Unit #4 - Lesson # 8 Exit Ticket: The seventh-grade class had 74 students in it last year. This
increase in the number of seventh grade students from last year to this year? Show all calculations.
year, the seventh-grade class has 86 students in it. To the nearest tenth, what was the percent
Unit #4
on til
Answer:

To get the slope, use the slope-intercept form and calculate the reciprocal of the slope of the given line .The slope of any line perpendicular to Y = 7x + 8 is -7.

The equation of any line perpendicular to Y = 7x + 8 is in the form of y = mx + b where m is the slope.

To get the slope, use the slope-intercept form and calculate the reciprocal of the slope of the given line.

The slope of the given line (Y = 7x + 8) is 7. Therefore, the slope of the line perpendicular to it is the reciprocal of 7, which is -7.

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The 6th term of the geometric sequence is -1/2.

Here we have to find the a6the term of the geometric sequence.

Data given:

The series = 512/243, -128/81, 32/27.....

The formula to find the nth term of the geometric sequence:

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where [tex]a_{n}[/tex] = nth term of the sequence

a = first term of the sequence

r = common ratio

common ratio(r) = -128/ 81 ÷ 512/ 243

                       = -128/81 × 243/512

                       = -3/4

Now we have to find the 6th term of the series.

[tex]a_{6}[/tex] = 512/ 243 (-3/4[tex])^{6-1}[/tex]

   = 512/243 (-3/4[tex])^{5}[/tex]

  = 512/243 × 243/1024

  = -512/1024

  = -1/2

Therefore the 6th term is -1/2.

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If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is:                              z = x−μ/ σ

The z-score indicates the number of standard deviations that the value x is above (right) or below (left) the mean μ. Values ​​of x greater than the mean have positive z values, and values ​​of x less than the mean have negative z values. The z-score of x is zero if x is equal to the mean.

The standard normal distribution is the normal distribution of standardized values ​​called z-scores. Z-scores are measured in units of standard deviation. For example, if the normal distribution has a mean of 5 and a standard deviation of 2, then the value 11 is 3 standard deviations above (or to the right of) the mean. Here's the calculation:

                      x = μ + (z)(σ)  

                         = 5 + (3)(2)

                         = 11

The standard normal distribution has zero mean and one standard deviation. The transformation

                                    z= x − μ/σ

gives the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.

The next two videos explain what it means to have a "normal" distributed data set.

If X is a random variable and follows a normal distribution with mean µ and standard deviation σ, the rule of thumb states within 1 standard deviation of the mean.

About 95% of the x-values ​​lie between –2σ and +2σ of the mean µ (within two standard deviations of the mean).

About 99.7% of the x-values ​​lie between –3σ and +3σ of the mean μ (within 3 standard deviations of the mean) .

Almost all x-values ​​are within 3 standard deviations of the mean.

1) +1σ and -1σ have z-scores of +1 and -1 respectively.

2) +2σ and -2σ have Z-scores of +2 and -2 respectively.

3) +3σ and -3σ have Z-scores of +3 and -3 respectively.

The rule of thumb is also known as the 68-95-99.7 rule.

The exact value used to calculate the median; further decreasing the minimum value or increasing the maximum value will not change the median value. Therefore, the median does not use all the information in the data and is therefore shown to be less efficient than the mean or average, which uses all the values ​​in the data. To calculate the average, add the observations and divide by that number.

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Answer: 2x(x^-4)(x^-2)

Answer:

2

Step-by-step explanation:

count your fingerssssssssssssd

Answer:

[tex]a. \: x = \frac{ - 13}{8} [/tex]

Step-by-step explanation:

[tex]1. \: - 6x - 3 = 2x + 10 \\ 2. \: - 3 = 2x + 10 + 6x \\ 3. \: - 3 = 8x + 10 \\ 4. \: - 3 - 10 = 8x \\ 5. \: - 13 = 8x \\ 6. \: \frac{ - 13}{8} = x \\ 7. \: x = \frac{ - 13}{8} [/tex]

After solving the given equation 3(-2x - 1) = 2(x + 5), we know that the value of x is (A) -13/8.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, we got the equation:

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

Now, solve for x as follows:

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

-6x - 3 = 2x + 10

-6x - 2x = 10 + 3

-8x = 10

x = -13/8

Therefore, after solving the given equation 3(-2x - 1) = 2(x + 5), we know that the value of x is (A) -13/8.

