Answer:
125 times
Step-by-step explanation:
30x5=150
25x5=125
In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6. Assume the population standard deviation is 5.8 hours. Find the 98% confidence interval for the population mean.
a. (17.5, 21.7)
b. (14.1, 23.2)
c. (18.3, 20.9)
d. (19.1, 20.4)
Answer:
[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]
[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]
And the best option for this case would be:
a. (17.5, 21.7)
Step-by-step explanation:
Information given
[tex]\bar X= 19.6[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma= 5.8[/tex] represent the population deviation
n=42 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom, given by:
[tex]df=n-1=42-1=41[/tex]
Since the Confidence is 0.98 or 98%, the significance would be [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.1[/tex], and the critical value would be [tex]t_{\alpha/2}=2.42[/tex]
Replacing we got:
[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]
[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]
And the best option for this case would be:
a. (17.5, 21.7)
Answer:
The 98% confidence interval for the population mean is between 17.5 hours and 21.7 hours.
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = ln(x), [1, 5]
Answer:
Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]
Step-by-step explanation:
We are given that a function
[tex]f(x)=ln(x)[/tex]
Interval [1,5]
The given function is defined on this interval.
Hypothesis of Mean Value Theorem:
(1) Function is continuous on interval [a,b]
(2)Function is defined on interval (a,b)
From the graph we can see that
The function is continuous on [1,5] and differentiable at(1,5).
Hence, the function satisfies the hypothesis of the Mean Value Theorem.
can someone help me with this please?!?
Answer:
The answer is 60cm^2.
hope it helps..
simplity 1-5(3 + 2-3)?
Answer:
-9
Step-by-step explanation:
1 - 5 (3 + 2 - 3)
1 − 5 ( 5 − 3 )
1 - 5 x 3
1 - 10
-9
Nina had 17 marbles in a bag. Her mother put a handful of marbles in the bag. When Nina counts her marbles, she discovers she now has 34 of them. Which of the following equations will help Nina solve for the number of marbles, m, that her mom put in the bag? 17 + 34 = m 17 + m = 34 17m = 34 m − 17 = 34
Answer:
17+m=34
Step-by-step explanation:
Nina had 17 marbles in a bag + the x amount of marbles that her mom gives her.
so 17+x=34
(x is the variable that I chose however it could be any variable, so it would also mean the same thing as 17+m=34)
Hope this helped!
Answer:
17 + m = 34.
Step-by-step explanation:
Nina had 17 marbles;
Mother put a handful of marbles, let's say m.
Now Nina has 34 marbles.
34 marbles is [=] 17 marbles Nina had before + m from her mother.
17 + m = 34 will be the right equation.
17 + 34 = m — wrong;17 + m = 34 — right;17m = 34 — wrong;m - 17 = 34 — wrong.www.g "You roll a fair six-sided die twice. Find the probability of rolling a 4 the first time and a number greater than 3 the second time."
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?
a.positive
b.zero
b.negative
c.undefined
Answer:
B. zero
Step-by-step explanation:
If the temperature is supposed to remain constant over time (the same) when working properly, then this means that there is no increase or decrease over time.
If there were a line to represent this, then it would be a straight line with a slope of 0 because the temperature would remain the same.
Please help asap!!!!!!!
Answer:Yes indeed!
Step-by-step explanation:
Your right!
Not sure of how I would solve this
A concession-stand manager buys bottles of water and soda to sell at a football game. The manager needs to buy a total of 4,500 drinks and have 25% more water than soda. Let w be the number of bottles of water and let s be the number of bottles of soda. Create a system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to bu
Answer: The equations are
w + s = 4500
2.25s = 4500
Step-by-step explanation:
Let w represent the number of bottles of water that the football manager bought.
Let s represent the number of bottles of soda that the football manager bought.
The manager needs to buy a total of 4,500 drinks. This means that
w + s = 4500
He also needs to have 25% more water than soda.
25% of soda = 25/100 × s = 0.25s
25% more of water than soda = s + 0.25s = 1.25s
The equation would be
1.25s + s = 4500
2.25s = 4500
The time to assemble the first unit on a production line is 8 hours. The learning rate is 0.81. Approximately how long will it take for the seventh unit to be assembled?
