Answer:
The answer is below
Step-by-step explanation:
a) For a normal model the sample size has to be equal or greater than 30 so that it can be a normal distribution.
b) Given that:
μ = 11.2 minutes, σ = 4.8 minutes, n = 45
The z score determines how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For x < 10 minutes
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.8/\sqrt{45} }= -1.68[/tex]
Therefore from the normal distribution table, P(x < 10) = P(z < -1.68) = 0.0465
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of. ... by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. ... How many square inches of wrapping paper were left over?
Answer:
380 square inches or 380 in²
Step-by-step explanation:
We are given 2 parameters in the question
A rectangular prism and a rectangular wrapping paper.
To solve the question above, we have to find the areas of these two parameters.
a) Formula for the area of the Rectangular Prism = 2(WL+ HL + HW)
The Rectangular Prism has the dimensions of Length × Width × Height = 8 inches by 9 inches by 10 inches
Where
L = Length = 8 inches
W = Width = 9 inches
H = Height = 10 inches
Area of the Rectangular Prism = 2[(9 × 8) + (10 × 8) + (9 × 10)]
= 2(72 + 80 + 90)
= 2(242)
= 484 in²
b) Formula for the area of a Rectangular shaped wrapping paper
= Length × Breadth
The wrapping paper has measurements of:
2 feet by 3 feet
Since the dimensions of the rectangular prism is in inches, we have to convert that of the rectangular prism to inches as well
1 foot = 12 inches
2 feet = 2 × 12 inches = 24 inches
3 feet = 3 × 12 inches = 36 inches
Area of the Rectangular shaped wrapping paper = Length × Width
= 24 in × 36 in
= 864 in²
The amount of square inches of wrapping paper left.
= Area of Rectangular wrapping paper - Area of Rectangular prism
= 864 in² - 484 in²
= 380 in²
c.
What is the capacity of the airplane?
An airplane is carrying 180 passengers. This is 9/10 of the capacity of the airplane. What is the capacity of the airplane?
Answer:
the capacity of the airplane be 200 passengers
Step-by-step explanation:
According to the question, the data provided is as follows
Number of passengers in an airplane = 180
Capacity = [tex]\frac{9}{10}[/tex]
Based on the above information
Let us assume the capacity of the airplane be x
So the equation would be
[tex]\frac{9}{10} \times x = 180\\\\\\x = \frac{1,800}{9}[/tex]
So x = 200
Therefore the capacity of the airplane be 200 passengers
We simply applied the above equation so that the capacity of the airplane could come
How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one quarter as long as I walked? Translate into expression, I will award brainiest!
Answer:
21h
Step-by-step explanation:
we know that
Speed = distance / time, and as such
distance = speed * time
From the question, we are given that ...
He biked for h hrs -> b
He walked for 2 * b = 2h -> w
He ran for (1/4)(w) = 1/4 * 2h = 1/2 h -> r
The total distance traveled will then be
total distance = distance biked + distance walked + distance ran
recall that we stated that
d = s * t, now we'd apply that here
distance biked = 10 * h = 10h
distance walked = 3 * 2h = 6h
distance ran = 10 * 1/2h = 5h
total distance = 10h + 6h + 5h
Total distance = 21h
Write the equation of the line that contains (8,0) and is parallel to the line -3x+4y=4
Answer:
y = (3/4)x - 6
Step-by-step explanation:
if line is parallel to -3x + 4y = 4, that means that they both have the same slope
Slope of that second line is 3/4.
now time to find the y-intercept
0 = 3/4*8 + b
therefore, b = -(3/4)*8 = -3*2 = -6
Therefore, equation of line is y = (3/4)x - 6
Bob decided to go to college, the cost of going to school will be $4,474 per semester, (there are 2 semesters per year) plus $389 per semester for books. His degree will take 4 years. If he wants to pay off his investment in 10 years or less what is the minimum increase in yearly salary he would need to earn upon finishing his degree.
Answer:
Step-by-step explanation:
1 semester = 4474
8 semester = 8* 4474 35792
1 semester books = 389
8 semester books = 8* 389 3112
Total 38904
If he is going to pay this off in 10 years, he would have to have an increase of 3890.40 (after all income taxes) to pay it off. Fewer years would mean dividing by the number of years.
So for 8 years for example, he would need 4863 every year.