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Correct question:
Solve for x.3(-2x - 1) = 2(x + 5)

A) -13/8

B) -3/4

C) 13/8

D) 3/4

A bijection between two sets is constructed below and also proved that it is both one-one and onto.

The phrase "one-to-one function" should not be mistaken with "one-to-one correspondence," which is used to describe bijective functions, in which each element in the codomain is a precise mirror image of a single element in the domain.

Any function that can work with the operations of two algebraic structures is said to be a homomorphism between them. An injective homomorphism is also referred to as a monomorphism for any commonly occurring algebraic structures, particularly vector spaces.

Let t∈T

Then,

t=2k+1, for some k∈Z

Let s=3k

Then,

s∈S and f(s)=2(s/3)+1

=2k+1

=t

Therefore, for every t∈T there exists s∈S such that f(s)=t

Thus, f is onto.

Hence,

f:S  ----> T is a bijective mapping

⇒|S|=|T|

Now, we have to define a mapping f:S ---?T

By f(x)=2(x/3)+1, ∀x∈S

Given,

S={3k|k∈Z} and T={2k+1:k∈Z}

We have to prove:

|S|=|T|

Let x, y∈ S with f(x)=f(y)

Then,

2(x/3)+1=2(y/3)+1

2(x/3)=2(y/3)

(x/3)=(y/3)

x=y

So, f is one-one

Now, we have proved that f is both one-one and onto.

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The theorems used are:

First blank: side-angle-side theorem

Second blank: CPCTC

Third blank: 200 feet

Fourth blank: 1,700 feet.

Wen two triangles have a pair of included congruent angles and two pairs of corresponding congruent sides, then both triangles are congruent to each other by the side-angle-side theorem.

Furthermore, if two triangles are known to be congruent to each other, the CPCTC states that "corresponding parts of corresponding triangles are congruent". This means all angles and all sides that corresponds to each other are congruent.

Therefore:

Using the side-angle-side theorem it can be shown that the two triangles are congruent to each other.

Then using CPCTC , the length of the road from the intersection to the first turn would be 200 feet.

The total length of the tour would be = 2(200 + 300 + 350)

= 1,700 feet.

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Using, SAS it can be shown that the two triangles formed are congruent. Then using ,-CPCTC the length of the road from the intersection to the first turn can be found to be 200 feet. Thus, the total length of the tour is 1,700 feet.

The SAS Triangle Theorem indicates that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

By the use of the corresponding parts of congruent triangles are congruent (CPCTC) rule, we can state that the missing side is 200 feet. If that is the case, then the total distance traveled can be obtained by adding all the lengths of triangles:

=200 + 200 + 300 + 350 + 350 + 300

= 1,700 feet.

Hence, te total length of the tour is 1,700 feet.

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Answer:

he perimeter of the equilateral triangle is $3(x + 1) = 3x + 3$.

Step-by-step explanation:

The perimeter of the equilateral triangle is $3(x + 1)$ since the sides are all equal and there are three sides. The perimeter of the other triangle is $2x + x + 4x - 7$, which is also equal to $3(x + 1)$

This is a table of values of three functions at selected values of x.

It is asking for h(f(-2))

Its saying, take f(-2), and take whatever you get from that and put it into h(x)

So, find f(-2).

