Answer:
The estimate is [tex]P__{hat}} \pm E = 0.37 \pm 0.0348[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 522
The sample proportion of students would like to talk about school is [tex]\r p__{hat}} = 0.37[/tex]
Given that the confidence level is 90 % then the level of significance can be mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645[/tex]
Generally the margin of error can be mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }[/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }[/tex]
=> [tex]E = 0.0348[/tex]
Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is
[tex]P__{hat}} \pm E[/tex]
substituting values
[tex]0.37 \pm 0.0348[/tex]
Question 3
Which of the following best describes the solution to the system of equations below?
-6x + y=-3
7x-y=3
The system of equations has exactly one solution where x = 6 and y = 3.
The system of equations has no solution.
The system of equations has infinitely many solutions.
The system of equations has exactly one solution where x = 0 and y=
-3
Answer:
The system has exactly one solution where x = 0 and y = -3.
Step-by-step explanation:
-6x + y = -3
7x - y = 3
(7x - 6x) + (y - y) = 3 - 3
x + 0 = 0
x = 0
7(0) - y = 3
0 - y = 3
-y = 3
y = -3
-6(0) + y = -3
0 + y = -3
y = -3
So, the system has exactly one solution where x = 0 and y = -3.
Hope this helps!
If the image is blurry the answer choices are -1,0,1,2,and 3. The question says select each correct answer
Answer:
12Step-by-step explanation:
There is no algebraic way to solve such an equation. It can be simplified to ...
[tex]-2x-6=-2^x-6\\\\2x-2^x=0\qquad\text{add $2x+6$}[/tex]
This has solutions at x=1 and x=2 as shown in the attached graph.
__
The second attachment shows the functions graphed on the same graph.
Find the volume of each solid. Round to the nearest tenth. IMG_7097.HEIC
Answer:
You didn't put an attachment to show what solid you wanted rounded
Step-by-step explanation:
Please help. I’ll mark you as brainliest if correct!
Answer:
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
Step-by-step explanation:
The last column is the solution
The rest of the columns are the coefficients of the variables
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
A basketball team plays half of its games during the day and half at night. Ten scores from day games and ten scores from night
games were randomly selected by the team's statistician. The following statistical information was calculated from the final game
scores.
Day Night
Mean 58 72
Median 46 63
Mode 50. 70
Range 21 33
Based on these samples, what generalization can be made?
A. The basketball team scored the same number of points in day games as night games.
OB. The basketball team scored more points in night games than in day games.
OC. The basketball team scored more points in day games than in night games.
OD. Not enough information is provided to draw any of these conclusions,
Option B
Because the average points scored in the night is more than that of the day
When a person throws a ball into the air, it follows a parabolic path that opens downward as shown in the figure to the right. Suppose that the ball's height in feet after t seconds is given by h(t)=-16t^2+32t+2. If possible, determine the time(s) when the ball was at a height of 14 feet.
Answer:
0.5 seconds and 1.5 seconds.
Step-by-step explanation:
h(t) = -16t^2 + 32t + 2
14 = -16t^2 + 32t + 2
16t^2 - 32t - 2 + 14 = 0
16t^2 - 32t + 12 = 0
8t^2 - 16t + 6 = 0
4t^2 - 8t + 3 = 0
(2x - 3)(2x - 1) = 0
2x - 3 = 0
2x = 3
x = 3/2
x = 1.5
2x - 1 = 0
2x = 1
x = 1/2
x = 0.5
So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.
Hope this helps!
A cosine function is graphed below. Use the drop-down menus to describe the graph. The amplitude of the graph is __ . The equation of the midline is __ . The period of the function is __ . The function is shifted __ left. The function is shifted __ units up.
Amplitude:4
Equation of Midline: 2
Period of function:3
Function shifted left:0.5
Function shifted up: 2
From the graphed cosine function we are given, we have;
1) Amplitude = 4
2) Equation of midline; m = 2
3) Period of the function = 3π
4) The function shifted 0.5 units left.
