Is 2x + y = 10 a linear function

Answer:

14π in.

Step-by-step explanation:

First, we use the area to find the radius.

A = πr²

πr² = 49π in.²

r² = 49 in.²

r = √(49 in.²)

r = 7 in.

Now, we use the radius to fins the circumference.

C = 2πr

C = 2 × π × 7 in.

C = 14π in.

Answer:

D: f(x) · g(x) =12x^2-25x+12

Step-by-step explanation:

we multiply the 2 equations

(3x-4)(4x-3)

12x^2-9x-16x+12

12x^2-25x+12

so d is the answer

hopes this helps please mark brainliest

The possible values for the width of rectangle are 24 and -28.

What is area of rectangle?

The area of a rectangle formula. Area of a Rectangle is A = l × b. Once the length and width of a rectangle are known, the area can be calculated. The area of the rectangle is calculated as a square unit by multiplying the length and width.

Let x is the width of rectangle.

As given a rectangle length  is 4 feet longer than it is wide.  

⇒ l = 4 + x

Since,

Area of rectangle = length x width

                      672 = (4 + x) x x

                      672 = 4x + x^2

     x^2 + 4x - 627 = 0

To find the value of x we can use the quadratic formula.

Here a = 1, b = 4, c = -672

[tex]x = \frac{-b +-\sqrt{b^2-4ac} }{2a} \\x = \frac{-4+-\sqrt{4^2-4(1)(-672)} }{2(1)} \\x = \frac{-4+-\sqrt{2704} }{2} \\x = \frac{-4+-52}{2} \\x = -2+-26[/tex]

⇒ x = -2 + 26,  x = -2 - 26

⇒ x = 24,         x = -28

Hence, the possible values for the width of rectangle are 24 and -28.

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Answer:

y - 2.5 = 2(x - 1)

Step-by-step explanation:

Here given slope is 2 and the point through which the straight line passes is (1, 2.5)

Let the equation be y = mx + c where m and c represent slope and y intercept respectively.

We know the slope, so we input that in our equation

y = 2x + c ------- i

This straight line also passes through (1, 2.5)

Putting the values in place of x and y we get,

2.5 = (2X1) + c

⇒ 2.5 = 2 + c

⇒ c = 2.5 - 2

⇒ c = 0.5

Now, putting value of c in i, we get

y = 2x + 0.5 -------- ii

It can also be written as y - 2.5 = 2(x - 1) ------- iii

this equation and ii are same and you can verify that by simplifying iii, by multiplying 2 and then shifting the -2.5 from LHS to RHS

The expression 6x - 2  is equivalent to 5x + 2(3x - 1) - 5x. Option (1) is Correct.

Expressions that function identically despite having distinct appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

The equality (=) sign is used to denote equivalent phrases. Since the values of both expressions are constant for all values of x, 3(x + 2) and 3x + 6 are equal expressions. 3x + 6 = 3 × 4 + 6 = 18.

Here the expression is : 5x + 2(3x - 1) - 5x ...... (1)

let x=1 put in equation 1

then we get,

=5(1)+2(3(1)-1)-5(1)

=5+6-2-5

=4

now verify with all Options: put x =1

6x - 2 = 6(1) -2

=6-2

=4 (Correct value)

Option 2:

6x + 2

=6(1)+2

=8 (wrong Option)

Option 3:

16x - 2

=16-2

=14  (wrong Option)

Option 4:

=16x + 2

=16+2

=18 (wrong Option)

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Correct Question:

Which of the following is equivalent to the expression below?

5x + 2(3x - 1) - 5x

1. 6x - 2

2. 6x + 2

3. 16x - 2

4. 16x + 2

Answer: $144

Step-by-step explanation: To find the price she gets paid for 1 hr we need to divide the money by the hours. So, 90 / 5 = 18.

So, now we know she gets paid 18 dollars an hour. So, we need to find out how much she earns in 8 hrs. So, we would simply multiply the 18 by the 8, to get $144.

Answer:

it is a 10% increase.

Step-by-step explanation:

3,036 - 2,760 = 276

276/2,760 · 100 = 10%

The given point estimators are unbiased and estimator b₁  is more efficient than b₂.

A statistic used to precisely estimate a population parameter is called an "unbiased estimator." An estimator's expected value must match the population parameter's value to be considered unbiased. The discrepancy between an estimator's expected value and the parameter value is known as bias. The estimator tends if this difference is not zero.

a) To show whether the given point estimators are unbiased, first, find whether the expected value of the given estimators is equal to the population parameter μ.

