The probability that a container with 2 defective diesel engines will be shipped when 8 engines are chosen at random is 1/45, calculated using combinations in Mathematics.
Explanation:The subject of this question is Mathematics, specifically involving probability and combinatorics. A container has 10 diesel engines, with 2 being defective. The company will only ship the container if none of the randomly selected 8 engines are defective. The probability that the container is shipped can be found by considering the number of ways to choose 8 engines that are not defective out of the 10 engines, relative to the total number of ways to choose 8 engines out of 10 without any restrictions. Since there are 2 defective engines, there are 8 non-defective engines in total.
To calculate this, we use combinations: The number of ways to choose 8 non-defective engines from the 8 available is given by 8 choose 8 (which is 1 way), while the total number of ways to choose any 8 engines from the 10 is given by 10 choose 8. The probability is the ratio of these two numbers.
Using the combination formula which is n choose k = n! / (k!(n - k)!), we can calculate:
8 choose 8 = 1 (since 0! = 1 by definition)10 choose 8 = 10! / (8!(10 - 8)!) = 45The probability is therefore 1/45. Hence, the probability that a container will be shipped, even though it contains 2 defective engines, when 8 engines are chosen at random is 1/45.
True or false:
1) If f'(c)=0, then f has a local maximum or minimum at x=c.
I think this one is false, but I'm not sure.
2) If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b].
3) The Mean Value Theorem can be applied to f(x) = 1/x^2 on the interval [-1, 1].
I'm pretty sure the last one is false.
1. False. [tex]f'(c)=0[/tex] does not necessarily mean that [tex]f(c)[/tex] is a maximum or minimum. It could just as easily be a saddle point. For example, consider the function [tex]f(x)=x^3[/tex] with [tex]f'(x)=3x^2=0[/tex] when [tex]x=0[/tex], yet [tex]f(x)<0[/tex] for [tex]x<0[/tex] and [tex]f(x)>0[/tex] for [tex]x>0[/tex].
2. True. If [tex]f'(x)=0[/tex] for all [tex]x[/tex] in [tex](a,b)[/tex], then [tex]f[/tex] must be constant on that interval.
3. False. In order for the MVT to apply, [tex]f[/tex] must be continuous on the closed interval. But [tex]\dfrac1{x^2}[/tex] does not exist at [tex]x=0[/tex].
The first statement about f'(c)=0 implying a local maximum or minimum is true. The second statement that if f'(x)=0 on an interval implies the function is constant is also true. Lastly, the Mean Value Theorem cannot be applied to f(x) = 1/x² on the interval [-1, 1] because the function is not continuous at x=0.
Explanation:True or false:
The statement 'If f'(c)=0, then f has a local maximum or minimum at x=c' is true. As part of calculus, this is the concept of the first derivative test. If the derivative of a function at a given point is zero, it means that point is a local minimum or maximum, or it could also be a point of inflexion.The statement 'If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b]' is true. This is based on the fact that if the derivative of a function is zero over an interval, the function will be constant in that interval.The statement that 'The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [-1, 1]' is indeed false. The Mean Value Theorem requires the function to be continuous over the closed interval and differentiable over the open interval. The function f(x) = 1/x² is not defined at x=0, hence it is not continuous in the interval [-1,1].Learn more about Calculus here:https://brainly.com/question/32512808
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Need help ASAP!! Use the graph to find the solution of the system of equations what is the solution?
A.(0,-4)
B.(0,-1)
C.no solution
D.(4,-3)
The solution is the point where the two lines meet. The answer is D.
Please help me with this!!!!!!!!!!
Answer:
True
Step-by-step explanation:
The incentre is equally distant from the triangles 3 sides and like centroids is always inside the circle.
Please help with this question!! I am out of points now!! I need this!
Answer:
m∠QRS = 30°
Step-by-step explanation:
An inscribed angle has half the measure of the intercepted arc.
(arc QS)/2 = 60°/2 = 30°
The measure of angle QRS is 30°.
For which intervals is the function negative? Select each correct answer.
ANSWER
(1,4)
(-∞,-3)
EXPLANATION
The interval where a portion of the graph is below the x-axis is where the graph is negative.
From the graph , the curve is below the x-axis on the interval (-∞,-3). Hence the graph is negative on this interval.
Also the graph is below the x-axis on the interval (1,4). This is also another interval where the graph is negative.
