Consider the numbers 9 and 12. What is the product of the greatest common factor and the least common multiple for the numbers?

Answer:

a) The lower bound of the confidence interval is below 4.50 minutes, which means that there is not sufficient evidence to say that the mean wait time for customers is longer than 4.50 minutes with a 98% level of confidence.

b) The null hypothesis is \(H_0: \mu \leq 4.50\), and the alternate hypothesis is \(H_a: \mu > 4.50\)

Step-by-step explanation:

Finding the confidence interval:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.98}{2} = 0.01\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.01 = 0.98\), so Z = 2.327.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 2.327\frac{2.1}{\sqrt{53}} = 0.67\)

The lower end of the interval is the sample mean subtracted by M. So it is 4.94 - 0.67 = 4.27 minutes

The upper end of the interval is the sample mean added to M. So it is 4.94 + 0.67 = 5.61 minutes.

a. Is there sufficient evidence to say that the mean wait time for customers is longer than 4.50 minutes with a 98% level of confidence?

The lower bound of the confidence interval is below 4.50 minutes, which means that there is not sufficient evidence to say that the mean wait time for customers is longer than 4.50 minutes with a 98% level of confidence.

b. State the null and alternative hypotheses for the test.

Testing if there is evidence to say that the mean wait time for customers is longer than 4.50 minutes, which is the alternate hypothesis.

So the null hypothesis is \(H_0: \mu \leq 4.50\), and the alternate hypothesis is \(H_a: \mu > 4.50\)

Answer: y=-3x-4

Step-by-step explanation:

Since we know slope, we can plug it into slope-intercept form to find the y-intercept by using the given points,

y=-3x+b

8=-3(-4)+b

8=12+b

b=-4

Now that we know the y-intercept, we can complete the slope-intercept form.

y=-3x-4

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

The equation of the line is y = (3/2)x - 1/2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).

Now,

The equation of a line.

y = mx + c

The line passes through points (3, 4) and (5, 7).

m = (7 - 4) / (5 - 3)

m = 3/2

Slope = 3/2 _____(1)

Now,

(3, 4) = (x, y)

4 = 3/2 x 3 + c

4 = 9/2 + c

c = 4 - 9/2

c = (8 - 9) / 2

c = -1/2

y-intercept = -1/2 ____(2)

Now,

y = mx + c

From (1) and (2),

y = (3/2)x - 1/2

Thus,

The equation of the line is y = (3/2)x - 1/2.

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The complete question.

Find the equation of a line that [passes through the point (2, 4), and (5, 7).

Answer:

m = - 1/2

Step-by-step explanation:

m = -4 - 1

4 - -6

- 5/10

m = - 1/2

Answer:

This is a function

Step-by-step explanation:

If you do the Vertical Line Test you can see that the line passes through only one dot at a time. Therefore it is a function. If the line passed through more than one dot at a time then it wouldn't be a function.

Answer:

The answer is 92%

Step-by-step explanation:

448/487=.92

Add the two groups together for total students:

487 + 448 = 935 total students.

The probability of not using a chrome book is the number of students not using one / total students.

Probability of not using a chromebook = 448/935

Answer:

ranus is a large planet with a volume of 6.833 x 1013 cubic kilometers. You could fit a little more than 63 Earths inside of Uranus, but like the other gas giants, it is not very dense. Comprised mostly of gas, the planet is only about 14.5 times more massive than Earth is.

Step-by-step explanation:

^

The factors of the original expression, u and v to produce a sum of simpler terms, the derivative of y with respect to x is: y' = -2x⁴ - x² - 10x + 15

Given the expression y = (3 - x²) (x³ - 5x + 5),

We need to find the derivative of y with respect to x.

We can find y' using two methods:

Method 1: Applying the Product RuleIf y = uv, then we know that y' = u'v + uv'Applying this formula to the given expression, We get:

y = (3 - x²) (x³ - 5x + 5)u = (3 - x²) and v = (x³ - 5x + 5)

Differentiating u and v, we get:u' = -2x and v' = 3x² - 5

Substituting these values into the formula for y', we get:

y' = u'v + uv' = (-2x) (x³ - 5x + 5) + (3 - x²) (3x² - 5)

Simplifying this expression, we get:

y' = -2x⁴ + 10x² - 10x - 3x² + 15 = -2x⁴ - x² - 10x + 15

Method 2: Multiplying the Factors to Produce a Sum of Simpler Terms to Differentiate

Expanding the given expression, we get:

y = 3x³ - 15x + 15 - x⁵ + 5x³ - 5x - 3x² + 15x² - 15x

Differentiating this expression, we get: y' = 9x² - 15 + 0 - 5x⁴ + 15x² - 5 - 6x + 30x - 15

Simplifying this expression, we get:

y' = -2x⁴ - x² - 10x + 15

Therefore, the derivative of y with respect to x is:y' = -2x⁴ - x² - 10x + 15

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Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

Answer:

28/10

14/5

3 - 1/5

Step-by-step explanation:

28/10

14/5

3 - 1/5

The whole numbers to make 2.8 in three different ways are 28/10,14/5, 3 - 1/5.

An entire quantity is an absolutely any high-quality wide variety that does not encompass a fractional or decimal component. because of this, as an example, the numbers 0, 1, 2, three, 4, 5, 6, and 7 are all whole numbers. Numbers that include -three, 2.7, or 3 ½ aren't whole numbers.

The complete numbers are a set of real numbers that consist of 0 and all superb counting numbers. while, excludes fractions, negative integers, fractions, and decimals. when you consider that, 1 is a positive integer and is a counting number. therefore, it is taken into consideration to be a whole wide variety.

sure, 0 is a rational variety. because we understand, a rational number may be expressed as p/q, in which p and q are integers and q isn't equal to 0. for this reason, we will explicit zero as p/q, wherein p is identical to zero and q is an integer.