5) The function shifted 2 units up.
1) The amplitude is the distance between the center line and the positive or negative peak of the graph. Now, the positive peak is 6 and the negative one is 2. Thus, Amplitude = 6 - 2 = 42) Equation of the midline is the line that divides the entire sinusoidal curve into 2 equal parts along the x-axis. Since amplitude is 4, then the equation of midline is; m = 4/2 ; m = 2.3) The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3π.4) Looking at the graph, ideally the coordinate (-0.5π, 6) should have been on the y-axis which is at (0π, 6). This means it was shifted by 0.5 units to the left side.5) The positive peak should be equal to the negative peak but in this case, positive is 6 and negative is 2. This means, for them to be equal, they have to each be 4. Thus, the graph was shifted by 2 units upwards .Read more; https://brainly.com/question/16280305
Help with inequality
Answer:
1. x>20 2. x≤1 3.x<4 4.x>9 5.x≥-13
3(x+4)-1=-7 plz help
Answer:
x = -6
Step-by-step explanation:
3(x+4)-1=-7
Add 1 to each side
3(x+4)-1+1=-7+1
3(x+4)=-6
Divide by 3
3/3(x+4)=-6/3
x+4 = -2
Subtract 4 from each side
x+4-4 = -2-4
x = -6
Answer:
- 6Step-by-step explanation:
[tex]3(x + 4) - 1 = - 7[/tex]
Distribute 3 through the parentheses
[tex]3x + 12 - 1 = - 7[/tex]
Calculate the difference
[tex]3x + 11 = - 7[/tex]
Move constant to R.H.S and change it's sign
[tex]3x = - 7 - 11[/tex]
Calculate
[tex]3x = - 18[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{ - 18}{3} [/tex]
Calculate
[tex]x = - 6[/tex]
hope this helps
Best regards!!
NEED HELP AS SOON AS POSSIBLE which interval describes where the graph of the function is negative
Answer:
2 < x < ∞
Step-by-step explanation:
We want where the value of y is less than zero
The value of the graph is less than zero is from x=2 and continues until x = infinity
2 < x < ∞
Answer:
[tex]\boxed{2 < x < \infty}[/tex]
Step-by-step explanation:
The value of y should be less than 0 for the graph of the function to be negative.
In the graph, when it startes from x is 2 the value becomes less than 0 and it keeps continuing until x is equal to infinity.
[tex]2 < x < \infty[/tex]
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 240240 engines and the mean pressure was 7.57.5 pounds/square inch (psi). Assume the population standard deviation is 1.01.0. The engineer designed the valve such that it would produce a mean pressure of 7.67.6 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.10.1 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.
Answer:
p-value = 0.1213 (to 4-decimal places)
Step-by-step explanation:
Given:
N = 240
mean = 7.5
s = 1.0
Solution
With N=240 and using the central limit theorem, distribution can be approximated as normal.
Let
Null hypothesis H0, mu = 7.6
Alternate hypothesis, mu not equal to 7.6 (two-tail test)
for
Alpha = 0.1 (two sided)
Z = sqrt(N)(mean – mu)/s = sqrt(240)(7.5-7.6)/1.0 = -1.54919
p-value
= P(|Z|>1.54919)
= 2P(Z>1.54919)
= 2(1-P(Z<1.54919)
=2(1-0.9393) (using normal distribution table)
=0.12134
Since alpha = 0.1 < p-value (0.1213), H0 that mean = 7.6 is not rejected.
(x*129)-3=126 what is x
Answer:
x should equal 1
Step-by-step explanation:
(1*129)-3=126
129-3=126
126=126
Answer:
x=1
Step-by-step explanation:
We can start by adding 3 to both sides to get rid of the -3
That leaves us with 129x=129
It ends up working out really evenly because by dividing both sides by 129, we are left with x=1
I need help!!! If none Of these are correct say none.
side angle side
explanation
because in two similar triangles the SAS congruence rule be obeyed
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.
