Answer:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we can find this probability:
[tex] P(X \geq 1)[/tex]
And we can solve this probability like this:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)[/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
Simplify the expression and then evaluate it for the given value of the variable:
(6−2x)+(15−3x) for x=−0.2
PLEASE HELP!!!!!!!!!!!!!!!!!
Answer:
-5x+2122Step-by-step explanation:
There are no factors outside the parentheses that need to be distributed, so the parentheses can be simply dropped:
6 -2x +15 -3x
The terms can be rearranged to put like terms next to each other:
-2x -3x +6 +15
and the like terms can be combined.
-5x +21 . . . . simplified expression
__
Put the value of x where x is, then do the arithmetic.
-5(-0.2) +21 = 1 +21 = 22
A survey was sent out to re-evalute the proportion of people who play games on pc computers, as the last study on the topic had been gathered four years prior. This survey was done specifically to test the possibility that fewer people are playing games on pc computers. The previous study found that 81% of people were playing games on pc computers. The current study, with 861 participants, found that 53% of people who responded play on a pc computer.
Calculate the p-value and determine if we should accept or reject H0 under alpha = 0.05.
Answer:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
Step-by-step explanation:
Info given
n=861 represent the random sample
[tex]\hat p=0.53[/tex] estimated proportion of people who responded play on a pc computer
[tex]p_o=0.81[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion decreases from 81%, the system of hypothesis are.:
Null hypothesis:[tex]p\geq 0.81[/tex]
Alternative hypothesis:[tex]p < 0.81[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]
The p value would be given by:
[tex]p_v =P(z<20.943)\approx 0[/tex]
The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81
A sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the 10% significance level.
x = 20, n = 36, sigma = 9, H0: mu = 25, H amu : < 25.
Answer:
[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-3.33)=0.000434[/tex]
For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.
Step-by-step explanation:
Information given
[tex]\bar X=20[/tex] represent the sample mean
[tex]\sigma=9[/tex] represent the population deviation
[tex]n=36[/tex] sample size
[tex]\mu_o =25[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
tzwould represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test the hypothesis that the true mean is lower than 25 and the system of hypothesis are:
Null hypothesis:[tex]\mu \geq 25[/tex]
Alternative hypothesis:[tex]\mu < 25[/tex]
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given:
[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-3.33)=0.000434[/tex]
For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.
Please help me answer the question, answer problem 1 and 2
please see the attached picture for full solution
Hope it helps...
Good luck on your assignment,
Avantraveling 20 miles per hour can stop in 60 feet. If a van is traveling 32 miles per hour what is it’s stopping distance
Section 1: Write the following times in 24-hour clock time:
a) 7:15 a.m -
b) 1:05 am
c) 2:01 p.m
d) 9:22 p.m
e) 12:25 am
Section 2: Write the following times in 12-hour clock time.
a) 1155 hours
b) 1005 hours
c) 1714 hours
d) 0756 hours
e) 1345 hours
Answer:
Section 1:
a) 7:15 a.m - 19:15
b) 1:05 am - 01:05
c) 2:01 p.m - 14:01
d) 9:22 p.m - 21:22
e) 12:25 am- 24:25
Section 2:
a) 1155 hours - 11:55am
b) 1005 hours -10:05am
c) 1714 hours - 5:14pm
d) 0756 hours - 7:56am
e) 1345 hours- 1:45pm
Answer:
12:25 am= 00:25
Step-by-step explanation:
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
Complete question:
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
a. How much cheese does Mai use per Pizza
b. At this rate how much cheese will she need to make 15 Pizza's
Answer:
a. ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. amount of cheese to make 15 pizzas= 2.5 × 15 = 37.5 ounces of cheese
Step-by-step explanation:
Mai is making a personal pizzas .For 4 pizza she uses 10 ounces of cheese. This means Mai uses 10 ounces of cheese in weight to make just 4 pizzas.
a. How much cheese does Mai use per Pizza
Not she uses 10 ounces of cheese to make 4 pizzas. Therefore,
If 4 pizzas requires 10 ounces of cheese
1 pizza will require ? ounces of cheese
cross multiply
ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. At this rate how much cheese will she need to make 15 Pizza's
Since she requires 2.5 ounces of cheese to make 1 pizza
? ounces of cheese will be required to make 15 pizzas
cross multiply
amount of cheese to make 15 pizzas = 2.5 × 15 = 37.5 ounces of cheese
Consider the following.x = t − 2 sin(t), y = 1 − 2 cos(t), 0 ≤ t ≤ 8πSet up an integral that represents the length of the curve.8π0 dtUse your calculator to find the length correct to four decimal places.
The length of the parametric curve (call it C ) is given by
[tex]\displaystyle\int_C\mathrm ds=\int_0^{8\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
We have
[tex]x=t-2\sin t\implies\dfrac{\mathrm dx}{\mathrm dt}=1-2\cos t[/tex]
[tex]y=1-2\cos t\implies\dfrac{\mathrm dy}{\mathrm dt}=2\sin t[/tex]
Now,
[tex]\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=5-4\cos t[/tex]
so that the arc length integral reduces to
[tex]\displaystyle\int_0^{8\pi}\sqrt{5-4\cos t}\,\mathrm dt[/tex]
which has an approximate value of 53.4596.
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'? 1.5 units 3 units 4.5 units 6 units
If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.
Dilation of an object simply means enlarging or shrinking of the object by a scale factor.Now, we are told that Triangle ABC was dilated to Triangle A'B'C' using the rule D₀,₄.What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.
Now, if the length of OB is 3/4, it means that the new dilated length is gotten from;Scale factor = new dilated length OB'/(³/₄)
new dilated length OB' = ³/₄ × 4
new dilated length OB' = 3 units
Read more on dilation at; https://brainly.com/question/8532602
Answer:
its 4 units trust just answered it
Step-by-step explanation:
Kristen wants to buy a Persian cat. She takes out a loan for $500 for one year. The bank charges
her an annual simple interest rate of 8%.
a. How much will she have to pay back at the end of the 1 year?
b. How much interest does she have to pay?
Answer:
a. How much will she have to pay back at the end of the 1 year?
Answer: $540
b. How much interest does she have to pay?
Answer: $40
Step-by-step explanation:
Simple interest for any amount p is given by
SI = p*r*t/100
where r is the annual rate rate of interest
t is the time
____________________________________________
Given
p= $500 (loan taken)
r = 8%
t = 1 year
SI = 500*8*1/100 = 40
Thus, $40 is the interest charged in a year.
Total money paid at the end of one year = loan taken + interest charged
= $500 + $40
= $540
a. How much will she have to pay back at the end of the 1 year?
Answer: $540
b. How much interest does she have to pay?
Answer: $40
Please help. I’ll mark you as brainliest if correct!
Answer:
a = 13
b = 0
Step-by-step explanation:
Conjugate of -3 + 2i is -3 - 2i
(-3 + 2i) (-3 - 2i)
We need to expand:
9 + 6i + -6i + -4i^2
-4i^2 =(-4)(-1) = 4
9 + 4 = 13
a = 13
b = 0
Please answer this correctly
Answer:
See below.
Step-by-step explanation:
The total is 20 friends. This means that we need to make each frequency into a fraction, then simplify to percentage.
1. 10/20 = 50%
2. 3/20 15%
3. 2/20 = 10%
4. 5/20 = 25%
Hope this helps! (Please consider giving brainliest)
Answer:
Bus: 50%
Walk: 15%
Bike: 10%
Car: 25%
Step-by-step explanation:
The total amount of friends is 20.
10 out of 20 is equal to 1/2, which is equal to 50%.
3 out of 20 is equal to 15%.
2 out of 20 is equal to 10%.
And 5 out of 20 is equal to 1/4, which is equal to 25%.
Please mark Brainliest if correct
Which set of three angles could represent the interior angles of a triangle? A 26 degrees, 51 degrees, 103 degrees B 29 degrees, 54 degrees, 107 degrees C 35 degrees, 35 degrees, 20 degrees D 10 degrees, 90 degrees, 90 degrees
Answer:
it is option A
Step-by-step explanation:
Alex and Bryan are giving an exam. The probability Alex gets an A is 0.9, the probability Bryan gets an A is 0.8 and the probability Alex gets an A and Bryan doesn't get an A is 0.1. What is the probability that either Alex or Bryan get an A.
Answer:
The probability that either Alex or Bryan get an A is 0.9
Step-by-step explanation:
Before we proceed to answer, we shall be making some important notation;
Let A = event of Alex getting an A
Let B = event of Bryan getting an A
From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1
We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)
We can use the addition theorem here;
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) .......................(i)
Also,
P(A) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) .........................(ii)
We can insert ii into i and we have;
P(A ∪ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) + P(B) - P(A ∩ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9
A farmer planted corn in two different fields. He planted 500 seeds of regular corn in Field A and 500 seeds of experimental corn in Field B. At
harvest time, more ears of corn had grown in Field A than in Field B. The farmer concluded that more corn grew in Field A because of the type
of corn planted.
Choose two other possible variables that could have caused more corn to grow in Field A.
Answer:
1. More pollination process in the regular corn planted in field A than that of field B.
2. Low pest and insect attack on corn planted in field A compared to that of B.
Step-by-step explanation:
1. Pollination is the process in which a plant becomes fertilized, so as to produced seeds. The process requires some agent which could be; air, human, wind etc.