Find x = -2, then see what f is there.

f(-2) = -1

So, find h(-1)

h(-1) = 0

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

The slope of the lines in the question are 0 and -1/2

Slope of a line is the change in y-coordinate with respect to the change in x-coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = y₂ - y₁ / x₂ - x₁

a)

Taking the two points;

m = 7 - 7 / 5 - (-1)

m = 0

The slope is equal to 0

b)

Using the same formula above;

m = y₂ - y₁ / x₂ - x₁

m = 0 - 2 / 5 - 1

m = -2 / 4

m = -1/2

The slopes are 0 and -1/2

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Answer: its the 3 anwers

Step-by-step explanation:

The angle between two lines having slopes as 1 and 1 is 0°. thus, the two lines coincide with each other.

The formula to find the angle between two lines having slop m1 and m2 is

tan θ= ± (m2 – m1 ) / (1+m1m2)

Substituting the value of slope in this equation

tan θ = ± (1-1)/ (1 + 1×1)

tan  θ =± 0

 θ=   [tex]tan^{-} (0)[/tex]

θ = 0°

When two straight lines cross, two sets of angles are created. The intersection creates two acute angles and two obtuse angles. The slopes of the intersecting lines have an impact on the angles' absolute values.

It is also important to note that because the slope of a line parallel to the y-axis is indeterminate, it is impossible to calculate the angle created by two lines intersecting.

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The congruence theorem that justifies the similar triangles of triangles EFH and GFH is given as follows:

D. AAS.

For the triangles EFH and GFH in this problem, we have that:

These three features are used to identify the congruence theorem as follows.

Then the congruence theorem that justifies the similar triangles of triangles EFH and GFH is the Angle-Angle-Side theorem, given by option D, as:

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Answer:

I have no idea sorry

Step-by-step explanation:

i'm in middle school

Answer:

x=22.5 please mark me as brainlyiest

Step-by-step explanation:

2(x-3)=49

2x-6=49

2x=55

x=22.5

Answer: x=10   x=-4

Step-by-step explanation:

[tex](x-3)^2=49\\\\(x-3)=7^2[/tex]

Extract the square root of both parts of the equation:

[tex]\sqrt{(x-3)^2}=\sqrt{7^2} \\\\x-3=б7\\\\x-3=7\\x-3+3=7+3\\x=10\\\\x-3=-7\\x-3+3=-7+3\\x=-4[/tex]

Answer:

3.054

i think

The height, ab, is 6 cm

The volume of the pyramid is 100 cm3.

we know that

ABC is a right triangle and we know that

∠ACB=45°

AC=hypotenuse------ 6√2 cm

sin 45=AB/AC----- AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm

AB=6 cm

we already know that the formula for getting the volume of a pyramid

volume of the pyramid=(1/3)*Area of the base*height

We will now Substitute all the values in the formula;

area of the base=50 cm²

height=6 cm

so

volume of the pyramid=(1/3)*50*6---->

1/3*300

300/3

1=00 cm³

volume=100 cm³

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Answer:

6, 100

Step-by-step explanation:

right on edge

Using the equation we know that the flowerbed is 2250 feet away from the hive.

A mathematical assertion that has an "equal to" symbol between two expressions with equal values is known as an equation.

As in 3x + 5 Equals 15, for instance.

So, let's say the flowerbed is feet away from the hive.

The bee travels directly from its hive at a speed of 20 feet per second to a flowerbed before returning at a speed of 12 feet per second.

Time = distance/speed

Therefore, the bee needed x/20 seconds to get to the flowerbed and x/12 seconds to fly back to the hive.

The bee spends a total of 20 minutes, or 2060 seconds, or 1200 seconds away from the hive. I

t spends 15 minutes, or 1560 seconds, at the flowerbed.

Consequently, the equation will be:

x/20 + x/12 + 900 = 1200

3x + 5x/60 = 300

8x = 60 * 300

8x = 18000

x =  18000/8

x = 22550

Therefore, using the equation we know that the flowerbed is 2250 feet away from the hive.

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Complete question:
A bee flies at 10 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 20 ​minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 22 minutes.

What equation can you use to find the distance of the flowerbed from the​ hive?

Answer:

17

Step-by-step explanation:

15 + 17 + 19= 51

The area of the rectangle in centimeter square is 2013 cm².

The area of a rectangle is the product of its length and width.

