Answer:
Equation of the axis of symmetry is: x = 3
Step-by-step explanation:
The equation
[tex]y=2x^2-12x+21[/tex]
is the equation of a parabola, of the form
[tex]y=ax^2+bx+c[/tex] whose vertex is located at the x-coordinate:
[tex]x_{vertex}=\frac{-b}{2\,a}[/tex]
Then, for our case the x position of the given parabola, is:
[tex]x_{vertex}=\frac{-b}{2\,a} \\x_{vertex}=\frac{12}{2\,(2)} \\x_{vertex}=3[/tex]
Then the equation of the axis of symmetry, which is a vertical line that goes through the vertex, would be given by:
x = 3
Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance. (Round your answer to one decimal place.)
The radioactive compound has a half-life of around 3.09 hours.
The period of time needed for a radioactive substance's initial quantity to decay by half is known as its half-life. The half-life of a drug may be calculated as follows if the rate of decay is proportionate to the amount of the substance existing at time t:
Let t be the half-life of the substance, then after t hours, the amount of the substance present will be,
100 mg × [tex]\dfrac{1}{2}[/tex] = 50 mg.
At time 6 hours, the amount of the substance present is,
100 mg × (1 - 3%) = 97 mg.
Given that the amount of material available determines how quickly something degrades,
The half-life can be calculated as follows:
[tex]t = 6 \times \dfrac{50}{ 97} = 3.09 \ hours[/tex]
Therefore, the half-life of the radioactive substance is approximately 3.09 hours.
Learn more about half-life:
brainly.com/question/24710827
#SPJ12
Which of these fractions is an improper fraction? 5/3 or 3/5
Answer:
5/3 is an improper fraction because 5 is higher then 3. So the correct way of writing it would be 1 2/3.
Step-by-step explanation:
5. The probability that a defect will occur over the surface of a semiconductor chip is 0.2. Assuming the occurrences of defects are independent, what is the probability that two out of nine chips selected with replacement will be defective
Answer:
P(X=2) = 0.302
Step-by-step explanation:
With the conditions mentioned in the question, we can model this variable as a binomial random variable, with parameters n=9 and p=0.2.
The probability of having k defective items in the sample of nine chips is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{9}{k} 0.2^{k} 0.8^{9-k}\\\\\\[/tex]
Then, the probability of having 2 defective chips in the sample is:
[tex]P(x=2) = \dbinom{9}{2} p^{2}(1-p)^{7}=36*0.04*0.2097=0.302\\\\\\[/tex]
A line passes through the points P(1,-6,7) and Q(-9,10,-5) find the standard parametric equations for the line, written using the base point P(1,-6,7) and the components of the vector PQ rightarrow.
x = _________, y = _________, z = __________.
Answer:
[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]
Step-by-step explanation:
We are given the coordinates of points P(1,-6,7) and Q(-9,10,-5).
The values in the form of ([tex]x,y,z[/tex]) are:
[tex]x_1=1\\x_2=-9\\y_1=-6\\,y_2=10\\z_1=7\\z_2=-5[/tex]
[tex]$\vec{PQ}$[/tex] can be written as the difference of values of x, y and z axis of the two points i.e. change in axis.
[tex]\vec{PQ}=<x_2-x_1,y_2-y_1,z_2-z_1>[/tex]
[tex]\vec{PQ} = <(-9-1), 10-(-6),(-5-7)>\\\Rightarrow \vec{PQ} = <-10, 16,-12>[/tex]
The equation of line in vector form can be written as:
[tex]\vec{r} (t) = <1,-6,7> + t<-10,16,-12>[/tex]
The standard parametric equation can be written as:
[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]
Find the volume of the cone.
4 cm
3 cm
V = [?] cm3
Round to the nearest tenth.
Answer:
Volume of a cone = 1/3πr²h
h = height
r = radius
r = 3cm h = 4cm
Volume = 1/3π(3)²(4)
= 36 × 1/3π
= 12π
= 36.69cm³
= 37cm³ to the nearest tenth
Hope this helps
Answer:
37.7
_______
NOT 37
Step-by-step explanation:
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]3^{2}[/tex] · [tex]4 = 12\pi = 37.69911 =[/tex] 37.7
Please answer this correctly
Answer:
The mode would decrease by 3
Step-by-step explanation:
The mode right now is 6, as there are 4 6's. However, closely behind it is 3, with 3 3's. If we replaced a 6 with a 3, we would have 4 3's and 3 6's. Find the difference between 6 and 3 and you answer should be 3.
