Find the area of the triangle below. Be sure to include the correct unit in your answer.​

For each variable, the possible values are:

a) T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b) X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

c) U = {0, 1, 2, 3, 4, 5, 6}

d) Z = {0, 1, 2}

Item a:

In total, there are 10 pumps, hence the possible values are all integers from 0 to 10, that is:

T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Item b:

In the first, there are 6 pumps, and in the second 4, hence, the difference ranges from -4 to 6, that is:

X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

Item c:

The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.

U = {0, 1, 2, 3, 4, 5, 6}

Item d:

Either none of the stations has exactly two pumps in use, or one has or both, hence the variable ranges from 0 to 2.

Z = {0, 1, 2}

The question is incomplete. The complete question is:

"The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)

a. T = the total number of pumps in use

b. X = the difference between the numbers in use at stations 1 and 2.

c. U = the maximum number of pumps in use at either station

d. Z = the number of stations having exactly two pumps in use"

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The answer is 2π

Hope this helps

1. The amount of money which the tanker driver receive per day during week days is R832.50 per day.

2. The total number of hours that the driver has worked in March 2022 is 216 hours.

We are given that regular pay rate per hour = R92.50 and regular work hours per day on weekdays = 9

The regular pay rate per day on weekdays:

= Regular pay rate per hour x Regular work hours per day on weekdays

= R92.50 x 9

= R832.50.

What is the total number of hours he has worked in March?

Available data

Number of weekdays in March 2022 = 22

Number of work hours per day on weekdays = 9

Number of work hours on Saturday = 4.5

Number of Saturdays in March 2022 = 4

Total work hours on weekday:

= Number of weekdays x Number of work hours per day on weekdays

= 22 x 9

= 198

Total work hours on Saturdays:

= Number of Saturdays x Number of work hours on Saturday

= 4 x 4.5

= 18

Now, the total number of work hours in March 2022 is computed as follows:

= Total work hours on weekdays + Total work hours on Saturdays

= 198 + 18

= 216 hours

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Complete question is;

The driver of the water tanker works for 5½ days per week and 9 hours per day on week days except on Saturdays where they work for a ½ day (4,5 hours). The rate per hour was R92,50 and the rate of pay was doubled on Saturdays. 2.1 Calculate the amount of money that the tanker driver receive per day during week days. 2.2 Determine the total number of hours that the driver has worked in March 2022

Answer:

80°

Step-by-step explanation:

140+140+x=360

280+x=360

x=80

Answer:

image

Step-by-step explanation:

image

The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

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Answer:

A. Most of the students collected 12 apples.

Step-by-step explanation:

The line plotted on the graph is demonstrating the 12 apples picked from the club. The students are on the y-axis since they are independent and apples are placed on the x axis. The line is intersecting the points on x-axis. There is average collection of 12 apples by each student.

Answer:

73.5

Step-by-step explanation:

7100 km = 4411.735 miles

1 minute = 60 secs

4411.735/60 = 73.5 miles/sec

Option (e) SE(u(x)) = 1 is incorrect about the sample correlation coefficient between two random variables X and Y based on a set of bi-variate points (X i , Yi )

The examination of the relationship between two variables is possible using bivariate analysis, which also has many real-world applications. It seeks to determine whether there is a link between the variables and how strong it is.

You can examine an association or causality hypothesis using bivariate analysis. It also aids in the prediction of dependent variable values based on changes in an independent variable.

The correlation coefficient (R) is a numerical value that ranges from -1 to 1. It reveals the strength of the linear relationship between the two specified variables.

The coefficient is referred to as Pearson's correlation coefficient when used to describe a linear regression.

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Answer:

5y/8w = x

Step-by-step explanation:

Answer:

The 90% for the average weights of men is between 137.24 lb and 185.76 lb.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 14

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.7709

The margin of error is:

M = T*s = 1.7709*13.7 = 24.26

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 161.5 - 24.26 = 137.24 lb

The upper end of the interval is the sample mean added to M. So it is 161.5 + 24.26 = 185.76 lb

The 90% for the average weights of men is between 137.24 lb and 185.76 lb.

The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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Answer:

A / commutative property

Step-by-step explanation:

Answer:

0.2, 0.21, 0.25 (1/4), 0.2666666 (4/15)

Step-by-step explanation:

Using z-scores, it is found that due to the higher z-score, Bryant had the better performance.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For Maravich, we have that the parameters are \(X = 2273, \mu = 1198, \sigma = 379\), hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2273 - 1198}{379}\)

Z = 2.84.

