What is the answer to the question below

Answer:

(3, 2), (2, 3)

Step-by-step explanation:

x + y = 5

xy = 6

Solve the first equation for x.

x = 5 - y

Substitute 5 - y for x in the second equation.

xy = 6

(5 - y)y = 6

5y - y² = 6

y² - 5y + 6 = 0

Factor.

(y - 2)(y - 3) = 0

y - 2 = 0  or y - 3 = 0

y = 2  or y = 3

Now substitute 2 for y in the first equation and solve for x.

x + y = 5

x + 2 = 5

x = 3

One solution is x = 3; y = 2, or (3, 2).

Now substitute 3 for y in the first equation and solve for x.

x + y = 5

x + 3 = 5

x = 2

Another solution is x = 2; y = 3, or (3, 2).

Answer: (3, 2), (2, 3)

The probability that the sample mean would differ from the population mean by less than 0.5 millimeters is 0.3970.

Given mean diameter of 145 millimeters, standard deviation of 6 millimeters.

We have to find out the probability that the sample mean would differ from the population mean by less than 0.5 millimeters.

μ=145 and ,σ=60 ,n=39 then

s=60/[tex]\sqrt{39}[/tex]=0.96

By finding the probability that the sample mean would differ by less than 0.5 mm equal to p value of Z when X=145+0.5=145.5 mm subtracted by the p value of Z when X==145-0.5=144.5 mm.

When X=145.5 mm

Z=(X-μ)/σ

By central limit theorem

Z=(145.5-145)/5

=0.5/0.96

=0.52

p value of 0.52=0.6985.

When X=144.5

Z=(144.5-145)/0.96

=-0.5/0.96

=-0.52

p value of -0.52=0.5-0.1985=0.3015

Required probability=0.6985-0.3015=0.3970.

Hence the probability that the sample mean would differ from the population mean by less than 0.5 mm is 0.3970.

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The incidence rate of varicella is 13 per 100 if there were 20 students and 5 of whom got vaccinated before fifth grade.

Given Total students of 100 in which 5 had varicella before entering fifth grade and 2 of whom developed  varicella during fifth grade.

We have to find the incidence rate of varicella means requirement of vaccine in proportion form.

So we want the incidence rate, which is the number of people who caught the disease who were at risk to it. So we have 20 people in the class in total. But we said that five of them already had it and they were told that they are immune. So we have 15 people in the class who are at risk, then two people caught it. and so the incidence rate is going to be two divided by 15, which you can check is Not .13 recurring. And so as a percentage We just times by 100 this is going to be 13/ 100.

Hence the incidence of varicella during the fifth grade is 13/100.

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[tex]|\Omega|=6^3\\|A|=3^3\\\\P(A)=\dfrac{3^3}{6^3}=\left(\dfrac{3}{6}\right)^3=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}=12.5\%[/tex]

Hello:

Okay, this problem should be taken in a series of steps:

What is the slope's formula?

  [tex]\rm\hookrightarrow \frac{y_2-y_1}{x_2-x_1}[/tex]

Okay, now let's use this knowledge  

10. (5,-19) and (-5,21)

       [tex]Slope = \frac{21--19}{-5-5} =\frac{40}{-10}=-4[/tex]

11. (12,1) and (12, -1)

      [tex]Slope = \frac{-1-1}{12-12} =\frac{-2}{0}[/tex]

12. (8,7) and (4,7)

     [tex]Slope = \frac{7-7}{4-7} =0[/tex]

Answer:

Hopefully that helps!

The volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

As we have given the volume of the larger cube is 120

Let v is the volume of the small shape.

[tex]\rm \dfrac{120}{v} =\left( \dfrac{4}{2} \right)^3[/tex]

After simplifying:

v = 120/8 cubic ft

or

v = 1.5 cubic ft

Thus, the volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.

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There are 25 males in village 3

The given parameters are:

Total males = 75

                 Male     Female   Total

Village 1   20              25

Village 2  30                            50

Village 3                     30

Total         75

The number of male in village 3 is calculated using:

Male = Total Male - Male in villages 1 and 2

So, we have:

Male = 75- (20 + 30)

Evaluate

Male = 25

Hence, there are 25 males in village 3

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Complete question

An island has three villages and the total number of males is 75. The first village has 20 males and 25 females. The second village has 50 people of whom 30 are males. The third village has 30 females.

Calculate the number of male in third village

Answer:

-7x^2 + 3x + 5

Step-by-step explanation:

-3x^2 + x + 5 - 4x^2 + 2x

Step-by-step explanation:

RS + ST = 8

(RS + ST)×RS = (4 + 2)×4

8 × RS = (4 + 2) × 4 = 6 × 4 = 24

RS = 24/8 = 3

RS + ST = 8

3 + ST = 8

ST = 5

Answer:

182 [tex]yd^{2}[/tex]

Step-by-step explanation:

Area of a parallelogram: bh

bh

= 13(14)

= 182 sq. yds

[489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.

n=400

sample mean (x)=500

sample standard deviation (s)=80

99% confidence interval for mean

α=0.01

critical value [tex]Z_{\frac{a}{z} }[/tex] =2.58

Standard error of sample mean Sx = [tex]\frac{s}{\sqrt[]{n} }[/tex] = [tex]\frac{80}{\sqrt[]{400} }[/tex] = [tex]\frac{80}{20}[/tex] = [tex]4[/tex]

∴ Sx = 4

Confidence interval (μ)

μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] [tex]\frac{s}{\sqrt[]{n} }\\[/tex]

μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] (Sx)

=500 ± 2.58(4)

=500 ±  10.32

lower limit = 500 - 10.32 = 489.68

upper limit= 500 + 10.32= 510.32

Hence, [489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.

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When you win 25% of the time based on the probability, this illustrates that the number of products picked will be 7 products.

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴

= 1/1296

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The triangle that represents the image is; Option B; Triangle X Y Z is reflected across line m and then is dilated to form smaller triangle X prime Y prime Z prime.

From the given transformation as seen in the attached image, we can say that;

In Option A, the triangle is first reflected across m and then reflected across the vertical line. Then, it is dilated.

In Option C, the triangle is reflected across m but the angles are not preserved.

In Option B, the triangle is reflected across m and then dilated and as such is a correct image similar to the original triangle.

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It's Option B.

(You can also call it the middle one, up to you <3)

The minimum number of flyers of each color distributed is 1.

In order to determine the minimum number of flyers of each color distributed, the common factor of 13 and 20 has to be determined. The factor of a number is a number that divides another number perfectly without any remainder.

Factors of 13 = 1, 13

Factors of 20 = 1, 2, 4, 5, 10, 20

Common factor = 1

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Answer:

[tex]f(x)=-2^x[/tex]

Step-by-step explanation:

So generally an exponential equation is expressed in the form: [tex]f(x)=a(b)^x[/tex] and: [tex]b=1+r\text{ or }b=1-r \text{ depending on whether it's decaying or growing}[/tex]. In this case we see that as x increased by 1, the y-decreases, BUT the absolute value is increasing, so it's really just reflected.

Plug in known values:

[tex]-2=a(b)^1[/tex]

[tex]-4=a(b)^2[/tex]

So if you think about it. you really have

-2 = a * b

-4 = a * b * b

since ab = -2, then we can substitute this into the second equation

-4 = -2 * b

-4 = -2b

Divide both sides by -2

b = 2

You can also deduce that b=2, by realizing to go from -2 to -4, you have to subtract 100% of -2 from -2. This means r=1, so b=1+1, b=2

Anyways, now it's time to solve for a, by plugging in a point as well as b.

-4 = a(2)^2

-4 = 4a

-1 = a

You can verify this by using the other point

-2 = -(2)^1

-2 = -(2)

-2 = -2

So the equation is: [tex]f(x)=-2^x[/tex]

Answer:

452.389 cubic feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for finding the volume of the cone: [tex]\pi r^2h/3[/tex]

Height= 12ft

Diameter= 6, radius= [tex]\frac{6}{2}[/tex]= 3

[tex]\frac{22}{7} *3^2*\frac{12}{3} \\\\\frac{22}{7} *3^2*2\\\frac{22}{7} *9*2\\\\\frac{22}{7} *18\\\\56.57[/tex]

Answer:

Step-by-step explanation:

Answer:

gradient= change in y intercept ÷change in x intercept

gradient=-2-0 ÷3-0

gradient=

An opinion poll survey based on a sample of a small section of people is likely to provide the most accurate results.

An opinion poll, often known as a poll or survey, is a human research survey of the general public from a specific sample. By asking a series of questions and extending generalizations into ratios or confidence intervals, opinion polls are often created to represent the opinions of a population. A person who conducts polls is referred to as a pollster.

An opinion poll is a survey that samples a tiny portion of the population in an effort to forecast election outcomes or gauge popular sentiment toward various concerns.

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The summary of the ruler placement postulate is given as:

This states that the points of a line can be matched and correspond to a set of points on the line and the set of real numbers,

Therefore, based on the fact that your question is incomplete, a general overview of the ruler placement postulate is given to give you a better understanding of the concept.

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Answer: You can measure the positive distance  between points A and B by using either point as zero

Step-by-step explanation:

Answer:

A, B, E and F.

Step-by-step explanation:

A triangles side must be larger than the difference of the other sides, and smaller than the sum of the other sides. So in this case we could create an equation such as, 9-7<x<9+7. From this equation we can conclude that this side can be between 2 and 16. So, A, B, E and F all work.

Answer:

3!

Explanation:

By calling a sunny weather "beautiful" and rainy weather "depressing", you're inserting your own opinion into the question- which makes it biased!

The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].

In this problem we must prove that one side of the equality is equal to the expression of the other side, requiring the use of algebraic and trigonometric properties. Now we proceed to present the corresponding procedure:

[tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex]

[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }[/tex]

[tex]\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}[/tex]

[tex]\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}[/tex]

[tex]\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}[/tex]

[tex]\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}[/tex]

[tex]\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}[/tex]

[tex]\tan \alpha + 1 + \cot \alpha[/tex]

[tex]\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1[/tex]

[tex]\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1[/tex]

[tex]\frac{1}{\cos \alpha \cdot \sin \alpha} + 1[/tex]

[tex]\sec \alpha \cdot \csc \alpha + 1[/tex]

The trigonometric expression [tex]\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}[/tex] is equivalent to the trigonometric expression [tex]\sec \alpha \cdot \csc \alpha + 1[/tex].

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Answer:

As x to negative infinity, y to negative infinity

Step-by-step explanation:

The number of hours it will take Brigid to fill 5 bushels of strawberries is; 5³/₅ hours

We are told that the scenario that Brigid represents is;

⁵/₈x + 1¹/₂ = 5

where x is is the number of hours she picks

Now, let us solve for x by converting the mixed fraction to improper fraction to get;

⁵/₈x + ³/₂ = 5

Multiply through by 8 to get;

5x + 12 = 40

Subtract 12 from both sides to get;

5x = 28

x = 28/5

x = 5³/₅ hours

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Answer:

Trinomial:  [tex]\boldsymbol{\text{x}^2 + 3\text{x} - 4}[/tex]

Dimensions: [tex]\boldsymbol{\text{x}+4} \text{ by } \boldsymbol{\text{x}-1}[/tex]

=======================================================

Explanation:

The big green square is x units by x units. Its area is [tex]\text{x} * \text{x} = \text{x}^2[/tex] which represents x squared.

The long vertical green rectangles are x units tall and 1 unit across. The area of one such rectangle is x times 1 = x. Since we have four of these green rectangles, so far we have x+x+x+x = 4x in additional area.

So far the area is [tex]\text{x}^2+4\text{x}[/tex]

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

All of the green areas mentioned so far are positive areas so to speak.

In contrast, the red areas are negative areas. They take away from the positive. You can think of it like a bank balance.

If a single green rectangle is x square units in area, then a red rectangle is negative x or -x

So we go from 4x to 4x-x = 3x

Then we subtract off 4 due to the 4 small squares

This gives a total area of [tex]\text{x}^2 + 3\text{x} - 4[/tex] and this represents the standard form of the polynomial area. It is a trinomial since it has 3 terms.

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

Now onto the dimensions.

Check out the diagram below. The overall figure is x+4 units across the horizontal dimension, and x-1 units tall along the vertical dimension.

If you were to use the FOIL rule, then you would find that [tex](\text{x}+4)(\text{x}-1) = \text{x}^2 + 3\text{x} - 4[/tex] which helps show how the two forms connect to one another.

This also helps show that area = length*width which is what we'd expect from any rectangular area.

Answer:

A

Step-by-step explanation:

The formula for circumference is π×diameter.

π×12= 37.6991, which can be rounded up to 38.

Answer:

Linear

Step-by-step explanation:

Notice that x values increase by 1 each row and that the y values increase by 5 each row. By definition, in linear functions, x and y values both increase by constant values. Going down each row, the y value increases by 5 as the x value increases by 1, so we know that the graph must be a linear function.

Function Type: linear

Equation: y = 5x + 7

Step-by-step explanation:

Newton's second law of motion describes the relationship between force and acceleration. They are directly proportional. If you increase the force applied to an object, the acceleration of that object increases by the same factor. In short, force equals mass times acceleration.

Both climbers rested on the wall at a constant height for 2 minutes.

The complete question is added as an attachment

From the attached graph, we have the following highlights

The above means that both climbers stopped for 2 minutes

Hence, the true statement about the climber's height is that (d) Both climbers rested on the wall at a constant height for 2 minutes.

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Answer: D: Both climbers rested on the wall at a constant height for 2 minutes.

Step-by-step explanation: i did the quiz edge 2022