Answer:
-3.1
Step-by-step explanation:
[tex]a=-1/4=-0.25\\\\-0.5(3a+4)+1.9a-1=\\\\-0.5(3*-0.25+4)+1.9*(-0.25)-1=\\-0.5(-0.75+4)+1.9*(-0.25)-1=\\-0.5(3.25)+1.9*(-0.25)-1=\\-1.625+1.9*(-0.25)-1=\\-1.625-0.475-1=\\-2.1-1=\\-3.1[/tex]
A negative value of Z indicates that
A. the number of standard deviations of an observation is to the right of the mean
B. the number of standard deviations of an observation is to the left of the mean
C. a mistake has been made in computations, since Z cannot be negative
D. the data has a negative mean
Answer:
We need to remember that the Z value comes froma normal standard distribution given by:
[tex] Z\sim N(\mu=0,\sigma=1)[/tex]
So then the mean is 0 and all the values in the left are negative. So then if we want to analyze that if A is negative then value of Z indicates that :
B. the number of standard deviations of an observation is to the left of the mean
Step-by-step explanation:
We need to remember that the Z value comes froma normal standard distribution given by:
[tex] Z\sim N(\mu=0,\sigma=1)[/tex]
And the z score formula is given by:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
So then the mean is 0 and all the values in the left are negative. So then if we want to analyze that if A is negative then value of Z indicates that :
B. the number of standard deviations of an observation is to the left of the mean
B. the number of standard deviations of an observation is to the left of the mean
A [tex]Z[/tex] score is a numerical measurement that describes a value's relationship to the mean of a group of values. The value of the [tex]Z[/tex] score tells you how many standard deviations you are away from the mean. A negative [tex]Z[/tex] score reveals the raw score is below the mean average. Also, a negative value of Z indicates that B. the number of standard deviations of an observation is to the left of the mean
For more information:
https://brainly.com/question/17756962?referrer=searchResults
In Vancouver, British Columbia, the probability of rain during a winter day is 0.42, for a spring day is 0.23, for a summer day is 0.16, and for a fall day is 0.51. Each of these seasons lasts one quarter of the year. If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
Answer:
31.82% probability that this day would be a winter day
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening
In this question:
Event A: Rain
Event B: Winter day
Probability of rain:
0.42 of 0.25(winter), 0.23 of 0.25(spring), 0.16 of 0.25(summer) or 0.51 of 0.25(fall).
So
[tex]P(A) = 0.42*0.25 + 0.23*0.25 + 0.16*0.25 + 0.51*0.25 = 0.33[/tex]
Intersection:
Rain on a winter day, which is 0.42 of 0.25. So
[tex]P(A \cap B) = 0.42*0.25 = 0.105[/tex]
If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
[tex]P(B|A) = \frac{0.105}{0.33} = 0.3182[/tex]
31.82% probability that this day would be a winter day
Heather has divided $6700 between two investments, one paying 8%, the other paying 5%. If the return on her investment is $428, how much does she have in each investment?
Answer:
First investment = $3100
Other investment = $3600
Step-by-step explanation:
Total investment made by Henry = $6700
Let one investment be x,
Then other investment = total investment - first investment = 6700 - x
A) For 8% interest, investment = x
dollar value of 8% investment = 8/100*x= 8x/100
A) For 5% interest, investment = 6700- x
dollar value of 8% investment = 5/100*(6700- x)= 5(6700- x)/100
Total return on both the investment = 8x/100 + 5(6700- x)/100
= (8x +33500 - 5x)/100 = (3x+33500)/100
Given that total return = 428
Therefore,
(3x+33500)/100 = 428
=> 3x+33500 = 428*100 = 42800
=> 3x = 42800- 33500 = 9300
=> x = 9300/3 = 3100
Thus, first investment = x = $3100
other investment = $(6700 - 3100) = $3600
which one doesn't belong ? + pls explain anything helps!! thx:)
The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The test statistic is
Answer:
Null hypothesis: [tex]\sigma^2 \leq 0.003[/tex]
Alternative hypothesis: [tex]\sigma^2 > 0.003[/tex]
And for this case the statistic is given by:
[tex] T= (n-1)\frac{s^2}{\sigma^2_0}[/tex]
And replacing we got:
[tex] T =(26-1) \frac{0.06^2}{0.003}= 30[/tex]
Step-by-step explanation:
We have the following info given:
[tex] n = 26[/tex] represent the sample size
[tex] s =0.06[/tex] represent the sample deviation
We want to test the following hypothesis:
Null hypothesis: [tex]\sigma^2 \leq 0.003[/tex]
Alternative hypothesis: [tex]\sigma^2 > 0.003[/tex]
And for this case the statistic is given by:
[tex] T= (n-1)\frac{s^2}{\sigma^2_0}[/tex]
And replacing we got:
[tex] T =(26-1) \frac{0.06^2}{0.003}= 30[/tex]
Convert 100 kilometers to meters.
Answer:
100,000 meters
Step-by-step explanation:
There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.
Answer:
it is 100000 kilometers
Step-by-step explanation:
use the metric system and you get 10000 kilometers.
Add the expressions four -2/3 B +1/4 a and 1/2 a+1/6b-7. What is the simplified some?
Answer:
I tried the question and I got. a/4-b/2-5/2
Step-by-step explanation:
I hope this helps
Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability 0.23 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent. Give your answer to four decimal places. a. What is the probability that both professors get their grants funded
Answer:
14.72% probability that both professors get their grants funded
Step-by-step explanation:
Independent events:
If two events, A and B are independent, the probability of both happening is:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question:
Event A: Professor Jane is funded
Event B: Professor Joe is funded.
Professor Jane has a probability of 0.64 of being funded.
This means that [tex]P(A) = 0.64[/tex]
Professor Joe has probability 0.23 of being funded.
This means that [tex]P(B) = 0.23[/tex]
What is the probability that both professors get their grants funded
[tex]P(A \cap B) = P(A)*P(B) = 0.64*0.23 = 0.1472[/tex]
14.72% probability that both professors get their grants funded
Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a horizontal or vertical tangent line. g
I suppose the curve is [tex]r(\theta)=e^\theta[/tex].
Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.
[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]
We have
[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]
[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]
[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]
[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]
The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:
[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]
[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]
(where [tex]n[/tex] is any integer)
The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:
[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]
[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]
The perimeter of the rectangle shown below is 24 feet. What's the length of side x?
8 ft.
4 ft
811
A. 3 feet
B. 4 feet
C. 14 feet
D. 6 feet
Answer:
b)4feet
Step-by-step explanation:
In a rectangle two sides are equal.
Perimeter is the distance around the rectangle thus.
length=24-8-4-8
length=4
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
Required:
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
Answer:
a) 0.65 mpg
b) Between 24.99 mpg and 28.01 mpg.
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, which is also called standard error, [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 = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
s = 0.65 mpg
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
From the: 50 - (98/2) = 1st percentile
To the: 50 + (98/2) = 99th percentile
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = -2.327*0.65[/tex]
[tex]X = 24.99[/tex]
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = 2.327*0.65[/tex]
[tex]X = 28.01[/tex]
Between 24.99 mpg and 28.01 mpg.
Select the action you would use to solve 4x = 16. Then select the property
that justifies that action.
A. Action: Divide both sides by 4.
B. Property: Multiplication property of equality.
C. Action: Multiply both sides by 4.
D. Property: Division property of equality.
E. Property: Addition property of equality.
O F. Action: Add 4 to both sides.
Answer:
A.
Step-by-step explanation:
Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.
[URGENT] Suppose A and B are dependent events. If P(A) = 0.4 and P(B A) = 0.8, what is
P(A B)?
Answer:
Option (B)
Step-by-step explanation:
If the probabilities of two events A and B are P(A) and P(B) then the conditional probability of an event that can be derived by the formula,
P(B | A) = [tex]\frac{P(A\cap B)}{P(A)}[/tex]
P(A ∩ B) = P(B|A) × P(A)
P(A ∩ B) = (0.8) × (0.4)
= 0.32
Therefore, Option (B) will be the correct option.
Answer:
Option B is correct.
Step-by-step explanation:
The standard error of the estimate measures the scatter or dispersion of the observed values around a __________________________________________________________
Answer:
True mean/population mean
Step-by-step explanation:
The standard error in this case gives an estimate on how far the values observed during the course of the experiment ate likely to be from the true mean/population mean.
Please answer this for me!!! 25 points to whoever answers this!!!!!!
Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers. His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8 markers, and 6 erasers. Sharon bought 6 pencils, 4 markers, and 7 erasers for $17.75. What is the cost of each item?
Answer:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Step-by-step explanation:
Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:
[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]
Solving the linear system:
[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]
The price of each item is:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
What is the area of the figure below 13 in length, 11 in width, 29 in and 13 in?
Answer:
B. 533in²
Step-by-step explanation:
Step 1: Find the area of the rectangle
A = lw
A = (29)13
A = 377
Step 2: Find the leg of the triangle
13 + 11 = 24
Step 3: Find the area of the triangle
A = 1/2bh
A = 1/2(24)(13)
A = 12(13)
A = 156
Step 3: Add the areas of the 2 figures together
377 + 156 = 533
Ten different numbers are written on pieces of paper and thrown into a hat. The sum of all the numbers is 205. What is the probability of selecting four numbers that have a sum greater than 82
Answer:
The probability is 40%
Step-by-step explanation:
a) There are ten pieces of paper with ten numbers
Probability of selecting four pieces of paper = 4/10 or 40%
Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%
Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.
b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes. In other words, it is a measure of the likelihood of an event (or measure of chance).