Answer:
4.428 hours
Step-by-step explanation:
If the learning rate is 0.81, the slope of the learning curve is:
[tex]b=\frac{ln(0.81)}{ln(2)} \\b=-0.304[/tex]
The time it takes to produce the n-th unit is:
[tex]T_n=T_1*n^b[/tex]
If T1 = 8 hours, the time required to produce the seventh unit will be:
[tex]T_n=8*7^{-0.304}\\T_n=4.428\ hours[/tex]
It will take roughly 4.428 hours.
what is the value of -x+ the absolute value of -y
Answer:
[tex]-x+| \: y\: |[/tex]
Step-by-step explanation:
[tex]-x+|-y|[/tex]
[tex]\mathrm{Apply\:absolute\:rule}: \left|-y\right|\:=| \: y\: |[/tex]
[tex]-x+| \: y\: |[/tex]
The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish from each of the 53 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have different mercury than the allowable amount?
Required:
State the random variable, population parameter, and hypotheses.
Answer:
Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.
The population parameter is the mean amount of mercury in the bass fish of Florida lakes.
The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.
The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
Step-by-step explanation:
The question is incomplete.
There is no data provided.
We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.
This is a hypothesis test for the population mean.
The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=53.
The sample mean is M=0.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=53-1=52[/tex]
This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The sum of Joe's and Sheila's ages is 115. Fourteen years ago, Joe was twice as old as Sheila. How old is Sheila now?
Answer: Sheila today = [tex]46\dfrac{1}{3}[/tex] yrs old
Step-by-step explanation:
J + S = 115 v⇒ J = 115 - S
Current Ages Ages 14 years ago
Joe (J) = 115 - S J - 14 = 2(S - 14)
Sheila (S) = S
Substitute J = 115 - S into the "14 years ago" equation
J - 14 = 2(S - 14)
(115 - S) - 14 = 2(S - 14)
111 -S = 2S - 28
111 = 3S - 28
139 = 3S
46 [tex]\frac{1}{3}[/tex] = S
It is odd that the result was not an integer. I wonder if you meant to type "Joe was twice as old as Sheila is today. That would change the equation to:
J - 14 = 2S
111 - S = 2S
111 = 3S
37 = S
Can somebody please help me with this question?
Answer: 6x^2
Step-by-step explanation:
The area of a triangle is 1/2bh
Thus, simply multiply 2x*3x = 6x^2
Hope it helps <3
Answer:
[tex]3 {x}^{2} [/tex]Solution,
Base(b)= 3x
Height(h) = 2x
Now,
Finding the area of triangle:
[tex] \frac{1}{2} \times b \times h[/tex]
[tex] \frac{1}{2} \times 3x \times 2x[/tex]
[tex] \frac{1}{2} \times 6 {x}^{2} [/tex]
[tex]3 {x}^{2} [/tex]
Hope this helps....
Good luck on your assignment....
Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system.
(1 -4 4 0 -2
0 2 -6 0 5
0 0 1 2 - 4
0 0 4 5 -1]
(Type an integer or a simplified fraction)
A. Replace row 4 by its sum with - 4 times row 3.
(Type an integer or a simplified fraction)
B. Replace row 2 by its sum with times row 4.
(Type an integer or a simplified fraction.)
C. Interchange row 3 and row 2.
Answer:
The correct option is (A)
A. Replace row 4 by its sum with - 4 times row 3.
[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]
w = 8
x = 17/2
y = 6
z = -5
Step-by-step explanation:
The given matrix is
[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&4&5&-1\end{array}\right][/tex]
To solve this matrix we need to create a zero at the 4th row and 3rd column which is 4 at the moment.
Multiply 3rd row by -4 and add it to the 4th row.
Mathematically,
[tex]R_4 = R_4 - 4R_3[/tex]
So the correct option is (A)
A. Replace row 4 by its sum with - 4 times row 3.
So the matrix becomes,
[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]
Now the matrix may be solved by back substitution method.
