b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.
Step-by-step explanation:
from the question, the number of successes is equal to 30
and it is more than the number of failures
for us to conduct this test such as the z test the data we are using should be a random sample from the population that we are interested in. the population should be at least as big as the sample by 10 times. first of all We need to check if the mean of the sample is normally distributed.
if 26 are successes out of a sample of 30, then failures would be 4. therefore option b is correct.
a data set includes 110 body temperatures of healthy adult humans having a mean of 98.1F and a standard deviation of 0.64F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans
Answer:
The 99% confidence interval is [tex]97.94 < \mu < 98.26[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 110
The sample mean is [tex]\= x = 98.1 \ F[/tex]
The standard deviation is [tex]\sigma = 0.64 \ F[/tex]
Given that the confidence level is 99% the level of significance i mathematically evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution, the values is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]
[tex]E = 0.1574[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]
[tex]97.94 < \mu < 98.26[/tex]
Answer:
Step-by-step explanation:
An online polling site posed this question: "How much stock do you put in long-range weather forecasts?" Among its Web site users, 38, 528 chose to respond Complete parts (a) through (c) below.
a. Among the responses received, 3% answered with "a lot". What is the actual number of responses consisting of "a lot"?
b. Among the responses received, 18, 566 consisted of "very little or none". What percentage of responses consisted of "very little or none"?
c. Because the sample size of 38, 528 is so large, can we conclude that about 3% of the general population puts "a lot" of stock in long-range weather forecasts? Why or why not?
A. No, because the sample is a voluntary response sample, so the sample is not likely to be representative of the population.
B. Yes, because the sample is so large, the margin of error is negligible.
C. No, because even though the sample size is so large, there is still a margin of error.
D. Yes, because the sample size is large enough so that the sample is representative of the population.
Answer:
(a) 1155.84
(b) 48.2%
(c) D
Step-by-step explanation:
The number of total responses is, N = 38,528.
(a)
It is provided that 3% answered with "a lot".
Compute the actual number of responses consisting of "a lot" as follows:
n (a lot) = N × P (a lot)
= 38528 × 0.03
= 1155.84
Thus, the actual number of responses consisting of "a lot" is 1155.84.
(b)
The number of responses consisting of "very little or none" is,
n (very little or none) = 18,566
Compute the percentage of responses consisted of "very little or none" as follows:
[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]
[tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]
The percentage is: 0.482 × 100% = 48.2%.
Thus, the percentage of responses consisted of "very little or none" is 48.2%.
(c)
As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.
Thus, making the sample statistic an unbiased estimator of the population parameter.
And proving that the sample is a true representative of the population.
Thus, the correct option is (D).
Please help me on question a
I would really appreciate it
Answer:
[tex]x = 3.6[/tex]
Step-by-step explanation:
To find the area of a rectangle, you multiply its length by its width. The formula is [tex]lw = a[/tex].
We already know the length, 5, and the area, 18, so we can plug it into the equation.
[tex]5\cdot w=18[/tex]
We can simplify this equation by dividing both sides by 5.
[tex]5\cdot w \div5 = 18\div5\\\\w = 3.6[/tex]
Hope this helped!
Answer: x= 13
Step-by-step explanation:
Find the fourth roots of 16(cos 200° + i sin 200°).
Answer:
See below.
Step-by-step explanation:
To find roots of an equation, we use this formula:
[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}(cos(\frac{\theta}{n}+\frac{2k\pi}{n} )+\mathfrak{i}(sin(\frac{\theta}{n}+\frac{2k\pi}{n})),[/tex] where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).
In this case, n = 4.
Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.
Part 2: Solving for root #1
To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by [tex]\frac{\pi}{180}[/tex] and simplify.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(0)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(0)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}} = 2(sin(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
Root #1:
[tex]\large\boxed{z^\frac{1}{4}=2(cos(\frac{19\pi}{36}))+\mathfrack{i}(sin(\frac{19\pi}{38}))}[/tex]
Part 3: Solving for root #2
To solve for root #2, follow the same simplifying steps above but change k to k = 1.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(1)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(1)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{2\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{2\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{2}))\\[/tex]
Root #2:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{7\pi}{9}))+\mathfrak{i}(sin(\frac{7\pi}{9}))}[/tex]
Part 4: Solving for root #3
To solve for root #3, follow the same simplifying steps above but change k to k = 2.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(2)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(2)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{4\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{4\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\pi))+\mathfrak{i}(sin(\frac{5\pi}{18}+\pi))\\[/tex]
Root #3:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{23\pi}{18}))+\mathfrak{i}(sin(\frac{23\pi}{18}))}[/tex]
Part 4: Solving for root #4
To solve for root #4, follow the same simplifying steps above but change k to k = 3.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(3)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(3)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{6\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{6\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{3\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{3\pi}{2}))\\[/tex]
Root #4:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{16\pi}{9}))+\mathfrak{i}(sin(\frac{16\pi}{19}))}[/tex]
The fourth roots of 16(cos 200° + i(sin 200°) are listed above.
