Answer: Working together, they can complete the task in 7 hours and 12 minutes.
Step-by-step explanation:
Ok, Briana needs 12 hours to complete the task.
Then we can find the ratio of work over time as:
1 task/12hours = 1/12 task per hour.
This means that she can complete 1/12 of the task per hour.
Henry needs 18 hours to complete the task, then his ratio is:
1 task/18 hours = 1/18 task per hour.
This means that he can complete 1/18 of the task in one hour.
If they work together, then the ratios can be added:
R = 1/12 + 1/18 = 18/(12*18) + 12/(18*12) = 30/216
we can reduce it to:
R = 15/108 = 5/36
So, working together, in one hour they can complete 5/36 of the task, now we can find the number of hours needed to complete the task as:
(5/36)*x = 1 task
x = 36/5 hours = 7.2 hours
knowing that an hour is 60 minutes, then 0.2 of an hour is 60*0.2 = 12 minutes.
then x = 7 hours and 12 minutes.
In a sample of 22 people, the average cost of a cup of coffee is $2.70. Assume the population standard deviation is $0.93. What is the 90% confidence interval for the cost of a cup of coffee
Answer:
$2.70+/-$0.33
= ( $2.37, $3.03)
Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)
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 = $2.70
Standard deviation r = $0.93
Number of samples n = 22
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
$2.70+/-1.645($0.93/√22)
$2.70+/-1.645($0.198276666210)
$2.70+/-$0.326165115916
$2.70+/-$0.33
= ( $2.37, $3.03)
Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)
Can someone please help me
Answer:
20
Step-by-step explanation:
If the two triangles are similar, then corresponding sides must share a constant ratio. This means that:
[tex]\dfrac{10}{6}=\dfrac{25}{15}=\dfrac{x}{12}[/tex]
Let's use the second ratio:
[tex]\dfrac{25}{15}=\dfrac{x}{12}[/tex]
Multiply both sides by 12:
[tex]\dfrac{25\cdot 12}{15}=x \\\\x=20[/tex]
Hope this helps!
Please answer this correctly
Answer:
Step-by-step explanation:
Baltimore orioles : 1,000,000 + 1,000,000 + 500,000
Click 2 full bag and 1 half bag
Kansas city royals : 1,000,000 +500,000
Click 1 full bag and 1 half bag
Newyork Yankees : 1,000,000 + 1,000,000 + 1,000,000 +1,000,000 +1,000,000 + 500,000
Click 5 full bag + 1 half bag
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then
[tex]n = 1537, \pi = \frac{353}{1537} = 0.2297[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507[/tex]
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
The length of a 95% confidence interval for mean Age is which of the following? (Because of potential roundoff, choose the closest.) Click here to reference the data needed to answer the question. a. 3.37 b. 3.72 c. 4.27 d. 3.11
Answer:
The length of a 95% confidence interval for mean Age is 3.72.
Step-by-step explanation:
The data is provided for the age of 100 adults.
The mean and standard deviation are:
[tex]\bar x=47.8\\\\s=9.3744[/tex]
As the sample size is too large the z-interval will be used for the 95% confidence interval for mean.
The critical value of z for 95% confidence level is, z = 1.96.
The length of a confidence interval is given by:
[tex]\text{Length}=2\cdot z_{\alpha/2}\cdot\frac{s}{\sqrt{n}}[/tex]
[tex]=2\times 1.96\times\frac{9.3744}{\sqrt{100}}\\\\=3.6747648\\\\\approx 3.67\\\\\approx 3.72[/tex]
Thus, the length of a 95% confidence interval for mean Age is 3.72.
An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2000 individuals, what is the approximate distribution of the number who carry this gene
Answer:
Brianliest!
Step-by-step explanation:
4
1 in 500
500 x 4 = 2000
4 in 2000
Find the volume of the cone.
4 cm
3 cm
V = [?] cm3
Round to the nearest tenth.
Answer:
Volume of a cone = 1/3πr²h
h = height
r = radius
r = 3cm h = 4cm
Volume = 1/3π(3)²(4)
= 36 × 1/3π
= 12π
= 36.69cm³
= 37cm³ to the nearest tenth
Hope this helps
Answer:
37.7
_______
NOT 37
Step-by-step explanation:
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]3^{2}[/tex] · [tex]4 = 12\pi = 37.69911 =[/tex] 37.7
If
f(x) = 13x + 1, then
f-1(x) =
Answer:
(x-1)/13
Step-by-step explanation:
y = 13x+1
To find the inverse, exchange x and y
x = 13y+1
Solve for y
Subtract 1 from each side
x-1 =13y+1-1
x-1 = 13y
Divide each side by 13
(x-1)/13 = y
The inverse is (x-1)/13
Answer:
f(x) = 13x + 1
To find the inverse let f(x) = y
y = 13x + 1
x = 13y + 1
13y = x - 1
y = (x-1)/13
The inverse is x-1/13.
Help solve attached question.
Answer:
[tex]\mathrm{12\sqrt{5} \: \: inches}[/tex]
Step-by-step explanation:
Use Pythagorean theorem, where:
[tex]a^2+b^2=c^2[/tex]
Substitute in the values.
[tex]24^2+12^2=c^2[/tex]
[tex]c^2=576+144[/tex]
[tex]c^2=720[/tex]
[tex]c=\sqrt{720}[/tex]
[tex]c=12\sqrt{5}[/tex]
[tex]c=26.83281[/tex]
What is the general form of the equation of the line shown? 2 x - y + 3 = 0 2 x - y - 3 = 0 x - 2 y - 3 = 0
Answer:
2x - y - 3 = 0
Step-by-step explanation:
Find slope-intercept form first: y = mx + b
Step 1: Pick out 2 points
In this case, I picked out (2, 1) and (0, -3) from the graph
Step 2: Using slope formula y2 - y1/x2 - x1 to find slope
-3 - 1/0 - 2
m = 2
Step 3: Place slope formula results into point-slope form
y = 2x + b
Step 4: Plug in a point to find b
-3 = 2(0) + b
b = -3
Step 5: Write slope-intercept form
y = 2x - 3
Step 6: Move all variables and constants to one side
0 = 2x - 3 - y
Step 7: Rearrange
2x - y - 3 = 0 is your answer
The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power. The probabilities that these two sources will be successfully developed and commercially viable in the next 10 years are 0.70 and 0.85, respectively. The successful development of these two energy sources are statistically independent. Determine the following: a. The probability that there will be energy supplied by these two alternative sources in the next 10 years. b. The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years.
Answer:
Step-by-step explanation:
a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S
Write the probability of energy supplied by these energy sources in the next 10 years
P(energy supplied) = P(S ∪ F) -----(1)
Rewrite eqn (1)
P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)
substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources
P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)
= 0.85 + 0.7 - (0.595)
= 1.55 - 0.595
= 0.955
Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955
B) write the probability of only one source of energy available
P(only one source of energy available) = [tex]P(\bar F S)[/tex] ∪ [tex]P( \bar S F)[/tex] ---(3)
Rewrite the equation (3)
P(only one source of energy available) =
[tex]=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)[/tex]
[tex]=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36[/tex]
Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36
A simple random sample of 5 months of sales data provided the following information: Month: 1 2 3 4 5 Units Sold: 94 105 85 94 92 (a) Develop a point estimate of the population mean number of units sold per month. x = (b) Develop a point estimate of the population standard deviation. If required, round your answer to two decimal places. s =
Answer:
a) x = 94 units/month
b) s = 51.50 units/month
Step-by-step explanation:
The adequate point estimation of the population mean and standard deviation are the sample mean and sample standard deviation.
a) Point estimation of the population (sample mean)
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(94+105+85+94+92)\\\\\\M=\dfrac{470}{5}\\\\\\M=94\\\\\\[/tex]
b) Point estimation of the population standard deviation (sample standard deviation)
[tex]s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{4}((94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2)\\\\\\s=\dfrac{206}{4}\\\\\\s=51.50\\\\\\[/tex]
Using statistical concepts, it is found that:
a) The point estimate for the population mean is of: [tex]\overline{x} = 94[/tex]
b) The point estimate for the population standard deviation is of: [tex]s = 7.18[/tex]
Item a:
The mean of a data-set is the sum of all observations in the data-set divided by the number of observations.The point estimate for the population mean is the sample mean.In this problem, the sample is: 94, 105, 85, 94, 92.
Thus, the mean is:
[tex]\overline{x} = \frac{94 + 105 + 85 + 94 + 92}{5} = 94[/tex]
Item b:
The standard deviation of a data-set is the square root of the sum of the differences squared between each observation and the mean, divided by one less than the number of values.The point estimate for the population standard deviation is the sample standard deviation.Then:
[tex]s = \sqrt{\frac{(94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2}{4}} = 7.18[/tex]
A similar problem is given at https://brainly.com/question/13451786
Which graph shows a function whose domain and range exclude exactly one value?
