ms. Torres has a box of scraps of wood. She measures the length of each scrap of wood to the nearest half inch results are represented on the line plot below.

The sequence of numbers, 7, 10, 17, 27, 44, 71, 115... in which each new term is given by the sum of the previous two terms, gives the sum of the first 10 terms as 1,265

A number sequence consists of a listing of numbers that are connected to each other by a rule.

The given sequence is presented as follows;

7, 10, 17, 27, 44, 71, 115..., [tex] a_{10}[/tex]

From the given sequence, we have;

a_n = a_{(n-1)} + a_{(n-2)}

The first 10 terms of the sequence is therefore;

7, 10, 17, 27, 44, 71, 115, (71+115), (115+(71+115)), ((71+115)+(115+(71+115)))

Which gives;

7, 10, 17, 27, 44, 71, 115, 186, 301, 487

The sum of the first 10 terms of the sequence is therefore;

7 + 10 + 17 + 27 + 44 + 71 + 115 + 186 + 301 + 487 = 1265

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Step-by-step explanation:

Since right angles are 90°

11 = 90°

12 = 90°

13 = 90°

The value of x is 6 degrees.

It is given in the question that:-

HI is parallel to JK and FG is the transversal intersecting HI at L and JK at M.

∠LMK = 115 degrees

∠MLI = (8x + 17) degrees

We have to find the value of x.

We know that,

Angles on the same side of the transversal sum up to 180 degrees.

Hence, we can write,

∠LMK + ∠MLI = 180 degrees.

115 + (8x + 17) = 180 degrees

8x + 132 = 180 degrees

8x = 180 - 132

8x = 48 degrees

x = 48/8 degrees

x = 6 degrees

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Answer: Carlos started with 38 comic books.

Step-by-step explanation:

33 - 14 = 19

19 x 2 = 38

According to the Empirical Rule, 99.7% percent of values in a normal distribution will fall between 1 standard deviations above the mean and 3 standard deviations above the mean.

The Empirical Rule is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:

In this context, we can reasonably infer and logically deduce that 99.7% of a normal distribution would fall within three (3) standard deviations of its mean in accordance with the Empirical Rule.

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Normal distributions are frequently employed in the natural and social sciences to describe real-valued regressors with uncertain distributions, normal distributions are essential to statistics.

The central limit theorem is one reason they are significant.

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Answer:

Step-by-step explanation:

Givens

OF =     RF

OU = UR

Draw a line from U to F

UF = UF                              Reflexive property.

Solution

ΔOUF = ΔRUF                    SSS

<O = < R                              Congruent parts are congruent when the triangles are congruent.

Answer:

[tex]P'(-6,4)[/tex]

Step-by-step explanation:

P(x,y) -> rotate 90 degrees -> P'(-y,x)

P'(-6,4)

:]

(Brainliest would be greatly appreciated :] )

Answer:

(xy-6)(y-3)

Step-by-step explanation:

i don't know if you needed this, but if you need this i can explain step by step

xy(y-3)-6(y-3). we take the common ones out and than simplify as:. (xy-6)(y-3)

Answer:

18 pi

Step-by-step explanation:

2xpixr d divided by 2 equals 9 pi x 2 x 9 =18

Answer:

1 and 2

and the greatest common divisor is 2

Answer:The total cost is $41.04

Step-by-step explanation:

The minimum sample size of the given condition is 89.

In given condition,

For 95% confidence level, critical value of z is z* = 1.96

The margin of error given is E = 1

Standard deviation ( α ) = 4.8

Final required sample size is;

n = [tex](\frac{z*\alpha }{E} )^{2}[/tex]

  = [tex](\frac{1.96 * 4.8}{1} )^2[/tex]

  = 88.51

n  ≅ 89

The minimum sample size of the given condition is 89.

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SOLUTION

Solve the inequality.

divide both sides by -4

Answer:

w - 20

Step-by-step explanation:

Remove the parenthesis by multiplying each term of (w + 5) by (-4)

-4(w + 5) + 5w = -4*w + 5*(-4) + 5w

                       = -4w - 20 + 5w

                       = -4w + 5w - 20

        Combine like terms. Like terms have same variable with same power.

                       = w - 20

Answer:

2 points

Step-by-step explanation:

According to the graph, the parabola has two x-intercept, where is (0,-2) and (0,-8).

We want to find where to put the parentheses on each expression to make the expression true.

First, we identify the symbols +, x, / and - to identify the pairs of numbers. For example, in the expression

we have two symbols (+, *).

Now, this would give us two pairs of expression where we can put the parentheses. That is, one possibility per symbol. So we have

and

Now, let us try the first choice. Remember that first we have to evaluate what is inside the parentheses. This would give us

which coincides to the value we wanted.

In the second case, we have the following symbols / and -

This would give us two pairs for grouping, namely

and

as before, we will first evaluet the first option

If we try the second option, we woud get

which would give us the correct value.

The volume of the cylinder is 502.4m³

Volume of the cylinder:

Volume of the cylinder can be calculated by the product of the area of base and height.

For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.

V = πr²h cubic units.

Given,

A cylinder with radius r and height h is inscribed in a cone with radius of 4m and height of 10m.

Here we need to find the volume of the cylinder,

We know that the values of,

Radius = 4m

height = 10m.

Now we have to apply the value on the formula, then we get,

V = π x (4)² x 10

Apply the value of π as 3.14 then we get,

V = 3.14 x 16 x 10

V = 502.4

Therefore, the volume of the cylinder is 502.4 m³.

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The required equation of the graph is y = x - 1.

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y = mx + c, where m is the slope and c is the y-intercept.

Given, the line passes through the points (-1, 0) and (0, 1).
Also, the y-intercept for the line = c = -1
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (1 - 0)/(0 - (-1)) = 1/1 = 1
y-intercept = c = -1
Therefore, equation of the standard line is y = mx + c, thus y = (1*x) + (-1)
Thus, the required equation of the graph is y = x - 1.

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The population of the city in 5 years is 3430386 as the population is increasing 10% per year

What is percentage and how to calculate?

Percentage is the ratio which can be expressed as fraction of 100. And to calculate percentage we multiply by 100.

We are given that population of a city is 2130000

And the population is increasing at a rate of 10%

We are asked to find the population after 5 years

The equation can be given as (1.1)^x*2130000

We put x =5

We get

[tex](1.1)^5*2130000\\1.61051*2130000\\=3430386[/tex]

Hence the population will be 3430386 after 5 years at a rate of 10% increase per year

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Answer: It is impossible for two obtuse angles to be a straight angle

Step-by-step explanation:

Definition of a straight angle: An angle that is exactly 180 degrees

Definition of obtuse angle: An angle that is more than 90 degrees

1)  X = obtuse angle

x > 90

Set minimum to test:

x = 91

2) Set up the question

(<= less than or equal to)

2x <= 180

3) Sub the first equation

2(91) <= 180

182 <= 180

4) Answer the question

It is impossible for two obtuse angles to be a straight angle

The probability of a simple event to occur is this:

In the question given, the favorable outcomes are either 8 or diamond.

In a deck of cards, there are 13 diamond cards and 4 eights however one of the diamond cards is also 8. Therefore, total favorable outcome is 13 + 4 - 1 = 16.

Of course, the total number of possible outcomes is 52. So, the probability of getting an eight or a diamond is:

The probability, in fraction, is 4/13.

In decimal form, it is 0.3077.

In percentage form, it is 30.77%

No, there is nothing wrong in the research that is done by the head of the institution. He said correct that the mean age of the full time students has declined.

Given above that a university's director of institutional research thought that the average age of full-time students was lowering. The average age of a full-time student in 1995 was 27.4 years old.

He registered all 4934 pupils for this and the average age was 27.1 years.

The fact that the inquiry concerns the average age of a full-time student makes this situation ideal. This is a trustworthy approach when the mean is calculated after accounting for all full-time students at the university.

Given that this is a left-tailed test, the hypothesis is also correct.

He rejected the null hypothesis because p = 0.0020.05.

The average age did decrease, in conclusion. The situation is ideal.

Therefore his hypothesis is absolutely correct. There is nothing wrong with it.

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then the  generator is the element which can generate whole set

therefore U(49) has 12 generator

What is meant by cyclic group?

A cyclic group is a group that can be generated by a single element. (the group generator). Cyclic groups are Abelian.

the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group.

elements of U(49) are {1,2,3,5,,7,11,,13,17,19,23,29,31,37,39,,41,47}

then the  generator is the element which can generate whole set

therefore U(49) has 12 generator

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pls tell me u understand the drawing

In 6 days 285 miles can be travelled.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

190  miles cover in 4 days.

let x miles travelled in 6 days

So, using proportion

190/4 = x/6

190 x 6 = 4x

4x= 1440

x= 285 miles.

Hence, in 6 days 285 miles can be travelled.

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Answer:

David's orchid: 20 +x

Pam's orchid: 25 + 0.75x

Step-by-step explanation:

Framing linear equations:

Cost of first 10 pounds = 10 * 2 = $ 20

Let the weight of additional apples picked = x pounds

Cost of 'x' pounds = 1 * x = $ x

Total cost = cost of first 10 pounds + cost of additional 'x' pounds

                = 20 + x

                     Entry fee = $ 10

Cost of first 10 pounds = 10 * 1.50 = $ 15

      Cost of 'x' pounds = 0.75*x = 0.75x

Total cost = Entry fee + cost of first 10 pounds + cost of additional 'x' pounds

                = 10 + 15 + 0.75x

                = 25 + 0.75x

If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.

Let the equation be

[tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]

Multiply both sides by 0.0375 / 12, and we get

[tex]$300000 \cdot \frac{0.0375}{12}=\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{\frac{0.0375}{12}} \cdot \frac{0.0375}{12}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{1875}{2}=300\left(1+\frac{0.0375}{12}\right)^{12 t}$$[/tex]

Switch sides of the equation,

[tex]$300\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{1875}{2}$$[/tex]

Divide both sides by 300, and we get

[tex]$\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{300}=\frac{\frac{1875}{2}}{300}$$[/tex]

Simplifying the above equation, we get

[tex]$\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{25}{8}$$[/tex]

Apply exponent rules, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right)$$[/tex]

Solving the above equation, then

[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right): \quad t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$[/tex]

[tex]$t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$$[/tex]

simplifying the above value of t, we get

t = 30.43236.

If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.

Therefore, the value of t = 30.43236.

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Answer:

1000

Step-by-step explanation:

Hello!

Use the Quotient Property of Exponents to evaluate the expression:

[tex]\frac{a^b}{a^c} = a^{b-c[/tex]

In this case, a is 10, b is 5, and c is 2.

If we simplify 10³, we should get 1000.