Which of the following is not an undefined term?
point, ray, line, plane
Answer:
Step-by-step explanation:
Ray
Answer:
ray
Step-by-step explanation:
ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray
hope this helps
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that:
Complete question is;
In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.
Answer:
P(has diabetes | positive) = 0.442
Step-by-step explanation:
Probability of having diabetes and being positive is;
P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)
We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.
Thus;
P(positive & has diabetes) = 0.08 × 0.95 = 0.076
P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)
P(negative & has diabetes) = 0.004
P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)
We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease
Thus;
P(positive & no diabetes) = 0.92 × 0.1 = 0.092
P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)
P(negative &no diabetes) = 0.828
Probability that a person selected having diabetes actually has the disease is;
P(has diabetes | positive) =P(positive & has diabetes) / P(positive)
P(positive) = 0.08 + P(positive & no diabetes)
P(positive) = 0.08 + 0.092 = 0.172
P(has diabetes | positive) = 0.076/0.172 = 0.442
Using formula:
[tex]P(\text{diabetes diagnosis})\\[/tex]:
[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]
[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]
[tex]\text{P(have been diagnosed with diabetes)}[/tex]:
[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]
[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]
Learn more about the probability:
brainly.com/question/18849788
In a sample of 22 people, the average cost of a cup of coffee is $2.70. Assume the population standard deviation is $0.93. What is the 90% confidence interval for the cost of a cup of coffee
Answer:
$2.70+/-$0.33
= ( $2.37, $3.03)
Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $2.70
Standard deviation r = $0.93
Number of samples n = 22
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
$2.70+/-1.645($0.93/√22)
$2.70+/-1.645($0.198276666210)
$2.70+/-$0.326165115916
$2.70+/-$0.33
= ( $2.37, $3.03)
Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)
A woman has a collection of video games and anime. she has 50 anime DVDs, and she has 70 video games. which it adds up to 120 items. if you divide them by 5, how many items does she have all together?
Answer:
24
Step-by-step explanation:
Since you are given almost everything, you just simply divide by 5=>
120/5 = 24
Hope this helps
What is the general form of the equation of the line shown? 2 x - y + 3 = 0 2 x - y - 3 = 0 x - 2 y - 3 = 0
Answer:
2x - y - 3 = 0
Step-by-step explanation:
Find slope-intercept form first: y = mx + b
Step 1: Pick out 2 points
In this case, I picked out (2, 1) and (0, -3) from the graph
Step 2: Using slope formula y2 - y1/x2 - x1 to find slope
-3 - 1/0 - 2
m = 2
Step 3: Place slope formula results into point-slope form
y = 2x + b
Step 4: Plug in a point to find b
-3 = 2(0) + b
b = -3
Step 5: Write slope-intercept form
y = 2x - 3
Step 6: Move all variables and constants to one side
0 = 2x - 3 - y
Step 7: Rearrange
2x - y - 3 = 0 is your answer
13. Two points P and Q, 10 m apart on level ground,
are due West of the foot B of a tree TB. Given that
TPB = 23° and TQB = 32°, find the height of tree
Answer: height = 13.24 m
Step-by-step explanation:
Draw a picture (see image below), then set up the proportions to find the length of QB. Then input QB into either of the equations to find h.
Given: PQ = 10
∠TPB = 23°
∠TQB = 32°
[tex]\tan P=\dfrac{opposite}{adjacent}\qquad \qquad \tan Q=\dfrac{opposite}{adjacent}\\\\\\\tan 23^o=\dfrac{h}{10+x}\qquad \qquad \tan 32^o=\dfrac{h}{x}\\\\\\\underline{\text{Solve each equation for h:}}\\\tan 23^o(10+x)=h\qquad \qquad \tan 32^o(x)=h\\\\\\\underline{\text{Set the equations equal to each other and solve for x:}}\\\tan23^o(10+x)=\tan32^o(x)\\0.4245(10+x)=0.6249x\\4.245+0.4245x=0.6249x\\4.245=0.2004x\\21.18=x[/tex]
[tex]\underline{\text{In put x = 21.18 into either equation and solve for h:}}\\h=\tan 32^o(x)\\h=0.6249(2.118)\\\large\boxed{h=13.24}[/tex]
A well known social media company is looking to expand their online presence by creating another platform. They know that they current average 2,500,000 users each day, with a standard deviation of 625,000 users. If they randomly sample 50 days to analyze the use of their existing technology, identify each of the following, rounding to the nearest whole number if necessary:
(a) Mean users.