Help me please I dont understand
Answer:
42°
Step-by-step explanation:
This is right triangle and sum of 2 angles is 90°:
y+48°=90°
so y= 90°- 48°= 42°
Prompt The cell-phone datafile is available in the Data section below. Once again, here is the research question for this lab. Based on a recent study, roughly 80% of college students in the U.S. own a smartphone. Is the proportion of smartphone owners lower at this university? Respond to each of the following in your initial post. State your hypotheses in symbolic form and in words. (The following should be clear in your answer: the population of interest and the meaning of the proportion p in terms of the variable Cell.) StatCrunch uses a normal model to estimate the P-value probability. Verify that normality conditions are met. Use StatCrunch to conduct the hypothesis test. (directions) Copy and paste the results (the StatCrunch output window) into your initial post. Give your P-value and interpret its meaning as a conditional probability. State a conclusion that answers the research question. Use a significance level of 5%. (Your answer should include the P-value and reference the population and the variable Cell.)
Answer:
Step-by-step explanation: i really would day if 80 % was college students it would be more then enogh
P-value and interpret its meaning as a conditional probability is 206
What is conditional probability?
conditional probability is a degree of the chance of an event taking place, for the reason that another event has already occurred. the particular technique is predicated on occasion B occurring with some kind of courting with every other event A.while conditional probabilities can offer extremely useful information, limited records are often furnished or to hand.
Learn more about conditional probability here:-https://brainly.com/question/10739947
#SPJ2
if x degree and 50 degree are co interior angles find the value of x degree
Answer:
x+50degree =180 (sum of co- interior angle)
x=180-50degree
x=130answer
The time it took for a man to walk from his house to the park and back was 2 hours. The distance from his house to the park is 7 miles. The rate at which he walked to the park was twice the rate at which he walked back. What is the man's rate (in mph) walking back to his house?
Answer:
5.25 mph
Step-by-step explanation:
Let r represent the rate at which the man walked back from the park. Then 2r is the rate at which he walked to the park. His total travel time is ...
time = distance/speed
total time = time to the park + time from the park
2 = 7/(2r) +7/r
2 = (7 +14)/(2r) . . . combine terms
r = 21/(2·2) = 5.25 . . . miles per hour
The man's rate walking back from the park is 5.25 miles per hour.
Select true or false for each equation
- 48 (134) = 1,608 True or False
- 7.3 • 0.14 = - 1.022 True or Flse
(- 0.28)(- 5.6) = - 1.568 True or False
(3/4)(- 1 1/3) = -1 True or False
Answer:
False
True
False
True
Step-by-step explanation:
Easiest and fastest way is to plug each equation into a calc and see if they match the values given. When you do so, you should get your answers.
n a nature conservatory, the ratio of butterflies to total number of flying insects is 36 to 100. There are 450 total flying insects. (a) Create a table for how many butterflies there are for 1, 50, and 100 flying insects. Show your work. (b) How many butterflies are in the conservatory? Show your work.
Answer:
There are 172 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 172
Thus, there are 172 butterflies in the conservatory.
Answer:
There are 162 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 162
Thus, there are 162 butterflies in the conservatory.
Look at picture please
Answer:
BCD
Step-by-step explanation:
Is that hegarty maths? Just curious. Anyway acute means a angle below 90
Answer:
∠C
Step-by-step explanation:
Angle A is incorrect because it is 90° and acute angles are LESS than 90°.
Angle B is incorrect because it is more than 90° which makes it obtuse.
Angle D is incorrect because it is more than 90° which makes it obtuse.
Angle C is correct because it is less than 90°.
In triangle △JKL, ∠JKL is right angle, KM and is an altitude. JL=20 and ML=15, find KL.
Answer:
KL = 17.32
Step-by-step explanation:
[tex]KL^{2} = (ML)(JL)\\KL^{2} = (15)(20)\\KL^{2} = 300\\\sqrt{KL^{2} } = \sqrt{300} \\KL = 17.32[/tex]
Find the midpoint of AC
Answer:
so the coordinates of mid-point of AC are (a/2,a/2)
Step-by-step explanation:
as the mid-point of AC is the same as the mid-point of BD
SO we will find the mid-point of BD
by using mid-point formula
[tex]M(x,y)=(\frac{x1+x2}{2} ,\frac{y1+y2}{2})\\M(x.y)=(\frac{0+a}{2},\frac{a+0}{2})\\ M(x,y)=(\frac{a}{2},\frac{a}{2})[/tex]
i hope this will help you :)
. Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito. (a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points) (b) 20% of Chipotle burritos weigh more than what weig
Complete Question
Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.
(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)
(b) 20% of Chipotle burritos weigh more than what weight
Answer:
a
[tex]P(X < 445 )= 0.3085[/tex]
b
[tex]k = 458.42[/tex]
Step-by-step explanation:
From question we are told that
The population mean is [tex]\mu = 450 \ g[/tex]
The variance is [tex]var = 100 \ g^2[/tex]
The consider weight is [tex]x = 445 \ g[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{var}[/tex]
substituting values
[tex]\sigma = \sqrt{ 100}[/tex]
[tex]\sigma = 10[/tex]
Given that weight of Chipotle burritos follows a normal distribution the the probability that a Chipotle burrito weighs less than x grams is mathematically represented as
[tex]P(X < x ) = P ( \frac{X - \mu }{\sigma } < \frac{x - \mu }{\sigma } )[/tex]
Where [tex]\frac{X - \mu }{\sigma }[/tex] is equal to z (the standardized values of the random number X )
So
[tex]P(X < x ) = P (Z < \frac{x - \mu }{\sigma } )[/tex]
substituting values
[tex]P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )[/tex]
[tex]P(X < 445 ) = P (Z <-0.5 )[/tex]
Now from the normal distribution table the value for [tex]P (Z <-0.5 )[/tex] is
[tex]P(X < 445 ) = P (Z <-0.5 ) = 0.3085[/tex]
=> [tex]P(X < 445 )= 0.3085[/tex]
Let the probability of the Chipotle burritos weighting more that k be 20% so
[tex]P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - 450}{10 } ) = 0.2[/tex]
From the normal distribution table the value of z for [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex] is
[tex]z = 0.8416[/tex]
=> [tex]\frac{k - 450}{10 } = 0.8416[/tex]
=> [tex]k = 458.42[/tex]
Solve the system by the method of elimination.
Answer:
no solution
Step-by-step explanation:
x-y = 2
-4x +4y = 4
Multiply the first equation by 4
4(x-y) = 2*4
4x -4y = 8
Add this to the second equation
4x -4y = 8
-4x +4y = 4
------------------------
0x + 0y = 12
0 =12 is never true so there is no solution
Answer:
no solutions
Step-by-step explanation:
work is shown
3. Maria is a veterinarian. She wants to know how the weight of a puppy is related to its length. To find out, Maria randomly selected 10 puppies that are two months old. She recorded the length and weight of each puppy in the table below. Part A. The data from the table are shown on the scatterplot. Draw an estimated line of best fit through the data points. (3 points) Part B. Use the scatterplot to answer these questions. a. What kind of correlation exists between the length and weight of the puppies? Explain. (2 points) b. Identify two points on the line of best fit that you drew in Part A. Use the two points to find the equation of the line. Write the equation of the best fit line in slope-intercept form. Show your work. (4 points: 1 point for identifying the coordinates of two points, 1 point for slope, 1 point for b-value, and 1 point for showing work)
Answer:
Part A. I chose points (7,1.3) and (48,9.8)
Part B. a. Positive correlation; b. y = 0.21x - 0.2
Step-by-step explanation:
Part A.
I chose the first and last points on the line — (7 in, 1.3 lb) and (48 in, 9.8 lb).
That put three points on the line, three above it, and four below.
Part B
a. Type of correlation
There is a positive correlation between the length of a puppy and its weight.
You would expect a longer dog to be bigger and weigh more than a shorter dog.
b. The equation for the line of best fit
The slope-intercept equation for a straight line is
y = mx + b
where m is the slope of the line and b is the y-intercept.
The line passes through the points (7,1.3) and (48, 9.8).
(i) Calculate the slope of the line
\begin{array}{rcl}
[tex]m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{9.8 - 1.3}{48-9}\\\\& = & \dfrac{8.5}{41}\\\\& = & \textbf{0.21 lb/in}\\\\\end{array}[/tex]
The slope of the line is 0.21 lb/in.
(ii) Locate the y-intercept
Put the slope and the coordinates of one point into the slope-intercept formula.
[tex]\begin{array}{rcl}y & = & mx + b\\1.3 & = & 0.21\times7 + b\\1.3 & = & 1.47 + b\\b & = & -0.2\\\end{array}[/tex]
The y-intercept is at (0,-0.2)
(iii) Write the equation for the line
y = 0.21x - 0.2
need some help thanks ;)
Answer:
137
Step-by-step explanation:
sum of angle in a circle = 360°
105 + 118 + x = 360
223 + x = 360
x = 360 - 223
x = 137