Answer:
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Step-by-step explanation:
The amount of Carbon-14 after t years is given by the following equation:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.
This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]
How many years will it take for carbon–14 to decay to 10 percent of its original amount?
This is t for which:
[tex]A(t) = 0.1A(0)[/tex]
So
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]
[tex]e^{-0.000124t} = 0.1[/tex]
[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]
[tex]-0.000124t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]
[tex]t = 18569.2[/tex]
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85
Complete Question
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. Suppose a random sample of 100 Americans is asked "Are you satisfied with the way things are going in your life?"
What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85
Answer:
The probability is [tex]P(X > 0.85 ) = 0.21745[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.82[/tex]
The value considered is x = 0.85
The sample size is n = 100
The standard deviation for this population proportion is evaluated as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]\sigma = \sqrt{\frac{0.82(1-0.82)}{100} }[/tex]
[tex]\sigma = 0.03842[/tex]
Generally the probability that probability the sample proportion who are satisfied with the way things are going in their life is greater than x is mathematically represented as
[tex]P(X > x ) = P( \frac{X - p }{ \sigma } > \frac{x - p }{ \sigma } )[/tex]
Where [tex]\frac{X - p }{ \sigma }[/tex] is equal to Z (the standardized value of X ) so
[tex]P(X > x ) = P( Z> \frac{x - p }{ \sigma } )[/tex]
substituting values
[tex]P(X > 0.85 ) = P( Z> \frac{ 0.85 - 0.82 }{ 0.03842 } )[/tex]
[tex]P(X > 0.85 ) = P( Z> 0.78084)[/tex]
from the standardized normal distribution table [tex]P( Z> 0.78084)[/tex] is 0.21745
So
[tex]P(X > 0.85 ) = 0.21745[/tex]
A Car Salesman sold $450000.00 in cars for the month of July.
He is paid a monthly salary of $6000.00 and 5% commission on
total sales. How much did he earn in July?
Answer:
$28,500
Step-by-step explanation:
$6,000 + 5% of $450,000 =
= $6,000 + 0.05 * $450,000
= $6,000 + $22,500
= $28,500
Which of the following box plot best represents the set of data below
Answer:
C. Box plot B
Step-by-step explanation:
A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.10 significance level, is there a relationship between job pressure and age.
(Round your answers to 3 decimal places.)
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 25 27 20
25 up to 40 49 53 40
40 up to 60 59 59 52
60 and older 35 42 44
H0: Age and pressure are not related. H1: Age and pressure are related.
Reject H0 if X2 > .
X2=
(Click to select)Reject Do not reject H0. Age and pressure (Click to select)areare not related.
Answer:
Reject H0
Age and pressure are related
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.
find the maximum value of c=6x+2y
Answer:
∞
Step-by-step explanation:
c can have any value you like.
There is no maximum. We say it can approach infinity.
__
Additional comment
There may be some maximum imposed by constraints not shown here. Since we don't know what those constraints are, we cannot tell you what the maximum is.
What is the equation of the line perpendicular to y=5x-3 that passes through the point (3, 5)?
Answer:
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]
Step-by-step explanation:
Hey there!
Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.
Look at the image below ↓
By looking at the image we can conclude that the equation for the perpendicular line is,
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].
Hope this helps :)
Answer:
[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]
Step-by-step explanation:
Part 1: Finding the new slope of the line
Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.
Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].
Part 2: Using point-slope formula and solving in slope-intercept form
Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].
Then, use the point-slope equation to get b, or the y-intercept of the equation.
