7. Solve 10x + 8 = 8x - (- 16) for x.

The algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.

What is an algebraic expression?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.).

The total number of eggs he collected =  12c + b.

Because 12 eggs are a dozen multiplied by unknown, you get a multiple of twelve then you add your broken eggs for the total.

Hence, the algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.

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Answer:

x>

Step-by-step explanation:

x>

A number a:

a

is more than 6

< 6

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer: 4x - 1

Step-by-step explanation:

Answer:

4x-2

Step-by-step explanation:

i did it

We have demonstrated the definition of an isosceles triangle.

What is an isosceles triangle?

An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.

The isosceles triangle has both two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.

The given diagram shows an isosceles triangle.

Hence, we have demonstrated the definition of an isosceles triangle.

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The given statement is True.

What is the Null Hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is possible to determine the probability that the null hypothesis is correct using statistical tests.

True. In a non-directional significance test of a correlation, the null hypothesis states that the population correlation is zero.

Hence, The given statement is True.

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Answer:

b) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9332 = 0.0668

c) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9997 = 0.0003

Answer:

a. El auto pesado ganará, ya que debido a su mayor masa tendrá una mayor fuerza de arrastre.

b. El auto ligero se detendrá en menos tiempo, debido a que su masa es menor, lo cual significa que tendrá una menor resistencia al movimiento.

Step-by-step explanation:

Answer:

Step-by-step explanation:

11. First option

12. 5p+4 > 14

> symbol is greater than and has an open circle, going right

Answer:

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

The graph indicates the inequality n ≤ 1, since highlighted part is to the left from the 1 and there is a closed circle.

Double both sides to get 2n:

And add 5 to both sides to get 7:

This is matching the option A.

The graph indicates the inequality p > 2, since highlighted part is to the right from the 2 and there is a open circle.

Multiply both sides by 5 to get 5p:

Add 4 to both sides to get 14:

This is matching the option A.

By using the concept of null space of a matrix, it can be calculated that

Nullspace of A = [tex]\{ \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} , \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}\}[/tex]

What is Nullspace of a matrix?

Nullspace of a matrix A is the solution of the equation AX= 0 where 0 is the zero matrix

[tex]\begin{bmatrix} 1 & -3 & 0 & -3 & 0 \\ 0 & 0 & 1 & 4 & 0 \\0 & 0 & 0 & 0 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix}[/tex]

We need to find Ax = 0

[tex]\begin{bmatrix} 1 & -3 & 0 & -3 & 0 \\ 0 & 0 & 1 & 4 & 0 \\0 & 0 & 0 & 0 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\0 \end{bmatrix}[/tex]

x - 3y - 3w = 0

x = 3y + 3w

z + 4w = 0

z = -4w

-t =  0

t = 0

[tex]\begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix} = \begin{bmatrix} 3y + 3w\\ y \\-4w \\ w\\0 \end{bmatrix}\\\\y \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} + w \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}[/tex]

Nullspace of A = [tex]\{ \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} , \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}\}[/tex]

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Complete Question

The complete question has been attached

After a dilation by a scale factor of (3/2) the vertices are A'(- 3, - 3), B'(6, - 3) and

(3/2, 3/2).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

A triangle has coordinates A(- 2, - 2), B(4, - 2) and C(1, 1).

After a dilation by a scale factor of (3/2) it will be A'(- 3, - 3), B'(6, - 3) and

(3/2, 3/2).

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The number of ways to contain 2 black card and 3 red cards are 84,500.

What is card deck?

A piece of specially made card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that has been imprinted with distinctive motifs is what is known as a playing card. Each card frequently has a finish on the front and reverse to make handling simpler.

There are 26 red card and 26 black card in a 52 card deck.

We have to find the number of ways contain 2 black card and 3 red cards.

Initial black card: 26 options

Secondly black card: 25 options

First caution: 26 options

Second warning: 25 options

Three red cards: 24 options

A total of,

26 x 25 x 26 x 25 x 24 = 10,140,000.

But since all orders are equal, we divide by the number of orders for a five card hand:

5 x 4 x 3 x 2 x 1 = 5! = 120

So,

10,40,000 / 120 = 84,500.

Hence, the number of ways to contain 2 black card and 3 red cards are 84,500.

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Answer:

  12 feet

Step-by-step explanation:

You want the length of the side of a square with a diagonal length of 12√2.

The diagonal of a square is the hypotenuse of a right triangle with equal-length sides. Such an isosceles right triangle has side lengths in the ratio ...

  1 : 1 : √2

That is, the hypotenuse is √2 times the side length.

The given hypotenuse is 12√2, so the side length is 12.

Each side of the bedroom is 12 feet.

On solving tthe question, we got by double integration [tex]\int\limits^0_1 \int\limits^1_2{100x^2+49y^2} \, dx dy = x(\frac{100x^2 + 147y^2}{3} )[/tex]

A function in two variables over a region in R2, or the real number plane, is referred to in mathematics as a double integral. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as follows:  ∬ R f ( x , y ) d A = ∬ R f ( x , y ) d x d y.

g[tex]\int\limits^0_1 \int\limits^1_2{100x^2+49y^2} \, dx dy \\ At first,\\ \int\limits^{} \,100x^2 dx = 100\int\limits^ {} \,x^2 dx \\ \int\limits^ {} \,x^2 dx = \frac{x^3}{3} \\[/tex]

[tex]the result - \frac{100x^3}{3}\\ now,\\\int\limits \, 49y^2dx = 49xy^2\\\\result - \frac{100x^3}{3} + 49xy^2\\\\On simplyfing-\\[/tex]

[tex]x(\frac{100x^2 + 147y^2}{3} )[/tex]

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the best approximation of the percent of scores that fell between 58.9 and 75.1 is 4.

The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.

Find the difference between these two figures and the mean, divide it by the standard deviation of 5.4, and you will know how many standard deviations 75.1 and 61.5 are above and below the mean:

(75.1−64.3)/5.4

=2sd

According to the empirical rule, 95% of data are within two standard deviations of the mean.

So, the answer is 4.

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The total number of schools such that 35% of it is 105 will be 300.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

Suppose the total number of students is x.

35% of x = 105

(35/100)x = 105

x = 105(100/35)

x = 300 students

Hence "The total number of schools such that 35% of it is 105 will be 300".

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To make a 49 pound bag of a mixture of peanuts and almonds that costs $6.85 per pound, the owner needs 15.98 pounds of peanuts and 33.02 pounds of almonds.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = pounds of peanuts in the mixture

y = pounds of almonds in the mixture

The owner wished to make a total of 49 pounds of mixture of peanuts ang almonds. Hence,

x + y = 49

x = 49 - y     (equation 1)

Bags of peanuts cost $2.2 per pound and bags of almonds cost $9.1 per pound, and the mixture should cost $6.85 per pound. Hence,

2.2x + 9.1y = 6.85(49)

2.2x + 9.1y = 335.65

Substitute equation 1 and solve for y.

2.2x + 9.1y = 335.65

2.2(49 - y) + 9.1y = 335.65

107.8 - 2.2y + 9.1y = 335.65

6.9y = 227.85

y = 33.02

pounds of almonds in the mixture = 33.02

Using equation 1, solve for x.

x = 49 - y

x = 49 - 33.02

x = 15.98

pounds of peanuts in the mixture = 15.98

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Hence, the ordered pair which replace  [tex](x,y)[/tex] is [tex](4,8)[/tex].

What is the function?

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

Here given function is

[tex]{(0, 1), (2, 6), (1, 7), (5, 7), (x, y)}[/tex]

So, the value which replace [tex](x,y)[/tex] is [tex](4,8)[/tex], because for the function every element have a single image.

Hence, the ordered pair which replace  [tex](x,y)[/tex] is [tex](4,8)[/tex].

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Physical attractiveness determined whether college freshmen who had been randomly paired for a welcome week dance liked each other.

Samples with natural or matched couplings are known as paired samples (sometimes referred to as dependent samples). This results in the creation of a data set where each data point from one sample is uniquely linked with a data point from the other sample. In statistics, paired data, also known as ordered pairs, refers to two variables in a population's individuals that are linked together to ascertain their association. We refer to two datasets that are identical in length and in which each observation can be "paired" with an observation from the other dataset as having "paired data." Each observation in one dataset must only be paired with one observation in the other dataset in order for the two datasets to be paired.

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Probability of two black Erminette chickens crossed is equal to 1/4.

As given in the question,

Erminette chickens are basically a chicken with a gene of black and white feathers.

There are two groups of chicken black feather chicken and white feather chicken.

All possible outcomes when Erminette chicken crossed each other are:

= { BB , BW, WB, WW}

Total number of outcomes are = 4

Favourable outcomes are ={ BB }

Number of favourable outcomes = 1

Probability of two black Erminette chickens crossed each other

= ( Favourable outcomes) / ( Total number of outcomes )

= 1 / 4

Therefore, probability of two black Erminette chickens crossed each other with the given condition is equal to 1/ 4.

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Surface are increasing at the rate of 8 square feet per second.

What is a sphere?

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its centre.

