Answer:
0.58 = 58% probability she passes both courses
Step-by-step explanation:
We have two events, A and B.
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In which:
[tex]P(A \cup B)[/tex] is the probability of at least one of these events happening.
P(A) is the probability of A happening.
P(B) is the probability of B happening.
[tex]P(A \cap B)[/tex] is the probability of both happening.
In this question:
Event A: Passes the first course.
Event B: Passes the second course.
The probability she passes the first course is 0.7.
This means that [tex]P(A) = 0.7[/tex]
The probability she passes the second course is 0.67.
This means that [tex]P(B) = 0.67[/tex]
The probability she passes at least one of the courses is 0.79.
This means that [tex]P(A \cup B) = 0.79[/tex]
What is the probability she passes both courses
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]0.79 = 0.70 + 0.67 - P(A \cap B)[/tex]
[tex]P(A \cap B) = 0.58[/tex]
0.58 = 58% probability she passes both courses
Which of the following relations is a function?
A{(1, 3), (2, 3), (4,3), (9. 3)}
B{(1, 2), (1, 3), (1.4), (1,5)}
C{(5, 4), (-6, 5), (4, 5), (4, 0)}
D{(6,-1), (1, 4), (2, 3), (6, 1)}
Chloe has a budget of $800 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?
Answer:
$42.10
Step-by-step explanation:
Assuming that she did not yet buy a costume for herself, 800 dollars divided among 18 people plus herself is equal to $42.10 maximum per person.
Answer:
44.44
Step-by-step explanation:
800 didvided by 18.
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.
a. Develop hypotheses that can be used to test whether the population proportion of those
who will use the coupons is sufficient to go national.
b. The file Eagle contains the sample data. Develop a point estimate of the population
proportion.
c. Use αα= .05 to conduct your hypothesis test. Should Eagle go national with the
promotion?
Answer:
a) Alternative hypothesis: the use of the coupons is isgnificantly higher than 10%.
Null hypothesis: the use of the coupons is not significantly higher than 10%.
The null and alternative hypothesis can be written as:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
b) Point estimate p=0.13
c) At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
Eagle should not go national with the promotion as there is no evidence it has been succesful.
Step-by-step explanation:
The question is incomplete.
The sample data shows that x=13 out of n=100 use the coupons.
This is a hypothesis test for a proportion.
The claim is that the proportion of coupons use is significantly higher than 10%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
The significance level is 0.05.
The sample has a size n=100.
The point estimate for the population proportion is the sample proportion and has a value of p=0.13.
[tex]p=X/n=13/100=0.13[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.0009}=0.03[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.13-0.1-0.5/100}{0.03}=\dfrac{0.025}{0.03}=0.833[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>0.833)=0.202[/tex]
As the P-value (0.202) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.
The area of this parallelogram is 120 ft2 find the value of h
Answer: 6
Step-by-step explanation:
A=bh plus 120 for A and 20 for B
120=20b
/20 divide by 20 each side
H=6
The school band is going to a competition. Five members play the flute. There are three times as many members who play the trumpet. There are eight fewer trombone players than trumpeters, and eleven more drummers than trombone players. There are twice as many members that play the clarinet as members that play the flute. There are four fewer tuba players than there are trombone player, but three more members play the French horn than play the trombone. The band director, his assistant and six parent volunteers are also going. How many seats are needed on the bus?
Answer:
76
Step-by-step explanation:
Flute players- 5
Trumpet player- 3 times flute players -15
Trombone players- 8 fewer than trumpet-7
Drummers- 11 more than trombone-18
Clarinet- 2 times flute- 10
Tuba-4 fewer than trombone-3
French horn- 3 more than trombone- 10
Band director- 1
Assistant-1
Volunteers- 6
5+15+7+18+10+3+10+1+1+6=76
pls help me hepl me
Answer:
b at most 199
Step-by-step explanation:so the total was 121 and there is a flat fee of 21.50 so you subtract that out and gat 99.5 since its .5 per mile its going to be divided giving 199 and that is the most she could have driven.
