Find the greatest common factor of
44
,
12
,
44,12,44, comma, 12, comma and
28
2828.

The statement which is true about the function is that the function is negative for all real values of x where x < –3 or x > –1.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function is,

\(f(x) = -(x +3)(x - 1)\)

It is positive, its value is above x-axis. For the function above, the solutions are,

\(x+3=0\\x=-3\\x-1=0\\x=1\)

The value of x is lies between,

\(-3 < x < 1\)

Thus, the statement which is true about the function is that the function is negative for all real values of x where x < –3 or x > –1.

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The segment of a triangle is the median of the triangle. This is the line that join a vertex of the triangle to the opposite side of the triangle.

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Step-by-step explanation:

speed = distance/time

so,

distance = speed × time

and

time = distance / speed = distance / distance/time

therefore,

T = 100/b + 200/c

as we have first 100 miles with the speed b, and the rest of the 300 miles trip is 300-100 = 200 miles with the speed c.

The require angle, angle ABD = 40 degrees

A bisector has two primary characteristics:

Any point along an angle's bisector is equally - spaced from the angle's sides.

The angle bisector divides the other side of a triangle in proportion to the other two sides.

Given : ∠ ABC is bisected by a ray BD

∠ ABC = 80°

Since the angle ABC is being bisected this means that the angles are equal

Let the bisected angle be x

thus we can write it mathematically as

x + x = 80

2x = 80

dividing both the sides as 2 we would get

x = 40 degrees

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If the sales tax in Brian’s area is 8.51%, then Brian pay in total is option (d) $507.96

Brian's credit card has an interest rate of 9.4% compounded monthly, which means that the interest is calculated based on the balance of the credit card at the end of each month. Therefore, the interest will accumulate over time, and Brian will have to pay more than the base price of $435.

Additionally, the sales tax in Brian's area is 8.51%, which means that he needs to pay this percentage of the total cost of his purchase as well.

To calculate how much Brian paid in total, we need to take into account the base price, the interest rate, and the sales tax.

First, let's calculate the total cost of the air conditioning unit including sales tax. The sales tax is 8.51% of the base price, which is:

8.51% x $435 = $37.02

So, the total cost of the air conditioning unit including sales tax is:

$435 + $37.02 = $462.04

Now, let's calculate how much Brian paid in interest. Since the interest rate is compounded monthly, we need to divide the annual rate by 12 to get the monthly rate. Therefore, the monthly interest rate is:

9.4% / 12 = 0.78333% (rounded to five decimal places)

Over a year and a half (or 18 months), the interest accumulated on Brian's credit card balance can be calculated using the following formula:

\(A = P(1 + r/n)^{nt} - P\)

where A is the total amount paid, P is the principal amount (which is the same as the base price of the air conditioning unit), r is the interest rate in decimal form, n is the number of times the interest is compounded per year (which is 12 in this case since the interest is compounded monthly), and t is the time in years (which is 1.5 in this case since Brian made monthly payments for a year and a half).

Substituting the values we have:

A = $435\((1 + 0.0078333)^{12\times1.5}\) - $435 = $45.92

Therefore, the total amount of interest paid by Brian is $45.92.

Finally, to calculate the total amount that Brian paid, we need to add the total cost of the air conditioning unit including sales tax and the total amount of interest paid:

$462.04 + $45.92 = $507.96

So, the correct answer is (d) $507.96, rounded to the nearest cent.

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Answer:

96

Step-by-step explanation:

20 percent of 80 is 16, and added to 80 would equal 96

The value of a in terms of b is given as \(a = 8b^3\)

Given the equation solved by Leo expressed as \(b=\frac{1}{2}\sqrt[3]{a-1}\)

We are to solve the equation for the variable "a"

Given;

\(b=\frac{1}{2}\sqrt[3]{a-1}\)

Cross multiply

\(2b=\sqrt[3]{a-1}\)

Cube both sides of the equation:

\((2b)^3=(\sqrt[3]{a-1})^3 \\8b^3=a-1\)

Add 1 to both sides of the equation:

\(8b^3+1=a-1+1\\8b^3=a\\Swap\\a=8b^3\)

Hence the value of a in terms of b is given as \(a = 8b^3\)

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Answer:

1887.6 ft³

Step-by-step explanation:

What is the volume of a cylinder with a height of 6.8 ft and a base with a radius of 9.4 ft, to the nearest tenth of a cubic foot?