(b) Standard deviation.
(c) Sample mean.
Using the Central Limit Theorem, it is found that the measures are given by:
a) 2,500,000.
b) 88,388.35.
c) 2,500,000.
What does the Central Limit Theorem state?By the Central Limit Theorem, the sampling distribution of sample means of size n for a population of mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] has the same mean as the population, but with standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Hence, we have that for options a and c, the mean is of 2,500,000 users, while for option b, the standard deviation is given by:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{625000}{\sqrt{50}} = 88,388.35.[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
how many dimes equal $12.60? (show your work)
Answer:
126
Step-by-step explanation:
0.1x=12.6
126
A drug company is testing a new drag which is supported to reduce blood pressure. From the nine people who are used as subjects, it is found that the average drop in blood pressure is 2.28 points, with a standard deviation of 0.82 points. What is the 95% confidence interval for the mean change in pressure?
Answer:
95% of the data falls between 0.64 and 3.92
Step-by-step explanation:
Using the Empirical Rule, 95% of the data will fall 2 standard deviations above and below the mean. Therefore, from the mean of 2.28, the lower change will be 2.28 - 2(0.82)= 0.64 and the upper change will be 2.28 + 2(0.82)= 3.92
If the terms of a polynomial do not have a GCF, does that mean it is not factorable?
What is AB? Geometry help please
Answer:
AB = 37 units.
Step-by-step explanation:
Solve for AB using the Pythagorean theorem:
c² = a² + b² (c being AB in this instance)
Plug in the values of the legs of the triangle:
c² = 12² + 35²
c² = 144 + 1225
c² = 1369
c = √1369
c = 37
Therefore, AB = 37.
A fence 6 feet tall runs parallel to a tall building at a distance of 6 feet from the building. We want to find the the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. Here are some hints for finding a solution: Use the angle that the ladder makes with the ground to define the position of the ladder and draw a picture of the ladder leaning against the wall of the building and just touching the top of the fence. If the ladder makes an angle 0.82 radians with the ground, touches the top of the fence and just reaches the wall, calculate the distance along the ladder from the ground to the top of the fence. equation editorEquation Editor The distance along the ladder from the top of the fence to the wall is equation editorEquation Editor Using these hints write a function L(x) which gives the total length of a ladder which touches the ground at an angle x, touches the top of the fence and just reaches the wall. L(x) = equation editorEquation Editor . Use this function to find the length of the shortest ladder which will clear the fence. The length of the shortest ladder is equation editorEquation Editor feet.
Answer:
12√2 feet ≈ 16.97 feet
Step-by-step explanation:
For the dimensions shown in the attached diagram, the distance "a" along the ladder from the ground to the fence is ...
a = (6 ft)/sin(x) = (6 ft)/sin(0.82) ≈ 8.206 ft
The distance along the ladder from the top of the fence to the wall is ...
b = (6 ft)/cos(x) = (6 ft)/cos(0.82) ≈ 8.795 ft
__
In general, the distance along the ladder from the ground to the wall is ...
L(x) = a +b
L(x) = 6/sin(x) +6/cos(x)
This distance will be shortest for the case where the derivative with respect to x is zero.
L'(x) = 6(-cos(x)/sin(x)² +sin(x)/cos(x)²) = 6(sin(x)³ -cos(x)³)/(sin(x)²cos(x²))
This will be zero when the numerator is zero:
0 = 6(sin(x) -cos(x))(1 -sin(x)cos(x))
The last factor is always positive, so the solution here is ...
sin(x) = cos(x) ⇒ x = π/4
And the length of the shortest ladder is ...
L(π/4) = 6√2 + 6√2
L(π/4) = 12√2 . . . . feet
_____
The ladder length for the "trial" angle of 0.82 radians was ...
8.206 +8.795 = 17.001 . . . ft
The actual shortest ladder is ...
12√2 = 16.971 . . . feet
√x+3 = √5x-1 Find the value of X
Answer:
x=1
Step-by-step explanation:
sqrt(x+3) = sqrt(5x-1)
Square each side
x+3 = 5x-1
Subtract x from each side
3 = 4x-1
Add 1 to each side
4 =4x
Divide by 4
x=1
Answer:
x= 1
Step-by-step explanation:
[tex]\sqrt{x+3}=\sqrt{5x-1}[/tex]
Square both sides.
x + 3 = 5x - 1
Subtract 3 and 5x on both sides.
x - 5x = -1 - 3
-4x = -4
Divide -4 into both sides.
