Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 200
x = 118
p = 118/200 = 0.59
q = 1 - 0.59 = 0.41
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.01 = 0.9
The z score corresponding to the area on the z table is 2.326. Thus, confidence level of 98% is 2.326
Therefore, the 98% confidence interval is
0.59 ± 2.326√(0.59)(0.41)/200
= 0.59 ± 0.08
The lower boundary is
0.59 - 0.08 = 0.51
The upper boundary is
0.59 + 0.08 = 0.67
The correct option is
B. We are 98% confident that the true proportion of all students receiving financial aid is between 0. 51 and 0. 67
Xzavion buys 1.2 pounds of strawberries. If each pound of strawberries cost $3.70, how much will he pay for the strawberries?
Answer:
$4.44
Step-by-step explanation:
$3.70 * 1.2 = $4.44
Answer:
$4.44
Step-by-step explanation:
What is slope of the line -3y=8x -5?
The slope of the line given by the equation -3y=8x-5 is -8/3. This is obtained by re-arranging the equation into slope-intercept form (y=mx+b), where 'm' is the slope.
Explanation:The equation given is -3y=8x-5. To find the slope of the line, we first need to convert this equation to the form y=mx+b, which is the slope-intercept form of a line. In this form, the coefficient 'm' represents the slope, and 'b' represents the y-intercept.
First, divide all terms by -3 to transform the equation. Doing so gives us y=-8/3x + 5/3. Thus, the slope of the line is -8/3. This means that for every increase of 1 unit on the x (horizontal) axis, y (on the vertical axis) will decrease by 8/3 units.
Different lines can have different slopes. A slope can be positive, negative, zero, or undefined. In this case, because our slope is -8/3, we have a line that slopes downwards when reading from left to right.
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Evaluate each expression
Answer:
a. 32
b. 27
c. 64
d. 36
e. 1/16
f. 1/9
Answer:
a.32
b.27
c.64
d.36
e.1/16
f.1/9
Step-by-step explanation:
Hope it helps.!
Activity
Serena is hitting golf balls at the driving range. When she hit a ball viith her 9-Iron, it stopped x yards in front of the 100-yard marker. She knows
she can hit a ball twice that far if she uses her driver. Complete the steps below to see how far Serena can hit a golf ball with her driver. Write an expression in terms of x that represents the distance Serena hit the gofl using her 9 - iron.
Final answer:
To find the distance Serena can hit a golf ball with her driver, we can multiply the distance with her 9-iron by 2.
Explanation:
To find the expression that represents the distance Serena hit the golf ball with her 9-iron, we know that the ball stopped x yards in front of the 100-yard marker. So, the distance Serena hit the ball with her 9-iron is 100 - x yards. To find how far Serena can hit a golf ball with her driver, which is twice as far as her 9-iron, we can multiply the distance with her 9-iron by 2. Therefore, the expression that represents the distance Serena can hit the golf ball with her driver is 2(100 - x) yards.
Question 1 (1 point)
Evaluate if t=-2, x=3 and z=5
4z + 3x -t
Answer:
27
Step-by-step explanation:
4(5) + 3(3) - 2
20 + 9 - 2
27
What does 55 represent y=55x+20
it is the slope its not that hard to figure out
If the volume of an object is 100cm3 and the density is 4g/cm3. What is the mass of the object in g?
Answer:
400g
Step-by-step explanation:
mass= density × volume
Substitute the given value of density and volume.
Mass of the object
= 4(100)
= 400g
I need help with #11 and #12 how do I do this?
Answer:
11. x = 6; y = 6.5
12. x = 2; y = 4
Step-by-step explanation:
In each figure, the hash marks on the lines indicate the parallel lines (marked with red arrows) are equally-spaced. That means the two expressions involving x are equal to each other, and the two expressions involving y are equal to each other.
__
11. 2x +1 = x +7
x = 6 . . . . . . . subtract (x+1) from both sides
and
3y -8 = y +5
2y = 13 . . . . add (8-y) to both sides
y = 6.5 . . . . divide by the coefficient of y
__
12. x +3 = 3/2x +2
1 = 1/2x . . . . . subtract (x+2)
2 = x . . . . . . . multiply by 2
and
2y -1 = 3y -5
4 = y . . . . . . add (5 -2y)
Answer:
11. x=6;y=6.5 12. x=2;y=4
Step-by-step explanation:
hope that helped
Multiply and simplify the following complex numbers: (1 + 2i) x (1 - 4i)
Answer:
9-2i
Step-by-step explanation:
(1 + 2i) * (1 - 4i)
(1*1)-(1*4i)+(2i*1)-(2i)*(4i)
(1)-(4i)+(2i)-(8i^2)
i^2 = -1
1-4i+2i+8
1-2i+8
9-2i
The multiplication and simplification of the complex numbers (1 + 2i) x (1 - 4i) results in 9 - 2i.
Explanation:To multiply and simplify the complex numbers (1 + 2i) and (1 - 4i), we must use the distributive property, just like in normal algebra. We get (1*1) + (1*-4i) + (2i*1) + (2i*-4i), which is 1 - 4i + 2i - 8i². But remember, in complex numbers, i² equals -1, so it simplifies further to 1 - 2i -8(-1), or 1 - 2i + 8, and finally, 9 - 2i which is our final, simplified result.
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In a certain Algebra 2 class of 28 students, 8 of them play basketball and 14 of them play baseball. There are 12 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball
Answer:
[tex]P(B \cup b) =\frac{4}{7}[/tex]
Step-by-step explanation:
Total Number of students, the Universal Set [tex]n(\mathcal{E})[/tex]=28
Let the number of those who play basketball =B
Let the number of those who play baseball =n
Number who play neither sport, [tex]n(B\cup b)'[/tex]=12
From Set Theory,
Since we want to determine the probability that a student chosen randomly from the class plays basketball or baseball, we only simply exclude those who play neither sports.
Mathematically,From Set Theory,
[tex]\mathcal{E}=n(B \cup b)+n(B \cup b)'\\28=n(B \cup b)+12\\n(B \cup b)=28-12\\n(B \cup b)=16[/tex]
The Probability that a student chosen randomly from the class plays basketball or baseball
[tex]P(B \cup b)=\frac{n(B \cup b)}{n(\mathcal{E})}\\=\dfrac{16}{28}\\ =\dfrac{4}{7}[/tex]
Answer:
4/7
Step-by-step explanation:
4/7
Solve for x in the equation x^2 - 4x-9= 29
I'm guessing 4+-√42 if u can understand it's the last one....
The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed. Given this information, the approximate percentage of the population with an IQ greater than 130 is closest to _________.
Answer:
2.28% is the approximate percentage of the population with an IQ greater than 130.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100
Standard Deviation, σ = 15
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(IQ greater than 130)
[tex]P( x > 130) = P( z > \displaystyle\frac{130 - 100}{15}) = P(z > 2)[/tex]
[tex]= 1 - P(z \leq 2)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 130) = 1 - 0.9772 = 0.0228 = 2.28\%[/tex]
2.28% is the approximate percentage of the population with an IQ greater than 130.
The approximate percentage of the population with an IQ greater than 130 will be 2.28%.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed.
Then the approximate percentage of the population with an IQ greater than 130 will be
The value of z-score
z = (130 - 100) / 15
z = 30 / 15
z = 2
Then the probability will be
P(x > 130) = P(z > 2)
P(x > 130) = 1 - P(z < 2)
P(x > 130) = 1 - 0.97725
P(x > 130) = 0.02275
Then the percentage will be
P = 0.02275 x 100
P = 2.275%
P ≅ 2.28%
More about the normal distribution link is given below.
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Order these to Least to greatest -3/4, -2, -1/4, 2
-2. -3/4, -1/4, 2
-2 = -2
-3/4 = -0.75
-1/4 = -0.25
2 = 2
Pink panda has $56.75 to spend today. she spends $13.45 on lunch, $16.32 on getting her nails done and $7.65 on cupcakes how much money does she have left
1) $56.75-$13.45=$43.3
2) $43.4-$16.32=$27.08
3) $27.08-$7.65=$19.43
Answer: she have left $19.43
51) Eloise had to solve a system of inequalities that contained an exponential growth function and a linear function with positive slope. She KNOWS that the two equations intersect at least once, and she was asked to state the interval where the linear > exponential. Which could be an answer to her system of inequalities? A) (-1, 3) B) (-1, [infinity]) C) (-[infinity], -1) D) (-[infinity], -1) ∪ (3, [infinity])
Answer:
Answer is A. (-1, 3)
Refer below.
Step-by-step explanation:
If the line and exponential function intersect only once then the line is tangent to the exponential at that point and therefore is always is below the exponential except at the point of intersection where there are equal.
If you reflect point A (3, 4) over
the y-axis, what is the reflected
point?
The rule for reflecting a point over the y-axis is this:
(x, y) ---> (-x, y)
The x term becomes the opposite and the y term stays the same
(3, 4) ---> (-3, 4)
Hope this helped! Let me know if you have any further questions!
~Just a girl in love with Shawn Mendes
The height of a trapezoid is 8 in. And its area is 64 in2. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases?
Answer:
5 and 11
Step-by-step explanation:
The area of a trapezoid is
A = 1/2 (b1+b2)*h
We know the height is 8 and the area is 64.
Let one of the bases is b and the other is b+6
64 = 1/2 (b+ b+6) *8
Combine like terms
64 = 4 (2b+6)
Divide each side by 4
64/4 = 4/4 *(2b+6)
16 = 2b+6
Subtract 6 from each side
16-6 = 2b+6-6
10 =2b
Divide each side by2
10/2 =2b/2
5=b
The second base is
5+6 =11
Need help please don’t be fake
We see that Angle C = 99.
Then we see that Angle A + 22 + Angle C = 180
Substitute in the 99
Angle A + 22 + 99 = 180
Angle A = 59
Given that the measure of ∠x is 123°, and the measure of ∠y is 51°, find the measure of ∠z. °
Answer:
The measure of angle z is 59°.
Step-by-step explanation:
Final answer:
To find the measure of ∠z when ∠x = 123° and ∠y = 51°, add the angles and subtract the sum from 180°.
Explanation:
Given:
∠x = 123°
∠y = 51°
To find ∠z:
Add ∠x and ∠y: 123° + 51° = 174°
Since the sum of angles in a triangle is 180°, subtract the sum of ∠x and ∠y from 180° to find ∠z: 180° - 174° = 6°
Hence, ∠z = 6°.
Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment on a sheet of paper.Consider the event that the first ball that is drawn is blue.
Answer:
[tex]\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\[/tex]
[tex]W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}[/tex]
Step-by-step explanation:
[tex]\text{If an urn contains two blue balls} (denoted \:B_1 \:and \:B_2) \text{and three white balls}[/tex],[tex](denoted \:W_1, W_2, \:and\: W_3)[/tex]
If One ball is drawn, its color is recorded, and it is replaced in the urn. Then another ball is drawn and its color is recorded.
The 25 Possible outcomes of this experiment are listed below:
[tex]\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\[/tex]
[tex]W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}[/tex]
The tree diagram of this event is also attached.
Which expression is NOT equivalent to −3/8·(−4+1/2)?
Drag this expression to the box.
Answer:
The answer to your question is the first option
Step-by-step explanation:
Original expression
-3/8 (-4 + 1/2)
First option -3/8 (-4) + (3/8)(1/2) This option is not equivalent because
they forgot the negative sign of the
second term.
Second option (-3/8)(-4) + (-3/8)(1/2) This option is equivalent to the
original. Distributive property
Third option (-3/2)(-3 1/2) This option is equivalent to the original
Fourth option (-3/8)(-3) + (-3/8)(-1/2) This option is equivalent to the original
Circle P has a circumference of approximately 75 inches.
What is the approximate length of the radius, ? Use 3.14 for
T. Round to the nearest inch.
va
12 inches
24 inches
38 inches
46 inches
Answer:
The answer to your question is 12 in
Step-by-step explanation:
Data
Circumference = 75 in
radius = ?
π = 3.14
Circumference is defined as the distance around the edge of a circle.
Formula
Circumference = 2 π radius
Solve for radius
Radius = Circumference / 2π
-Substitution
Radius = 75 / 2(3.14)
-Simplification
Radius = 75/6.28
-Result
Radius = 11.94 in ≈ 12 in
Answer:
1) 12in
Step-by-step explanation:
The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.
Find the length of the missing side. (Use the Pythagorean theorem)
Answer:
20
Step-by-step explanation:
12square + 16 square=400
Square root it = 20
Answer:
Step-by-step explanation:
a^2+b^2=c^2
144+256=?
144+256=400
the square root of 400 is 20
so the missing side is 20
Grace had 4 3/8 yards of elastic. She used 1 2/3 yards of the elastic to make bracelets for her friends. How many yards of elastic does she have now?
A. 6 1/24
B. 3 7/24
C. 2 17/24
D. 3 17/24
Answer: D. 3 17/24
Step-by-step explanation:
4 3/8 - 1 2/3
Lawrence father gave him 200 baseball card declines purchases 25 baseball cards to add to his collection of weeks after starting his collection when Lawrence will have more than 750 baseball cards in his collection
Answer:
The inequality is [tex]25w+200> 750.[/tex]
Step-by-step explanation:
The question is incomplete so the complete question is attached below:
Now, to write an inequality that can be used to find [tex]w[/tex], the number of weeks after starting his collection when Lawrence will have more than 750 baseball cards in his collection.
Let the number of weeks be [tex]w.[/tex]
Number of cards Lawrence purchases each week = 25.
Number of cards Lawrence's father gave him = 200.
Total number of cards Lawrence will have more than in his collection = 750.
Now, to write an inequality that can be used to get the number of weeks after starting his collection when Lawrence will have more than 750 baseball cards in his collection:
[tex]25\times w+200>750[/tex]
[tex]25w+200> 750.[/tex]
Therefore, the inequality is [tex]25w+200> 750.[/tex]
You are building a sandbox for your little sister. You want to make sure that she has 200 cubic ft. Of space to play. Give a possible length, width, and height of the sandbox.
Answer:
10x10x2
Step-by-step explanation:
10 * 10 * 2 = 200
Ken can walk
40
4040 dogs in
8
88 hours.
How many dogs can Ken walk in
12
1212 hours?
Answer:
Hey. I'm not sure if you have typos, but if you're saying ''Ken can walk 40 dogs in 8 hours, how many dogs can Ken walk in 12 hours", the answer is 60.
Step-by-step explanation:
So, we get our answer by dividing the amount of dogs Ken can walk by the amount of hours. 40/8 = 5. He walks 5 dogs an hour. Now that we know he walks 5 dogs an hour, we can multiply by 5 for each hour. 5 (Dogs/Hour) x 12 (Hours the dogs were walked) = 60, and that is our final answer.
Each of forty-one pet owners was asked, "Does your pet eat more dry food or wet food?" Here are the results. Among the cat owners,6 chose "Dry food" and 8 chose "Wet food". Among the dog owners, 14 chose "Dry food" and 13 chose "Wet food".
No, pet does not eat more dry food than wet food.
Here's the detailed explanation of the table:
Dog Owners: Among the owners of dogs, 6 prefer to feed their pets wet food, while 11 prefer to feed them dry food.Cat Owners: Among the owners of cats, 12 prefer to feed their pets wet food, which is typically more common for cats due to their need for higher moisture content in their diet, and 15 prefer to feed them dry food.The numbers in the table are called "frequencies," and they show how many responses fell into each category. The table allows us to quickly see and compare the food preferences of dog and cat owners. For instance, we can observe that:
More cat owners prefer wet food for their pets compared to dog owners (12 versus 6).More dog owners prefer dry food compared to wet food (11 versus 6).Similarly, more cat owners prefer dry food compared to wet food, but the preference is less pronounced (15 versus 12).This table does not provide the total number of respondents in each category, but since we know that there are 44 pet owners in total, we could infer additional information if needed.
For example, we can calculate the total number of dog owners (6 + 11 = 17) and the total number of cat owners (12 + 15 = 27) from the table.
The completed table is given below.
The complete question is given below:
There are 5 red pens, 4 black pens, and 1 blue pen in a box. What is the probability of pulling out a black pen two times in a row with replacement?
A. 8/10
B. 4/10
C. 16/100
D. 4/25
Answer:
D. 4/25
Step-by-step explanation:
To find probability, you multiply 4/10 by 4/10. You should get 16/100, which simplifies to 4/25.
On Friday, 112 grocery shoppers bought a candy bar from the checkout line and 588 grocery shoppers did not. What percentage of shoppers did NOT buy a candy bar?
Answer: 84%
Step-by-step explanation:
112 grocery shoppers bought a candy bar and 588 grocery shoppers did not.
Number of grocery shoppers that bought candy bar = 112
Number of grocery shoppers that did not buy candy bar= 588
Total number of grocery shoppers= 112+588 = 700
Percentage of shoppers did not buy a candy bar= 588/700 × 100
= 0.84 × 100
= 84%
Answer:
0.84 = 84%
Step-by-step explanation:
First we need to find the total number of grocery shoppers.
If 112 bought a candy bar and 588 did not, the total number of grocery shoppers is:
588 + 112 = 700
Now, to calculate the percentage of grocery shoppers that didn't buy a candy bar, we make a division between the number of grocery shoppers that didn't buy a candy bar and the total number of grocery shoppers:
588 / 700 = 0.84 = 84%