Answer:
9 years
Step-by-step explanation:
Let's call the amount of years x. We can write
42 + x = 3(8 + x)
42 + x = 24 + 3x
2x = 18
x = 9
The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Answer:
The correct answer is the first one of your list of options:
"Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points."
Step-by-step explanation:
Since the y-intercept is -6, then the point (0, -6) is a point on the line.That is x = 0 and y = -6. From there you move according to the slope value "2 = 2/1" which means two units of rise when the run is one.
Then, from (0, -6) move up 2 units and then right one unit. The new point should also be a point on the line. Join the two points with a line to graph the function.
According to creditcard , the mean outstanding credit card debt of college undergraduate was $3173 in 2010. A researcher believes that this amount has decreased since then.
Required:
a. Determine the null and alternative hypotheses.
b. Explain what it would mean to make a Type I and Type Il error.
Answer:
a. The null and alternative hypothesis can be written as:
[tex]H_0: \mu=3173\\\\H_a:\mu< 3173[/tex]
b. A Type I error is made when a true null hypothesis is rejected. In this case, it would happen if it is concluded that the actual mean outstanding credit card debt of college undergraduate is significantly less than $3173, when in fact it does not.
A Type II error is made when a false null hypothesis is failed to be rejected. In this case, the actual mean outstanding credit card debt of college undergraduate is in fact less than $3173, but the test concludes there is no enough evidence to claim that.
Step-by-step explanation:
We have a prior study of the mean outstanding credit card debt of college undergraduate that states that it was $3173 in 2010.
A researcher believes that this amount has decreased since then.
Then, he has to perform a hypothesis test where the null hypothesis states that the mean is still $3173 and an alternative hypothesis that states that the actual credit card debt is significantly smaller than $3173.
The null and alternative hypothesis can be written as:
[tex]H_0: \mu=3173\\\\H_a:\mu< 3173[/tex]
to prove triangleABC is isosceles, which of the following statements can be used in the proof?
&
given circleR, how is it known that QS = YT?
(idk the answers i guessed)
Answer:
Step-by-step explanation:
In an isosceles triangle, the base angles are equal. This also means that the length of two sides of the triangle are equal. Looking at triangle ABC, to prove that it is an isosceles triangle, then
Angle CAB = angle CBA
For the second question, to determine how it is known that QS is equivalent to YT, we would recall that the diameter of a circle passes through the center and from one side of the circle to the other side. Assuming R is the center of the circle, then QS and YT are the diameters of the circle and also the diagonals of the rectangle. Thus, the correct option is
The diameters act as diagonals
The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000586 mm. Assume a random sample of 59 sheets of metal resulted in an x¯ = .2905 mm. Calculate the 95 percent confidence interval for the true mean metal thickness.
Answer:
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm
The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
The scores on a recent statistics test are given in the frequency distribution below. Construct the corresponding relative frequency distribution. Round relative frequencies to the nearest hundredth of a percent if necessary.Scores frequency0-60 461-70 1071-80 1281-90 491-10 5A. Scores frequency0-60 15.5%61-70 22.1%71-80 31.3%81-90 16.2%91-10 14.9%B. Scores frequency0-60 12.5%61-70 20.1%71-80 37.3%81-90 15.2%91-10 14.9%C. Scores frequency0-60 11.43%61-70 28.57%71-80 34.29%81-90 11.43%91-10 14.29%D. Scores frequency0-60 0.20%61-70 0.20%71-80 0.49%81-90 0.03%91-10 0.09%
Answer:
C
Step-by-step explanation:
The scores in a recent statistics test are given in the frequency distribution below.
[tex]\left|\begin{array}{c|cc}$Scores&$Frequency\\---&--\\0-60&4\\61-70&10\\71-80& 12\\81-90&4\\91-10&5\\----&--\\$Total&35\end{array}\right|[/tex]
The relative frequency is calculated in the table below.
[tex]\left|\begin{array}{c|c|c}$Scores&$Frequency&$Relative Frequency\\---&--&-----\\0-60&4&\dfrac{4}{35}\times 100=11.43\% \\\\61-70&10&\dfrac{10}{35}\times 100=28.57\%\\\\71-80& 12&\dfrac{12}{35}\times 100=34.29\%\\\\81-90&4&\dfrac{4}{35}\times 100=11.43\%\\\\91-10&5&\dfrac{5}{35}\times 100=14.29\%\\----&--&---\\$Total&35&100\end{array}\right|[/tex]
Therefore, the relative frequency table is that in Option C.
Which phrases can be used to represent the inequality 6.5 x + 1.5 less-than-or-equal-to 21? Select two options. The product of 6.5 and the sum of a number and 1.5 is no more than 21. The sum of 1.5 and the product of 6.5 and a number is no greater than 21. The product of 6.5 and a number, when increased by 1.5, is below 21. The product of 6.5 and a number, when increased by 1.5, is at most 21. The sum of 1.5 and the product of 6.5 and a number is at least 21.
Answer:
The option with “at most” and “no more than”
Step-by-step explanation:
These two phrases mean “greater than or equal to”
1. The sum of 1.5 and the product of 6.5 and a number is no greater than 21.
2. The product of 6.5 and a number, when increased by 1.5, is at most 21.
What is inequality ?In which mathematical expression both sides are not equal, i.e. one side is greater or less or greater equal or less equal than other side, is called inequality.
Example : 4x+5>3x-2
What are the required phrases ?The given inequality is [tex]6.5x+1.5\leq 21[/tex]
Firstly, The sum of 1.5 and the product of 6.5 and a number (say x) is 6.5x+1.5, which is no greater than 21, i.e. [tex]6.5x+1.5\leq 21[/tex]
Again, The product of 6.5 and a number (say x) is 6.5x, when increased by 1.5, it will be 6.5x+1.5 which is at most 21, i.e. [tex]6.5x+1.5\leq 21[/tex]
Hence, the correct options are,
1. The sum of 1.5 and the product of 6.5 and a number is no greater than 21.
2. The product of 6.5 and a number, when increased by 1.5, is at most 21.
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Match each correlation coefficient, r, to its description.
r = −0.08
r = −0.83
r = 0.96
r = 0.06
1.) strong negative correlation
2.) weak positive correlation
3.) weak negative correlation
4.) strong positive correlation
The answers are in order
r = −0.08 --> weak negative correlation
r = −0.83 --> strong negative correlation
r = 0.96 --> strong positive correlation
r = 0.06 --> weak positive correlation
The match of each correlation is given by,
r = −0.08 implies a weak negative correlation
r = −0.83 implies a strong negative correlation
r = 0.96 implies strong positive correlation
r = 0.06 implies weak positive correlation.
We have given that,
The correlation coefficient, r, to its description.
A B
r = −0.08 strong negative correlation
r = −0.83 weak positive correlation
r = 0.96 weak negative correlation
r = 0.06 strong positive correlation
We have to match the given relation
What is the positive and negative correlation?If the correlation coefficient is greater than zero, it is a positive relationship. Conversely, if the value is less than zero, it is a negative relationship.
So the correct match is,
r = −0.08 implies a weak negative correlation
r = −0.83 implies strong negative correlation
r = 0.96 implies strong positive correlation.
r = 0.06 is implies weak positive correlation.
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Find the amount in an account where $500 is invested at 2.5% compounded continuously for period of 10 years
Hi
500 *1.025^10 ≈ 640.04
Find the length of AC in a triangle
Answer:
9.35
Step-by-step explanation:
AAS formula is easier if you add 12+90 then subtract it from 180, thats angle A.
then just write out the formula
sinA/a = sinB/b
1)5/6 of 3/4÷7/8×2/2
2)3/2of3/4÷8/2
Step-by-step explanation:
[tex] (\frac{5}{6} \times \frac{3}{4} ) \times \frac{8}{7} \times 1 \\ = \frac{5}{8} \times \frac{8}{7} \\ = \frac{5}{7} [/tex]
[tex]( \frac{3}{2} \times \frac{3}{4} ) \times \frac{2}{8} \\ = \frac{9}{8} \times \frac{2}{8 } \\ = \frac{9}{32} [/tex]
In the multiplication sentence below, which numbers are the factors? Check
all that apply.
7x3 = 21
Answer:
The factors are 7 and 3
Step-by-step explanation:
The factors of a multiplication sentence are the numbers that are being multiplied for the product (or answer).
What is the total surface area of a rectangular prism whose net is shown 29 in. 25in. 25.in. Venus do not delete my question you hater
Answer:
V = 18125 in^3
Step-by-step explanation:
Surface Area of Rectangular Prism:
V = 18125 in^3
Step-by-step explanation:
Surface Area of Rectangular Prism:
S = 2(lw + lh + wh)
length l = 25 in
width w = 25 in
height h = 29 in
diagonal d = 45.7274535 in
total surface area S_tot = 4150 in^2
lateral surface area S_lat = 2900 in^2
top surface area S_top = 625 in^2
bottom surface area S_bot = 625 in^2
volume V = 18125 in^3
The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 23x − 132, y = 0; about the y−axis
Answer:
V = 23π/6
Step-by-step explanation:
V = 2π ∫ [a to b] (r * h) dx
y = −x² + 23x − 132
y = −(x² − 23x + 132)
y = −(x − 11) (x − 12)
Parabola intersects x-axis (line y = 0) at x = 11 and x = 12 ----> a = 11, b = 12
r = x
h = −x² + 23x − 132
V = 2π ∫ [11 to 12] x (−x² + 23x − 132) dx
V = 23π/6
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the planex + 9y + 4z = 27.
Answer:
81/4
Step-by-step explanation:
From the given information; we are to use Lagrange multipliers to find the volume of the largest rectangular box
The coordinate planes and the vertex given in the plane is x + 9y + 4z = 27.
By applying Lagrange multipliers, we have;
[tex]fx = \lambda gx[/tex]
where;
[tex]f: V = xyz[/tex]
[tex]g : x + 9y + 4z = 27[/tex]
From; [tex]fx = \lambda gx[/tex]
[tex]yz = \lambda[/tex] --------- equation (1)
From; [tex]fy = \lambda gy[/tex]
[tex]xz = 9 \lambda[/tex] --------- equation (2)
From; [tex]fz = \lambda gz[/tex]
[tex]xy = 4 \lambda[/tex] --------- equation (3)
Comparing and solving equation (1),(2) and (3);
[tex]\lambda x = 9 \lambda y = 4 \lambda z[/tex]
divide through by [tex]\lambda[/tex]
x = 9 y = 4z
3x = 27
x = 27/3
x = 9
From x = 9y
9 = 9 y
y = 9/9
y = 1
From
x = 4z
9 = 4 z
z = 9/4
Thus; the Volume of the largest rectangular box = 9 × 1 × 9/4
= 81/4
Simplify: 1. (x−1)+(12−7.5x) 2. b−(4−2b)+(3b−1) 3. (2p+1.9)−(7−p)
Answer:
1. -6.5x+11
2. 6b-5
3. 3p-5.1
Step-by-step explanation:
[tex]1. \\(x-1)+(12-7.5x)=\\x-1+12-7.5x=\\x-7.5x-1+12=\\-6.5x-1+12=\\-6.5x+11\\\\2.\\b-(4-2b)+(3b-1)=\\b-4+2b+3b-1=\\b+2b+3b-4-1=\\3b+3b-4-1=\\6b-4-1=\\6b-5\\\\3.\\(2p+1.9)-(7-p)=\\2p+1.9-7+p=\\2p+p+1.9-7=\\3p+1.9-7=\\3p-5.1[/tex]
Express $0.\overline{1}+0.\overline{01}+0.\overline{0001}$ as a common fraction.
Answer:
[tex]\dfrac{1213}{9999}[/tex]
Step-by-step explanation:
We are required to express [tex]0.\overline{1}+0.\overline{01}+0.\overline{0001}[/tex] as a common fraction.
The bar on top of the decimal part indicates the decimal number is a repeating decimal.
Therefore:
[tex]0.\overline{1}=\dfrac{1}{10-1}= \dfrac{1}{9}\\\\0.\overline{01}=\dfrac{1}{100-1}= \dfrac{1}{99}\\\\0.\overline{0001}=\dfrac{1}{10000-1}= \dfrac{1}{9999}\\\\\\$Therefore$:\\0.\overline{1}+0.\overline{01}+0.\overline{0001} \\=\dfrac{1}{9}+\dfrac{1}{99}+\dfrac{1}{9999}\\\\=\dfrac{1213}{9999}[/tex]
Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y= -x +4
Answer: V = [tex]\frac{64}{3}\pi[/tex]
Step-by-step explanation: A solid formed by revolving the region about the x-axis can be considered to have a thin vertical strip with thickness Δx and height y = f(x). The strip creates a circular disk with volume:
V = [tex]\pi. y^{2}.[/tex]Δx
Using the Disc Method, it is possible to calculate all the volume of these strips, giving the volume of the revolved solid:
V = [tex]\int\limits^a_b {\pi. y^{2} } \, dx[/tex]
Then, for the region generated by y = - x + 4:
V = [tex]\int\limits^4_0 {\pi.(-x+4)^{2} } \, dx[/tex]
V = [tex]\pi.\int\limits^4_0 {(x^{2}-8x+16)} \, dx[/tex]
V = [tex]\pi.(\frac{x^{3}}{3}-4x^{2}+16x )[/tex]
V = [tex]\pi.(\frac{4^{3}}{3}-4.4^{2}+16.4 - 0 )[/tex]
V = [tex]\frac{64}{3}.\pi[/tex]
The volume of the revolved region is V = [tex]\frac{64}{3}.\pi[/tex]
The evaluation of the definite integral that represents the volume of the solid is [tex]\mathbf{\dfrac{64 \pi}{3}}[/tex]
Using the Disk Method to determine the volume of a solid formed by revolving the region about the x-axis and the interval [a, b]; we have:
[tex]\mathbf{V = \int ^b_a \pi (y)^2 \ dx}[/tex]
where;
b = 4a = 0[tex]\mathbf{V = \int ^4_0 \pi \Big[-x +4 \Big]^2 \ dx}[/tex]
[tex]\mathbf{V =\pi \int ^4_0\Big[-x^2 -8x+16 \Big] \ dx}[/tex]
[tex]\mathbf{V =\pi \Big[\dfrac{x^3}{3} -4x^2+16x \Big]^4_0 \ dx}[/tex]
[tex]\mathbf{V =\pi \Big[\dfrac{4^3}{3} -4(4)^2+16(4) -0 \Big]}[/tex]
[tex]\mathbf{V =\dfrac{64 \pi}{3}}[/tex]
Therefore, we can conclude that the evaluation of the definite integral that represents the volume of the solid is [tex]\mathbf{\dfrac{64 \pi}{3}}[/tex]
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Help me please thank you
Answer:
104 degrees
Step-by-step explanation:
The angle of the whole set of lines is 140 degrees. In addition, the partial angle of it is also given--which is 36 degrees. In order to solve for the remaining part, Subtract 36 degrees from 140 degrees to get 104 degrees.
Tell whether the following set is an empty set or not.
A = {A quadrilateral having 3 obtuse angles}
Answer:
It is not an empty set
Step-by-step explanation:
A quadrilateral with 3 obtuse angles is possible.
A obtuse angle has a measure of more than 90 degrees and less than 180 degrees.
Let’s say three angles are measuring 91 degrees in a quadrilateral.
91 + 91 + 91 + x = 360
x = 87
The measure of the fourth angle is 87 degrees which is less than 360 degrees and is a positive integer, so it is possible.
Answer:
It is not an empty set
Step-by-step explanation:
Obtuse angles are angles greater than 90 and less than 180.
There are quadrilaterals having 3 obtuse angles and they are possible.
If we imagine 3 obtuse angles of 91 degrees (obtuse angle), the 4th angle will be
360-91-91-91
=> 87 degrees
So, This quadrilateral can be constructed!
And also with 92, 93, 94 and so on!
So, Set A is not an empty set!
HELP!! Find the GCF for the list. -6x^2, 15x^3 Find the GCF for the polynomial 32xy-18x^2
Answer:
Step-by-step explanation:
GCF: -6x^2 and 15x^3 the GCF is 3x^2
the GCF for this polynomial is 2x(16y-9x)
HELP PLEASE ITS FOR PLATO
Answer:
i think it might be A. 0.2
Step-by-step explanation:
Perform the indicated operation.
Answer:
√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.
Answer:
[tex] 7\sqrt{3} [/tex]
Step-by-step explanation:
[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]
please simplify this
Answer:
The answer is 4√3 - 6
Steps
(8√6mn + 6√8mn ) / 2√2mn
Factor out 2√mn from the expression
That's
2√mn × ( 4√6 - 3√8) / 2√2mn
Next reduce the fraction with 2
We have
√mn × ( 4√6 - 3√8) / √2mn
Factor √2 from the denominator
√mn × ( 4√6 - 3√8) / √2(√mn)
√mn will cancel each other
we get
( 4√6 - 3√8) / √2
Simplify the radical expression
That's
( 4√6 - 3× 2√2) / √2
= ( 4√6 - 6√2) / √2
Rationalize the surd
We get
( 4√6 - 6√2) / √2 × (√2 / √2)
= ( 4√6 - 6√2) (√2) / (√2)²
= 4√12 - 12 / 2
= (8 √3 - 12) / 2
Factor out 2 from the numerator
That's
2( 4 √ 3 - 6 ) /2
2 will cancel each other
so the final answer will be
4√3 - 6
Hope this helps you
Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally. Define the following in terms of the study. Give examples where appropriate.