Please help me out please
Answer:
400 units³
Step-by-step explanation:
The volume (V) of the square pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
where h is the perpendicular height.
Consider the right triangle formed by a segment from the vertex to the midpoint of the base and the slant height ( the hypotenuse )
Using Pythagoras' identity on the right triangle
h² + 5² = 13²
h² + 25 = 169 ( subtract 25 from both sides )
h² = 144 ( take the square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
Area of square base = 10² = 100, hence
V = [tex]\frac{1}{3}[/tex] × 100 × 12 = 4 × 100 = 400
Juanita and Nina are bowling together. The probability of Juanita getting a strike next game is 24%. The probability of Nina getting a strike next game is 0.17. Which of these events is more likely?
(Choice A)
A
Juanita gets a strike next game.'
(Choice B)
B
Nina gets a strike next game.
(Choice C)
C
Neither. Both events are equally likely.
Answer:
Step-by-step explanation:
0.24 is greater than 0.17, and therefore J's getting a strike next game is more likely.
The event that is more likely is Juanita gets a strike next game.
What is a probability?
Probability is the likelihood that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that Juanita would have a strike is higher than that of Nina. Thus, it is more likely that Juanita gets a strike next game.
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Adriana's computer code 20% less than jocelyn's computer. Adriana's computer cost $640. Adriana's computer cost 15% more than corbins computer. Write an equation that could be used to find the cost of jocelyn's computer
Answer:
640 = 0.80·j
Step-by-step explanation:
Let j represent the cost of Jocelyn's computer (in dollars). Adriana's computer cost 20% less, so has a cost that is 0.80·j. We are told that amount is $640, so we can write the equation ...
640 = 0.80·j
A principal of $3100 is invested at 5.5% interest, compounded annually. How much will the investment be worth after 7 years?
Answer:
$4501.51
Step-by-step explanation:
Because you're compounding annually, which is only once per year, you can use a simple formula:
[tex]A(t)=P(1+r)^{t}[/tex]
Filling in our info gives us
[tex]A(t)=3100(1+.055)^7[/tex]
Do the adding inside the parenthesis and then raise 1.055 to the 7th power to get
A(t)= 3100(1.454679161)
A(t)= $4509.51
PLEASE HELP ASAP 60 POINTS + BRAINLIEST TO RIGHT/BEST ANSWER!
Answer:
see explanation
Step-by-step explanation:
Given
P(x) = x³ + 7x² + 4x, then
P(a) = a³ + 7a² + 4a ← substitute x = a into polynomial
To evaluate P(- 2) substitute a = - 2 into P(a)
P(- 2) = (- 2)³ + 7(- 2)² + 4(- 2) = - 8 + 28 - 8 = 12
Since P(- 2) ≠ 0 then (x + 2) is not a factor of P(x)
Answer:
12
Step-by-step explanation:
(-2)³ + 7(-2)² + 4(-2)
12
How many solutios are there for the following triangle:
A=9 C=4 c=12*
Answer Choices:
a. 0 solutions
b. 1 solution
c. 2 solutions
d. infinite solutions
I would personally go w/ b or c
There is exactly one solution for this triangle, and the correct answer is: b. 1 solution
To determine the number of solutions for the given triangle with angles A, C, and side c, we can use the Law of Sines, which states that in any triangle:
[tex]\[\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
Given:
- Angle A = 90 degrees (since it is a right angle, we assume A is the right angle for the purpose of this solution)
- Angle C = 4 degrees
- Side c = 12 units (opposite to angle C)
Since angle A is 90 degrees, we know that this triangle is a right-angled triangle. In a right-angled triangle, the other two angles must add up to 90 degrees. We are given one of those angles, C, which is 4 degrees. Therefore, the third angle, B, which is opposite side b, can be calculated as:
[tex]\[B = 90^\circ - C = 90^\circ - 4^\circ = 86^\circ\][/tex]
Now, we have all three angles: A = 90°, B = 86°, and C = 4°. The sum of angles in any triangle is 180 degrees, and in this case:
[tex]\[A + B + C = 90^\circ + 86^\circ + 4^\circ = 180^\circ\][/tex]
This confirms that the angles are consistent with the angles of a triangle.