Therefore more pollination of the corn planted in field A than those in B would lead to more yield (ears of corn harvested) than that of B.
2. Pests and insects are agents which could reduce the yield of the corn after harvest. Comparing the two fields A and B, if the corn planted in field A were not affected by pests or insects, while those planted in B were affected, then more ears of corn would be harvested in field A.
Answer:
a,c, And gg gamer
Step-by-step explanation:
— 3х + 7 < 19 ?
Help plz
Answer:
x > -4
Step-by-step explanation:
— 3х + 7 < 19
Subtract 7 from each side
— 3х + 7-7 < 19-7
-3x < 12
Divide each side by -3, remembering to flip the inequality
-3x/-3 > 12/-3
x > -4
Just like any of your two-step equations, in this inequality,
start by isolating the x term which in this case is -3x by
subtracting 7 from both sides.
This gives us -3x < 12.
Solving from here, we divide both sides by -3.
However, when solving inequalities, you need to watch out.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.
So we end up with x > -4.
Which explains how to find the quotient of the division below? - 3 1/3 divided by 4/9 Write Negative 3 and one-third as Negative StartFraction 13 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 13 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 9 and three-fourths. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction, and find the reciprocal of StartFraction 4 over 9 EndFraction as StartFraction 9 over 4 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 9 over 4 EndFraction. The quotient is Negative 7 and StartFraction 6 over 12 EndFraction = Negative 7 and one-half. Write Negative 3 and one-third as Negative StartFraction 9 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 9 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and one-third. Write Negative 3 and one-third as Negative StartFraction 10 over 3 EndFraction. Then, rewrite Negative 3 and one-third divided by StartFraction 4 over 9 EndFraction as Negative StartFraction 10 over 3 EndFraction times StartFraction 4 over 9 EndFraction. The quotient is Negative 1 and StartFraction 13 over 27 EndFraction = Negative 1 and StartFraction 13 over 27 EndFraction
Answer:
The answer is D
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A 10 foot tree create a shadow that is 15 feet long. Find the angle of elevation of the sun
The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long is 33.69 degrees
To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.
Given that:
The tree's height is 10 feet.
The length of the shadow is 15 feet.
Let's assume that the tree's height is "h" feet.
Length of its shadow is represented by "s" feet
The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.
The angle can be determined using the tangent function.
[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]
Now, substitute the given values:
[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]
[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]
The angle of elevation can be obtained by taking the inverse tangent of 2/3
angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]
angle of elevation ≈ 33.66 degrees
So, the angle of elevation of the sun is approximately 33.69 degrees.
Learn more about angle of elevation here:
https://brainly.com/question/31006775
#SPJ4
Which graph has a slope of 1/4?
Answer:Please include images of the graphs!
Step-by-step explanation:
Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.
Use the following equation to get the slope:
m (slope) = (y₂ - y₁)/(x₂ - x₁)
Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:
(x₁ , y₁) & (x₂ , y₂)
In this equation, make sure that the slope (m) will equal 1/4 (given).
The full equation that you will use is:
1/4 = (y₂ - y₁)/(x₂ - x₁)
Find the graph that will satisfy this equation.
at an ice cream shop, thirty cups of ice cream costs $105. what is the cost of one cup of ice cream? what is the cost of 18 cups of ice cream??
Hey there! :)
Answer:
Price per cup: $3.5
Price for 18 cups: $63.
Step-by-step explanation:
To find the cost of a single cup of ice cream, we can set up an equation where 'x' equals the price of a cup of ice cream.
30x = 105
Divide both sides by 30:
x = $3.5.
To find the cost of 18 cups, simply multiply this price by 18:
18 × 3.5 = $63 dollars. This is the price for 18 cups of ice cream.
The diagram shows a rectangle and a square.
Diagram
accuratel
The rectangle is 2 cm long and 6 cm wide.
The perimeter of the rectangle is the same as the perimeter of the square.
Work out the length of one side of the square.
Answer:
4 cm
Step-by-step explanation:
The side of the square will be the average of the two sides of the rectangle with the same perimeter.
Formulas for the perimeters are ...
P = 2(L+W)
P = 4s
Equating these gives ...
4s = 2(L+W)
s = (L +W)/2 . . . . . divide by 4
For the given side lengths, ...
s = (2 cm +6 cm)/2 = (8/2) cm = 4 cm
The length of one side of the square is 4 cm.
Fuel Efficiency of Cars and Trucks Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28.1 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true mean gas mileage with 95% confidence.
Answer:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
Step-by-step explanation:
Information given
[tex]\bar X= 28.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma =4.7[/tex] represent the population standard deviation
n=40 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
A factory received a shipment of 10 generators, and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
Answer:
A) 0.026
B) 0.130
Step-by-step explanation:
Complete Question
A factory received a shipment of 10 generators and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
(A) If a sample of 4 generators is selected, find the probability that all in the sample are defective.
(B) If a sample of 4 generators is selected, find the probability that none in the sample is defective.
Solution
A) This is a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 4
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 4) = ⁴C₄ (0.40)⁴ (0.6)⁴⁻⁴ = 0.0256 = 0.026 to 3 d.p.
B) n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 0
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 0) = ⁴C₀ (0.40)⁰ (0.6)⁴⁻⁰ = 0.1296 = 0.130 to 3 d.p.
Hope this Helps!!!
What’s the correct answer for this?
Answer:
B and F
Step-by-step explanation:
When we'll slice a triangular prism, a square and triangle would be formed
Akmal, Bakri and Cadin share their mother medical expenses which cost RM4200. Cadin pays RM2100 while akmal pays three quarters of Bakri amount. Find the ratio of the expenses shared by Akmal to Bakri to Cadin
Answer:
The ratio of the expenses shared by Akmal to Bakri to Cadin is 7 : 4 : 3
Step-by-step explanation:
The 3 of them shares their mother medical expenses which cost RM4200 . There mother medical expenses is RM4200 in total. Cadin pays RM2100 which is half of their mother medical expenses. Then Akmal pays three quarters of Bakri amount.
Let
The amount Bakri pays = a
Akmal pays = 3/4 of a
Akmal pays = 3/4a
Therefore,
a + 3a/4 = 2100
4a + 3a/ 4 = 2100
7a/4 = 2100
cross multiply
7a = 8400
divide both sides by 7
a = 8400/7
a = 1200
Therefore,
Bakri pays =RM 1200
Akmal pays = 3/4 × 1200 =RM 900
The ratio of the expenses shared by AKmal to Bakri to Cadin is expressed as 2100 : 1200 : 900. Divide through by 300
7 : 4 : 3
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Measure of arcURN = 270°
In radians:
270° = 270π/180
270° = 3π/2
Now
Area of sector = 1/2r²∅
= 1/2(10)²(3π/2)
= 50(3π/2)
= 75π
A certain car can travel on a highway for 350 miles on 15 gallons of gas and in a city for 280 miles on 18 gallons of gas. If the car uses twice as many gallons for city driving as for highway driving, what is the car's average number of miles per gallon? Express your answer to the nearest whole number.
Answer:
The car's average 18 number of miles per gallon
Step-by-step explanation:
The car has different efficiencies depending if its used on highway or city streets.
The efficiency on a highway is:
[tex]E_h=\dfrac{350}{15}\;\text{miles/gal}=23.33\;\text{miles/gal}[/tex]
The efficiency for city driving is:
[tex]E_c=\dfrac{280}{18}\;\text{miles/gal}=15.56\;\text{miles/gal}[/tex]
We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.
Then, we can calculate how many miles makes the car on average as:
[tex]E=\dfrac{1}{3}E_h+\dfrac{2}{3}E_c\\\\\\E=\dfrac{1}{3}\cdot 23.33+\dfrac{2}{3}\cdot15.56=7.78+10.37=18.15\;\text{miles/gal}[/tex]
n th term of quadratic sequence 3, 11 , 25, 45
The first differences are 8, 14, 20.
The second differences are 6.
Half of 6 is 3, so the first term of the sequence is 3n^2.
If you subtract 3n^2 from the sequence you get 0,-1,-2,-3 which has the nth term of -n + 1.
Therefore your final answer will be 3n^2 - n + 1
In 1990, there were 4,500 deaths due to lung diseases in miners aged 20 to 64 years. The expected number of deaths in this occupational group, based on age-specific deaths rates from lung diseases in all males aged 20 to 64 years, was 1,800 during 1990. What is the standardized mortality ratio (SMR) for lung disease in miners
Answer:
2.5
Step-by-step explanation:
We have that the standardized mortality ratio (SMR) is the relationship between the number of deaths observed in a year, that is, those that occurred and the number of expected deaths, that is, those that were predicted.
SMR = observed / expected
therefore if we replace we have:
SMR = 4500/1800
SMR = 2.5
Which means that the standardized mortality ratio (SMR) is 2.5
n a group of 40 people, 10 people are healthy. The 30 unhealthy people have either high blood pressure, high cholesterol, or both. Suppose 15 have high blood pressure and 25 have high cholesterol. If a person is randomly selected from this group, what is the probability that they have both high blood pressure and high cholesterol
Answer:
If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.
Step-by-step explanation:
We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:
[tex]N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10[/tex]
We can calculate the probability that a random person has both high blood pressure and high cholesterol as:
[tex]P(\text{HBP and HC})=\dfrac{10}{40}=0.25[/tex]
