During the period of time that a local university takes the phone registrations, calls come in at the rate of one every two minutes.
A) What is the probability of three calls in ten minutes?
B) What is the probability of more than 3 calls in ten minutes?

In factored form, the same expression is thus:

8(x² + 2x + 3)

The expression can be factored to provide the common factor of 8:

8x² + 16x + 24 = 8(x² + 2x + 3)

We must now factor the quadratic expression within the parenthesis. The quadratic formula can be used:

x = [-b ± sqrt(b² - 4ac)] / 2a

We have a = 1, b = 2, and c = 3 for the formula x2 + 2x + 3. When we plug these numbers into the quadratic formula, we get:

x = [-2 ± sqrt(2² - 4(1)(3))] / 2(1)

x = [-2 ± sqrt(-8)] / 2 x = (-1 ± i√2)

The quadratic expression does not factor over the real numbers because the discriminant (\(b^{2}\) - 4ac) is negative. As a result, the factored equivalent expression is:

8(\(x^{2}\)+2x+3) = 8(x - (-1 + i2))(x - (-1 - i2))

8x²+16x+24 = 8(x+1)(x+3)

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

Answer:

x=24/13

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

times both sides by 8

x = 24/13

24/13 = 1.8

This means that a linear relationship exists among the variables.

When the data points on a scatterplot cluster along a straight line, it indicates that there is a linear relationship between the two variables being plotted.

The scatterplot visually shows that as one variable increases or decreases, the other variable also increases or decreases in a proportional manner, following a straight-line pattern.

The correlation coefficient is an estimation of the strength and direction of the linear relationship between two variables. A positive correlation coefficient indicates that as one variable increases, the other variable also increases, while a negative correlation coefficient indicates that as one variable increases, the other decreases.

The magnitude of the coefficient implies the strength of the relationship, with a value of 1 showing a perfect positive correlation and a value of -1 showing a perfect negative correlation.

To know more about linear relationship, here

https://brainly.com/question/13828699

#SPJ4

--The given question is incomplete; the complete question is

"A student conducting a research study was told by her professor to use a scatterplot in conjunction with calculating the correlation coefficient. She discovered that the data points clustered along a straight line; this means that:  

A. The student cannot determine if a relationship exists.

B. No relationship exists between variables.

C. A nonlinear relationship exists among the variables.

D. A linear relationship exists among the variables."--

Answer:

Functions: 2

Not a Function: 1 and 3

Step-by-step explanation:

1 and 3 cross over each other and don't go in a straight line.

Whilst, 2 does technically go in a straight line.

Answer:

-3/4

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -4 - -7)/(-2-2)

   ( -4+7)/(-4)

    3/-4

   -3/4

The objective function that has the same slope (parallel) as the given function $4x + 2y = 20 is

option d. $2x + $4y = $20.

To determine which objective function has the same slope as $4x + 2y = 20, we need to rearrange the given equation into slope-intercept form, y = mx + b, where m represents the slope. In this case, we have:

$4x + $2y = $20

$2y = -$4x + $20

y = -2x + 10.

By comparing this equation with the slope-intercept form, we can see that the slope is -2. Therefore, we need to find the objective function with the same slope. Among the options, option d, $2x + $4y = $20, has a slope of -2 since its coefficient of x is 2 and its coefficient of y is 4 (2/4 simplifies to -1/2, which is the same as -2/1). Thus, option d is the correct answer.

Learn more about Objective function here:

brainly.com/question/2500020

#SPJ11

If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;

P = l+l+w+w

P= 2(l+w)

60 = 2( 17+w)

60 = 2( 17+w)

17+w= 60/2

17+ w = 30

w = 30-17

w = 13cm

Therefore the height of the train ticket is 13cm

learn more about perimeter of a rectangle

https://brainly.com/question/10452031

#SPJ1

Answer:

35/72 yards of ribbon

Step-by-step explanation:

The quadratic inequality defined on the graph is given as follows:

y ≥ 2/3(x + 3)² - 24.