For Bryant, we have that the parameters are \(X = 2832, \mu = 1123, \sigma = 433\), hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2832 - 1123}{433}\)

Z = 3.95.

Due to the higher z-score, Bryant had the better performance.

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Answer:

The answer would be B

Step-by-step explanation:

Answer:       5.1 x 10⁻¹ kg

To find the mass of water in the bottle, we can multiply the mass of one molecule by the number of molecules.

By using dimensional analysis, or by cancelling out units, we can figure out what to multiply or divide. Dimensional analysis uses fractions written with units. Dividing the same unit cancels out units we don't need.

To solve:

We are looking for the mass of H₂O in the bottle.

The units we need in the answer are:      \(\displaystyle{ \frac{kg}{bottle} }\)

The question tells us:

Our equation puts the fractions in an equation, making them multiply to get the units we need.

\(\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\ =\ \frac{kg}{bottle}\)

Why is this equation correct?

Remember that dividing the same unit will cancel them out. In the equation, we have H₂O in a numerator and H₂O in a denominator. So, H₂O will cancel out. In the end, we will only have kg in the numerator and bottle in the denominator.

Take the equation we wrote. Now that we know our equation gives us the right units, we only need the front part.

\(\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\)

Cancel out H₂O:

\(=\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1} \ *\ \frac{(1.7*10^{28})}{1\ bottle}}\)

Simplify the equation:

\(=\displaystyle{ \frac{(3 * 10^{-29})*(1.7*10^{28})\ kg}{1\ bottle}\)

\(=\displaystyle{ \frac{3 * 10^{-29}*1.7*10^{28}\ kg}{1\ bottle}\)

Use exponent rules to multiply 10⁻²⁹ with 10²⁸:

\(=\displaystyle{ \frac{3 *1.7*10^{28-29}\ kg}{1\ bottle}\)

\(=\displaystyle{ \frac{3*1.7*10^{-1}\ kg}{1\ bottle}\)

Multiply within the numerator to simplify:

\(=\displaystyle{ \frac{5.1*10^{-1}\ kg}{1\ bottle}\)

∴ The mass of water in the bottle is 5.1 x 10⁻¹ kg.

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Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

In the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

Row echelon form suggests that: Each row's leading (first) entry must be

Each following row's first entry must be on a new column to the right.

All rows with zero entries are listed below rows with non-zero items.

If the leading entry in each column is the only nonzero element in that column, reduced echelon form also results from echelon form conditions.

According to the definitions we see that, in the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

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The probability distribution for the number of empty balls is,

I.(3, 0, 0), II.(0, 3, 0) and III.(0, 0, 3).

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment).

The binomial probability is \(^nC_xp^{n-x}q^x\).

Given, Each of the three balls is randomly placed into one of three bowls.

Therefore, It can be I.(3, 0, 0), II.(0, 3, 0) and III.(0, 0, 3).

So, The probability distribution would be, P(1) + P(2) + P(3).

= 1/3 + 1/3 + 1/3.

= 1.

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Answer:

Step-by-step explanation:

X: -2, -1, 0, 1, 2,...

Y: -2, -1, 0, 1, 2,...

(y=x)

Answer:

Please give more info

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The value of y in the given inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.

To solve any inequalities, apply the same knowledge used to solve a normal algebraic equation by isolating the value of the variable.

The given inequality is 4y + 1/5 ≤ 4/5. To solve for the value of y, follow the steps below:

4y + 1/5 ≤ 4/5 [given]

Subtract 1/5 from both sides of the inequality:

4y ≤ 4/5 - 1/5 [subtraction property of equality]

4y ≤ 3/5

Multiply both sides by 1/4:

4y × 1/4 ≤ 3/5 × 1/4

y ≤ (3 × 1) / (5 × 4)

y ≤ 3/20

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Answer:

6+3x=w

Step-by-step explanation:

6 *more* more always means +

and then three *times* times always means *

so it would equal 6+3x=w

The product of the expression is given as  1/4x²y²

Remember that an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). It can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient

The given expression is  (3x⁵y²)/(xy)  * (6xy²) / (9x³y)

Multiply through to have

{(3x⁵y²)(6xy²)} / {(xy)(xy)}

⇒( 18x⁶y⁴) / (72x⁴y²)

Simplify to get

Therefore the value of the expression is 1/4x²y²

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Answer:

OK. I misread the question. Sorry.

7/1.75 = 4

4 * 3/4 = 12/4 = 3 cups of milk

4 * 1 = 4 cups of flour

Answer:

That's the surface area........

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65