Answer:
2.5% of adults are intellectually disabled by this criterion
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 105
Standard deviation = 16
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
What percent of adults are intellectually disabled by this criterion
Below 73
73 = 105 - 2*16
So 73 is 2 standard deviations below the mean.
Of the 50% of the measures that are below the mean, 95% are within 2 standard deviations of the mean, that is, between 73 and 105. The other 100 - 95% = 5% are below 73. So
0.05*0.5 = 0.025
0.025*100 = 2.5%
2.5% of adults are intellectually disabled by this criterion
I don’t know how to do this, what’s the area?
Answer:
Hello!
Step-by-step explanation:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.
So,you have to multiply.
Hope this helps.
Solve for x in the diagram below.
Answer:
x = 20
Step-by-step explanation:
The three angles form a straight line so they add to 180 degrees
x+ 100 +3x = 180
Combine like terms
100+4x= 180
Subtract 100 from each side
100+4x-100= 180-100
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
Answer:
[tex]x = 20 \: \: degrees[/tex]
Step-by-step explanation:
Angles in a straight line = 180 degrees
[tex]x + 3x + 100 = 180 \\ 4x + 100 = 180 \\ 4x = 180 - 100 \\ 4x = 80 \\ \frac{4x}{4} = \frac{80}{4} \\ x = 20 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A bird of species? A, when? diving, can travel six times as fast as a bird of species B top speed. If the total speeds for these two birds is 224 miles per hour
Answer:
Maximum speed of bird A is [tex]192\,\,\frac{mi}{h}[/tex]
Maximum speed of bird B is [tex]32\,\,\frac{mi}{h}[/tex]
Step-by-step explanation:
This is a problem with two unknowns: Max speed of bird A (we name that "A"), and max speed of bird B (we call that "B"). Now we can create two equations with these two unknowns, based on the info provided:
Equation 1): based on the phrase "bird A can travel six times as fast as bird B" we write:
[tex]A=6\,*\, B\\A=6B[/tex]
Equation 2): based on the phrase; "the total speeds for these two birds is 224 miles per hour", we write:
[tex]A+B=224\,\,\frac{mi}{h}[/tex]
Now, we use the first equation to substitute A in the second equation, ad then solve for the unknown B:
[tex]A+B=224\,\,\frac{mi}{h}\\(6B)+B=224\,\,\frac{mi}{h}\\7B=224\,\,\frac{mi}{h}\\B=\frac{224}{7} \,\,\frac{mi}{h}\\B=32\,\,\frac{mi}{h}[/tex]
Now we can solve for the other unknown "A" using the substitution equation and the value of B we just found:
[tex]A=6B\\A=6\,(32\,\,\frac{mi}{h})\\A=192\,\,\frac{mi}{h}[/tex]
100 thousands equal to ---lakhs
Answer:one lakh....
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 thnk me...
Answer:
1 Lakh = 100 Thousands
Step-by-step explanation:
which of the following expressions is equal to 2X^2 +8
Answer:
The question is not clear.
Step-by-step explanation:
Normally it helps to rewrite 8 as
8 = 2 * 2 * 2 = 2³
However the question is not clear.
There are no following expressions given...
By 2X^2 +8,
do you mean 2*x² + 8, or do you mean 2*x^(2 + 8)
or did you perhaps mean 2^(x+8)
Next time, please add a picture.
Answer:
(2x-4i)(x+2i)
According to the Mortgage Bankers Association, 21% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of seven mortgages was selected. What is the standard deviation of this distribution
Answer:
The standard deviation for the number of delinquent mortgages in the sample is 1.08.
Step-by-step explanation:
For each mortgage, there are only two possible outcomes. Either it is delinquent, or it is not. The probability of a mortgage being delinquent is independent of other mortgages. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
21% of U.S. mortgages were delinquent last year.
This means that [tex]p = 0.21[/tex]
A random sample of seven mortgages was selected.
This means that [tex]n = 7[/tex]
What is the standard deviation of this distribution
[tex]\sqrt{V(X)} = \sqrt{7*0.21*0.79} = 1.08[/tex]
The standard deviation for the number of delinquent mortgages in the sample is 1.08.
Please help! Will give Brainliest!
