2 Determine whether the table represents a linear relationship. If so, state the slope of
the line.
X
2
3
4
5
сл
y
14
21
28
35
X
-2
-1
0
1
y
10
5
0
-5
x
2
3
4
5
y
48
72
90
114

The exterior angle with angle d is equivalent to 141 degrees, and the value of x is equal to 10.

We must keep in mind that the total of all the angles in a triangle equals 180 degrees in order to solve this puzzle.

The given angles are-

Using that formula in this case;

Thus, sum of all angles is 180°.

m < d + m < e + m < f = 180°

(2x + 19)° + (3x + 24)° + 87° = 180°

x = 10°

But if angle D is on a straight line, it is possible to find its exterior angle because angle D plus its exterior angle add up to 180 degrees.

Suppose y = external angle.

m < d + y = 180°

2x + 19 + y = 180°

And x = 10°

2(10) + 19 + y = 180°

y = 141°

Thus, the measure of the degree measure of the exterior angle is found as  141°.

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The correct question is-

In triangle DEF, m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°. Determine the degree measure of the exterior angle to ∠D.

54°

39°

141°

126°

The account in which there was a mistake in the calculation of the simple interest is account B.

We know that the interest is an amount of money that is obtained on top of the initial money that was deposited. The initial money that you deposit in the account is called the principal. The rate is the percentage at which the interest is calculated and the time is the period that has elapsed since the deposit was made.

Given that;

I = PRT/100

I = interest

P = principal

R = rate

T = time

For account A

I = 200 * 3.9 * 1/100

I = $7.8

For account B;

I = 400 * 2.7 * 1/100

I = $10.8

We can see that there must have been a calculation error as the interest in account B was being calculated.

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99% confidence interval would be (10.78,11.82) for the true mean of the damaged items.

Variability is measured by the variance. It is determined by averaging the squared deviations from the mean.

The degree of dispersion in your random sample collection is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.

You may determine the average distance between each number and the mean using the standard deviation, which is obtained from variance. It is the variance's square root.

Both metrics capture distributional variability, although they use different measurement units:

Standard deviation is represented in the same units as the initial values (e.g., meters).

Larger units are used to express variation.

How to solve?

n = 12

Average = 11.3

Variance = 0.49

Standard deviation = √0.49=0.7

so, we need to find 99% confidence interval.

At 99% confidence , z = 2.58

So, interval would be

x±z* σ/√n = 11.3 ±2.58* 0.7/√12

=11.3±0.521

=(11.3 - 0.521,11.3 +0.521

= (10.78, 11.82)

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The number of children take greek and hebrew = 2

In this question, we have been given that in a class of 30 children, 20 take latin, 14 take greek, and 10 take hebrew.

So, n(s) = 30

Let set a: children taking Latin language

n(a) = 20

set b: children taking Greek language

n(b) = 14

set C: children taking Hebrew language

n(c) = 10

no child takes all three languages

⇒ n(a ∩ b ∩ c) = 0

And eight children take no language

⇒ n(S) -  n(a ∪ b ∪ c) = 8

So, n(a ∪ b ∪ c) = 8

This means, 22 children taking languages.

Of those 22 kids, 14 take Greek and 10 take Hebrew.

14+10 = 24

This means, at least 2 children must taking Greek and Hebrew.

Since no child takes all three languages, the children taking Greek and Hebrew can't be taking Latin. Since 20 of the 22 kids are taking Latin, that means at most 2 are taking Greek and Hebrew.

Therefore, 2 children take greek and hebrew

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The length of diameter of the base of the cone will be 112 cm. Hence, option b is correct.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

Use the equation of Pythagoras's theorem,

106² = 90² + r²

r² = 106² - 90²

r = √3136

r = 56 cm.

Then, the diameter will be,

D = 2r

D = 2(56)

D = 112 cm.

