When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that the first die is 3 or that doubles are rolled.
Step-by-step explanation:
The space comprising all possible outcomes (sample space) is represented by the 6×66×6 matrix formed by the possible pairs representing the outcome of dice:
From the above sample space, there are six events wherein the first die is 44 (all elements of the fourth row in the matrix). That is, n(F)=6n(F)=6. Moreover, there are six events wherein doubles are rolled (all diagonal elements in the matrix). That is, n(D)=6n(D)=6. The result (4,4)(4,4) is the intersection of both events. That is, n(D∩F)=1n(D∩F)=1.
Therefore, the possibility/probability that the first die is 4 or that doubles are rolled is computed as follows:
P(D∪F)=P(D)+P(F)−P(D∩F)=n(D)n(S)+n(F)n(S)−n(D∩F)n(S)=636+636−136=1136P(D∪F)=P(D)+P(F)−P(D∩F)=n(D)n(S)+n(F)n(S)−n(D∩F)n(S)=636+636−136=1136
A surveyor has a surveyed a triangular plot of land. One side of the plot lies along countryside road. This side is 400 ft long. The second side is the gore road, which intersects countryside road at an angle of 88 degrees. The third side of this plot of land is 550 ft long. Determine the distance of the gore road that makes up the unknown side of the plot to the nearest foot
Answer:
tanga bono ulaga kase tatamadtamad
Convert the polar representation of this complex number into its rectangular form: z=4(cos120 + isin 120)
Please help!!! I will mark brainliest!!!!!!!!
Answer:
The answer is D
Step-by-step explanation:
took the test
The polar expression of a complex number in its rectangular form 4(cos120° + i sin120°) = -2 + 2√3 i.
What is the polar form of a complex number?Let Z = a + ib be a complex number in the cartesian form represented by point P(a, b) in the complex plane then Z = r cos∅ + i r sin∅ =r is called the polar form of a complex number.
We have.
z = 4(cos120° + i sin120°)
z = 4(cos(90 + 30)° + i sin(90 + 30)°)
Using trigonometry
cos (90 + ∅) = -sin ∅ and sin (90 + ∅) = -cos ∅
So, 4( -sin (30)° + i cos (30)°)
= 4 ( -1/2 + i √3/2)
= -4(-1/2) + i 4(√3/2)
= -2 + 2√3 i
Thus, the rectangular form is 4(cos120° + i sin120°) = -2 + 2√3 i.
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which of the following could be effectively used to reduce friction (a) water (b)petrol (c) kerosene (d) grease
Answer:
( d ) grease
Step-by-step explanation:
Grease could be effectively used to reduce friction.
i will give Brainiest if you are right
Answer:
F. 4 ÷ 5
Step-by-step explanation:
x^2+8x+4=0 using quadratic formula
Answer:
-4±2√3
Step-by-step explanation:
quadratic formula: (-b±√(b²-4ac))/(2a)
a = 1
b = 8
c = 4
(-8±√(8²-4*1*4))/(2*1)
(-8±√(64-16))/(2)
(-8±√48)/(2)
(-8±4√3)/(2)
-4±2√3
A student wants to write an expression for, all of the elements which are in set A AND all of the elements in set B.” Which expression below matches the statement? (A ‘U B’). (A U B). (A n B) P(A n B)
A student wants to write an expression for, all the elements which are in set A and all the elements in set B. Then, the expression matches the statement is (A n B), which is read as A intersection B. Thus, option B is correct.
What is intersection?The intersection of two sets A and B, denoted by display by (A ∩ B). It is the set containing all elements of A that also belong to B, or, alternatively, all elements of B that also belong to A. The symbol is sued for the intersection is ∩. This is defined as that the element of A and B are is a single set.
Therefore, option B is correct.
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You randomly select one card from a 52-card deckFind the probability of selecting a black ace or a red nine
Answer:
2/52 + 2/52 = 4/52
Find the measure of line segment TU. Assume that lines which appear to be tangent to the circle are tangent.
A)
14
B)
16
18
D)
20
Given:
A figure of a circle. A secant SU and a tangent SR is drawn to the circle from the external point S.
To find:
The measure of the line segment TU.
Solution:
According to the secant tangent segment theorem, the square of tangent is equal to the product of secant and external segment of the secant.
Using secant tangent segment theorem, we get
[tex]SR^2=SU\times ST[/tex]
[tex](40)^2=(32+2x-2)\times (32)[/tex]
[tex]1600=(30+2x)(32)[/tex]
[tex]1600=960+64x[/tex]
Subtract both sides by 960.
[tex]1600-960=64x[/tex]
[tex]640=64x[/tex]
Divide both sides by 64.
