Answer:
49
Step-by-step explanation:
Margin of error = critical value × standard error
ME = CV × SE
The critical value at 98% confidence is z = 2.326.
Standard error is SE = σ / √n.
4 = 2.326 × 12 / √n
n = 49
A random sample of 18 graduates of a certain secretarial school typed an average of 80.6 words per minute with a standard deviation of 7.2 words per minute. Assuming a normal distribution for the number of words typed per minute, compute the 95% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.
Answer: ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 80.6 words per minute
Standard deviation r = 7.2
Number of samples n = 18
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
80.6+/-1.96(7.2/√18)
80.6+/-1.96(1.697056274847)
80.6 +/- 3.33
= ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
someone answer this
Answer:
16
Step-by-step explanation:
The right triangle shown is a 30:60:90 triangle.
30:60:90 right triangles have a 1:sqrt(3):2 ratio between their sides.
Since the side opposite from the 30 degree is 8, and x is opposite from the 90 degree angle, 8 and x have a 1:2 ratio, or 8:16.
if the base of a right angled triangle is 4cm and its area is 20cm^2, find its height
answer will be 10cm² as i calculate it
Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?
Answer:
He is incorrect. Ray RO and ray RL are not opposite rays.
Step-by-step explanation:
Two angles are linear pair if they are supplementary and share a leg.
∠ORP and ∠LRP are not supplementary, because ray RO and ray RL are not opposite rays.
Therefore, ∠ORP and ∠LRP are not linear pair.
correct me if this is wrong
find the arc length of the particle circle
Answer:
Is there a picture or graph or..
Step-by-step explanation:
Step-by-step explanation:
arc length = (radians * radians) . 90° is π/2 radians. Arc length is (π/2×4). So the answer is 2π.
01:30:4
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the
solution set of this problem?
Answer:
x<_ 21
Step-by-step explanation:
5(x+27)>_ =6(x+26)
5x +135 >_ 6x +156
5x >_6x +21
-x>_21
x<_21
Which graph represents the function f(x) = |x| – 4? On a coordinate plane, an absolute value graph has a vertex at (0, 4). On a coordinate plane, an absolute value graph has a vertex at (negative 4, 0). On a coordinate plane, an absolute value graph has a vertex at (0, negative 4). On a coordinate plane, an absolute value graph has a vertex at (4, 0).
Answer:
(0, -4)
Step-by-step explanation:
The graph that represents the function is (c) on a coordinate plane, an absolute value graph has a vertex at (0, -4)
The equation of the function is given as:
[tex]f(x) = |x| - 4[/tex]
The above function is an absolute value function shifted down by 4 units
Hence, the graph that represents the function is a graph that has its vertex at (0,-4)
Read more about absolute value graphs at:
https://brainly.com/question/2166748
Solve 3(a + 3) – 6 = 21.
Answer:
a=6
Step-by-step explanation:
to find the value of a you need to simplify the equation first. so...
3(a+3)-6=21 (you remove the bracket first)
3a+9-6=21
3a+3=21 (you collect the like terms then)
3a=21-3
3a=18 (then you both divide both sides by 3 to find the value of a)
a=18/3
a=6
to check your answer substitute 3 instead of a
3(a+3)-6=21
3(6+3)-6=21
3(9)-6=21 (according to BODMAS since multiplication comes first you multiply 3 with 9 before subtracting it from 6.)
29-6=21
21=21
Answer:6
Step-by-step explanation:
3(a + 3) - 6 = 21
3(a + 3) = 21 + 6
3(a + 3) =27
a + 3. = 27 ÷ 3
a + 3. = 9
a. = 9 - 3
a. = 6
what is the solution set for the equation (x-2)(x-8)=0
Answer:
x=2 x =8
Step-by-step explanation:
(x-2)(x-8)=0
Using the zero product property
x-2 = 0 x-8 = 0
x=2 x =8
Answer:x = 2 and x = 8
Step-by-step explanation:
( 2 - 2)( 8 - 8)
(0)(0)
=0
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Density = Mass / Volume
D = 3/0.2
D = 15 kg/m³
Answer:
density=mass/volume
d=3kg/0.2m3
=15kgm-3
what is X:
|4x−1|=3
|x|=−4
Answer:
1
Step-by-step explanation:
A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 10 kilograms of the 40% silver alloy?
Answer:
the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
Step-by-step explanation:
Suppose, the weight of the alloy with 50% silver content is x kilograms.
As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be: kilograms
The percentage of silver content in the mixed alloy is 40%. So the equation will be calculated as
[tex]0.5x+0.25(10-x)=0.4\times10\\0.5x+2.5-0.25x=4\\0.25x=1.5\\\Rightarrow x=\frac{1.5}{0.25} = 6[/tex]
So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
g(-4)
Please help!!
Answer:
1
Step-by-step explanation:
g(-4) means what is the y value when x is -4.