-4x/-4 = -4/-4
x = 1
Can someone please explain how to do this problem? The websites instructions are very poor. Rewrite [tex]\frac{2}{x^{2} -x-12}[/tex] and [tex]\frac{1}{x^{2}-16 }[/tex] as equivalent rational expressions with the lowest common denominator.
Answer: x = -5
Step-by-step explanation:
If you factor each denominator, you can find the LCM.
[tex]\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\[/tex]
Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.
2(x + 4) = 1(x + 3)
2x + 8 = x + 3
x + 8 = 3
x = -5
An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2000 individuals, what is the approximate distribution of the number who carry this gene
Answer:
Brianliest!
Step-by-step explanation:
4
1 in 500
500 x 4 = 2000
4 in 2000
find the are of the kite.
a. 96 ft^2
b.192 ft^2
c.64 ft^2
d.348 ft^2
Answer:
A
Step-by-step explanation:
The area of a kite is half of the product of the length of the diagonals, or in this case 16*12/2=96 square feet. Hope this helps!
Answer:
a. 96 ft^2
Step-by-step explanation:
You can cut the kite into 2 equal triangle halves vertically.
Then you can use the triangle area formula and multiply it by 2 since there are 2 triangles.
[tex]\frac{1}{2} *12*8*2=\\6*8*2=\\48*2=\\96ft^2[/tex]
The kite's area is a. 96 ft^2.
Which graph shows a function whose domain and range exclude exactly one value?
Answer:
C (the third graph)
Step-by-step explanation:
This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.
Answer:
see below
Step-by-step explanation:
This graph has an asymptote at y = 0 and x=0
This excludes these values
The domain excludes x =0
The range excludes y=0
given the diagram below what is cos (45degree)?
Answer:
[tex]1/\sqrt{2}[/tex]
Answer:
B
Step-by-step explanation:
Lard-O potato chips guarantees that all snack-sized bags of chips are between 16 and 17 ounces. The machine that fills the bags has an output with a mean of 16.5 and a standard deviation of 0.25 ounces. Construct a control chart for the Lard-O example using 3 sigma limits if samples of size 5 are randomly selected from the process. The center line is ____. The standard deviation of the sample mean is ____. The UCL
Answer:
- The center line is at 16.5 ounces.
- The standard deviation of the sample mean = 0.112 ounce.
- The UCL = 16.836 ounces.
- The LCL = 16.154 ounces.
Step-by-step explanation:
The Central limit theorem allows us to write for a random sample extracted from a normal population distribution with each variable independent of one another that
Mean of sampling distribution (μₓ) is approximately equal to the population mean (μ).
μₓ = μ = 16.5 ounces
And the standard deviation of the sampling distribution is given as
σₓ = (σ/√N)
where σ = population standard deviation = 0.25 ounce
N = Sample size = 5
σₓ = (0.25/√5) = 0.1118033989 = 0.112 ounce
Now using the 3 sigma limit rule that 99.5% of the distribution lies within 3 standard deviations of the mean, the entire distribution lies within
(μₓ ± 3σₓ)
= 16.5 ± (3×0.112)
= 16.5 ± (0.336)
= (16.154, 16.836)
Hope this Helps!!!
A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimate μ. (Round your answers to four decimal places.)
Required:
a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?
b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?
Answer:
a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.
b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
In this question, we have that:
[tex]\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]
a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?
This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.
Due to the Central Limit Theorem, Z is:
[tex]Z = \frac{X - \mu}{s}[/tex]
X = 205
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{205 - 200}{5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
X = 195
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{195 - 200}{5}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587.
0.8413 - 0.1587 = 0.6426
0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.
b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?
This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.
X = 210
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{210 - 200}{5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772.
X = 195
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{190 - 200}{5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.
(a): The required probability is [tex]P(195 < \bar{x} < 205)=0.6826[/tex]
(b): The required probability is [tex]P(190 < \bar{x} < 200)=0.9544[/tex]
Z-score:
A numerical measurement that describes a value's relationship to the mean of a group of values.
