the 5−kg slender bar is released from rest in the horizontal position shown.

Answer:

The first choice

Step-by-step explanation:

7/8 x + 3/4 = -6

6 (x/8) + 3/4 = -6

the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1. Multiply this answer by the common denominator (18) to get the final answer: -5/2.

To solve this fraction division problem, first convert the fractions to have a common denominator. To do this, multiply the denominator of the first fraction (-1/3) by the denominator of the second fraction (6), and the denominator of the second fraction (6) by the denominator of the first fraction (-1/3). This will change the fractions to -5/18 and 5/18, respectively.

Next, divide the numerators of the fractions. Since the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1.

Multiply this answer by the common denominator (18) to get the final answer: -5/2.

learn more about number here

https://brainly.com/question/10547079

#SPJ4

The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.

acc to our question-

The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.

The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.

learn more about counterexamples click here:

https://brainly.com/question/24881803

#SPJ13

Answer:

so $90

about 10

The amount of pay received if the sales are $ 150 can read in the graph by first locate 150 in the axis because the x axis represent the sales and the y is pay. After locating go straight up to the line and read its y value and it is about $90

If you drove 150 miles the amount of gallons in the tank is about 11

im sorry if im wrong

The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Median is better than mean as it is not affected by extremely high or low values in the same way that the mean is

The median is a measure of central tendency, like the mean, but it is not affected by extremely high or low values in the same way that the mean is. Because of this, the median is often a better measure of central tendency when there are outliers in the data, or when the data is skewed (not normally distributed). For example, consider the following set of numbers: 1, 2, 3, 100. The mean of these numbers is 26, but the median is 3, which is a better representation of the "typical" value in this set.

However, the mean is still a useful measure and has its own advantages. For example, the mean is sensitive to every value in the data set, so it can provide a more comprehensive summary of the data. Additionally, the mean is easier to work with mathematically than the median, so it is often used in statistical tests and calculations.

Learn more about median here: brainly.com/question/14532771

#SPJ4

Answer:

The correct solution is B

Step-by-step explanation:

2x - 6 = 22

2x = 28

x = 14

hi

Correct answer is B

2X-6 =22

2X-6 +6 = 22 +6

2X =28

2X/2 = 28/2

X=14

We can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division.

The result of a multiplication operation is a product.

There are four different methods for multiplying: addition, long multiplication, grid multiplication, and drawing lines.

So, we have:
5/8 and 4

5/8 is in the form p/q which represents the fraction that must be multiplied by 4.

Now, calculate the product as follows:

5/8 * 4

5/2

Therefore, we can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

Know more about multiplication here:

brainly.com/question/10873737

#SPJ4

Answer:

67

Step-by-step explanation:

Each time the number goes up by 7. After 9 moretimes 4 will increase by 63.

4+63=67.

The 10th term should be 67

A regular polygon has side's length 5 units and exterior angle 120°. Its perimeter is 15 units.

If a polygon has equal sides and angles, it is said to be regular. A regular triangle is therefore an equilateral triangle, and a regular quadrilateral is a square.

In a regular polygon, the following holds:

exterior angle = 360° : number of sides

Information available in the problem:

exterior angle = 120°

Hence, the number of sides = 360° /120° = 3.

Therefore, it is a an equilateral triangle with sides 5 units.

The perimeter = 3 x 5 units = 15 units.

Learn more about polygon here:

https://brainly.com/question/27083382

#SPJ4

Answer: Let's represent the value of car 1 as x. Then, the value of car 2 is 3/4 of x, and the value of car 3 is 4/5 of the value of car 2.

So, we can write the following equations:

x = (3/4) * y

y = (4/5) * z

Where y is the value of car 2, and z is the value of car 3.

Adding all the values, we have:

x + y + z = 1115900

We can substitute the values of y and z in terms of x:

x + (3/4) * x + (4/5) * (3/4) * x = 1115900

Simplifying the expression on the left side, we get:

7/4 * x = 1115900

Finally, dividing both sides by 7/4, we get:

x = 359900

So, the value of car 1 is $359900, the value of car 2 is (3/4) * x = (3/4) * 359900 = 269925, and the value of car 3 is (4/5) * (3/4) * x = (4/5) * (3/4) * 359900 = 213140.

Step-by-step explanation:

Answer: the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.

Step-by-step explanation:

Let's call the value of car 1 "x".

From the first ratio, we know that the value of car 2 is 4/3 times greater than the value of car 1, and the value of car 3 is 3/4 times greater than the value of car 1.

So, the value of car 2 is 4/3 * x, and the value of car 3 is 3/4 * x.

From the second ratio, we know that the value of car 2 is 8/5 times greater than the value of car 3.

So, the value of car 2 is 8/5 * (3/4 * x) = 6/5 * x.

The total value of all three cars is $1115900, so we can set up an equation to solve for x:

x + 4/3 * x + 3/4 * x = 1115900

Expanding and simplifying the right side:

x + 4/3 * x + 3/4 * x = 1115900

8/3 * x = 1115900

x = 1115900 * 3 / 8

x = 467125

So, the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.

Answer:

Step-by-step explanation:

In an analysis of variance, you reject the null hypothesis when the F ratio is:
b. much larger than 1.

Here's a step-by-step explanation:
1. The null hypothesis states that there are no significant differences among the groups being compared.
2. Variance is the measure of how much the individual data points in a dataset vary from the mean.
3. The F ratio is the ratio of two variances, specifically, the variance between group means and the variance within groups.
4. When the F ratio is much larger than 1, it indicates that the variance between group means is much larger than the variance within groups.
5. This suggests that there is a significant difference among the group means, leading to the rejection of the null hypothesis.

Visit here to learn more about null hypothesis:

brainly.com/question/28920252

#SPJ11

Answer:

x = 1/6

Step-by-step explanation:

6x = 1

x = 1/6

Answer:

x = 1/6

Step-by-step explanation:

3x + 4 = 9x + 3

collect ' like terms'

the smaller terms should be the ones crossing the = sign

4 - 3 = 9x - 3x

1 = 6x

x = 1/6

Answer:

a) 2000000 kilobytes

b)20 000 000 bytes

Answer:

6 5/12

Step-by-step explanation:

77/12 as a mixed fraction will be 6 5/12

Answer:

6 5/12

Step-by-step explanation:

77/12 is the same as saying 77 divided by 12, the numerator is always going to be divided by the denominator. This means that if you divide 77 by 12 you will get a number like 6.4 but we dont want any decimals, we are just looking for how many times 12 can go into 77, which is 6 and we can take the leftover 5 and make it the new numerator over 77, somyou would get 6 5/12 and to check this answer, multiply 12 by 6 and add 5 and you should get what you started with, 77/12

Answer:

Proof given by contradiction.

Step-by-step explanation:

Given that:

\(n \geq 2\)

To prove:

\(n\) is prime if and only if no positive integer > 1 and \(\leq\) \(\sqrt n\) divides \(n\).

Solution:

First of all, let \(n\) is a composite number i.e. not a prime number such that:

\(n =a\times b\)

and \(a\) and \(b\) are prime and \(a\) divides \(n\) and \(b\) also divides \(n\).

Let \(\sqrt n = p\)

or \(n = p\times p\)

1. \(\underline{a < p}\):

\(a\) is prime and is a divisor of \(n\).

2. \(\underline{a>p}\):

\(n = a\times b = p\times p\)

We have assumed that \(a > p \Rightarrow b <p\)

\(b\) is a prime number and is a divisor of \(n\).

But we are given that no prime number \(\leq \sqrt n\) divides \(n\) but we have proved that \(b < \sqrt n\) divides \(n\).

So, it is a contradiction to our assumption.

Therefore, our assumption is wrong that  \(n\) is a composite number.

Hence, proved that \(n\) is a prime number.

Answer:

1. The cost of equity can be derived from the share price, which is the present value of the expected dividend one year from now(using the present value of growing perpetuity) as shown below:

share price=D1/(r-g)

share price=$500

D1=expected dividend one year from now=$4

r=cost of equity=unknown

g=constant growth rate=9%

$500=$4/(r-9%)

$500*(r-9%)=$4

r-9%=$4/$500

r=($4/$500)+9%

r=9.8

the Cost of Equity for the project is 9.8%

2. Compute the relevant cost of debt for this project is 5.53%

Market Value= 1,150

Face Value= 1,000

Term= 5 years, 10 semi-annual periods

Coupon Rate= 9%, 4.5% semi-annual rate

Tax Rate= 30%

N=10(semiannual coupons in 5 years)

PMT=45(semiannual coupon=face value*coupon rate/2=$1000*9%/2=$45)

PV=-1150(current market price)

FV=1000(face value of the bond is $1,000)

CPT(press compute)

I/Y=2.762766%(semiannual yield)

annual yield=2.762766%*2

annual yield=5.53%

3. The weighted average cost of capital is the sum of equity and the after-tax cost of debt multiplied by their respective market value weights