[tex]\begin{aligned}E(b_1) &= E(0.10X_1 + 0.20X_2 + 0.40X_3 + 0.30X_4)\\&=0.10E(X_1) + 0.20E(X_2) + 0.40E(X_3) +0.30E(X_4)\\&=0.10\mu+0.20\mu+0.40\mu+0.30\mu\\&=\mu\\E(b_2) &= E(0.25X_1 + 0.25X_2 + 0.30X_3 + 0.20X_4)\\&=0.25E(X_1) + 0.25E(X_2) + 0.30E(X_3) +0.20E(X_4)\\& = 0.25\mu + 0.25\mu + 0.30\mu + 0.20\mu\\&=\mu \end{aligned}[/tex]

Therefore, both estimators are found to be unbiased.

b) To show which estimator is more efficient, first, find the two-point estimators' variance.

[tex]\begin{aligned}V ar(b_1)&= Var(0.10X_1+0.20X_2+0.40X_3+0.30X_4)\\&= 0.10^2V ar(X_1)+0.20^2Var(X_2)+0.40^2Var(X_3)+0.30^2Var(X_4)\\&= 0.10^2\sigma^2+ 0.20^2\sigma^2+ 0.40^2\sigma^2 + 0.30^2\sigma^2\\&=0.3\sigma^2\\Var(b_2)&= Var(0.25X_1+0.25X_2+0.30X_3+0.20X_4)\\&= 0.25^2Var(X_1)+0.25^2Var(X_2)+0.30^2Var(X_3)+0.20^2Var(X_4)\\&= 0.25^2\sigma^2 + 0.25^2\sigma^2 + 0.30^2\sigma^2 + 0.20^2\sigma^2\\&= 0.255\sigma^2\end{aligned}[/tex]

From this, we can say that Var(b₁) > Var(b₂). Therefore, b₁ is more efficient.

The complete question is -

Let X₁, X₂, X₃, and X₄ be a random sample of observations from a population with mean μ and variance σ². Consider the following two-point estimators:

b₁ = 0.10X₁ + 0.20X₂ + 0.40X₃ + 0.30X₄, and

b₂ = 0.25X₁ + 0.25X₂ + 0.30X₃ + 0.20X₄

(a) Show that both estimators are unbiased.

(b) Which estimator is more efficient, b₁ or b₂? Explain in detail.

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If the sample size increases while the variability remains the same, then the standard error decreases.

Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.

SE = SD / √n

where SE = standard error

SD = sample standard deviation

n = sample size

Variability refers to the statistical dispersion of data which is expressed through the range, variance, or standard deviation.

Increasing the sample size, n, while having the same variability, will result to a lower value for the standard error.

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Answer:In step 1 the equation should be 1/4r=8

Step-by-step explanation:

1/4r+2=10

  -2        -2

1/4r=8

r=32

The error was instead of subtracting 2 from each side Yusuf added 2 to the ten. The correct way would be.

1/4r + 2 = 10

      - 2   -  2

1/4r = 8

÷1/4   ÷1/4

r = 32

Hence, the vectors of the length  [tex]2[/tex] making an angle of [tex]60[/tex] degree with the x-axis is [tex]P= < -\sqrt2,-1 >[/tex].

What are vectors?

A vector is a Latin word that means carrier. Vectors carry a point [tex]A[/tex] to point [tex]B[/tex]. The length of the line between the two points [tex]A[/tex] and [tex]B[/tex] is called the magnitude of the vector and the direction of the displacement of point [tex]A[/tex] to point [tex]B[/tex] is called the direction of the vector [tex]AB[/tex].

Here given that,

The vector of length [tex]2[/tex] making an angle of [tex]60[/tex] degree with the x-axis.

Given length is [tex]||P||=2[/tex]

[tex]P=||P|| < cos\theta,sin\theta > \\\\P=2 < cos(210),sin(210) > \\\\P=2 < \frac{-\sqrt3}{2},\frac{-1}{2} > \\\\P= < 2(-\frac{\sqrt3}{2}),2(-\frac{1}{2}) > \\\\P= < -\sqrt2,-1 >[/tex]

Hence, the vectors of the length  [tex]2[/tex] making an angle of [tex]60[/tex] degree with the x-axis is [tex]P= < -\sqrt2,-1 >[/tex].

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"Parameter" is the descriptive measure of the population. The description, that if the data refuses the assumption of a parameter is the main goal of the tests of hypothesis.

There are many population parameters. Some examples of the population parameters include:

In general, it is not possible to measure the parameters of a population, as it requires to collect information from each and every member of the population. That is why, 'sample statistics' is conducted.

What is a sample statistics?

In sample statistics, samples are collected from each and every aspect of the population and then the samples are tested in order to derive a conclusion. For example: the mean diastolic blood pressure of more than one sample, the mean body weight of more than one population, etc.

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In a rhombus, all sides are the same length, and the opposite angles are equal. The diagonals also bisect each other at 90 degrees.

We know that,

A rhombus has two congruent acute and two congruent obtuse angles.

Here we use the terms  x and y to represent the angles.

where x is the acute angle

The angles total 360 degrees.

So far, we have:

2(x+y) = 360

By dividing both sides by 2 , we get,

x + y = 180

We can assume y is 3 times larger than x,

That is y = 3x

As a result, the equation becomes,

x + 3y = 180

Calculate the total

4x = 180

As a result, the acute angle is 45 degrees.

Hence we proved that y is 3 times larger than x.

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a) The average weight is 195 pounds b)The probability that the maximum safe weight will be exceeded is 0.4840 = 48.40% c) The probability that the maximum safe weight will be exceeded is 0.3539 = 35.39%.

In statistics, the standard deviation measures how widely distributed or how much a group of values can vary. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Normal Probability Distribution:

The z-score formula can be used to address problems with normal distributions.

The zscore of a measure X in a set with mean and standard deviation can be calculated as follows:

Z=[tex]\frac{x-u}{\alpha }[/tex]

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. Subtracting 1 by the p value, we get the probability that the value of the measure is greater than X.

(a) If 46 people are on the elevator, and their total weight is s 8970 pounds, what is their average weight?

This is s 8970  divided by 46, that is s 8970 /46 = 195pounds.

Their average weight is 195 pounds.

Z=[tex]\frac{x-u}{\alpha }[/tex]

=> Z=195-177/70

=>Z=0.25 pvalue of 0.5160

1 - 0.5160 = 0.4840

(b) If a random sample of 46 adult men ride the elevator ,the probability that the maximum safe weight will exceed or not

The weights of adult U.S. men have mean 177 pounds and standard deviation 71 pounds, which means that

Z=[tex]\frac{x-u}{\alpha }[/tex]

=> Z = 195 -177/71

=> Z=0.25 pvalue of 0.6461

=> 1-0.6461=0.3539

Therefore a) The average weight is 195 pounds b)The probability that the maximum safe weight will be exceeded is 0.4840 = 48.40% c) The probability that the maximum safe weight will be exceeded is 0.3539 = 35.39%.

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The value of the stock yield will be;

⇒ 3.1%

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Now,

Since, McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Hence, The value of the stock yield is;

⇒ 2.80/90.24  ×  100

⇒ 0.0310 × 100

⇒ 3.1%

Thus, The value of the stock yield will be;

⇒ 3.1%

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Binary Variable is  a variable that can only be 1 or 0. Binary variables are categorical variables that can take only one of two values, are usually represented as Boolean (True or False) or integer variables (0 or 1), and usually have no attributes indicates that it exists.

Binary variables have only two states, such as 0 or 1. 0 defines the variable does not exist, 1 defines the variable exists. For example, for the patient-defining variable Smoker , 1 means the patient smokes and 0 means the patient does not smoke. Binary variables can be viewed as if they were scaled by intervals, which can lead to misleading clustering results. Therefore, a method that defines binary data is essential for computing dissimilarities.

Binary data is data whose unit can take on only two possible states. These are often labelled as 0 and 1 in accordance with the binary numeral system and Boolean algebra. Binary data occurs in many different technical and scientific fields, where it can be called by different names including bit (binary digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics.

Binary data is used to represent one of two conceptually opposite values. "correct" or "incorrect".

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Answer: ABC and AED are congruent by SSS. SSS is if three sides of a triangle are congruent to 3 sides of another triangle, then the triangles are congruent. AB and AE are both 7, BC is congruent to ED and CA is congruent to DA because of the tick marks.

Distance that plane has flown is 2812.5 feet.

What do you mean by trignometry?

Trigonometry  “triangle” is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan. Let's see how these ratios or functions are evaluated in the case of right triangles.

It is given that a plane rises from take-off and flies at an angle of 9° with the horizontal runway. It has gained 450 feet

Let the distance be x

According to the question:

sin 9 = 450/x

0.16 = 450/x

x = 450/0.16

x = 2812.5

Therefore, distance that plane has flown is 2812.5 feet.

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When you are doing a survey of the time it takes for a person to run 100m, the unit that you would you use is seconds.

A unit of measurement is a definite magnitude of a quantity that is defined and adopted by convention or law and is used as a standard for measuring the same type of quantity. Any other such quantity can be expressed as a multiple of the unit of measurement. A length, for example, is a physical quantity.

A unit is any standard that is used to compare measurements. Unit conversions allow measurements of a property to be converted from one unit to another, such as centimeters to inches.

In this case, time is measured in seconds.

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The 95% confidence interval for difference in mean drying times of two type of paints is (4.90, 17.50). This suggests that Type A takes between 4.90 and 17.50 hours more to dry than type B paint.

Given that,

A paint's formula was altered by the manufacturer to hasten drying time. 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were randomly chosen at random and applied on comparable surfaces. The drying periods were measured in hours. The following are the statistics in brief.