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Answer:

(a)  Other zeros:  3i  and  -4-i

(b)  9

(c)  10

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z^*=a-bi[/tex] .  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if R(x) is a polynomial with real coefficients, and 3i is a root of R(x)=0, then its complex conjugate -3i is also a root of R(x)=0.

Similarly, if -4+i is a root of R(x)=0, then its complex conjugate -4-i is also a root of R(x)=0.

The degree of the polynomial is the greatest of the exponents of its various terms.  

The degree of R(x) with just the given roots (including the complex conjugates) is 6, which includes 2 real zeros.

As the actual degree of R(x) is 13, the maximum number of real zeros would be 7 more than the given real zeros.

Therefore, the maximum number of real zeros that R(x) can have is 9.

For each complex root there is also a complex conjugate root.

We have been given 2 complex zeros and 2 real roots, so when we include the complex conjugates, the degree of R(x) is 6.

The actual degree of R(x) is 13, so the maximum number of non-real zeros is 6 more (as they come in pairs) than the already given 4 non-real zeros.  Therefore, the maximum number of non-real zeros that R(x) can have is 10.

The ant travels at a pace of 1/15 mins per centimeters.

What is Pace?

Meaning of pace is rate of movement.

Pace is the inverse of speed.

If speed is measured in units of distance per unit of time then pace is measured in units of time per unit of distance.

We know speed is total distance travelled in the total time taken

speed = distance/time

According to the given question:

Ant travels 30cm in every 2 minutes

Distance travelled by ant = 30 cm

Time taken to travel this distance = 2 minutes

Therefore, speed of the ant is

30/2 = 15 cm per min

Now pace = inverse of speed

pace = 1/15 min per cm

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Hence, the equation of parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] is

[tex]y=-6(x-4)^2+4[/tex].

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

The parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] .

Here [tex](x,y)=(3,-2)[/tex] and [tex](x_1,y_1)=(4,4)[/tex]

The general formula is

[tex]y=a(x-x_1)^2+y_1[/tex]       ....[tex](1)[/tex]

Substitue the given values in the equation [tex](1)[/tex], we get

When [tex](x_1,y_1)=(4,4)[/tex]

[tex]y=a(x-4)^2+4[/tex]

When [tex](x,y)=(3,-2)[/tex]

[tex]-2=a(3-4)^2+4\\\\-2=a(-1)^2+4\\\\-2=a+4\\\\a+4+2=0\\\\a+6=0\\\\a=-6[/tex]

So, the equation is of thr form

[tex]y=-6(x-4)^2+4[/tex]

Hence, the equation of parabola in vertex from vertex [tex](4,4)[/tex] point [tex](3,-2)[/tex] is

[tex]y=-6(x-4)^2+4[/tex].

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The appropriate design for testing the significance of the difference between the means is called an independent-samples t-test.

The Independent Samples t- test analyzes the means of two separate groups to observe if there is statistical support that the population mean values are statistically substantially different.

A parametric test is said to be the Independent Samples t Test and the Independent t Test is another name for this test. Both examine the significance of a discrepancy between two means.

Independent-sample t tests compare scores on the same variable for the two different groups of cases, whereas paired-sample t tests compare scores on two different variables for the same group of instances.

When doing a t-test, it is usual to make the following assumptions: like the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and an equality of variance in standard deviation.

The appropriate design for testing the significance of the difference between the means is - b. independent-samples t-test.

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The condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).

In mathematics, a polynomial with integer values (also called a numerical polynomial) has an integer value for each integer n.

Contrary to popular belief, every polynomial with integer coefficients has integer values.

For instance, when t is an integer, the polynomial takes on integer values.

So, polynomials are the sums of terms of the form kˣⁿ, where k is any number and n is a positive integer.

A description of polynomials, such as the polynomial 3x+2x-5.

The concepts of degree, standard form, monomial, binomial, and trinomial are all covered in this section.

Therefore, the condition that p(x)/q(x) is an integer for any number of inputs of integers x is satisfied by the integer polynomials p and q. It's not necessary for q(x) to split p(x).