The coordinates of the vertex of the quadratic function are given as follows:

(-3, -24).

Hence the quadratic function is given as follows:

y = a(x + 3)² - 24.

In which a is the leading coefficient.

When x = 3, y = 0, hence the leading coefficient a is obtained as follows:

0 = a(3 + 3)² - 24

36a = 24

a = 24/36

a = 2/3.

Hence:

y = 2/3(x + 3)² - 24.

The quadratic function has a solid curve, and the values above it are pained, hence the inequality is given as follows:

y ≥ 2/3(x + 3)² - 24.

More can be learned about quadratic functions at https://brainly.com/question/1214333

#SPJ1

g(x) is basically transformed f(x). First, let's focus on f(x) graph. Notice how the graph has slope of 1 and intersect y-axis at (0,0).

Which means that our equation for f(x) is:

\( \large{f(x) = x}\)

Now then we focus on g(x). g(x) is f(x+k). That means if f(x) = x then f(x+k) would mean substitute x = x+k in the equation.

\( \large{f(x + k) = x + k }\\ \large{g(x) = x + k}\)

Next, we want to find the value of k. In the slope-intercept form or y = mx+b where m = slope and b = y-intercept. Notice the g(x) graph and see that the graph intersects y-axis at (0,4). Therefore k = y-intercept = 4.

\( \large{g(x) = x + 4}\)

Answer

Answer: 4

Step-by-step explanation:

answer is b Answer:

Step-by-step explanation:

When we identify a nonsignificant finding, p relates to alpha in the following way:

b. p is less than or equal to alpha.

Explanation:

In hypothesis testing, a p-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. On the other hand, alpha is the level of significance or the probability of rejecting the null hypothesis when it is true.

The common convention is to set the level of significance at 0.05 or 0.01, which means that if the p-value is less than alpha, we reject the null hypothesis. On the other hand, if the p-value is greater than alpha, we fail to reject the null hypothesis.

Therefore, when we identify a nonsignificant finding, it means that the p-value is greater than the alpha, and we fail to reject the null hypothesis. Hence, option (b) is the correct answer.

The appropriate "Null-Hypothesis" would be (a) population proportion is equal to 0.60.

In hypothesis testing, the null-hypothesis (H₀) represents the default assumption or claim that is being tested. It is generally stated as an equality or a specific value that is being tested against an alternative hypothesis (H₁).

In this case, the null-hypothesis is stating that the population proportion is equal to a specific value of 0.60. The alternative hypothesis, which is not provided in the options, would state a different relationship or inequality, such as the population proportion being greater than or less than 0.60.

The other options (b) the population proportion is not equal to 0.60 and (c) the sample-proportion is equal to 0.60, are not appropriate null hypotheses because they do not directly test population proportion.

Therefore, the correct option is (a).

Learn more about Hypothesis here

https://brainly.com/question/31853971

#SPJ4

The given question is incomplete, the complete question is

Which of the following would be appropriate null hypothesis?

(a) the population proportion is equal to 0.60

(b) the population proportion is not equal to 0.60

(c) the sample proportion is equal to 0.60

(d) all these choices are true.

The appropriate null hypothesis would be a. The population proportion is equal to 0.60.

In hypothesis testing, the null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often denoted as H0. The null hypothesis is typically the opposite of the alternative hypothesis, which suggests that there is a significant difference or relationship.

For the given options:

Based on the given options, the appropriate null hypothesis would be:

About appropriate null hypothesis here:

https://brainly.com/question/31853971

#SPJ11a. The population proportion is equal to 0.60.

Answer:

Step-by-step explanation:

The discriminant comes from the quadratic formula. We use the discriminant to determine, before factoring, what types of solutions we can expect when we do factor. In the quadratic formula, the discriminant is under a square root sign. If the number under a square root sign is negative (meaning the discriminant is negative), we will not have real number solutions because you can't have a negative number under a square root. So a is your choice.

Answer:

a

Step-by-step explanation:

Answer: $10

Step by step explanation:

Let the cost of the green fabric be g

Then, the cost of the blue fabric will be g+2.