Answer:
C (the third graph)
Step-by-step explanation:
This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.
Answer:
see below
Step-by-step explanation:
This graph has an asymptote at y = 0 and x=0
This excludes these values
The domain excludes x =0
The range excludes y=0
for a sample size of 115 and a population parameter of 0.1,what is the standard deviation of the normal curve that can be used to approximate the binomial probability histogram. Round your answer to three decimal places
A.0.028
B.0.054
C.0.043
D.0.035
Answer:
A) 0.028
Step-by-step explanation:
Given:
Sample size, n = 115
Population parameter, p = 0.1
The X-Bin(n=155, p=0.1)
Required:
Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.
To find the standard deviation, use the formula below:
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
Substitute figures in the equation:
[tex]\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.1 * 0.9}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.09}{115}}[/tex]
[tex] \sigma = \sqrt{7.826*10^-^4}[/tex]
[tex] \sigma = 0.028 [/tex]
The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028
If the terms of a polynomial do not have a GCF, does that mean it is not factorable?
What is the answer? x^2-y^2=55
Answer:
To solve for x we can write:
x² - y² = 55
x² = y² + 55
x = ±√(y² + 55)
To solve for y:
x² - y² = 55
y² = x² - 55
y = ±√(x² - 55)
A polynomial is factorable, but it is not a perfect square trinomial or a
difference of two squares. Can you factor the polynomial without finding the GCF?
Answer:
So in this problem, we're told that a polynomial is fact herbal and it's not a perfect square. Try no meal or a difference of two squares. Can you factor the pie? Nomi bite or polynomial without finding the G C F. So no Jacey after is allowed. So if it's not a perfect squared, try no meal. So not a perfect square. We know it's not this, and we also know it's not a difference of two squirt if it's not any of these or if it's not either of these, but we can't find the G. C F. There are three different ways we could find the factored form. You could do it by grouping where you separating the polynomial into two parts and factor them individually before combining. You could also use the sum or a difference of cubes. This is for a cubic or a um, polynomial of third degree, and you could also use fractional or negative exponents. So even if you can't find the G c f or use these methods, there are still three ways you can factor the
Step-by-step explanation:
Glad i could help!
Calculate balloon volume for each balloon at maximum inflation from the circumference data. (You will have to assume that the balloon was a perfect sphere.) To calculate balloon volume, first find the radius (in cm) of the balloon by using the formula C = 2πr. Then, use the radius' value in the formula V = (4/3)πr3 to calculate volume (in cm3). Show all your work, place units on all numbers (even those within the calculations), and express your answers with appropriate sig figs. (12 pts)
Answer:
r₁ = 3.583cm
V₁= 192.55cm³
r₂= 5.176cm
V₂ = 580.283cm³
r₃ = 5.255cm
V₃ = 607.479cm³
Step-by-step explanation:
assuming circumferences of each balloons are given as follows C₁ = 22.5cm, C₂ = 32.5cm and C₃ = 33cm
Recall C = 2πr
volume of a sphere is 4/3πr³
Find the volume of a right circular cone that has a height of 4.2m and a base with a radius of 3.4m
Answer:
about 50.8 cubic meters
Step-by-step explanation:
The formula for the volume of a cone is ...
V = (1/3)πr²h
Put the given values into the formula and do the arithmetic.
V = (1/3)π(3.4 m)²(4.2 m) = 16.194π m³
__
For π to calculator precision, this is ...
V ≈ 50.84 m³
For π = 3.14, this is ...
V ≈ 50.82 m³
I Am Thinking of a number. 1/12 of it equals 6. 1/3 of it equals_________.
Answer:
24
Step-by-step explanation:
hello
let's note x the number we are looking for
[tex]\dfrac{x}{12}=6\\<=> x = 6*12=72[/tex]
so 1/3 of it equals
[tex]\dfrac{72}{3}=24[/tex]
another way to see it is that 12=4*3
so 1/3 of it equals 6*4=24
hope this helps
Which of these fractions is an improper fraction? 5/3 or 3/5
Answer:
5/3 is an improper fraction because 5 is higher then 3. So the correct way of writing it would be 1 2/3.
Step-by-step explanation:
HURRY TIMEDD!!!!!
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has? The discriminant is −4, so the equation has 2 real solutions. The discriminant is −4, so the equation has no real solutions. The discriminant is 35, so the equation has 2 real solutions. The discriminant is 35, so the equation has no real solutions.
