If X is a factor of Y and Y is a factor of Z then X is a factor of Z. If so then how



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Answer:

21 (but see note)

Step-by-step explanation:

I am thinking you are showing the symbols for absolute values ( the vertical  lines) so the absolute value of negative 9 is 9 and absolute value of positive 12 is 12 so it's just 9+12

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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Answer:

First recipe needs = 3/8

Second recipe needs = 5/8

Step-by-step explanation:

Given:

Two recipes needs butter = 1 pound

One recipe needs 1/4 pound more

Find:

Each recipe needs butter

Computation:

Assume;

First recipe needs = x

Second recipe needs = x + (1/4)

Two recipes needs butter = First recipe needs + Second recipe needs

x + x + (1/4) = 1

2 x = 1 - (1/4)

2 x = 3/4

x = 3/8 pound

First recipe needs = 3/8

Second recipe needs = x + (1/4) = (3/8) + (1/4) = 5/8

Second recipe needs = 5/8

Answer:

a) GH¢15x

b) GH¢15

Step-by-step explanation:

a) To find the cost function, C(x), given that it is linear, we need to find the slope and y-intercept of the line that represents the cost to produce x units of the product. We can use the point-slope form of a line to find the cost function: C(x) = mx + b, where m is the slope and b is the y-intercept.

We have two points: (100, GH¢1,500) and (0, GH¢0), which represents the cost to produce 100 units and 0 units, respectively. The slope can be found by dividing the change in y by the change in x:

m = (GH¢1,500 - GH¢0) / (100 - 0) = GH¢15

The y-intercept can be found by plugging in one of the points and solving for b:

GH¢1,500 = (GH¢15)(100) + b

GH¢1,500 = GH¢1,500 + b

b = GH¢0

So the cost function is C(x) = GH¢15x + GH¢0.

b) To find the average cost per item to produce 50 units and 300 units, we need to divide the total cost by the number of units produced.

For 50 units:

C(50) = GH¢15 * 50 + GH¢0 = GH¢750

Average cost = C(50) / 50 = GH¢15

For 300 units:

C(300) = GH¢15 * 300 + GH¢0 = GH¢4,500

Average cost = C(300) / 300 = GH¢15

Answer:

Step-by-step explanation:

S.I =720×6×5/100×365

=21600/36500

=0.59178

So balance will be 720+0.59178

=720.59178

Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining  $2,000 in her savings account.

Future value = $20,000

Simple interests rate = 1.5%

The return rate on bonds= 4.5%

The return rate on stocks = 6.2%

Total amount made on invests =  $942

Time period = 1 year

Let us assume that the amount of money Emily invested = x

Amount invested in stock = y

If the amount is twice = 2y

The interest earned = x * 0.015

Interest on bond = 2y * 0.045

Interest on stocks = y * 0.062

The equation will be:

(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942

0.015x + 0.152y = 942  ------ Equation 1

Total future value is given as $20,000

x + 2y + y = 20000

x + 3y = 20000

x = 20000 - 3y

Substituting the x value in the first equation:

0.015(20000 - 3y) + 0.152y = 942

300 - 0.045y + 0.152y = 942

0.107y = 642

y = 6000

Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.

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If the value of a = 5 and c = √21  then the value of b = 2i, b = -2i.

In this problem, we have one leg and the hypotenuse.

Let the equation be a² + b² = c²

substitute the values in the above equation, we get

5² +b² = (√21)²

25+b²=21

Move 25 to the right side

b² = -4

For x² = f(a) the solutions are \($x=\sqrt{f(a)},-\sqrt{f(a)}$\)

\($$b=\sqrt{-4}, b=-\sqrt{-4}$$\)

simplifying the above equation, we get

\(& \sqrt{-4}=2 i \\\)

\(& -\sqrt{-4}=-2 i \\\)

b = 2i, b = -2i

Therefore, the value of b = 2i, b = -2i.

