giving barinly to someone who answers in a complete sentence and who is write



Approximate √15 to the nearest integer.
Explain how you got your answer. ​

Answers

Answer 1

The square root of 15 is approximately 4.

To approximate the square root of 15, we can find the perfect squares that are closest to 15. The perfect squares that are closest to 15 are 9 and 16. Since 15 is closer to 16, we can say that the square root of 15 is slightly less than 4.

Another approach could be:

The square root of 15 is approximately 3.87. Rounding to the nearest integer gives us 4. To round a number, we look at the number following the place value we are rounding to. If it is greater than or equal to 5, we round up. If it is less than 5, we round down. In this case, the digit following the ones place is 8, which is greater than 5, so we round up to 4.


Related Questions

(5 points)
If ABCD is a parallelogram, what is the measure of D
A/9x + 5
16x
C
B

Answers

If ABCD is a parallelogram, then the measure of D is 68

From the property of parallelogram the opposite angels are equal so < DAB = < DCB so < DAB will become 16x.

        9x + 5 + 16x(<DAB) = 180 ....... because it is straight line.

        25x + 5 = 180

        25x = 180 - 5

        25x = 175

            x = 7

now let's substitute in the angle < DAB( 16x): 16 × 7= 112To get < ADC lets use the property of parallelogram which says that adjacent angles are supplementary. which means

          <ADC+ <DAB= 180

          <ADC+ 112 = 180

          < ADC= 180 - 112

          < ADC = 68

Therefore, the measure of D is 68

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a student needs 11 more classes to graduate. if she has met the prerequisites for all the classes, how many possible schedules for next semester could she make if she plans to take 4 classes?

Answers

We can conclude that the number of possible schedules for next semester could she make is 7920.

In more mathematical terms, the factorial of a number (n!) is equal to

n(n-1). For example, if you want to calculate the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

Given that,

The student needs 11 more classes to graduate.

And, possible schedules for next semester could she make if she plans to take 4 classes

Based on the given expression, the calculation is as follows:

The combination formula is given to be:

[tex]n_{C} _{r} =\frac{n!}{r!(n-r)!}[/tex]

= [tex]11_{C} _{4}[/tex] ! * 4 !

= [tex]\frac{11 !}{4!(11-4)!}[/tex]  * 4 !

= [tex]\frac{11!}{4!7!}[/tex] * 4 !

= [tex]\frac{11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1*7*6*5*4*3*2*1}[/tex] * 4 !

We can cancel the coefficients,

= [tex]\frac{11*10*9*8}{4*3*2*1}[/tex] * 4 !

= [tex]\frac{7920}{24}[/tex] * 4 !

= 330* 4 !

= 330 * 4*3*2*1

= 7920

Therefore,

We can conclude that the number of possible schedules for next semester could she make is 7920.

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What is the solution of the equation x2 - 12x = 8?

Answers

The solution of the equation is x = 6±2√11.

What is a quadratic equation?

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

Here, we have

Given: x² - 12x = 8

Now, we factorize the given equation and find the solution.

x² - 12x = 8

x² - 12x - 8 = 0

We apply here the quadratic formula.

= (-b ±√b²-4ac)/2

= (12 ±√12²-4×1×(-8))/2

= (12±√144+32)/2

= (12±√176)/2

= (12±4√11)/2

= 6±2√11

Hence, the solution of the equation x² - 12x = 8 is 6±2√11.

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Answer question #8
Give a short answer responding the question that’s being asked
The response written in the box isn’t correct so I need help

Answers

The conclusion is that the angle which measures 120° is not Acute angle.

What are angles ?

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.

In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:

The acute angle ranges from 0° to 90°.The obtuse angle ranges from 90° to 180°.Right Angle: The angle that is 90 degrees precisely.Direct Angle: the angle that is exactly 180 degreesReflex Angle: The angle between 180 degrees and 360 degrees that is bigger than 180 degrees.360-degree full rotation: The whole rotation of an angle.

Angle B measures 120°.

Here the angle is more than 90° so the angle is not acute.

The conclusion is that the angle which measures 120° is not Acute angle.