The equation will be:

5b + 8g = 62

where, b = blue and g = green

Since b = g+2, this will be:

5b + 8g = 62

5(g+2) + 8g = 62

5g + 10 + 8g = 62

Collect like terms

5g + 8g = 62 - 10

13g = 52

Divide both side by 13

13g/13 = 52/13

g = 4

Green yard cost $4

Since blue = g + 2 = 4+2 = $6

Blue yard cost $6

The combined cost will be:

= $4 + $6

= $10

Answer:

-4/9 is a rational number

Step-by-step explanation:

Rational numbers are the numbers you can make by dividing one integer by another, so in other words a fraction.

Answer

4/9 belongs to rational numbers (D).

Explanation

(Lol moderator deleted everyone's answers so I'm gonna answer).

First I'll give you a definition of each choice.

Integers: Integers don't include decimals or fractions. Integers are positive and negative numbers. So basically it's this; (..., -3, -2, -1, 0, 1, 2, 3, ...). The '...' means numbers from infinity to the next number. I hope this makes sense Imao.

Whole numbers: whole numbers are integers, except they don't include negative numbers. Whole numbers include 0 (zero)... (0, 1, 2, 3, ...)

Natural numbers: natural numbers are whole numbers but they don't include 0 (zero)... (1, 2, 3, ...)

Rational numbers: rational numbers are numbers that can be expressed as a fraction. This includes repeating decimals such as 0.333 repeating. Rational numbers also include integers, because if you put the number over one, that is a fraction. Rational numbers are basically every number except for the radicals of some numbers (such as the square root of 3) and pi.

So now let's just see which one 4/9 is.

Well, 4/9 is not an integer, whole number, or natural number because it is a fraction.

But 4/9 can be expressed as a fraction (well, it already is one) meaning it is a rational number.

Answer:

Girls = 16

Total students = 40

Step-by-step explanation:

40% of the students are girls, this means 60% of the students are boys.

To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.

Also let's convert the percentages to decimals by moving the decimal two places left.

40% = 0.4 and 60% = 0.6

\(\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16\)

Now let's find the total number of students by adding the number of girls to the number of boys.

16 + 24 = 40

The corresponding equation is 4q + 3p = 22.

What is the slope of a line ?

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's b in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate. Locate two locations along the chosen line and find their coordinates.

Find the y-coordinate difference between these two places (rise). Find the difference between the x-coordinates of these two points (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope is defined as the relationship between the rise, or vertical change, between two points and the change, or horizontal change, between the same two points and can be represented as an equation.

Given that, coordinates are (p, 1/2) and (-8, q), slope is 3/4.

m = (y2 - y1)/(x2 - x1)

34 = (q - 1/2)/-8 - p

-24 - 3p = 4q - 2

4q + 3p = 22

The corresponding equation is 4q + 3p = 22.

Learn more about slope of a line here:

https://brainly.com/question/3493733

#SPJ1

With a critical value of 1.96 and a margin of error of 0.022, the standard error is 0.011.

To find the standard error, we can use the formula for the margin of error, which is:
Margin of Error = Z* × Standard Error
Given that the margin of error is 0.022 and the critical value (Z*) is 1.96, we can rearrange the formula to find the standard error:
Standard Error = Margin of Error / Z*
Standard Error = 0.022 / 1.96
Standard Error = 0.011224
Rounded to three decimal points, the standard error is 0.011.

Given a confidence interval with a critical value of 1.96 and a margin of error of 0.022, the standard error is approximately 0.011.

To know more about standard error, click here

https://brainly.com/question/13179711

#SPJ11

The ladder is 13 m long and leans against a window 5 m high, then the ladder leaned to the other side without moving its feet to reach the 12 m high window.

if we imagine a leaning ladder it will look like a right triangle and it will remind us of the Pythagorean theorem. do you remember the pythagorean theorem?

The Pythagorean theorem explains the relationship or relationship between the lengths of the sides of a right triangle.

The Pythagorean theorem reads: "The square of the length of the hypotenuse (hypotenuse) in a right triangle is equal to the sum of the squares of the lengths of the other sides".

in the picture, let's say if the width of the street is a, the height of the window is b and the length of the stairs is c.

in this case we will find the width of the street, namely a, then we use formula a² = c² - b² .

then it will be

b = 12

c = 13

a² = c² - b²

a² = 13² - 12²

a² = 169 - 144

a² = 25

a = 5

Answer:300

Step-by-step explanation:

Because the total area planted (240 square feet) is going to be composed of an area of flowers (x) and an area of vegetables, you can say x + y ≤ 240 (because he will use UP TO 240 square feet)

Because the area of vegetables will be AT LEAST twice the area of flowers, you can say y ≥ 2x

Answer:

Step-by-step explanation:

8x + 23

Answer:

x > 3

Step-by-step explanation:

Here, we want to write the inequality represented

We start by looking at the value on which we have the circle

It is on the value 3

we can also see that the circle is unshaded and also that, the graph faces the right direction

As the circle

is unshaded, we have it that we only use the inequality without the equal to

So we have the representation as;

x > 3

Answer:

Step-by-step explanation:

25*60%=15 on the backpack

25-15= 10 on the binder

Step-by-step explanation:

the backpack was 15 dollars and the binder was 10

Answer:

0

Step-by-step explanation:

g(x) = x-6

- g(x) = -x+6

g(x) + -g(x) = x-6 + -x+6

                 = x-x -6+6

                   =0

Option 3) Sometimes is the correct answer, Sometimes an equilateral triangle is similar to a scalene triangle.

If the respective sides are proportional and the corresponding angles are congruent, two triangles are comparable. An equilateral triangle has three congruent sides and three congruent angles, so any triangle that is similar to an equilateral triangle must also have three congruent angles. However, a scalene triangle has no congruent sides and no congruent angles, so it is possible for a scalene triangle to be similar to an equilateral triangle only if it has the same angle measurements as an equilateral triangle, but with different side lengths. Therefore, a scalene triangle can be similar to an equilateral triangle, but it is not always the case.

In general, if two triangles are similar, it means that they have the same shape but possibly different sizes. In the case of an equilateral triangle and a scalene triangle, if they are similar, then it means that the scalene triangle has the same angles as the equilateral triangle, but its sides are of different lengths. So it is possible for a scalene triangle to be similar to an equilateral triangle, but not in all cases.

Learn more about equilateral triangle here:

https://brainly.com/question/17556213

#SPJ4

Answer:

median number of snow days is 4

Step-by-step explanation:

Listed in order from least to greatest:

2

3

3

3

4

5

6

7

8

There are 9 numerals on this list.  Because this count is odd, the median is simply the middle value, which here is 4.  This is the median number of snow days.

Answer:

2 snow days

Step-by-step explanation:

Harry will have a gross margin of $5,290.

If the cost of each shirt is $12.90 and 1,000 shirts are purchased, then the total cost of 1,000 shirts is:

$12.90 x 1,000 = $12,900

If Harry sells 800 shirts at a 50% markup, then he sells them for:

$12.90 x 1.5 = $19.35

Harry sells the 200 remaining shirts at a 30% reduction from the selling price:

$19.35 x 0.7 = $13.55

The gross margin (markup) is the difference between the selling price and the cost per shirt. For the 800 shirts sold at a markup, the gross margin per shirt is:

$19.35 - $12.90 = $6.45

So the gross margin for the 800 shirts is:

$6.45 x 800 = $5,160

For the 200 shirts sold at a discount, the gross margin per shirt is:

$13.55 - $12.90 = $0.65

So the gross margin for the 200 shirts is:

$0.65 x 200 = $130

Therefore, the total gross margin for all 1,000 shirts is:

$5,160 + $130 = $5,290

Harry will have a gross margin of $5,290.

Learn more about :

gross margin : brainly.com/question/14721252

#SPJ11