Find x=-4, and when x=-4. y=1
Answer:
1
Step-by-step explanation:
Find the values of x in the figure below. Express your answer in simplest radical form.
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...
A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from a large university and they produce a mean score of 183 with a standard deviation of 12. Use a 0.05 level of significance to test whether the mean score for students from this university is greater than 160. use the P-value method of testing hypotheses.
Answer:
[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
And the p value would be:
[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]
Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160
Step-by-step explanation:
Information provided
[tex]\bar X=183[/tex] represent the sample mean
[tex]s=12[/tex] represent the sample standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =160[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is greater than 160, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 160[/tex]
Alternative hypothesis:[tex]\mu > 160[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
And the p value would be:
[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]
Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160
Identify the domain of a radical function with an odd index.
Answer:When n is an odd number, [tex]\sqrt[n]{a}[/tex] is a real number for all values of a. Then, the domain is the real domain.
Among fatal plane crashes that occurred during the past 55 years, 415 were due to pilot error, 96 were due to other human error, 169 were due to weather, 622 were due to mechanical problems, and 68 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it?
Answer:
Relative frequency:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
The most serious threat to aviation safety is, according to this data, "mechanical failures". It can be improved by more rigorous inspection and better maintenance policies and execution.
Step-by-step explanation:
We have the data for fatal plane crashes. The sum of plane crashes is
We can calculate the relative frequency as:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
We can see that the most frequent cause is "mechanical problems", with a relative frequency of 0.45.
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
Which of the following functions is graphed below
Answer:
B
Step-by-step explanation:
you will get alot of points if you answer this explain your answer
Answer:
The surface area of stand is 46 feet.
First
taking the upper rectangular prism only.
so we get
l=3
w=1
h=3
surface area of rectangular prism = 2lw+2lh+2hw
= 2×3×1+2×3×3+2×3×1
= 30
taking the lower rectangular prism only.
surface area of rectangular prism = 2lw+2lh+2hw
=2×7×2+2×1×7+2×2×1
=46
add both the rectangular prism.
we get,
30+46
76
Yes, $15 is enough
Taking out the square of all the rectangle the total would be 52m²
52/25×6.79 ( as 6.79 dollars for 25 m²)
$14.1232
Answer:
freecoins
Step-by-step explanation:
For all the people that have to do algebra and dont want to do it yourself there is a website or you can download it on your phone its called*** MATH PAPA*** ****IT SHOWS YOU STEP BY STEP AND GIVES YOU THE ANSWER*** Just input the equation
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the total number of rooms in the house. Consequently the appraiser decided to fit the simple linear regression model, ^y=β0+β1x , where y= the appraised value of the house (in thousands of dollars) and x= the number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained:
Answer:
Step-by-step explanation:
Hello!
The statistical model predicts the appraised value of houses in a section of the county East Meadow (Y) in relationship with the number of rooms of the house (X)
For a sample of n=64 houses the simple linear regression was estimated:
^Y= 74.80 + 24.93X
Range of X: 5 - 11
Range of Y: 160 - 300 ($ thousands of dollars)
Interpretation of the estimates of the y-intercept and the slope
y-intercept:
74.80 thousand dollars is the estimated average value of a house in a section of the county East Meadow when the house has zero rooms.
Slope:
24.93 [tex]\frac{thousand dollars}{rooms}[/tex] is the modification of the estimated average value of a house in a section of the county East Meadow when the number of rooms increases on one.
I hope this helps!
M5-3/2x less than or equal to 1/3
Answer: choice A
Step-by-step explanation:
by rearranging the initial inequality you’ll get
[tex]\frac{3}{2} x\leq 5-\frac{1}{3}[/tex]
which equals
[tex]\frac{3}{2} x\leq\frac{14}{3}[/tex]
then multiply both sides by 2/3
[tex]x\leq \frac{28}{9}[/tex]
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below. Three lines of math. The first line, StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis. The second line, StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half EndFraction x minus x plus 4. The third line StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half EndFraction x plus 4. StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half Endfraction x minus x plus 4. StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half Endfraction x plus 4. When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ? –1 –negative StartFraction one-half EndFraction 0 StartFraction one-half EndFraction.
Answer:
x = 0
Step-by-step explanation:
Given
Karissa begins to solve the equation ...
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)[/tex]
Her work is correct and is shown below. Three lines of math.
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)\qquad\text{given}\\\\\dfrac{1}{2}x-7+11=\dfrac{1}{2}x-x+4\qquad\text{eliminate parentheses}\\\\\dfrac{1}{2}x+4=-\dfrac{1}{2}x+4\qquad\text{collect terms}[/tex]
When she subtracts 4 from both sides, the result is ...
[tex]\dfrac{1}{2}x=-\dfrac{1}{2}x[/tex]
Find
What is the value of x?