[tex](y-y_{1})=m(x-x_{1})[/tex]
[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]
Why 200/3 doesn’t work
Answer:
it does work
i think u mean why is it not whole
but it is not a whole number
Step-by-step explanation:
200/3=66.6(6 is repeating)
for example if u have 200 chocolates and u give them to 3 people
everyone will have 66
and u will have 2 left
2/3 is also 0.66(6 repeating)
66+0.66(6repeating)
=66.66(6repeating0
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
-ZYLYNN JADE ARDENNE
Answer:
Step-by-step explanation:
it does not work as a whole number.
but it does work in simple division with fraction.
200 / 3 = 66 and [tex]\frac{2}{3}[/tex]
Identify the factors of x2 − 4x − 12.
(x + 4)(x − 3)
(x − 4)(x + 3)
(x − 2)(x + 6)
(x + 2)(x − 6)
Answer:
(x + 2)(x - 6)
Step-by-step explanation:
We are given the equation: x² - 4x - 12. Let's factor this.
First, look at the integer factor pairs of -12:
-1, 12
-2, 6
-3, 4
1, -12
2, -6
3, -4
We would like to find a pair whose sum is -4. Inspecting each pair, we realise that only the pair 2, -6 works because 2 + (-6) = -4.
Thus, our factors are:
x + 2 (from the 2)
x - 6 (from the -6)
The factored form of our given quadratic is:
(x + 2)(x - 6)
~ an aesthetics lover
If one number is five more than another number, and the smaller number is half of the larger number, what are the two numbers?
Answer:
Larger number = 10Smaller number = 5Step-by-step explanation:
Let larger number be x
Let smaller number be y
[tex]x = 5 + y[/tex]---> equation (i)
[tex]y = \frac{1}{2} x[/tex]
[tex]x = 2y[/tex]-----> equation (ii)
Equate equation (i) and (ii),
[tex]5 + y = 2y[/tex]
Move variable to L.H.S and change its sign:
Similarly, Move constant to R.H.S and change its sign
[tex]y - 2y = - 5[/tex]
[tex] - y = - 5[/tex]
The difference sign (-) will be cancelled on both sides
[tex]y = 5[/tex]
Putting the value of y in equation (ii) in order to find the value of X ( larger number)
[tex]x = 2y[/tex]
Plug the value of y
[tex] = 2 \times 5[/tex]
Calculate the product
[tex] = 10[/tex]
Hence,
Smaller number = 5
Larger number = 10
Hope this helps..
Best regards!!
Answer:
10 and 5
Step-by-step explanation:
Let the first number be x.
Let the second number be y.
x = 5 + y
y = 1/2x
Plug y as 1/2x in the first equation.
x = 5 + (1/2x)
Solve for x.
Subtract 1/2x on both sides.
x - 1/2x = 5 + 1/2x - 1/2x
1/2x = 5
Multiply both sides by 2.
2(1/2x) = 2(5)
x = 10
Plug x as 10 in the second equation.
y = 1/2(10)
Solve for y.
y = 5
x = 10
y = 5
The two numbers are 10 and 5.
10 is the larger number.
5 is the smaller number.
Which represents the value of c?
Which of the following is a correct tangent ratio for the figure?
Answer:
C) tan(39°) = 11/15
Step-by-step explanation:
SohCahToa
tangent = opposite / adjacent
The given angle is 39°. The angle directly opposite of 39° is 11 and the angle adjacent to 39° is 15.
Answer:
tan(39°) = 11∕15
Step-by-step explanation:
11) $ 8,000 is invested in an account that yields 6% interest per year. After how many years will the account be worth 13709.60$ if the interest is compounded monthly?
Answer:
[tex]\large \boxed{\sf \ \ 9\text{ years} \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all, a few remarks:
>>> 1 year is 12 months, right?
>>> Monthly compounding means that each month we compute the interest and they will be included in the investment for the next month.
>>> 6% is an interest per year, it means that to compute the interest for 1 month we need to compute by 6% multiplied by [tex]\dfrac{1}{12}[/tex]
Let's do it !
