Write an equation (slope-intercept form) of the line
passing through the point (-20, 4)
that is perpendicular to the line
2x + 5y = 10.
y =
Blank 1:

Using the normal distribution and the central limit theorem, the probabilities are calculated as follows:

a) One meter stick greater than 100.17 cm: 0.1357 = 13.57%.

b) Group of 10 with mean less than 100.3: 0.1711 = 17.11%.

c) Group of 44 with mean greater than 100.08: 0.0918 = 9.18%.

d) Group of 50 with mean between 100.05 and 100.07: 0.5222 = 52.22%.

e) 92nd percentile of sample of 24: 100.09.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the Central Limit Theorem, the z-score formula can be given as follows:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The mean and the standard deviation of the lengths are given as follows:

[tex]\mu = 100.06, \sigma = 0.1[/tex]

For item a, we have that n = 1 and the probability is one subtracted by the p-value of z when X = 100.17, hence:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.17 - 100.06}{\frac{0.1}{\sqrt{1}}}[/tex]

Z = 1.1

Z = 1.1 has a p-value of 0.8643.

1 - 0.8643 = 0.1357.

For item b, we have that n = 10 and the probability is the p-value of Z when X = 100.03, hence:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.03 - 100.06}{\frac{0.1}{\sqrt{10}}}[/tex]

Z = -0.95

Z = -0.95 has a p-value of 0.1711.

For item c, we have that n = 44 and the probability is one subtracted by the p-value of Z when X = 100.08, hence:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.08 - 100.06}{\frac{0.1}{\sqrt{44}}}[/tex]

Z = 1.33.

Z = 1.33 has a p-value of 0.9082.

1 - 0.9082 = 0.0918 = 9.18%.

For item d, we have that n = 50 and the probability is the p-value of Z when X = 100.07 subtracted by the p-value of Z when X = 100.05, hence:

X = 100.07:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.07 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]

Z = 0.71.

Z = 0.71 has a p-value of 0.7611.

X = 100.05:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{100.05 - 100.06}{\frac{0.1}{\sqrt{50}}}[/tex]

Z = -0.71.

Z = -0.71 has a p-value of 0.2389.

0.7611 - 0.2389 = 0.5222 = 52.22%.

For item e, we have that n = 24, and the 92th percentile is X when Z = 1.405, hence;

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]1.405 = \frac{x - 100.06}{\frac{0.1}{\sqrt{24}}}[/tex]

x - 100.06 = 1.405 x 0.0204

X = 100.09.

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The Maximum height of the object is 2888.9 feet which is at 23.06 seconds

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let h represent the height of an object after t seconds. Given that:

h(t) = -4.9t² + 226t + 283

The maximum height is at h'(t) = 0, hence:

h'(t) = -9.8t + 226

-9.8t + 226 = 0

9.8t = 226

t = 23.06 s

h(23.06) = -4.9(23.06)² + 226(23.06) + 283 = 2888.9

Maximum height is 2888.9 ft

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Given data:

The series is 1 + 2 + 4 + 8 + 16 + 32 + ....

The given series is G.P because the common ratio for GP is,

Here, the common ratio is 2.

Sum of the first five numbers ,

Here, a is first term that is 1

r is common ratio that is 2

n is the number

Therefore, sum is given as

Thus, the sum of first five terms is 31

The correct option is (2).

Answer: The median and mean of height of students is not equal, the median is greater.

Step-by-step explanation:

Definition of Median:

Median is the middle value in the picture. To find the median, order the numbers and see which one is in the middle value of the list.

in this picture, first, we order the numbers in numerical order:

1,1,1,2,2,3,3,5,6,6

Find the middle number:

1,1,1,2,2,3,3,5,6,6

As above, 3 is the middle number, then we find which bar represents the median of height of students:

1+1+1+2+2+3 = 10 students

Referring back to the chart, if we add the first 2 bars together, we will get 6+2 = 8 students, but the median number is 10 students, that means the median will be at the third bar, median of height of students = 62-64.

Definition of Mean:

Mean is the sum of the numbers divided by the number of numbers.

In this picture, the Mean will be

(2+6+5+6+3+3+2+1+1+1) / 10

= 3 students

which means the mean height of students = 60-62.

Answer:

u did not addd the pic

Step-by-step explanation:

Answer: 1.3660254037844

-0.36602540378444

Step-by-step explanation:

By using conversion factor, if Lorraine prepared a 2.5 gallon pot filled with tomatoes to be canned in jars and each jar will hold 1.25 quarts of tomatoes, then Lorraine can fill 8 jars  

The quantity of tomatoes prepared by Lorraine = 2.5 gallon

The quantity of tomatoes can be filled in one jar = 1.25 quarts

We know

1 gallon = 4 quarts

First convert the quantity of tomatoes prepared by Lorraine from gallon to quarts

2.5 gallon =  2.5×4 = 10 quarts

How many jars can Lorraine fill = The quantity of tomatoes prepared by Lorraine/The quantity of tomatoes can be filled in one jar

we have to use division

= 10/1.25

= 8 jars

Hence, if Lorraine prepared a 2.5 gallon pot filled with tomatoes to be canned in jars and each jar will hold 1.25 quarts of tomatoes, then Lorraine can fill 8 jars

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The value of k = -10 in f(x).

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

The amount "left over" after a calculation is the remainder. The integer that remains after multiplying one integer by another to create an integer quotient is known as the remnant in mathematics.

Given that,

f(x) = x³ + kx + 13

The remainder when f(x) is divided by x + 1 is 22,

Here, the f(x) is divided by x+1

Hence, x = -1

Substitute x = -1 in f(x)

22 = f(x) = x³ + kx + 13

22 = f(-1) = (-1)³ + k(-1) + 13

22 = -1 –k +13

22 = -k +12

K = -10

Therefore, the value of k = -10 in f(x).

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Answer:

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

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we want to find is 1/3.

Using point-slope form, the equation is

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

Answer:

  A: y = 10

  B: ∠A = 42; ∠C = ∠D = 138

Step-by-step explanation:

Given vertical angles A and B, with A marked 5y-8 and B marked 42, you want to know the value of y and the measures of supplementary angles C and D.

Vertical angles A and B are congruent, so we have ...

  ∠A = ∠B

  5y -8 = 42

  5y = 50 . . . . . . . add 8

  y = 10 . . . . . . . divide by 5

As we noted above, angle A has the same measure as vertical angle B:

  ∠A = 42

Angle C forms a linear pair with angle B, so is supplementary:

  ∠C = 180 -∠B = 180 -42

  ∠C = 138

Angle D is a vertical angle to angle C (and is also supplementary to angle B).

  ∠D = 138

With the aid of subjective judgment, we can describe the number of girls as; A. The number of girls is significantly low.

Subjective judgement is simply defined as something that is subjective is based on personal opinions and feelings rather than on facts.

Now, we are told to assume that 600 births are randomly selected and 26 of the births are girls.

Now, we see that the total number of births are assumed as 600.

Now, since only 26 of that size are seen to be girls, then it means that;

Percentage that are girls = (26/600) * 100 = 4.33%

Thus, using subjective judgement we see that the percentage that are girls is so low that it is even lower than 5%. Thus, we can say that The number of girls is significantly low.

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Using it's concept, the probabilities are given as follows:

a) Type A die and orange: 1/10 = 0.1.

b) Blue: 23/30

c) Type B, if blue: 8/23.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

For item a, the probability that a type A dice is chosen is:

3/5.

As there are 5 dices, 3 of type A and 2 of type B.

The probability that a type A dice comes up orange is:

1/6.

As it has six faces, one of which is orange.

Then the probability of an orange type A dice being chosen is:

3/5 x 1/6 = 1/10 = 0.1.

For item b, the probability of blue is divided as follows:

Hence the probability of a blue dice is:

p = 5/6 x 3/5 + 4/6 x 2/5 = 23/30

For item c, we apply the conditional probability, hence the probability is given as follows:

p = (4/6 x 2/5)/(23/30) = (8/30)/(23/30) = 8/23.

Dividing the probabilities of type B and blue by the probability of blue.

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Answer:

D). Angle B ≈ Angle E

Step-by-step explanation:

ASA means that for the relation to be true, there not only has to be the 3 given proportionate values, but 2 have to be angles and 1 has to be a side.

Since we already have the 1 side, option 1 and 2 are voided.

Then since we already have Angle A and D option 3 is as well, so through this we know the answer is number 4 or Angle B = Angle E

Hope this helps.

The volume of this triangular prism 7yd x 7yd x 8yd is calculated as 196 [tex]yd^3\\[/tex] as per answered with the correct unit.

A prism is a kind of a polyhedron in geometry that has n number of parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the present first base, and the n faces.

