Answer:
With 99% confidence the proportion of all smart phones that break before the warranty expires is between 0.041 and 0.069.
Step-by-step explanation:
We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.055.
[tex]p=X/n=97/1750=0.055[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.055*0.945}{1750}}\\\\\\ \sigma_p=\sqrt{0.00003}=0.005[/tex]
The critical z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.005=0.014[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.055-0.014=0.041\\\\UL=p+z \cdot \sigma_p = 0.055+0.014=0.069[/tex]
The 99% confidence interval for the population proportion is (0.041, 0.069).
Jimmie invested $13,000 at 5.23% compounded monthly.
What will Jimmie's account balance be in 42 years?
Answer:
116370.197$
Step-by-step explanation:
Jimmie invested $13,000 at 5.23% compounded monthly.
Jimmie's account balance (B) after 42 years:
B = principal x (1 + rate)^time
= 13000 x (1 + (5.23/100)/12)^(42 x 12)
= 116370.197$
A survey of enrollment at 35 community colleges across the United States yielded the following figures:
6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622
a. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."
b. Construct a histogram of the data.
c. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
d. Calculate the sample mean.
e. Calculate the sample standard deviation.
f. A school with an enrollment of 8000 would be how many standard deviations away from the mean?
Answer: (a) The chart is in the first attachment named table frequency.
(b) The histogram is in the second attachment named frequency vs. enrollment
(c) Mode
(d) x = 9071.4
(e) s = 6677.64
(f) It is -0.16 standard deviation away
Step-by-step explanation:
(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.
(d) To calculate sample mean of a frequency data:
1) Find the midpoint for each interval;
2) Multiply each midpoint for its correspondent frequency;
3) Sum up each multiplication obtained in the previous step;
4) Sum up all the frequencies;
5) Divide the sum in step 3 by the sum in step 4;
For this chart:
x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]
x = 9071.4
(e) To find the standard deviation:
1) With each midpoint, calculate its square;
2) Multiply the midppoint square by its correspondent frequency;
3) Use the following formula to determine the sample standard:
s = √∑f.M² - n(μ)² / n-1
For this chart:
s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]
s = 6677.64
(f) To find how many standard deviations away is the enrollment:
z = [tex]\frac{8000-9071.4}{6677.64}[/tex]
z = - 0.16
8000 enrollments are -0.16 standard deviations away from the mean.
Sandy can fold 6 towels in 3 minutes. If she continues at this rate, how many minutes will it take her to fold 36 towels?
Hey there! :)
Answer:
x = 18 minutes.
Step-by-step explanation:
To solve this equation, set up a ratio.
# of towels over time taken:
[tex]\frac{6}{3} = \frac{36}{x}[/tex]
Cross multiply:
6x = 108
Divide both sides by 6:
6x/6 = 108/6
x = 18 minutes.
Answer:
In eighteen minutes she will have folded all 36
Please answer this correctly
Answer:
0
Step-by-step explanation:
3 cards
P( odd) = 1 odd/ 3 cards = 1/3
No replacement
2 cards 6,8
No odds
P( odd) = 0/2
P( odd, no replacement, odd) = 1/2 * 0 = 0
How would I Evaluate 8×5÷10?
Answer:
4
Step-by-step explanation:
8×5÷10
PEMDAS says multiply and divide from left to right
40÷10
4
Answer:
4
Step-by-step explanation:
Follow the PEMDAS order of operations
8*5=40
40÷10=4
=4
OR
8x5÷10
8x0.5=4
=4
Have a good day and stay safe!
A tabletop has an area of 12 square feet and a perimeter of 16 ft. What are the dimensions of the table? 2 ft by 6 ft 2 ft by 8 ft 4 ft by 3 ft 4 ft by 4 ft
Answer:
2 ft by 6
Step-by-step explanation:
The dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Since, the area of a rectangle is:
Area = length x width
We know that the area of the table is 12 square feet,
So, we can write:
12 = length x width
And, use the formula for the perimeter of a rectangle:
Perimeter = 2 x length + 2 x width
We know that the perimeter of the table is 16 feet, so we can write:
16 = 2 x length + 2 x width
Now we have two equations with two variables (length and width), which we can solve simultaneously as.
Let's rearrange the second equation to solve for length:
16 = 2 x length + 2 x width
16 - 2 x width = 2 x length
8 - width = length
Now we can substitute this expression for length into the first equation:
12 = length x width
12 = (8 - width) x width
12 = 8w - w²
We can rearrange this equation into standard quadratic form:
w² - 8w + 12 = 0
Now we can use the quadratic formula:
where a = 1, b = -8, and c = 12
w = (-(-8) ± √((-8)² - 4(1)(12))) / 2(1)
w = (8 ± √(16)) / 2
w = 4 ± 2
Hence, w = 2
w = 6
So the possible values for the width are 2 and 6.
If the width is 2 feet, then the length is:
length = 8 - width = 6 feet
If the width is 6 feet, then the length is:
length = 8 - width = 2 feet
Therefore, the dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.
Learn more about the rectangle visit:
https://brainly.com/question/2607596
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Suppose that early in an election campaign, a telephone poll of 800 registered voters shows that 460 favor a particular candidate. Just before Election Day, a second poll shows that 520 of 1,000 registered voters now favor that candidate. At the 0.05 significance level, is there sufficient evidence that the candidate's popularity has changed?
Answer:
Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion that support the candidate has significantly changed.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=800 has a proportion of p1=0.58.
[tex]p_1=X_1/n_1=460/800=0.58[/tex]
The sample 2, of size n2=1000 has a proportion of p2=0.52.
[tex]p_2=X_2/n_2=520/1000=0.52[/tex]
The difference between proportions is (p1-p2)=0.05.
[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]
As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.
Answer:
to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]
The resulting function can be written as
[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]
Step-by-step explanation:
Hello,
f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0
and [tex]f(x)\geq 0[/tex]
so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]
and then we can write
[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]
hope this helps
Prime factorization of 45
A. 2³×5
B. 3²×5
C. 5²×3
D. 5²×9
Answer:
Hello, your answer is:
B. 3²×5
Step-by-step explanation:
Prime factorization of 45 is:
45 = 9 x 5
= 3²×5
Hope this helps you.. Good Luck
Answer:
B. 3² × 5
Step-by-step explanation:
45 can be written as a product of its prime factors.
45 = 3 × 3 × 5
45 = 3² × 5
there are 11 people in an office with 6 different phone lines. if all the lines begin to ring at once, how many groups of 6 people can answer these lines?
T_11
Expect_6 phones
This is a permutation problem
Therefore 11p6= 11!/(11-6)! = (5!*6*7*8*9*10*11)/5! = 6*7*8*9*10*11 (ANSWER)
Answer:
one group
Step-by-step explanation:
there is only one group of six people in the office since the office only has 11 people.
The mean of 100 numerical observations is 51.82 what is the value of all 100 numbers
Answer: 5182
To get the value of all 100 numbers you would need to multiply.
Step-by-step explanation:
51.82x100= 5182
A farmer divided his land into 2 groups of sections randomly. There is no difference in the quality of the soil between the 2 groups of land. He used Type A seeds in the first group and Type B seeds in the second group. After 3 months, the heights of the crops are measured across the two groups of land sections. Is the study observational or experimental? If it is an experiment, what is the controlled factor?
Answer:
Experiment
Time..
Step-by-step explanation:
It is an experimental study. An experimental study is a type of study in which all conditions are under the control of the researcher.
The control factor in this case may includes the time...before measurements.
Here we must answer different things about the experiment that the farmer performed. We will see that this is an experiment and the controlled factors are:
Quality of the soil.Wheater.Hours of daylight.What he did is divide his land in two equal parts, and then use different types of seeds in each one of the two parts.
After 3 months, he measures the height of the crops.
The questions are:
Is the study observational or experimental?
It is experimental, because the farmer assigned two areas and he decided what type of seed went into each area.
If it is an experiment, what are the controlled factor?
The controlled factors are the things that are the same for both of the groups of sections and that are relevant for the growth of the seeds. These things are:
Quality of the soil.Wheater.Hours of daylight.If you want to learn more about experiments, you can read:
https://brainly.com/question/11256472
Find the value of x that makes A||B
Answer:
For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15°
a rectangle has a length that is 5 inches grater than is width and is area is 104 square inches, The equation (x+5) x=104 represent the situation, where x represents the width of the retangle
Answer:
width = 8 inches; length = 13 inches
Step-by-step explanation:
(x + 5)x = 104
x^2 + 5x - 104 = 0
(x - 8)(x + 13) = 0
x - 8 = 0 or x + 13 = 0
x = 8 or x = -13
Since the width of a rectangle cannot be a negative number, we discard the answer x = -13.
x = 8
The width is 8 inches.
The length is 8 + 5 = 13.
The length is 13 inches.
A penny, a nickel, a dime, and a quarter are tossed. What is the probability of obtaining exactly two tails on the tosses?
Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.
Answer:
m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)
Step-by-step explanation:
Use sin to solve m∠A
sin x = 12/42 Simplify
sin x = 0.2857 Use the negative sin to solve for x
sin^-1 x = 17 degrees
Add together all of the angle measures to solve for m∠B
17 + 90 + x = 180 Add
107 + x = 180
-107 -107
x = 73 degrees
Use Pythagorean Theorem to solve for b
12^2 + x^2 = 42^2 Simplify
144 + x^2 = 1764
-144 -144
x^2 = 1620 Take the square root of both sides
x = 40
A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?
Answer:
50 miles
Step-by-step explanation:
hello,
let's note x the number of miles travelled heading west,
it takes 1 hour to travel 25 miles
so it takes x/25 hours to travel x miles
we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles
so in 7-x/25 hours it travels 19(7-x/25) miles
we can write, as the total distance is 145 miles
[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]
we can verify
50 miles heading West takes 2 hours
in 5 hours it travels 19*5 = 95 miles
the total is 145 miles
so this is correct
hope this helps
Please answer this correctly
Answer:
100%
Step-by-step explanation:
First, let's determine the probability for each of the conditions.
For P(greater than 2), we will have the cards 3, 4, 5, 6, 7, and 8.
For P(less than 3), we will have the cars 2.
In other words, every single card fits the conditions.
Thus, P(greater than 2 or less than 3)=7/7=100%
100%
Answer:
100%
Step-by-step explanation:
Greater than 2 is 3, 4, 5, 6, 7, 8
And less than 3 is 2 so that’s all the numbers which is 100%
a bag contains only red and blue counters the probability that a counter is blue is 0.58 A counter is picked at random What is the probability that it is red
Answer:
0.42
Process:
1 - 0.58
0.42
A club has 20 women and 17 men and needs to form a committee of six members. How many committees are possible if the committee must have at least two men?
Answer:
2,022,456 committees
Step-by-step explanation:
From the above question, we are given the following information:
Number of women = 20
Number of men = 17
In order to form a committee of six members with at least 2 men, the number of ways we can do this is 5 ways and they are:
a) A committee of 6 men
b) A committee of 5 men and 1 woman
c) A committee of 4 men and 2 women
d) A committee of 3 men and 3 women
e) A committee of 2 men and 4 women
To solve for this we use the combination formula which is given as:
C(n, r) = nCr = n!/r!(n - r)!
Hence, the number of committees that are possible if the committee must have at least two men is calculated as
A committee of 6 men or A committee of 5 men and 1 woman or A committee of 4 men and 2 women or A committee of 3 men and 3 women or A committee of 2 men and 4 women
=[C(17, 6)]+ [C(17,5) × C(20,1)] + [C(17,4) × C(20,2)] + [C(17,3) × C(20,3)] + [C(17,2) × C(20,4)]
= [17!/6!(17 - 6)!] + [17!/5!(17 - 5)! × 20!/1!(20 - 1)!] + [17!/4!(17 - 4)! × 20!/2!(20 - 2)!] + [17!/3!(17 - 3)! × 20!/3!(20 - 3)!] + [17!/2!(17 - 2)! × 20!/4!(20 - 4)!]
= [12376] + [ 6188 × 20] + [2380 × 190] + [680 × 1140] + [ 136 ×4845]
= 2,022,456 committees
Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?
Answer:
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Uniform distribution from 0 to 4.8 seconds.
This means that [tex]a = 0, b = 4.8[/tex]
61% of the time a person will wait at least how long before the wave crashes in?
This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]
[tex]x = 4.8*0.39[/tex]
[tex]x = 1.872[/tex]
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
What tool is used to draw circles
Answer:
Pair of compasses.
Step-by-step explanation:
These are used to inscribe circles/arcs.
Compasses are used in maths, navigation,e.t.c.
Hope it helps.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 130
x = 69; 90% confidence
a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603
Answer:
d. 0.459 < p < 0.603
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.531.
[tex]p=X/n=69/130=0.531[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]
The 90% confidence interval for the population proportion is (0.459, 0.603).
What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answer:
[tex]y = 4x-3[/tex]
Step-by-step explanation:
The coordinates are (-0.5,-5) and (2,5)
Finding the slope, m:
=> Slope = [tex]\frac{rise}{run}[/tex]
=> Slope = [tex]\frac{5+5}{2+0.5}[/tex]
=> Slope = [tex]\frac{10}{2.5}[/tex]
=> Slope = 4
Now, y-intercept, b:
Taking any of the two coordinate and putting it in the slope intercept equation:
=> Point = (x,y) = (2,5)
So, x = 2, y = 5
=> [tex]y = mx+b[/tex]
=> 5 = (4)(2) + b
=> 5 = 8 + b
=> b = 5-8
=> b = -3
Now, Putting in slope intercept equation:
=> [tex]y = mx+b[/tex]
=> [tex]y = 4x-3[/tex]
Gradient (m) = x2-x1
y2-y1
considering
y1 = -5 y2 = 5
x1 = -0.5. x2 = 2
m = 2-(-0.5)
5-(-5)
m = 5.5
10
m = 11. = 0.55
20
equation of a line is given by
y-y1 = m+(x-x1)
y-(-5) =0.55 + {x-(-0.5)}
y+5 = 0.55 + x+0.5
making y the subject
y = 0.55 +0.5 -5 + x
y = -3.95 + x
A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?
Answer:
41°, 56°, 83°
Step-by-step explanation:
We can find the largest angle from the law of cosines:
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab))
C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°
Then the second-largest angle can be found the same way:
B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°
Of course the third angle is the difference between the sum of these and 180°:
A = 180° -82.8192° -55.7711° = 41.4096°
Rounded to the nearest degree, ...
the angles of the triangle are 41°, 56°, 83°.
In geometry the set of all points is called ---- ?
Answer:
it may be locus. because is a set of point and line is formed the locus of points.
In geometry, the set of all points is called space.
What are collinear points?In Mathematics and Geometry, collinear points can be defined as three or more points that all lie on the same straight line (single line). This ultimately implies that, two (2) planes intersect at a line.
For example, we can infer and logically conclude that a sphere would have all points in space that are 4 units from a point.
Generally speaking, the set of all points is referred to as a space in geometry.
Read more on collinear points here: brainly.com/question/24391959
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QUESTION 4
The expected value can be used to calculate the overall grade for a course by using the
earned value for each grade category and its category weighted probability. Calculate the
overall grade given the following grade data:
Grade Category
Earned Value
Weighted Probability
Homework
95
20%
Quiz
80
20%
Test
75
45%
Project
90
15%
Enter your answer as a numeric. For example, if your answer is 78.23%, enter 73.23.
Answer:
82.25%
Step-by-step explanation:
95*0.2 + 80*0.2 + 75*0.45 + 90*0.15 = 82.25%
[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!
Answer:
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
Step-by-step explanation:
[tex]\frac{5x-11}{2x^2+x-6}[/tex]
Factor the denominator.
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
The fraction cannot be simplified further.
Answer:
[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]solution,
[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]
Hope this helps..
what is 18576939*47 Thanks!!!!!
Answer:
873116133
Step-by-step explanation:
18576939 × 47
Multiply the numbers.
= 873116133
Answer: 873116133
Step-by-step explanation:
‘Hope this helps:)
What is the solution to the equation below? Round your answer to two decimal places. 4+4•log2 x=4
Answer:
Option (C)
Step-by-step explanation:
Given expression is,
[tex]4+4\times \text{log}_2(x)=14[/tex]
By subtracting 4 from both the sides of the equation.
[tex]4\times \text{log}_2(x)=14-4[/tex]
Now divide the equation by 4
[tex]\text{log}_2(x)=\frac{10}{4}[/tex]
[tex]\text{log}_2(x)=2.5[/tex]
[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]
[tex]x=(2)^{2.5}[/tex]
[tex]x = 5.657[/tex]
x ≈ 5.66
Therefore, Option C will be the correct option.
4+4•log2 x=14
x= 5.66