," or "equal," as well as by assigning a numerical value that is a multiple of the unit of measurement.

Let the number of ounces in a juice box means, there are  number of ounces in a box.

The term "number of" is referred as quantity.

Therefore, the number of ounces in a juice box is an example of quantitative.

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Answer:  The correct answer is x > −5.733333  (the second and third buttons (">" and "-5.73") shown in the screenshot)

Step-by-step explanation:

Solve the inequality:

−1.5x−3.1 < 5.5

Step 1 - Add 3.1 to both sides

−1.5x − 3.1 + 3.1 < 5.5 + 3.1

−1.5x < 8.6

Step 2 - Divide both sides by -1.5

−1.5x / -1.5 < 8.6 / -1.5

x > −5.733333

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Answer:

y = -3/8 x - 4

Step-by-step explanation:

y-(-7) = -3/8 (x-8)

y+7 = -3/8x + 3

y = -3/8 x +3 - 7

y = -3/8 x -4

The numbers which are divisible by 3 are 6, 6, 6, and 9.

What is the divisibility of 3?

The rule of three states that a number is completely divisible by three if the sum of its digits is divisible by three.

Consider the number 308: To determine whether 308 is divisible by three, add the digits together (i.e. 3+0+8= 11). Check to see if the total is divisible by three.

From the given numbers the numbers which are divisible by 3 are:

                         6, 6, 6, and 9.

Hence, The numbers which are divisible by 3 are 6, 6, 6, and 9.

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As per the given condition of the forty percent students from the science program are 8th grader out of total 50 students present in the class , then number of students which are not 8th grader are 30 students.

As given in the question,

Total number of students present in the class of science program = 50

Percent of students present in the class of science program are of 8th graders = 40 percent

Let y be the number of student not present in the class of science program

( 100 - 40 )% of 50 = y  

⇒ 60 % of 50 = y

⇒ (60/100) × 50 = y

⇒ y = ( 60 × 50) / 100

⇒ y= 3000/100

⇒ y = 30 students

Therefore, for the given condition of the forty percent students from the science program are 8th grader out of total 50 students present in the class ,then number of students which are not 8th grader are 30 students.

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The length of ladder is 11.5 m.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

Let the length of ladder = y

And distance of bottom of ladder from the wall = X

According to the given,

Length of ladder y =

√(7² + x²)

Since, the bottom of the ladder is moved 1 meter farther away from the wall, so

Length of ladder y = √(5² +(x+1)²)

as in both equation y is equated

√(7² + x²) = √(5² +(x+1)²)

square root will get cancel on both sides

(7² + x²) = (5² +(x+1)²)

49 + x² = 25 + x² +1+2x

cancelling x² on both sides

49 = 26 +2x

2x = 23

x =11.5 meters

Hence the length of ladder is 11.5 m

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Answer:

x = 20

Step-by-step explanation:

<KOP and <OPN are alternate angles, therefore, they are equal to one another.

[tex]4x + 38 = 118 \text{ // Subtract 38}\\4x + 38 - 38 = 118 - 38\\\to 4x = 80 \text{ // Divide by 4}\\\frac{4x}4 = \frac{80}4\\\to x = 20[/tex]

The area of the shaded region between the curves f(x) and g(x), using integrals, is of:

126.54 units².

The curves are classified as follows:

Then, between an interval [a,b], the area is given by the definite integral between a and b of the subtraction of these two curves, as follows:

[tex]A = \int_{a}^{b} f(x) - g(x) dx[/tex]

The shaded region is divided into two intervals, as the upper and the lower curve change, as follows:

The area on the first interval is of:

[tex]A_1 = \int_{-4}^{0} x^3 + x^2 - 20x dx[/tex]

[tex]A_1 = 0.25x^4 + 0.33x^3 - 10x^2|_{x = -4}^{x = 0}[/tex]

Applying the Fundamental Theorem of Calculus, the first area is of:

A1 = -0.25(-4)^4 - 0.33(-4)³ + 10(-4)² = 117.12 units squared.

The second area is of:

[tex]A_2 = \int_{0}^{1} -x^3 - x^2 + 20x dx[/tex]

[tex]A_2 = -0.25x^4 - 0.33x^3 + 10x^2|_{x = 0}^{x = 1}[/tex]

Hence:

A2 = -0.25 - 0.33 + 10 = 9.42 units squared.

Then the total area is of:

117.12 + 9.42 = 126.54 units².

The region is given by the image shown at the end of the answer.

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Answer: 54, if there are 9 pages with 6 photos each, then you would do 6 x 9 = 54.