That number is obtained by dividing 38904 / 8
In 6 years he would need
38904/6 = 6484 extra dollars.
Answer:
Answer is C. $11,700
Step-by-step explanation:
Zoom In
In Exercises 1-4, use the figure shown. Find the length of each segment.
U
-6-5-4-3-2-1
0
1
2 3
4 5
6 7
8
1. RS =
2. RT =
3. ST
4. RU=
oooo
For Exercises 5-7, use the figure shown.
5. What is PQ?
6. What is QR?
7. What is PR?
Points A, B, C, and D on the figure below are collinear. Use the figure for
Exercises 8 and 9
A
3x
4x
13
8. If AC = 24, what is AB?
9. If BC = 15, what is BD?
Use the figure shown for Exercises 10-13.
10. What is m_PTR?
11. What is m_PTQ?
12. What is m2QTS?
13. Understand Luis said that m2 QTR = 80
Explain Luis's error
Answer/Step-by-step Explanation:
When calculating the length of a segment on a number line, the absolute value of the difference between one point on the numberline, and another point is what we're looking for.
1. Length of RS = |-5 - (-2)| = |-5 + 2| = |-3|
RS = 3
2. Length of RT = |-5 - 2| = |-7|
RS = 7
3. Length of ST = |-2 - 2| = |-4|
ST = 4
4. Length of RU = |-5 - 8| = |-13|
RU = 13
5. Given that the following coordinates:
P = 3
Q = 8
R = 14
5. PQ = |3 - 8| = |-5| = 5
6. QR = |8 - 14| = |-6| = 6
7. PR = |3 - 14| = |-11| = 11
Given that points A, B, C, and D are collinear, and AB = x, BC = 3x, CD = 4x - 13
8. If AC = 24,
BC can be calculated as follows:
AB + BC = AC
[tex] x + 3x = 24 [/tex]
Solve for x
[tex] 4x = 24 [/tex]
Divide both sides by 4
[tex] x = 6 [/tex]
Thus,, BC = 3x = 3(6) = 18
BC = 18
9. If BC = 15, BD can be calculated as follows:
Find the value of x first
BC = 3x
15 = 3x
Divide both sides by 3
5 = x
x = 5.
BD = [tex] 3x + (4x - 13) [/tex]
Plug in the value of x
BD = [tex] 3(5) + (4(5) - 13) = 15 + (20 - 13) [/tex]
BD = [tex] 15 + 7 = 22 [/tex]
BD = 22
10. m<PTR = 80° (taking the reading at the top from 0°)
11. m<PTQ = 45°
12. m<QTS = 128 - 45 = 83°
13. Luis read m<QTR wrongly, what he measured was the whole of <PTR.
According to the angle addition theorem, m<QTR = 80 - 45 = 35°.
For each of the following vector fields
F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potentialfunction f (that is, ∇f = F) with f(0,0)=0. If it is not conservative, type N.
A. F(x,y)=(−16x+2y)i+(2x+10y) j f(x,y)= _____
B. F(x,y)=−8yi−7xj f(x,y)=_____
C. F(x,y)=(−8sin y)i+(4y−8xcosy)j f(x,y)=_____
(A)
[tex]\dfrac{\partial f}{\partial x}=-16x+2y[/tex]
[tex]\implies f(x,y)=-8x^2+2xy+g(y)[/tex]
[tex]\implies\dfrac{\partial f}{\partial y}=2x+\dfrac{\mathrm dg}{\mathrm dy}=2x+10y[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy}=10y[/tex]
[tex]\implies g(y)=5y^2+C[/tex]
[tex]\implies f(x,y)=\boxed{-8x^2+2xy+5y^2+C}[/tex]
(B)
[tex]\dfrac{\partial f}{\partial x}=-8y[/tex]
[tex]\implies f(x,y)=-8xy+g(y)[/tex]
[tex]\implies\dfrac{\partial f}{\partial y}=-8x+\dfrac{\mathrm dg}{\mathrm dy}=-7x[/tex]
[tex]\implies \dfrac{\mathrm dg}{\mathrm dy}=x[/tex]
But we assume [tex]g(y)[/tex] is a function of [tex]y[/tex] alone, so there is not potential function here.