Choose the equation of the horizontal line that passes through the point (−5, 9). y = −5 y = 9 x = −5 x = 9
Answer:
y = 9
Step-by-step explanation:
Since we are trying to find a horizontal line, our line would have to be y = [a number]. That takes our x = -5 and x = 9 out as answer choices. We are left with y = -5 and y = 9. y = 9 is correct because the horizontal line is the y-values, and since in (-5, 9), our y-value is 9, our line is y = 9.
The left and right page numbers of an open book are two consecutive integers whose sum is 389. Find these page numbers
Step-by-step explanation:
Maybe the page numbers can be 143 and 246
143 + 246 = 389
Answer:
194 and 195
Step-by-step explanation:
x = 1st page
x + 1 = 2nd page
x + x + 1 = 389
2x + 1 = 389
2x = 388
x = 194
x + 1 = 195
The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the mean steer weight is 1100lbs. Find the probability that the weight of a randomly selected steer is between 920 and 1730lbs round to four decimal places.
Answer:
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Step-by-step explanation:
Step(i):-
Given mean of the Population = 1100 lbs
Standard deviation of the Population = 300 lbs
Let 'X' be the random variable in Normal distribution
Let x₁ = 920
[tex]Z = \frac{x-mean}{S.D} = \frac{920-1100}{300} = - 0.6[/tex]
Let x₂ = 1730
[tex]Z = \frac{x-mean}{S.D} = \frac{1730-1100}{300} = 2.1[/tex]
Step(ii)
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(x₁≤ x≤x₂) = P(Z₁≤ Z≤ Z₂)
= P(-0.6 ≤Z≤2.1)
= P(Z≤2.1) - P(Z≤-0.6)
= 0.5 + A(2.1) - (0.5 - A(-0.6)
= A(2.1) +A(0.6) (∵A(-0.6) = A(0.6)
= 0.4821 + 0.2257
= 0.7078
Conclusion:-
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Answer:
0.7975
Step-by-step explanation:
The function f(x) = -x2 + 40x - 336 models the daily profit, in dollars, a shop makes for selling donut
combos, where x is the number of combos sold and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? Show
the work that leads to the answer. (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? Show
the work that leads to the answer. (5 points)
(10 points)
Answer:
This question should be worth atleast 20 points
Step-by-step explanation:
a. For the vertex, input the funtion into the calculator, and see where the turning piont is, that is the vertex.
b. Solve using this vormula.
x= (-b ±[tex]\sqrt{b^2 - 4ac}[/tex])/2a
you will get two asnwrs, both are correct.
Quadrilateral DEFG is rotated 180° about the origin to create quadrilateral D'E'F'G'. In which quadrant does G' lie? A. I B. II C. III D. IV
Answer:
B. II
Step-by-step explanation:
G is in quadrant IV. The quadrant that is across the origin from that is quadrant II.
G' will lie in quadrant II
Answer:
B. 11
Step-by-step explanation:
I NEED HELP PLEASE THANKS!
Jenny is sitting on a sled on the side of a hill inclined at 15°. What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds? (Show work)
Answer:
23.29 lbs
Step-by-step explanation:
The force on Jenny due to gravity can be resolved into components perpendicular to the hillside and down the slope. The down-slope force is ...
(90 lbs)sin(15°) ≈ 23.29 lbs
In order to keep Jenny in position, that force must be balanced by an up-slope force of the same magnitude.
if p(A)=0.30,p(B)=0.40and p(AB) =0.20,then p(A/B) is
Answer:
p(A|B) = 2/3Step-by-step explanation:
Given p(A)=0.30,p(B)=0.40and p(A∩B) =0.20,then p(A/B) is expressed as shown:
p(A|B) = p(A∩B)/p(A)
p(A|B) means B is independent and A depends on B.
