Keisha, a scheduler at Mangel-Wurzel Transport, gets a call from a regular customer needing to move 70.3 m^3 of rock and soil, which Keisha knows from previous experience has an average density of 880 kg/m^3. Keisha has available a dump truck with a capacity of 9 m^3 and a maximum safe load of 5300. kg. Calculate the number of trips the dump truck will have to make to haul the customer's load away.

Nothing further can be done with this topic. Please check the expression entered or try another topic.

log 5 x ( 2 x − 4)=3x+2

Answer: like what are you supposed to be doing

Step-by-step explanation:

Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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Answer:    192

Step-by-step explanation:

You multiply 6 x 16 x 2

Answer:

1/12

Step-by-step explanation:

the probability of landing on 6 is 1/6 and the probability of a tails is 1/2, so 1/6*1/2=1/12

The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

From the information provided above, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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

\(\sqrt[4]{a}^3\)

Consider an expression expressed as xⁿ

The expression can be expanded as

xⁿ = x * x * x .... in n places

Using the above as a guide, we have the following:

\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)

Apply the exponent rule of indices

\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)

Apply the power rule of indices

\(\sqrt[4]{a}^3 = a^\frac34\)

Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)

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Sarah's statement, "Now I have enough paint to finish," concerning her demand for a gallon of paint, is TRUE because the required quantity is complete.

The quantity or number of gallons of paint made available for Sarah's use can be computed using the mathematical operations of either addition or subtraction.

In this case, we use the addition operation.  The quantities offered by her friend and husband can be added to the quantity of paint that she has available to determine if they add up to a gallon.

One can also decide to subtract the separate quantities from one gallon.

The available quantity of paint = 3/10

The quantity brought by a friend = 3/10

The quantity brought by the husband = 4/10

The total quantity of pain = 1 (3/10 + 3/10 + 4/10)

Thus, we can conclude that Sarah made a true claim of having a sufficient quantity of paint to finish after the donations.

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Answer:

£2.38

Step-by-step explanation:

£1.40 divided by 2.5kg = 0.56

0.56 x 4.25kg = £2.38

Answer:

\(x=15^\circ\)

Step-by-step explanation:

Please refer to the attached figure for labeling of given diagram:

We are given the following angles:

\(\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ\)

Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.

Using property of vertically opposite angles:

\(\angle EOF = \angle AOB = 7x^\circ\)

Line CD is a straight line, so \(\angle COD = 180^\circ\)

Also,

\(\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ\)

Hence, answer is \(x = 15^\circ\).

Using the binomial distribution, it is found that:

a) There is a 0.0501 = 5.01% probability that you need to contact four people.

b) You expect to contact 1.82 students until you find one who lives within five miles of you.

c) The standard deviation is of 1.22 students.

d) 0.3369 = 33.69% probability that 3 of them live within five miles of you.

e) It is expected that 2.75 students live within five miles of you.

For each student, there are only two possible outcomes. Either they live within 5 miles of you, or they do not. The probability of a student living within 5 miles of you is independent of any other student, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

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

The parameters are:

In this problem:

Item a:

This probability is P(X = 0) when n = 3(none of the first three) multiplied by 0.55(the fourth does live within five miles), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{3,0}.(0.55)^{0}.(0.45)^{3} = 0.091125\)

\(p = 0.091125(0.55) = 0.0501\)

0.0501 = 5.01% probability that you need to contact four people.

Item b:

The expected number of trials in the binomial distribution until q successes is given by:

\(E = \frac{q}{p}\)

In this problem, \(p = 0.55\), and 1 trial, thus \(q = 1\), hence:

\(E = \frac{1}{0.55} = 1.82\)

You expect to contact 1.82 students until you find one who lives within five miles of you.

Item c:

The standard deviation of the number of trials until q successes are found is given by:

\(S = \frac{\sqrt{q(1 - p)}}{p}\)

Hence:

\(S = \frac{\sqrt{0.45}}{0.55} = 1.22\)

The standard deviation is of 1.22 students.

