Answer:
A 90% confidence interval for the mean mathematics SAT score is (440, 478).
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{1-0.9}{2} = 0.05[/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]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/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 = 1.645*\frac{116}{100} = 19[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 459 - 19 = 440
The upper end of the interval is the sample mean added to M. So it is 459 + 19 = 478
A 90% confidence interval for the mean mathematics SAT score is (440, 478).
The 90% confidence interval for the SAT score is between 440 and 478.
mean (μ) = 459, standard deviation (σ) = 116, sample (n) = 100, confidence = 90% = 0.90
α = 1 - C = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05
The z score of α/2 is equal to the z score of 0.45 (0.5 - 0.05) which is equal to 1.645.
The margin of error (E) is given by:
[tex]E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.645*\frac{116}{\sqrt{100} } =19[/tex]
The confidence interval = μ ± E = 459 ± 19 = (440, 478)
The 90% confidence interval for the SAT score is between 440 and 478.
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What is the value of 6/x+2x,when x=3
Answer:
8
Step-by-step explanation:
6/3 + 2 x 3
6/3 + 6
2 + 6=8
Answer:
[tex]2/3[/tex]
Step-by-step explanation:
[tex]\frac{6}{3x}[/tex]
[tex]\frac{6}{3(3)}[/tex]
[tex]\frac{6}{9} =\frac{2}{3}[/tex]
Write the following statement as a unit rate: 18 laps in 6 minutes
Answer:
3 laps per minute
Step-by-step explanation:
Take the number of laps and divide by the minutes
18/6 = 3 laps per minute
Answer:
3 laps per min
Step-by-step explanation: divide 18 and 6
A trapezoid has an area given by A =1-2(b1+b2)h,where b1,is the length of one base, b2 is the length of the other
base, and h is the height. If the trapezoid has an area of 14 square units, solve for b in terms of the other variables.
Answer:
b1 = (28/h) -b2
Step-by-step explanation:
Filling in the given value for A, you have ...
14 = (1/2)(b1 +b2)h
Multiply by 2/h:
28/h = b1 +b2
Subtract b2:
b1 = (28/h) -b2
what is the following quotient? 1/1+sqrt3
Answer:
4 answer
Step-by-step explanation:
The quotient 1 / (1 + √3) is (- 1 +√3) / 2.
Option D is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 / (1 +√3)
Rationalize the denominator.
1 / (1 +√3) x (1 -√3) / (1 -√3)
{ a² - b² = (a + b) (a - b) ]
(1 -√3) / (1 - 3)
(1 -√3) / -2
-(1 -√3) / 2
(- 1 +√3) / 2
Thus,
The final expression is (- 1 +√3) / 2
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5 customers buy 10,15,20,25,30 toffees respectively from 1 shop. But the the person who bought 20 toffees forgot to pay .if the shopkeeper makes 20% profit what will be his profit or loss from these five customers of the person who forgot to pay at pay his amount had paid his amount?
50% profit ,60% profit, 40% loss ,20% loss.
Answer:
40% profit
Step by step Explanation:
Profit percentage
=( profit/cost price) * 100
0.2 = profit/cost
10+15+20+25+30= 100
Let's assume the cost price of the items is $1 each
Cost price total= $100
Profit made when buyer of 20 toffe didn't say was
0.2=profit/cost
0.2*100 =$20
If the$ 20 paid.
Total profit = $40
So percentage profit now
40/100 * 100 = 40%
The shopkeeper makes a loss of 40% and this can be determined by using the given data.
Given :
5 customers buy 10,15,20,25,30 toffees respectively from 1 shop. But the person who bought 20 toffees forgot to pay.The shopkeeper makes a 20% profit.The following steps can be used in order to determine the profit or loss the shopkeeper makes:
Step 1 - The total number of toffees can be calculated as:
[tex]\rm Total \; Toffees = 10 +15 + 20+ 25+ 30\\\rm Total \; Toffees = 100\\[/tex]
Step 2 - Now, let the cost of 1 toffee be $1. So, the cost of 80 toffees is $80.
Step 3 - So, the value of 20% profit by selling 80 toffees be 'x'. So, the value of 'x' is:
[tex]x = \dfrac{20}{100}\times 80[/tex]
[tex]x = \$16[/tex]
Step 4 - Now, let the profit or loss be 'y'. So, the value of 'y' is:
[tex]y = \dfrac{20}{80}\times 16[/tex]
[tex]y = \$4[/tex]
Step 5 - So, the loss percentage is 40%.
Therefore, the correct option is C).