WACC=(cost of equity*weight of equity)+(after-tax cost of debt*weight of debt)

cost of equity=9.80%

the market value of equity raised=shares issued*market price of the share

the market value of equity raised=80,000*$500

the market value of equity raised=$40 million

weight of equity=market value of equity/total amount raised

weight of equity=$40 million/$100 million

weight of equity=40.00%

weight of debt=1-weight of equity

weight of debt=1-40.00%

weight of debt=60.00%

after-tax cost of debt=bond yield*(1-tax rate)

the after-tax cost of debt=5.53%*(1-30% )

the after-tax cost of debt=3.87%

WACC=(9.80%*40.00%)+(3.87%*60.00%)

WACC= 6.2426% or 6.24%

Therefore the WACC is 6.2426% or 6.24% rounded off to 2decimal place

4. Determine the initial cash flow for the project =$100 million

The initial cash outlay is the sum of the plant and machinery and net working capital investment required to commence the project

Plant and machinery= $80 million

Networking capital = $20 million

Total Initial Cash Flow= $100 million

5. Determine the earnings before taxes for years 1 through 5

Year

1 2 3 4 5

Revenue

120,000,000 120,000,000 120,000,000 120,000,000 120,000,000

Expenses

(80,000,000) (80,000,000) (80,000,000) (80,000,000) (80,000,000)

Depreciation (20,000,000) (15,000,000) (11,250,000) (8,437,500) (6,328,125)

EBT

20,000,000 25,000,000 28,750,000 31,562,500 33,671,875

Step-by-step explanation:

5. Depreciation schedule:

Year 1 = 80 × 25% = 20

Year 2 = (80-20) × 25% = 15

Year 3 = (80-20-15) × 25% = 11.25

Year 4 = (80-20-15-11.25) × 25% = 8.4375

Year 5 = (80-20-15-11.25-8.4375) × 25% = 6.328125

EBT = revenue - Expenses - depreciation

Year 1 = 120 - 80 - 20 = 20 Million

Year 2 = 120-80- 15 = 25 Million

Year 3 = 120-80- 11.25 = 28.75 Million

Year 4 = 120-80- 8.4375 = 31.5625 Million

Year 5 = 120-80- 6.328125 = 33.671875Million

The cost of equity of the project through the use of Gordan's formula will be 9.87%.

It should be noted that the price of stock is computed thus:

= Previous dividend + Growth / Cost of equity - Growth

Po = Do + g/Ke - g

500 = 4 + 9%/Ke - 9%

500 = 4 + (0.09 × 4) / Ke - 9%

500 = 4.36/Ke - 9%

500(Ke - 9%) = 4.36

500Ke = 4.36 + 45

500Ke = 49.36

Ke = 49.36/500

Ke = 9.87%

The cost of debt will be:

= Interest rate (1 - Tax rate)

= 9% × (1 - 30%)

= 9% × 0.7

= 6.30%

The amount of the cost of debt will be:

= $1000 × 6.30%

= $63.00

Learn more about cost of equity on:

https://brainly.com/question/14041475

The  statement that can be considered true ,Data set represents the number of hours spent studying per week, it means that 25% of the individuals surveyed studied for 2.5 hours or less per week. Option C) is the correct answer.

The first quartile of a data set is 2.5, the statement that can be considered true about the data values is that 25% of the values in the data set are less than or equal to 2.5.

The first quartile, denoted as Q1, is a measure of central tendency that divides a data set into four equal parts. It represents the value below which the first 25% of the data lies. In this case, since the first quartile is 2.5, it implies that 25% of the data values in the set are less than or equal to 2.5.

This information provides insights into the distribution and spread of the data set. For example, if the data set represents the number of hours spent studying per week, it means that 25% of the individuals surveyed studied for 2.5 hours or less per week.

It's important to note that without further information about the data set, we cannot make any specific conclusions about the maximum or minimum values, the distribution shape, or the values within the other quartiles. Additional statistical measures and analysis would be needed to determine those aspects.

To know more about Data .

https://brainly.com/question/29642782

#SPJ11

The full question will be :

What statistical measure represents the value below which the first 25% of the data lies in a data set?

Options:

a) Median

b) Mean

c) First quartile (Q1)

d) Third quartile (Q3)

Answer:

x=9

Step-by-step explanation:

angle A =angle B (because they are corresponding angles)

5x-5=3x+13

5x-3x=13+5

2x=18

x=18/2

x=9

angle A=5x-5

=5*9-5

=45-5

=40

angle B=3x+13

=3*9+13

=27+13

=40

Answer:

A = B

5X-5 = 3X+13

5X-3X. =13+5

2X =18

X = 9

5X-5

(5×9)-5

45-5

=40

ANGLE A=ANGLE B =40

Answer:

volume: 49280 cm³  and   curved S.A = 5826.64 cm²

Explanation:

using similarities:

\(\sf \frac{45 + h2}{28} = \frac{h2}{7}\)

\(\sf 315 + 7h2 = 28h2\)

\(\sf 315 = 28h2-7h2\)

\(\sf 315 = 21h2\)

\(\sf 15 = h2\)

total height of the cone: 45 + 15 = 60 cm

solve for volume:

\(\sf volume \ of \ cone \ = \frac{1}{3} \pi r^2 h\)

\(\sf volume \ of \ cone \ = \frac{1}{3} \pi (28)^2 (60)\)

\(\sf volume \ of \ cone \ = 15680\ *\frac{22}{7}\)

\(\sf volume \ of \ cone \ = 49280 \ cm^3\)

First find the slant height using Pythagoras theorem -

\(\sf l^2 = r^2 + h^2\)

\(\sf l =\sqrt{ r^2 + h^2}\)

\(\sf l =\sqrt{ (28)^2 + (60)^2}\)

\(\sf l =66.212 \ cm\)

solve for curved surface area:

\(\sf curved \ surface \ area = \pi rl\)

\(\sf curved \ surface \ area = \pi (28)(66.2)\)

\(\sf curved \ surface \ area =5826.64 \ cm^2\)

The statement mentioned in question when translated to form expression is 5 + 6x ≥ 30.

Let us assume the number other than 6 to be x. Now remember that the overall result is atleast 30. The word indicates that minimum result will be 30 and it can be more than that. Hence, we will use inequality sign rather than equal. Forming the expression -

5 + 6x ≥ 30

Rewriting the expression for value of x

6x ≥ 30 - 5

Performing subtraction on Right Hand Side of the equation

6x ≥ 25

x ≥ 25/6

Hence, the number will be less than or equal to 25/6.

Learn more about inequality -

https://brainly.com/question/24372553

#SPJ4

The solution to the system of linear inequalities x ≥ 3 and y≤ 2.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

This is represented on a coordinate plane, is a region that satisfies both inequalities. It is the half-plane formed by the line x= 2 and above the line y= 3 .

x ≥ 3

y ≤ 2.

It can be represented on a coordinate plane as a region that satisfies both inequalities.

To graph the solution, we first plot the line x = 2 on the coordinate plane. Since x <= 2, this line represents the boundary of the solution. Everything to the left of the line x = 2 is included in the solution.

Next, we plot the line y = 3. Since y less than 3, everything above the line y = 3 is included in the solution.

The solution set is x ≥ 3 and y≤ 2

Learn more about inequalities here:

https://brainly.com/question/27425770

#SPJ1

Answer:

Step-by-step explanation:

The graph starts at x = - 3 and ends x = 2. For all x between -3 and 2, there points on the graph. Hence the domain, in interval notation, is written as

[-3 , 2]

We have closed circles at x = - 3 and x = 2 because -3 and 2 are included in the domain which is indicated by the closed brackets at x = - 3 and x = 2.

The range is the set of possible output values, which are shown on the y-axis.

This is why our graph goes from (-3,8) to (2,3)

Let the distance from the corner is x.

The length of diagonal -12 inch.

the fiure show a right angle triangle

Apply the pythagoras theorem to find the values of x

Pytahgoras theorem state as the square of the hypotenuse is equal to sum of the squre of perpendicular and the square of base of right angle triangle,

In the given figure we have,

Hypotenuse=12

Base=x

Perpendicular=x

Substutute the value in the pythagoras theorem

The corner will be at a distance of 8.5 inch.

The probability that at least $15$ cents worth of coins come up heads is

P(H)=1/16

This is further explained below.

Generally, We are doing a simultaneous toss of four coins. How likely is it that every coin will land with the head side facing up?

It has been established by everyone who has participated so far that the solution is 116, which can be written as

(1/2)4=1/16.

On the other hand, a person who is just starting out can benefit from another method to see things.

I'm going to go ahead and make the assumption that each coin is balanced and that each side has an equal chance of facing up.

Each coin has the potential to exist in either of two states (heads or tails). Therefore, there are

2^4 = 16 different permutations (states) that the four coins may be in together as a group.

Only one of these possible permutations results in all heads. This results in the correct value of 1/16.

Read more about probability

https://brainly.com/question/795909

#SPJ1

Answer:

Step-by-step explanation:

f(-9)= 2(-9) - 3 = -18 - 3 = -21

f(-3)= 2(-3) - 3 = -6 - 3 = -9

f(1)= 2(1) - 3 = 2 - 3 = -1

Answer:

x = 12

Step-by-step explanation:

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

From the picture attached,

Length of Hypotenuse = 13

Length of leg 1 = 5

Length of leg 2 = x

By substituting these values in the formula,

(13)² = 5² + x²

169 = 25 + x²

169 - 25 = x²

144 = x²

(12)² = x²

x = 12