16. Simplify each expression for x = 4.
a. --5x-4
-54
b. 7x-3
94-3

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

An ordered pair consists of two items. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it might be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

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Answer:

D

Step-by-step explanation:

Answer:

Answer:

25 degrees

Step-by-step explanation:

arc divided by 2 = angle

50/2=25

Answer:

The force of friction is 19.1 N

Step-by-step explanation:

According to Newton's second law, the net force acting on the bag is equal to the product between its mass and its acceleration:

where

is the net force

m is the mass

a is the acceleration

The bag is moving at constant speed, so its acceleration is zero:

Therefore the net force is zero as well:

Here we are interested only in the forces acting along the horizontal direction, therefore the net force is given by:

where

is the horizontal component of the applied force, with

F = 22.5 N

is the force of friction

And solving for , we find

The congruent triangles in this problem are given as follows:

Triangles A and B.

Two figures are classified as congruent if their side lengths are the same.

If we rotate triangle B 180º over it's base, we have that it will have a similar format to triangle A, and also with the same side lengths.

Hence the congruent triangles in this problem are given as follows:

Triangles A and B.

With triangle C, no rotation would make it like A and B, with the same side lengths, hence it is not congruent to any of the triangles in this problem.

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Answer:

yes

Step-by-step explanation:

3x+7x+2x = 12x

-5+10 = 5

so it's = 12x+5

Answer:

It's most likely spposed to be 22

Step-by-step explanation:

Answer: 91.65

Part 1: You will need to find the average by adding 108, 72, and 95. This will give you 275. Now you divide the sum by the amount of numbers there are which is 3 numbers. 275/3 would be 91.6

Part 2: Now that you have all four numbers you should repeat the process, 108 + 72 + 95 + 91.6 which is 366.6 now divide by four, and you have 91.65.

Let me know if this was correct!

After inspecting the graph, when x=0  y is 6 so the constant is +6 which is Positive

What is polynomial function ?

A polynomial characteristic is a function that includes handiest non-bad integer powers or simplest tremendous integer exponents of a variable in an equation like the quadratic equation, cubic equation, and so forth. for example, 2x+5 is a polynomial that has exponent same to one.

Given ,

The graph is a polynomial function.

This is an odd degree polynomial since end behavior is +infinitely when x is positive and -infinity when x is negative

For an even degree polynomial en behavior will be positive regardless of the sign as a negative number raised to an even power is always positive

The leading coefficient is positive other wise the function would be flipped around the x axis

Inspect the graph. when x=0  y is 6 so the constant is +6 which is Positive

Hence , After inspecting the graph, when x=0  y is 6 so the constant is +6 which is Positive

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Answer: He rented the bike for 10 hours

Step-by-step explanation:

Note that the probability that a person selected at random would test positive for this disease is 0.06894.

We are given that the detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease.

This means:
P(positive results | do not have disease) = 0.05

We also know that the test gives a negative result 0.3 percent of the time for people who have the disease. What this means is that the test gives a positive result 99.7 percent of the time for people who have the disease.

Thus,
P(positive results |  have disease) = 0.997;

Then, we know that

large-scale studies have shown that the disease occurs in about 2 percent of the population. That is P(have disease) = 0.02, P(do not have disease) = 0.98

Thus, the probability that a person selected randomly would test positive is:
P(positive results) = P( Positive results ∩ have disease) + P(Positive results ∩ do not have disease)

= P(have disease) P (Positve results | have disease) + P(do not have disease)  P(Positive results) | do not have disease)

= (0.02 x 0.0997) + (0.98 x 0.05)
= 0.06894

Thus, it is right to state that the likelihood that a person selected at random would test positive for this disease is 0.06894.

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The domain of a function is defined as the set of all possible input values for which the function is defined. For instance, if we have a function f(x) = 3x + 5, the domain is all real numbers because the function is defined for all values of x.

Similarly, if we have a function that assigns to each pair of positive integers the first integer of that pair, the domain is the set of all possible pairs of positive integers. To understand the domain of the function that assigns to each pair of positive integers the first integer of that pair, let us consider some examples. Suppose we have the pairs (1, 3), (2, 4), (5, 7), (6, 8), and (9, 10). The function would assign the values 1, 2, 5, 6, and 9 to these pairs, respectively. Therefore, the domain of the function is the set of all positive integers. This is because for any pair of positive integers (a, b), the function assigns the value a, which is also a positive integer. On the other hand, if we consider pairs that include non-positive integers, such as (0, 3), (-1, 2), or (-5, -7), the function is not defined because there is no first positive integer in these pairs. Therefore, the domain of the function is restricted to positive integers.

