Answer:
The required sample size 'n' = 97 .41 hours
Step-by-step explanation:
Explanation:-
Given standard deviation of the Population 'σ' = 3 hours
Given the Margin of error = [tex]\frac{1}{2} hour[/tex]
The Margin of error is determined by
[tex]M.E = \frac{Z_{\frac{\alpha }{2} S.D} }{\sqrt{n} }[/tex]
Given level of significance ∝ = 0.10 or 0.90
Z₀.₁₀ = 1.645
[tex]\frac{1}{2} =\frac{1.645 X 3}{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]\sqrt{n} = 2 X 1.645 X 3[/tex]
√n = 9.87
Squaring on both sides, we get
n = 97.41 hours
Final answer:-
The required sample size 'n' = 97.41 hours
As part of a physics experiment, Ming drops a baseball from the top of a 315-foot building. To the nearest tenth of a second, for how many seconds will the baseball fall? (Hint: Use the formula h = 16t^2, which gives the distance h, in feet, that a free-falling object travels in t seconds.)
Answer: 4.4 seconds
Step-by-step explanation:
h(t) = -16t² + 315
Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0
0 = -16t² + 315
-315 = -16t²
[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]
Answer:
≈ 4.44 sec
Step-by-step explanation:
h= 315 ft
h= 16t²
315 = 16t²
t²=315/16
t=√315/16 ≈ 4.44 sec
Need help please :) thanks
In rhombus MNOP, mMNO = 24. What is the measure of PMO
A lumber company is making boards that are 2564.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 21 is made, and it is found that they have a mean of 2567.0 millimeters with a variance of 121.00. A level of significance of 0.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=21-1=20[/tex]
the p value for this case would be given by:
[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
Step-by-step explanation:
Information given
[tex]\bar X=2567[/tex] represent the mean height for the sample
[tex]s=\sqrt{121}= 11[/tex] represent the sample standard deviation
[tex]n=21[/tex] sample size
[tex]\mu_o =2564[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true mean is equal to 2564 mm, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2564[/tex]
Alternative hypothesis:[tex]\mu \neq 2564[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=21-1=20[/tex]
the p value for this case would be given by:
[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
Three kinds of tickets were sold for a concert. Child tickets are $6, adult tickets are $12, and student tickets are $8. A total of 204 tickets were sold, bringing in a total of $2,008. If 4 more adult tickets were sold than the total number of student and child tickets combined, how many student tickets were sold? Type in your numerical answer only; do not type any words or letters with your answer.
Answer:
The number of children's tickets sold =12The number of adult's tickets sold =100The number of student's tickets sold =92Step-by-step explanation:
Let the number of children's tickets sold =c
Let the number of adult's tickets sold =a
Let the number of student's tickets sold =s
A total of 204 tickets were sold, therefore: c+a+s=204
Child tickets are $6, adult tickets are $12, and student tickets are $8.
Total revenue =$2,008
Therefore:
6c+12a+8s-2008
We are also told that 4 more adult tickets were sold than the total number of student and child tickets combined.
c+s=a+4
We then solve the resulting system of equation.
c+a+s=2046c+12a+8s=2008c+s=a+4Substituting c+s=a+4 into the first equation
c+a+s=204
a+4+a=204
2a=204-4
2a=200
a=100
Substitute a=100 into the second and third equation
6c+12(100)+8s=2008
6c+8s=2008-1200
6c+8s=808
From the third equation
c+s=100+4
c=104-s
Substitute c=104-s into 6c+8s=808
6(104-s)+8s=808
624-6s+8s=808
2s=808-624
2s=184
s=92
Since c=104-s
c=104-92
c=12
Therefore:
The number of children's tickets sold =12The number of adult's tickets sold =100The number of student's tickets sold =92given a 60 month car loan at 4.71%, explain how much your monthly payments would be for a $18,400 car and what your TOTAL COST would be given that interest.
Answer:
$23161.10
Step-by-step explanation:
Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t
Step 1: Convert months to years
60 months/12 month/year = 5 years
Step 2: Plug in known variables
A = 18400(1 + 0.0471)^5
Step 3: Solve
When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.
Find the value of x for which line a is parallel to line b. 34 32 68 56
Answer
value of x is 34 degrees
Step-by-step explanation:
Someone please help ASAP
Answer:
[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]
Step-by-step explanation:
hello,
saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]
means that 1 is a root of this expression, so it comes
1+1-1-k=0
<=> 1-k=0
<=> k = 1
Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot
Answer:
[tex]x=2$\pm$\sqrt{42}[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]
Formula:
A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:
[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]
Where [tex]D= b^{2} -4ac[/tex]
Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]
a = 1
b = -4
c= -38
Calculating D,
[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]
Now, finding the roots:
[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]
So, the solution is:
[tex]x=2$\pm$\sqrt{42}[/tex]
Answer is A or the first one
What is the conjugate?
2x2 + √3
Answer: 2x²-√3
Step-by-step explanation:
Another way to say the conjugate is the opposite. All you have to do is to change the sign in the binomial, which is 2x²+√3. When you change the sign, it becomes 2x²-√3.