Answer:
Second option is the correct choice.
Step-by-step explanation:
"The discriminant is −4, so the equation has no real solutions."
[tex]x^2-4x+5=0\\\\a=1,\:b=-4,\:c=5:\\\\b^2-4ac=\left(-4\right)^2-4\cdot \:1\cdot \:5=-4[/tex]
Best Regards!
Answer: B
The discriminant is −4, so the equation has no real solutions.
Step-by-step explanation:
Just took quiz EDG2021
Mark Brainliest
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.45 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are operating. Assume that the components operate independently. (Round your answers to four decimal places.)
Required:
Find the probability that the subsystem operates longer than 1000 hours.
Answer:
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The components operate independently. 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.
Eight components:
This means that [tex]n = 8[/tex]
Probability of 0.45 of failing in less than 1,000 hours.
So 1 - 0.45 = 0.55 probability of working for longer than 1000 hours, which means that [tex]p = 0.55[/tex]
Find the probability that the subsystem operates longer than 1000 hours.
We need at least four of the components operating. So
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{8,4}.(0.55)^{4}.(0.45)^{4} = 0.2627[/tex]
[tex]P(X = 5) = C_{8,5}.(0.55)^{5}.(0.45)^{3} = 0.2568[/tex]
[tex]P(X = 6) = C_{8,6}.(0.55)^{6}.(0.45)^{2} = 0.1569[/tex]
[tex]P(X = 7) = C_{8,7}.(0.55)^{7}.(0.45)^{1} = 0.0548[/tex]
[tex]P(X = 8) = C_{8,8}.(0.55)^{8}.(0.45)^{0} = 0.0084[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2627 + 0.2568 + 0.1569 + 0.0548 + 0.0084 = 0.7396[/tex]
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 80% confident that you estimate 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}{1.28})^2}=655.36[/tex]
And rounded up we have that n=656
Step-by-step explanation:
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 80% of confidence, our significance level would be given by [tex]\alpha=1-0.80=0.20[/tex] and [tex]\alpha/2 =0.10[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=\pm 1.28 [/tex]
Solution to the problem
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)
Since we don't have prior info for the proportion of interest we can use [tex]\hat p=0.5[/tex] as estimator. 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}{1.28})^2}=655.36[/tex]
And rounded up we have that n=656
factorization of expression 4z(3a+2b-4c)+(3a+2b-4c)
Answer:
(3a+2b-4c)[4z+1]
Step-by-step explanation:
4z(3a+2b-4c)+(3a+2b-4c)
Factor out (3a+2b-4c)
(3a+2b-4c)[4z+1]
Answer:
3a+2b-4c)[4z+1]
Step-by-step explanation:
4z(3a+2b-4c)+(3a+2b-4c)
Factor out (3a+2b-4c)
(3a+2b-4c)[4z+1]
In the matrix equation below, what are the values of x and y?
Answer: x=3 y=1
Step-by-step explanation:
What transformations to the linear parent function, f(x) = x, give the function
g(x) = 4x - 2? Select all that apply.
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
O c. Horizontally stretch by a factor of 4.
O D. Shift left 2 units.
Answer:
A. Shift down 2 units.
B. Vertically stretch by a factor of 4.
Step-by-step explanation:
Given the function
f(x)=x
If we stretch y vertically by a factor of m, we have: y=m·f (x)
Therefore:
Vertically stretching f(x) by a factor of 4, we have: 4x.
Next, if we take down f(x) by k units we have: y= f(x)-k
Therefore: Taking down 4x by 2 units, we obtain:
g(x)=4x-2
Therefore, Options A and B applies.
What is AB? Geometry help please
Answer:
AB = 37 units.
Step-by-step explanation:
Solve for AB using the Pythagorean theorem:
c² = a² + b² (c being AB in this instance)
Plug in the values of the legs of the triangle:
c² = 12² + 35²
c² = 144 + 1225
c² = 1369
c = √1369
c = 37
Therefore, AB = 37.
How many units of insulin are in 0.75 ML a regular U – 100 insulin
Answer:
0.75 ML of insulin contains 75 units of insulin
Step-by-step explanation:
U - 100 insulin hold 100 units of insulin per ml
This means that:
1 ML = 100 units
∴ 0.75 ML = 100 × 0.75 = 75 units
Therefore 0.75 ML of insulin contains 75 units of insulin
What is the relative change from 6546 to 4392
Answer:
The relative change from 6546 and 4392 is 49.04
Step-by-step explanation: