Final answer:
The area of decorative paper needed, given the dimensions of length and width, is calculated as 50 square centimeters.
Explanation:
To answer the question about the area of decorative paper required, we need to use the formula for the area of a rectangle which is length times width. However, the given dimensions of a = 5 centimeters, w = 10 centimeters, and h = 6 centimeters seem to describe a box or a prism rather than a flat piece of paper. If the decorative paper is meant to cover the side of the box, then the relevant dimensions are likely length and width, not including the height. Assuming the decorative paper is to cover a flat surface, the formula for the area is A = length × width. Therefore, the required area of decorative paper is A = 5 cm × 10 cm = 50 square centimeters.
(2CQ) Write the repeating decimal as a fraction .15
Answer:
c. [tex]\frac{5}{33}[/tex]
Step-by-step explanation:
The given decimal is [tex]0.\bar {15}[/tex]
Let [tex]y=0.\bar {15}...(1)[/tex]
Multiply equation (1) by 100.
[tex]100y=15.\bar {15}...(2)[/tex]
Subtract equation (1) from equation (2)
[tex]\Rightarrow 100y-y=15.\bar {15}-0.\bar {15}[/tex]
[tex]\Rightarrow 99y=15[/tex]
Divide both sides by 99.
[tex]\Rightarrow y=\frac{15}{99}[/tex]
Simplify;
[tex]\Rightarrow y=\frac{5}{33}[/tex]
The recurring decimal 0.15 can be converted to the fraction 5/33.
To convert the repeating decimal 0.15 to a fraction, follow these steps:
Let x be the repeating decimal: x = 0.151515...
Express this equation by multiplying both sides by 100 to shift the decimal point two places: 100x = 15.151515...
Next, subtract the original equation from this new equation: 100x - x = 15.151515... - 0.151515...
This simplifies to: 99x = 15
Solve for x by dividing both sides by 99: x = 15/99
Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3: x = 5/33
Therefore, the repeating decimal 0.15 can be expressed as the fraction 5/33.
It was 8 degrees at nightfall. The temperature dropped 10 degrees by midnight. what was the temperature at midnight?
Answer: The temperature would be -2 degrees at midnight.
Step-by-step explanation:
If you take 8 and minus 10 then you get -2!
Answer:
-2
Step-by-step explanation:
hope it will help youu!!!
Graph the function. Describe its position relative to the graph of the indicated function
Answer:
C
Step-by-step explanation:
If the parent function is function [tex]y=f(x)[/tex] and [tex]a>0,[/tex] then
the graph of the function [tex]y=f(x-a)[/tex] is translated a units to the right graph of the parent function; the graph of the function [tex]y=f(x+a)[/tex] is translated a units to the left graph of the parent function;the graph of the function [tex]y=f(x)+a[/tex] is translated a units up graph of the parent function;the graph of the function [tex]y=f(x)-a[/tex] is translated a units down graph of the parent function.In your case, the grapgh of the function [tex]y=2^x+2[/tex] is translated 2 units up the graph of the function [tex]y=2^x.[/tex]
Answer:
To graph the function, we first need to know what means:[tex]f(x)=2^{x} +2[/tex] relative to [tex]f(x)=2^{x}[/tex]
This is called translation of functions, and it refers to the movement of a specific function, either upwards, downwards, leftwards or rightwards. To be able to translate a function, we have to use the next rules.
Moving upwards or downwards.If we sum a number to the whole function, we are gonna move that function upwards. For example, if we have [tex]f(x)=x^{2}[/tex] and sum 3 to it, we would have [tex]f(x)=x^{2} +3[/tex], which is the same function but moved 3 units upwards.If we subtract a number to the whole function, we are gonna move that function downwards. For example, if we have [tex]f(x)=x^{2}[/tex] and subtract 3 from it, we would have [tex]f(x)=x^{2} -3[/tex], which is the same function but moved 3 units downwards.In this case, the problem is saying that we have to move the function upwards by two units, because [tex]f(x)=2^{x} +2[/tex] is the same function as [tex]f(x)=2^{x}[/tex], but moved 2 units upwards.
In addition, the graph is attached, there you can see the difference between those two functions, you will se that they are the same, but one is moved two units upwards.
lily worked 3 hours more than andrea. together they worked a total of 16 hours. andrea worked a hours. Which equation represents this situation?
A. a+3=16
B. a+6=16
C. a+(a-3)=16
D. a+(a+3)=16
Answer:
The times were Lily 9.5 hours and Andrea 6.5 hours.
Equation "D" is correct using those numbers.
Step-by-step explanation:
Courney buys 2bags of apples.Each bag has 20 apples.How many apples does she buy?
Find the measure of angle B.
A) 90
B) 180
C) 120
D) 60
Answer:
C) 120 degrees
Step-by-step explanation:
m<A + m<B + m<C = 180
45 + m<B + 15 = 180
m<B + 60 = 180
m<B = 120
The answer is C) 120
USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let x = number of prisoners out of five on parole who become repeat offenders. x 0 1 2 3 4 5 P(x) 0.211 0.378 0.216 0.162 0.032 0.001 (a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) How does this number relate to the probability that none of the parolees will be repeat offenders? This is the complement of the probability of no repeat offenders. These probabilities are not related to each other. This is twice the probability of no repeat offenders. This is five times the probability of no repeat offenders. These probabilities are the same. (b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) (d) Compute μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.) μ = prisoners (e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.) σ = prisoners
Answer:
a) 0.789, this is the complement of the probability of no repeat offenders; b) 0.411; c) 0.033; d) μ = 1.429; e) σ = 9.58
Step-by-step explanation:
For part a,
The probability that no parolees are repeat offenders is 0.211. This means the probability of at least one is a repeat offender is the complement of this event. To find this probability, subtract from 1:
1-0.211 = 0.789.
For part b,
To find the probability that 2 or more are repeat offenders, add together the probability that 2, 3, 4 or 5 parolees are repeat offenders:
0.216+0.162+0.032+0.001 = 0.411.
For part c,
To find the probability that 4 or more are repeat offenders, add together the probabilities that 4 or 5 parolees are repeat offenders:
0.032+0.001 = 0.033.
For part d,
To find the mean, we multiply each number of parolees by their probability and add them together:
0(0.211)+1(0.378)+2(0.216)+3(0.162)+4(0.032)+5(0.001)
= 0 + 0.378 + 0.432 + 0.486 + 0.128 + 0.005 = 1.429
For part e,
To find the mean, we first subtract each number of parolees and the mean to find the amount of deviation. We then square it and multiply it by its probability. Then we add these values together and find the square root.
First the differences between each value and the mean:
0-1.429 = -1.429;
1-1.429 = -0.429;
2-1.429 = 0.571;
3-1.429 = 1.571;
4-1.429 = 2.571;
5-1.429 = 3.571
Next the differences squared:
(-1.429)^2 = 2.0420
(-0.429)^2 = 0.1840
(0.571)^2 = 0.3260
(1.571)^2 = 2.4680
(2.571)^2 = 6.6100
(3.571)^2 = 12.7520
Next the squares multiplied by the probabilities:
0(2.0420) = 0
1(0.1840) = 0.1840
2(0.3260) = 0.652
3(2.4680) = 7.404
4(6.6100) = 26.44
5(12.7520) = 63.76
Next the sum of these products:
0+0.1840+0.652+0.7404+26.44+63.76 = 91.7764
Lastly the square root:
√(91.7764) = 9.58
Probabilities are used to determine the outcomes of events.
The probability that one or more are repeat offenders is 0.789The probability that two or more are repeat offenders is 0.411The probability that four or more are repeat offenders is 0.033The standard deviation of repeat offenders is 1.093The expected number of repeat offenders is 1.429The table is given as:
[tex]\left[\begin{array}{ccccccc}x &0 &1 &2 &3 &4 &5 &P(x) &0.211 &0.378 &0.216& 0.162 &0.032 &0.001\end{array}\right][/tex]
(a) Probability that one or more are repeat offenders
This is represented as: [tex]P(x \ge 1)[/tex]
Using the complement rule, we have:
[tex]P(x \ge 1) = 1 - P(x = 0)[/tex]
So, we have:
[tex]P(x \ge 1) = 1 - 0.211[/tex]
[tex]P(x \ge 1) = 0.789[/tex]
The probability that one or more are repeat offenders is 0.789
(b) Probability that two or more are repeat offenders
This is represented as: [tex]P(x \ge 2)[/tex]
Using the complement rule, we have:
[tex]P(x \ge 2) = 1 - P(x = 0) - P(x = 1)[/tex]
So, we have:
[tex]P(x \ge 2) = 1 - 0.211 - 0.378[/tex]
[tex]P(x \ge 2) = 0.411[/tex]
The probability that two or more are repeat offenders is 0.411
(c) Probability that four or more are repeat offenders
This is represented as: [tex]P(x \ge 4)[/tex]
So, we have:
[tex]P(x \ge 4) = P(x = 4) + P(x = 5)[/tex]
[tex]P(x \ge 4) = 0.032 + 0.001[/tex]
[tex]P(x \ge 4) = 0.033[/tex]
The probability that four or more are repeat offenders is 0.033
(d) The expected number of repeat offenders
This is calculated as:
[tex]\mu = \sum x \times P(x)[/tex]
So, we have:
[tex]\mu = 0 \times 0.211+ 1\times 0.378 + 2 \times 0.216 + 3 \times 0.162 + 4 \times 0.032 + 5 \times 0.001[/tex]
[tex]\mu = 1.429[/tex]
The expected number of repeat offenders is 1.429
(e) The standard deviation
This is calculated as:
[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]
[tex]\sum (x^2 \times P(x))[/tex] is calculated as:
[tex]\sum (x^2 \times P(x)) = 0^2 \times 0.211+ 1^2 \times 0.378 + 2^2 \times 0.216 + 3^2 \times 0.162 + 4^2 \times 0.032 + 5^2 \times 0.001[/tex]
[tex]\sum (x^2 \times P(x)) = 3.237[/tex]
So, we have:
[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]
[tex]\sigma = \sqrt{3.237 - 1.429^2}[/tex]
[tex]\sigma = \sqrt{1.194959}[/tex]
[tex]\sigma = 1.093[/tex]
The standard deviation of repeat offenders is 1.093
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Suppose that a and b are integers, a ≡ 11 ( mod 19), and b ≡ 3 ( mod 19 ) .find integer c with0 ≤ c ≤ 18 such that
a.c ≡ 13 a ( mod19).
b.c ≡ 8 b( mod19).
c.c ≡ a − b( mod19).
d.c ≡ 7 a + 3 b( mod19).
e.c ≡ 2 a 2 + 3 b 2 ( mod19). f) c ≡ a 3 + 4 b 3 ( mod19).
To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic. For each congruence, we substitute the given values of a and b and simplify the congruences to solve for c. The possible values of c are then determined using the Chinese Remainder Theorem when appropriate.
Explanation:To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic:
a) To find c such that a.c ≡ 13a (mod 19), we divide both sides of the congruence by a. This gives us c ≡ 13 (mod 19).
b) To find c such that b.c ≡ 8b (mod 19), we divide both sides of the congruence by b. This gives us c ≡ 8 (mod 19).
c) To find c such that c.c ≡ a - b (mod 19), we square both sides of the congruence. This gives us c^2 ≡ (a - b)^2 (mod 19). Since we know a ≡ 11 (mod 19) and b ≡ 3 (mod 19), we substitute these values and simplify the congruence to c^2 ≡ 8 (mod 19). To solve this quadratic congruence, we can use the Chinese Remainder Theorem to find the two square roots of 8 modulo 19, which are 7 and 12. Therefore, c ≡ 7 (mod 19) or c ≡ 12 (mod 19).
d) To find c such that c.c ≡ 7a + 3b (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 7(11) + 3(3) ≡ 4 (mod 19). Similar to part (c), we use the Chinese Remainder Theorem to find the square roots of 4 modulo 19, which are 2 and 17. Therefore, c ≡ 2 (mod 19) or c ≡ 17 (mod 19).
e) To find c such that c.c ≡ 2a^2 + 3b^2 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 2(11^2) + 3(3^2) ≡ 2(121) + 3(9) ≡ 149 ≡ 2 (mod 19). Therefore, c ≡ ±4 (mod 19).
f) To find c such that c ≡ a^3 + 4b^3 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c ≡ 11^3 + 4(3^3) ≡ 11^3 + 4(27) ≡ 11^3 + 4(8) ≡ 11 + 32 ≡ 17 (mod 19). Therefore, c ≡ 17 (mod 19).
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On a winter morning, the temperature before sunrise was 11 degrees. The temperature then rose by 1/2 degree each hour for 7 hours before dropping by 2 1/4 each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours/
Answer:
7.75 F
Step-by-step explanation:
you will do 7/2 *
convert 2.25 to imporper fraction
multiply the denomintor
Answer:
7.75
Step-by-step explanation:
Explain how to solve 4x 2- 5x = 16 by completing the square. What are the solutions?
Is there a way to calculate sin, cos, and tan without a calculator?
If so, could you please do it with this problem...
Tan(90°) = DE/4
Also, could you please explain it step by step.
Thanks!
Answer:
yes, and no
Step-by-step explanation:
There are a few trig functions that are "simple" and can be memorized. Usually, these are the ones for angles of 0°, 30°, 45°, 60°, 90°. See below for a table.
To solve an equation like this for DE, you multiply both sides of the equation by 4 (cancelling the denominator).
4·tan(90°) = DE
The tangent of 90° is "infinity." So, the length of DE will be infinite for an angle of 90°.
_____
Trig functions of multiple angles and half angles can be derived from those in the table using the appropriate formulas. The math can get messy fast.
Of course, SOH CAH TOA reminds you of the relationships between trig function values and right triangle side measures. You may not know the angle measure (and it may be irrelevant), but you can find the trig function value.
Answer:
See below.
Step-by-step explanation:
You can find them by constructing a right angled triangle with the given angle and measuring the sides giving sin = opposite / hypotenuse , cos = adjacent / hypotenuse and tan = opposite / adjacent ( SOH-CAH-TOA).
For tan 90 degrees you think of an 'imaginary' triangle where opposite side = hypotenuse and the adjacent side = 0 ( in fact a vertical line!) .Now tan x = opposite / adjacent = opposite / 0 which is indeterminate. There is no value for the tan of 90 degrees and so there is no solution to your problem.
What is the value of the square root of 15 to the nearest tenth? Show or explain how you got your answer.
Answer:
3.9
Step-by-step explanation:
A calculator is useful for this.
Which is an equation of a direct proportion? y=−2x y=12x−2 y=−2x+3 y=4x
Answer: First option and last option.
Step-by-step explanation:
By definition, an equation of direct proportion has the following form:
[tex]y=kx[/tex]
Where k is the constant of proportionality.
The equation of the line [tex]y=mx+b[/tex], where m is the slope and b the y-intercept.
When b=0, means that the line passes through the origin. Therefore, it would be:
[tex]y=mx[/tex]
(which is similar to [tex]y=kx[/tex])
Then, the slope of the line would be the constant of proportionality.
By definition, the slope can be positive or negative.
Keeping on mind the information above, you can see that the equation that have that form are:
[tex]y=-2x\\\\y=4x[/tex]
Answer:
y=−2x
Step-by-step explanation:
I got it right on Imagine math.
The mean incubation time of fertilized eggs is 21 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.(a) Determine the 20th percentile for incubation times.(b) Determine the incubation times that make up the middle 39% of fertilized eggs.
Answer:
a) 20.16; b) 20.49 and 21.51
Step-by-step explanation:
We use z scores for each of these. The formula for a z score is
[tex]z=\frac{X-\mu}{\sigma}[/tex].
For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.
Using this, 21 as the mean and 1 as the standard deviation,
-0.84 = (X-21)/1
-0.84 = X-21
Add 21 to each side:
-0.84+21 = X-21+21
20.16 = X
For part b, we want the middle 39%. This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want
50-19.5 = 30.5% = 0.305 and
50+19.5 = 69.5% = 0.695.
Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:
-0.51 = (X-21)/1
-0.51 = X-21
Add 21 to each side:
-0.51+21 = X-21+21
20.49 = X
0.51 = (X-21)/1
0.51 = X-21
Add 21 to each side:
0.51+21 = X-21+21
21.51 = X
The 20th percentile for incubation times is approximately 20.16 days. The incubation times that make up the middle 39% of fertilized eggs fall between roughly 20.5 days and 21.5 days.
Explanation:This question focuses on statistics and their application in a biological context, specifically about the incubation time of fertilized eggs. In statistics, the normal distribution is a common continuous probability distribution that is symmetric about the mean.
(a) The 20th percentile of the normal distribution can be found using the z-table or a calculator that has the capability. Using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value in the data set, μ is the mean, and σ is the standard deviation, a Z-score associated with the 20th percentile is approximately -0.84. So the incubation time in days for the 20th percentile is (0.84 * 1) + 21 = 20.16 days.
(b) Similarly, to find the incubation times that make up the middle 39% of the fertilized eggs, note that since this is symmetric, this implies the incubation times falls between the 30.5 percentile and the 69.5 percentile. Using the formula Z = (X - μ) / σ and the Z-table, the Z-scores associated with these percentiles are approximately -0.5 and 0.5 respectively. Hence the incubation time falls between (0.5 * 1) + 21 = 20.5 days and (0.5 * 1) + 21 = 21.5 days
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What is the coefficient of q in the sum of these two expressions
(2/3q-3/4(-1/6q-r)
The coefficient of q in the sum of the two expressions is 17/24.
We have,
The given expression is:
(2/3q - 3/4(-1/6q - r))
Let's simplify this expression step by step:
Step 1: Distribute -3/4 to (-1/6q - r):
(2/3q - 3/4 * -1/6q + 3/4 * r)
Step 2: Simplify the multiplication of fractions:
(2/3q + 1/8q + 3/4 * r)
Step 3: Combine like terms:
(17/24q + 3/4 * r)
Thus,
The coefficient of q in the sum of the two expressions is 17/24.
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The coefficient of q in the sum of the expressions is found by simplifying the terms individually and then combining them. After finding a common denominator and adding the terms, the coefficient of q is 19/24.
Explanation:To find the coefficient of q in the sum of the given expressions (2/3q - 3/4*(-1/6q - r)), we first need to simplify the expression step by step. Starting with the second term, we distribute the -3/4 across the parentheses:
-3/4 * (-1/6q) = 3/4 * 1/6 * q = 1/8q-3/4 * (-r) = 3/4 * rNow adding this to the first term:
(2/3q + 1/8q) - (3/4)rTo add the q terms, they need to have a common denominator. The common denominator for 3 and 8 is 24. We convert both fractions:
2/3q = (2*8)/(3*8)q = 16/24q1/8q = (1*3)/(8*3)q = 3/24qNow we can add them:
16/24q + 3/24q = 19/24qThe coefficient of q in the sum of the given expressions is 19/24.
In Las Vegas, Nevada, stores charge a 4.6\%4.6%4, point, 6, percent state sales tax and a 3.65\%3.65%3, point, 65, percent county sales tax. Yuki is purchasing a handbag priced at \$220$220dollar sign, 220 before tax. How much sales tax does Yuki pay for her handbag purchase? \$
Answer:
18.15
Step-by-step explanation:
Percent means per hundred, so we can convert 4.6% and 3.65% to equivalent decimals.
4.6%= 4.6 divided by 100 = 0.046
3.65%= 3.65 divided by 100 = 0.0365
Since both sales tax rates apply to $220, we can add the two rates.
0.046 + 0.0365= 0.0825
0.0825 x 220 = 18.15
And so, Yuki pays$18.15 in sales tax for her handbag purchase.
A bag contains 1 blue, 2 green, and 3 red marbles, as shown. What is the probability of drawing a green marble out of the bag without looking?
ANSWER
[tex] P(G)= \frac{1}{3}[/tex]
EXPLANATION
The number of green marbles in the bag is
[tex]n(G) = 2[/tex]
The total number of marbles in the bag is
[tex]n(S)=1+2+3 = 6[/tex]
The probability of selecting a green marble from the bag without looking is
[tex]P(G)= \frac{n(G)}{n(S)} [/tex]
Substitute the values to get,
[tex]P(G)= \frac{2}{6} [/tex]
[tex]P(G)= \frac{1}{3} [/tex]
Answer:
The probability of drawing a green marble out of the bag without looking = 1/3
Step-by-step explanation:
It is given that, a bag contains 1 blue, 2 green, and 3 red marbles
Therefore total number of marble in the bag = 1 + 2 + 3 = 6
To find the probability
Total number of marble = 6
Number of green marble = 2
The probability of drawing a green marble = 2/6 = 1/3
A poll reported that 66% of adults were satisfied with the job the major airlines were doing. suppose 15 adults are selected at random and the number who are satisfied is recorded. complete parts (a) through (e) below.
The statistical technique applicable here is simple random sampling and binomial distribution. The formula for a binomial distribution is used to estimate the probabilities of a specific number of satisfactions among the randomly selected 15 adults. The average number and variability can also be calculated for this binomial distribution.
Explanation:This question is about statistics, particularly a technique called simple random sampling. In the given scenario, it's reported that 66% of adults are satisfied with the major airlines' job. We're asked to conjecture about a scenario where 15 adults are chosen at random and the number who are satisfied is observed.
First, this scenario is modeled with a binomial distribution. A binomial distribution is appropriate here because you're considering a certain number of 'trials' (15 adults), and for each trial, there are two possible outcomes - the adult is either satisfied or not satisfied with the airlines. The 'success' probability (satisfaction) remains constant (66%).
A. If we want to know the probability of exactly x adults satisfied, the formula for a binomial distribution is used: P(X = k) = C(n, k) * (p^k) * ((1 - p)^(n - k)), where C(n, k) is combinations of n things taken k at a time, n is number of trials (15), p is the probability of success (66% or 0.66), and k is the number of successes we want exact probability for.
B. If we want to know the expected value or the average number of adults satisfied, it's simply n*p, in this case 15*0.66 = 9.9, meaning, on average, about 10 adults out of 15 should be satisfied according to the poll report.
C. If we want to compute the variability, we can calculate the standard deviation. For a binomial distribution, the standard deviation, sigma, is square root of [ n*p*q ], where q = 1-p is the probability of 'failure', or an adult not satisfied.
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To show that polygon ABCDE is congruent to polygon FGHIJ, a must be used to make the two polygons coincide. A sequence of two transformations that can be used to show that polygon ABCDE is congruent to polygon FGHIJ is
Is there answer choices?
Susan collected 1,470 stickers and placed them in her sticker book if there are 35 stickers on each page of her sticker book how many pages of stickers does Susan have
All you need to do is divide 1470 by 35, which is 42.
Grades on a standardized test are known to have a mean of 1000 for students in the US. The test is administered to 453 randomly selected students from Queens College, and they obtained an average grade of 1013 and a standard deviation of 108. a. Construct a 95 % confidence interval for the true average test score for Queens College students. b. With 5% significance level, Is there a statistical evidence that Queens College students perform differently than other students in the US? The same 453 students selected earlier are now given a two-hour tutoring session and then asked to take the test a second time. The average change in their test scores is 9 points, and the standard deviation of the change is 60 points. Assume the changes are from a Normal distribution. c. You are asked by the school administration to study whether students have performed better in their second attempt. State in terms of , the relevant null and alternative hypothesis in conducting this study. d. Compute the t statistic for testing against ; obtain the p- value for the test. e. Do you reject at the 5% level? At the 1% level? f. Provide a short summary of your conclusions from this study. Comment on the practical versus statistical significance of this estimate.
Answer:
a: 1003 < µ < 1023
b: See attached photo for answers
c: see below
d and e: See second attached photo
f: See below
Step-by-step explanation:
a. to find a confidence interval, first find the error with the formula,
E = Z(σ/√n) where Z is the value of the z-score that relates to the confidence level, σ is the standard deviation of the population (or of the sample if the population standard deviation isn't given), and n is the sample size
For this problem, E = 1.96(108/√453) = 9.95 = 10
Now add and subtract that value form the sample average...
x - E < µ < x + E becomes 1013 - 10 < µ 1013 + 10
simplifies to 1003 < µ < 1023
b. See attached photo for hypothesis test results...
c. H0: µ = 1013
Ha: µ > 1013 (claim)
They want to test if it's greater than their first attempt, so this claim becomes the alternate hypothesis. We're testing against their first attempt, that's why µ = 1013, not 1000
d and e. See second attached photo for hypothesis test results...
f. There is enough evidence to support the claim that the students second attempt was an improvement from their first attempt. They happened to take a 2 hour tutoring course between tests. This doesn't prove that the tutoring was effective thought. It very well might have been effective, but also, the students taking the test again means they've already seen the test and know what to expect, which could have also boosted their scores.
Given the table below for selected values of f(x), use 6 left rectangles to estimate the value of
.
x
1
3
4
6
7
9
10
f(x)
4
8
6
10
10
12
16
Numerical Answers Expected!
Answer for Blank 1:
Divide the area into 6 portions and find the sum of each one to find the value of the final integral:
f(x)dx = 2(8+4)/2 + 1 (8+6)/2 + 2 (6+10)/2 + 1(10+10)/2 + 2 (10+12)/2 + 1 (12+16)/2
= 12 + 7 + 16 + 10 + 22 + 14 = 81 sq units
Answer:
Step-by-step explanation:
Given is a table of x, f(x) as below
x 1 3 4 6 7 9 10
f(x) 4 8 6 10 10 12 16
Mid pt 6 7 8 10 11 14
width of
interval 2 1 2 1 2 1
dA1 12 7 16 10 22 14
area = area of all rectangles= 81 sq units.
How would you solve mathematical problem?
Answer:
[tex]r=\dfrac{I}{Pt}[/tex]
Step-by-step explanation:
Solve this the way you do any "solve for" problem. Locate the variable of interest and identify what has been done to it. Undo that.
Here, the variable of interest is "r". It has been multiplied by Pt. We undo that multiplication by dividing by that product:
[tex]I=Prt\\\\\dfrac{I}{Pt}=\dfrac{Prt}{Pt}\\\\\dfrac{I}{Pt}=r \quad\text{simplify}[/tex]
Based on the experimental probability, predict the number of times that you will roll a 5 if you roll the number cube 300 times.
Rolling a 5 in 300 rolls: Probability of 1/6 [tex]*[/tex] 300 ≈ 50 times.
Sure, let's break it down step by step:
1. Understand Experimental Probability : Experimental probability is based on actual outcomes from an experiment or trial. It's calculated by dividing the number of favorable outcomes by the total number of outcomes.
2. Identify the Probability of Rolling a 5 : Since a standard number cube has 6 faces numbered 1 through 6, each face has an equal probability of 1/6 of showing up in a single roll.
3. Calculate the Probability of Rolling a 5 : The probability of rolling a 5 is 1/6, since there's one favorable outcome (rolling a 5) out of the total 6 possible outcomes.
4. Use Probability to Predict Outcomes : To predict how many times you'll roll a 5 in 300 rolls, multiply the probability of rolling a 5 by the total number of rolls.
Let's calculate:
Probability of rolling a 5 = 1/6
Total number of rolls = 300
Number of times you'll roll a 5 = (Probability of rolling a 5) * (Total number of rolls)
= (1/6) [tex]*[/tex] 300
≈ 50
So, based on experimental probability, you can predict that you will roll a 5 approximately 50 times if you roll the number cube 300 times.
You get paid $18 for 3 hours of work. How much money would make if you worked 7 hours?
Answer:
$42
Step-by-step explanation:
Divide $18 by 3 to get a unit rate of $6 per hour. Then, multiply by 7 hours to get $42.
What is the discriminant of the polynomial below? 2x^2+3x-7
Answer:
Option C. [tex]65[/tex]
Step-by-step explanation:
we know that
The discriminant of a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]D=b^{2}-4ac[/tex]
in this problem we have
[tex]2x^{2} +3x-7[/tex]
so
[tex]a=2\\b=3\\c=-7[/tex]
substitute
[tex]D=3^{2}-4(2)*(-7)[/tex]
[tex]D=9+56[/tex]
[tex]D=65[/tex]
The discriminant of the giving polynomial is 65. The correct option is C. 65
The discriminant of a quadratic functionFrom the question, we are to determine the discriminant of the given polynomial
The given polynomial is
2x²+3x-7
This is a quadratic function
The discriminant of a quadratic function is simply the value in the square root of the quadratic formula
That is,
Discriminant, D = b² - 4ac
In the given quadratic function, 2x²+3x-7
a = 2, b = 3 and c = -7
∴ D = 3² -4(2)(-7)
D = 9 +56
D = 65
Hence, the discriminant of the giving polynomial is 65. The correct option is C. 65
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A student stands 50 feet away from the front of a building and measures the angle of elevation to the top of the building. From the student's eye level 5 feet off the ground, the angle of elevation to the top of the building is 30^\circ. Approximately, what is the height of the building?
Answer:
The height of the building is approximately [tex]34\ ft[/tex]
Step-by-step explanation:
Let
h------> height of the building from the student's eye level
H----> height of the building from the ground (H=h+5 ft)
we know that
[tex]tan(30\°)=\frac{h}{50}[/tex]
[tex]h=tan(30\°)(50)=28.87\ ft[/tex]
Find the height of the building H
[tex]H=h+5=28.87+5=33.87\ ft[/tex]
The height of the building is approximately [tex]34\ ft[/tex]
A rectangular prism has the dimensions 8 feet by 3 feet by 5 feet. What is the surface area of the prism?
Answer:
A=158
Step-by-step explanation: SA = 2 × l × w + 2 × l × h + 2 × w × h
Answer: Option D
(D) 158 square feet
Step-by-step explanation:
A=2(wl+hl+hw)=2·(3·8+5·8+5·3)=158ft²
A gear in a watch turns clockwise, in 1° sections, a total of 300 times. How many degrees has the gear turned?
Answer:
300°
Step-by-step explanation:
This may seem really strange and counterintuitive to you, but when you turn 1° 300 times, you have turned 300°.
_____
If you don't want to add it up ...
1° + 1° + 1° ... + 1° . . . . . 300 times
you can use multiplication. It was invented as a shortcut to repeated addition:
1° × 300 = 300°
The gear has turned a total of 300 degrees.
To solve this problem, we need to consider the information given and apply basic multiplication. The gear turns in 1° sections, and it does so a total of 300 times. Since each section is 1°, we can simply multiply the number of sections by the size of each section to find the total degrees turned.
So, the calculation is as follows:
Number of sections = 300
Size of each section = 1°
Total degrees turned = Number of sections × Size of each section
Total degrees turned = 300 × 1°
Total degrees turned = 300°
Therefore, the gear has turned 300 degrees in total.
Tom bought 5 t-shirts from a store. After he bought the t-shirts, his account balance showed a change of −$65.25. What would have been the change to Tom's account balance had he bought only 1 t-shirt from the store?
Answer:
It would be $13.05
Step-by-step explanation:
Since you're dividing negative $65.25 with a negative number of 5 stores. The five stores are negative because he bought from those stores. So, when dividing the 2 negatives you get a positive $13.05.
If Tom has bought only one t-shirt the change to Tom's account balance
would have been - $13.05.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Tom bought 5 t-shirts from a store.
After he bought the t-shirts, his account balance showed a change of
- $65.25.
Assuming all 5 t-shirts cost the same so the cost of 1 t-shirt would be
= - (65.25/5).
= - 13.05 dollars.
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