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Ramón makes nectar for a hummingbird feeder by mixing 8 cups of water with 2 cups of sugar. Tiffany makes nectar by mixing 9 cups of water with 3 cups of sugar. Whose nectar is more sugary? Explain.​

Answers

Answer: Tiffany

Step-by-step explanation: Ramon Ratio 8:2 can be reduced to 1 cup of sugar every 4 cups of water. Tiffany Ration is 9:3 which is reduced to 1 cup of sugar every 3 cups of water.

What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
Question 15

Answers

The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

How to obtain the cubic polynomial?

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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Mia went into a grocery store and where they sell apples for $2 each and mangos $1.50 each. Let x represent the number of apples and y represent the number of mangos she can buy.


Problem part 1: Mia has $20 to spend. Which inequality can be used to represent this situation?



Problem part 2: If Mia decided to buy 3 mangos, determine the maximum number of apples that she could buy.

Answers

The inequality that can be used to represent this situation is 2x + 1.50y ≤ 20.

The maximum number of apples she can buy is 7 apples.

How to represent inequality?

Mia went into a grocery store and where they sell apples for $2 each and mangos $1.50 each.

where

x = number of applesy = number of mangoes

Therefore, let's represent the inequality when Mia has to spend 20 dollars.

2x + 1.50y ≤ 20

If Mia decide to buy 3 mangoes , the maximum number of apples she can buy can be calculated as follows:

2x + 1.50y ≤ 20

2x + 1.50(3) ≤ 20

2x + 4.5 ≤ 20

2x ≤ 20 - 4.5

2x ≤ 15.5

x ≤ 15.5 / 2

x ≤ 7.75

Therefore, the maximum she can buy is 7 apples.

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A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left

Answers

A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).

Define translation.

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given

A triangle with coordinates (1,1) (4,2) (3,5)

The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.

We multiply all of the numbers by 3 since we are translating the entire triangle down three units.

Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.

A = (1 - 5, 1 - 3)

B = (4 - 5, 2 -3)

C = (3 - 5, 5 - 3)

New coordinates will be:

A = (-4,-2)

B = (-1,-1)

C = (-2, 2)

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PLEASE HELP ME!!!!!! THIS IS DUE ON FRIDAY!!!!!! (There is another part)

Answers

Answer:

it's c trust me I had the same problem

Find the surface area 5 4 7 6 8 triangular

Answers

The surface area of the triangular prism is 136 square units

How to determine the surface area

From the question, we have the following parameters that can be used in our computation (see attachment):

Rectangles (2) = 7 units by 5 unitsRectangles (1) = 7 units by 6 unitsTriangles (2) = 4 units by 6 units

The surface area of the triangular prism is the sum of the areas of the above shapes

So, we have

Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6

Evaluate

Surface area = 136

Hence, the surface area is 136 square units

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Help meee please !!!???

Answers

Answer:

Step-by-step explanation:

it is c

Answer: A have a good day

By rounding to 1 significant figure, estimate
101
×
52

Answers

The significant figure by multiplying 101 with 52 is 5000.

What is significant figures?The number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value is referred to as significant figures. At the first non-zero digit, we begin counting significant figures.A number's first significant figure is the first digit that is not zero.To round to the nearest one, ten, hundred, thousand, and so on, change all digits to the right of the rounding digit to zeroes.

Here given,

101 x 52

Round 101 to 100 and 52 to 50, then multiply together to get 5000.

Significant Figures: 1

Decimals: 0

The significant notation: 5e+3

Therefore the significant notation is 5000.

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4 Describe at least two different transformations or sequences of transformations that
transform square A to square B.

Answers

The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).

Does the order of transformations matter in functions?

Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.

The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

rotation 90° CCW about the point (-1, -1)

Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

reflection across the line y=x

reflection across the line x=-1

Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.

b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.

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Which ordered pair is a solution of the
equation?
-3x + 5y = 2x + 3y

Answers

Answer:

Solve the equation for [tex]{y}[/tex].

[tex]y=\frac{5x}{2}[/tex]

Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.

Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(0,0)}[/tex]

Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex](1,\frac{5}{2})[/tex]

Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(2,5)}[/tex]

These are three possible solutions to the equation.

[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]

Let’s set up steps to solve for the ordered pair.

