The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.
A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.
n = 50 makes up the sample size.
Furthermore, the sample variance is s² = 20
The following is the formula for both the variance confidence interval:
σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]
Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.
The 90% confidence interval's lower bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)
= 32.54
The 90% confidence interval's upper bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)
= 96.86
Consequently, the confidence level for the distribution's variance is (96.86, 32.54).
Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).
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the number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. what is the estimate of the population proportion of defectives?
The estimate of the population proportion of defectives is 0.05.
Given that,
There are 10 different samples of 50 observations, that is, total of 500 observations.
To find : The estimate of the population proportion of defectives
And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25
Thus, the point estimate for the population proportion defectives will be,
=25/500=0.05
or just obtain the individual proportion of each sample and then take their average to obtain the same result.
Thus, the point estimate for the population proportion defectives will be 0.05
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justin went to the track at bobcat stadium and performed the 1.5-mile run test to estimate his vo2max. he completed 1.5 miles in 11 minutes and 25 seconds. what is his estimated vo2max? round your answer to the first decimal place.
3Justin's estimated Vo2 max is 25.8(mL*kg*min)
What is Vo2 max ?
The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.
Here using vo2 max fomula 1.5 miles ,
=> VO2 max = 3.5+483/Time
Here Time= 11 min 25 sec = 25/60 = 0.41 min
Then time=11.42 mins. Now,
=> VO2 max = 3.5+ 483/11.41
=> VO2 max = 3.5+42.3
=>VO2 max = 25.8(mL*kg*min)
Hence His estimated Vo2 max is 25.8(mL*kg*min)
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a basket contains 13 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen? a) 165 b) 11 c) 121 d) 220 e) 9 f) none of the above.
Answer:
None of the above
Step-by-step explanation:
if 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home?
The probability that fewer than 60 adults will work from home will be 2%.
we have to use the Normal probability distribution to find the probability
In a normal distribution with mean μ, SD σ, z-score Z of a measure X is given by
Z = (X-μ)/ σ
here,
15% adults work from home , So p= 0.15
n = 500
∴ μ = np = 500(0.15) = 75
σ = [tex]\sqrt{np(1-p)}[/tex]
σ = 7.98
Now we have selected adults(60) less than n (500)
So using the continuity correction , the probability is P(X< 60 - 0.5)
= P( X< 59.5)
which is the p-value of Z when X = 59.5
∴ Z = (X-μ)/ σ
Z = (59.5 - 75)/7.98
Z = - 1.98
so the p-value is 0.02
0.02 = 2% probability that fewer than 60 adults will work from home.
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The Coast Guard cutter Angelica travels at 30 knots from its home port of Corpus Christi on a course of 95 degrees for 2 hrs and then changes to a course of 185 degrees for 2 hrs. Find the distance and the bearing from the Corpus Christi port to the boat.
The distance and bearing of the boat from the port areas follows;
The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.
What is a bearing in mathematics?A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.
The speed at which the Coast Guard cutter travels = 30 knots
Bearing of the Coast Guard cutter Angelica = 95°
The time the coast guard travels in the initial direction = 2 hours
The direction the Coast Guard cutter changes to = 185°
Time of traveling in the new direction = 2 hours
30 knots = 55.56 km/hr
The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km
The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km
From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle
The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15
The distance f the boat from the port is approximately 157.15 kilometers
The base angles of an isosceles right triangle are 45°
Therefore, the bearing is 95° + 45° = 150°
The bearing from the port to the boat is 150°
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Lines AB and CD (if shown) are straight lines. Find x .
Answer:
x = 20
Step-by-step explanation:
We know that a straight line is 180 degrees. We also know that the line A and B is a supplementary angle.
We subtract 180 - 110 which will come out to 70 which is the value of angle B
We know that angles D and E are 90 degrees and since D and C is 180 degrees, that means C and E is equal to 90 degrees as well.
Since B is equal to 70 degrees, we subtract 90 - 70 to get 20 degrees which is the value of x
Kylie just accepted a job at a new company where she will make an annual salary of $67000. Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000. How much would Kylie make as a salary after 3 years working for the company? What would be her salary after t years?
The amount that Kylie make as a salary after 3 years working for the company is $76000.
Her salary after t years will be 67000 + 3000t.
How to calculate the value?In this situation, Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000 every years.
Her salary after three years will be:
= $67000 + ($3000 × 3)
= $67000 + $9000
= $76000
Her salary after t years will be:
= 67000 + (3000 × t)
= 67000 + 3000t
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Which triangle congruence postulate or theorem proves that these triangles are
congruent?
The angle-side-angle (ASA) Congruence theorem proves that
ΔABC and ΔPQR are congruent triangles.
We know that the angle-side-angle ASA Congruence theorem states that if two angles and the side between these angles of one triangle are equal to two angles and the side between then of another triangle then those two triangles are congruent.
In given triangles ABC and PQR,
∠ABC ≅ ∠PQR
BC ≅ QR
∠BCA ≅ ∠QRA
so, by ASA Congruence theorem ΔABC ≅ ΔPQR
Therefore, the angle-side-angle (ASA) Congruence theorem proves that
ΔABC and ΔPQR are congruent triangles.
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Which expression is equivalent to 4f^2
e
/
1
4f
Answer:
4f^2/3 divided 1/4f 16f^3/3 f/3 3/16f^3 3/f
✓ Lets use algebra and simplify:[tex]\frac{\frac{4f^{2}}{3}}{\frac{1}{4f}} \\=\frac{4f^{2}}{3}* \frac{4f}{1} \\=…
Please help now !!!!!!
Answer:
The tablet costs more than the smartphone
Step-by-step explanation:
1 year tablet = $1.50
1 year smartphone = $0.02x12months = $0.24
3z + 6(z-5) = -48
What does this equal please help
Answer: z=-2
Step-by-step explanation:
3z+6z-30=-48
9z-30=-48
9z-30=-48+30
9z=-18
z=-2
There are 4 consecutive even integers that add up to 4. What is the value of the least integer?
The value of the least integer is -1/2 or -0.5.
How to calculate the value?Based on the information given, let the integers be represented as:
x
x + 1
x + 2
x + 3
Since they all add to 4, this will be:
x + x + 1 + x + 2 + x + 3 = 4
4x + 6 = 4
Collect like terms
4x = 4 - 6
4x = -2
Divide
x = -2 / 4
x = - 1/2
Therefore, the least is - 1/2
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Step up an inequality for this situation below. Define your variable, but do not solve. (2 points – 1 defined variable, 1 point correct inequality).
Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?
The lessons can a student take if they pay no more than $175 is 25x + 50 < 175.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
In the 12U Softball division, Olivia gets chosen. What is Olivia's age? Olivia's age is unknown to you because the word "equals" is missing. However, since you are aware that she should be under or equal to 12, you can write Olivia's Age 12. This is a real-world example of an inequality.
given:
Per lesson charges= $25
Recital f= $50
Total money can be spend= $175
let the number of lessons taken be x.
So, the inequality is
25x + 50 < 175
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Which of the following shows an example of two irrational numbers being multiplied to get a rational number?
Answer:
[tex]\sqrt{2}[/tex] × [tex]\sqrt{8}[/tex] And [tex]\sqrt{2}[/tex] ×[tex]\sqrt{3}[/tex]
Step-by-step explanation:
3x9 are both whole numbers and 0x[tex]\sqrt{5}[/tex] has only one irrational number
Answer:
C) √2 × √8---------------------------
Option A3 × 9 = 27No, all three numbers are rationalOption B0 × √5 = 0No, one irrational number multipliedOption C√2 × √8 = √16 = 4Yes, two irrational numbers multiplied to get a rational numberOption D√2 × √3 = √6No, √6 is still irrational numberair is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. how fast is the surface area of the balloon changing when the radius is 5 centimeters?
The rate of change of the surface area of the balloon is 32cm²/sec
We know that volume of the sphere is,
V = 4/3πr³
Given,
dV / dt = +200
r = 5cm
d(SA) / dt = ?
dV / dt = 4πr² dr/dt
80 = 4π (25) dr/dt
dr / dt = 0.8 / π
SA = 4πr²
d(SA) / dt = 8πr dr / dt
d(SA) / dt = 8π × 5 × 0.8 / π
d(SA) / dt = 32cm²/sec
Hence the rate of change of the surface area is 32cm²/sec
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Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.
The statement which is true about this equation is that: C. The equation has no solution.
What is no solution?In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.
This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.
From the information provided above, we have this equation:
3(-y + 7) = 3(y + 5) + 6
Opening the bracket, we have the following:
-3y + 21 = 3y + 15 + 6
Next, we would rearrange the equation by collecting like terms as follows:
-3y + 21 = 3y + 21 (no solution)
-3y - 3y = 21 - 21
-6y = 0
y = -0/6
y = 0
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10 plus the difference of 6 and 2
Answer: 14
Step-by-step explanation: 10 + (6-2) = 14
Find a polynomial function of least degree having only real
coefficients, a leading coefficient of 1, and zeros of 4 and
3 + i.
The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Given,
In the question:
A leading coefficient of 1, and zeros of 4 and 3 + i.
To find the polynomial function of least degree having only real coefficients.
Now, According to the question;
The function has 4 and 3 + i .
As, i's roots
So, 3 - i is also its root a leading coefficient of 1 .
So, The function of polynomial is :
f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]
To solve the function;
f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
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In a pack of Skittles, 20% are red. If 13 are red, how many skittles were in the entire bag?
The total number of skittles in the bag will be 65.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that In a pack of Skittles, 20% are red. If 13 are red. The total number of skittles will be calculated as,
N = ( 13 / 20 ) x 100
N = 130 / 2
N = 65
Therefore, the total number of skittles in the bag will be 65.
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What is the slope of a line that is parallel to the line y = x 2?
It is 5:15 now. What time was it 9 hours and 15 minutes ago?
Answer:
8:00
Step-by-step explanation:
Calculate time
It is 5:15 now.
Subtract 15 minutes
5:00
Subtract 9 hours
subtract 5 hours
12:00
Then subtract 4 hours
8:00
Mrs. sisneros ran 3 miles in 27 minutes on monday. she ran 5 miles in 50 minutes on wednesday. on which day did mrs. sisneros run at a faster rate? what was that rate?
Friday hope that this helps
As the value of c increase toward infinity, what happens to the values of g(x) = 3x - 19
Oliva is making granola bars. She will use 17.9 ounces of pastachios, 12.6 ounces of almonds,12.5 ounces of walnuts, and 12.5 ounces of cashews. This amount makes 25 bars. How many ounces of nuts are in each granola bar?
The required number of ounces of nuts would be 1/2 in each granola bar.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
She will use 12.5 ounces of walnuts to make 25 granola bars which is given in the question.
To determine the number of ounces of nuts in each granola bar
Let the number of ounces of nuts in each granola bar would be x
As per the given situation, we can write a ratio as
12.5 ounces : 25 bars = x ounces : 1 bars
⇒ 12.5 / 25 = x / 1
⇒ 1/2 = x
⇒ x = 1/2
Thus, the required number of ounces of nuts would be 1/2 in each granola bar.
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help is needed, please and thank you
Answer:
f(- 5) = 7
Step-by-step explanation:
f(- 5) means what is the value of y when x = - 5
locate x = - 5 on the x- axis, go vertically up to meet the graph at (- 5, 7 ), then
f(- 5) = 7
Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!
The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
In this question we have been given an expression.
We need to identify the property that is used to multiply two binomials.
(3x+5)(2x+7)=2x(3x+5)+7(3x+5)
Consider two binomials,
(3x+5)(2x+7)
= (2x+7)(3x+5) ...............(commutative property)
= 2x(3x+5)+7(3x+5) ................(distributive property)
Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
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a sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies? responses 15.1 15.1 15.3 15.3 16.3 16.3
The mean sleep time is 16.54 hours per day for newborn babies
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."It is a statistical idea with significant financial implications. The idea is applied in a number of financial areas, such as business appraisal and portfolio management, although not exclusively.acc to our question-
z-score = (x - μ)/σ, where x is the score , μ is the mean and σ is thestandard deviationA sleep time of 15.9 hours per day for a newborn babyx = 15.9 hoursAt the 10th percentile of the distribution of sleep times for all newborn babiesThat means we want to find z-score corresponding to 0.1 (10/100 = 0.1)By using the normal distribution tablez = -1.28The standard deviation is 0.5 hourσ = 0.5Substitute these values in the rule above-1.28 = (15.9 - μ)/0.5Multiply both sides by 0.5-0.64 = 15.9 - μAdd μ to both sides-0.64 + μ = 15.9add -0.64 to both sidesμ = 15.9 + 0.64 = 16.54The mean sleep time is 16.54 hours per day for newborn babies.
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in a right triangle, the longer leg is two more than three times the shorter leg, and the area of the triangle is 400. what is the length of the shorter leg?
The length of the shorter leg is 16 units which was found using the given data.
What exactly is a quadratic equation?A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.
Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.
We know that,
Area of triangle = 1/2(larger leg)(shorter leg)
400=1/2(larger leg)(shorter leg) Equation(1)
larger leg = 2 + 3(shorter leg)
We need to substitute this in Equation(1)
400 = 1/2[2+3(shorter leg)](shorter leg)
800 = 2(shorter leg) + 3(shorter leg)²
3(shorter leg)² + 2(shorter leg) - 800 = 0
Solving this quadratic equation,
we get, shorter leg = - 16 or +16
Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.
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IM GIVING BRAINLY I NEED HELP ASAPP
Answer:
C
Step-by-step explanation:
Rate change = Change in Y/ Change in Xy=mx+cand for graph, rate change is 10(10 units change in Y for every 1 unit change in X) whereas another function's rate change is 4
C= is y-intercept
and in graph its -6 whereas in function its -8, so graph has higher y-intercept
Graph: Rate of change = 10, y-intercept = -6
Function: Rate of change = 10, y-intercept = -8
Simplify by expressing fractional exponents instead of radicals 8 sqrd x^2 y^4
After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.
Exponent:
Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.
Given,
Here we have the expression 8√(x²y⁴).
Now, we need to simplify the fractional exponents.
When we rewritten the expression like the following,
=> 8√(x²y⁴)
While we looking at these expression we know that, the number 8 can be written as the multiple of 2,
So, it can be written as,
=> 8√(x²y⁴) = 2³√(x²y⁴).
So, in the simplified form it can be written as,
=>8√(x²y⁴) = 2³(x²y⁴)¹/₂.
Therefore, the simplified form is 2³(x²y⁴)¹/₂.
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