Answer:
Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.
Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.
Step-by-step explanation:
The Empirical 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.
Within what limits do the active minutes for 95% of the people in each group fall
By the Empirical Rule, within 2 standard deviations of the mean.
Mildly obese:
Mean = 373, standard deviation = 61.
373 - 2*61 = 251 minutes
373 + 2*61 = 495 minutes
Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.
Lean people:
Mean = 525, standard deviation = 104
525 - 2*104 = 317 minutes
525 + 2*104 = 733 minutes
Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.
11+11=4, 22+22=16, 33+33?
Sequence= 4, 16
Difference=12
16+12=28
Answer is...
33+33=28
A square of area 36cm2 is cut to make two rectangles, A and B The ratio of Area A to Area B is 2 : 1 Work out the dimensions of rectangle A and B
(Need help with this question)
Answer:
Given..hope it helps
Step-by-step explanation:
Area of square= 36cm2 = total area
Side of square= √36= 6cm
Ratio a:b = 2:1
so let's take total area as 3x
while a is 2x and b is 1x
3x= 36 (given)
x= 36/3 = 12
so area of each rectangle--
area A= 2x= 24cm2
area B= x= 12cm2
While finding the dimensions, they both have a common length since they are from the same square which will be 6cm (side)
So,
Dimensions of rectangle A= 6cm * 4cm
Dimensions of rectangle B= 6cm * 2cm
Solve -3(2x - 9) = -3.
Answer:
X=4
Step-by-step explanation:
1. Distribute 3 to 2x and -9
2. You will get "6x-27 = -3"
3. Next, add 27 to -27 and -3
4. You will get "6x = 24"
5. Then, you will divide 6x and 24 by 6
6. You will get "6x/6 = 24/6"
7. The 6 will cancel the 6 in 6x.
8. Then, you will divide 24 and 6. which will give you the answer of 4
9. Add the "X=..." and...
10. You will get the answer of "X=4"
6(x/2 + 4) greater than or equal to 9
Answer:
Greater than 9.
Step-by-step explanation:
[tex]6(x/2 + 4)[/tex]
[tex]3x+24[/tex]
Find the volume of the prism.
The volume is cubic meters.
Alex needs
80
cm
80 cm80, start text, space, c, m, end text of thread for a sewing project. The thread is on a spool with a circumference of
10
cm
10 cm10, start text, space, c, m, end text.
How many times must Alex unwind the spool to get the length of thread he needs?
Answer:
8 full turns
Step-by-step explanation:
80 cm is 8 times 10 cm, so is 8 times around the spool.
Alex must unwind 8 full turns of thread from the spool.
__
He must unwind it once.
Answer:
8 in total turns
Step-by-step explanation:
Find the value of x for which the figure below is a parallelogram
Answer:
x = 2
Step-by-step explanation:
Well the diagonals bisect each other.
4x = 8
x = 2
Answer:
x = 2
Step-by-step explanation:
5x = 3x+4
2x = 4
x = 2
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
6x^2 -2x -6
Step-by-step explanation:
f(x) = 6x^2 -4
g(x) = 2x+2
f(x) - g(x) = 6x^2 -4 - (2x+2)
Distribute the minus sign
6x^2 -4 - 2x-2
Combine like terms
6x^2 -2x -6
Answer:
b
Step-by-step explanation:
6x^2
2x
-4+2=-2
what is the solution? X - 7 > -6
Answer:
x > 1
Step-by-step explanation:
Add 7 to both sides
x > 1
What is the slope of the line?
A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds x=20.6 months and s=8 months. Test the claim that u=18.7 months at the 0.05 significance level.
Answer:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/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 is not significantly different than 18.7
Step-by-step explanation:
Information given
[tex]\bar X=20.6[/tex] represent the sample mean
[tex]s=8[/tex] represent the sample standard deviation
[tex]n=11[/tex] sample size
[tex]\mu_o =18.7[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypotesis to test
We want to verify if the true mean is equal to 18.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu =18.7[/tex]
Alternative hypothesis:[tex]\mu \neq 18.7[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/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 is not significantly different than 18.7
Please help. I’ll mark you as brainliest if correct!!!!
Answer:
a= 2/5
b= -3/5
Step-by-step explanation:
We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator
[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]
This simplifies to:
[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]
This further simplifies to:
[tex]\frac{-3i +2}{5}[/tex]
Can be rewritten as:
[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]
a = 2/5
b = -3/5
can someone please help me it’s urgent!!!!!
Answer:
6/4
Explanation:
If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.
Hope this helps!
Dustin is buying carpet for the living room. How many square feet of carpet will he need to buy?
Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
F(x)=2x-6 and g(x)=3x+9,find (f+g)(x)
Answer: 5x-3
Step-by-step explanation:
(f+g)(x) means f(x)+g(x). Knowing this, we add the 2 functions together.
2x-6+3x+9
5x-3
The freezer contains vanilla and chocolate ice cream. Chocolate ice cream contains 12 servings less than vanilla. How many servings of vanilla ice cream are in the freezer if there are a total of 40 servings of ice cream? (Solve by building an equation)
Answer:
26 servings
Step-by-step explanation:
Let the number of servings of vanilla ice cream be x.
Number of servings of chocolate ice cream
= x -12
(since it has 12 servings less than vanilla)
Total servings= servings of chocolate+ vanilla
x + x-12= 40
2x -12 =40 (simplify)
2x= 40 +12 (+12 on both sides)
2x= 52 (simplify)
x= 52 ÷2
x= 26
Therefore, there are 26 servings of vanilla ice cream in the freezer.
Please help. I’ll mark you as brainliest if correct!
Answer:
a= -3/8
b= 1/8
Step-by-step explanation:
To remove i from the denominator, we need to multiply the numerator and denominator by -i
[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]
This simplifies to
[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]
This further simplifies to
[tex]\frac{i-3}{8}[/tex]
This can be rewritten as
[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]
a= -3/8
b= 1/8
Answer:
[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]
Step-by-step explanation:
[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]
from a deck of 52 cards, what is the probability of getting a four or diamond.
Answer:
4/13
Step-by-step explanation:
There are 13 diamonds in a deck and 3 fours that aren't diamond
13+3=16
16/52 = 4/13
Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. Give the limit when the sequence converges.
{(-1.00000005)^n}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. The sequence diverges by oscillation.
b. The sequence converges monotonically. It converges to:________
c. The sequence converges by oscillation. It converges to:________
d. The sequence diverges monotonic ally.
Answer:
a
Step-by-step explanation:
(-1.00000005)^n
as n becomes very large, the function increases in both positive and negative direction.
If n=1, -1.00000005
if n=2, 1.0000001
if n= 3, -1.00000015
if n=20, 1.000001
if n=21, -1.00000105
An amount was invested at % r per quarter. What value of rwill ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
42.67%
Step-by-step explanation:
The annual growth factor for interest at annual rate r compounded quarterly is ...
(1 +r/4)^4
You want that value to be 1.5:
1.5 = (1 +r/4)^4
1.5^(1/4) = 1 +r/4
(1.5^(1/4) -1) = r/4
4(1.5^(1/4) -1) = r ≈ 0.426728
The rate r must be about 42.67%.
_____
Comment on the wording
We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."
The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."
someone pls pls pls help me
Answer:
A, C, D, E
Step-by-step explanation:
According to the rational root theorem, any rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
The constant is 8, and its divisors are 1, 2, 4, 8.
The leading coefficient is 6, and its divisors are 1, 2, 3, 6.
So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:
A, 2/3C, -8D, 4E, -1/6What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
A quadrilateral inscribed in a circle has its opposite angles adding up to 180°
So
<NOP + <M = 180
4x+8x-24 = 180
12x = 180+24
12x = 204
Dividing both sides by 12
x = 17
<NOP = 4(17)
= 68°
The equation 4x-45=y is used to find your profit y in dollars from buying $45 of supplies and washing cars for $4 what does the x stand for
A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mean 3125 and standard deviation 250. Calculate the approximate 90th percentile for the distribution of the total contributions
Answer:
The 90th percentile for the distribution of the total contributions is $6,342,525.
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 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.
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.