In conclusion, the domain of a function that assigns to each pair of positive integers the first integer of that pair is the set of all positive integers. Any pair of positive integers can be used as an input to this function, and the function will assign the first integer of that pair as its output. However, if the input pair contains any non-positive integer, the function is not defined.

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The function that assigns to each brace of positive integers the first integer of that brace is a function of two variables,  generally denoted by f( x, y) =  x. This function maps  dyads of positive integers onto their first  equals only.

In order to determine the sphere of this function, we need to specify the set of all  dyads of positive integers that can be inputted into thefunction.

The  sphere is the set of all possible inputs for which the function is defined. In this case, since the function takes  dyads of positive integers as input, the  sphere consists of all possible  dyads of positive integers.

We can denote the  sphere by the set D =  ( x, y)| x> 0 and y> 0}.  

Functions are  fine constructs that take in one or  further inputs and give out a single affair.

The  sphere of a function is the set of all possible input values for which the function is defined.

For case, the  sphere of a function that takes in real  figures and gives out their places is the set of all real  figures.

In this case, the  sphere of the function that assigns to each brace of positive integers the first integer of that brace is the set of all possible  dyads of positive integers.

The function is  generally denoted by f( x, y) =  x.

This means that the function takes in two inputs, x and y, and gives out x as the affair.

For case, if we input the brace( 2,5) into the function,

we get f( 2,5) =  2 as the input. also, if we input the brace( 7,9), we get f( 7,9) =  7 as the output.In order to determine the  sphere of this function, we need to specify the set of all  dyads of positive integers that can be inputted into the function.

Since the function takes  dyads of positive integers as input, the  sphere consists of all possible  dyads of positive integers. We can denote the  sphere by the set D =  ( x, y)| x> 0 and y> 0}.  

This means that the  sphere consists of all  dyads( x, y) where both x and y are positive integers.  

In conclusion, the  sphere of the function that assigns to each brace of positive integers the first integer of that brace is the set of all possible  dyads of positive integers. The  sphere can be denoted by the set D = {( x, y)| x> 0 and y> 0}. The function takes in two inputs, x and y, and gives out x as the affair.

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Answer:

m=-9/7

Step-by-step explanation:

An equation of slope-intercept form describing this relationship. Use ordered pairs of the form​ the equation, y = 640x + 4760

Since there were 4760 electric vehicles in 1998, when x=0 (indicating 0 years have passed since 1998), y=4760. There were 1,920 more electric vehicles on the road after three years. 1920 / 3 = 640 is the average rate of change every year. Between 1998 and 2001, there were 640 more automobiles every year.Our slope measures m=640. By dividing the change in y by 4760, or 1920, we can determine the slope.The y-intercept is just the starting point, or x=0. At this point, x=0. The y-intercept is shown here: (0, 4760). Equation of slope intercept: y = 640x + 4760 where b=4760.

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Answer: ?

Step-by-step explanation: Is that the whole question? I don't really understand the question.

The percentage of illicit drug users in the US are African American is a. 14%

According to data from the National Survey on Drug Use and Health, in 2019, 14.5% of African Americans reported using illicit drugs in the past month, compared to 12.4% of the overall population. While African Americans are overrepresented in state prisons for drug offenses, they do not use drugs at a significantly higher rate than other racial and ethnic groups.

It's important to note that drug use is a complex issue with many social and economic factors at play. It's crucial to approach drug use and addiction with a public health perspective that prioritizes prevention, treatment, and harm reduction over punitive criminal justice approaches.

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Your question is incomplete, but probably the complete question is :

57% of people in state prisons for drug offenses in the US are African American. What percentage of illicit drug users in the US are African American?

a. 14%

b. 28%

c. 42%

d. 56%

Answer:

Rs 6900

Step-by-step explanation:

To calculate the tax amount the girl should pay in a year, we need to determine the taxable income and then apply the corresponding tax rates.