(C)
[tex]\dfrac{\partial f}{\partial x}=-8\sin y[/tex]
[tex]\implies f(x,y)=-8x\sin y+g(x,y)[/tex]
[tex]\implies\dfrac{\partial f}{\partial y}=-8x\cos y+\dfrac{\mathrm dg}{\mathrm dy}=4y-8x\cos y[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy}=4y[/tex]
[tex]\implies g(y)=2y^2+C[/tex]
[tex]\implies f(x,y)=\boxed{-8x\sin y+2y^2+C}[/tex]
For (A) and (C), we have [tex]f(0,0)=0[/tex], which makes [tex]C=0[/tex] for both.
Calculate the expected value of the given random variable X. This exercise assumes familiarity with counting arguments and probability. (Round your answer to one decimal place.) X is the number of green marbles that Suzan has in her hand after she selects seven marbles from a bag containing six red marbles and five green ones.
Answer:
The expected value of:
X = 3 green marbles
Step-by-step explanation:
Number of marbles in a bag = 11
Make-up of the bag = 6 red and 5 green marbles
Sussan selects 7 marbles from the bag
The probability of collecting from 5 of the green marbles = 0.45
The probability of collecting from 6 of the red marbles = 0.55
The expected value of X = the probability of selecting a green marble multiplied by the number of marbles selected
= 0.45 x 7
= 3 green marbles
how do i solve this absolute value equation |x-2| + 5 = 2?
Answer:
No solutions
Step-by-step explanation:
First, isolate the absolute value:
|x-2| + 5 = 2
|x - 2| = -3
An absolute value can never equal to a negative number
So, there are no solutions
Write the rational number 0.3 in the form ab , where a and b are integers.
Answer:
[tex]\frac{a}{b} = \frac{3}{10}[/tex]
Step-by-step explanation:
Given
[tex]Number = 0.3[/tex]
Required
Represent as [tex]\frac{a}{b}[/tex]
Let [tex]\frac{a}{b} = 0.3[/tex]
This can be further written as
[tex]\frac{a}{b} = \frac{0.3}{1}[/tex]
Multiply the numerator and denominator by 10
[tex]\frac{a}{b} = \frac{0.3 * 10}{1 * 10}[/tex]
[tex]\frac{a}{b} = \frac{3}{10}[/tex]
Since 3 and 10 are both integers, then
[tex]\frac{a}{b} = \frac{3}{10}[/tex]
Which number line models this expression? -2+2
solve the system of equations below
5x+2y=9
2×-3y=15
Answer:
The solution is (3, -3)
Step-by-step explanation:
5x + 2y = 9
2x - 3y = 15
Use elimination by addition/subtraction. Multiply the first equation by 3 and the second by 2, obtaining:
15x + 6y = 27
4x - 6y = 30
----------------------
19x = 57
This yields x = 3.
Substituting 3 for x into 5x + 2y = 9, we get 5(3) + 2y = 9, or
15 + 2y = 9, or
2y = -6
This yields y = -3.
The solution is (3, -3)
16 equals 9x + 4 - 5x solve for x
Answer:
x = 3
Step-by-step explanation:
Step 1: Write out equation
16 = 9x + 4 - 5x
Step 2: Combine like terms
16 = 4x + 4
Step 3: Subtract 4 on both sides
12 = 4x
Step 4: Divide both sides by 4
3 = x
Step 5: Rewrite
x = 3
if four tires can be changed in 3/4 of an hour gow long would it take to change 19 cars
Answer:
14.25 hours
Step-by-step explanation:
Four tires = 3/4 of an hour
=> 1 car = 3/4 of an hour
=> 19 cars = ?
=> If 1 = 3/4
=> 19 = 3/4 x 19
=> 3/4 x 19
=> 57/4
=> 14.25 hours
So, it would take 14.25 hours for 19 car's tires to be changed.
Given the function, g(x)=5x^5/x^3-2x+1, choose the correct horizontal asymptote. none y = 0 y = 1 y = 3
Answer: NONE
Step-by-step explanation:
Consider that m is the degree of the numerator and n is the degree of the denominator.
The rules for horizontal asymptote (H.A.) are as follows:
If m > n then no H.A. (use long division to find the slant asymptote)
If m = n then H.A. is y = leading coefficient of numerator/leading coefficient of denominator
If m < n then H.A. is y = 0
Given: g(x) = 5x⁵/(x³ - 2x + 1)
--> m = 5, n = 3
Since m > n then there is no H.A.
