Answer:
GCF of 1/3 and 1/4 is 1/12
LCM of 1/3 and 1/4 is 1
Step-by-step explanation:
1/12(3 + 4) would be distributed/factored form from GCF
Given the equation - 2x + 7y = -25 find the
value of y if the ordered pair (2,y) is a solution.
A 19.5
B -3
C -19.5
D 3
Answer:
y=-3
Step-by-step explanation:
-2x+7y=-25
put x=2 in the above equation
-2(2)+7y=-25
-4+7y=-25
adding 4 on both sides
-4+4+7y=-25+4
7y=-21
dividing 7 on both sides
7y/7=-21/7
y=-3
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
Explain why the initial value of any function of the form f(x) = a(b^x) is equal to a. no sample response
Answer:
Basically, it is a because the b elevated to the zero results in 1, which multiplies a. Then the initial value is a.
Step-by-step explanation:
The initial value of a function f(x) is f(0), that is, the value of f when x = 0.
Format:
[tex]f(x) = ab^{x}[/tex]
The initial value is f(0). So
[tex]f(x) = ab^{x}[/tex]
[tex]f(0) = ab^{0}[/tex]
Any non-zero value elevated to the zero is 1.
So
[tex]f(0) = ab^{0} = a*1 = a[/tex]
Basically, it is a because the b elevated to the zero results in 1, which multiplies a. Then the initial value is a.
Answer:
SAmple Answer Edge 2020-2021
Step-by-step explanation:
When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a.
The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation.
y''-25y= 4; y1=e^-5x
a. y2(x) = ?
b. yp(x) = ?
Answer:
a) y₂ (x) = e ⁵ˣ
Complementary function
[tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]
b) particular integral
[tex]P.I = y_{p} = \frac{-4}{25}[/tex]
Step-by-step explanation:
step(i):-
Given differential equation y''-25y= 4
operator form
⇒ D²y - 25 y =4
⇒ (D² - 25) y =4
This is the form of f(D)y = ∝(x)
where f(m) = D² - 25 and ∝(x) =4
The auxiliary equation A(m) =0
⇒ m² - 25 =0
m² - 5² =0
⇒ (m+5)(m-5) =0
⇒ m =-5 , 5
Complementary function
[tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]
This is form of
[tex]y_{C} = C_{1} y_{1} (x) + C_{2} y_{2} (x)[/tex]
where y₁ (x) = e⁻⁵ˣ and y₂ (x) = e ⁵ˣ
Step(ii):-
Particular integral:-
[tex]P.I = y_{p} = \frac{1}{f(D)} \alpha (x)[/tex]
[tex]P.I = y_{p} = \frac{1}{D^{2} -25} 4[/tex]
= [tex]= \frac{1}{D^{2} -25} 4e^{0x}[/tex]
put D = 0
The particular integral
[tex]y_{p} = \frac{1}{ -25} 4[/tex]
[tex]P.I = y_{p} = \frac{-4}{25}[/tex]
Conclusion:-
General solution of given differential equation
[tex]y = y_{C} +y_{P}[/tex]
[tex]y = C_{1} {e^{-5x} } + C_{2} {e^{5x} } -\frac{4}{25}[/tex]
The function C(x)=−10x+1764 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $32?
Answer:
42
Step-by-step explanation:
(-10*42+1764)/42
The blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 1.3 years. What warranty should be provided so that the company is replacing at most 6% of their blenders sold?
Answer:
A warranty of 6.185 years should be provided.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 8.2, \sigma = 1.3[/tex]
What warranty should be provided so that the company is replacing at most 6% of their blenders sold?
The warranty should be the 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.55.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.55 = \frac{X - 8.2}{1.3}[/tex]
[tex]X - 8.2 = -1.55*1.3[/tex]
[tex]X = 6.185[/tex]
A warranty of 6.185 years should be provided.
Please answer this correctly
Answer:
The second graph.
Step-by-step explanation:
0-9: 6 numbers
10-19: 2 numbers
20-29: 1 number
30-39: 3 numbers
40-49: 1 number
50-59: 2 numbers
60-69: 0 numbers
70-79: 5 numbers
80-89: 3 numbers
90-99: 1 number
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.
On a coordinate plane, point B(–6, 1) is translated to B prime(–3, –2). Indira uses these steps to find a rule to describe the translation. Step 1 Substitute the original coordinates and the translated coordinates into (x, y) right-arrow (x + a, y + b): B (negative 6, 1) right-arrow B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2) Step 2 Write two equations: Negative 6 + a = negative 2. 1 + b = negative 3. Step 3 Solve each equation: Negative 6 + a = negative 2. a = negative 2 + 6. a = 4. 1 + b = 3. b = negative 3 minus 1. b = negative 4. Step 4 Write the translation rule: (x, y) right-arrow (x + 4, y minus 4) Which corrects Indira’s first error? Indira should have substituted B (negative 6, 1) right-arrow B prime (negative 3 + a, negative 2 + b) = B prime (negative 6, 1) in Step 1. Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2. Indira should have solved the equations to find that a = negative 8 and b = negative 2 in Step 3. Indira should have written the translation rule (x, y) right-arrow (x minus 4, y + 4) in Step 4.
Answer:
Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.
Step-by-step explanation:
Point B(-6, 1) to B'(-3, -2)
Steps to achieve B"
-6+a= -3 ⇒ a= -3+6= 3
1+b= -2 ⇒ b= -2-1= -3
-----------------
Step 1 Substitute the original coordinates and the translated coordinates into (x, y) right-arrow (x + a, y + b): B (negative 6, 1) right-arrow B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2)
Step 2 Write two equations: Negative 6 + a = negative 2. 1 + b = negative 3. wrong stepStep 3 Solve each equation: Negative 6 + a = negative 2. a = negative 2 + 6. a = 4. 1 + b = 3. b = negative 3 minus 1. b = negative 4.
Step 4 Write the translation rule: (x, y) right-arrow (x + 4, y minus 4)
----------------
Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.Answer:
Indira should have written the equations Negative 6 + a = negative 3 and 1 + b = negative 2 in Step 2.
Step-by-step explanation:
point B(–6, 1) goes to B prime(–3, –2)
-6 goes to -3 which means we add 3
1 goes to -2 which means we subtract 3
x+a = x' y+b = y'
-6+a = -3 1 + b = -2
Add 6 Subtract 1
a = -3+6 b = -2-1
a = +3 b = -3
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!!!
given the diagram below what is cos (45degree)?
Answer:
[tex]1/\sqrt{2}[/tex]
Answer:
B
Step-by-step explanation:
The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 8 in-state applicants results in a SAT scoring mean of 1144 with a standard deviation of 25. A random sample of 17 out-of-state applicants results in a SAT scoring mean of 1200 with a standard deviation of 26. Using this data, find the 90% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean score of in-state applicants
x2 = sample mean score of out-of-state applicants
s1 = sample standard deviation for in-state applicants
s2 = sample standard deviation for out-of-state applicants
n1 = number of in-state applicants
n2 = number of out-of-state applicants
For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (8 - 1) + (17 - 1) = 23
z = 1.714
x1 - x2 = 1144 - 1200 = - 56
Margin of error = z√(s1²/n1 + s2²/n2) = 1.714√(25²/8 + 26²/17) = 18.61
Confidence interval = - 56 ± 18.61
Yearly healthcare expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation equal to $500. A sample of 36 families was selected and the mean and standard deviation were was found to be $3250 and $400 respectively. What is the probability of healthcare expenses in the population being greater than $4,000?
Answer:
The probability of healthcare expenses in the population being greater than $4,000 is 0.02275.
Step-by-step explanation:
We are given that yearly healthcare expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation equal to $500.
Let X = yearly healthcare expenses of a family
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{ X-\mu}{\sigma} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean expense = $3,000
[tex]\sigma[/tex] = standard deviation = $500
Now, the probability of healthcare expenses in the population being greater than $4,000 is given by = P(X > $4,000)
P(X > $4,000) = P( [tex]\frac{ X-\mu}{\sigma} }[/tex] > [tex]\frac{4,000-3,000}{{500}{ } }[/tex] ) = P(Z > 2) = 1 - P(Z [tex]\leq[/tex] 2)
= 1 - 0.97725 = 0.02275
The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.
