Answer:
a) 23.73% probability that all five of them have a landline
b) 76.27% probability that at least one of them does not have a landline
c) 99.90% probability that at least one of them does have a landline
Step-by-step explanation:
For each household, there are only two possible outcomes. Either it has landline service, or it does not. The probability of a household having landline service is independent of other households. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
25% of households in a certain country had no landline service.
This means that 100-25 = 75% have, so [tex]p = 0.75[/tex]
Pick five households form this country at random.
This means that [tex]n = 5[/tex]
a) what is the probability that all five of them have a landline?
This is P(X = 5).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.75)^{5}.(0.25)^{0} = 0.2373[/tex]
23.73% probability that all five of them have a landline
b) what is the probability that at least one of them does not have a landline?
Either all have, or at least one does not have. The sum of the probabilities of these events is 100%.
From a), 23.73% probability that all five of them have a landline
100 - 23.73 = 76.27
76.27% probability that at least one of them does not have a landline
c) what is the probability that at least one of them does have a landline?
Either none have a landline, or at least one has. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.75)^{0}.(0.25)^{5} = 0.0010[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0010 = 0.9990[/tex]
99.90% probability that at least one of them does have a landline
P(x)=3x² + 4x³-8+x⁴-7x Degree; Type; Leading coefficent;
Answer:
Degree: 4; Type: quartic; Leading coefficient: 1
Step-by-step explanation:
What is the product of the polynomials below?
(3x2 - 2x - 3)(5x2 + 4x + 5)
Answer:
15x^4+2x^3-8x^2+2x-15
Step-by-step explanation:
Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.
Answer:
r = -10*cos(t)
Step-by-step explanation:
To write the rectangular equation in polar form we need to replace x and y by:
[tex]x=r*cos(t)\\y=r*sin(t)[/tex]
Replacing on the original equation, we get:
[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]
Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:
[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]
Evelyn pets the box with 1 inch cubes with represents does not show how evelyn can’t find the volume of the box
Question Correction
Evelyn packed this box with 1 inch cubes. Which expression does not show how Evelyn can find the volume of the box?
(A)6+6+6+6+6+6 (B) 2 X 3 X 6 (C) 2 + 3 + 6 (D) 6 X 6Answer:
(C) 2 + 3 + 6
Step-By-Step Explanation
In the diagram,
Height = 6 Units Length =2 Units Width =3 UnitsVolume = Height X Length X Width
= 6 X 2 X 3
=36 cubic units
Consider the options:
(A)6+6+6+6+6+6 =36 cubic units
(B) 2 X 3 X 6 =36 cubic units
(C) 2 + 3 + 6 = 11 cubic units
(D) 6 X 6 =36 cubic units
Out of the option, that which is not equivalent to 36 cubic units is:
(C) 2+3+6
Therefore, it does not show how Evelyn can find the volume of the box.
Answer:
2+3+6
Step-by-step explanation:
i just did it
A box is 24 inches long, 10 inches wide, and 10 inches deep. About how many cubic feet is the box?
Answer:
1.3888888 ft^3
Step-by-step explanation:
We need to find the volume
V = l*w*h
V = 24*10*10
V =2400 in^3
We want cubic ft
Divide by 12 for each foot
12*12*12 = 1728 ft^3
2400/1728 =1.3888888 ft^3
Answer:
[tex] = 1.388889 {ft}^{3} [/tex]
Step-by-step explanation:
[tex]v = whl \\ = 10 \times 24 \times 10 \\ = 2400 {in}^{3} [/tex]
we know that,
[tex]1 \: \: in = 0.833333ft \\ x = 2400 \\ use \: \: cross \: \: \: multipication \\ 2400 = 0.833333x \\ \frac{2400}{0.833333} = \frac{0.833333x}{0.833333} \\ x = 1.388889 {ft}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Anthony brought an 8 -foot board. He cut off 3/4 of the board to build a shelf and gave 1/3 of the rest to his brother for an art project. How many inches long was the piece Anthony gave to his brother?
Answer: 7.2 inches
Step-by-step explanation:
3/4th of 8 feet = 6 ft.
Balance = 2 feet
1/3 of 2 feet = 2/3 = 0.67 ft = 8 inches
What is the ratio 16 : 12 in its simplest form?