Next, we can find the length of side b using the Law of Sines:
[tex]\[\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
[tex]\[\frac{\sin(86^\circ)}{b} = \frac{\sin(4^\circ)}{12}\][/tex]
Since 86° and 4° are acute angles and sine of an acute angle is unique, there will be a unique positive value for b. This means there is only one possible length for side b that will satisfy the conditions of the triangle.
Therefore, there is exactly one solution for this triangle, and the correct answer is:
b. 1 solution
What is the sum of the infinite geometric series represented by
A. 240
B. 135
C. 360
D. 720
Answer:
the answr is a 240
Step-by-step explanation:
beacuse you have to desept the question
Answer:
240 is the answer
Subtract (5x + 3) from (9x – 7).
A. 4x – 4
B. 4x + 10
C. 4x – 10
D. –4x + 10
D is the correct answer
the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
To subtract (5x + 3) from (9x - 7), we need to distribute the negative sign to all the terms in (5x + 3) and then perform the subtraction term by term.
(9x - 7) - (5x + 3)
= 9x - 7 - 5x - 3
Now, combine like terms:
= (9x - 5x) + (-7 - 3)
= 4x - 10
So, the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
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Please please help me
Answer:
BF = 30
Step-by-step explanation:
Each midsegment is half the length of the parallel side of the triangle. CE is 60 and is parallel to BF, so BF = 60/2 = 30.
What is the value of term a^4?
Answer:
135Step-by-step explanation:
[tex]\text{We have the recursive formula of a series:}\\\\a_1=5\\a_n=3a_{n-1}\\\\a_2=3a_{2-1}=3a_1\to a_2=3(5)=15\\\\a_3=3a_{3-2}=3a_2\to a_3=3(15)=45\\\\a_4=3a_{4-1}=3a_3\to a_4=3(45)=135[/tex]
A chord of a circular clock is 48 inches long, and its midpoint is 7 inches from the center of the circle. What is the radius of the clock to the nearest whole number?
ANSWER
The radius is 25 inches
EXPLANATION
From the diagram, the radius of the circle is AC.
From the Pythagoras Theorem,
[tex] {r}^{2} = {7}^{2} + {24}^{2} [/tex]
[tex]r^{2} = 49 + 576[/tex]
Simplify
[tex]r^{2} = 625[/tex]
Take positive square root,
[tex]r = \sqrt{625} [/tex]
[tex]r = 25[/tex]
Hence the radius is 25 inches
I am running out of points!! Please help me!!
ANSWER
[tex]165.6 \degree[/tex]
EXPLANATION
The measure of arc AC corresponds to 22% + 24%=46%
The complete angle of the circle is 360°.
Therefore the measure of arc AC is
[tex] = \frac{46}{100} \times 360[/tex]
This simplifies to
[tex]165.6 \degree[/tex]
The correct answer is A.
Please help me?????????
Given an implication of the form [tex]P\implies Q[/tex]
The equivalent implication is [tex]\lnot Q \implies \lnot P[/tex]
So, you have to negate both propositions and invert the order:
If a triangle is not isosceles, then it's not equilateral.
You drop a ball from a height of 10ft. Each bounce the ball gains only 90% of its height back. How high does the ball bounce on its 6th bounce? Starting amount: decay rate: equation: answer:
Answer:
6th bounce: 40%
Starting amount: 100%
Decay rate: 10%
Equation: 100% - 10% - 10% - 10% - 10% - 10% - 10% =
Step-by-step explanation:
100% - 10% - 10% - 10% - 10% - 10% - 10% = 40%. 40% is the answer.
Using an exponential function, it is found that on the 6th bounce, the ball bounces up 5.31 ft.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
You drop a ball from a height of 10ft, hence A(0) = 10.Each bounce the ball gains only 90% of its height back, hence r = 0.1.Then, the height after the nth bounce is given by:
[tex]A[n] = 10(0.9)^n[/tex]
After the 6th bounce, we have that:
[tex]A[6] = 10(0.9)^6 = 5.31[/tex]
On the 6th bounce, the ball bounces up 5.31 ft.
More can be learned about exponential functions at https://brainly.com/question/25537936
PLEASE HELP ME ON THESE 2 QUESTIONS!!!
THANK U!!!
Answer:
Step-by-step explanation:
You might see this a bit easier if you change the 5/4 * pi into degrees.
pi/180 = 5/4*pi / x This is the proportion. Change 5/4 into a decimal
pi/180 = 1.25 *pi / x Cross multiply
x * pi = 1.25 pi * 180 Divide by pi
x = 1.25 * 180
x = 225 degrees.
The fraction of the area of the sector is angle/360
The fraction of the area of the sector is 225/360
The fraction of the area area of the sector is 5/8 Reduced.
225: 3*3*5*5
360 = 2*2*2*5*3 *3
Cancel out the common factors
3 * 3 * 5
which leaves 5/8
Two
-3x^2 + 5x - 2 - 2x^2 + 4x + 2
- 5x^2 + 9x (the 2's cancel)
a = - 5
b = 9
c = 0
Identify the measure of arc HD◠.
Answer:
The measure of arc HD is 20°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
In the triangle of the figure , the measure of the third interior angle is equal to
180°-92°-38°= 50°
50°=(1/2)[(102+18)°-arc HD]
100°=[120°-arc HD]
arc HD=120°-100°=20°
Answer:
arc HD = 20°
Step-by-step explanation:
Let point N be the point where secant RL intersect the circle, point M be the point of intersection for chords NL and KH, and point S be the vertex of the triangle formed by secants KH and RD.
It is given that m∠SRM = 38∘ and m∠RMS = 92∘. Use the Triangle Sum Theorem to determine m∠MSR.
m∠MSR = 180° − 92∘ − 38∘ = 50∘
It is also given that mPN = 18∘ and mNK = 102∘. So, mPK = 18∘ + 102∘ = 120∘.
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,
m∠MSR= 1 /2 (mPK − mHD)
Substitute the known values and solve for mHD.
50∘ = 1/2 (120∘ − mHD)
Multiply by 2.
100 = 120∘ − mHD
Simplify.
mHD = 20
Therefore, the measure of arc HD is 20∘.
The double number lines show the ratio of minutes to days. How many minutes are in 222 days? minutes
2880
Step-by-step explanation:
Final answer:
To find out how many minutes are in 222 days, multiply the number of days (222) by the number of hours in a day (24) and then by the number of minutes in an hour (60). The result is 319,680 minutes.
Explanation:
The student is asking how many minutes are in 222 days. We begin the conversion using the provided information:
There are 24 hours in 1 day
There are 60 minutes in 1 hour
Now, we just need to multiply the number of days by the number of hours in a day, and then by the number of minutes in an hour, to get our answer.
222 days × 24 hours/day × 60 minutes/hour = 319,680 minutes
There are 319,680 minutes in 222 days.
Ameekah is working with consecutive integers
Consecutive numbers: 1, 2, 3, 4, 5.
As we can see it's the latest plus 1
So,
x, x + 1, x + 1 + 1, x + 1 + 1 + 1
x, x + 1, x + 2, x + 3 and so on
So it's x + 1.
For this case we have that by definition, a consecutive number is obtained by adding a unit to the previous one.
Example:
n, n + 1, n + 2, n + 3 ...
So:
If "x" is the first number of Ameekah, its second number to form a series of consecutive integers must be:
x + 1, that is, add "1" to the previous number.
Answer:
x + 1
Option B
lim (-x^2 + 6x-8)
x->-3
[tex]\bf \lim\limits_{x\to 3}~-x^2+6x-8\implies \lim\limits_{x\to 3}~-(3)^2+6(3)-8\implies 1[/tex]
Answer:
2///////////////////////////
Find the Geometric Mean of 8 and 50. Be sure to show your work!
Answer:
20
Step-by-step explanation:
The geometric mean of n numbers is the n-th root of their product. For two numbers, it is the square root of their product:
geometric mean = √(8·50) = √400 = 20
The answer is: 20
My work: √8*50 = √400 = 20
You have to take the square root of 8 multiplied by 50. With that, you would get 400, which is still squared because you have to get the numbers inside of the square root to one number. After that, you can now take the square root of the number that is inside of it, which in this case it is 400. The square root of 400 is 20.
I hope this helps!
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Simplify.
Answer: [tex]\bold{B)\quad \dfrac{x-2}{x+1}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2+5x-14}{x^2+8x+7}\\\\\\=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}\\\\\\=\dfrac{x-2}{x+1}[/tex]
99 PLZ HELP BRAINLIEST Which strategy would not correctly solve this story problem?
There are 14 bikes for sale at a bicycle store. Four of the bikes are black, 5 are white, and the rest are red. How many bikes are red?
A.
Translate into an equation. 4 + 5 + r = 14
B.
Use logical reasoning. There were 14 bikes to start with. Subtract the number of black bikes (4) and subtract the number of white bikes (5). The remaining bikes must be red.
C.
Work backward. Start with 14 bikes and add 4. Then subtract 5. The number left is the number of red bikes.
D.
Draw a diagram. Draw 14 circles. Cross out 4 of the circles and then cross out 5 more circles. Color the remaining circles red.
Which strategy would not correctly solve this story problem?
Billy put up some balloons for a party. He had 4 times as many green balloons as red ones. There were 3 red balloons. During a game, 2 green balloons popped. Then another 5 green balloons popped. How many green balloons did Billy have left?
A.
Use objects to model the problem. Use toothpicks to represent the green balloons. Count out a total of 4 groups of 3 toothpicks. Remove 2 toothpicks and then 5 more. Count the remaining toothpicks to find the number of green balloons left.
B.
Work backwards. Start by adding the number of green balloons that popped (5 + 2) Then multiply the sum by 4. Subtract the number of red balloons (3) and that gives the number of green balloons that were left.
C.
Use logical reasoning. Step 1. Multiply 3 × 4 to figure out the total number of green balloons. Step 2. Add 2 + 5 to figure out how many green balloons popped. Step 3. Subtract the sum in Step 2 from the product in Step 1 to find out the number of green balloons that were left.
D.
Translate into an equation. (3 × 4) – (2 + 5) = g
Which strategy would not correctly solve this story problem?
Comic books cost $1, paperback books cost $3, and hardcover books cost $5 at the used book store. Sara bought 2 comic books, 5 paperbacks, and 2 hardcover books. How much money did Sara spend?
A.
Use objects to model the problem. Use coins to represent $1. Drop 1 coin into a jar 2 times for the cost of comic books. Drop 3 coins into the jar 5 times for the cost of the paperbacks. Drop 5 coins into the jar 2 times for the cost of the hard cover books. Count the coins in the jar.
B.
Draw a diagram. Draw 2 squares and write $1 inside each. Draw 5 circles and write $3 inside each. Draw 2 triangles and write $5 inside each. Add all the dollar amounts inside the shapes to find the total Sara spent.
C.
Use logical reasoning. Sara bought 2 comic books at $1 each for a total of $2. She bought 5 paperbacks at $3 each for a total of $15. She bought 2 hard cover books at $5 each for a total of $10. So Sara adds $2 + $15 + $10 to find the total amount she spent.
D.
Translate into an equation. (1 + 3 + 5) × (2 + 5 + 2) = n
Answer:
is this all apart of the answers or separate questions??
Step-by-step explanation:
1. B
2.C
3.C
4.A
5.D
if m AD=98 and m CD=120 Whats is m
Answer:
The measure of arc BC is 44°
Step-by-step explanation:
we know that
m arc AD+m arc DC+m arc BC+m arc AB=360° ----> by complete circle
substitute the given values and solve for m arc BC
98°+120°+m arc BC+98°=360°
m arc BC+316°=360°
m arc BC=360°-316°=44°
Answer:
109Step-by-step explanation:
I need help ty ty ty :-)
Answer:
First Answer: y + 4 = -3(x - 3)
Second Answer: y - 5 = (-3/4)(x - 4)
Step-by-step explanation:
That answer was correct :)
Answer:
1. y + 4 = -3(x - 3)
2. Second Answer: y - 5 = (-3/4)(x - 4)
:)))
John and George together raked 7/8 if the yard. John raked 3/4 of that amount. What part of the yard did john raked?
Answer:
1
8
Step-by-step explanation:
What do we know:
John and George raked 7/8 of the yard.
John raked 3/4 of 7/8
What we need to know is:
How much did George rake?
How? Subtract the fractions given.
7 - 3
8 4
To do this we must make the denominator (bottom) number the same. How? Find the least common denominator for 8 and 4. Basically what is the lowest number that both 8 and 4 can be divided.
Answer is 8
8 divided by 8 is 1
4 divided by 8 is 2
so
7 - 3 ×2 6
8 4 ×2 = 8
7 _ 6 = 1
8 8 8 is how much George raked.