Answer:

54 pictures

Step-by-step explanation:

9 pages, 6 pictures in each page, 9*6=54

Answer:

  (6)  The functions f and g are not inverses

Step-by-step explanation:

You want to know which of several statements proves f(x) = (9x+9)/7 and g(x)=(7x+9)/9 are inverses of each other.

The inverse of f(x) can be found by solving ...

  x = f(y)

  x = (9y +9)/7

  7x = 9y +9

  7x -9 = 9y

  y = (7x -9)/9

The plus sign in f(x) turns into a minus sign in its inverse function. g(x) is not the inverse of f(x).

The functions f and g are not inverses.

__

Additional comment

As answer choice (2) suggests, graphs of inverse functions will be reflections of each other in the line y=x. The attached graph shows they are not, hence f(x) is not the inverse of g(x).

The correct statement that correctly verifies the two functions f(x) = (9x + 9) / 7 and g(x) = (7x + 9) / 9 is the functions f and g are not inverses

The inverse of a function is solved by making the input function equal to the output function

the inverse of f(x) = (9x + 9) / 7

f(x) = y = (9x + 9) / 7

7y = 9x + 9

9x = 7y - 9

x = (7y - 9) / 9

changing the input and output of the new functions

hence f⁻¹ =  (7x - 9) / 9

Since f⁻¹ ≠ g(x) the last option is the correct option

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Konrad will buy 2 shorts and one T-shirt.

Marek will buy 3 T-shirts and 2 caps.

Ming will buy 2 T-shirts and one cap and one short.

What is a selective principle in mathematics?

A selection principle is a rule in mathematics that asserts the possibility of obtaining mathematically significant objects by selecting elements from given sequences of sets. Selection principle theory investigates these principles and their relationships to other mathematical properties.

The price of each short is $20.98.

The price of each T-shirt is $12.49.

The price of each cap is $7.59.

The price of each pair of shoes is $16.50.

Konrad can buy only 3 items so he can buy 2 shorts and one T-shirt

So the total amount spent by Konrad = 2*20.98 + 12.49

                                                              = 41.96 + 12.49

                                                              = 54.45 dollars

which is less than $55.

Marek can buy only 5 items so he can buy 3 T-shirts and 2 caps.

So the total amount spent by Marek = 3*12.49 + 2*7.59

                                                              = 37.47 + 15.18

                                                              = 52.65 dollars.

which is less than $55.

Ming can buy only 4 items so he can buy 2 T-shirts and one cap and one short.

So the total amount spent by Ming = 2*12.49 + 7.59 + 20.98            

                                                          = 53.55 dollars.

which is less than $55.

Hence,

Konrad will buy 2 shorts and one T-shirt.

Marek will buy 3 T-shirts and 2 caps.

Ming will buy 2 T-shirts and one cap and one short.

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The roller coaster has a deceleration of 3 meters per second.

In this problem we need to calculate the magnitude of the deceleration experimented by the roller coster, which is under uniform accelerated motion. This can be easily found by means of the following formula:

a = (v' - v) / t

Where:

If we know that v = 20 m / s, v' = 2 m / s and t = 6 s, then the magnitude of the deceleration of the roller coster is:

a = [(2 m / s) - (20 m / s)] / 6 s

a = - 18 m / s / 6 s

a = - 3 m / s²

The magnitude of deceleration is 3 meters per square second.

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Answer:

4 is the correct answer to your question

Answer:

...

8 (4 - a) = 2a

32 - 8a = 2a

32 = 2a + 8a

32 = 10a

32/10 = 10a/10

32/10 = a

16/5 = a OR

3.2 = a

Correct

After simplification,  the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].

In the given question,

We have to factor the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].

The given expression is [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].

The given all term having negative power. So make the term in positive we can write it as

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}+\frac{1}{x^{3/2}}+\frac{1}{x^{5/2}}[/tex]

Taking 1/[tex]x^{1/2}[/tex] from the left side

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1+\frac{1}{x}+\frac{1}{x^2})[/tex]

Now solving the bracket by multiply and divide [tex]x^2[/tex] in each term.

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1\times\frac{x^2}{x^2}+\frac{1}{x}\times\frac{x^2}{x^2}+\frac{1}{x^2}\times\frac{x^2}{x^2})[/tex]

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2}{x^2}+\frac{x}{x^2}+\frac{1}{x^2})[/tex]

Simplifying the bracket

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2+x+1}{x^2})[/tex]

[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{x^2+x+1}{x^{5/2}}[/tex]

Hence, the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].

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Answer:

-21

Step-by-step explanation:

put 1/4 as x and solve the equation:
8*(1/4) - 23
= 8/4 - 23
= 2 - 23
= -21

Find the negative reciprocal of the original line and use point slope formula y-y1=m(x-x1)  to find the perpendicular line.

y= -x+3