[tex]\dfrac{640}{64}=x[/tex]
[tex]10=x[/tex]
Now, the measure of the line segment TU is:
[tex]TU=2x-2[/tex]
[tex]TU=2(10)-2[/tex]
[tex]TU=20-2[/tex]
[tex]TU=18[/tex]
Therefore, the correct option is C.
What is the value of x? Show your work in arriving at your answer.
The value of x is 18.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
First, both angles shown are equal to each other.
5x + 5 = 95
Next, the opposite side of the equation to isolate x value (5x).
5x + 5 (-5) = 95 (-5)
5x = 90
Finally, we need to divide both sides of the equation by 5.
5x / 5 = 90 / 5
x = 18
The final answer: x = 18
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solve y=(1/2)x exponential graph
The value of the exponential graph y = ( 1/2 )ˣ is graphed
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
y = ( 1/2 )ˣ be equation (1)
On simplifying the equation , we get
y = 1 / (2ˣ)
Now , the graph of the function y = ( 1/2 )ˣ will be a slanting line which will not touch the x axis and passes through the point y = 1
The graph of the function y = ( 1/2 )ˣ is given below
Hence , the function is solved and the graph is plotted
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All exponential functions can be written in many forms. Write the function f(t)=90,000(1.3)^t in the form f(t)=ab^t/5. Round all coefficients to four decimal places.
The expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
What is an exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
Given that, we have to express the function [tex]f(t) = 90,000(1.3)^t[/tex] in the form of [tex]f(t) = ab^{\frac{t}{5} }[/tex]
Comparing both the functions,
[tex]b^\frac{t}{5} = (1.3)^t[/tex]
We can write, [tex](1.3)^t[/tex] as
[tex](1.3)^t = (1.3^5)^\frac{t}{5}[/tex]
[tex]= 3.71^\frac{t}{5}[/tex]
Therefore, the equation ca be written as, [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
Hence, the expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
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the ratio of the number of goat to the number of sheep is 3:1. The sheep are 10 in numbers. how many goats are in the gardens and many animals are there?
Answer:
30 goats, and 40 animals
Step-by-step explanation:
so since the problem says 10 goats are in the garden, and the ratio of sheep to goats is 3:1 you do 3*10. it's basically saying for every 1 goat you have 3 sheep. so if you take away the 0 from 30 and 10 you get 3:1. : )
Two people leave from the same point. One travels 12 meters north. The other travels 9 meters east. How far apart are they?
Answer:
It would be 3 meters apart
The midpoint M of the line segment AB is (1,3). If the coordinate of B is (-5,7), what is the coordinate of the point A
Answer:
( 7,-1 )
Step-by-step explanation:
Please help me with this question!!
Answer:
y=8(0.5)^x
Step-by-step explanation:
We can find the value of b, which is the rate. The rate is 0.5 because the y value is consistently going down by 2. A is the first value, which is 8. y=8(0.5)^x
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Which of these is NOT a statistical question?
A.
What were the sixth grade student scores of the final exam?
B.
How many boxes of candy did each member of SGA sell?
C.
How many apps do my classmates have on their phones?
D.
Which class had the highest average on the pre-test?
Answer:
A.
What were the sixth grade student scores of the final exam?
write the equation 0.3x^2+5x-7=0 in standard form and then choose the value of “b”
70
50
5
Answer:
b = 5
Step-by-step explanation:
The given equation is :
[tex]0.3x^2+5x-7=0[/tex] .......(1)
It is in the form of quadratic equation. The general form of a quadratic equation is as follows :
[tex]ax^2+bx+c=0[/tex] .....(2)
Comparing equations (1) and (2), we get :
a = 0.3, b = 5 and c = -7
Hence, the value of b is equal to 5.
(REPOST) PLS HELP Al uses a box in the shape of a rectangular prism as shown in the diagram to for his coin collection.
What is the volume of this box?
192in³
275in³
37512 in³
425in³
Answer:
4 x 8.5 x 12.5 =425 (multiple hight x width x length)
The volume of the box is [tex]425in^{3}[/tex]
Answer:
425 in³
Step-by-step explanation:
V = whl
12 1/2 · 8 1/2 · 4 = 425
Which rectangle has side lengths of 7 units and 8 units?
The rectangle that has side lengths of 7 units and 8 units is (a) a rectangle that has an area of 56 square units
How to determine the rectangleFrom the question, we have the following parameters that can be used in our computation:
Side lengths of 7 units and 8 units
These parameters can be represented as
Length = 7 units
Width = 8 units
Using the options in the question as a guide, we have the following computations
We start by calculating the area of the rectangle
The area of the rectangle can be calculated using the following area formula
Area = length * width
Substitute the known values in the above equation, so, we have the following representation
Area = 7 * 8
Evaluate
Area = 56
Hence, the rectangle is (a)
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Complete question
Which rectangle has side lengths of 7 units and 8 units?