Solution
Karissa can determine the value of x by adding 1/2x to both sides:
[tex]x=0[/tex]
Answer:
Option C (0)
Step-by-step explanation:
Please answer this correctly
So if we know the perimeter of the circle we can find it's radius using the formula for perimeter:
[tex]p = 2\pi(r)[/tex]
So we can solve for radius:
[tex]r = \frac{10.71}{2\pi} [/tex]
Then we can plug this radius into the formula for the area of a circle:
[tex]a = \pi {r}^{2} [/tex]
[tex]a = \pi( \frac{10.71}{2\pi} ) ^{2} [/tex]
Then it only wants a quarter of that area so we divide that value by 4 which upon simplification becomes the answer:
[tex]2.28 {ft}^{2} [/tex]
Answer:
[tex] \boxed{Area \: of \: quarter \: circle = 7.065 \: square \: feet} [/tex]
Given:
Perimeter of quarter circle = 10.71 feet
To find:
Area of quarter circle
Step-by-step explanation:
First we need to calculate the radius of quarter circle:
Let the radius of quarter circle be 'r'
[tex]Perimeter \: of \: quarter \: circle = \frac{\pi r}{2} + 2r[/tex]
[tex] \implies 10.71 = \frac{\pi r}{2} + 2r \\ \\ \implies 10.71 = \frac{\pi r}{2} +2r \frac{2}{2} \\ \\ \implies 10.71 = \frac{\pi r}{2} + \frac{4r}{2} \\ \\ \implies 10.71 = \frac{\pi r + 4r}{2} \\ \\ \implies 10.71 \times 2 = \pi r + 4r \\ \\ \implies 21.42 = \pi r + 4r \\ \\ \implies 21.42 = (\pi + 4)r \\ \\ \implies 21.42 = (3.14 + 4)r \\ \\ \implies 21.42 = 7.14r \\ \\ \implies 7.14r = 21.42 \\ \\ \implies r = \frac{21.42}{7.14} \\ \\ \implies r = 3 \: ft[/tex]
[tex] Area \: of \: quarter \: circle = \frac{\pi {r}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times {(3)}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3.14 \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{28.26}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =7.065 \: {ft}^{2} [/tex]
Grandmother bought enough cat food for her four cats to last for 12 days. On her way home she brought back two stray cats. If she gives each cat the same amount of food every day, how many days will the cat food last
Answer:
The number of days the cat food will last is 8 days.
Step-by-step explanation:
In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.
Assume that each cat consumes x portions of food each day.
Then the four cats will consume, 4x portions of food each day.
Then in 12 days the amount of food consumed by the 4 cats will be:
Total amount of cat food = 12 × 4x
= 48x.
Now, it is provided that she on her way home she brought back two stray cats.
Then the six cats will consume, 6x portions of food each day.
Compute the number of days the cat food will last as follows:
[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]
[tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]
Thus, the number of days the cat food will last is 8 days.
Solve for the value of x
Answer:
x = 8
Step-by-step explanation:
The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...
4 +7x = 60
7x = 56 . . . . . . subtact 4
x = 8 . . . . . . . . .divide by 7
Type answer as integer proper fraction or mixed number
Answer:
[tex]9\dfrac{5}{6}[/tex]
Step-by-step explanation:
[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]
Hope this helps!
A box plot is shown below:
What is the median and Q1 of the data set represented on the plot?
Median = 31; Q1 = 26
Median = 30; Q1 = 26
Median = 31; Q1 = 20
Median = 30; Q1 = 20
Answer:
Step-by-step explanation:
Hello!
I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values
When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.
In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.
The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.
Watching the example, the median is 33
I hope this helps!
Answer: D
Step-by-step explanation:
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 250 companies to invest in. After 1 year, 135 of the companies were considered winners; that is, they outperformed other companies in the same investment class. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested Upper H 0: pequals0.5 versus Upper H 1: pgreater than0.5 and obtained a P-value of 0.1030. Explain what this P-value means and write a conclusion for the researcher.
Answer:
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
The population proportion is equal to 0.5
Step-by-step explanation:
Step (i):-
Given random sample size ' n' = 250
Sample proportion 'p'
[tex]p= \frac{x}{n} = \frac{135}{250} = 0.54[/tex]
Given Population proportion P = 0.5
Q = 1-P = 1-0.5 =0.5
Null Hypothesis : H₀ : P = 0.5
Alternative Hypothesis : H₁ : P≥ 0.5
Step(ii):-
Test statistic
[tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.54-0.5}{\sqrt{\frac{0.5 X 0.5}{250} } }[/tex]
Z = 1.2903
Level of significance α = 0.05
Z₀.₀₅ = 1.96
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
Step(iii):-
P- value
The probability of test statistic
P(Z > 1.2903) = 0.5 - A ( 1.2903)
= 0.5 - 0.4015
= 0.0985≅ 0.10
i) P- value =0.10 > α = 0.05
null hypothesis is accepted
Conclusion:-
The population proportion is equal to 0.5