Volume(V) = [tex]4\pi r^3[/tex]

            [tex]\frac{dV}{dt} =\frac{4\pi }{3} \times3r^2\times\frac{dr}{dt} =4\pi r^2.\frac{dr}{dt} \\\\\boxed{\frac{dr}{dt} =\frac{1}{4\pi r^2} (\frac{dV}{dt} )}[/tex]

             [tex]V=36\pi \\\\\frac{4}{3} \pi r^3=36\pi \\\\r^3=\frac{108}{4} =27\\\\\boxed{r=3}\\\\\boxed{\frac{dV}{dt} =12}[/tex]

Surface area(S) = [tex]4\pi r^2[/tex]

                        [tex]\frac{dS}{dr} =8\pi r\times\frac{dr}{dt} \\\\\frac{dS}{dt} =\frac{8\pi r}{4\pi r^2} \times\frac{dr}{dt}\\\\ \frac{dS}{dt}=\frac{2}{r} \times \frac{dV}{dt} =\frac{2}{3} \times12=8\\\\\boxed{\frac{dS}{dt} =8}[/tex]

Hence, the surface area increasing at the rate of 8 square feet per second.

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After solving,  41.67 Hz wing beats the dragonfly performs per second.

In the given question, if the video is shot at 190 frames per second, then we have to find how many wing beats the dragonfly performs per second.

From the given question,

Frames per one wing beat = 6 frames

Video shot at = 250 frames per second

We firstly find the time period

So, Time period (T) = 6/250

T= 0.024 s

Snce we have to find how many wing beats the dragonfly performs per second.

Per second number of wing beats = 1/T

Per second number of wing beats = 1/0.024

Per second number of wing beats = 41.67 Hz

Hence, 41.67 Hz wing beats the dragonfly performs per second.

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The right question is;

A frame by frame analysis of a slowmotion video shows that a hovering dragonfly takes 6 frames to complete one wing beat.

If the video is shot at 190 frames per second, how many wing beats does the dragonfly perform per second?

Answer:

7 + 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a

([tex]\sqrt{2}[/tex] + 5)(1 + [tex]\sqrt{2}[/tex])

each term in the second factor is multiplied by each term in the first factor, that is

[tex]\sqrt{2}[/tex](1 + [tex]\sqrt{2}[/tex]) + 5(1 +[tex]\sqrt{2}[/tex]) ← distribute parenthesis

= [tex]\sqrt{2}[/tex] + 2 + 5 + 5[tex]\sqrt{2}[/tex] ← collect like terms

= 7 + 6[tex]\sqrt{2}[/tex]

There is a 1 in 4 probability, or 25%, that the envelope will contain just one letter with the proper address.

Tanya wrote four distinct letters that she was going to send to four different addresses. She prepared an envelope with the correct address for each letter. The probability that only 1 letter will be placed into the envelope with the correct address if the 4 letters are randomly placed into the 4 envelopes is

1 in 4, or 25%

(4c4/4c1).

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The value of the required integral is 50π  where C is the positively oriented circle x2+y2=25

We are given a vector F = -yi + xj. A vector is a quantity with magnitude and direction that is commonly represented by a directed line segment, with length representing magnitude and orientation in space representing direction. We need to use the tangential vector form of Green's Theorem to compute the circulation integral ∫CF⋅dr where C is the positively oriented circle x² + y² = 25

Let the value of the integral be represented by the variable "I".

I = ∫∫[(/x)(x) - (/y)(-y)]dA

I = ∫∫[(1 - (-1)]dA

I = ∫∫2dA

I = 2∫∫dA

I = 2×(Area of the circle)

I = 2*(πr²)

I = 2*(π*25)

I = 50π

Hence, the value of the required integral is 50π.

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113 % = 1893per capacity

Step-by-step explanation:

first you have to calculate the 113 feet with its equation then calculate the quation with the number 69 divisible by it then divide it and your answer is there

We know that in statistics, the Type II error happens when the null hypothesis is false but fails to get rejected.

Type II error in this scenario will be when the researcher claim 65% of college students will graduate with debt is false but fails to be rejected.

A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false. A type II error produces a false negative, also known as an error of omission.

For example, a test for a disease may report a negative result when the patient is infected. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect.

A Type II error can be contrasted with a type I error is the rejection of a true null hypothesis, whereas a type II error describes the error that occurs when one fails to reject a null hypothesis that is actually false. The error rejects the alternative hypothesis, even though it does not occur due to chance.

Given : The null hypothesis, , is: researchers claim that 65% of college students will graduate with debt.

Then , Type II error in this scenario will be when the researcher claim 65% of college students will graduate with debt is false but fails to be rejected.

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For the given statement option C  increase, wider and decrease , narrower is correct.

What is confidence interval?

A confidence interval is computed at a designated confidence level; the  95% confidence level is most common, but other levels, such as 90% or  99%, are sometimes used.

When constructing a confidence interval, if the level of confidence increases, the margin of error must Increase and the confidence interval will be Wider.

Hence  Increase; wider is the correct answer.

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