In your problem P(A)=0.65, P(A∩B) =0.1
Substituting the given values,
p(A|B) = 0.2/0.30
p(A|B) = 2/10 * 10/3
p(A|B) = 2/3
pls help help me pls
Answer:
b
Step-by-step explanation:15 x 5 = 75 and 20 x 4 = 80 making 155 and 15 x 3 = 45 and 20 x 2 = 40 making 85
A car is traveling on Michigan Street towards Ward Street. The car planes to turn right into Ward Street. what is the angle measure of the turn.
Pls help ASAP
Find all solutions to the equation.
7 sin2x - 14 sin x + 2 = -5
If yall can help me for Pre-Calc, that would be great.
-Thanks.
If the equation is
[tex]7\sin^2x-14\sin x+2=-5[/tex]
then rewrite the equation as
[tex]7\sin^2x-14\sin x+7=0[/tex]
Divide boths sides by 7:
[tex]\sin^2x-2\sin x+1=0[/tex]
Since [tex]x^2-2x+1=(x-1)^2[/tex], we can factorize this as
[tex](\sin x-1)^2=0[/tex]
Now solve for x :
[tex]\sin x-1=0[/tex]
[tex]\sin x=1[/tex]
[tex]\implies\boxed{x=\dfrac\pi2+2n\pi}[/tex]
where n is any integer.
If you meant sin(2x) instead, I'm not sure there's a simple way to get a solution...
Given
f(x) = 2x2 + 1
and
g(x) = 3x - 5
find the following.
f-g
Answer:
The answer is
2x² - 3x + 6Step-by-step explanation:
f(x) = 2x² + 1
g(x) = 3x - 5
To find f - g(x) subtract g(x) from f(x)
That's
f-g(x) = 2x² + 1 - (3x - 5)
= 2x² + 1 - 3x + 5
= 2x² - 3x + 6
Hope this helps you
How does a perpendicular bisector divide a triangle
A heavy rope, 30 ft long, weighs 0.4 lb/ft and hangs over the edge of a building 80 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.How much work W is done in pulling half the rope to the top of the building
Answer:
180 fb*lb
45 ft*lb
Step-by-step explanation:
We have that the work is equal to:
W = F * d
but when the force is constant and in this case, it is changing.
therefore it would be:
[tex]W = \int\limits^b_ a {F(x)} \, dx[/tex]
Where a = 0 and b = 30.
F (x) = 0.4 * x
Therefore, we replace and we would be left with:
[tex]W = \int\limits^b_a {0.4*x} \, dx[/tex]
We integrate and we have:
W = 0.4 / 2 * x ^ 2
W = 0.2 * (x ^ 2) from 0 to 30, we replace:
W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)
W = 180 ft * lb
Now in the second part it is the same, but the integral would be from 0 to 15.
we replace:
W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)
W = 45 ft * lb
Following are the calculation to the given value:
Given:
[tex]length= 30 \ ft\\\\mass= 0.4 \ \frac{lb}{ft}\\\\edge= 80 \ ft \\\\[/tex]
To find:
work=?
Solution:
Using formula:
[tex]\to W=fd[/tex]
[tex]\to W=\int^{30}_{0} 0.4 \ x\ dx\\\\[/tex]
[tex]= [0.4 \ \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{4}{10} \times \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{2}{10} \times x^2]^{30}_{0} \\\\= [\frac{1}{5} \times x^2]^{30}_{0} \\\\= [\frac{x^2}{5}]^{30}_{0} \\\\= [\frac{30^2}{5}- 0] \\\\= [\frac{900}{5}] \\\\=180[/tex]
Therefore, the final answer is "[tex]180\ \frac{ lb}{ft}[/tex]".