Steps 1-4 in attachment (#4 below)
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.
Answer:
g(x) = 2|x|g(x) = -2|x|g(x) = -2|x| -3g(x) = -2|x-1| -3Step-by-step explanation:
1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...
g(x) = 2|x|
__
2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.
g(x) = -2|x|
__
3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.
g(x) = -2|x| -3
__
4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...
g(x) = -2|x -1| -3
A man driving a car leaves a point A drives up to 32.5 km in a direction of 070. A cyclist leaves the same point in a direction 130 travelling. After some few hours both drivers are 80 km apart. Use this information to answer 3 questions. (1). What is the distance covered by the cyclist at this time in 2 d.p. (2). Find the bearing of Cyclist from the Car. correct to 1 d.p. (3). Find the shortest distance between the car and the line of path of the cyclist, in 2 d.p.
Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.
An artist is trying to choose 5 covers for children’s books. There are 10 different covers to choose from. How many ways can the artist choose covers? (It’s a permutation and combination kind of problem)
Answer:
252
Step-by-step explanation:
The order of the books isn't important, so we'll use combinations.
The number of ways to choose 5 books from 10 is:
₁₀C₅ = 10! / (5! (10 − 5)!)
₁₀C₅ = 10! / (5! 5!)
₁₀C₅ = 10×9×8×7×6 / (5×4×3×2×1)
₁₀C₅ = 252
I need help pls someone:(
Answer:
7/30
Step-by-step explanation:
here it is ill mark you as brainliest if the answer is correct.
Answer:
A = 1168.67 cm²
Step-by-step explanation:
[tex]A=2\pi rh+2\pi r^{2}[/tex] Use this equation to find the surface area
[tex]A=2\pi (6)(25)+2\pi (6)^{2}[/tex] Multiply
[tex]A=2\pi (150)+2\pi (36)[/tex] Multiply
A = 942.48 + 226.19 Add
A = 1168.67 cm²
Answer:
1169.14cm2
Step-by-step explanation:
The surface area is that area which you can feel. Now there are two circles one at the top and one at the bottom.
These areas are expressed as;
π×r2 { remember area of a circle}.
Therefore for the two areas we have twice the area of once since they are the same. Hence we have:
2×π×r2.
Secondly, there is still another area we haven't talked about yet. It's the area you feel at the side and this area curls into a circular fashion.
Now let's assume the two circles are the top and bottom are knocked off , we would have a shape that looks like a rectangle.
Now area of a rectangle is the multiplication of both sides. In this case the side would be the height,h and the circumference of the circle since the rectangle forms into a circle when she try to join both edges together.
Hence the area of this Shape would be;
2πr{circumference} × h=2πrh
Hence the total surface area would be;
2πr2 + 2πrh.
Substituting the giving values we have;
Note: to obtain raduis,r ; we divide the diameter by 2.
2 × 22/7 × 6^2 + 2 × 22/7 × 6× 25
2×22/7(36+150)
44/7(186)= 8184/7
=1169.1429cm2
=1169.14cm2{ to 2 decimal place}
3] The population of a
village is 4800. There are
1200 men, 1620 women
480 boys and the rest are
girls.
(a) How many girls are
in the village?
(b) Calculate the
percentage of men in
the village.
Answer:
A) 1500 girls
B) 25% are men
Step-by-step explanation:
I hope this helps
What is the area of triangle ABC?
3 square units
0 7 square units
11 square units
15 square units
[tex]the \: answer \: is \: 7 \: square \: units \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. What is the probability that the next customer will request mid-grade gas and fill the tank
Answer:
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Step-by-step explanation:
In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:
probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks
probability that the next customer will request mid-grade gas and fill the tank= 30%*60%
probability that the next customer will request mid-grade gas and fill the tank= 0.1800
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Which equation is equivalent to One-fourth + x =Negative StartFraction 5 over 4 EndFraction? Select all that apply.