Darren picked 25 flowers that he plans to divide evenly into 3 vases. He will use as many flowers per vase as he can, but may have flowers left
Answer:
So the number of flowers per vase
= 8 flowers per vase
Remainder= one flower
Step-by-step explanation:
Darren picked 25 flowers that he plans to divide evenly into 3 vases.
Number of Flowers touse per vase
= 25/3
Number of flowers to use per case
= 8.33
Number of flowers to use per case
= 8 1/3
We can see that it's 8 flowers per vase the a remainder of one flower Left.
So the number of flowers per vase
= 8 flowers per vase
Remainder= one flower
Answer: 8
Remainder: 1
Which of the following equations shows the correct way to apply the Commutative Property of Addition?(1 point) 2×(4+3)=(2×4)+3 7+y=y+7 a+(c+b)=(a+c)+b 5+5=8+2
Answer:
B. 7 + y = y + 7
Step-by-step explanation:
Commutative property of addition describe an equation in which the order of addition has no effect on the outcome of the sum. The result of addition of the expressions on the left hand side is the same as that on the right hand side. It requires only an addition to property.
In the given question, the equation that shows the correct application of commutative law of addition is; 7 + y = y + 7
Of the 80 trees planted, 2 out of 5 survived the winter. How many trees died during the winter?
Answer:
48 died
Step-by-step explanation:
2 out of 5 survived that means 5-2 = 3
3 out of 5 died
Multiply that fraction that died by the total number
3/5 * 80
48
Bessy has 6 times as much money as Bob, but
when each earns $6, Bessy will have 3 times as
much money as Bob. How much does each have before
and after earning the $6?
Answer:
Before: Bob, $4; Bessy, $24After: Bob, $10; Bessy, $30Step-by-step explanation:
Let x represent the amount of money Bob starts with. Then Bessy starts with 6x. After they have each earned $6, the relationship of their amounts is ...
(6x +6) = 3(x +6)
6x +6 = 3x +18
3x = 12
x = 4
Bob starts with $4; Bessy with $24.
After earning $6, Bob has $10; Bessy has $30.
Help Solving This Problem
Answer:
65oz for 6.99 dollars
Step-by-step explanation
8-i/6+i =(simplified in form a + bi)
Answer:
[tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i
Step-by-step explanation:
Given
[tex]\frac{8-i}{6+i}[/tex]
Multiply numerator/ denominator by the conjugate of the denominator.
The conjugate of 6 + i is 6 - i, thus
= [tex]\frac{(8-i)(6-i)}{(6+i)(6-i)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{48-14i+i^2}{36-i^2}[/tex] → substitute i² = - 1
= [tex]\frac{48-14i-1}{36+1}[/tex]
= [tex]\frac{47-14i}{37}[/tex]
= [tex]\frac{47}{37}[/tex] - [tex]\frac{14}{37}[/tex] i
Emily made 75% of the basket she attempted .If she make 9 basket ,how many attempts did she make.
Answer:
6.75
Step-by-step explanation:
9x0.75=6.75
Answer:
Correct answer is 6.75
Step-by-step explanation:
75% x 9 = 6.75
Jerome and eric start their hike at point a and follow the trail in the counterclockwise direction. they stop at point w to eat lunch. how manu total miles have jerome and erick hicked when they stop for lunch
Answer:
12.5 feet
Step-by-step explanation:
The distance in a coordinate geometry is calculated using: [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]. Jerome and Eric have hiked 12.4 miles when they stopped to eat.
To do this, we make use of distance formula
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
From the figure, we have the following points:
[tex]A = (4,4)[/tex]
The other points between A and W in counterclockwise are:
[tex]B=(6,2)[/tex]
[tex]C = (8,2)[/tex]
[tex]D = (8,4)[/tex]
[tex]E = (10,6)[/tex]
[tex]W = (8,8)[/tex]
Distance AB is:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]AB = \sqrt{(4 - 6)^2 + (4 -2)^2} =\sqrt{8} =2.8[/tex]
Distance BC is
[tex]BC = \sqrt{(6 - 8)^2 + (2 -2)^2} =\sqrt{4} =2[/tex]
Distance CD is
[tex]CD = \sqrt{(8 - 8)^2 + (2 -4)^2} =\sqrt{4} =2[/tex]
Distance DE is :
[tex]DE = \sqrt{(8 - 10)^2 + (4 -6)^2} =\sqrt{8} =2.8[/tex]
Distance EW is:
[tex]EW = \sqrt{(10-8)^2 + (6 -8)^2} =\sqrt{8} =2.8[/tex]
So, distance AW is:
[tex]AW = AB + BC + CD + DE + EW[/tex]
[tex]AW = 2.8 + 2+ 2 + 2.8 +2.8[/tex]
[tex]AW = 12.4[/tex]
Read more about distance in coordinate geometry at:
https://brainly.com/question/3715220
What is the difference between a yard and a meter? give me the actual distance
difference in cm
Answer:
The difference is 8.56 cm. ( the metre is longer than the yard).
Step-by-step explanation:
1 yard = 36 inches
= 36 * 2.54
= 91.44 cm
1 metre = 100 cm.
Which statement represents the situation described below? The cost c of a shirt is less than $27.50. A. c > 27.50 B. c < 27.50 C. c = 27.50 D. 27.50 < c
Answer:
B c < 27.50
Step-by-step explanation:
The cost c of a shirt is less than $27.50
In representing equality
< Represent less than
= Represent equal to
> Represent greater than
Other representation includes
< = Less than or equal to
>= Greater than or equal to
/= Not equal to
The cost c of a shirt is less than $27.50
C< 27.50
Find the distance between the points (-12, 10) and (16, 10)
Two separate samples receive two different treatments. The first sample has n = 9 with SS = 710, and the second has n = 6 with SS = 460. Compute the pooled variance for the two samples.
Answer:
The pooled variance for the two samples is 90
Step-by-step explanation:
Here in this question, we are interested in computing the pooled variance for the two given samples.
From the question;
n1 = 9
ss1 = 710
n2 = 6
ss2 = 460
The pooled variance can be calculated using a mathematical formula as shown below;
S^2 =( ss1 + ss2)/(n1 + n2 -2)
where S^2 refers to the pooled variance of both samples.
Plugging the values into the equation, we have ;
S^2 = (710 + 460)/9 + 6 -2 = 1170/13 = 90
the regular price of a tshirt is 14.80. today tshirts are on sale for 0.8 of their regular price. how much will eliason spend if he buys 6 tshirts today
Answer:(14.80-0.8)*6=84
Step-by-step explanation:
Answer:
71.04
Step-by-step explanation:
0.8×14.80=11.84
11.84×6=71.04
4 hundred thosands 16 thousands 4 hundreds 21 tens 12 ones equals what
Answer:
56622
Step-by-step explanation:
Simplify into numbers.
40000 + 16000 + 400 + 210 + 12
Add.
56622
The value of 4 hundred thousands 16 thousands 4 hundreds 21 tens 12 ones is 416622
Given,
4 hundred thousands 16 thousands 4 hundreds 21 tens 12 ones
We need to find the number that equals the given above.
What is the place value of a number?Example:
456789
4 - hundred thousands
5 - ten thousands
6 - thousands
7 - hundreds
8 - tens
9 - ones
Find the number for 4 hundred thousands 16 thousands 4 hundreds 21 tens 12 ones.
4 hundred thousands = 400,000
16 thousands = 16,000
4 hundreds = 400
21 tens = 210
12 ones = 12
We get,
= 400,000 + 16,000 + 400 + 210 + 12
= 416622
Thus the value of 4 hundred thousands 16 thousands 4 hundreds 21 tens 12 ones is 416622
Learn more about place value in a given number here:
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does a regular pentagon tessellate and why
Answer:
No, a regular pentagon does not tessellate.
In a tessellation, all the angles at a point have to add to 360 degrees, as this means there is no overlap, nor are there gaps. To find the interior angle sum of a pentagon, we use the following formula:
(n-2)*180 (where n is the number of sides)
We plug in the number of sides (5) and get:
Angle sum = (5–2)*180
Angle sum = 3*180
Angle sum = 540
Regular pentagons have equal sides and equal angles, so to find the size of the interior angle of a pentagon, we divide the angle sum by 5 and get 108 degrees for every angle.
As I said before, the angles at a point need to add up to 360, so we need to know if 108 divides evenly into 360. If it does, the shape tessellates, and, if it doesn’t, the shape does not.
360/108 = 3.33333…
This means that a regular pentagon does not tessellate.
Hope this helps!