Answer:
a) 0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers
b) 0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers
c) 1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be 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.
Standard deviation of 500 kilometers
This means that [tex]\sigma = 500[/tex]
a. Assuming the mean is 1500 kilometers, what is the probability of a northward displacement of less than 500 kilometers?
Mean of 1500 km means that [tex]\mu = 500[/tex]
The probability is the pvalue of Z when X = 500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 1500}{500}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.0228 = 2.28% probability of a northward displacement of less than 500 kilometers.
b. Assuming the mean is 1200 kilometers, what is the probability of a northward displacement of less than 500 kilometers?
Now [tex]\mu = 1200[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 1200}{500}[/tex]
[tex]Z = -1.4[/tex]
[tex]Z = -1.4[/tex] has a pvalue of 0.0808
0.0808 = 8.08% probability of a northward displacement of less than 500 kilometers.
c. If, in fact, the northward displacement is less than 500 kilometers, which is the more plausible mean, 1200 or 1500 kilometers?
1200 kilometers, because in this case, the will be a higher probability of a northward displacement that is less than 500 kilometers.
The height (in inches) of males in the United States is believed to be Normally distributed. The average height of a random sample of 50 American adult males is 69.72 inches and the standard deviation of the 50 heights is s = 4.23. The best pint estimate for the average height if males in the United States is_____inches. Give answer to the hundredths place.
Answer:
69.72 inches.
Step-by-step explanation:
The best point estimate for the average height if males in the United States is...
For large samples, as we have here, the best point estimate is the sample mean. In this question, the sample mean is of 69.72 inches, so the answer is 69.72 inches.
7. An equilateral triangle has sides of length 6.2cm, correct to the nearest millimetre.
Complete the statement about the perimeter, Pcm, of the triangle.
Five family members are going to a play. A service charge of $2 is added to the cost of each ticket. The family is willing to pay $250 or less for the five tickets. What is the greatest amount the family is willing to pay for each ticket? PLEASEE HELPPP ME
250 ÷5 = 50
$50
Hope this helps!
Lamar buys 0.8 gallon of gas to use in the lawnmower the price of the gas is 2.95$ per gallon how much does Lamar play for the gas
Answer:$2.36
Step-by-step explanation:
2.95 x .8 = 2.36
6x-1/2=1 solve this equation
Answer:
cross ❌ multiply
6x-1=2
6x=2+1
6x=3
divide both sides by 6
x=1/2
Solve for n:5*8^3n+1=80
Answer:
8^(3n+1) = 80/5
8^(3n+1) = 16
(2^3)^(3n+1) = 2^4
2^(3*(3n+1) = 2^4
Having same power so;
9n+3 = 4
9n = 4-3
9n = 1
n = 1/9
Someone help me on this please
Answer:
b
Step-by-step explanation:
there are 65 cookies in a jar. the probability of randomly choosing an oatmeal cookie from the jar is 40% how many of the cookies are oatmeal cookies pls help
Answer:
25
Step-by-step explanation:
help me someone please
A company makes wax candles shaped like rectangular prisms. Each candle is 5 cm long, 3cm wide, and 10cm tall. If the company used 3900 cm3 of wax, how many candles did they make?
Answer:
26 candles
Step-by-step explanation:
19. A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively.19a. Describe the shape of the sampling distribution of the sample mean in this case.19b. Find the mean and standard error of the sampling distribution of the sample mean.19c. What is the probability that the mean age exceeds 73 years
Answer:
a) Approximately normal.
b) The mean is 75 years and the standard deviation is 0.8485 years.
c) 0.9909 = 99.09% probability that the mean age exceeds 73 years
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Sample of 50 retirees
This means that [tex]n = 50[/tex]
Mean age and standard deviation are 75 and 6 years
This means that [tex]\mu = 75, \sigma = 6[/tex]
a. Describe the shape of the sampling distribution of the sample mean in this case
By the Central Limit Theorem, approximately normal.
b. Find the mean and standard error of the sampling distribution of the sample mean.
By the Central Limit Theorem, the mean is 75 and the standard error is [tex]s = \frac{6}{\sqrt{50}} = 0.8485[/tex]
c. What is the probability that the mean age exceeds 73 years?
This is 1 subtracted by the pvalue of Z when X = 73.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{73 - 75}{0.8485}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a pvalue of 0.0091
1 - 0.0091 = 0.9909
0.9909 = 99.09% probability that the mean age exceeds 73 years
what is the mean of the ages of the dance instructors?
IM GIVING BRAINLIEST‼️
Answer:
the answer to this is 25
Answer: 25
To find mean you first need to add up all the ages, which gives you 125. Then you divide that number by how many people. In this case it's 5, so divide 125 by 5 which gives you 25. And that's your answer.
Hope this helped you!
WILL MARK B!
Please I need help I have a quiz
Answer:
a) 2x² - x + 3 = x(2x + 1) - 2x
<=> 2x² - x + 3 = 2x² + x - 2x
<=> 3 - x = - x
<=> 3 = 0
=> no solution
b) x/2 - x/3 - x/4 = 1/12
[tex] \frac{6x}{12} - \frac{4x}{12} - \frac{3x}{12} = \frac{1}{12} \\ \\ \frac{ - x}{12} = \frac{1}{12} \\ \\ = > - x = 1 \\ \\ \\ < = > x = 1[/tex]
=> the euqation has the solution x = 1
c) |x - 5| = 2|x|
=> x - 5 = 2x
or x - 5 = -2x
<=> x = -5
or 3x = 5
<=> x = -5
x = -5or x = 5/3
d) defined conditions: 2 - x 》 0
<=> x 《 2
we have:
[tex] \sqrt{x + 4} = 2 - x \\ < = > x + 4 = (2 - x) {}^{2} \\ < = > x + 4 = {x}^{2} - 4x + 4 \\ < = > {x}^{2} - 5x = 0 \\ < = > x(x - 5) = 0 \\ [/tex]
<=> x = 0 (because x 《 2)
e)
[tex] \sqrt{5} = \frac{1}{25 {}^{x} } \\ = > 5 = \frac{1}{25 {}^{2x} } \\ < = > 5.25 {}^{2x} = 1 \\ < = > 5.5 {}^{4x} = 1 \\ < = > 5 {}^{4x + 1} = 1 \\ = > 4x + 1 = 0[/tex]
<=> x = -1/4
Answer:
[tex]a) [x: - \infty < x < \infty ][/tex]
[tex]b)[x: - 1][/tex]
[tex]c) [x:- \frac{5}{3} ][/tex]
[tex]d) [x: 3, 0][/tex]
[tex]e) [x: - \frac{1}{4} ][/tex]
Can someone actually helped me? People will answer and deleted their comment I really need help
Congruent Angle
Vertical Angle
Adjacent Angle
Complementary Angle
Supplementary Angle
Answer:
14) ∠CBE = 118° supplementary to 62°
15) ∠ABF = 28° complementary to 62°
16 ∠CBA = 152° because it is vertical to ∠DBF
Step-by-step explanation:
14) ∠CBE = 180° - 62° = 118°
15) ∠ABF = 90° - 62° = 28°
16) ∠DBF = 90°+ 62° = 152°
∠CBA = ∠DBF
The vertices of APQR are P(-3, 8) Q(-6,-4), and R(1, 1). If you reflect APQR across the x-axis, what will be the coordinates of the vertices of the image AP'Q'R'?
Answer:(-3,-8),(-6,4),(1,-1)
Step-by-step explanation:
Given
Vertices of the triangle are
[tex]P(-3,8), Q(-6,-4),R(1,1)[/tex]
Coordinates (a,b) when reflected about x-axis is given as (a,-b) i.e. Y coordinate changes its sign
[tex]\therefore P\rightarrow P'(-3,-8)\\\Rightarrow Q\rightarrow Q'(-6,4)\\\Rightarrow R\rightarrow R'(1,-1)[/tex]
Find the vertex of the parabola y=2x^2+10x+8
Answer:
Step-by-step explanation:
Put the equation into vertex form.
y = 2x² + 10x + 8
= 2(x² + 5x) + 8
= 2(x² + 5x + 2.5²) - 2·2.5² + 8
= 2(x+2.5)² - 4.5
vertex (-2.5, -4.5)
Help me plsss first person with the right answer gets Brainliest
Answer:
D
Step-by-step explanation:
Have a nice day!
SOMEONE PLEASE HELP NO LATE RESPONSES JUST PLEASE ASAP
Answer:
93.5
Step-by-step explanation:
this is on ttm or imagine math
Answer:
I think the answer is A as well
Step-by-step explanation:
Answer:
a a a a a a a a a a a a a
Step-by-step explanation:
75% of n is 45. n is what percent of 90?
Answer:
66.67%
Step-by-step explanation:
75 /100 = .75
.75n = 45
45/.75 = 60
60 is n
60/90 = .666667
.666667 * 100 = 66.67%
Answer: for this problem, I will be using proportions.
Step-by-step explanation:
Find n
45 x 100 = 4,5000
4,5000 / 75 = 60
n = 60
60 x 100 = 6,000
6,000 / 90 = 66.66%
So, n is equal to 60 and n is 66.66% of 90.
I just need these three questions fine, they should be easy, 7th grade level
1) A graph is linear when the line on a graph is a straight line with no curves.
2) A proportional graph means that as x increases, y increases and when x decreases, y decreases and their ratio always stays the same.
3) (I don't know what type of equation you mean but this is my guess)
Division is the last step of an equation.