PLEASE I NEED HELP ASAP
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
A 11 gram sample of a substance that's
used to treat thyroid disorders has a k-
value of 0.1247.
Enter the correct answer.
N = Noekt
DONE
No = initial mass (at time t = 0)
ĐOO
t?
N = mass at time t.
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answer: 55.6 days
Step-by-step explanation:
[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]
represent 5 20 30 25 10 on a pie chart
Answer :
I have solved for the points.
Explanation :
Just get a protractor and plot out the angles into a circle. Starting with the largest angle.
Given a = 4 and b= -2, evaluate -Ib-al.
-2
-6
6
Explain how to translate the statement into an equation. Use n for the variable. Thirteen less than a number is four EXPLAIN:
start here
Answer:
13-n=4
Subtract both sides by 13
-n=-9
n=9
Step-by-step explanation:
13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you
A nighttime cold medicine’s label indicates the presence of 600 mg of acetaminophen in each fluid ounce of the drug. The FDA randomly selects 65 1-ounce samples and finds the mean content is 595 mg with a standard deviation of 20 mg. Is there evidence that the label is incorrect? Use a= .05.
Answer:
[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]
And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg
Step-by-step explanation:
Information given
[tex]\bar X=595[/tex] represent the sample mean
[tex]s=20[/tex] represent the sample standard deviation
[tex]n=65[/tex] sample size
[tex]\mu_o =600[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is different from 600 mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 600[/tex]
Alternative hypothesis:[tex]\mu \neq 600[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]
And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg
Find the distance from the point (1, 4) to the line y = 1/3x – 3. A) 2(square root) 10 units B) 4 units C) 4(square root) 2 units D) 20 units
Answer:
Distance between line and point =
4√5 -3/2√10
Step-by-step explanation:
Distance between the line is
= √ ((9-0)²+(0+1)²)
= √ (89+1)
= √90
= 3√10
Half of the line = 3/2√10
Distance of one side of the line and the point.
= √((9-1)²+(0-4)²)
= √((8)²+(-4)²)
=√64+16
= √80
= 4√5
Distance between line and point =
4√5 -3/2√10
Answer: 2 square root 10 units
Step-by-step explanation: A
Evaluate f(x) = x2 + 1 for f(-1)
Answer: -1
Step-by-step explanation:
to calculate f(-1), you know that x = -1. so all you have to do is substitute:
f(-1) = (-1)2 + 1
f(-1) = -2 + 1
f(-1) = -1
Answer:
0
Step-by-step explanation:
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm.Use function notation to complete the following tasks
a. Represent the area (in square cm) of a circle whose radius is 4 cm.
b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm.
Answer:
(a)f(4) square cm.
(b)f(10.91)-f(10.9) Square centimeter.
Step-by-step explanation:
f(r)=the area of a circle (in square cm) that has a radius of r cm.
(a)Area (in square cm) of a circle whose radius is 4 cm.
Since r=4cm
Area of the circle = f(4) square cm.
(b) When the radius of the increases from 10.9 to 10.91 cm.
Area of the circle with a radius of 10.91 = f(10.91) square cm.Area of the circle with a radius of 10.9 = f(10.9) square cm.Change in the Area = f(10.91)-f(10.9) Square centimeter.
Which table shows the correct methods used to justify the solution steps?
3 (x minus 5) + 7 x = 65
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, distributive property, addition property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, combine like terms, addition property of equality, division property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, addition property of equality, combine like terms division property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, addition property of equality, distributive property.
Answer:
B.
Step-by-step explanation:
The correct table that shows the justified solution steps is the second table.
The correct option is B.
The correct table that shows the justified solution steps is:
A 2-column table with 4 rows.
Column 1: Solution step
3x - 15 + 7x = 65
10x - 15 = 65
10x = 80
x = 8
Column 2: Method to Justify
Distributive property
Combine like terms
Addition property of equality
Division property of equality
In this table, the solution steps are correctly listed in the first column, showing the step-by-step process of solving the equation. The methods to justify each step are accurately provided in the second column, demonstrating the mathematical properties used at each stage.
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A stock lost 7 1/8 points on Monday and then another 1 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stock for these three days?
Answer:
It was gained 4 1/4 points.
Step-by-step explanation:
- 7 1/8 - 1 5/8 + 13 = - 8 6/8 + 13 = - 8 3/4 + 13 = - 8 - 3/4 + 12 + 4/4 = 4 1/4
Given: AD≅ BC and AD ║ BC Prove: ABCD is a parallelogram. Assemble the proof by bragging tiles to the statements and reasons column.
Answer:
Step-by-step explanation:
A parallelogram is a quadrilateral with congruent opposite sides and pair of opposite angles.