A box of chocolates contains five milk chocolates, three dark chocolates, and four white chocolates. You randomly select and eat three chocolates. The first piece is milk
chocolate, the second is white chocolate, and the third is milk chocolate. Find the probability of this occuring.
Answer:
60/220
Step-by-step explanation:
we use combination,
[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]
[tex]5 \times 4 \times 3 = 60[/tex]
then, all divided by,
[tex] (\frac{12}{3}) = 220 [/tex]
[tex]60 \div 220[/tex]
The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{5}{12}[/tex]
Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is
[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{11}[/tex]
Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{10}[/tex]
Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is
[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]
Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
Learn more about Probability:
https://brainly.com/question/795909
determine each unknown addend ___ + 41=-18
Answer:
-59
Step-by-step explanation:
x+41=-18
x= -18-41
x = -59
there are 12 eggs in one box and 12 boxes in one crate. how many eggs are in a shipment of 24 crates
Answer:
Step-by-step explanation:
12 eggs in one box
12 boxes = 1 crate
12 x 12 = 144 eggs
144 x 24 crates = 3456 eggs
Answer:
3,456 eggs
Step-by-step explanation:
There are 12 eggs in one box and 12 boxes in one crate. To find out how many eggs are in a crate, multiply 12 and 12
12*12=144
144 eggs in one crate.
We want to find out what how many eggs are in 24 creates. We know there are 144 eggs in 1 crate. Therefore, we can multiply 144 and 24.
144*24=3,456
There are 3,456 eggs in 24 crates.
Stock prices used to be quoted using eighths of a dollar. Find the total price of the transaction. 400 shares of national semi at 135 1/2
Answer:
The value is [tex]T = \$54200[/tex]
Step-by-step explanation:
From the question we are told that
The number of shares is n = 400
The rate of each share is [tex]k = 135\frac{1}{2} = 135.5[/tex]
Generally the total price is mathematically represented as
[tex]T = 400 * 135.5[/tex]
[tex]T = \$54200[/tex]
Which point is located at (5, –2)?
Explanation:
The origin is the center of the grid. This is where the x and y axis meet. The location of this point is (0,0).
Start at the origin and move 5 places to the right. Note how the x coordinate is 5 which tells us how to move left/right. Positive x values mean we go right.
Then we go down 2 spots to arrive at point D. We move down because the y coordinate is negative.
You could also start at (0,0) and go down 2 first, then to the right 5 to also arrive at point D. Convention usually has x going first as (x,y) has x listed first.
Answer:
Point D is located at (5, -2)
Step-by-step explanation:
The coordinates are in the form of (x,y) so that means the point has the x value of 5 and the y value of -2
22. f(x) is stretched horizontally by a factor of 2 and reflected across the x-axis. Which choice shows the correct representation of f(x) after these transformations?
Options:
A. –f(1/2x)
B. f(–2x)
C. –f(2x)
D. f(–1/2x)
Answer:
A. -f(1/2 x)
Step-by-step explanation:
Reflextion about the x-axis is
f(x) -> -f(x)
and horizontal dilation is
f(x) -> f(-x/b) where b is the factor of dilation.
so the proper answwer is
A. -f(1/2 x)
F(x)=2x+6,g(x)=4x^2 find (f+g)(x)
Work Shown:
(f+g)(x) = f(x) + g(x)
(f+g)(x) = 2x+6 + 4x^2
(f+g)(x) = 4x^2+2x+6
What does "C" represent and how do you evaluate this?
[tex]_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36[/tex]
Explain how to perform a two-sample z-test for the difference between two population means using independent samples with known.
Answer:
The steps 1-7 have been explained
Step-by-step explanation:
The steps are;
1) We will verify that the population standard deviations are known and that the population is normally distributed which means the sample size must be a minimum of 30.
2) We will state the null and alternative hypothesis
3) We will determine the critical values from the relevant tables
4) From the critical values gotten, we will determine it's corresponding region where it can be rejected.
5)We will calculate the value of the test statistic from the formula;
z = [(x1' - x2') - (μ1 - μ2)]/√[((σ1)²/n1) + ((σ2)²/n2)]
6) If the value of the test statistic gotten from step 5 above falls in the region of rejection noted in step 4,then we will reject the null hypothesis
7) After rejection of the null hypothesis, we will now give a decision/conclusion on the claim.