1. Eliminate x on the left side

-3x + 5y + 3x = 2x + 3y + 3x

5y = 5x + 3y

2. Eliminate y on the right side

5y - 3y = 5x

2y = 5x

3. Divide both sides by the coefficient of y

2 / 2 = 1
5 / 2 = 5/2

4. Simplify

y = 5/2x

The ordered pair(s) representative of the solution to this equation would be (2, 5), (0, 0), or (1, 5/2).

suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked. (i) define the random variable of interest and state how the variable is distributed. (ii) determine the expected value of the random variable and interpret the expected value in context.

Answers

i) The random variable is the number of suspicious transmissions reviewed until finding the first blocked one and the random variable is distributed usinng geometric distribution

ii) The expected value of the random variable: 2.5 which means the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.

In this question we have been given a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history.

Based on past history, the specialist blocks 40 percent of the suspicious transactions.

so, p = 0.40

i. Let X represent the number of suspicious transmissions reviewed until finding the first blocked one.

We will use a geometric distribution to model the first transmission.

ii. We know that according to the geometric model the expected value of the random variable would be.

E(X) = 1/p ,

       = 1/0.4

       = 2.5

This means, the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.

Therefore,  i) the random variable: the number of suspicious transmissions reviewed until finding the first blocked one.

ii) the expected value of the random variable: 2.5

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The complete question is:

At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions.

Suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked.

(i) Define the random variable of interest and state how the variable is distributed.

(ii) Determine the expected value of the random variable and interpret the expected value in context.

The sum of the digits of a certain two digit number is 13. Twice the tens digit exceeds the unit digit by 2. What is the number?

Answers

Answer:

Step-by-step explanation:

6.5

O
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 0≤x≤ 4.
x
0
1
2
32
4
5
3
6
12
24
48
96

Answers

The average rate of change of the function at the interval 0 ≤ x ≤ 4 is 11.25

How to determine the average rate of change

From the question, we have the following parameters that can be used in our computation:

x  0   1   2   3  4   5

y 3   6  12   24 48 96

The interval is given as

0 ≤ x ≤ 4

On the table, we have

x = 0 and y = 3

x = 4 and y = 48

This means that

f(0) = 3 and f(4) = 48

The average rate of change is then calculated as

Average rate of change = [f(4) - f(0)]/[4 - 0]

Substitute the known values in the above equation, so, we have the following representation

Average rate of change = [48 - 3]/[4 - 0]

Evaluate

Average rate of change = 11.25

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miguel is mixing up a salad dressing. regardless of the number of servings, the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?

Answers

44 is the proportion of the botched dressing will be olive oil.

Given, Miguel is mixing up a salad dressing. regardless of the number of servings,

the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if he accidentally doubles the vinegar and forgets the sugar altogether,

we have to find the proportion of the botched dressing that will be olive oil.

first we will find the amount of the even mixture of salt, pepper and sugar.

as, olive oil + vinegar + even mixture of salt, pepper and sugar = 100

58 + 14 + mixture of salt, pepper and sugar = 100

mixture of salt, pepper and sugar = 100 - 72

mixture of salt, pepper and sugar = 28

if he mixed doubles of the vinegar i.e. 28 then olive oil be,

x + 28 + 28 = 100

x = 100 - 56

x = 44

Hence, 44 is the proportion of the botched dressing will be olive oil.

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When solving an equation, Henry gets to the last line of his work and is left with “3 = 3”. What does this mean? * 4 points A. The solution is 3. B. There is only one solution. C. There is no solution. D. There are infinite solutions.

Answers

This mean there are infinite solutions.

What does this mean?

Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.

Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.

Any value for the Variable would make the equation true, according to infinite solutions.

We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,

such as

3=3 or 3x=3x, then. Finite solutions exist.

This mean there are infinite solutions.

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Which equations are true for x = –2 and x = 2? Select two options
O x2 – 4 = 0
O x2 = –4
O 3x2 + 12 = 0
O 4x2 = 16
O 2(x – 2)2 = 0

Answers

The only two options with equations that are true for x = –2 and x = 2 are;

Option A: x² - 4 = 0

Option D: 4x² = 16

How to identify the correct domain value?

The domain of a function is the set of all input values  for which the function is possible.