I need help please.
Answer:
[tex] {120m}^{3} [/tex]
Remember to find the volume it is the
length x height x breadth
A music therapist was interested in investigating whether listening to music or composing music had an influence on both anxiety levels and oxygen saturation in children who were hospitalized for asthma-related illnesses. Thirty-two children spent 20 minutes listening to classical waltzes played on a piano. On a different day, they spent 20 minutes composing their own short pieces of music using a software program.
When listening to music: For the physiological measure, the critical value for t was larger than the test statistic for the observed data. For the anxiety measure, the critical value for t was smaller than the test statistic for the observed data.
When composing music: For the physiological measure, the critical value for t was larger than the test statistic for the observed data. For the anxiety measure, the critical value for t was larger than the test statistic for the observed data.
When writing the results of the music therapist's study, which of these statements reflects the correct conclusions that should be drawn from the results and then included as part of the interpretation paragraph?Question 8 options:
a) Music therapists should make pediatric asthma patients compose music in order to increase their oxygen saturation.
b) Music therapists should make pediatric asthma patients listen to music in order to reduce their anxiety.
c) Pediatric asthma patients should listen to music in order to increase their oxygen saturation.
d) Additional information is needed to draw a proper conclusion.
Answer:
The correct conclusion is;
d) Additional information is needed to draw a proper conclussion
Step-by-step explanation:
The given parameters are;
When listening to music;
Physiological measure Critical t > Test statistic Accept H₀
Anxiety measure Critical t < Test statistic Reject H₀
When composing music;
Physiological measure Critical t > Test statistic Accept H₀
Anxiety measure Critical t > Test statistic Accept H₀
When the test statistic is larger the critical 't'
Therefore, the test suggest that there is no difference between physiological and anxiety influence of composing music on pediatric asthma patients
There is sufficient statistical evidence to suggest that listening to music has an influence on the anxiety of pediatric asthma patients however, the nature of the influence is not specified and more information is needed to draw a proper conclusion
HELP ME PLEASE I HAVEE 5 MINNS lEft HELP
Answer:
im going to guess the last answer. theone that i can't see
Step-by-step explanation:
Patrick randomly selects a marble from a bag , records the color and then returns the marble to the bag . After 40 trials , he has recorded 14 red marbles 12 blue marbles yellow marbles and 4 green marbles Which of the following experimental probabilities is correct based on his record ?
Answer: A
Step-by-step explanation:
6 1/5 - 4 2/4=? help I need it now pls thx u.
Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 11 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is: the absolute tolerance is /-0.0001
Answer:
0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they stay for the same company for more than five years, or they do not. Graduates are independent. This means that 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 percent of all college graduates hired by companies stay with the same company for more than five years.
This means that [tex]p = 0.08[/tex]
Sample of 11 college graduates:
This means that [tex]n = 11[/tex]
The probability, rounded to four decimal places, that in a random sample of 11 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is: the absolute tolerance is +-0.0001
The tolerance means that the answer is rounded to four decimal places.
The probability is P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{11,2}.(0.08)^{2}.(0.92)^{11} = 0.1662[/tex]
0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years
What is the product?
(**(3x2-2) (4x2 +5x)
.
O 12x + 15x8 - 8x8 - 10x5
O
12x24 + 15x12 - 8x8 - 10x4
O 12x9-10x5
O 12x24 - 10x4
The product of the expression (3x² - 2) (4x² + 5x) is 12x⁴ + 15x³ - 8x² - 10x.
What is Multiplication?
Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given expression is (3x² - 2) (4x² + 5x).
This can be written as,
(3x² - 2) (4x² + 5x) = 3x² (4x² + 5x) - 2 (4x² + 5x)
We have to use distributive property here.
a(b + c) = ab + ac for any three numbers or expressions, a, b and c.
(3x² - 2) (4x² + 5x) = 3x² (4x² + 5x) - 2 (4x² + 5x)
= (12x⁴ + 15x³) - (8x² + 10x)
= 12x⁴ + 15x³ - 8x² - 10x
Hence the product is 12x⁴ + 15x³ - 8x² - 10x.
To learn more about Multiplication of Expressions, click :
https://brainly.com/question/29052794
#SPJ7
Oi please help me it’s to hard
-4x - 18 = 46
need help
Answer:
x=−16
Step-by-step explanation:
−4x−18=46
Add 18 to both sides
−4x−18+18=46+18
−4x=64
Divide both sides by -4
-4x/4=64/-4
x=−16
Answer:
x= -16
Step-by-step explanation:
Let's solve your equation step-by-step.
−4x − 18 = 46
Step 1: Add 18 to both sides.
−4x − 18 + 18 = 46 + 18
−4x = 64
Step 2: Divide both sides by -4.
−4x / −4 = 64 / -4
x=−16
Hope it helps T-T