The formula for the volume of a cylinder is given as:

πr²h

From the above question,

r = 9.4 ft

h = 6.8 ft

The volume of the cylinder =

π × 9.4² × 6.8

= 1887.61966 ft³

Approximately = 1887.6 ft³

The point estimate for µ is 25.2 years, with a margin of error to be determined. The 99% confidence interval for µ is (24.06, 26.34) years.

a. The point estimate for µ, the population mean, is obtained from the sample mean, which is 25.2 years. The margin of error represents the range within which the true population mean is likely to fall. To determine the margin of error, we need to consider the sample variance, which is 16.4, and the sample size, which is 100. Using the formula for the margin of error in a t-distribution, we can calculate the value.

b. To calculate the 99% confidence interval for µ, we need to consider the point estimate (25.2 years) along with the margin of error. Using the t-distribution and the sample size of 100, we can determine the critical value corresponding to a 99% confidence level. Multiplying the critical value by the margin of error and adding/subtracting it from the point estimate, we can establish the lower and upper bounds of the confidence interval.

The resulting 99% confidence interval for µ is (24.06, 26.34) years. This means that we can be 99% confident that the true population mean falls within this range based on the sample data.

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Answer: 7/10

Step-by-step explanation:

multiply 4/5 by 7/8=28/40 or 7/10

m > 650 miles

A mileage over 650 miles makes company A cheaper than B.

1) Gathering the data

Company A

$127 (unlimited mileage)

Company B

$75 + 0.08m

2) To find out the mileage that makes Company A cheaper than Company B, we can write out the following:

3) Hence when we drive over 650 miles the Company A becomes cheaper than B.

Two numbers that satisfy the conditions of having a sum of 20 and a product of 96 are 8 and 12. This can be answered by the quadratic equation.

Let's call the two numbers we're looking for "x" and "y". We know from the problem that:

x + y = 20

xy = 96

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:

y = 20 - x

We can substitute this expression for y into the second equation:

x(20 - x) = 96

Expanding the left side, we get:

20x - x^2 = 96

Rearranging terms:

x^2 - 20x + 96 = 0

This is a quadratic equation that we can solve using the quadratic formula:

x = (20 ± sqrt(20^2 - 4(1)(96))) / (2(1))

x = (20 ± 4) / 2

So we have two possible solutions:

x = 12 or x = 8

If x = 12, then y = 8 (from the equation y = 20 - x). We can check that these values satisfy both conditions:

12 + 8 = 20

12 * 8 = 96

Therefore, the two numbers that satisfy the conditions are 8 and 12

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If the null hypothesis is not rejected when it is false, this is called a type II error.

A type II error occurs when there is a failure to reject a false null hypothesis. It is also known as a "false negative" result. This type of error can be minimized by increasing the sample size or using a more sensitive test. It is important to be aware of the potential for type II errors when interpreting the results of a statistical test.

It is important to be clear that a null hypothesis is a statement that is formulated to be tested in a statistical test. The null hypothesis generally states that there is no significant difference between two groups, or that there is no effect of a particular variable.

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Answer:

The sample included only those people who chose to complete the survey.

Step-by-step explanation:

Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.

Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.

A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.

B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.

C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.

D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.

E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.

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The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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Answer:

(x−7,y+5)

A p e x n dat

a. Two populations.

b. Qualitative (categorical) data.

c. Proportion stats.

d. Null hypothesis: p1 = p2 (The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch). Alternative hypothesis: p1 > p2 (The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch).

e. Z-test for two proportions.

f. P-value.

g. A small P-value provides convincing evidence to support Phoebe's hunch that older students are more likely to bring a bag lunch than younger students.

h. 95% confidence interval to estimate the difference in proportions.

What is hypothesis?

A hypothesis is a proposed explanation or assumption that is tested through research and data analysis. It is a statement that suggests a relationship or difference between variables or phenomena and serves as a basis for scientific investigation.

a. There are two populations in this problem: the population of seniors and the population of sophomores.

b. This is a problem about qualitative (categorical) data since we are examining whether students bring a bag lunch or not.

c. We will use the proportion stats option in StatCrunch to complete this problem.

d. Null hypothesis (H0): The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch.

Alternative hypothesis (Ha): The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch.

e. The test statistic is the z-test for two proportions.

f. The P-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

g. The strength of the P-value determines the level of evidence against the null hypothesis. If the P-value is small (below the significance level), it provides strong evidence against the null hypothesis. In this case, a P-value less than 0.05 (assuming significance level α = 0.05) would suggest convincing evidence to support Phoebe's hunch.

h. To construct a 95% confidence interval to estimate the difference in proportions, we use the formula:

Confidence interval = (p1 - p2) ± z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the critical value corresponding to the desired confidence level (in this case, z value for a 95% confidence level).

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Answer:

0.4

Step-by-step explanation:

hegarty maths

Answer: f(x) = 10in*cos(x*2*pi/60s) + 10in*sin(x*2*pi/60s) + 108in.

Step-by-step explanation:

When we have a circular motion, we can write this as:

f(x) = A*sin(k*x + f) + A*cos(k*x + f) + C.

where:

k is a constant that depends on the period.

f is a phase shift.

C is the mean height of the circular motion, in this case will be equal to the height of the center, that is 9ft.

C = 9ft.

A is the amplitude of the motion, in this case is equal to the radius, that is equal to the lenght of the second hand

A = 10in

But we should write both quantities in the same units, so we have:

1ft = 12in

then:

C = 9ft = 9*12in = 108in

Then our equation is:

f(x) = 10in*cos(k*x + f) + 10in*sin(k*x + f) + 108in

now, x = 0s coincides with the noon

so at x = 0s, the second hand is pointint to the twelve, this means that is in the max height, so we have:

F(0s) = 10in*cos(0 + f) + 10in*sin(0 + f) + 108 in

Now, the maximum value will be when the value inside the sinusoidals is 0.

(because cos(0) = 1 and sin(0) = 0)

then we have that f = 0.

Now, we know that it takes 60 seconds to do a full revolution, and for the sinusodial functions the period is 2*pi

Then we have:

c*60s = 2*pi

c = 2*pi/60s.

Then the equation is:

f(x) = 10in*cos(x*2*pi/60s) + 10in*sin(x*2*pi/60s) + 108in.

Answer:

B : 5/6cos(pi/30x)+9

Step-by-step explanation:

Edge 2020

The value of opposite side of angle θ would be,

⇒ EF

Since, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that,

A right triangle EFD is shown in figure.

And, At angle E, right angle is shown.

We know that;

The Opposite side of a angle is called perpendicular side.

Hence, The value of opposite side of angle θ would be,

⇒ EF

Thus, Option A is true.

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The expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

The management of First American Bank faces a decision regarding the installation of an emergency power generator to mitigate potential losses from physical catastrophes such as power failures or fires.

To evaluate this decision, we can use decision tree analysis.

Without the generator, there is a 10% chance of a power outage. In the event of an outage, there is a 0.05 probability of very large losses ($80 million) and a 0.95 probability of slight losses ($1 million). To calculate the expected loss from not installing the generator, we can use the following formula:

Expected loss = (probability of outage) x [(probability of large loss x large loss amount) + (probability of slight loss x slight loss amount)]

Expected loss = 0.1 x [(0.05 x $80 million) + (0.95 x $1 million)]
Expected loss = 0.1 x [$4 million + $950,000]
Expected loss = 0.1 x $4.95 million
Expected loss = $495,000

Now let's compare this expected loss to the cost of installing the emergency power generator, which is $800,000. Since the expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.

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Answer:

its C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

To calculate \(\frac{{f(x+h) - f(x)}}{h}\) for the function \(f(x) = ax^3\), we need to substitute the expressions into the formula and simplify.

\(f(x+h) = a(x+h)^3\\\\f(x) = ax^3\)

Now we can calculate the difference:

\(f(x+h) - f(x) = a(x+h)^3 - ax^3\)

Expanding \((x+h)^3\):

\(f(x+h) - f(x) = a(x^3 + 3x^2h + 3xh^2 + h^3) - ax^3\)

Simplifying:

\(f(x+h) - f(x) = ax^3 + 3ax^2h + 3axh^2 + ah^3 - ax^3\)

The terms \(ax^3\) cancel out:

\(f(x+h) - f(x) = 3ax^2h + 3axh^2 + ah^3\)

Now we can divide by h:

\(\frac{{f(x+h) - f(x)}}{h} = \frac{{3ax^2h + 3axh^2 + ah^3}}{h}\)

Canceling out the common factor of h:

\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3axh + ah^2\)

Now, we evaluate this expression again by setting h = 0:

\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3ax(0) + a(0)^2\)

\(= 3ax^2\)

Therefore, when we evaluate the expression by setting h = 0, we get \(3ax^2\).

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The Raj's AMTI who itemised deductions providing their financial records for 2022 is 478,000.

AMT ( Alternative Minimum Tax ) is applied to high economic income by setting a limit on these benefits to reduce taxpayer's regular tax.

As per the question,

⇒ The Alternative Minimum Tax for taxpayers is triggered when a tax preference item is a type of income. In IRS' tax formula, preference items are added to the amount of AMT income.

⇒ AMTI   =   Taxable income + AMT positive adjustments + AMT

                     preferences

               =    370000 + 33000 + 75000

AMTI       =    478000

Therefore, 478,000 is the AMTI of Raj in the year 2022 i.e. option d is correct.

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The complete question is

Answer:

George gets 13 runs in the fifth game

Step-by-step explanation:

He gets x in the fifth game so, ( 23 · 4 + x ) + 5 = 21

So 92 + x = 105
    -92         -92

       x = 13

The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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Answer: don't ask for help unless you have the problem there XD

Step-by-step explanation: common sense

Answer:

P = 2 !

Step-by-step explanation:

15p = 31 = 61

        -31   -31

-----------------------

Thus, P = 2. Hope this helps! <3