Is the point \displaystyle (1,2)(1,2) a solution to the system of equations \displaystyle y-10x=-8y−10x=−8 and \displaystyle y=-8x+10y=−8x+10?

YES
NO

To use the integral test, we need to evaluate the following integral: ∫[infinity]1 6/5x dx Using integration by substitution with u = 6/5x, we get: ∫[infinity]1 6/5x dx = (5/6)∫[infinity]6/5 1 du.

Evaluating this integral gives us: (5/6)∫[infinity]6/5 1 du = (5/6)(1/u)|[infinity]6/5 = (5/6)(0 - 5/6) = -25/36 Since the integral evaluates to a finite value, and the series has the same general term as the function being integrated, we can conclude that the series is convergent by the integral test.

The new limits for the integral will be 5 (lower) and infinity (upper). ∫(5 to infinity) 6/u * (1/5) du. Thus, the integral is divergent. Since the integral is divergent, the original series Σ (n = 1 to infinity) 6/(5n) is also divergent.

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Answer:

Choice C

Step-by-step explanation:

Point D is in the 4th quadrant where we generally have points in the form (x, -y).

To reflect about the y-axis from quadrant 4, (x,-y) becomes (-x-y). This both coordinates become negative. See it?

So, D becomes (-4, -1).

To reflect about the y-axis from quadrant 1, (x, y) becomes (-x, y).

So, points E and F become (-5, 2) and (-1, 2), respectively.

In other words, the x-coordinate becomes negative. See it?

Answer: Choice C

The probability that chad gets at least 2 heads on 3 flips is 1/2 which was found using the sample space.

Given: To decide who will pay for lunch, Jeff and Chad decide to flip a coin three times. Chad chooses heads, and in order to win and have Jeff pay for his lunch, he must get heads at least twice out of three times.

Let,

H = Heads

T = Tails

Sample space =  {HHH, HTH,THH,TTH, HHT, HTT,THT,TTT​}

Total number of possible outcomes = 8

Probability that chad gets at least 2 heads is given as:

P(A)=P(getting two heads)+P(getting 3 heads)

= 3/8 + 1/8

= 4/8

= 1/2

Therefore,  the probability chad gets at least 2 heads on 3 flips is 1/2 which was found using the sample space.

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Step 1: Write the system of equations

Step 2: Using Elimination method

Hence the new equations are

An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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Answer:

\(f(g(x)) = 2x - 1\)

Step-by-step explanation:

learn composite functions

There are 2.5 pounds in 40 ounces.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor.

Given,

There are 16 ounces in 1 pound.

then, pounds in 1 ounce = 1/16

expression z/16 represents number of pounds

where z represents the number of ounces.

For 40 ounces,

Number of pounds = 40/16

                                = 2.5 pounds

Hence, 2.5 pounds are there in 40 ounces.

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Answer:

9x^2 - 36x + 35.

Step-by-step explanation:

One would be (x - 5/3)(x - 7/3)   <------ in factor form.

Getting rid of the fractions by multiplying each term by 3:

= (3x - 5)(3x - 7)

Converting to standard form

= 3x*3x -7*3x - 5*3x + 35

= 9x^2 - 36x + 35.

Answer:

60 degrees

Step-by-step explanation:

just add 33 and 27

Answer:

60°C

Step-by-step explanation:

27 - (-33) = 27+33 = 60

Area:

Approximately 211.24 square feet

Explanation:

Im going to assume you are asking for the surface area of a sphere with a diameter of 8.2ft. The equation to find this is: \(A = 4\pi r^2\)

Firstly, we need to convert the diameter to the radius. The diameter is always twice the length of the radius, so the radius must be 4.1ft

Plug this value in:

\(A = 4\pi (4.1)^2\\A = 4\pi(16.81)\\A = 211.24\)

The probability Amaya will bring pizza one day and peanut butter and jelly the next day is 143/961.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Amaya bought peanut butter and jelly sandwich = 11

Amaya bought sandwich = 7

Amaya bought pizza= 13

Total outcomes = 13+ 7 + 11 = 31

So, the probability Amaya will bring pizza one day and peanut butter and jelly the next day

= 13/31 x 11/31

= 143/961

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Answer:

Step-by-step explanation:

say that mystery number is x

5*x-27=83

5*x=83+27

5*x=110

x=22

Answer:

22

Step-by-step explanation:

5x-27=83

           +27

5x=110

x=110/5

x=22

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

The first one is 12

The second one is -12

Just multiply, and remember the negative signs.

Answer:

1st Question- Positive Twelve

Second Question- Negative Twelve

Step-by-step explanation:

In Costello et al. (2003), the independent variable that was not manipulated by the research team was the gender of the participants.

The study examined the effects of different levels of alcohol consumption on cognitive performance and mood states in young adults. Participants were assigned to different alcohol consumption groups based on their self-reported drinking habits. However, the gender of the participants was not manipulated, and the study included both male and female participants. This means that any differences in the results based on gender cannot be attributed to the research team's manipulation of the independent variable, but rather to other factors that may have affected the results.

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A test of nonverbal intelligence is a type of cognitive assessment that measures an individual's ability to solve problems and think abstractly without the use of language.

Unlike traditional intelligence tests that rely heavily on verbal abilities such as vocabulary, reading, and verbal reasoning, nonverbal intelligence tests use visual-spatial and abstract reasoning tasks that do not require the use of language.

Nonverbal intelligence tests can be particularly useful for individuals who have language or communication difficulties, such as those with speech and language disorders, or those who are non-native speakers of the language in which the test is administered. They can also be used to assess individuals who have difficulty with traditional tests due to visual or hearing impairments.

Examples of nonverbal intelligence tests include Raven's Progressive Matrices, the Naglieri Nonverbal Ability Test (NNAT), and the Universal Nonverbal Intelligence Test (UNIT). These tests typically involve completing visual pattern recognition and completion tasks, spatial reasoning tasks, and other nonverbal problem-solving tasks.

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The equation of the line that passes through the points (0,-2) and (3,2) is  4x-3y-6 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

The points are (0,-2) and (3,2)

To find the equation of the line,

Find slope by using formula  m = (y₂-y₁)/(x₂-x₁)

m = (2-(-2))/(3-0)

m = 4/3

The equation of line is,

y-y₁ = m (x-x₁)

y-(-2) = 4/3(x-0)

y+2 = 4/3x

3y+6 = 4x

4x-3y-6 = 0

The required equation of line is 4x-3y-6 = 0.

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Answer:

first

2/5m + 8/5

second

22/5

third

11

The Dot plots clearly display clusters/gaps of data and outliers.

Twelve teachers attended a seminar on mathematical problem-solving. their attitudes were measured before and after the seminar.

a positive number change attitude indicates that a teacher's attitude toward math became more positive.

The twelve change scores are as follows:

3 8 -1 2 0 5 -3 1 -1 6 5 -2

First, we arrange the data in increasing order

-3,-2,-1,-1,0,1,2,3,5,5,6,8

Dot plots clearly display clusters/gaps of data and outliers. In dot plots, the frequency axis is not necessary but you need to count to find the frequency.

n=12 is even.

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To know how much lemonade you can buy with $320, we first need to determine the price of a pint of ice cream. Since you can buy 80 pints with $320, the price of one pint of ice cream is $320 divided by 80, which equals $4.

Next, we need to find the price of a glass of lemonade, which is 3.2 times less than the price of ice cream. Therefore, the price of a glass of lemonade is $4 - (3.2 * $4) = $4 - $12.8 = -$8.8.

Since the price of lemonade is negative, it indicates that you will receive money back for every glass of lemonade you buy. However, since you cannot have a negative quantity of lemonade, the answer would be zero.

In summary, with $320, you can buy zero glasses of lemonade.

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Answer:

A

Step-by-step explanation:

The answer is A because in the triangle, the two smaller sides added up have to be more than the bigger side, or equal, if it is a right triangle. so 4 is the smallest 4+6=10, so it does not work, but lets see if it is a right triangle

4^2+6^2=16+36=52. it would have to equal 100 to be a right triangle. Use Pythagorean thereon.

For a triangle, the any two sides must be greater than the third side.The measure of AC cannot be equal to 4

A triangle has three sides and angle. For a triangle, the any two sides must be greater than the third side.

Given the following parameters

AB = 10 and

BC = 6

The measure of AC must be 8 for the theorem above to be true

6 +8 > 10

6 +10 > 8

10 + 8 > 6

Hence the measure of AC cannot be equal to 4

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Answer:

(6m² + 12m + 2) / (6m + 1)

Step-by-step explanation:

multiply both sides by m.

we get m² - 1 = 6m

move the -1 to the other side, so it becomes +1

m² =  6m + 1

so m² + 1/m² = (6m + 1) + 1/(6m + 1)

get a common denominator by squaring (6m + 1)

(6m + 1)².

we now have (6m + 1)² / (6m + 1)  + 1/(6m + 1).

we now add the numerators.

(6m + 1)² + 1 = (6m² + 6m + 6m + 1) + 1 = 6m² + 12m + 2.

numerator over denominator = (6m² + 12m + 2) / (6m + 1)

Answer:

there is no solution

Step-by-step explanation:

You would use distributive property first to get

12x+36 = 8x+36 + 4x

by combining like terms, you would get 12x+36 = 12x+36, meaning there is no solution to this equation

The area under the curve over [2,5] is 24.

Given function is f(x) = 2xIntervals [2, 5] is given and it is to be divided into subintervals.

Let us consider n subintervals. Therefore, width of each subinterval would be:

$$
\Delta x=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}
$$Here, we are using right-hand end point. Therefore, the right-hand end points would be:$${ c }_{ k }=a+k\Delta x=2+k\cdot\frac{3}{n}=2+\frac{3k}{n}$$$$
\begin{aligned}
\therefore R &= \sum _{ k=1 }^{ n }{ f\left( { c }_{ k } \right) \Delta x } \\&=\sum _{ k=1 }^{ n }{ f\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ 2\cdot\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ \frac{12}{n}\cdot\left( 2+\frac{3k}{n} \right) }\\&=\sum _{ k=1 }^{ n }{ \frac{24}{n}+\frac{36k}{n^{ 2 }} }\\&=\frac{24}{n}\sum _{ k=1 }^{ n }{ 1 } +\frac{36}{n^{ 2 }}\sum _{ k=1 }^{ n }{ k } \\&= \frac{24n}{n}+\frac{36}{n^{ 2 }}\cdot\frac{n\left( n+1 \right)}{2}\\&= 24 + \frac{18\left( n+1 \right)}{n}
\end{aligned}
$$Take limit as n → ∞, so that $$
\begin{aligned}
A&=\lim _{ n\rightarrow \infty  }{ R } \\&= \lim _{ n\rightarrow \infty  }{ 24 + \frac{18\left( n+1 \right)}{n} } \\&= \boxed{24}
\end{aligned}
$$

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Given function f(x) = 2x. The interval is [2,5]. The number of subintervals, n is 3.

Therefore, the area under the curve over [2,5] is 21.

From the given data, we can see that the width of the interval is:

Δx = (5 - 2) / n

= 3/n

The endpoints of the subintervals are:

[2, 2 + Δx], [2 + Δx, 2 + 2Δx], [2 + 2Δx, 5]

Thus, the right endpoints of the subintervals are: 2 + Δx, 2 + 2Δx, 5

The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, we have to find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. The width of each subinterval is:

Δx = (5 - 2) / n

= 3/n

Therefore,

Δx = 3/3

= 1

So, the subintervals are: [2, 3], [3, 4], [4, 5]

The right endpoints are:3, 4, 5. The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, Δx is 1, f(x) is 2x

∴ f(c1) = 2(3)

= 6,

f(c2) = 2(4)

= 8, and

f(c3) = 2(5)

= 10

∴ S = f(c1)Δx + f(c2)Δx + f(c3)Δx

= 6(1) + 8(1) + 10(1)

= 6 + 8 + 10

= 24

Therefore, the Riemann sum is 24.

To calculate the area under the curve over [2, 5], we take the limit of the Riemann sum as n → ∞.

∴ Area = ∫2^5f(x)dx

= ∫2^52xdx

= [x^2]2^5

= 25 - 4

= 21

Therefore, the area under the curve over [2,5] is 21.

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Answer:

Not a function

Step-by-step explanation:

For 0 in the domain (input), there are two possible values in the output (range). This goes against the definition of a function, where every element in the domain must have only one value in the range.

Hope this helps!

7.051 can be written as the fraction 7051/1000.

To express 7.051 as a fraction in the form of p/q, we need to identify the decimal places and convert them to the corresponding fractional parts.

Since 7.051 has three decimal places, we multiply it by 1000 to move the decimal point three places to the right, which gives us 7051.

Now, the numerator (p) of the fraction will be 7051, and the denominator (q) will be the corresponding power of 10, which is 1000.

Therefore, 7.051 can be expressed as 7051/1000.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

In this case, the GCD of 7051 and 1000 is 1, so the fraction is already in its simplest form.

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to express the range of possible values that the number could take, we write the number as:
x = 40 ± 5.

When we round a number to a certain number of significant figures, we are essentially estimating the value of the number based on the level of precision we require. In the case of rounding to 1 significant figure, we are rounding the number to the nearest power of 10 that has only one non-zero digit. For example, 40 has one significant figure, while 45 has two significant figures.

However, when we round a number, we introduce an error in our estimate. This error is due to the fact that the true value of the number may be closer to the midpoint between two adjacent values than to the value we have rounded to. In the case of rounding to 1 significant figure, the error interval is equal to half the value of the least significant digit.

In other words, if we round a number to 1 significant figure, the true value of the number could be as much as 5 units less or 5 units more than the rounded value. Therefore, to express the range of possible values that the number could take, we write the number as:

x = 40 ± 5

This means that the true value of x could be anywhere between 35 and 45, inclusive. In other words, we are 95% confident that the true value of x falls within this range.
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Answer:

1. is equilateral and 2. is scalene

Step-by-step explanation:

Isosceles triangle is when it has 2 equal angles and sides

Scalene has all different angles and sides.

Option C is not a characteristic of both surveys and observational studies.

What are some examples of observational studies?

In an observational study, researchers watch participants while they engage in certain behaviours or tasks without directing them towards any particular strategies or modes of behaviour.

                              An observational research, for instance, may be chosen by a scientist to investigate how human consumption of water influences dietary habits.

Which of the following best describes an observational study's characteristics?

While doing an observational study, the researcher relies solely on what they see to provide an answer to their research topic. No controls or treatment groups are used, and the study participants are not interfered with or otherwise manipulated.

In Option C we are given that in a survey Data are collected about a population which need not be true every time.

Thus, Option C is the correct answer.

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The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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