We claim that the average weight of our "product" is 50 pounds, with a standard deviation of 2 pounds. We take a sample of 50 units, with a mean of 49.95 pounds and a standard deviation of 1.9999 pounds. What is a 95% prediction interval for the mean weight of the NEXT unit of production from our process? Use Z for ease of calculation.
Answer:
49.95+/-0.5543
= ( 49.3957, 50.5043) pounds
the 95% confidence interval (a,b) = ( 49.3957, 50.5043) pounds
And to 2 decimal points;
the 95% confidence interval (a,b) = ( 49.40, 50.50) pounds
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 = 49.95 pounds
Standard deviation r = 1.9999 pounds
Number of samples n = 50
Confidence interval = 95%
z value(at 95% confidence) = 1.96
Substituting the values we have;
49.95+/-1.96(1.9999/√50)
49.95+/-1.96(0.282828570338)
49.95+/-0.554343997864
49.95+/-0.5543
= ( 49.3957, 50.5043) pounds
Therefore, the 95% confidence interval (a,b) = ( 49.3957, 50.5043) pounds
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
Evaluate: (4 + 6 • 3) + 3
Answer:
[tex]25[/tex]
Step-by-step explanation:
[tex](4 + 6 \times 3) + 3[/tex]
[tex]=(4 + 18) + 3[/tex]
[tex]=(22) + 3[/tex]
[tex]=22+3[/tex]
[tex]=25[/tex]
Answer:25
Step-by-step explanation:
Pemdas
(4+6*3)+3
(Parentheses and Multiplication first)
4+18
22+3
Then addition
22+3=25
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
what is the inverse of the function f(x)=2x+1?
Answer:
Option 1.
Step-by-step explanation:
[tex]y=2x+1[/tex]
[tex]x=2y+1[/tex]
[tex]x-1=2y[/tex]
[tex]\frac{x-1}{2} = \frac{2y}{2}[/tex]
[tex]\frac{x-1}{2} = y[/tex]
[tex]\frac{1}{2}x -\frac{1}{2} = y[/tex]
Answer:
see the attachment
Step-by-step explanation:
You can find the inverse by swapping the variables and solving for y.
y = f(x) . . . . . original function
x = f(y) . . . . . variables swapped
x = 2y +1
x -1 = 2y . . . subtract 1
(x-1)/2 = y . . . divide by 2
y = (1/2)x -1/2 . . . expand
If the inverse function is named h(x), then it is ...
h(x) = x/2 -1/2
Que es el teorema del factor
Answer:
En álgebra, el teorema del factor es un teorema que vincula factores y ceros de un polinomio. Es un caso especial del teorema del resto polinómico.
Step-by-step explanation:
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.
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
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]
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]
finding angle measures between intersecting lines.
Answer: x=45°
Step-by-step explanation:
Angles opposite from each other are equal. The angle 160 degrees in red on the bottom encompasses two angles: BEG and CEG. Angle BEG is on the opposite side as FEA which means it is equal to x.
Since angle FED on the other side is 115, you subtract 115 from 160 to get 45 degrees.
Answer: x=45°
The angle BEG, which is opposite to the angle FEA, is determined to be 45 degrees.
According to the information provided, in a figure with an angle of 160 degrees (red angle on the bottom), there are two angles labeled as BEG and CEG. It is stated that the angle BEG is opposite to the angle FEA, making them equal, so we can represent this angle as x.
Additionally, it is mentioned that the angle FED on the other side measures 115 degrees.
To find the value of x, we subtract 115 degrees from the angle of 160 degrees.
=160-115
= 45
Thus, the solution is x = 45°.
For more details about the angle visit the link below: https://brainly.com/question/16959514
#SPJ4
pls help me I would be happy if do
Answer:
a prism is a three dimensional shape with the same width all the way through.
Step-by-step explanation:
Step-by-step explanation:
i think this will help.
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(1) Given
(2) Definition of midpoint
(3) Transitivity
(4) PWP (Parts Whole Postulate)
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
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
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]
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