Options:
(A)x = StartFraction 6 over 4 EndFraction
(B)x = Negative StartFraction 6 over 4 EndFraction
(C)x minus one-fourth = negative StartFraction 5 over 4 EndFraction
(D)x = negative three-halves
(E)x = negative three-fourths
Answer:
(B)x = Negative StartFraction 6 over 4 EndFraction
[tex]-\dfrac{6}{4}[/tex]
(D)x = negative three-halves
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
We want to determine which fraction is equivalent to
[tex]\dfrac{1}{4}+x=-\dfrac{5}{4}\\$First, we collect like terms$\\x=-\dfrac{5}{4}-\dfrac{1}{4} \\\\=\dfrac{-5-1}{4}\\=-\dfrac{6}{4}\\x=-\dfrac{6}{4}[/tex]
This value of x is the result in Option B.
Reducing [tex]-\dfrac{6}{4}[/tex] to its lowest form:
[tex]-\dfrac{6}{4}=-\dfrac{3}{2}[/tex] which is Option D.
Therefore, the correct options are: B and D
if teta is an angle in right angle triangle if tan teta = 3/4 then find sin teta?
Answer:
[tex] \frac{3}{5}[/tex]
Step-by-step explanation:
The adjacent sides are 3 and 4. Thus the hypotenuse is: (by Pythagoras Theorem)
$=\sqrt{3^2+4^2}$
$=\sqrt{25}$
$=5$
Now by definition of $\sin$, we get:
$\sin \theta= \frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5}$
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none select none. When m<7=m<4
Answer:
Option (2). None
Step-by-step explanation:
A quadrilateral ABCD has been given with a property,
m∠7 = m∠4
Option (1). AB║ DC
For AB║DC, angle 7 and angle 3 should measure the same.
(By the property of alternate angles)
Therefore, by the given property we can not deduce AB║DC.
Option (3). AD║BC
For AD║BC, angle 7 and angle 3 must be equal in measure.
(By the property of alternate angles)
Therefore, by the given property we can not deduce AD║DC
Option (2). None will be the answer.
Michael has a weekly food budget of $62. If he plans to budget the same amount for each of the 7 days of the week, what is the maximum amount he can spend on food each day?
Answer:
62/7
Step-by-step explanation:
The budget illustrates ratios and proportions.
The maximum amount to spend on food each day is $8
The given parameters are:
[tex]\mathbf{Budget = \$62}[/tex]
[tex]\mathbf{Days = 7}[/tex]
So, the daily budget is:
[tex]\mathbf{Daily = \frac{Budget}{Days}}[/tex]
So, we have:
[tex]\mathbf{Daily = \frac{\$62}{7}}[/tex]
[tex]\mathbf{Daily = \$8.85714285714}[/tex]
Remove decimal parts (do not approximate)
[tex]\mathbf{Daily = \$8}[/tex]
Hence, the maximum to spend each day is $8
Read more about ratios and proportions at:
https://brainly.com/question/13114933
Some of the stock in a winery has been found to be infected by Brettanomyces. You independently sample 80 barrels from the winery, and find that 28 of them are infected. Carry out a hypothesis test to evaluate the claim that half of the wine barrels are infected. What is closest to the p-value that you obtain
Answer:
Step-by-step explanation:
If half of the wine barrels are infected, it means that the proportion of infected wine is 0.5
We would set up the hypothesis test.
For the null hypothesis,
p = 0.5
For the alternative hypothesis,
p < 0.5
Considering the population proportion, probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 28
n = number of samples = 80
P = 28/80 = 0.35
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.35 - 0.5)/√(0.5 × 0.5)/80 = - 2.68
From the normal distribution table, the area below the test z score in the left tail 0.0037
Therefore,
p value = 0.0037
Assuming a significance level of 0.05, therefore,
Since alpha, 0.05 > than the p value, 0.0037, then we would reject the null hypothesis.
Barry has $30.00 to spend on soft drinks
for a party. A case of soft drinks costs
$4.65. Which inequality can be used to find how many cases (c) of soft drinks
Barry can purchase?
Answer:
30 ≥ 4.65x
Step-by-step explanation:
He cannot purchase more than $30, so the amount that he buys must always be less than 30.
Find the probability. Enter your answer as a simplified fraction.
Picking a purple marble from a jar with 14 green and 14 purple marbles.
Answer:
1/2
Step-by-step explanation:
14 green and 14 purple marbles = 28 marbles
P( purple) = purple/ total
= 14/28
=1/2
Pls help I really need help
Answer:
7. [tex]x \leq 5[/tex]
8. [tex]x\geq 4[/tex]
9. x < 5
10. x < -7
11. x < 45
12. [tex]x\geq -10[/tex]
13. x < -7
14. x < 45
15. [tex]x\leq 50[/tex]
16. [tex]w\geq 16[/tex]
18. q > 4
Step-by-step explanation:
What is the symbol for pi?
Answer:
π
Step-by-step explanation:
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose from, 55 types of sandwiches, and 44 types of chips. How many different value meal packages are possible?
Answer:
159,720
Step-by-step explanation:
Calculation of how many different value meal packages are possible at Ron's Subs :
The meal package at Ron's Subs are:
Drink 66
Sandwich 55
Bag of chips 44
Since we are looking for the how many different value meal packages are possible that means we have to multiply all the three value meal package with each other.
Hence,
Drink 66 ×Sandwich 55 ×Bag of chips 44
=159,720
Therefore 159,720 is the number of different value meal packages that are possible at Ron's Subs
On a number line, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with number a. For example b= 11/4 when a= -11/4
A) b=-a
B) -b=-a
C) b-a=0
D) b(-a)=0
Answer:
B and A
Step-by-step explanation:
So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.
Wyoming fisheries contend that the mean number of cutthroat trout caught during a full day of fly-fishing on the Snake, Buffalo, and other rivers and streams in the Jackson Hole area is 4.0. To make their yearly update, the fishery personal asked a sample of fly-fishermen to keep a count of the number caught during the day. The numbers were: 4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6. At the 0.05 significance level, can we conclude that the mean number caught is greater than 4.0?
Answer:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
Step-by-step explanation:
We have the following data given:
4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6
The sample mean and deviation from these data are:
[tex]\bar X=4.5[/tex] represent the sample mean
[tex]s=2.680[/tex] represent the sample deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =4[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to verify if the true mean is equal to 4, the system of hypothesis would be:
Null hypothesis:[tex]\mu =4[/tex]
Alternative hypothesis:[tex]\mu \neq 4[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the the info we got:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
Last years freshman class at big state university totaled $5330 students. Of those, $1258 received a merit scholarship to help offset tuition cost their freshman year. The amount a student received was N($3464, 489). If the cost of full tuition was $4450 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?
Answer:
2.17% of students who received a merit scholarship did not receive enough to cover full tuition
Step-by-step explanation:
Problems of normally distributed samples are solved using 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.
In this question, we have that:
[tex]\mu = 3464, \sigma = 489[/tex]
If the cost of full tuition was $4450 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?
This is 1 subtracted by the pvalue of Z when X = 4450. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4450 - 3464}{489}[/tex]
[tex]Z = 2.02[/tex]
[tex]Z = 2.02[/tex] has a pvalue of 0.9783.
1 - 0.9783 = 0.0217
2.17% of students who received a merit scholarship did not receive enough to cover full tuition
find the mean of x,2x,3x,4x,5x
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{No. OfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
The mean, also known as the average of x, 2x, 3x, 4x, and 5x is 3x as per the concept of Simplifying.
To find the mean of x, 2x, 3x, 4x, and 5x, we need to add up all the values and divide by the total number of values.
In this case, we have five values.
Mean = (x + 2x + 3x + 4x + 5x) / 5
Simplifying the numerator:
Mean = (15x) / 5
Mean = 3x
Therefore, the mean of x, 2x, 3x, 4x, and 5x is 3x.
The mean, also known as the average, represents the central tendency of a set of values. In this case, the mean is 3x, which indicates that on average, the values x, 2x, 3x, 4x, and 5x are three times the value of x.
To learn more about the mean;
brainly.com/question/13451489
#SPJ6
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 25.325.3 milligrams and standard deviation of 2.72.7 milligrams for a sample of n equals 9n=9 cigarettes. Construct a 9090% confidence interval for the mean nicotine content of this brand of cigarette.
Answer:
The 90% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 9 - 1 = 8
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595
The margin of error is:
M = T*s = 1.8595*2.7 = 5
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 25.3 - 5 = 20.3 milligrams
The upper end of the interval is the sample mean added to M. So it is 25.3 + 5 = 30.3 milligrams.
The 90% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.