Answer:
4 : 3
Step-by-step explanation:
16 : 12 can be simplified by 4 to get 4 : 3
Answer:
[tex]4:3[/tex]
Step-by-step explanation:
[tex]16 : 12[/tex]
The common highest factor of the ratio is 4.
Simplify the ratio.
[tex]16 \div 4:12 \div 4[/tex]
[tex]4:3[/tex]
What is the square root of 28
Answer:5. 291503
Step-by-step explanation:
√28
2√7
5. 291503
Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ Pls help.
Answer:
-56/9
Step-by-step explanation:
By Vieta's formulas,
$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get
$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,
$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$
helpp i cant understand this question
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 90% confident that you esimate is within 2.5% of the true population proportion. How large of a sample size is required
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]
And rounded up we have that n=1076
Step-by-step explanation:
Information given
[tex]ME= 0.025[/tex] represent the desired margin of error
Solution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and . And the critical value would be given by:
[tex]t_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
We can assume that the best estimate for the true proportion is [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.025[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]
And rounded up we have that n=1076
European car company advertises that their
car gers 9.4 Kilometers per liter of gasoline. Convert
this figure to miles per galllon
Answer:
22.11 miles per gallon
Step-by-step explanation:
1 km = 0.621371 miles
1 litre = 0. 264172 gallon
Given
Mileage of car = 9.4 Milometers per liter of gasoline
Mileage of car = 9.4 Km/ litres
now we will use 0.621371 miles for Km and 0. 264172 gallon for litres
Mileage of car = 9.4 * 0.621371 miles/ 0. 264172 gallon
Mileage of car = 9.4 * 2.3521 miles/ gallon
Mileage of car = 22.11 miles/ gallon
Thus, 9.4 Km/litres is same as 22.11 miles per gallon.
An employee earns a 25% commission rate on his sales. One day he earned $175. What was his amount of sales?
Answer:
sales = $700
Step-by-step explanation:
he earned commission of 175
this is 25% of sales
if 25% = 175
what about 100%
sales = (100*175)/25
sales = $700
Answer:700
Step-by-step explanation:
A) estimate the value of 9.9^2 x 1.79 B)estimate the value of V^(square root) 97.5/1.96 Thanks.
Answer:
Below in bold.
Step-by-step explanation:
A). 9.9^2 is close to 10^2 = 100
Round 1.79 to 1.8
So an estimate is 1.8 * 100
= 180.
B). √97.5 / 1.96
( I am assuming that the square root is of 97.5 only).
is approximately equal to √100 / 2
= 10/2
= 5.
Q2 (i). A line “t” is parallel to 3y = 6x + 9. Find the slope of this line “t”. (ii) Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line “r”. plz can anyone tell me by doing the practice on the copy I will be thankful
Answer: 6 and -1/6
Step-by-step explanation:
solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.
Answer:
1) 2
2) -1/2
Step-by-step explanation:
1) 3y= 6x+9
y= 2x+3
Slope is 2
Parallel line "t" has the same slope, it will have equation:
y= 2x+b
2) y =2x+3
Perpendicular line"r" has a slope opposite-reciprocal to this, so the slope will be -1/2, the equation for line"r" is:
y= -1/2x +b
The gradient of the line is same as slope and it is -1/2 for line"r"
How many different ways can the letters of "kissing" be arranged?
Answer:1260
Step-by-step explanation:
Kissing has 7 letters, and there are 2 paris of the same letter.
[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260
Can someone please help me would appreciate it so much
Simplify.
3√45
Answer:
3√45
= 9√5
= 20.12461
Answer:
[tex]9\sqrt{5}[/tex]
Step-by-step explanation:
To simplify this radical, you want to first find the prime factorization of the radicand, which happens to be 45.
The lowest square root factor of 45 is 3.
Now, the radical looks like this:
[tex]\sqrt{3^2\cdot \:5}\\=\sqrt{5}\sqrt{3^2}[/tex]
Of course, The square root of a squared number is still the same number so...
[tex]=3\sqrt{5}[/tex]
Now, we aren't done here, as the 3 which was multiplied by the square root of 45 is still existent so...
[tex]=3 \cdot 3\sqrt{5} \\=9\sqrt{5}[/tex]
#SpreadTheLove<3
The concern of a study by Beynnon et al. (A-4) were nine subjects with chronic anterior cruciate ligamenttears. One of the variables of interest was the laxity of the anteroposterior, where higher values indicate more knee instability. The researchers found that among subjects with ACL-deficient knees, the mean laxity value was 17.4mm with a standard deviation of 4.3mm.
(a) What is the estimated standard error of the mean?
(b) Construct the 99 percent confidence interval for the mean of the population from which the nine subjects may be presumed to be a random sample.
(c) What is the precision of the estimate?
(d) What assumptions are necessary for the validity of the conidence interval you constructed?
Answer:
a) Standard error of the mean = 1.433 mm
b) 99% confidence interval = (12.6, 22.2)
c) The precision of the estimate = 4 816
d) The assumptions that are necessary for the validity of the conidence interval constructed include
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.
- The sample must be a normal distribution sample or approximate a normal distribution and the best way to establish this is when the population distribution where the sample was extracted from is normal or approximately normal.
Step-by-step explanation:
a) Standard error of the mean is given as
σₓ = (σ/√n)
σ = Sample standard deviation = 4.3 mm
n = sample size = 9
σₓ = (4.3/√9) = 1.433 mm
b) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 17.4 mm
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 9 - 1 = 8.
Significance level for 99% confidence interval
(100% - 99%)/2 = 0.5% = 0.005
t (0.005, 8) = 3.36 (from the t-tables)
Standard error of the mean = 1.433 mm
99% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 17.4 ± (3.36 × 1.433)
CI = 17.4 ± 4.816
99% CI = (12.584, 22.216)
One crate orė
99% Confidence interval = (12.584, 22.216)
c) The precision of the estimate is gven as the length of the, margin of error of the confidence interval. The precision of the estimate = 4.816
d) They include
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.
- The sample must be a normal distribution sample or approximate a normal distribution and the best way to establish this is when the population distribution where the sample was extracted from is normal or approximately normal.
Hope this Helps!!!
X is a normally distributed random variable with the standard deviation of 4.00.Find the mean of X when 64.8%
Answer:
μ = 9.504
Step-by-step explanation:
I get complete question that is x is a normally distributed random variable with a standard deviation of 4.00. find the mean of x when 64.8% of the area lies to the left of 11.02
given data
standard deviation = 4
solution
we know that that
X ∞ Normal ( μ , 4²) ...............1
so Probability P will be express as
P ( X < 11.02 ) = 64.8%
so here
P ( Z < [tex]\frac{11.02- \mu }{4}[/tex] ) = 0.648
Z for 0.648 = [tex]\frac{11.02- \mu }{4}[/tex]
0.379 = [tex]\frac{11.02- \mu }{4}[/tex]
solve it we get
μ = 9.504
3. How many different arrangements can be made with the letters in the word
POWER?
O A 100
B 25
OC 20
OD 120
Answer:
D. 120
Step-by-step explanation:
Array formula: A (n, p) = n! / (n -p)!
At where:
n = Total number of elements in the set.
p = Quantity of elements per arrangement
A (5.5) = 5! / (5-5)! = (5x4x3x2x1) / 0!
By definition: 0! = 1
Then: 120/1 = 120
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.55 inches.
Required:
a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
b. What percentage of men are SHORTER than 6 feet 3 inches?
c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
d. What percentage of women are TALLER than 5 feet 11 inches?
Answer:
a) 1.93
b) 97.32% of men are SHORTER than 6 feet 3 inches
c) 2.71
d) 0.34% of women are TALLER than 5 feet 11 inches
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
For man, [tex]\mu = 69.8, \sigma = 2.69[/tex]
A feet has 12 inches, so this is Z when X = 6*12 + 3 = 75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 69.8}{2.69}[/tex]
[tex]Z = 1.93[/tex]
b. What percentage of men are SHORTER than 6 feet 3 inches?
Z = 1.93 has a pvalue of 0.9732
97.32% of men are SHORTER than 6 feet 3 inches
c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
For woman, [tex]\mu = 64.1, \sigma = 2.55[/tex]
Here we have X = 5*12 + 11 = 71.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{71 - 64.1}{2.55}[/tex]
[tex]Z = 2.71[/tex]
d. What percentage of women are TALLER than 5 feet 11 inches?
Z = 2.71 has a pvalue of 0.9966
1 - 0.9966 = 0.0034
0.34% of women are TALLER than 5 feet 11 inches
The line of reflection is the ____. y-axis, center of rotation, x-axis
Answer:The line of reflection is the y axis
Step-by-step explanation:
Working together Wayne and his son Garth can mow the lawn in 30 min, but if Wayne mow the lawn alone then it takes 1h 15min. Find how long does it take for Garth to mow their lawn if he does it alone.
Answer:
105
Step-by-step explanation:
1h and 15 minutes is 75 minutes so
30+75=
70+30=100
100+5=105
Answer:
105
Step-by-step explanation:
I copied the other dude
Which of the following verified the triangle COW is similar to triangle PIG? Ignore the answer I filled in I didn’t meant to pick that one.
Answer:
D. SSS theorem
Step-by-step explanation:
The triangles have similarity by 3 sides:
4/12=5/15=7/21So the answer is SSS
What is the distance between the following points?
Answer:
D. d = [tex]\sqrt{58}[/tex]
Step-by-step explanation:
Use the distance formula: d = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2} }[/tex]
The two points are (6, -2) and (3, -9)
Plug the values into the formula:
d = [tex]\sqrt{(3 - 6)^{2}+ (-9 + 2)^{2} }[/tex]
Simplify
d = [tex]\sqrt{(-3)^{2}+ (-7)^{2} }[/tex]
d = [tex]\sqrt{9+ 49 }[/tex]
d = [tex]\sqrt{58}[/tex]
I hope this helps :))
2÷3 ? 4÷5 A. > B. < C. =
Answer: B
Step-by-step explanation:
To know the inequality, we can divide the numbers on each side to see what belongs in the middle.
0.67 ? 0.80
We can see that 0.67 is smaller than 0.8. Therefore, the inequality should be <.
0.67<0.8
Can someone organize these from least to greatest
-4.8 * 3.2 [least],
4.32/3,
-2 3/5 - (-1 2/5),
2 1/4 + (-1 2/5) [greatest]
Step-by-step explanation:
-4.8 * 3.2 = -15.36
4.32 / -3 = -1.44
-2 3/5 - (-1 2/5) = -2 3/5 + 1 2/5 = -2.6 + 1.4 = -1.2
2 1/4 + (-1 2/5) = 2 5/20 - 1 8/20 = 17/20 = 0.85
In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random variable.
Answer:
The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.
Step-by-step explanation:
The question is incomplete:
The probability distribution is:
x P(x)
0 0.30
1 0.40
2 0.20
3 0.06
4 0.04
The mean can be calculated as:
[tex]M=\sum p_iX_i=0.3\cdot 0+0.4\cdot 1+0.2\cdot 2+0.06\cdot 3+0.04\cdot 4\\\\M=0+0.4+0.4+0.18+0.16\\\\M=1.14[/tex]
(pi is the probability of each class, Xi is the number of topping in each class)
The standard deviation is calculated as:
[tex]s=\sqrt{\sum p_i(X_i-M)^2}\\\\s=\sqrt{0.3(0-1.14)^2+0.4(1-1.14)^2+0.2(2-1.14)^2+0.06(3-1.14)^2+0.04(4-1.14)^2}\\\\s=\sqrt{0.3(-1.14)^2+0.4(-0.14)^2+0.2(0.86)^2+0.06(1.86)^2+0.04(2.86)^2}\\\\ s=\sqrt{0.3(1.2996)+0.4(0.0196)+0.2(0.7396)+0.06(3.4596)+0.04(8.1796)}\\\\s=\sqrt{0.3899+0.0078+0.1479+0.2076+0.3272}\\\\ s=\sqrt{ 1.0804 }\\\\s\approx 1.04[/tex]
Answer:
mean: 1.14; standard deviation: 1.04
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue
graph?
A grocery store bought ice cream for $2.80 per half gallon and stored it in two freezers. During the night, one freezer malfunctioned and ruined 12 half gallons. If the remaining ice cream is sold for $3.96 per half gallon, how many half gallons did the store buy if they made a profit of $66.16?
Steps:
Add 47.52 to both sides
Divide both sides by 1.16
x= 98
Description:
The first step is to add 47.52 to both sides then simplify it then divide the both sides by 1.16. And your answer will equal as x=98.
Answer: x= 98
Please mark brainliest
Hope this helps.