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The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:

32/12 and 27/12.

The mixed numbers in the context of this problem are given as follows:

The fractions that represent each number are given as follows:

The least common factor of 3 and 4 is given as follows:

3 x 4 = 12.

Hence the equivalent fractions are given as follows:

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This is the coordinate plane shown below:

The horizontal axis is x-axis and the vertical axis is the y-axis.

See that the coordinate plane is broken down into 4 quadrants.

• Top Right - 1st quadrant

• Top Left - 2nd quadrant

• Bottom Left - 3rd quadrant

• Bottom Right - 4th quadrant

Now, we can plot a pair of point (x,y) on the coordinate plane.

We can have 4 types of points:

• (x positive, y positive) >>> falls in 1st quadrant

• (x negative, y positive) >>> falls in 2nd quadrant

• (x negative, y negative) >>> falls in 3rd quadrant

• (x positive, y negative) >>> falls in 4th quadrant

Let's plot 4 types of points in each coordinate and show in coordinate plane.

Let's plot:

A=(2,2)

B=(-2,2)

C=(-2,-2)

D=(2,-2)

In coordinate plane, they are:

Answer:

The question has a mistake

Step-by-step explanation:

11d+7c= 172.5

10d+7c= 155.8

By subtraction;

1d+ 0c = 16.7

1d = 16.7

11×16.7+7c=172.5

7c = 172.5-11*16.7

You will get a negative answer yet the cost cannot be negative.

Answer:

I believe the answer is 1/12

Step-by-step explanation:

the volume of a rectangular prism is length × width × height

Answer:

\( \frac{1}{12} \: cubic \: foot\)

Step-by-step explanation:

\(V_{box} = lbh \\ = 1 \frac{1}{2} \times \frac{1}{6} \times \frac{1}{3} \\ \\ = \frac{ \cancel3}{2} \times \frac{1}{6} \times \frac{1}{ \cancel3} \\ \\ = \frac{1}{12} \: cubic \: foot\)

Answer:

2

Step by Step Explanation

Keep Change Flip

3/4x8/3=24/12=2

Answer:

2

Step-by-step explanation:

3/4 divided by 3/8

3/4 x 8/3

cross simplify to get

1/4 x 8/1

cross simplify again to get

1 x 2 = 2

Answer:

$5.86

Step-by-step explanation:

The total was $36.31

We were given the price of 1, which was $1.15

$36.31-$1.15 = $35.16 remaining

Since the other 6 friends ordered the same meal, they would have paid the same price, so we would divide by 6

$35.16/6 = $5.86

Answer:five million six hundred seventy-three thousand one hundred fifty-four. 5,000,000 + 600,000 + 70,000 + 3,000 + 100 + 50 + 4. I'm pretty sure that's right

Step-by-step explanation:

Answer:

5,673,154

Expanded Form - 5,000,000 + 600,000 + 70,000 + 3,000 + 100 + 50 + 4

Word Form - five million, six hundred seventy-three thousand, one hundred fifty-four.

Hope it helped!

Answer:

 ƒ(x) = (x - 2)^2 + 1

Step-by-step explanation:

To make f(x) be a translation of the graph of g(x) by (h, k), write it as ...

 f(x) = g(x -h) +k

You want to translate g(x) = x^2 by (2, 1), 2 units right and 1 unit up, so the function f(x) is ...

 f(x) = g(x -2) +1

Answer:

24.50

Step-by-step explanation:

1.40 per pound so 17 x 1.40= 23.80

1.40/2= .70 this is for the half pound

so now add 23.80+.70=24.50

Answer:

85 square inches.

Step-by-step explanation:

The area of a triangle can be found by the formula \(1/2bh\), assuming b is the base and h is the height.

If b is 17 inches and h is 10 inches:

\(1/2(17)(10)\)

\(1/2(170)\)

\(A = 85\)

Therefore, the area is 85 square inches.

Using the combination formula, it is found that she can select the shirts in 775,200 ways.

The order in which the shirt are chosen is not important, hence, the combination formula is used to solve this question.

Combination formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem:

\(T = C_{17,3} \times C_{20,3} = \frac{17!}{3!14!} \times \frac{20!}{3!17!} = 680 \times 1140 = 775200\)

She can select the shirts in 775,200 ways.

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9514 1404 393

Answer:

  x = 10; WX = 5; HJ = 10

Step-by-step explanation:

The hash marks indicate that points W and X are midpoints of their respective segments. That makes WX a midline of the triangle. The midline is always half the length of the base (HJ). We can use this fact to write an equation relating the lengths.

  HJ = 2·WX

  x = 2(x -5) . . . .substitute the given expressions

  x = 2x -10 . . . . eliminate parentheses

  10 = x . . . . . . . add 10-x to both sides

This value of x tells you that ...

  HJ = x = 10

  WX = x -5 = 5

Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

Answer:

13

Step-by-step explanation:

4w-10=42

4w=52

w=52/4

w=13

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

Answer:

D) Simultaneously compare several population means.

Step-by-step explanation:

ANOVA (Analysis of Variance) was developed by Ronald Fisher.

ANOVA ie Analysis of Variance, is collection of statistical models & linked estimation processes, like variation among & between groups. It is used in analysing differences among various means.

So, it is used to : D) Simultaneously compare several population means.

Nominal Data, t test, population proportions are not uses of ANOVA.

Answer:

3/5 < 2/3 < 3/4

Step-by-step explanation:

36/60  = 3/5

40/60     = 2/3

45/60     = 3/4