The taxable income is calculated by subtracting the tax-free allowance from the girl's early income:

Taxable Income = Early Income - Tax-Free Allowance

Taxable Income = 150,000 - 100,000

Taxable Income = 50,000

Now, we can calculate the tax amount based on the given tax rates:

For the first 20,000 rupees, the tax rate is 12%:

Tax on First 20,000 = 20,000 * 0.12

Tax on First 20,000 = 2,400

For the remaining taxable income (30,000 rupees), the tax rate is 15%:

Tax on Remaining 30,000 = 30,000 * 0.15

Tax on Remaining 30,000 = 4,500

Finally, we add the two tax amounts to get the total tax she should pay in a year:

Total Tax = Tax on First 20,000 + Tax on Remaining 30,000

Total Tax = 2,400 + 4,500

Total Tax = 6,900

Therefore, the girl should pay 6,900 rupees in tax in a year.

Answer:

D Identity Property

Step-by-step explanation:

The identity property is whenever you multiply a number by one, it will always stay the same number.

⇒Let the two unknowns be x and y

It is said that their sum is -7 mathematically it can be written as

\(x+y=-7\)

Their product can be written mathematically as

⇒ x×y=6

\(xy=-6\)

As a results you can see that we have a system of equation that we have to solve and we can solve it by substitution

let us derive the third equation from the first equation by making x the subject of the equation

As a results we have x=-7-y

Now let us substitute the equation to the second equation .

\((-7-y)(y)=6\\-7y-y^{2} =6\\-y^{2} -7y-6=0\\-(y^{2} +7y+6)=0\\y^{2} +7y+6=0\\(y+6)(y+1)=0\\y+6=0\\\\or\\y+1=0\\y=-6\\\\or \\y=-1\)

when y =-1

x=-7-(-1)

x=-7+1

⇒x=-6

When y=-6

x=-7-(-6)

x=-7+6

⇒x=-1

Note there was no need of finding the values of x

the two numbers are

Answer:

it is 6°. because 10 degree - 4 degree = 6 degree

A = area of triangle + area of rectangular + half of the circle area

_________________________________

triangle area = 1/2 × base × height

triangle area = 1/2 × 3 × 5 = 15/2 = 7.50

☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆

rectangular area = length × width

rectangular area = 6 × 5 = 30

☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆

circle half area = 1/2 × pi × radius^2

circle half area = 1/2 × 3.14 × 3^2

circle half area = 1.57 × 9

circle half area = 14.13

_________________________________

A = 7.50 + 30 + 14.13

A = 51.63 m^2

Answer:

\( \frac{29}{9} \)

Step-by-step explanation:

3.2 repeating = 3.2222....

let's make it equal to x

x = 3.2222....

we want to eliminate the infinitely repeating digits, so let's multiply 3.2222.... by 10 and equate it to 10x

3.2222.... × 10 = 32.2222....

10x = 32.2222....

Now we have

x = 3.2222....

10x = 32.2222....

They both have an infinite number of repeating twos so subtract x from 10x to get rid of the repeating digits after the decimal point

Rewriting it as

10x = 32.2222....

x = 3.2222....

10x - x = 9x and 32.2222.... - 3.2222.... = 29

equate both

9x = 29

divide both sides by 9

x = 29/9

The equation 3x-4y=36 can be rewritten in slope-intercept form (y=mx+b), which makes it easier to identify the y-intercept. The following equations is an equivalent form of 3 x-4 y=36, the correct answer is (H) y-6=3/4(x+4).

The equation

3x-4y=36

can be rewritten in slope-intercept form (y=mx+b),

which makes it easier to identify the y-intercept.
The equation

(F) y=-3/4x-9

is not an equivalent form because the slope is different (-3/4 instead of 4/3) and the y-intercept is not the same.
The equation

(H) y-6=3/4(x+4)

is an equivalent form of the given equation. It has the same slope (3/4) and the y-intercept is (0,6), which is different from the y-intercept of the given equation.
The equation

(G) y+6=3/4(x-4)

is not an equivalent form because the slope is different (3/4 instead of 4/3) and the y-intercept is not the same.
The equation (I)

y=3/4x-9

is not an equivalent form because the slope is the same (3/4) but the y-intercept is not the same.
Therefore, the correct answer is (H) y-6=3/4(x+4).

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From the given questions data the relation B and relation C is not a function.

What is the function?

A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, for a relationship to be a function, each input can only be associated with one output.

Using this definition, we can determine which of the given relations is not a function by checking whether each input is associated with exactly one output.

A. The inputs in relation A are 5, -2, 4, and -6. Each of these inputs is associated with exactly one output (4, 2, 1, and 2, respectively). Therefore, relation A is a function.

B. The inputs in relation B are -6, 4, -2, and 5. However, both -6 and 4 are associated with the output 4, so they violate the requirement that each input can only be associated with one output. Therefore, relation B is not a function.

C. The inputs in relation C are 4, -2, 4, and -6. The input 4 is associated with two different outputs (4 and 1), so relation C is not a function.

D. The inputs in relation D are -2, 4, 5, and -6. Each of these inputs is associated with exactly one output (4, 2, 1, and 5, respectively). Therefore, relation D is a function.

Therefore, the answer is relation B and relation C is not a function.

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The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.

The surface area of a cone is calculated using the following formula:

Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.

In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.

l² = 12² + 42²

l² = 1764

l = 42.01 meters

The surface area of the cone is then calculated as follows:

Surface area = πr² + πrl

Surface area = 3.14 * 12² + 3.14 * 12 * 42.01

Surface area = 1,670.5 square meters

Here are some additional explanations:

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Answer:

... what figure?

Step-by-step explanation:

you forgot to add a picture

Answer:

ummmm what...?........

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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Answer:

y=9x-4

OR

y-5=9(x-1)

(both are correct and equal)

Step-by-step explanation:

Parallel means slope is the same, so the slope of the equation should be 9.

Using point slope form:

\(y-5=9(x-1)\)

Which would be:

\(y=9x-4\)

in slope intercept form.

Hey there!

Answer:

y = 9x - 4

Step-by-step explanation:

The other guy already gave the explanation soo... but I got the same answer

Good luck!!  :D

The answer to statements regarding Taylor's theorem is;

a)TRUE

b) TRUE

(a) True. Taylor's theorem is a generalization of the mean value theorem.

The mean value theorem states that for any two points in the domain of a function,

there is at least one point between them on the graph of the function where the slope of the function equals the average rate of change between the two points.

Taylor's theorem is a more general statement of this theorem, where a function is approximated by a Taylor polynomial,

which is a finite sum of terms of the form \($(x-a)^n$\) multiplied by the derivative of the function at \($a$\).

(b) True. If\($p_n$\) is the nth Taylor polynomial for\($f$\) at a point \($x_0$\), then the first n derivatives of \($p_n$\) and \($f$\) are equal near the point \($x=x_0$.\)

This is because the Taylor polynomial of a function is its best linear approximation. Therefore, the derivative of the polynomial will be equal to the derivative of the function up to the order of the polynomial.

So, the first \($n$\) derivatives of the polynomial and the function will be equal near the point \($x=x_0$\).

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There may have been some bias or non-randomness in the selection process of the children for the community project.

To test whether the children were randomly selected, we can conduct a hypothesis test using the following steps:

Step 1: State the null and alternative hypotheses

Null hypothesis: The proportion of low-income children in the sample is equal to the proportion of low-income children in the population (i.e., p = 0.80).

Alternative hypothesis: The proportion of low-income children in the sample is not equal to the proportion of low-income children in the population (i.e., p ≠ 0.80).

Step 2: Determine the level of significance

Assuming a level of significance of 0.05, we want to find out whether the sample provides strong evidence to reject the null hypothesis in favor of the alternative hypothesis.

Step 3: Calculate the test statistic

We can use the z-test for proportions to calculate the test statistic, which measures the number of standard errors between the sample proportion and the population proportion under the null hypothesis.

z = (p - p) / √[p(1-p) / n]

where:

p = sample proportion

p = hypothesized population proportion

n = sample size

Using the given information, we have:

p = 0.74

p = 0.80

n = 200

Plugging in the values, we get:

z = (0.74 - 0.80) / √[(0.80)(1-0.80) / 200] = -2.33

Step 4: Determine the p-value

We need to find the probability of obtaining a z-score as extreme as -2.33 or more extreme (in either direction) if the null hypothesis is true. This is the p-value.

Using a standard normal distribution table or calculator, we find that the p-value is approximately 0.0202.

Step 5: Make a decision

Since the p-value (0.0202) is less than the level of significance (0.05), we reject the null hypothesis. This means that there is strong evidence to suggest that the sample proportion of low-income children is significantly different from the population proportion. In other words, it is unlikely that the sample was randomly selected from the population.

Therefore, further investigation may be needed to identify the potential sources of bias and take corrective actions.

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