Item d:

This probability is P(X = 3) when n = 5, hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{5,3}.(0.55)^{3}.(0.45)^{2} = 0.3369\)

0.3369 = 33.69% probability that 3 of them live within five miles of you.

Item e:

The expected value of the binomial distribution is:

\(E(X) = np\)

Hence:

\(E(X) = 5(0.55) = 2,75\)

It is expected that 2.75 students live within five miles of you.

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Answer/Step-by-step explanation:

Given,

10x - 3y = 3

3x + 10y = 30

Rewrite both equation in slope-intercept form, y = mx + b.

Where, m = slope of the line.

Thus,

✔️10x - 3y = 3

-3y = -10x + 3

y = 10/3x - 1

Slope of this line would be 10/3

✔️3x + 10y = 30

10y = -3x + 30

y = -3/10x + 3

The slope of this line is -³/10.

✔️The two lines are pendivukar to each other because the slope of one is the negative reciprocal of the other.

Answer:

B

Step-by-step explanation:

I'm not sure if it's right but you can try it

Answer:

answer: 30 in sq

Hope that helps!

Answer:

See below!

Step-by-step explanation:

254, 202, 284, 269, 151, 258, 202

Mean of the data:

\(\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}\)

Median of data:

Arrange the data in increasing order.

151, 202, 202, 254, 258, 269, 284

The middle value = 254

So,

Mode in data:

The mode, here, is 202. (occurring 2 times.)

So,

\(\rule[225]{225}{2}\)

Answer:

center is (5/2,2) and the radius is 4

Step-by-step explanation:

Answer: A

Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.

Answer:

CD=16

Step-by-step explanation:

If XY is median then CD equals 16

Length of CD = 16 .

An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure.

Given,

Isosceles trapezoid ABCD with median XY.

Median cuts the non-parallel lines of trapezoid in two equal parts.

then,

AX = 8

AB = 2 × AX

AB = 2 × 8

AB = 16

ABCD is isosceles trapezoid

So, Unparallel lines are equal,

AB = CD

⇒ CD = 16 unit.

Hence, 16 unit is length of CD.

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Answer:

45

Step-by-step explanation:

Ratio is 2girls:3boys

if there were 27 boys, we would have the following ratio:

2g    xg

--- = ---

3b     27b

To get from 3 to 27, multiply by 9.

Now, do the same for the numerator.

Now we know we have 18 girls!

We can add:

27 boys and 18 girls=

45 members!

Answer:

15:24, 20:32 and 40:64.

Step-by-step explanation:

hope this helps

Answer:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Step-by-step explanation:

The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and  lastly 16:10 because they both have a 2 as factors.

Answer:

I answered your duplicate question. Make sure to check out the answer, and I hope it helps!

The required amount to be paid into the fund each period is $1535.21. which the correct answer would be option (B).

Lee Associates borrowed $60,000 in total. The corporation intends to establish a sinking fund to repay the debt after 12 years.

Assuming a semiannual compounding rate of 8%,

As per the given information, the required solution would be as:

Amount to be paid into the fund each semi-annual period will be

= Loan Amount/((1+r/2)²ⁿ⁻¹)/(r/2))

= 60000/(((1+8%/2)²ˣ¹²⁻¹)/(8%/2))

= $1535.21

Thus, the required amount to be paid into the fund each period is $1535.21.

Hence, the correct answer would be an option (B).

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Answer:

y=mx+b m= rise/run b= y-intercept (0,b)

hope this helps

Step-by-step explanation:

The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

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Out of the population being surveyed, the one that could result in a sample statistic but not a parameter is; B: 50

A sample statistic is a piece of information you get from a fraction of a population.

A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

Now, we are told that a population consists of 5000 people. This means that the sample statistic could be the sample mean which could be 50 but certainly not 5000 as the sample statistic can't be same as the population.

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The correct answer is true

Answer:

True hope this helps!

Answer:

Some students were asked how many books they were carrying in their backpacks. The data is given in this frequency table. What is the mean number of pens carried by these students in their backpacks?

Pens      Frequency 

0                 4

1                 5

2                 8

3                 4

4                 3

5                 1

A.2

B.3.5

C.4

D.5.5