For sums of size n, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sqrt{n}*\sigma[/tex]
In this question:
[tex]n = 2025, \mu = 3125*2025 = 6328125, \sigma = \sqrt{2025}*250 = 11250[/tex]
The 90th percentile for the distribution of the total contributions
This is X when Z has a pvalue of 0.9. So it is X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{X - 6328125}{11250}[/tex]
[tex]X - 6328125 = 1.28*11250[/tex]
[tex]X = 6342525[/tex]
The 90th percentile for the distribution of the total contributions is $6,342,525.
hord
12 cm
5 cm
Resu
5 cm
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the
height of the prism is placed inside the prism, as shown in the figure.
SUME
The volume of the space outside the pyramid but inside the prism is
cubic centimeters,
Answer:
The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.
Step-by-step explanation:
To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.
The prism and pyramid's bases is 25 cm²
The pyramid's height is 12÷2 or 6 cm
The volume formula for a prism is l×w×h
The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h
The area of the prism is 5×5×12 or 300 cm³
The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³
300 cm³-75 cm³=225 cm³
The volume outside the pyramid but inside the prism is 225 cm³.
Determine whether the following procedure is a binomial experiment.
If it is not, explain why. Drawing 5 marbles from a bag with 10 red, 8 green and 12 yellow marbles without replacement and finding out how many of these five are green.
a. Yes, this is a binomial experiment.
b. No, the outcomes cannot be classified into two categories.
c. No, the trials are not independent
Answer:
C. The trails are not independent.
The probability of drawing one marble will not be independent of others thus option (c) is correct.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Drawing 5 marbles from a bag with 10 red, 8 green, and 12 yellow marbles without replacement.
In without replacement, the remaining balls in each draw will go to be decreased thus they will be dependent events so binomial distribution will not be applied.
Hence "One marble's likelihood of being drawn won't be independent of the other marbles".
For more information about the probability,
brainly.com/question/11234923
#SPJ5
Twice the difference of a number and 4 is equal to three times the sum of the number and 6. Find the number.
The number is
Answer:
-26
Step-by-step explanation:
2(x-4)=3(x+6)
2x-8=3x+18
2x-2x -8 = 3x-2x +18
-8 =X+18
-8-18=x+18-18
-26 = x
The value of the unknown number is -26.
Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number x.
Twice the difference of a number and 4 = 2(x-4)
Three times the sum of the number and 6 = 3(x+6)
So, equation is 2(x-4)=3(x+6)
⇒ 2x-8=3x+18
⇒ 3x-2x=-8-18
⇒ x=-26
Therefore, the value of the unknown number is -26.
To learn more about an equation visit:
https://brainly.com/question/1529522.
#SPJ2
A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: Sample Service Life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 What is the mean of the sampling distribution of sample means when the service life is in control
Answer:
[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
For the given scenario, it is known from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours.
On three recent production batches, he tested service life on random samples of four headlamps.
We are asked to find the mean of the sampling distribution of sample means when the service life is in control.
Since we know that the population is normally distributed and a random sample is taken from the population then the mean of the sampling distribution of sample means would be equal to the population mean that is 500 hours.
[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]
Whereas the standard deviation of the sampling distribution of sample means would be
[tex]\text {standard deviation} = s = \frac{\sigma}{\sqrt{n} } \\\\[/tex]
Where n is the sample size and σ is the population standard deviation.
[tex]\text {standard deviation} = s = \frac{20}{\sqrt{4} } \\\\ \text {standard deviation} = s = \frac{20}{2 } \\\\ \text {standard deviation} = s = 10 \: hours \\\\[/tex]
Find the area of the trapezoid to the nearest tenth.
Answer:
2.2 metres squared
Step-by-step explanation:
We need to find the area of this trapezoid.
The area of a trapezoid is denoted by:
[tex]A=\frac{(b_1+b_2)h}{2}[/tex], where [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel bases and h is the height
Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.
Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:
2.0 ÷ √2 = √2 ≈ 1.414 ≈ 1.4
Thus, the height is h = 1.4 metres. Now plug all these values we know into the equation to find the area:
[tex]A=\frac{(b_1+b_2)h}{2}[/tex]
[tex]A=\frac{(0.9+2.3)*1.4}{2}=2.2[/tex]
The answer is thus 2.2 metres squared.
~ an aesthetics lover
NEED HELP ASAP
Solve the equation or inequality for the unknown number. Show your work.
Answer:
5
Step-by-step explanation:
3(14+x) = 57
42 +3x = 57
3x = 15
x = 5