Learn more:
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Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. The lengths of W C and C Y are congruent. Which best explains if quadrilateral WXYZ can be a parallelogram? WXYZ is a parallelogram because diagonal XZ is bisected. WXYZ is not necessarily a parallelogram because it is unknown if CZ = CY. WXYZ is a parallelogram because ZC + CX = ZX. WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Answer: The answer is D
Step-by-step explanation:
Edge 2021
The true statement is (d) WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
What are quadrilaterals?Quadrilaterals are shapes with four sides
What are parallelograms?Parallelograms are quadrilaterals that have equal and parallel opposite sides
The quadrilateral is given as:
WXYZ
Also, we have:
WC = CY
The given parameters are not enough to determine if the quadrilateral is a parallelogram or not
Hence, the true statement is (d) WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
Read more about quadrilaterals and parallelograms at:
https://brainly.com/question/1190071
There is a set of 100 obserations with a mean of 46 and a standard deviation of 0. What is the value of smallest obserstion in a set?
Answer:
Solution = 46
Step-by-step explanation:
I believe you meant standard deviation. Standard deviation is defined as the variation of the data set, or the differences between the values in this set. In order for the standard deviation to be 0, all values should be the same.
Now if the mean is 46, the smallest possible number of each value in the data set should be 46 as well. This is considering the mean is the average of the values, and hence any number of values in the data set being 46 will always have a mean of 46. Let me give you a demonstration -
[tex]Ex. [ 46, 46, 46 ], and, [46, 46, 46, 46, 46]\\Average = 46 + 46 + 46 / 3 = 46,\\Average = 46 + 46 + 46 + 46 + 46 / 5 = 46[/tex]
As you can see, the average is 46 in each case. This proves that a data set consisting of n number of values in it, each value being 46, or any constant value for that matter, always has a mean similar to the value inside the set, in this case 46. And, that the value of the smallest standard deviation is 46.
c. Find the price of 16 shirts if 5 costs GH¢80
Answer:
16 shirts = GH¢256
Step-by-step explanation:
If 5 shirts cost GH¢80
Let's determine the price of 16 shirts by cross multiplying the values
This method of evaluating answers is one of the essential methods .
It's just Making sure that the values within each side of the wall to symbol crosses each other.
But one shirt = GH¢80/5
one shirt = GH¢16
So
5 shirts= GH¢80
16 shirts = (16 shirts * GH¢80)/5 shirts
16 shirts = GH¢1280/5
16 shirts = GGH256
Find the length of a leg of a right triangle (in inches) if the other leg measures 9 in. and the hypotenuse measures 19 in. Round to the nearest thousandth. __________________ in
Answer:
a = 16.733
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
a^2 + 9^2 = 19^2
a^2 = 19^2 - 9^2
a^2 = 361-81
a^2 =280
Taking the square root of each side
sqrt(a^2) = sqrt(280)
a = 16.73320053
Rounding to the nearest thousandth
a = 16.733
Which equation represents the line passing through points A and C on the graph below? On a coordinate plane, point A is at (2, 3), point B is at (negative 2, 1), point C is at (negative 4, negative 3), and point D is at (4, negative 5). y= negative x minus 1 y = negative x + 1 y = x minus 1 y = x + 1
The equation that represents the line that passes through the points A and C is y = x + 1
What is a linear equation?A linear equation is an equation that has a constant rate or slope, and is represented by a straight line
The points are given as:
(x,y) = (2,3) and (-4,-3)
Calculate the slope, m using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{-3 -3}{-4 - 2}[/tex]
Evaluate
m = 1
The equation is then calculated as:
y = m *(x - x1) + y1
So, we have:
y = 1 * (x - 2) + 3
Evaluate
y = x - 2 + 3
This gives
y = x + 1
Hence, the equation that represents the line that passes through the points A and C is y = x + 1
Read more about linear equations at:
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Answer:
y = x + 1
Step-by-step explanation:
Edge2020
Stuck Right now, Help would be appreciated :)
Answer:
C. c = (xv - x) / (v - 1).
Step-by-step explanation:
v = (x + c) / (x - c)
(x - c) * v = x + c
vx - vc = x + c
-vc - c = x - vx
vc + c = -x + vx
c(v + 1) = -x + vx
c = (-x + vx) / (v + 1)
c = (-x + xv) / (v + 1)
c = (xv - x) / (v + 1)
So, the answer should be C. c = (xv - x) / (v + 1).
Hope this helps!
Four different digits from 1 to 9 are required to open a safe.
1. The sum of the digits is 20.
2. The first digit is greater than the third.
3. The second and fourth digits differ by at least 5.
4. Exactly two digits are squares.
5. The first and fourth digits add up to a prime number.
6. The fourth digit is the lowest.
Can you find the four-digit combination?
Answer: 5942
Step-by-step explanation:
Clue 4 states exactly two of the digits = 1, 4, or 9
Clue 1 leaves us with the following combinations:
1, 9, 2, 8
1, 9, 3, 7 eliminate by clue 5
4, 9, 2, 5
1, 4, 7, 8
Clue 5 directs us to the following order for 1,9,2,8
2 __ __ 1 --> 2981 or 2891 eliminate by clue 2
9 __ __ 8 --> 9128 or 9218 eliminate by clue 6
9 __ __ 2 --> 9182 or 9812 eliminate by clue 6
Clue 5 directs us to the following order for 4,9,2,5
5 __ __ 2 --> 5492 or 5942 eliminate 5492 by clue 2
9 __ __ 2 --> 9452 or 9542 eliminate by clue 3
Clue 5 directs us to the following order for 1,4,7,8
4 __ __ 1 --> 4781 or 4871 eliminate by clue 2
The only combination not eliminated is 5-9-4-2, which satisfies all six clues.
1) 5 + 9 + 4 + 2 = 20
2) 5 > 4
3) 9 - 2 > 5
4) 4 & 9 but not 1 are included
5) 5 + 2 = 7, which is a prime number
6) 2 < 5, 9, 4
evaluate -x+4 when x = -2
Answer:
6Step-by-step explanation:
f(x)=-x+4
f(-2)=-(-2)+4
f(-2)=+2+4
f(-2)=6
Answer:
6
Step-by-step explanation:
-(-2)+4=___
+(+2)+4=6
Suppose that you collect data for 15 samples of 30 units each, and find that on average, 2.5 percent of the products are defective. What are the UCL and LCL for this process? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round up negative LCL values to zero. Round your answers to 3 decimal places.)
Answer:
The UCL is [tex]UCL = 0.054[/tex]
The LCL is [tex]LCL \approx 0[/tex]
Step-by-step explanation:
From the question we are told that
The quantity of each sample is n = 30
The average of defective products is [tex]p = 0.025[/tex]
Now the upper control limit [UCL] is mathematically represented as
[tex]UCL = p + 3 \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]UCL = 0.025 + 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]
[tex]UCL = 0.054[/tex]
The upper control limit (LCL) is mathematically represented as
[tex]LCL = p - 3 \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]LCL = 0.025 - 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]
[tex]LCL = -0.004[/tex]
[tex]LCL \approx 0[/tex]
evaluate -x+4 when x = -2
Answer:
6
Step-by-step explanation:
=> -x+4
Given that x = -2
=> -(-2)+4
=> 2+4
=> 6
Answer:
6
Step-by-step explanation:
You just have to input -2 into the statement and then solve
= -(-2) + 4
= 2+ 4
= 6
Nika baked three loaves of zucchini bread. Each cake needed StartFraction 17 over 4 EndFraction cups of flour. Which expression shows the best estimate of the number of cups of flour that Nika used? 4 + 4 + 4 = 12 5 + 5 + 5 = 15 4 + 4 + 4 = 16 17 + 17 + 17 = 51
Answer:
(A)4 + 4 + 4 = 12
Step-by-step explanation:
Each of Nika's cake needed 17/4 cups of flour. Now, we know that:
[tex]\dfrac{17}{4}=4.25 \approx 4[/tex]
Therefore, for three loaves of bread, the best estimate of the number of cups of flour Nika used is:
4 + 4 + 4 = 12
The correct option is A.
Answer:
The correct answer is A.)4 + 4 + 4 = 12