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Answer:

When x is 1, y=7

When x is 2, y=10

When x is 3, y= 13

Step-by-step explanation: Plug in each number for x and solve

Answer:

If x=1, y=7

If x=2, y=10

If x=3, y=13

Step-by-step explanation:

For every equation substitute x in y = 3x + 4, with the value you want.

For example the first one says when x=1, so simply substitute x with 1 in y = 3x + 4.

So it'll look something like this:

y = 3(1) + 4.

Simply solve the equation from there, and you'll get y=7, and we know that x is already equal to 1.

So if x=1, then y=7

The t critical value and confidence interval must be determined.

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.

The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level.

For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.

The sample size, sample variability, and confidence level are all variables that have an impact on the width of the CI.

Assuming all other factors remain constant, a larger sample results in a narrower confidence interval, while a sample with more variability results in a wider confidence interval.

According to our question-

At a confidence level of 90%, we have α = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05.

Degree of freedom = 4-1 = 3

When we look this up in the t critical value table,

t critical = 2.353

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Answer:

first step is to minus 28.7 - 6.7=22 (I did the minus because I want to get the remaining length of the rope )

step 2 : is to divide 22 by 2 (because the question said they should divide it into two pieces )

then the answer you get from the division of 22/2 which is 11 that would be the final answer

meaning each tire swing is 11m

Answer: 258 \(yard^{2}\)

Step-by-step explanation: To find the surface area you add the area of all the sides. And the unit for a surface area is unit (yards) squared.

Front: 5 • 9 = 45

Back: 5 • 9 = 45

Left: 6 • 5 = 30

Right: 6 • 5 = 30

Top: 9 • 6 = 54

Bottom: 9 • 6 = 54

45 + 45 + 30 + 30 + 54 + 54 = 258.

Therefore, the end behavior of the function f(x) is: f(x) → 0- as x → -∞ and f(x) → 1 as x → ∞.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

To determine the end behavior of the function f(x) = (-4x³+ 7x + 9)/(8x⁶ - 9x⁴ - 2x), we need to consider the limit of the function as x approaches positive or negative infinity.

As x approaches negative infinity, the highest power of x in the numerator is -4x³, which will dominate the function. The highest power of x in the denominator is 8x⁶, which will also dominate the function. Therefore, we can simplify the function to:

f(x) ≈ (-4x³)/(8x⁶) = -1/(2x³)

As x approaches negative infinity, the denominator of this simplified function will become very large (since x³ becomes very negative), causing the function to approach 0 from the negative side:

f(x) → 0- as x → -∞

As x approaches positive infinity, the highest power of x in the numerator and denominator are both 8x⁶. Therefore, we can simplify the function to:

f(x) ≈ (8x⁶)/(8x⁶) = 1

As x approaches positive infinity, the function will approach 1 from the positive side:

f(x) → 1 as x → ∞

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Complete question:

Consider the following rational function fff. f(x)=\dfrac{-4x^3+7x+9}{8x^6-9x^4-2x}f(x)= 8x 6 −9x 4 −2x −4x 3 +7x+9 ​ f, left parenthesis, x, right parenthesis, equals, start fraction, minus, 4, x, cubed, plus, 7, x, plus, 9, divided by, 8, x, start superscript, 6, end superscript, minus, 9, x, start superscript, 4, end superscript, minus, 2, x, end fraction Determine fff's end behavior. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to -\inftyx→−∞x, \to, minus, infinity. f(x)\tof(x)→f, left parenthesis, x, right parenthesis, \to as x\to \inftyx→∞x, \to, infinity.

Answer:

-9x/2 + 15/2

Step-by-step explanation:

(15-9x)* 1/2

15(1/2)-9x 1/2

15/2 -9x *1/2

15/2-9x/2

-9x/2 + 15/2

Answer:

21/2 ( SEE IMAGE BELOW)

Step-by-step explanation:

Calculate the product

15- 9/2

Calculate the Differnce

21/2

so the answer is 21/2

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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The cost to rent one shed of the rectangular prism shaped shed is $2772.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.

Volume of prism= BH

where B= area of base and H= height

B= 11*7 = 77 feet²

H= 12 feet

Volume= 77*12=924 cubic feet

Cost =$3 per cubic foot

Total cost= 3*924= $2772

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Answer: The boys ate half a pie more than the girls did (5/10 more).

Step-by-step explanation:

2/5 = 4/10

The difference between 9/10 and 4/10 is 5/10, or one half, so that's your answer.

The total cost to the nearest cent is $194.25

The TV costs of $185

The markup is 5%

The total cost can be calculated as follows

185 + (185 × 5/100)

= 185 + (185 × 0.05)

= 185 + 9.25

= 194.25

Hence the total cost to the nearest cent is $194.25

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Answer:

2

Step-by-step explanation:

mum

Answer:

I think you can go with:

The margin of error is equal to half the width of the entire confidence interval.

so  try .74 ±   =   [ .724 , .756] as the confidence interval

Step-by-step explanation:

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.

Using this information, we can set up equations to solve for the variables.

From the given information, we have -

AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)

BE = x + 2

DE = BE = (x + 2) = g (since diagonals bisect each other at point E)

We also know that opposite sides of a parallelogram are parallel.

Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -

10/1 = 2y/1

10 = 2y

y = 5

Now we can use equation (1) to solve for x -

2x - 5 = 5x - 17

12 = 3x

x = 4

Finally, we can use x to solve for g -

(x + 2) = g

(4 + 2) = g

g = 6

Therefore, the values of x, y, and g are 4, 5, and 6, respectively.

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If my allotted budget for a week in $500, and considering I spend $400 dollars as my complete expenses up till the end of the week, (since no information about my expenses is the question statement), the amount that I will be able save from my budget is $100, calculated using basic subtraction.

As per the question statement, my allotted budget for a week in $500 and there is no further information about my expenses for the week. Hence, Let us consider that I had to spend $400 dollars as my complete expenses for the week.

We are required to calculate the amount that I will be able save from my budget.

To solve this question, we simply have to subtract my total week's expenses from my weekly budget, i.e., \([(500-400)=100]\).

Hence, I will be able to save upto $100 from my weekly budget.

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The probability that a random sample of 21 has a mean between 564 and 587 is of:

0.2641 = 26.41%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

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

The parameters for this problem are given as follows:

\(\mu = 555, \sigma = 72, n = 21, s = \frac{72}{\sqrt{21}} = 15.7\)

The probability that a random sample of 21 has a mean between 564 and 587 is the p-value of Z when X = 587 subtracted by the p-value of Z when X = 564, hence:

X = 587:

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

By the Central Limit Theorem

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

Z = (587 - 555)/15.7

Z = 2.04

Z = 2.04 has a p-value of 0.9798.

X = 564:

Z = (564 - 555)/15.7

Z = 0.57

Z = 0.57 has a p-value of 0.7157.

0.9798 - 0.7157 = 0.2641 = 26.41%.

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Answer:

  3.1 seconds

Step-by-step explanation:

The diver will hit the water when the height is zero.

  0 = -5t^2 +11t +13

Using the quadratic formula, we find the solutions to be ...

  t = (-11 ±√(11^2 -4(-5)(13)))/(2(-5)) = (-11 ±√381)/-10

The positive solution is

 t = 1.1 +√3.81 ≈ 3.1 . . . seconds

The diver will hit the water after 3.1 seconds.

His estimated monthly income should be $480.

Answer:

C

Step-by-step explanation:

the answer is C sense that makes the most sense with the problem

Answer:

2.83333333333

Step-by-step explanation:

(3 2/5) / (1 1/5) = 2.83333333333

Answer:

85/30 or 2.833333333

Step-by-step explanation:

When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.

It is also much easier to solve after you convert these numbers to improper fractions.

In this case,

3 2/5 = 17/5

1 1/5 = 6/5

17/5 ÷ 6/5

17/5 x 5/6

85/30 (17/6 reduced)

or

2.83333333333333333333

Answer:

log4 (70)

Step-by-step explanation:

log4(7) + log4(10) = log4(7 * 10 ) = log4(70)