Now, we are given the domain values as  x = –2 and x = 2.

a) x² - 4

f(-2) = (-2)² - 4

= 0

f(2) = (2)² - 2

= 0

b) x² = -4

f(-2) = (-2)²

= 4

f(2) = (2)²

= 4

c) 3x² + 12

f(-2) = 3(-2)²  + 12

= 24

f(-2) = 3(2)²  + 12

= 24

d) 4x²

f(-2) = 4(-2)²

= 16

f(2) = 4(2)²

= 16

e) 2(x - 2)²

f(-2) = 2(-2 - 2)²

= 32

f(2) = 2(2 - 2)²

= 0

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Find the volume of the pyramid.

Answers

Answer:

180 ft^3

Step-by-step explanation:

volume of the pyramid = (1/3)(area of base) (height)

v= 1/3×(10×12÷2)×(9)

= 180 ft^3

Answer:

answer on the picture.....

1-36) what is the sum of 2 + (1/5 + 1/5² + 1/5³ +...,.. +... 1/(5 to power n) ..)
help how

Answers

Answer:

[tex]\displaystyle \frac{9}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]

The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,

- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r


Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]

Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]



Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]

A website offers a coupon to 50\%50%50, percent of its visitors, selected at random, each day. Yasemin visits the website for 444 days. What is the probability that yasemin will not be offered a coupon on at least one of the days she visits the website? round your answer to the nearest hundredth. P(\text{at least one day without coupon})=p(at least one day without coupon)=p, left parenthesis, start text, a, t, space, l, e, a, s, t, space, o, n, e, space, d, a, y, space, w, i, t, h, o, u, t, space, c, o, u, p, o, n, end text, right parenthesis, equals.

Answers

The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

What is mean by Probability?

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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Complete the equation of the line whose yyy-intercept is (0,-1)(0,−1)left parenthesis, 0, comma, minus, 1, right parenthesis and slope is 444.

Answers

The complete equation in the slope-intercept form is y = 4x-1.

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation is,

y - y₁ = m (x - x₁)

And the standard form of the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

From the question, we have

m = 4 and coordinates of b is (0, -1).

So, the equation is,

y + 1 = 4 (x - 0)

y +1 = 4x

y = 4x-1

Therefore, the equation is y = 4x-1.

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A cryotherapy chamber uses extreme cold to reduce muscle soreness. A chamber is currently 0°F. The temperature in the chamber is dropping 2.5°F every second. Identify an inequality that represents the numbers of seconds $s$ that can pass for the temperature to drop below -20 °F

Answers

Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.

Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.

The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.

We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.

Dividing both sides by 2.5, we get the final inequality: $s$ > 7.

Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.

cross-tabulation can only be used for two variables; each variable must have well-defined labels. true false

Answers

The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false

The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that  that present the results of the entire group of respondents

The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "

The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables

The cross tabulation can be used for two or more variables

Therefore, the the given statement is false

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What is the product of the two largest one-digit primes and the largest two-digit prime?

Answers

Answer:

see below

Step-by-step explanation:

A prime number is a whole number that cannot be exactly divided by another number other than itself and 1.

The two largest one digit prime numbers are 7 and 5. The product of them is 7×5=35.

The two largest two digit prime numbers are: 89 and 97.

89×97=8633

2
Write the answer in each blank.
Of these numbers
745 281 578 170
is the smallest
is the largest

Answers

Answer:

170 is the smallest

745 is the largest

Step-by-step explanation:

It is what it is

please help me I don’t get this

Answers

The operations between functions are:

a) h(f(3)) = 5

b) (f×g)(4) = -8

c) f(  g(h(0))) -1

How to operate with functions?

The first thing we want to find is a composition, we want to find:

h(f(3))

That means that we need to evaluate h(x) in f(3), look at the graph and you can see that f(3) = -4

Replacing that we get:

h(f(3)) = h(-4)

And on the graph, we can see that h(-4) = 5

then h(f(3)) = 5

b) Now we have the product:

(f×g)(4) = f(4)*g(4)

Again, looking at the graph:

f(4) = -4

g(4) = 2

Then:

(f×g)(4) = f(4)*f(4)

(f×g)(4) = -4*2

(f×g)(4) = -8

c) Finally we have other composition:

f(  g(h(0)))

So we have 2 compositions, first we find:

h(0) = 5

f(  g(h(0))) = f(g(5))

Then:

g(5) = 0

f(  g(5)) = f(0)

Finally, look at the graph and you can see that f(0) = -1

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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 10(1.01)

Answers

The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

What is the exponential growth function?

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

Calculation:

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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