If the values of area and one of the sides of a rectangle is given the other one can be found by forming a suitable equation.

The length and width of the given rectangle can be written in cm as follows,

The length is given as 24 × 2.54 = 60.96 cm

And, the width is 13 × 2.54 = 33.02 cm

Now, the area of the rectangle can be obtained by taking the product of length and width as follows,

Area = 60.96 × 33.02

        = 2012.89

Which can be approximated as 2013 cm².

Hence, the area of the rectangle is obtained as 2013 cm².

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Answer:

Sure! The formula for simple interest is I = P x R x T, where I is the interest, P is the principal, R is the interest rate, and T is the time.

To find the interest, you would plug in the values for P, R, and T and solve the equation. For example, if you have a principal of $500, an interest rate of 10%, and a time of 5 years, the formula would look like this: I = 500 x 0.1 x 5 = $250.

To find the principal, you would rearrange the formula to solve for P. This would give you P = I / (R x T). Using the same values as before, the formula would look like this: P = 250 / (0.1 x 5) = $500.

To find the interest rate, you would rearrange the formula to solve for R. This would give you R = I / (P x T). Using the same values as before, the formula would look like this: R = 250 / (500 x 5) = 0.1.

To find the time, you would rearrange the formula to solve for T. This would give you T = I / (P x R). Using the same values as before, the formula would look like this: T = 250 / (500 x 0.1) = 5.

I hope this helps! Let me know if you have any other questions

The following two methods are used to write a linear function;

1.  Write linear functions from graph

2. Write linear equation from slope and ordered pairs

Given,

Steps to write linear functions;

The slope and the y-intercept are the two pieces of data required to build a linear function. Once these two variables have been established, you can replace m and b with them in the slope-intercept equation y = mx + b.

There are two methods;

1. Write linear functions from graph

2. Write linear equation from slope and ordered pairs;

We only have half the information if we are provided the slope and an ordered pair. Although we now know the slope, we still need to determine the y-intercept. The following steps can be used to calculate this using the slope-intercept form:

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Answer: x = 13/4

Step-by-step explanation:

Easy, let's use x to define the number:

3x + 5 = 7x - 8

We take the 3x to the other side:

5 = 4x - 8

We take the 8 to the other side:

13 = 4x

x = 13/4

The interquartile range of the given data set is 2.16.

The given data is 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22 and 3.26.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1

The  order of the given data is 1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02.

Here,

Q1= 1/4 (n+1) = 11/4= 2.75

= 2.22

Q3 = 3/4 (n+1) = 8.25

= 4.38

Q2 =4.38-2.22

= 2.16

Therefore, the interquartile range of the given data set is 2.16.

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Answer:We can write the following equation.

C = 5000+200S

where C is cost and S = sugar transported in tons.

Plot is given in attached fig.

Step-by-step explanation:

The minimum revenue by selling tickets will be $363 thus there will be no solution.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose x is the number of hot dogs sold and y is the number of hamburgers sold.

As per the given,

hot dog for 6$ and a hamburger for 8$

6x + 8y = total cost

6x + 8y = 1106

Total x + y = 106

By substitution,

6(106 - y) + 8y = 1106

636 - 6y + 8y = 1106

2y = 470

y = 235

And, x = -129

Since the number cannot be negative thus it will be an incorrect question.

Hence "There won't be a solution because the minimum revenue from ticket sales will be $363.".

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Answer:

Step-by-step explanation: D-days, W=weeks

7d times 6w=42 d

Answer:

The strongest correlation is 0.87. In general, a correlation is a measure of the strength and direction of a linear relationship between two variables. Correlation values range from -1 to 1, with -1 indicating a perfect negative linear relationship, 0 indicating no linear relationship, and 1 indicating a perfect positive linear relationship. Among the numbers you have provided, 0.87 is the only one that is greater than 0, indicating a positive linear relationship between the two variables. This means that as one variable increases, the other variable also tends to increase. This is the strongest possible positive linear relationship, making 0.87 the strongest correlation among the numbers you have provided.

Step-by-step explanation: