Answer:
The Mean and Standard deviation for the given data would be as follows:
μ =79.7
б =7.81
Step-by-step explanation:
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.
Frequency Distribution
Given that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i\\}[/tex])
[tex]\frac{50+59}{2} = 54.5\\ \\\frac{60+69}{2} = 64.5\\ \\\frac{70+79}{2} = 74.5\\\\\frac{80+89}{2} = 84.5\\ \\\frac{90+99}{2} = 94.5\\ \\\frac{100+109}{2} = 104.5[/tex]
As we know,
Mean (μ) =∑ [tex](x_{i}f_{i})[/tex]/∑[tex]f_{i}[/tex]
= { (54.5 * 2) + (64.5 * 313) +(74.5 * 1419)+(84.5*1503)+(94.5*319) + (104.5*9)/ (2+313+1419+1503+319)
∵ μ = 79.7
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]
by putting the values, we get
∵ б = 7.81
Hence, μ = 79.7 and б=7.81 are the correct answers.
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3. Multiply the polynomials (a² + 3a-7) and (2a²-a + 4). Simplify the answer. Show your work.
Answer:
Answer:
[tex]2a^{4} + 5a^{3} - 13a^{2} + 19a - 28[/tex]
Step-by-step explanation:
What is the surface area of the cylinder below?
Answer:
Surface Area = 378.25
Step-by-step explanation:
Comment
It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.
Area lids
diameter = 11.4
radius = d/2
radius = 11.4/2
radius = 5.7
Area = pi * r^2
Area = (3.14 * 5.7^2) * 2 There are 2 lids.
Area = 102.01 yd^2
Area body
This is found by finding the circumference of the lid and multiplying by the height
Circumference
C = 2*pi*r
2*r = the diameter
2*r = 11.4
C = 3.14*11.4
C = 35.80
Area body
Area body = C* h
h = 7.8
Area body = 35.80 * 7.8
Area body = 279.24
Total Area = 102.01 + 279.24 = 378.25
For what values of x is the following polynomial expression undefined?
x^2+4x+32/x^2−x−10∗2x^2+4x^3/x^2+3x÷x^2+3x+2/x
The values of x for which the expression [tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]is undefined are 0,[tex]\sqrt{41} /2[/tex] and imaginary numbers.
Given Expression :x^2+4x+32/x^2−x−10∗2x^2+4x^3/x^2+3x÷x^2+3x+2/x
We have to find out those values of x for which the expression does not exists.
[tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]
We have to take LCM of the expression which is equal to [tex]x^{3}(x^{2}-x-10)(2x^{2} +4x^{3})[/tex]
LCM is the smallest positive integer that is divisible by both the numbers whose LCM is found.
and it is present in the denominator.
Expression if exists cannot take denominator equal to 0.
So, by putting LCM equal to zero we find
x=0,x=imaginary numbers and x=[tex]\sqrt{41} /2[/tex].
Hence the given expression have not take values of x=0,[tex]\sqrt{41} /2[/tex], imaginary number.
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10,000,000,000 is which power of ten? 21 -1 10 100
Answer:
10
Step-by-step explanation:
There are ten zeros therefore in standard form it is 1 x 10 to the power of 10 or [tex]10_{12}[/tex]
what is the fraction 2500 of 3600
Answer:
25/36
Step-by-step explanation:
put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's
there are 48 tables at a school.
3/8 of the tables are in the dining hall.
the rest are shaded equally between 5 classrooms.
how many tables are in the main hall
Total: 48
DIning Hall: 48(3/8)=18
so theres 30 left for the classes
30/5(#of classes)=6 per class
\Triangle X Y Z is shown. Angle X Z Y is 63 degrees. The length of X Z is 2.7 and the length of X Y is 2.8.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
Which is the approximate measure of angle Y? Use the law of sines to find the answer.
52°
59°
64°
67°
Solve the formula d = rt for t
What is the slope of the line that passes through the points (6, 2) and (4, 10)? −4 −14 14 4
Answer:
-4
Step-by-step explanation:
The equation for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
m: Slope
(6, 2) = [tex](x_1, y_1)[/tex]
(4, 10) = [tex](x_2, y_2)[/tex]
Substitute these values into the equation:
[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]
Therefore the slope is -4.
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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the slope of the line that passes through the points? 2 points given
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract
[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate
[tex]\bf{-4}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope\;-4}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
*30pts*What is the value of x in the triangle?
Answer:
A.4
Step-by-step explanation:
Using the sine rule
sin(α)/A equals sin(β)/B
From the question & inserting values,
sin(90°)/8 equals sin(30°)/x
∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8
∴x equals 4
You can learn more on the sine rule in case you get confused.
Answer:
A
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 8 ( divide both sides by 2 )
x = 4
The SAT is the most widely used test in the undergraduaté admissions process, Scores on the math portion of the SAT are believed to
be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire
is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take
to ensure that the margin of error is below 20?
(You may find it useful to reference the z table. Round intermediate calculations to at
least 4 decimal places and "2" value to 3 decimal places. Round up your final answer to the nearest whole number.)
Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:
[tex]6\sigma = 800 - 200[/tex]
[tex]\sigma = 100[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
To ensure a margin of error of 20, we solve for n when M = 20, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.96 \times 100[/tex]
[tex]\sqrt{n} = 1.96 \times 5[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 5)^2[/tex]
n = 96.04.
Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.
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Which of the following points lies on the graph of the function y = 2*3^x? a. (1, 0) c. (3, 6) b. (2, 9) d. (0, 2) Please select the best answer from the choices provided A B C D
The point which lies on the graph of the given function is; Choice D; (0, 2).
Which of the following points lies on the graph of the function y = 2*3^x?The point which lies on the graph of the given function; y = 2*3^x is it's y-intercept. The y-intercept which corresponds to the value of y when variable X is set to zero.
Hence, y = 2*3^0;
y = 2 ×1 = 2.
Hence, the point is; (0,2).
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Question 7 of 10
Classify the following triangle. Check all that apply.
Answer:
A,C,E
(if you find a better answer choose that.)
Step-by-step explanation:
This one has two acute angles and one obtuse.
This one is a scalene.
So, tick A,C,E
A cooler contains five colas, seven root beers, and four ginger ales. Three people grab a drink at random, one at a time. a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
The probabilities are:
a) P = 0.024
b) P = 0.5
How to get the probabilities?
a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.
There are 5 colas, and 16 drinks in total, so the probability is:
P = 5/16
The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:
Q = 4/15
Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:
Z = 4/14
The joint probability is:
prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024
b) If the two first persons grabed colas, then in the cooler we have:
3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.
Then the probability of grabbing a root beer is:
p = 7/14 = 1/2 = 0.5
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You must make 3 shots in a row to win the fairs basketball game. The hoop is uneven and the backboard curved. Only 5 players out of 100 win the game. What percentage of players do not win.
Answer:
95%
Step-by-step explanation:
5 player won, meaning 95 player didn't.
This means that 95% of the players didn't win.
Fig. R24 shows a flower vase whose circular base is parallel to its circular top.
Use the dimensions in the figure to calculate the curved surface area of the flower vase
Answer:
operant conditioning and schedules of reinforcement
in a study of birth orders and intelligence, IQ test were given to 18 and 19 years old men to estimate the size of difference, if any, between the main IQs of firstborn sons and second born sons. The following data for 10 firstborn sons and 10 second born sons are consistent with the means and standard deviation's reported in the article. It is reasonable to assume that the samples come from populations that are approximately normal. First born numbers are 107, 113, 84, 126, 99, 95, 98, 109, 91, 90. Second born numbers are 112, 92, 102, 86, 97, 106, 105, 116, 109, 95. construct a 95% confidence interval for the difference in mean IQ between first born and second born sons. Let them one denote the main IQ of firstborn sons.
In a study of birth orders and intelligence, IQ tests were given to 18 and 19 years old men to estimate the size of the difference, we have that [tex]|t|=0.618\leq t_c =2.101[/tex] and for this reason, we cannot reject the null hypothesis.
What are the Test Statistics?Null and Alternative Hypotheses
[tex]H_o: \mu_{1} = \mu_{2}\\\\Ha: \mu_1 \neq \mu_2 .[/tex]
Since the population standard deviations are unknown, we will apply a t-test on the means of the two populations, using two independent samples.
The degrees of freedom are df = 18, and the significance threshold is set at alpha = 0.05, based on the data presented. If we assume that the population variances are the same, we can calculate the degrees of freedom in this way:
The rejection region for this two-tailed test is R = \{t : |f| > 2.101}
Therefore the Test Statistics is
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
t=0.618
In conclusion. we have that [tex]|t|=0.618\leq t_c =2.101[/tex]
For this reason, we cannot reject the null hypothesis.
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Please help whilst I try to solve as well.
Answer:
Step-by-step explanation:
Answer:
420 cm³Step-by-step explanation:
we find the volume as if it were a parallelepiped and we remove the volume of the missing part.
8 * 6 * 10 = 480 cm³
480 - 2 * 3 * 10 = 420cm³
Rewrite the expression as a fraction.
Answer:
4/15
Step-by-step explanation:
in fractions, the number that goes on top is the dividend (the first number in the division problem) which is 4 in this case and the number that goes on the bottom of the fraction is the divisor, which is 15 in this case. therefore, the answer is 4/15.