At the beginning, we have:
$8,000
After 1 month, we will have:
[tex]8000 + 8000\cdot \dfrac{6\%}{12}=8000\cdot (1+ \dfrac{6}{1200})= 8000\cdot (1+ \dfrac{1}{200})[/tex]
After 2 months, we will have:
[tex]8000\cdot (1+ \dfrac{1}{200})\cdot (1+ \dfrac{1}{200})=8000\cdot \left(1+ \dfrac{1}{200}\right)^2[/tex]
After n months, we will have
[tex]8000\cdot \left(1+ \dfrac{1}{200}\right)^n=8000\cdot \left(1.005\right)^n[/tex]
We are looking for n such that
[tex]8000\cdot \left(1.005\right)^n=13709.60\\\\ln(8000)+ n\cdot ln(1.005)=ln(13709.60)\\\\\\n = \dfrac{ln(13709.60)-ln(8000)}{ln(1.005)}=108[/tex]
So, we need 108 months to reach this amount, which means 108/12=9 years.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
6th grade math , help me please :)
Answer:B
Step-by-step explanation:
which of the binomials below is a factor of this trinomial? 8x^2 + 10x-3
Answer:
The factors are (4x-1) and (2x+3)
Step-by-step explanation:
The factors of 8x^2 + 10x -3 can be found by grouping terms
8x^2 - 2x + 12x - 3
2x (4x -1) + 3(4x-1)
(4x-1)(2x+3)
11. A certain brand of margarine was analyzed to determine the level of polyunsaturated fatty acid (in percent). A sample of 6 packages had an average of 16.98 and sample standard deviation of 0.31. Assuming normality, a 99% confidence interval for the true mean of fatty acid level is:
Answer: (16.47, 17.49)
Step-by-step explanation:
Formula for confidence interval for the true mean if population stanmdard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Two tailed critical value.
We assume that the level of polyunsaturated fatty acid is normally distributed.
Given,
n= 6
degree of freedom = n-1 =5
[tex]\overline{x}[/tex] = 16.98
s= 0.31
significance level[tex](\alpha)[/tex] =1-0.99=0.01
Two tailed t- value for degree of freedom of 5 and significance level of 0.01 = [tex]t_{\alpha/2}=4.0317[/tex] [by student's t-table]
Now , the 99% confidence interval for the true mean of fatty acid level is:
[tex]16.98\pm 4.0317(\dfrac{0.31}{\sqrt{6}})\\\\=16.98\pm 4.0317(0.126557)\\\\=16.98\pm 0.51024\\\\=(16.98-0.51023,\ 16.98+0.51023)\\\\=(16.46977,\ 17.49023)\approx (16.47,\ 17.49)[/tex]
Hence, a 99% confidence interval for the true mean of fatty acid level is: (16.47, 17.49)
Which expression is equivalent to the expression below? StartFraction 6 c squared + 3 c Over negative 4 c + 2 EndFraction divided by StartFraction 2 c + 1 Over 4 c minus 2 EndFraction StartFraction 3 c (2 c minus 1) Over 2 c + 1 EndFraction StartFraction negative 3 c (2 c + 1) squared Over 4 (2 c minus 1) squared EndFraction 3c –3c
Answer:
its D. -3c
Step-by-step explanation:
just took the test
The expression that is equivalent to the expression [(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)] is; -3c
The fraction we are given to work with is;[(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)]
Simplifying the fraction equation by factorization gives:[3c(2c + 1)/(-2(2c - 1))] ÷ [(2c + 1)/(2(2c - 1)]
Now, in division of fractions, we know that;3/2 ÷ 1/5 is the same as; 3/2 × 5/1
Applying this same method to our question gives;
[3c(2c + 1)/(-2(2c - 1))] × [(2(2c - 1)/(2c + 1)]
2(2c - 1) is common and will cancel out to get; 3c(2c + 1)/(-1/(2c + 1))2c + 1 is common and will cancel out to get; -3cRead more about simplification of fractions at;https://brainly.com/question/6109670