The bases are all translated into all cross-sections that are parallel to them.

The volume of this prism can be found by applying the formula

1/2 Area x Height

= 1/2 x 7 x 7 x 8

= 196 [tex]yd^3\\[/tex]

V=Bh

V=Bh, where B can be said as the base area and h as the height, is the formula for a prism’s volume. The prism has a rectangular base.

The total area that any kind of prism takes up in three dimensions is known as its volume. It is defined in mathematically as the result of the base’s area and length.

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By using the method of addition, the equation is 12x + 1.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The sum is the entire value, and the addends are the integers that are being added. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum.

Given that,

5x - 4 > 12 adding 4 to both sides;

5x - 4+ 4 > 12 + 4

5x > 16 dividing both sides by 5;

x > 16/5

12x + 5-4

12x + 1

Therefore, the equation is 12x + 1.

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Answer:

you accidentally put x+6 for the 1st part

Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.

The future value formula is given by:

[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]

In which:

For this problem, the parameters are given as follows:

P = 2000, r = 0.06, n = 10.

Hence the value of the account will be of:

[tex]V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right][/tex]

V(10) = $26,361.59.

The complete problem is:

"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).

What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"

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Answer:

True

Step-by-step explanation:

The following rational fractions is graphed below?

f(x) = 1/ is the rational function seen in the given graph (x - 4)

How Are Graphs of Asymptotes Functions Interpreted?

The vertical asymptote of the graph is located at x = 4.

Let's determine each function's vertical asymptote.

We set the denominator equal to 0 to determine the vertical asymptote.

A) x + 4 = 0\sx = -4

That's incorrect

B) 4x = 0 x = 0 Invalid

C) The denominator is erroneous since it lacks a variable.

D) x - 4 = 0\sx = 4

So, this is true.

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This just means that the y coordinate will  always be 3 for all coordinates of x that means that the y coordinate of the point ( -7,1) will change to

(-7,3)

Answer:

g(7) = 21

Explanation:

To calculated g(7), we need to replace x by 7 in g(x) as:

Therefore, g(7) is equal to 21

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

ATTACHED IS THE SOLUTION

Answer:

x= 12

Step-by-step explanation:

8/4 = 2

2x6 = 12

Apply right triangle proportions:

20 (16) = x (x)

320 = x^2

√320 = x

x = 8√5

We are given w^2 + 5w and we are asked to identify the terms for each of its parts.

First, let's start with w. The letter w is used to represent an unknown value. Thus, it is called a variable.

ext, 2. Here, 2 is useda as an exponent of w in the first term.

Meanwhile, 5 is used as a multiplier or a numerical coefficient of w in the second term.

Finally, the expression w^2 + 5w is

The sales of the number of hammers that give the maximum revenue of 32400 is 1800

The equation of the revenue function is given as

R = 36x − 0.01x2

Rewrite the equation properly as a quadratic function

So, we have the following equation

R = 36x − 0.01x^2

Differentiate the above function

So, we have the following equation

R' = 36 - 0.02x

Set the differentiated function to 0

So, we have the following equation

36 - 0.02x = 0

This gives

0.02x = 36

Divide both sides by 0.02

So, we have

x = 1800

In (a), we have

36 - 0.02x = 0

0.02x = 36

x = 1800

Substitute x = 1800 in R = 36x − 0.01x^2

So, we have

R = 36 x 1800 − 0.01 * 1800^2

Evaluate

R = 32400

Hence, the maximum revenue is 32400

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Answer:Hence, the measure of angle whose measure is 32∘ less than its supplement is 74∘.

Step-by-step explanation:

Using a system of equations, it is found that 4 tangerines will balance one apple.

The equations are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

For this problem, the variables are given as follows, considering the situation described:

For the first picture, one apple and one tangerine balance one grapefruit, hence:

a + t = g.

For the second picture, one banana and one tangerine balance one apple, hence:

b + t = a.

For the third picture, two grapefruits balance three bananas, hence:

2g = 3b.

g = 1.5b.

Replacing on the first equation, we have that:

a + t = 1.5b.

From the second equation, we have that:

b = a - t.

Hence, replacing on the first:

a + t = 1.5(a - t)

1.5a - 1.5t = a + t

0.5a = 2t

a = 4t

Hence 4 tangerines will balance one apple.

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Answer:

A

Step-by-step explanation:

if you feel cold your body will tell your brain or give feedback to make you think or say its cold