Given: parallelogram ABCD
AD≅ BC
AD ║ BC
Thus;
<ABC + DAB = [tex]180^{o}[/tex] (supplementary angle property)
ΔABD = ΔCBD (each diagonal divides a parallelogram into two congruent triangles)
<ABC = <ADC (both pairs of opposite angles are congruent)
<DAB = <BCD (both pairs of opposite angles are congruent)
AB ≅ CD (opposite sides are congruent)
AB ║ DC (pair of opposite sides are parallel)
Therefore, the quadrilateral ABCD is a parallelogram.
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
This is algebra solving linear equations
P+7/20=19/20
Answer:
P = [tex]\frac{19}{7}[/tex] or the decimal answer is 2.71
Step-by-step explanation:
the equation of straight line passing through the point (2,3)&perpendicular to the line 4x-3y=10 is
Answer:
4y = -3x +18
Step-by-step explanation:
Let's get the gradient from this line equation first.
4x-3y=10
4x-10=3y
Y= 4/3x -10/3
The gradient is 4/3.
For a line perpendicular to another line.
M*M'= -1
M= -/(4/3)
M = -3/4
So the gradient to be used is -3/4
Formula for solving is
(Y-y1)/(x-x1)= M
X1= 2
Y1= 3
M = -3/4
(Y-y1)/(x-x1)= M
(Y-3)/(x-2)= -3/4
4(y-3)= -3(x-2)
4y -12 = -3x +6
4y = -3x +18
Can someone help me please
Answer:
Option (2)
Step-by-step explanation:
The given table represents the relation between the velocity and the time for an object is falling under the gravity.
Change in velocity with respect to time is directly proportional so the change is linear.
Acceleration due to gravity of this object is defined by the slope of the line joining the ordered pairs given in the table.
Let the two points lying on the line are (0, 0) and (1, 9.8)
Slope of the line passing through two points = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
= [tex]\frac{9.8-0}{1-0}[/tex]
= 9.8 [tex]\frac{m}{s^{2} }[/tex]
Option (2) will be the answer.
Jose can assemble 12 car parts in 40 minutes. How many minutes
would be needed to assemble 9 parts7
Answer:
12/40=0.3
0.3 car parts per minute
9 / 0.3 = 30 minutes
30 minutes for 9 parts
Hope this helps
Step-by-step explanation:
Jose required 30 minutes to assemble 9 parts.
Jose assemble 12 car parts in 40 minutes. Time consumed by jose to assemble 9 parts to be calculated.
In mathematics it deals with numbers of operations according to the statements.
Here,
40 minute = 12 parts
40/12 = 1 part
Time to assemble 9 parts: = 40/12 x 9
= 10/3 x 9
= 30
Thus, Jose required 30 minutes to assemble 9 parts.
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Which will provide the largest yield on an annuity after 30 years with 6% annual interest, compounded monthly? Annuity A: Deposit $2400 per year. Annuity B: Deposit $600 per quarter. Annuity C: Deposit $72,000 one lump sum.
Answer:
Annuity C: Deposit $72,000 one lump sum
Step-by-step explanation:
The yield is improved when the money is on deposit for a longer period.
If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.
If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.
Annuity C will provide the largest yield.
7th grade math I need help with this
Answer:
each bag of candy is $6.00
Step-by-step explanation:
1 bag would cost $6.00
1×$6.00=$6.00
6 bags × $6.00 = $36.00
Answer:
the constant of proportionally is 6
the prices of 6 bags of candy is 36
Step-by-step explanation:
to find the constant u divide 6 by 1 to find how they multiplying it by
the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36
hope this helps
Pls and thank u i need help
Answer: see table below
Step-by-step explanation:
Simply add the digit on the left to the digit on the top
1, 2 --> 1 + 2 = 3
3, 4 --> 3 + 4 = 7
4, 2 --> 4 + 2 = 6
6, 6 --> 6 + 6 = 12
[tex]\begin{array}{c|c|c|c}&\underline{\quad 2\quad }&\underline{\quad 4\quad }&\underline{\quad 6\quad }\\\underline{\quad 1 \quad}&\bold{\underline{\quad 3\quad}}&\underline{\quad 5\quad}&\underline{\quad 7\quad}\\\underline{\quad 2 \quad}&\underline{\quad 4\quad }&\underline{\quad 6\quad }&\underline{\quad 8\quad}\\\underline{\quad 3 \quad}&\underline{\quad 5\quad }&\bold{\underline{\quad 7\quad}}&\underline{\quad 9\quad}\\\end{array}[/tex]
[tex]\begin{array}{c|c|c|c}{\underline{\quad 4 \quad}&\bold{\underline{\quad 6\quad }}&\underline{\quad 8\quad }&\underline{\quad 10\quad }\\\underline{\quad 5 \quad}&\underline{\quad 7\quad}&\underline{\quad 9\quad}&\underline{\quad 11\quad}\\\underline{\quad 6 \quad}&\underline{\quad 8\quad }&\underline{\quad 10\quad }&\bold{\underline{\quad 12\quad}}\\\end{array}[/tex]
Which expression are equivalent to 4m-2+(-8m)
Answer:
combine 4m -8m to get -4m
[tex] - 4m - 2[/tex]
Answer:
− 4m-2
Step-by-step explanation: