8 more than 3 times a number is the same as -5 times the number.

a. x = -1
b. x = 1
c. x = -2

The sum of the first 30 terms of the arithmetic series is 1560

From the question, we are to determine the sum of the first 30 terms of the series

Using formula,

[tex]S_{n} = \frac{n}{2}(a + l)[/tex]

Where [tex]S_{n}[/tex] is the sum of the nth term

n is the number of terms

a is the first term

and [tex]l[/tex] is the last term

From the given information,

n = 30

a = 3

[tex]l[/tex] = 101

Thus,

[tex]S_{30} = \frac{30}{2}(3+ 101)[/tex]

[tex]S_{30} = 15(104)[/tex]

[tex]S_{30} = 15 \times 104[/tex]

[tex]S_{30} = 1560[/tex]

Hence, the sum of the first 30 terms of the arithmetic series is 1560

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Answer:

B. (5,12,13)

Step-by-step explanation:

The only answer with two side lengths that are greater than the largest side length.

Calculating the circumference of a circle based on the circle's diameter.

What kind of problems can a quantum computer solve?

10 Difficult Problems Quantum Computers can Solve Easily-

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The complete question is -

Which type of mathematical problem is too complex for a classical computer to solve efficiently?

a. converting an irregular fraction to an approximate decimal value

b. multiplying two numbers that both have a large number of digits

c. finding two prime factors that result in a specific value when multiplied

d. calculating the circumference of a circle based on the circle's diameter

Answer: No

Step-by-step explanation:

There is only one pair of congruent angles that can be determined, but to prove triangles similar, there needs to be two pairs of congruent angles.

Step-by-step explanation:

[tex]f(x) = ln( \frac{1}{x} ) [/tex]

To find the derivative, notice we have a function 1/x inside of another function, ln(x)

We use what we call the chain rule,

It states that

derivative of a '

[tex] \frac{d}{dx} f(g(x)) = f '(g(x)) \times \: g '(x)[/tex]

Here f is ln(x)

f is 1/x

So first, we know that

[tex] \frac{d}{dx} ( ln(x) = \frac{1}{x} [/tex]

so

[tex]f'(g(x)) = \frac{1}{ \frac{1}{x} } [/tex]

We know that

[tex]g'(x) = - \frac{1}{ {x}^{2} } [/tex]

So we have

[tex]x \times - \frac{1}{ {x}^{2} } = \frac{ - 1}{x} [/tex]

Answer:

The ¨mandatory dues¨ asked by the unions are not much (practically none), since it´s a voluntary system implemented, normally all the members pay a ¨agency fee¨ but not more than that, this changes depending on the personal involvement with the union.

a natural person can refuse the membership at any moment, without issues, and this way avoid any kind of activity with the union, including contributing with money (dues) or duties.

However, when this happens, the person it´s restricted to certain activities like participate in union elections, general or important meetings, and the contribution in the bargain for the collective elections is banned as well, these as main aspects to highlight.

If one doesn't pay they union dues, they will not be able to participate in collective bargaining with owners.

Only the real representatives of the union could participate in collective bargaining with owner (in which they could negotiate the new term of the salary with the owner). Without paying their dues, they're still haven't been acknowledged as the member of union.



Hope this helps have a great day!

Answer:

1. pi.      2.49-12.25pi

Step-by-step explanation:

Answer:

  (c)  f(x) = 3(x -3)(x -7)

Step-by-step explanation:

The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.

The graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...

  (x -3)(x -7) . . . . . . . . eliminates choices A and D

The vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.

Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)

Putting these observations together, we have determined the equation of the function to be ...

  f(x) = 3(x -3)(x -7) . . . . . . matches choice C

Answer:

[tex] y = \frac{4}{3} x + 5[/tex]

Step-by-step explanation:

The slope is

[tex] \frac{ - 3 - 1}{ - 6 - ( - 3)} = \frac{4}{3} [/tex]

Substituting into point-slope form,

[tex]y - 1 = \frac{4}{3} (x + 3) \\ \\ y - 1 = \frac{4}{3} x + 4 \\ \\ y = \frac{4}{3} x + 5[/tex]

The percentage of tardiness among the 102 pupils is 2.94.

According to the query,

Course A: Total number of students = 102

                   Number of tardy students = 3

Percent of students tardy in course A = (number of tardy students/total  

                                                                   number of students) * 100

  =(3/102)*100

  = 2.941

  ≈2.94

In case of course B: Total number of students = 85 & tardy student = 5

So, the percent of tardy student = (5/85)*100 = 5.88 %

Therefore, it is concluded that the percentage of student tardiness in course A is 2.94.

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These are independent events

and probability of drawing red marble is 1/3

and probability of drawing two blue marble is 1/2 ,1/2.

According to the statement

A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.

And we have to find the probability of tossing a head and drawing a red marble. and probability of drawing two blue marbles if the first marble is not replaced.

here we solve this problem by Probability

So, Probability of drawing red marble = Number of red marble / total number of marbles.

Probability = 2/6

Probability = 1/3.

Then

Probability of drawing blue marbles = number of blue marbles /total marbles

Probability = 3/6

Probability = 1/2.

1st blue marble Probability =1/2

2nd blue marble Probability = 1-(1/2) = 1/2.

These are non dependent events because they do no affect the probability of each others.

So, These are independent events

and probability of drawing red marble is 1/3

and probability of drawing two blue marble is 1/2 ,1/2.

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The value of sample size n in this statement according to a confidence interval is 350.

According to the statement

we have a given that the value of error and population proportion and we have to find the value of sample size.

So, we know that the

confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Here

p represent the real population proportion of interest

ρ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

z represent the critical value for the margin of error

So, The population proportion have the following distribution  

P≈n ( p, ([p (1-p)]/n)^1/2)

Here In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by  α = 1 - 0.95 = 0.05

and α/2 = 0.025 And the critical value would be given by:  

z = 1.96

And on this case we have that ME = ±0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got the value

n = 0.35(1-0.35) / (0.05/1.96)^2

so, the value becomes

n = 350.

So, The value of sample size n in this statement is 350.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05?

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Answer: (2, 18)

Step-by-step explanation:

When x=2, [tex]f(2)=2(3)^{2}=18[/tex].

So, it should pass through (2, 18).

Answer:

(2, 18)

Step-by-step explanation:

i posted this at 1:19 in the morning, good day

Answer:

[tex]6x^{2} -24x-10[/tex] with remainder -5

Answer:

[tex]6^2-24x-10-\frac{5}{x+4}[/tex]

In other words, [tex]6x^2-24x-10[/tex] is the answer and -5 is the remainder

Step-by-step explanation:

I used long division for this, and I uploaded an image for the steps. The final answer I got was [tex]6x^2-24x-10-\frac{5}{x+4}[/tex]

Answer:

11.  [tex]\frac{\sqrt{2} }{2}[/tex]

12. [tex]\sqrt{3}[/tex]

13. [tex]\frac{\sqrt{3} }{2}[/tex]

14. [tex]\frac{\sqrt{3} }{3}[/tex]

15. [tex]\sqrt{2}[/tex]

16. [tex]\frac{2\sqrt{3} }{3}[/tex]  

Step-by-step explanation:

Hope this helps

The area of the circle is 78.5 unit square.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

The formula for area of circle is;

Area = [tex]\pi[/tex](radius)²

The distance between the two points are calculated by distance formula.

[tex]\begin{aligned}&d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \\&d=\text { distance } \\&\left(x_{1}, y_{1}\right)=\text { coordinates of the first point } \\&\left(x_{2}, y_{2}\right)=\text { coordinates of the second point }\end{aligned}[/tex]

Calculation for the area of the circle;

As, the radius of the circle is xy.

The distance between x and y points will be calculated by the distance formula.

x=(0,3)  y=(-3,-1)

[tex]\begin{aligned}&d=\sqrt{\left(-3-0\right)^{2}+\left(-1-3\right)^{2}} \\\end{aligned}[/tex]

[tex]\begin{aligned}&d=\sqrt{\left(-3\right)^{2}+\left(-4\right)^{2}} \\\end{aligned}[/tex]

[tex]\begin{aligned}&d=\sqrt{25} \\\end{aligned}[/tex]

[tex]d=5[/tex]

As, distance between x and y point is 5 units which is the radius of the circle.

Area of circle = [tex]\pi[/tex](radius)²

                      = 3.14×(5)²

                      = 78.5

Therefore, the area of the circle is 78.5 unit square.

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Using proportions, it is found that out of the next 1500 pizzas, she should expect 420 pan style pizzas.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The proportion of pan style pizzas is given as follows:

294/(284 + 313 + 159 + 294) = 0.28.

Hence, out of 1500 pizzas, this amount is equivalent to:

0.28 x 1500 = 420

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Answer:927652832

Step-by-step explanation:

using long multiplication step by step multiply.

1) Quadrilateral PAST, TX=AX, [tex]\overline{TP} \parallel\overline{AS}[/tex] (given)

2) [tex]\angle XPT \cong \angle XSA[/tex] and [tex]\angle XTP \cong \angle XAS[/tex] (alternate interior angles theorem)

3) [tex]\triangle TXP \cong \triangle AXS[/tex] (AAS)

4) [tex]\overline{TP} \cong \overline{AS}[/tex] (CPCTC)

5) PAST is a parallelogram (a quadrilateral with two pairs of opposite congruent sides is a parallelogram)

(Adding to the other person's answer)

For the 5th step reason, put this: A quadrilateral is a parallelogram if a pair of opposite sides are parallel and congruent.

It won't work to just say something like the def. of parallelograms.

Using translation concepts, the graph that represents a reflection across the x-axis of [tex]g(x) = \frac{3}{4}(3)^x[/tex] is:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A reflection across the x-axis of g(x) means that:

f(x) = -g(x).

g(x) increases from the second quadrant into the first, hence for f(x) it will be from quadrant 3 into quadrant 4.

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Answer:

Option B

Step-by-step explanation:

Edge 2022

If the sample of bacteria is growing at an hourly rate of 15% continuously and the  bacteria began with 11 bacteria then there will be 244.178 samples bacteria after 21 hours.

Given growth of bacteria 15% ,bacteria at beginning 11.

We have to find the number of sample of bacteria after 21 hours.

We have to first form exponential function which shows the growth of bacteria in variable t.

Exponential function which shows the sum is y=P[tex]e^{rt}[/tex]

where P is initial amount ,

r is rate and

y is the sum

So in our problem P=11 and r=0.15

y=11*[tex]e^{0.15t}[/tex]

To find the  samples after 21 hours we have to put t=21.

y=11[tex]e^{0.15*21}[/tex]

y=11*[tex]e^{3.1}[/tex]

y=11*22.198  ([tex]e^{3.1}[/tex]=22.198 from e table)

y=244.178

Hence the samples after 21 hours will be 244 approximately.

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The height of the mountain from a point a sea level is approximately 1496.650 meters.

First, we construct the geometric diagram of the situation and find all needed angles and sides to determine the height of the mountain. First, we determine the missing side x by the law of sines:

Law of sines

1000 m/sin 3° = x/sin 14.261°

x ≈ 4706.886 m

Now we determine the height of the mountain by trigonometric functions:

h = 100 m + (4706.886 m) · sin 17.261°

h ≈ 1496.650 m

The height of the mountain from a point a sea level is approximately 1496.650 meters.

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The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

According to the question,

Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.

First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.

Mean: 10*3 = 30

Standard deviation: 5*3 = 15

Secondly "change of origin" when every score in a data set by a constant, its mean get  added or subtracted by the same constant and standard deviation remains constant.

Applying change of origin in the above mean and standard deviation  

Mean: 30 - 4 = 26

Standard deviation: Remains same = 15

Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

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For the given tree diagram of the experiment consisting of two trials, P(D) = 0.74

A method that can be infinitely repeated and has a clearly defined range of potential outcomes, or sample space, is referred to as an experiment or trial in probability theory. If there are multiple possible outcomes from an experiment, it is considered to be random; if there is just one, it is said to be deterministic.

Calculation of P(D) for the given experiment:

From the first branch of the tree, P(D) = 0.7 × 0.6

P(D) = 0.42

From the second branch of the tree, P(D) = 0.8 × 0.4

P(D) = 0.32

Hence, the probability of getting D in the experiment is,

P(D) = P(D) from first branch of the tree + P(D) from the second branch of the tree

P(D) = 0.42 + 0.32

P(D) = 0.74

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Answer:

g and f are inverse functions because g(f(x)) = f(g(x)) = x

Step-by-step explanation:

Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):

[tex]f(g(x))=f(\frac{x+6}{7})=7(\frac{x+6}{7} )-6=x+6-6=x[/tex]

Now, let's find g(f(x)):

[tex]g(f(x))=g(7x-6)=\frac{(7x-6)+6}{7} =\frac{7x}{7}=x[/tex]

There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:

[tex]f(x)=y=7x-6[/tex]

Swap x and y:

[tex]x=7y-6[/tex]

Solve for y:

[tex]x+6=7y\\y=\frac{x+6}{7}[/tex]

Notice that we got g, which means f and g are inverse.

Based on the Roni using a lawn mower and Allie pushing one, Roni would be able to mow 0.71 of the field.

Assume that the part of the field that Roni would mow is x.

The relevant equation would be:

x/30 + x/75 = 1

5x/150 + 2x/150 = 1

7x / 150 = 1

x = 21.43

In 30 minutes, Roni would have mowed:

= 21.43 / 30

= 0.71

Full question is:

Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.

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Answer:

Step-by-step explanation:

Day 1 = 2 birds

day 2 = 3 birds

day 3 = 9 birds

day 4 = 8 birds

day 5 = 1 bird

On day 1 the points are (1,2)

On day 5 the points are (5,1)

(I am picking these for the points because I don't know your options for the selecting area.)

we use this formula y2-y1/x2-x1

2-5/1-1

3/0

our answer is infinite which is the relation and this is an infinite function

Answer:

◘ (1, 2)

◘ (2, 3)

◘ 3

◘ is

◘ each value of Day corresponds to exactly one value of Number of birds

Explanation:

◘◘ In the graph, Days represents the x-axis, and Number of birds represents the y-axis. Therefore each marked point on the graph can be thought of as a Cartesian coordinate. This means that the answers for the first and second question could be any of (1, 2), (2, 3), (3, 9), (4, 8), or (5, 1).

◘ In the graph, we can see that the point above Day 2 corresponds to 3 on the Number of birds axis, which means on day 2, 3 birds visited the feeder.

◘ The relation shown is a function because each value of Day corresponds to exactly one value of Number of birds. A function is a relationship that provides one output for each input, and this graph follows that.

South Florida Water Management

The South Florida Water Management District is a regional governmental agency that manages the water resources in the southern half of the state, covering 16 counties from Orlando to the Florida Keys and serving a population of 9 million residents.

Water management is the control and movement of water resources to minimize damage to life and property and to maximize efficient beneficial use. Good water management of dams and levees reduces the risk of harm due to flooding.

Water management is the activity of planning, developing, distributing and optimum use of water resources under defined water polices and regulations.

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The value of n is 99

Integers are the set of numbers including all natural numbers and 0. They are part of the real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered whole numbers.

Natural numbers together with zero (0) are referred to as whole numbers. We know that natural numbers refer to the set of counting numbers starting from 1, 2, 3, 4 and so on. Simply put, integers are a set of numbers without fractions, decimals, or even negative integers. It is a collection of positive integers and zero. Or we can say that integers are the set of non-negative integers.

Integers are the set of natural numbers togethe with the number 0. In mathematics, the set of integers is given as {0, 1, 2, 3, ...}, denoted by the symbol W.

W = {0, 1, 2, 3, 4, …}

All natural numbers are integers.

All integers are real numbers.

It is given that If n a whole number, and 0.01 is between 1/n and 1/n+2, then we need to find the value of n.

1/n+2 < 0.01 < 1/n

1/n+2 < 1/100 < 1/n

n< 100 < n +2

Put n = 99, then we get

99 < 100 < 101

Hence the value of n is 99.

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