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The relationship between RS and RT is RT is the base of this isosceles triangle.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

We know the sum of all the interior angles in a triangle is 180°.

Given, A triangle RST,

So, ∠S + ∠T + ∠R = 180°.

50° + 65° + ∠R = 180°.

∠R = 65°.

This is an isosceles triangle with two similar sides RS and ST.

The relation between RS and RT is RT is the base of this isosceles triangle.

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Answer:

Your answer is 22.

Tu respuesta es 22. Además, no hablo español, usé Translate

Answer:5/8

Step-by-step explanation:

[tex]\begin{gathered} \boxed{ \sf \frac{3}{4} - \frac{1}{8}} = \\ \\ \sf \frac{8 \div 4 \times 3 - 8 \div 8 \times 1}{8} = \\ \\ \sf\frac{6 - 1}{8} = \\ \\ \sf \boxed{ \sf\frac{5}{8}} \end{gathered}[/tex]

Therefore, the result of this subtraction of fractions is five eighths.

How to subtract unlike fractions:

Heterogeneous fractions are fractions that have different denominators.

To subtract heterogeneous fractions we follow these steps:

The value of n is 25  according to standard deviation in the question.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

s = 30 minutes

C.I. = 99%

mean = 15 minutes

z value for 99% = 2.58

mean = z*s/√n

15  = 2.58 * 30 / √n

√n = 5.06

n = 25

Hence the value of n is 25 .

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Answer: $0.95

Step-by-step explanation:

7.90 - 1.25 = 6.65

6.65 divided by 7 = 0.95

The value of a $500 certificate after one year is $525.

The amount that actually enrol is 3000

From the question, we have the following parameters that can be used in our computation:

Expected enrolment = 70%

Actual enrolment = 30%

Number of applicants = 10000

This means that

Actual = Actual enrolment * Number of applicants

Substitute the known values in the above equation, so, we have the following representation

Actual = 30% * 10000

Evaluate

Actual = 3000

Hence, the amount  is 3000

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Answer: 1st point : 0,-1 second point : 1,0

Step-by-step explanation: the y intercept is -1. The slope is 2/1 rise over run. Two rise 1 over

The probability that the horse will not win the race is 0.7500.

The mathematical branch known as probability deals with determining the possibility of an event occurring. The conversions between probability and odds are feasible. This is because the odds are determined by dividing the likelihood that an event will occur by the likelihood that it won't.

Here, the odds of a horse winning a race are given as 2 to 6. Then, the probability of winning the horse race is calculated as,

[tex]\begin{aligned}\text{Odds}&=\frac{p}{1-p}\\\frac{2}{6}&=\frac{p}{1-p}\\2(1-p)&=6p\\2-2p&=6p\\2&=6p+2p\\8p&=2\\p&=\frac{2}{8}\\&=\frac{1}{4}\end{aligned}[/tex]

Then, the probability of not winning the horse race is,

[tex]\begin{aligned}q&=1-p\\&=1-\frac{1}{4}\\&=\frac{3}{4}\\&=0.75\end{aligned}[/tex]

The answer is 0.75. Therefore, the correct option is option c.

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The statement of the given hypothesis is False.

What is hypothesis testing?

Hypothesis testing is a statistical analysis that looks at a sample to see if the findings are representative of the population. Depending on the type of data used and the goal of the research, the analyst will choose a certain approach.

Given:  A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.

">" sign implies that right-tailed test i.e., one-tailed right-sided.

Hence, the given statement is False.

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The missing values are as shown below:

A.) 15

B.) 1 year

C.) $50

D.) 1.5%

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The percentage equation goes thus:

Interest earned = principal * rate * time

A)

Principal: $100 Interest rate: 5% Time in years: 3 Interest earned

Interest earned = $100 * 0.05 * 3

Interest earned = $15

B.)