Type A                 Type B

Sample-1             Sample-2

x₁ = 76.3 hrs        x₂ = 65.1 hrs

s₁ = 4.5 hrs          s₂ = 5.1 hrs

n₁ = 11                   n₂ = 9

We have to create a 98% confidence interval for the range 1–2, which represents the difference in the average drying time for paint cans of types A and B.

We know that,

Consider about Type A, which is the original paint, and Type B, which is the changed paint.

The difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type is within a 98% confidence interval, and it is as follows:

4.90 < μ₁ - μ₂ < 17.50

Therefore, The 95% confidence interval for difference in mean drying times of two type of paints is (4.90, 17.50). This suggests that Type A takes between 4.90 and 17.50 hours more to dry than type B paint.

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The following are parallelograms' essential characteristics: The opposing sides are parallel. The opposing parties are in agreement (they have the same length).

The four most crucial characteristics of a parallelogram are: A parallelogram has two opposed sides that are parallel to one another and have equal measurements. A parallelogram has equal opposite angles. The interior angles of a parallelogram sum to 360°. A parallelogram's subsequent angles should be supplementary (180°).

A quadrilateral having opposite sides that are equal and parallel is called a parallelogram. A parallelogram's opposing angle is also equal. A parallelogram is essentially a twisted rectangle.

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(B) All mathematic teachers who attended the conference.

Option B is the correct option.

The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are the focus of the science of statistics.

A statistic is a numerical representation of a sample property. One example of a statistic is the average number of points students in one math class got at the conclusion of the term if we assume that class to be representative of the population of all math classrooms.

Due to their role in assisting decision-making, statistics are crucial. To track progress, evaluate performance, identify issues, and set priorities, governments, organizations, and corporations all gather statistics.

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The Remainder in the Synthetic division is three, for given problem

1 |__1___2__-3__3 is 3.

So, the correct option is option(c).

The Synthetic Division:

It is defined as the method of dividing the polynomial by the binomial is known as the synthetic division. It stands for polynomial division. Here, the division principle is performing in the coefficient of the polynomial.

We have given that the synthetic division is

1 |__1___2__-3__3

We find out the remainder in the synthetic division :

Multiply the carry-down value (i.e 1) by the test zero on the left, and carry the result(i.1×1 = 1) up into the next column inside:

1 | 1 2 -3 3

|______________

1

Add down the column( 2+1 = 3) :

1 | 1 2 -3 3

|____1_________

1 3

Multiply the previous carry-down value (i.e 3) by the test zero, and carry the new result up into the last column:

1 | 1 2 -3 3

|____1____3____

1 3 0

1 | 1 2 -3 3

|____1____3___0_

1 3 0 3

three, last carry-down value is the remainder.

Therefore, the remainder is 3. The option c is correct.

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Complete question:

What is the remainder in the synthetic division problem below?

a. 6

b. 4

c. 3

d. 5

According to the T distribution, the correct option is (d) All the above

T distribution:

In statistics, t-distribution is used in all forms of t-tests. Where the T-tests are all classified as inferential statistical tests and will follow all of the same steps required to complete the process of null hypothesis significance testing. And it defines the exact shape of the t-distribution is governed by the degrees of freedom. And the t-distribution is associated with a degrees of freedom equal to the sample size minus a value of 1.

Given,

Here we need to find the correct option according to the T distribution.

As per the given options, the correct answer is best represented by option D. All of the above are correct.

Because, the t-distribution, along with the normal distribution, both assume data is normally distributed in the population.

When the sample size increases towards 30, the t-distribution will resemble the normal distribution, provided the data in the population is normally distributed.

If it is correct to state that the tails of the t-distribution are thicker compared to the normal distribution.

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The evidence suggests that the average distance hiked by each visitor has decreased to less than 25 kilometers, so the null hypothesis is rejected.

The p-value is the probability of getting a test statistic result at least as extreme as the one observed, given that the null hypothesis is true. If the p-value is less than the chosen level of significance (which is 0.05 in this case), then the null hypothesis is rejected. In this case, since the p-value is less than 0.05, the null hypothesis is rejected. This means that there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 25 kilometers.

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Answer:

y=8

Step-by-step explanation:

9y-7y=20-4

2y=16

y=16/2

y=8

Answer:

m = [tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

1. take any two points on the line

2. figure out the vertical change between both points, known as the rise

3. figure out the horizontal change between both points, known as the run

4. slope is defined as the variable m and is the [tex]\frac{rise}{run}[/tex]

40 pounds of salami are purchased by a deli for its renowned grinder sandwiches. An illustration of an intermediate good is salami.

Given fill-in-the-blank;

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of___ goods.

The answer for this case is Intermediate.

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of Intermediate goods.

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