Which statements about the sum of the interior angle measures of a triangle in Euclidean and non-Euclidean geometries are true? A. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees. B. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees. C. In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees. D. In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees. E. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
Answer:
its b and e
Step-by-step explanation:
The statements given in options B and E are true so options B and E are right options.
Given some statements we have to determine that which of the following statements are true
The given statements are as follows
A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.
B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.
C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.
D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
We know some facts about each type of geometry
In Euclidean geometry plane is used to plot the points and line.
In spherical geometry uses the sphere to plot the points and circles
Elliptical geometry is such a geometry where no parallel lines exists.
The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with and they can be written down in the following points
In Euclidean geometry the sum of interior angles of a triangle is 180° In spherical or elliptical geometry the sum of interior angles of a triangle is more than 180° In hyperbolic geometry the sum of interior angles of a triangle is less than 180°So from the above observations we can conclude that statements given in options B and E are true so options B and E are right options.
For more information please refer to the link given below
https://brainly.com/question/4637858
Do men and women run a 5 kilometer race at the same pace? Here are boxplots of the time (in minutes) for a race recently run in Chicago. Write a brief report discussing what these data show.
Answer:
yes
Step-by-step explanation:
Reduce the following fraction to lowest terms: 8/14
Answer:
4/7
Step-by-step explanation:
divide both by two for its simplest form
Answer:4/7
Step-by-step explanation
Divide both the numerator and denominator by 2
The result for the numerator is 8/2=4
that of the denominator is 14/2=7
Therefore the resultant answer is 4/7
Which of the following is an arithmetic sequence? A.-2, 4, -6, 8, ... B.2, 4, 8, 16, ... C.-8, -6, -4, -2, ...
Answer:
C. -8, -6, -4, -2, ...
Step-by-step explanation:
An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.
A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.
B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.
C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.
Hope this helps!
Following is a portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal.
ANOVA
df SS MS F Significance F
Regression 1 1575.76
Residual 8 349.14
Total 9 1924.90
Coefficient Standard Error t Stat P-value
Intercept 6.1092 0.9361
Usage 0.8931 0.149
A) Write the estimated regression equation (to 4 decimals).
B) Use a t test to determine whether monthly maintenance expense is related to usage at the .05 level of significance (to 2 decimals, if necessary).
1. Reject the null hypothesis
2. Do not reject the null hypothesis
C) Monthly maintenance expense______to usage.
1. Is related
2. Is not related
D) Did the estimated regression equation provide a good fit?
1. yes
2. no
E) Explain.
Answer:
Explained below.
Step-by-step explanation:
The ANOVA and Regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal is provided.
(A)
The estimated regression equation equation is:
[tex]y=6.1092+0.8931x[/tex]
Here,
y = maintenance expense (dollars per month)
x = usage (hours per week) for a particular brand of computer terminal
(B)
Consider the Regression output.
The hypothesis to test whether monthly maintenance expense is related to usage is:
H₀: The monthly maintenance expense is not related to usage, i.e. β = 0.
Hₐ: The monthly maintenance expense is related to usage, i.e. β ≠ 0.
Compute the test statistic as follows:
[tex]t=\frac{b}{S.E._{b}}=\frac{0.8931}{0.149}=5.99[/tex]
Compute the p-value as follows:
[tex]p-value=2\times P (t_{8}<5.99}=0.00033[/tex]
The null hypothesis will be rejected if the p-value is less than the significance level.
p-value = 0.00033 < α = 0.05
Reject the null hypothesis.
(C)
Monthly maintenance expense is related to usage.
(D)
Yes, the estimated regression equation provide a good fit.
Since the regression coefficient is significant it can be concluded that the regression equation estimated is a good fit.
From the regression output given, the solution to the questions given are outlined thus ;
[tex] Null \: hypothesis : H_{0} : β = 0 [/tex] [tex] Alternative \: hypothesis : H_{1} : β ≠ 0 [/tex]1.)
Regression equation :
y = bx + c b = slope ; c = interceptHence, the estimated regression equation is;
y = 0.8931x + 6.10922.)
We can calculate the T-statistic value thus ;
[tex] T-statistic = \frac{b}{SE_{b}}[/tex] [tex]SE_{b} = Standard \: error \: of \: slope[/tex] df = 8Hence, the T-statistic is given as ;
[tex] T-statistic = \frac{0.8931}{0.149} = 5.99[/tex]
Pvalue (2 tailed) = 0.00033
Decison Region :
[tex] Reject \: H_{0} \: if \: Pvalue \: < \: α [/tex]Since 0.00033 < 0.05 ; we reject the Null hypothesis.