(a) a rectangle that has an area of 56 square units
(b) a rectangle that has a perimeter of 56 square units
(c) a rectangle that has an area of 65 square units
(b) a rectangle that has a perimeter of 6 units
The value of a new car decreases by 10% in the first year.How much will a car be worth after one year if it’s an initial value was $40,000?
Answer:36,000
Step-by-step explanation: if ten percent of 100 is 10 we can use the same concept on 40000 by dividing it by 10 because 10% can be roughly said as 1/10 so 1/10 of 40000 is 4000 which we will subtract 40000 by which results in 36000
Hope this can help you
Any help please, - What is the area for this?
Answer:
109.18
Step-by-step explanation:
Subtract 13.4-7.2 then solve the triangle (base x height) getting 32.86. Next solve the rectangle getting 76.32. Then add all of it concluding in 109.18.
A mechanic charges $45 per hour for labor plus $55 for a computer diagnostic test. The mechanic charges a customer $595 to repair a vehicle. How many hours did the mechanic spend on the repair?
Answer:
The mechanic spent 12 hours on the repair.
Step-by-step explanation:
$595-$55=£540. £540 is the total of the amount the mechanic charges for an hour, MINUS the computer diagnostic testTo find out how many hours the mechanic spent on the repair, we have to do $540 divided by $45, which is 12.The mechanic spent 12 hours on the repair.
Help on this question ASAP PLEASE!!!
The time t in seconds that it takes a car to accelerate to ask mph can be described by T=0.001×0.7 32X^2 +15.417X +603.738 how fast in miles per hour is the car going after 8.55 seconds
The miles per hour that the car is going after 8.55 seconds is 610.79 miles per hour.
How to calculate the time taken?From the information Illustrated, it should be noted that the t in seconds that it takes a car to accelerate to ask mph can be described by T = 0.001 × 0.732X² + 15.417X + 603.738.
In this case, it is important to note that x in the function simply represents the seconds.
Therefore, based on the information, the miles per hour is the car going after 8.55 seconds will be:
T = 0.001 × 0.732X² + 15.417X + 603.738.
T = 0.001 × 0.732(8.55)² + 15.417(8.55) + 603.738
T = 0.001 × 53.511 × 131.815 + 603.738
T = 610.79
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Jayla has a makeup mirror like the one shown below, which measurement is closest to the area of the mirror in square inches?
Answer:
D. 113.1 in^2
Step-by-step explanation:
Choose the exponential function that is true for these points: (0, 1) and (1,
2).
Oy=4"
Oy = 32
Oy = 2
Answer:
If you have two points, (x1, y1) and (x2, y2), you can define the exponential function that passes through these points by substituting them in the equation y = abx and solving for a and b. In general, you have to solve this pair of equations: y1 = abx1 and y2 = abx2, .
Step-by-step explanation:
A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 38 minutes. The owner has randomly selected 27 customers and delivered pizzas to their homes. What hypotheses should the owner test to demonstrate that the pizza delivery will not be successful
Answer:
Read step by step explanation
Step-by-step explanation:
The owner already knows that the limit for the average time delivered pizzas is 38 minutes. So we conclude
1.-The resulting mean from sample data ( x ) ( 27 customers) need to be smaller than 38 minutes, any value of sample above 38 minutes means more time for the delivery action and will indicate a failure for the future project
2.-As sample size is smaller than 30 the test has to be t-student one tail test to the left
Test hypothesis
Null hypothesis H₀ x = 38
Alternative hypothesis Hₐ x < 38
We should test at a significance level α = 0,05 (α = 5%)
If the result of the test is to accept H₀ delivery project won´t be implemented, if on the other hand, H₀ is rejected then in the condition of the alternative hypothesis we accept Hₐ the sample indicates that we have a smaller average time than 38 minutes.
Michelle brought an apple cut in 4 for $0.10 per piece. How much should she pay for 3 dozen pieces
Answer:
$0.90
Step-by-step explanation:
[tex]\frac{4}{10}=0.4[/tex]
3 dozen = 36
[tex]\frac{36}{0.4} =\frac{y}{0.1}[/tex]
0.4 × y = 36 × 0.1
0.4y = 3.6
0.4y ÷ 0.4 = 3.6 ÷ 0.4
y = 9
There was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.4% each year.
Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.
Write an exponential function showing the relationship between y and t.
The exponential function can be written as y = 700e^-0.094t.
What is the exponential function?We know that the term function would have to do with a mathematical rule that we can use to be able to obtain specific values. Now we have to know that there was a sample of 700 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.4% each year.
We can use;
N = Noe^-rt
N = amount at time t
No = Amount at the beginning
r = decay rate
t = time taken
Thus we have; y = 700e^-0.094t
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