Given that,
mean=200
Standard deviation=50
[tex]n=100[/tex]
[tex]\mu_{\bar{x}}=200[/tex]
[tex]\sigma{\bar{x}} =\frac{\sigma}{\sqrt{n} } \\=\frac{50}{\sqrt{100} }\\ =5[/tex]
Part(a):
within [tex]5=200\pm 5=195,205[/tex]
[tex]P(195 < \bar{x} < 205)=P(-1 < z < 1)\\=P(z < 1)-P(z < -1)\\=0.8413-0.1587\\=0.6826[/tex]
Part(b):
within [tex]10=200\pm 10=190,200[/tex]
[tex]P(190 < \bar{x} < 200)=P(-1 .98 < z < 1.98)\\=P(z < 2)-P(z < -2)\\=0.9772-0.0228\\=0.9544[/tex]
Learn more about the topic Z-score:
https://brainly.com/question/5512053
Can someone help me with this please
Answer:
21
Step-by-step explanation:
so this is the way i learned it
compare side to side so CA is 12 and LM is 9 so its 4/3
CB is 8 LN is 6 so its 4/3
so AB is 8 so MN would have to be 4/3 which would made MN 6 so MNL would be 21
Answer:
21
Step-by-step explanation:
ΔLMN ≅ ΔABC with a scale factor of 0.75
If Line AB is similar to Line MN, then Line MN is 6.
Perimeter of ΔLMN
9+6+6=
15+6=
21
The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average age in the sample was 31 years with a standard deviation of 3.8 years.The Margin of error of the 99% confidence interval for the average age of the consumers is a.1.90 years b.2.13 years c.4.10 years d.1.65 years
Answer:
a.1.90 years
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{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
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.
In this question:
[tex]n = 25, \sigma = 3.8[/tex]
So
[tex]M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90[/tex]
So the correct answer is:
a.1.90 years
Compute the determinant using a cofactor expansion across the first row. Also compute the determinant by a cofactor expansion down the second column. StartAbsoluteValue Start 3 By 3 Matrix 1st Row 1st Column 3 2nd Column 0 3rd Column 3 2nd Row 1st Column 2 2nd Column 3 3rd Column 3 3rd Row 1st Column 0 2nd Column 4 3rd Column negative 2 EndMatrix EndAbsoluteValue
Answer:
Step-by-step explanation:
It is given that
[tex]\Delta=\begin{vmatrix}3&0&3\\2 &3&3\\0 &4&-2\end{vmatrix}[/tex]
By cofactor expansion across the first row, we get
[tex]\Delta=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}[/tex]
[tex]\Delta=3\left[(-1)^{1+1}\begin{vmatrix}3&3\\4&-2\end{vmatrix}\right]+0\left[(-1)^{1+2}\begin{vmatrix}2&3\\0&-2\end{vmatrix}\right]+3\left[(-1)^{1+3}\begin{vmatrix}2&3\\0&4\end{vmatrix}\right][/tex]
[tex]\Delta=3\left[-18\right]+0\left[(-1)(-4)\right]+3\left[8\right][/tex]
[tex]\Delta=-54+0+24[/tex]
[tex]\Delta=-30[/tex]
Therefore, the value of determinant is -30.
By cofactor expansion across the second column, we get
[tex]\Delta=a_{12}C_{12}+a_{22}C_{22}+a_{32}C_{32}[/tex]
[tex]\Delta=0\left[(-1)^{2+1}\begin{vmatrix}2&3\\0&-2\end{vmatrix}\right]+3\left[(-1)^{2+2}\begin{vmatrix}3&3\\0&-2\end{vmatrix}\right]+4\left[(-1)^{3+2}\begin{vmatrix}3&3\\2&3\end{vmatrix}\right][/tex]
[tex]\Delta=0\left[(-1)(-4)\right]+3\left[(-6)\right]+4\left[(-1)3\right][/tex]
[tex]\Delta=-18-12[/tex]
[tex]\Delta=-30[/tex]
Therefore, the value of determinant is -30.
for a sample size of 115 and a population parameter of 0.1,what is the standard deviation of the normal curve that can be used to approximate the binomial probability histogram. Round your answer to three decimal places
A.0.028
B.0.054
C.0.043
D.0.035
Answer:
A) 0.028
Step-by-step explanation:
Given:
Sample size, n = 115
Population parameter, p = 0.1
The X-Bin(n=155, p=0.1)
Required:
Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.
To find the standard deviation, use the formula below:
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
Substitute figures in the equation:
[tex]\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.1 * 0.9}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.09}{115}}[/tex]
[tex] \sigma = \sqrt{7.826*10^-^4}[/tex]
[tex] \sigma = 0.028 [/tex]
The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028