3.)
Hence, we conclude that monthly expense is related to usage.
4.)
Since, the correlation Coefficient, β ≠ 0 ; Yes, the correlation provides a good fit as it is significant.
Learn more :https://brainly.com/question/18558175
Simplify 6.92 to the exponent of 1000
Answer:
Whatever is raised to the power of 0 is 1
SO the answer is 1
How do i do this equation
-3(-2y-4)-5y-2=
Answer:
combined like terms and then follow the order of operations.
Step-by-step explanation:
How many vehicles have been driven less than 200 thousand kilometers?
The number of vehicles that drove less than 200, 000 km is 12 vehicles
How to find the vehicle that drove less than 200 thousand km?The bar char represents the distance in thousand of km vehicles drove.
3 vehicle drove for 50 thousand kilometres.
4 vehicle drove for 100 thousand kilometres.
5 vehicle drove for 150 thousand kilometres.
Therefore, the total vehicle that drove for less than 200 thousand kilometres is as follows:
total vehicle that drove for less than 200, thousand km = 3 + 4 + 5 = 12 vehicles
learn more on linear bar chart here: https://brainly.com/question/3101280
#SPJ1
Answer:
2
Step-by-step explanation:
The Triangle shown below has an area of 12 Units^2.
Find X
10
6
Answer:
4
Step-by-step explanation:
I got it right on Khan
The value of x is 4.
What is Triangle?A triangle is a polygon in two dimensional geometry. I has three sides and three angles along with three vertices.
Area of a triangle = [tex]\frac{1}{2}[/tex] × b × h
where b is the base of the triangle and h is the length of height of the triangle.
The given triangle is an obtuse triangle which has an angle equal to greater than 90 degrees. So the height of the triangle is found by drawing a perpendicular line from the base to the opposite vertex.
Here, height = x and base length = 6
Area = 12 units²
[tex]\frac{1}{2}[/tex] × 6 × h = 12
6 × h = 12 × 2
6 × h = 24
h = 24/6
h = 4 units.
Hence the length of the height which is x is 4 units.
To learn more about Triangles, click on the link given below :
https://brainly.com/question/2773823
#SPJ2
PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
1)
1/5 of the students earned a C
2)
3% more students earned an A then B
3)
20% of the students earned a D
4)
1/4 of the class earned a B
Answer:
Option (3)
Step-by-step explanation:
From the picture attached,
Bar graph sketched shows the grades earned by the students in an exam.
Number of students who achieved the grade A = 17
Number of students who achieved grade B = 14
Number of students with grade C = 5
Number of students with grade D = 9
Total students who took the exam = 17 + 14 + 5 + 9 = 45
Option (1)
"[tex]\frac{1}{5}[/tex] of the students earned a C"
Fraction of students who earned C = [tex]\frac{\text{Students who earned C}}{\text{Total students}}[/tex]
= [tex]\frac{5}{45}[/tex]
= [tex]\frac{1}{9}[/tex]
Therefore, this option is incorrect.
Option (2)
"3% more students earned an A then B"
Percentage of students who earned A = [tex]\frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{17}{45}\times 100[/tex]
= 37.78%
Percentage of students who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{14}{45}\times 100[/tex]
= 31.11%
Difference in percentage = 37.78 - 31.11
= 6.67%
Therefore, this option is not correct.
Option (3)
"20% of the students earned a D"
Percentage of students who earned D = [tex]\frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{9}{45}\times 100[/tex]
= 20%
Option (3) is the correct option.
Option (4)
" [tex]\frac{1}{4}[/tex] of the class earned a B"
Fraction of class who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}[/tex]
= [tex]\frac{14}{45}[/tex]
Therefore, Option (4) is not correct.
I need help ASAP THANK YOU
Answer:
174 cm²
Step-by-step explanation:
The figure given is a prism with isosceles trapezoid as base.
Its surface area can be calculating the area of each face that makes up the prism, and summing all together.