Principa;" $500 Interest rate: 4% Time in years: interest earned: $20

Interest earned = principal * rate * time

20 = 500 * 0.04 * time

20 = 20 * time

Time = 20 / 20 = 1

Time = 1 year

C.)

Principal: Interest rate:10% Time in years: 7 Interest earned:$35

Interest earned = principal * rate * time

$35 = principal * 0.1 * 7

$35 = principal * 0.7

Principal = $35 / 0.7

Principal = $50

D.)

Principal: $200 Interest rate: Time in years:2 Interest earned: $6

Interest earned = principal * rate * time

$6 = $200 * rate * 2

$6 = $400 * rate

Rate = $6/$400

Rate = 0.015 = 1.5%

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It will take the new crew 8 hours to paint the new apartment.

Two quantities are said to be in inverse proportion if an increase in one leads to a decrease in the other quantity and a decrease in one leads to an increase in the other quantity". In other words, if the product of both the quantities, irrespective of a change in their values, is equal to a constant value, then they are said to be in inverse proportion.

if it takes both crews 4 hours to paint the crew and both crew worked at same rate.

Then it will take the new crew 4 x 2 hours to complete the apartment which is 8 hours.

In conclusion, the new crew will complete the apartment in 8 hours

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The distance between the two towns is 49 km

What is average speed?

Average speed is calculated by dividing distance by time (eg miles/hour).

The entire distance traveled by the object in a specific amount of time is its average speed. A scalar quantity, average speed, exists. The magnitude serves as its representation, and it lacks direction.

A body's average speed is its mean value over a given amount of time. Since a moving body's speed fluctuates over time and is not constant, an average speed formula is required. The total time and total distance numbers can be used, even with fluctuating speed, and with the aid of the average speed formula, we can get a single value to represent the entire motion.

Difference in times = 12:42 - 11:32 = 1.17 hours

Formula:

Distance = speed * time

               = 42 * 1.17

              = 49 km

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The ratio of 13 to 25 is 13/25 because 13 is a prime number

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.

In this question, we have to find the ratio between 13 to 25

To do this, we simply divide 13 by 25

13÷25 = 13/25

This is so because the two numbers are not divisible as 13 is a prime number.

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Answer: If A is true, then B must be true.

Probability which is randomly selected race participants with finishing time less than 165 minutes is equal to 0.84.

As given in the question,

Mean 'μ' = 149 minutes

Standard deviation 'σ' = 16 minutes

Probability of randomly selected race for finishing time less than 165 minutes

⇒ P( X < 165 ) = P [(X - μ)/σ < (165 -149)/16]

                       = P  [(X - μ)/σ < 1]

                       = P ( z < 1 )

Probability is associated with 1,2,3 standard deviation of 68%, 95% and 99.7%

Empirical rule = 68 - 95 - 99.7

P ( z < 1 ) = 0.5 + 0.68/2

               = 0.5 + 0.34

               = 0.84

Therefore, the probability for randomly selected participants whose finishing time is less than 165 minutes is 0.84.

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Answer:

Step-by-step explanation:

84% is the answer for Knewton Alta Stats

Therefore, L has a relative and absolute minimum when x = 400 m

The area is as defined as the amount of space occupied by any shape in two dimensions. Whereas, Perimeter is the boundary or the outline of a flat shape.

Let x = length of the side parallel to the river

     y = length of each of the other two sides

Then xy = 80,000, so y = 80,000/x

Minimize:  L = length of the fence

L = x + 2y

  = x + 160,000/x, where x > 0

L' = 1 - 160,000/x2 = (x2 - 160,000)/x2

L' = 0 when x = 400 or -400

Since x can't be negative, x must be 400.

When 0 < x < 400, L' < 0.  So, L is decreasing.

When x > 400, L' > 0.  So L is increasing.

Therefore, L has a relative and absolute minimum when x = 400 m

                                                                                    y = 80,000/x = 200 m

The fence is shortest if the side parallel to the river has length 400 m and the other 2 sides each have length 200 m.  

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