Paulo is flying a kite as shown
in the right. Find the length of the kite string.
The length of the kite string is 50 ft
How to determine the length of the kite string?The string and the kite form a right triangle.
So, the length can be calculated using Pythagoras theorem as follows:
c^2 = 30^2 + 40^2
This gives
c^2 = 2500
Take the square roots
c = 50
Hence, the length of the kite string is 50 ft
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Use the given sample data to find Q3.
49 52 52 52 74 67 55 55
The given sample data the Q3=61
We begin by ordering the data from smallest to largest.
Next, find the median of the data.
The data set has 8 values, so the two middle values are 52 and 55.
49 52 52 52 55 55 67 74
What is the formula for the median?Median = (52 + 55) / 2
Median= 53.5
The third quartile (Q3) is the 25th percentile or the median of the upper half of the data.
To find the median of all the values that lie above 53.5.
Q3 = (55 + 67)/ 2
Therefore the Q3=61
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I need help with my geometry proof homework from 2-3
Answer: Tbh i don’t know anything besides that all the angles are equal to another and you have to prove it. I would just say: “90 degrees = 90 degrees
Sorry mate I can’t help
Step-by-step explanation:
Write an equation of the line that passes through a pair of points: On a coordinate plane, a line goes through (4, 1) and (5, 2). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 Please select the best answer from the choices provided A B C D
Answer:
b. y = x - 3
Step-by-step explanation:
The general form of the equation of the line is y = mx + c.
1) Find for m (gradient) using the following formula:
m = y2 - y1 / x2 - x1
Substitute the values into it and solve for m.
m = 2 - 1 / 5 - 4
m = 1 / 1
m = 1
2) Substitute into m of the y = mx + c.
y = 1x + c
3) Choose one the coordinates that the line goes through ((4, 1) or (5, 2)) to find c (y-intercept). I will choose (4, 1). Then, substitute your chosen coordinates into your newfound equation (y = 1x + c)
1 = 1(4) + c
1 = 4 + c
1 - 4 = c
-3 = c
Substitute -3 in place of c.
y = 1x - 3, which can be simplified to y = x - 3. Therefore, the correct choice is b.
What are the roots for the quadratic equation below?
3x^2+9x-2=0
Answer:
[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Quadratic equation: ax² + bx + c = 0, where a ≠ 0
Given: 3x² + 9x - 2 = 0
⇒ a = 3, b = 9, c = -2
Substitute the given values into the formula and simplify:
[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Therefore, the correct answer is A.
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What’s the vertex of this graph??
Answer:
(4, -3)
Step-by-step explanation:
A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)
which is the correct graph for the inequality
35. Use the Change of Base Formula to evaluate logs 92. Then convert logs 92 to a logarithm in base 3. Round to the n
2.810; log3 55.2
2.810; log3 21.903
1.964, log3 55.2
4.522; log3 21.903
100 students take a test. The mean score of the results is 88% with a standard deviation of 4%. Considering that the results were normally distributed, what is the median of the graph, what scores are within 2 standard deviations away, and how many student's scores would be within 1 standard deviation from the mean?
Using the Empirical Rule, it is found that:
Scores between 80% and 96% are within 2 standard deviations of the mean.68 scores are within one standard deviation of the mean.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:
88 - 2 x 4 = 80%.88 + 2 x 4 = 96%.68% are within 1 standard deviation of the mean, hence, out of 100:
0.68 x 100% = 68 scores.
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There are nine baseball players in the cafeteria The number of baseball players is one less than twice the number of golfers find the number of golfers
Using a system of equations, it is found that the number of golfers in the cafeteria is of 5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of baseball players.Variable y: Number of golf players.The number of baseball players is one less than twice the number of golfers, hence:
x = 2y - 1.
Since x = 9:
9 = 2y - 1
2y = 10
y = 5.
There are 5 golfers in the cafeteria.
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Drainpipe comes in lengths of 2.5 metres. A man wants to buy drainpipe to fit down
one side of his house from the ground to the gutter.
Estimate how many lengths he will need.
lengths
The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that the distance from the man side of the house to the gutter is 15 m, since the drainpipe comes in lengths of 2.5 m, hence:
Number of drainpipe needed = 15 m / 2.5 m = 6
The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.
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The required quantity of drainpipe is mathematically given as six.
L=6
What is the lengths he will need?Generally, Let's say the distance from the male side of the house to the gutter is 15 meters. Since the length of the drainpipe typically comes in increments of 2.5 meters, we may reason as follows:
In conclusion, The required quantity of drainpipe is equal to 15 meters divided by 2.5 meters, which is equal to six.
L=15/2.5
L=6
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