There are 6 faces. Their dimensions and areas can be calculated as follows:
2 isosceles trapezium:
It has 2 parallel bases, (a and b), of 4cm and 6cm,
Height (h) = 2.8cm
Area = ½(a+b)*h
Area = ½(4+6)*2.8
Area = ½(10)*2.8 = 5*2.8 = 14 cm²
4 rectangles of different dimensions:
Rectangle 1 (down face): l = 10cm, b = 4cm
Area = 10*4 = 40 cm²
Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm
Area = 2(l*b) = 2(10*3) = 60cm²
Rectangle 4 (top face) = l = 10cm, b = 6cm
Area = 10*6 = 60cm²
Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²
Carolyn and Paul are playing a game starting with a list of the integers $1$ to $n.$ The rules of the game are: $\bullet$ Carolyn always has the first turn. $\bullet$ Carolyn and Paul alternate turns. $\bullet$ On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list. $\bullet$ On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed. $\bullet$ If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers. For example, if $n=6,$ a possible sequence of moves is shown in this chart: \begin{tabular}{|c|c|c|} \hline Player & Removed \# & \# remaining \\ \hline Carolyn & 4 & 1, 2, 3, 5, 6 \\ \hline Paul & 1, 2 & 3, 5, 6 \\ \hline Carolyn & 6 & 3, 5 \\ \hline Paul & 3 & 5 \\ \hline Carolyn & None & 5 \\ \hline Paul & 5 & None \\ \hline \end{tabular} Note that Carolyn can't remove $3$ or $5$ on her second turn, and can't remove any number on her third turn. In this example, the sum of the numbers removed by Carolyn is $4+6=10$ and the sum of the numbers removed by Paul is $1+2+3+5=11.$ Suppose that $n=6$ and Carolyn removes the integer $2$ on her first turn. Determine the sum of the numbers that Carolyn removes.
Answer:
The sum of the numbers that Carolyn removes is 5.
Step-by-step explanation:
The provided instruction for the game are:
Carolyn always has the first turn. Carolyn and Paul alternate turns.On each of her turns, Carolyn must remove one number from the list such that this number has at least one positive divisor other than itself remaining in the list.On each of his turns, Paul must remove from the list all of the positive divisors of the number that Carolyn has just removed.If Carolyn cannot remove any more numbers, then Paul removes the rest of the numbers.The value of n is supposed as 6.
And it is also provided that Carolyn removes the integer 2 on her first turn.
The table displaying the outcomes of the game are as follows:
Player Removed Remaining
Carolyn 2 1, 3, 4, 5, 6
Paul 1 3, 4, 5, 6
Carolyn 3 4, 5, 6
Paul 6 4, 5
Carolyn None 4, 5
Paul 4, 5 None
The sum of the numbers that Carolyn removes is:
S = 2 + 3 = 5
Thus, the sum of the numbers that Carolyn removes is 5.
I believe the answer is 8, but I am not sure.
On a class trip with 40 students, 14 are male. What percentage of the class is female?
66%
60%
65%
58%
Answer:
65%
Step-by-step explanation:
If 14 are male, then 26 are female.
To find the percent female, divide the number of females by the total.
26/40 = 0.65
So, the percentage of the class that is female is 65%
Answer:
C. 65%
Step-by-step explanation:
We know that of the 40 total students, 14 are male, which means the remaining students are female.
To find how many are female, we subtract 14 from 40:
40 - 14 = 26 females
Percentage is simply a part divided by a whole, multiplied by 100. Here, the "part" is the number of females, which is 26. The "whole" is the total number of students, which is 40. So, we have:
(26 / 40) * 100 = 65
The answer is thus C, 65%.
~ an aesthetics lover
A rectangular vegetable garden will have a width that is 2 feet less than the length, and an area of 48 square feet. If x represents the length, then the length can be found by solving the equation: x(x-2)=48 What is the length, x, of the garden?
Answer:
[tex]x {}^{2} - 2x = 48[/tex]
[tex]x { }^{2} - 2x - 48 = 0[/tex]
using quadratic formula,
[tex] - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac} \div 2a[/tex]
[tex]2 + \sqrt{196} \div 2[/tex]
[tex]2 + 14 \div 2[/tex]
[tex]x = 8[/tex]
or
[tex]x = - 6[/tex]
help help help help help help
Answer:
75 yards long and 90 yards wide.
Step-by-step explanation:
Let's first find the perimeter of the main rectangle:
100x2 + 65x2 =
330
_________________________________________
Next we need to find two numbers that match:
75 and 90
75x2 + 90x2 =
330
_________________________________________
75x90 is 6750 (More Area)
100x60 is 6500 (Less Area)
What is the solution to the following system of equations? 3x-2y=12 6x - 4y = 24
Answer:
D question,somewhat confusing, itsit's like simultaneous equation,but values are different
Answer:
x = 4 + 2y/3
Step-by-step explanation:
is -54 rational number whole number or integersis
Answer:
-54 is a integer and rational number
Step-by-step explanation:
