Answer:
65°
Step-by-step explanation:
The sum of the measures of complementary anfglwes is 90°.
Let a = the measure of the complement.
m<1 + a = 90
25 + a = 90
a = 65
Albert jumped 100 times in 97.5 seconds. Round off the time taken to the nearest second.
The required round of the time 97.5 is 98 seconds.
Given that,
Albert jumped 100 times in 97.5 seconds. To round off the time taken to the nearest second.
The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
in 97.5 seconds 0.5 in the tenth place is close to 1,
So the round off the number will be 98 seconds,
Thus, the required round of the time 97.5 is 98 seconds.
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Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48.3 ppm and a standard deviation of 8 ppm. The Environmental Protection Agency takes a random sample of 40 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 48.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate comp
Answer:
0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.
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 establishes 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.
Mean of 48.3 ppm and a standard deviation of 8 ppm.
This means that [tex]\mu = 48.3, \sigma = 8[/tex]
Sample of 40:
This means that [tex]n = 40, s = \frac{8}{\sqrt{40}}[/tex]
Find the probability that the disposal of such capacitors will be regulated.
Sample mean above 48.5, which is 1 subtracted by the p-value of Z when X = 48.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48.5 - 48.3}{\frac{8}{\sqrt{40}}}[/tex]
[tex]Z = 0.16[/tex]
[tex]Z = 0.16[/tex] has a p-value of 0.5636.
1 - 0.5636 = 0.4364
0.4364 = 43.64% probability that the disposal of such capacitors will be regulated.
Eight trials are simulated. The results are shown in the table.
Simulation
109 105 112 110
115 106 108 109
What is the estimated margin of error, using standard deviation?
Answer:
3.33
Step-by-step explanation:
I just took the test! :D
The estimated margin of error, using standard deviation is 3.33.
What is the estimated margin of error, using standard deviation?The margin of error shows an estimated percentage, or that surrounds a guess related to the real value of the population. For example, a confidence interval that has a margin of error tells you that your findings will be within the real population value of the time.
Typically, the higher the standard deviation, the more dispersed the data is. Understanding standard deviation is an essential part of calculating the margin of error for your data. If you do not have the value for your sample data proportion.
Standard deviation describes variability within a single sample, while standard error describes variability across multiple samples of a population. Standard deviation is a descriptive statistic that can be calculated from sample data, while standard error is an inferential statistic that can only be estimated.
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Patel made a rectangular garden in his family's backyard. 24 ft What is the perimeter of the garden? A 336 feet B 76 feet C 48 feet D 38 f
Answer:
336+76+48+38= 498
Step-by-step explanation:
add all those sides up because it is just the perimeter
Answer:
336+76+48+38= 498
Step-by-step explanation:
Find the missing side.
Answer:
90-30=60
Its 60 because its a right angle triangle
I need help with this, please
none of the above
Step-by-step explanation:
SSS - only two legs are defined so this doesn't apply
SAS - the two legs of one triangle are not proportional to the legs of the other triangle.
AA - only one angle is defined to be congruent to the other (the rule requires two)
if f(x)= 9+3x, find f(-2)
Answer:
f(-2) =3
Step-by-step explanation:
f(x) = 9+3x
Let x=-2
f(-2) = 9+3(-2)
= 9-6
= 3
f ( -2 ) = 9 + 3( - 2 )
f ( -2 ) = 9 - 6
f ( -2 ) = 3
75,15,3 find the 6th term
Fill in the blanks. Suppose the probability at a light bulb factory of a bulb being defective is 0.11. If a shipment of 133 bulbs is sent out, the number of defective bulbs in the shipment should be around __________, give or take __________. Assume each bulb is independent.
Answer:
The number of defective bulbs in the shipment should be around 15, give or take 4.
Step-by-step explanation:
For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Suppose the probability at a light bulb factory of a bulb being defective is 0.11
This means that [tex]p = 0.11[/tex]
Shipment of 133 bulbs:
This means that [tex]n = 133[/tex]
Mean and standard deviation:
[tex]E(X) = np = 133*0.11 = 14.63[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{133*0.11*0.89} = 3.61[/tex]
Rounding to the nearest integers:
The number of defective bulbs in the shipment should be around 15, give or take 4.
Allen buys 1 square yard of cloth. He cuts out a rectangular piece of cloth that measures 2/5 yd by 3/4 yd. What is the area of cloth that he cuts?
Area is length x width
Area = 2/5 x 3/4
When multiplying fraction, multiply the numerators by each other and the denominators by each other:
Area = 2/5 x 3/4 = (2 x3)/(5 x 4) = 6/20
6/20 reduces to 3/10
Area = 3/10 square yards
Consider the circle.
If points W and X are the endpoints of a diameter on the circle, what is the value of x?
Answer:
x = 18Step-by-step explanation:
Find the diagram attached
If W and X are the endpoints of a diameter on the circle, this means that arc WX is 180degres
Since the angle at the vertex is half the angle at the intercepted arcs.
<V = 1/2(arcWX)
4x+18 = 1/2*180
4x+18 = 90
4x = 90-18
4x = 72
x = 72/4
x = 18
Hence the value of x is 18
WILL GIVE U BRAINLIEST
What is the value of x?
A. 100 degrees
B. 50 degrees
C. Not enough info
D. 60 degrees
Answer:
B. 50
Step-by-step explanation:
180-80=100
100 divided by two equal angles is 50.
brainliest for answer
4/15 !! hope it helps loll
A bag contains 5 blue, 4 red, 7 black and 2 white marbles. What is the probability of selecting a marble that is NOT white?
Answer:
8/9 (simplified)
Step-by-step explanation:
Total marbles = 18
Total of marbles not white = 16
Numerator = 16 / Denominator = 18
= 16/18
= 8/9 (simplified)
Total number of marble=18
probability of getting white marble = 2/18 =1/9
Now,
probability of not getting white marble = 1 - 1/9 = 8 / 9
Street G has a slope of zero and goes through (3 , -10). Write this street’s equation in slope intercept form.
Answer:
y = 0x + (-10) or y = 0x - 10
Step-by-step explanation:
y= 0x + b
-10= 0(3) + b
-10 = b
Which gives you the equation
y= 0x + (-10)
A 36-foot-tall tree that is leaning toward the sun casts a 40-foot-long shadow when the sun is at a
41° angle of elevation. Approximately how many degrees does the tree lean?
a. 1°
c. 4°
b. 2°
d. 7°
Answer:
64degrees
Step-by-step explanation:
Give the following
Height of tree H = 36feet
length of the shadow L = 40feeet
Requires
Angle of eleation
Using the SOH CAH TOA identity
Sin theta = opposite/hypotenuse
Sin theta = H/L
Sin theta = 36/40
SIn theta = 0.9
theta = arcsin0.9
theta = 64.16
Hence the required angle is 64degrees
which of the following triangle is an obtuse triangle
Answer:
An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees.
A rectangle has a length of (x+6) units and a width of (x - 5) units.
What is the area of the rectangle in terms of x?
A (x^2 – 30) square units
B (x^2 +30) square units
C (x^2– x+30) square units
D (x^2+– 30) square units
Answer:
x² +x -30
Step-by-step explanation:
A = length * width = (x+6)(x-5) = x² -5x+6x-30= x²+x -30
Help!!!!!!Solve for X. Round to the nearest tenth of a degree, if necessary.
Could someone help me define each word please?
Answer:
.
Step-by-step explanation:
.
Answer:
Ok!
Step-by-step explanation:
Religion: the belief and worship in what is usually a god
Bones: pieces of hard whitish tissiue in a skeloton
Agriculture: the practice of farming
Artifacts: historical objects
1 point
A water tank in the form of a rectangular prism is 80 meters long and 50 meters wide. What is the volume of the water in the tank,
if the water is 40 meters deep?
Answer:
160000m³
Step-by-step explanation:
Volume of a rectangular prism= A x h
V= l x b x h
V= 80x 50 x 40
V= 160000m³
PLEASE HELP! I've had to ask this question FOUR times now.
For a linear regression, what is the value of the following data to three decimal places? X 1 4 6 7 9 11 2016 22 14 O A. 0.949 O B.-0.949 O C. 0.901 D. 0.901
9514 1404 393
Answer:
A. 0.949
Step-by-step explanation:
Use your favorite calculator or spreadsheet to compute the correlation coefficient.
r ≈ 0.949
_____
Additional comment
The values of y generally increase as the values of x increase--with only one exception. This tells you the correlation coefficient is positive and fairly high. Of the two positive choices 0.901 and 0.949, the higher one is the better guess.
A triangle has dimensions 5, 9, and 12. A similar triangle is drawn with a scale
factor of 1.2. What are the dimensions of the new triangle?
The answer?
Answer:
i need more informatiion
Step-by-step explanation:
What percent of 15 is 45?
Answer:
Step-by-step explanation:
let the number be x %
according to the question the equation is
x% of 15=45
x/100*15=45
15x=45*100
x=4500/15
x=300
therefore x=300%
5th grade math. correct answer will be marked brainliest
210 - 30 = 180
180 ÷ 15 = 12
12 weeks
It would take her 12 weeks to pay for the DVD player.
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
Under Age of 18 Over Age of 18
n1 = 500 n2 = 600
Number of accidents = 180 Number of accidents = 150
We are interested in determining if the accident proportions differ between the two age groups.
Q1. Let P, represent the proportion under and p, the proportion over the age of 18. The null hypothesis is:_____.
a. pu - po < 0.
b. pu - po > 0.
c. pu - P ≠ 70.
d. Pu - Po = 0.
Q2. The 95% confidence interval for the difference between the two proportions is:____.
a. (150, 180).
b. (0.25, 0.36).
c. (0.055, 0.165).
d. (0.045, 0.175).
Answer:
Q1 z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the that means have no difference
Q2 CI 95 % = ( 0,056 ; 0,164 )
Step-by-step explanation:
Sample information for people under 18
n₁ = 500
x₁ = 180
p₁ = 180/ 500 p₁ = 0,36 then q₁ = 1 - p₁ q₁ = 0,64
Sample information for people over 18
n₂ = 600
x₂ = 150
p₂ = 150 / 600 p₂ = 0,25 then q₂ = 1 - p₂ q₂ = 1 - 0,25 q₂ = 0,75
Hypothesis Test
Null hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
The alternative hypothesis indicates that the test is a two-tail test.
We will use the approximation to normal distribution of the binomial distribution according to the sizes of both samples.
Testin at CI = 95 % significance level is α = 5 % α = 0,05 and
α/ 2 = 0,025 z (c) for that α is from z-table:
z(c) = 1,96
To calculate z(s)
z(s) = ( p₁ - p₂ ) / EED
EED = √(p₁*q₁)n₁ + (p₂*q₂)/n₂
EED = √( 0,36*0.64)/500 + (0,25*0,75)/600
EED = √0,00046 + 0,0003125
EED = 0,028
( p₁ - p₂ ) = 0,36 - 0,25 = 0,11
Then
z(s) = 0,11 / 0,028
z(s) = 3,93
Comparing z(s) and z (c) z(s) > z(c)
z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the idea of equals means
Q2 CI 95 % = ( p₁ - p₂ ) ± z(c) * EED
CI 95% = ( 0,11 ± 1,96 * 0,028 )
CI 95% = ( 0,11 ± 0,054 )
CI 95 % = ( 0,056 ; 0,164 )
A survey of 35 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated. You're testing the claim that the mean difference is greater than 0.7. From the sample, the mean difference was 0.95, with a standard deviation of 0.44. Calculate the test statistic, rounded to two decimal place
Answer:
The test statistic is t = 3.36.
Step-by-step explanation:
You're testing the claim that the mean difference is greater than 0.7.
At the null hypothesis, we test if the mean difference is of 0.7 or less, that is:
[tex]H_0: \mu \leq 0.7[/tex]
At the alternate hypothesis, we test if the mean difference is greater than 0.7, that is:
[tex]H_1: \mu > 0.7[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that [tex]\mu = 0.7[/tex]
A survey of 35 people was conducted to compare their self-reported height to their actual height.
This means that [tex]n = 35[/tex]
From the sample, the mean difference was 0.95, with a standard deviation of 0.44.
This means that [tex]X = 0.95, s = 0.44[/tex]
Calculate the test statistic
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}[/tex]
[tex]t = 3.36[/tex]
The test statistic is t = 3.36.
Of 60 randomly chosen students from a school surveyed,16 chose aquarium as their favorite fiel trip.There are 720 students in the school.predict the number of student in the school who chose aquarium
Answer:
192 students
Step-by-step explanation:
60 randomly students surveyed
16 chose aquarium as their favorite field trip.
720 students in total.
[tex]\frac{16}{60}[/tex] = [tex]\frac{?}{720}[/tex] =
720 × 16 ÷ 60 =
192 students
Pedro thinks that he has a special relationship with the number 5. In particular, Pedro thinks that he would roll a 5 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Pedro will roll a 5. (Note you will need to find the probability of getting a four when rolling a fair 6-sided die like we did in chapter 3 so that you can compare p to this value.)
(a) State the null and alternative hypotheses for testing Pedro's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =", ">=", or "<=" and express any values as a fraction e.g. p = 1/3) H0 = Ha =
(b) Now suppose Pedro makes n = 38 rolls, and a 5 comes up 8 times out of the 38 rolls. Determine the P-value of the test: P-value =
(c) Answer the question: Does this sample provide evidence at the 5 percent level that Pedro rolls a 5 more often than you'd expect? (Type: Yes or No)
Answer:
1.)
H0 : p = 1/6
H1 : p > 1/6
2.)
Pvalue = 0.3029
3.)
No
Step-by-step explanation:
Probability of rolling 5 in a 6-sided die by chance :
Number of 5's = 1
Number of 6 = 6
p = 1/6
The Null hypothesis :
H0 : p = 1/6
Since Pedro thinks he'd roll more than just by chance ;
Alternative hypothesis :
H1 : p > 1/6
Given that :
n = 38 ` x = 5
Phat = x / n = 5 / 38
Teat statistic : (phat - p) / √p(1-p)/n
1-p = 1 - 1/6 = 5/6
phat - p = 5/38 - 1/6 = −0.035087
√p(1-p) /n = (1/6 * 5/6) / 30 = √0.0046296 = 0.0680
Test statistic = −0.035087 / √0.0046296 =
Test statistic = −0.515673
Using the Pvalue calculator :
Pvalue at 0.05 , 1 - tail = 0.3029
Pvalue = 0.3029
Hence, at α = 0.05
Pvalue > α ;
There is no evidence to support Pedro's claim
Assume that we want to estimate the mean IQ score for the population of statistics students. How many statistics students must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 3 IQ points of the population mean? The Standard Deviation is 15.
Answer:
97 students must be randomly selected for IQ tests.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The Standard Deviation is 15.
This means that [tex]\sigma = 15[/tex]
How many statistics students must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 3 IQ points of the population mean?
This is n for which M = 3. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]3 = 1.96\frac{15}{\sqrt{n}}[/tex]
[tex]3\sqrt{n} = 1.96*15[/tex]
Simplifying both sides by 3
[tex]\sqrt{n} = 1.96*5[/tex]
[tex](\sqrt{n})^2 = (1.96*5)^2[/tex]
[tex]n = 96.04[/tex]
Rounding up(as with a sample size of 96 the margin of error will be slightly above 3):
97 students must be randomly selected for IQ tests.