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A cylindrical metal pipe has a diameter of 8.4 millimeters
and a height of 10 millimeters. Ahole cut out of the center
has a diameter of 6 millimeters,
What is the volume of metal in the pipe? Use 3.14 for
and round the answer to the nearest tenth of a cubic
millimeter
8.4 mm
© 282.6 mm
271.3 mm
553.9 mm
836.5 mm
thand
Next
Submit
Answer:
C. 271.44 [tex]mm^3[/tex]
Step-by-step explanation:
We need to first find the volume of the pipe, then find the volume of the hole and then subtract the volume of the hole from the volume of the pipe.
The diameter of the pipe is 8.4 mm. This means its radius is:
8.4/2 = 4.2 mm
The height of the pipe is 10 mm
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h - height
Therefore, the volume of the cylinder without the hole is:
[tex]V = \pi * 4.2^2 * 10\\\\V = 554.18 mm^3[/tex]
The diameter of the hole is 6 mm. Its radius is:
6/2 = 3 mm
The volume of the hole is:
[tex]V = \pi * 3^2 * 10\\\\V = 282.74 mm^3[/tex]
The volume is:
554.18 - 282.74 = 271.44 [tex]mm^3[/tex]
Answer:
B. 271.3 [tex]mm^{3}[/tex]
Step-by-step explanation:
Volume of the outer cylinder minus the volume of the inner cylinder returns the volume of the metal outer ring that surrounds the hole.
Graded Problem Set Jenna needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
She needs $6,949.65 in the account today.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
In this question:
She needs $9,000 in 3 years, so [tex]t = 3, A(t) = A(3) = 9000[/tex]
9% annual interest, so [tex]r = 0.09[/tex]
1 compounding, so [tex]n = 1[/tex]
How much money needs to be in the account today so she will have enough to pay for the repairs
We need to find P.
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]9000 = P(1 + \frac{0.09}{1})^{1*3}[/tex]
[tex]P(1.09)^{3} = 9000[/tex]
[tex]P = \frac{9000}{(1.09)^{3}}[/tex]
[tex]P = 6949.65[/tex]
She needs $6,949.65 in the account today.
Find the equation of the line that passes through (−4, 8) with slope −3. Write in slope-intercept form. F y = – 3x – 4 G y = – 4x + 3 H y = 3x + 4 J y = 4x – 3
Answer: y=-3x-4
Step-by-step explanation:
Since we know slope, we can plug it into slope-intercept form to find the y-intercept by using the given points,
y=-3x+b
8=-3(-4)+b
8=12+b
b=-4
Now that we know the y-intercept, we can complete the slope-intercept form.
y=-3x-4
Solve for x.
6(x - 1) = 9(x + 2)
X = -8
X = -3
X = 3
x = 8
Answer:x=-8
Step-by-step explanation:
Write a cost function for the cost c to rent a car for d days
Answer:
cost = c*d
Step-by-step explanation:
Unless the cost is calculated by the time (hours) or mileage, we can use the number of days in the calculation.
Everyday is one unit of c, so c times the number of days it is used gives us the cost. Simply multiply the number of days by cost per day to get the total cost.
What’s the correct answer for this?
Answer:
167
Step-by-step explanation:
10) Which diagram represents the figure with the greatest volume?
[A]
[C]
4 in
4 in
4 in
4 in
4 in
[B]
[D]
0
4 in
4 in
4 in
Answer:
see below
Step-by-step explanation:
You don't even need to do any math for this one.
All of the other figures will fit inside the first figure with space left over. Obviously, the first figure has the greatest volume.
The Cube is the diagram with the greatest volume which is 64 inch³.
What is the Volume of a solid shape?The volume of a solid body represents the space occupied by the body.
For example:
Volume of Cube = (side)³
Volume of Sphere = 4/3 π (radius)³
Volume of Cylinder = π (radius)² (height)
Volume of Cone = ⅓ pi (radius)² (height)
How to solve the problem?We will just put the value of radius, side, and height in the formula of the Volume of the corresponding diagrams.
Volume of the given Cube = (4)³ = 64 inch³
Volume of the given sphere = 4/3 π (2)³ = 8(4/3)π = 33.51 inch³
as the radius of the sphere is 2 inches, because the diameter of the sphere is 4 inches.
Volume of the given Cylinder = π (2)² (4) =50.26 inch³
as the radius of the Cylinder is 2 inches, because the diameter of the Cylinder is 4 inches.
Volume of the given Cone = ⅓ π (2)² (4) = 16.76 inch³
as the radius of the Cone is 2 inches, because the diameter of the Cone is 4 inches.
Thus, we come to the conclusion that the Cube is the diagram with the greatest volume which is 64 inch³.
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solve system by substitutition or elimination.
9x-8x=9
-18x+16y=-18
Answer:
1. 9x-8y=9
2. -18x+16y= -18 ⇒ -9x+8y= -9 ⇒ 9x-8y=9
as we see both equations are same, it means the lines overlap and there is infinite number of solutions
A circle has a diameter of 10 feet. What is the area of the circle? Leave answers in terms of π.
Answer:
25pi
Step-by-step explanation:
If the circle has a diameter of 10, it has an radius of 5. The area of a circle is pi*r^2. If r=5, then it is 25pi.
Answer:
25π feet^2
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr^2
We are given the diameter, but we need to find the radius. The radius is half of the diameter, or
r=d/2
We know the diameter is 10 feet. Therefore, we can substitute 10 in for d.
r=10/2
Divide 10 by 2
r=5
The radius is 5 feet.
Now we know the radius, and can substitute it into the area formula.
a=πr^2
r=5
a=π*5^2
Evaluate the exponent.
5^2 is equal to 5*5, which is 25.
a=π*25
a=25π
Add appropriate units. Area always uses units^2, and the units in this problem are feet.
a=25π feet^2
The area of the circle is 25π square feet
Please answer this question and thank you !! Will give you brainliest !!
Answer:
D
Step-by-step explanation:
Two lines are parallel if they have the same slope
y= mx+bthose with same m,
It only appears in the last option where m= -5 for both lines, so option d
What’s the correct answer for this? Select two answer choices
Answer:
D and F
Step-by-step explanation:
In the attached file
What is 75/2\3 for my math homework
Step-by-step explanation:
75 ÷ 2/3 = 12.5
This is the correct answer
Answer:
The answer is 225/2 or 112 1/2 or 112.5
Step-by-step explanation:
When a number is divided by a fraction, you have to convert it into multiply by making the fraction upside down :
[tex]75 \div \frac{2}{3} [/tex]
[tex] = 75 \times \frac{3}{2} [/tex]
[tex] = \frac{75 \times 3}{2} [/tex]
[tex] = \frac{225}{2} [/tex]
[tex] = 112 \frac{1}{2} \: or \: 112.5[/tex]
A cement walkway of uniform width has been built around an in-ground rectangular pool. the area of the walkway is 1344 square feet. the pool itself is 80 feet long by 20 feet wide. what is the width of the walkway?
Answer:
6 feet.
Step-by-step explanation:
Dimensions of the Pool =80 feet long by 20 feet wide
Area of the walkway =1344 square feet.
If the width of the walkway=w
Length of the Larger Rectangle =80+2wWidth of the Larger Rectangle =20+2wArea of the Walkway =Area of the Larger Rectangle - Area of the Pool
[tex]1344=(80+2w)(20+2w)-(80*20)\\1344=80*20+160w+40w+4w^2-80*20\\4w^2+200w=1344\\4w^2+200w-1344=0\\We factorize\\4(w^2+50w-336)=0\\4(w^2-6w+56w-336)=0\\w(w-6)+56(w-6)=0\\(w-6)(w+56)=0\\w-6=0$ or $ w+56=0\\w=6$ ft or $ w=-56$ \\Therefore, the width of the walkway , w=6 feet.[/tex]
11. In your own words, describe how to view the
hean of a set of numerical data in two different
ways: in terms of leveling out and as a balance
point. In each case, give an example to illustrate.
20% of the people in a community use the emergency room at in one year,find the probability that at most three used the emergency room for a sample of 10 people
Answer:
The probability that at most three used the emergency room for a sample of 10 people is 0.8791.
Step-by-step explanation:
The random variable X can be defined as the number of people in a community using the emergency room.
The probability that a person uses the emergency room is, p = 0.20.
A sample of n = 10 people are selected.
A person using the emergency room is independent of others.
The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.20.
The probability mass function of X is provided as follows:
[tex]P(X=x)={10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x};\ x=0,1,2,3...[/tex]
Compute the probability that at most three used the emergency room as follows:
P (X ≤ 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
[tex]=\sum\limits^{3}_{x=0}{{10\choose x}\ (0.20)^{x}\ (1-0.20)^{10-x}}\\\\=0.10737+0.26844+0.30199+0.20133\\\\=0.87913\\\\\approx 0.8791[/tex]
Thus, the probability that at most three used the emergency room for a sample of 10 people is 0.8791.
What is x X/5=15. ⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️⌚️
Answer:
x=3
Step-by-step explanation:
15/5=3 now I gotta get 20 chatacters
Answer:
[tex]x=75[/tex]
Step-by-step explanation:
[tex]\frac{x}{5} =15[/tex]
[tex]x=15 \times 5[/tex]
[tex]x=75[/tex]
Solve the equation.
C +9 = 3.7
Answer:
C= -5.3
Hope this helps!
Brainliest?
Answer:
C = -5.3
Step-by-step explanation:
C+9=3.7
Subtract 9 from both sides
C+9-9=3.7-9
Simplify
C = -5.3
Pick 3 cards from a standard 52-card deck. Find the P(of at least 1 red card).
Does this experiment represent a binomial probability situation? Explain why or why not.
Answer:P(BBR) = 1/2 × 25/51 × 26/50 = 13/102 if cards are not replaced.
P(RBB) = 1/2 × 26/51 × 25/50 (simplified 1/2) = 13/102
P(BRB) = 1/2 × 26/51 ×25/50 (simplified 1/2) = 13/102
Step-by-step explanation: P(B) at first step is 26 cards out of a possible 52 therefore 26/52 (or simplified 1/2). We then have 25 black cards left out of a possible 51 therefore 25/51. The final card then has to be red to meet the criteria, we have 26 red cards still out of a possible 50 therefore 26/50.
This would be an example of binomial probability as at each step there are only 2 options R or B.
A fish tank has a base, B, with an area, in square inches, modeled by B(x) = 2x^2 + 6x + 4. The height, H, in inches, is modeled by H(x) = x + 3. Find the equation that models the fish tank’s volume, V, in cubic inches.
A. V(x) = 2x^2 + 7x + 7
B. V(x) = 2x^2 + 5x + 1
C. V(x) = 2x^3 + 12x^2 + 22x + 12
D. V(x) = 2x^3 + 8x^2 + 10x + 4
Answer:
C. V(x) = 2x^3 + 12x^2 + 22x + 12
Step-by-step explanation:
The volume of a fish tank is the multiplication of the area of the base by the height.
In this question:
Area of the base: [tex]B(x) = 2x^{2} + 6x + 4[/tex]
Height: [tex]H(x) = x + 3[/tex]
Volume:
[tex]V(x) = B(X)*H(x) = (2x^{2} + 6x + 4)(x + 3) = 2x^{3} + 6x^{2} + 4x + 6x^{2} + 18x + 12 = 2x^{3} + 12x^{2} + 22x + 12[/tex]
So the correct answer is:
C. V(x) = 2x^3 + 12x^2 + 22x + 12
Sloane kicked a soccer ball at a speed of 48 feet per second. If the ball never leaves the ground, then it can be represented by the function H(t) = −16t2 + 48t. Determine the time the ball traveled. t = 0.33 seconds t = 3 seconds t = 16 seconds t = 48 seconds
Answer:
t = 3 seconds
Step-by-step explanation:
I took the test and i got it right.
The time the given ball traveled for is required.
The time the ball traveled was t = 3 seconds
Equation of motionThe given equation is [tex]H(t)=-16t^2+48t[/tex]
The ball never leaves the ground so the height of the ball is 0.
[tex]0=-16t^2+48t[/tex]
Solving the equation we get
[tex]-48t=-16t^2[/tex]
Dividing the equation by [tex]t[/tex] on both sides
[tex]\Rightarrow 48=16t[/tex]
Dividing the equation by 16 on both sides
[tex]\Rightarrow t=\dfrac{48}{16}\\\Rightarrow t=3\ \text{s}[/tex]
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Can someone please help me with this question? I really don't get it. Your help would be much appreciated. :) What is the length of CD to the nearest tenth?
Answer:
5.7
Step-by-step explanation:
The altitude of a right triangle divides it into two smaller triangles, all three of which are similar.
ΔABC ~ ΔADB ~ ΔBDC
Writing and solving a proportion:
AD / BD = BD / CD
(x + 3) / 5 = 5 / (2x + 3)
(x + 3) (2x + 3) = 25
2x² + 9x + 9 = 25
2x² + 9x − 16 = 0
x = [ -9 ± √(81 − 4(2)(-16)) ] / 2(2)
x = [ -9 ± √(81 + 128) ] / 4
x = (-9 ± √209) / 4
x = -5.86 or 1.36
Since x can't be -5.86, x = 1.36. So the length of CD is:
CD = 2(1.36) + 3
CD = 5.7
How do I find x to the nearest tenth?
Answer:
x=18.9
Step-by-step explanation:
The football team makes a profit of 20% on all sales of jerseys. During one season, the total sales on jerseys were $2625. How much was the profit?
Answer:
2625*0.2= $525 in profit
Pls brainliest!!
There are 25 students in a class. Sixteen of those students are boys. What percent of the class are girls?
Answer:
36% of the students are girls
Step-by-step explanation:
(Boys) 16/25 = 64%
(Girls) 9/25 = 36%
Answer:
36%
Step-by-step explanation:
you first do 25 minus 16 to find out how many girls are in the class which is 9
now u do 9/25 = ?/100 to find out the percent of girls
9 times 100 divided by 25 which gives u 36%
hope this helps
Find the Ratio of 250m to 1.5km
Answer:
Step-by-step explanation:
1 km= 1000m
1.5 km = 1 x 1000 + 500
1000 + 500
1500m
1500 m : 250 m
750 m : 125 m
150 m : 25 m
30 m : 5 m
6 m : 1m
0.0