The sample:
a. The sample is all of the people taking skiing or snowboarding lessons.
b. The sample is all of the children taking skiing or snowboarding lessons.
c. The sample is a group of the people taking skiing or snowboarding lessons.
d. The sample is a group of the children taking skiing or snowboarding lessons.
Answer:
Option D
Step-by-step explanation:
A sample can be described as a small part or potion that is intended to describe what the whole population is like.
In this study, the sample is a group of the children taking skiing or snowboarding lessons: this group is taken out of the whole population of children taking skiing or snowboarding lessons.
John comes across a recent survey and wants to gauge the strength of the results.
Which of the following would best reflect upon the researcher.
O a margin of error of +/- 10%
O a margin of error of +/- 3%
O a margin of error of +/- 98%
O a margin of error of +/-8%
Answer:
A margin of error of +/- 3%
Step-by-step explanation:
Strenght of surveys:
The lesser the margin of error, the more precise, stronger, the confidence interval is.
The margin of error depends of the number of people surveyed. The more people are surveyed, lower the margin of error is, giving a stronger interval.
In this question:
We want the smaller margin of error, which is given by:
A margin of error of +/- 3%
Four swimmers, Daniela, Camille, Brennan, and Amy, compete on a relay team. For the first race of the year, Daniela begins the relay. The other three swimmers can swim in any order. The sample space, S, for the event is shown below. S = {CBA, CAB, BAC, BCA, ACB, ABC} After the first race, it is determined that Camille is a strong finisher and should be the final swimmer in the race.
Answer:
A = {CBA, CAB, BCA, ACB}
Step-by-step explanation:
Answer: A. {CBA, CAB, BCA, ACB}
Step-by-step explanation: Id appreciate it if anyone else could explain why that is the answer. (?)
HELP! WILL GIVE BRAINLIEST!
Answer:
(2x+16) + (x) = 180
Step-by-step explanation:
The opposite angles of a quadrilateral inscribed inside a circle will be supplementary angles, meaning that A+C=180, and B+D=180. A+C is not given in the answers below, but B+D is, so that is the correct answer.
Hope this helps! Please give brainliest!!
Answer:
C
Step-by-step explanation:
Opposite angles of a quadrilateral are supplementary
Please answer this question in two minutes
Answer:
W = (18,0)
Step-by-step explanation:
I found the slope of the line from point M to point V. The slope is -3.875. I continued this slope starting with point V to find the coordinates of point W. The coordinates of point W are (18,0).
I graphed the coordinates and the line of VW on the graph below.
A company determined that the marginal cost, Upper C prime (x )of producing the xth unit of a product is given by Upper C prime (x )equalsx Superscript 4minus2x. Find the total cost function C, assuming that C(x) is in dollars and that fixed costs are $6000.
Answer:
C(x) = 0.2x^5 - x^2 + 6000
Step-by-step explanation:
Given in the question are restated as follows:
Marginal cos = C'(x) = x^4 - 2x ...................... (1)
Note that marginal cost (C'(x)) refers to the change in the total cost (C(x)) as a result of one more unit increase in the quantity produced. That is, MC refers to the additional cost incurred in order to produce one more unit of a good.
Therefore, TC can be obtained by integrating equation (1) as follows:
C(x) = ∫C'(x) = ∫[x^4 - 2x]dx
C(x) = 1/5x^5 - 2/2x^2 + F ................................ (2)
Where F is the fixed cost. Since the fixed cost is given as $6,000 in the question, we substitute it for F into equation (2) and solve as follows:
C(x) = 0.2x^5 - x^2 + 6000 ......................... (3)
Equation (3) is the total cost function C.
Unknown angle problems
Answer: x =40
Step-by-step explanation:
x +x +100 = 180 They form a straight line so they add to 180 degrees.
2x + 100 = 180 solve for x by combining like terms
-100 -100 subtract 100 from both sides
2x = 80 Divide both sides by 2
x =40
Answer:
x might be 40°.
Step-by-step explanation:
angle on a straight line =180°
x+100+x =180
2x =180-100
2x=80
2x/2=80/2
x=40°