Bonus:
The solution is given by
Eq. 1
-3z = 15
z = -15/3
z = -5
Eq. 2
y + 2z = -4
y + 2(-5) = -4
y - 10 = -4
y = -4 + 10
y = 6
Eq. 3
2x - 6y + 0z = 5
2x - 6(6) = 5
2x - 12 = 5
2x = 12 + 5
2x = 17
x = 17/2
Eq. 4
w - 4x + 4y + 0z = -2
w - 4(17/2) + 4(6) = -2
w - 34 + 24 = -2
w - 10 = -2
w = -2 + 10
w = 8
pls help help help hepl
Answer:
C
Step-by-step explanation:
undefined slope means tat the denominator=0 in the equation
m=y2-y1/x2-x1
A: m=-1-1/1+1=-2
B;2-2/2+2=0
C: 3+3/-3+3 = 6/0 undefined
D: 4+4/4+4=1
two bags contains 10 balls each. Every round you choose with equal probability one of the two bags and pick out a ball. After a while, you choose an empty ball. What is the probability for the other bag to contain exactly 4 balls at that time？
Answer:
6.10%
Step-by-step explanation:
For every round since we are choosing with equal probability, then the probability of choosing from either of the bags is 1/2
Here, this scenario is only possible when a particular bag has been chosen 10 times and the other bag has been chosen 6 times ( meaning a particular bag has been emptied and for a particular bag to be emptied, all of its content would have been picked)
Now on the 17th trial, an empty bag is chosen
Therefore the required probability will be;
16C0 * (1/2)^10 * (1/2)^6 * 1/2 = 0.0610 = 6.1%
If x=3 then what is y the equation is 2x -y=5 if you have the answer lets d a t e I m f e m a l e. T a n g ie_man 18 snap without spaces.
Answer:
y = 1Step-by-step explanation:
Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;
[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]
Hence, the value of y is 1
What is the greatest common factor of 36 and 44?
Answer:
GCF - 4
Step-by-step explanation:
36 - 1, 2, 3, 4, 6, 9, 12, 18, 36
44 - 1, 2, 4, 11, 44
Hope this helps! :)
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc)
Answer:
GOOGLE :)
equation:
y=mx+b
m= slope (how steep the line is(negative is \ positive is /))
b= y intercept (where it is on the vertical line(up and down line))
step by step
1. locate y intercept and plotthe point
2.from that point use slop to find second point and plot
Identify the parts (include: terms, coefficients, variables and
constants) of the following expression and translate it into a
verbal expression:
2(3x - 2y) + 7
Answer:
x=9
Step-by-step explanation:
3x subtracted by 2y
is 1 then 1 multiplied by 2 is 2 then 7 + 2 is 9
PEMDAS
I already completed part 1 as pictured, I need help solving part 2. Part 2: (c) How many new homes were completed in the 12-month period through January 2011, and how did that compare to the number of new homes started in 2010? If necessary, round your answer to the nearest whole number. In the 12 month period through January 2011, there were 423,831 new homes completed, which was _________ fewer OR more than the number of new homes in 2010.
Answer:
423,831104,840 fewerStep-by-step explanation:
Given:
281,000 homes sold through Jan 2011 was 66.3% of homes completed
378,000 homes was a 28.5% decrease from starts in 2010
Find:
(i) Homes completed in 12 months through Jan 2011
(ii) Comparison to homes started in 2010
Solution:
(i) Using the given relation, we can find homes completed through Jan 2011.
281,000 = 0.663×completed
completed = 281,000/0.663 = 423,831
__
(ii) Similarly, we can find the number of 2010 starts:
starts(1 -28.5%) = 378,000
starts = 378,000/0.715 = 528,671
The relation of completions in 2011 to starts in 2010 is ...
423,831 -528,671 = -104,840
__
Through Jan 2011, there were 423,831 homes completed, which was 104,840 fewer than the number of starts in 2010.
_____
Comment on your question
Your problem statement supplies the answer to the first question in 2(c). Part 1(b) tells you the relation between starts in 2011 and in 2010, so you can easily figure starts in 2010 from your answer to that question.
help asapppp....thanks
Answer:
a) -8x^3 + x^2 + 6x
b)16x^2 -9
c) 24x^4 + 37x^3 +13x^2 -18x
Step-by-step explanation:
a) distribute -2x to x and 4x^2 then do the same for the other part and then add the ones w the same exponent.
b) do foil ( multiply first outside inside last) which will be 4x times 4x then 4x times 3 then -3 times 4x and 3 times -3. add like exponents
c) do the same as above
Suppose you invest $ 2,000 at 45% Interest
compounded daily. F(t) represents value of investments
in t years
A) Find equation For F(+)
B) use equation to find how much account will
be worth in 30 years round to nearest cent
C) How much you should invest now in
order to have 14.000 in 9 years round to the nearest cent
Answer:
You will have $29,000 in 30 years, and you need to start with about $2,772.28 to make $14,000 in 9 years
Step-by-step explanation:
To find the total investment use the equation [tex]A = P(1 + rt)[/tex]
Where A equals total investment, P is your start investment, r is your rate, and t is time.
[tex]A=2,000(1+(0.45 * 30))[/tex]
[tex]A=2,000(1+13.5)[/tex]
[tex]A=2,000*14.5[/tex]
[tex]A=29,000[/tex]
To find the start investment use the equation [tex]P = A / (1 + rt)[/tex]
[tex]P=14,000/(1+(0.45*9))[/tex]
[tex]P=14,000/(1+4.05)[/tex]
[tex]P=14,000/5.05[/tex]
[tex]P=2,772.28[/tex]
Given: y ll z
Prove: m25+ m2 2 + m26 = 180°
L
A
M
1
2
3
y
4
5
6
7
Z
С
B
Assemble the proof by dragging ties to
the Statements and Reasons columns.
Answer:
As per the properties of parallel lines and interior alternate angles postulate, we can prove that:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Step-by-step explanation:
Given:
Line y || z
i.e. y is parallel to z.
To Prove:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Solution:
It is given that the lines y and z are parallel to each other.
[tex]m\angle 5, m\angle 1[/tex] are interior alternate angles because lines y and z are parallel and one line AC cuts them.
So, [tex]m\angle 5= m\angle 1[/tex] ..... (1)
Similarly,
[tex]m\angle 6, m\angle 3[/tex] are interior alternate angles because lines y and z are parallel and one line AB cuts them.
So, [tex]m\angle 6= m\angle 3[/tex] ...... (2)
Now, we know that the line y is a straight line and A is one point on it.
Sum of all the angles on one side of a line on a point is always equal to [tex]180^\circ[/tex].
i.e.
[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ[/tex]
Using equations (1) and (2):
We can see that:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Hence proved.
Answer: yes
Step-by-step explanation: yes
Follow the properties of the equality given for the steps to solve the following equation:
-3(x-4)+5=-x-3
(answers and steps in photo)
Answer:
Step-by-step explanation:
-3x+12+5= -x-3 -3x+17 = -x-317 = 2x-320 =2xx=10Question 1 of 16,
The area of a trapezoid is 189 cm . The height is 14 cm and the length of one of the parallel sides is 8 cm. Find the length of the second parallel side.
Answer:
19cm
Step-by-step explanation:
The area of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).
Given:
Area = 189 Square cm
Height, h=14cm
a=8cm
We want to find the value of the other parallel side, b.
Substitution of the given values gives:
[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]
The length of the second parallel side is 19cm.
The valve was tested on 250 engines and the mean pressure was 7.3 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 7.2 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answe
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 7.2
For the alternative hypothesis,
H1: µ ≠ 7.2
This is a two tailed test.
Since the population standard deviation is given, the test statistic would be the z score determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 7.2
x = 7.3
σ = 0.8
n = 250
z = (7.3 - 7.2)/(0.8/√250) = 1.976
Test statistic is 1.976
Please help meeeeeeeee
Answer:
The lines will intersect infinitely many times, because they are identical.
Step-by-step explanation:
Let's change the equations of the lines into (y=mx+b) form.
6x-4y=2 Divide by 2.
3x-2y=1 Move x and divide by -2.
-2y=1-3x ---> y= -1/2+3/2x
The equation of the first line is y=3/2x- 1/2
-2y+3x=1
-2y=1-3x
y = 3/2x -1/2
The equation of the second line is y = 3/2x- 1/2.
The lines are identical- infinitely many intersections.
Step-by-step explanation:
I think the answer is third because it doesn't has a solution.