In the above question, we need to from 3 probability questions and then give solutions for them
Example 1 : A coin is tossed three times. What is the probability of getting at least one head?
Solution : A coin is tossed 3 times then
Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]
Total number of ways = 2 × 2 × 2 = 8
Favorable Cases = 7
P (A) = 7/8
OR
Probability (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8
Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the probability that the drawn ball is
(i) black
(ii) not black
Solution :
Total number of balls in the bag are = 3 + 4 = 7 balls
Number of favorable outcomes or number of black balls in the bag = 4
(i) Probability getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]
P(black ball) = [tex]\frac{4}{7}[/tex]
(ii) Probability getting no black balls = 1 - P(black ball)
= 1 - [tex]\frac{4}{7}[/tex]
= [tex]\frac{3}{7}[/tex]
Example 3 : Given two dice, what is the likelihood of receiving the number 7?
Mathematical probability - There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6
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In ΔUVW, \overline{UW}
UW
is extended through point W to point X, \text{m}\angle UVW = (3x+16)^{\circ}m∠UVW=(3x+16)
∘
, \text{m}\angle WUV = (2x+8)^{\circ}m∠WUV=(2x+8)
∘
, and \text{m}\angle VWX = (8x-18)^{\circ}m∠VWX=(8x−18)
∘
. Find \text{m}\angle WUV.m∠WUV.
The value of the angle m∠WUV will be equal to 36°.
Triangle may be defined as a closed figure having three sides and three interior angles. The above question can be solved by using the exterior angle theorem of triangle. The exterior angle of a triangle theorem states that the measure of the angle formed, when one side of a triangle is extended, is equal to the sum of the opposite interior angles of that triangle. Applying the exterior angle of a triangle theorem:
m∠WUV + m∠UVW = m∠VWX
Substitute the values of angles.
(2x + 8) + (3x + 16) = (8x - 18)
5x + 24 = 8x - 18
5x - 8x = -24 - 18
-3x = -42
=> x = -42/-3
=> x = 14
So, the angle m∠WUV = 2x + 8
Putting in the value of x
m∠WUV = 2(14) + 8
m∠WUV = 28 + 8
m∠WUV = 36° which is required value.
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In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was
and mass was decreasing by
500 grams
8% per day. Determine the mass of the radioactive
sample at the beginning of the 13th day of the experiment. Round to the nearest tenth
(if necessary).
Answer: a13=310.7
Step-by-step explanation:
Formula= an=a1r^n-1
a13=1100(0.9)13-1
a13=310.7
let v be a vector space over a field of characteristic not equal to two. (a) let u and v be distinct vectors in v. prove that {u, v} is linearly independent if and only if {u v, u − v} is linearly independent. (b) let u, v, and w be distinct vectors in v. prove that {u, v, w} is linearly independent if and only if {u v, u w, v w} is linearly independent.
Thus {u, v} is linearly independent if and only if {u v, u − v} is linearly independent
It is given that {u,v} be a linearly independent set of a set S.
This means that there exist constant a,b such that if:
au+bv=0
then a=b=0
Now we are asked to prove that:
{u+v,u-v} is a linearly independent set.
Let us consider there exists constant c,d such that:
c(u+v)+d(u-v)=0
To show: c=d=0
The expression could also be written as:
cu+cv+du-dv=0
( Since, using the distributive property)
Now on combining the like terms that is the terms with same vectors.
cu+du+cv-dv=0
i.e.
(c+d)u+(c-d)v=0
Since, we are given that u and v are linearly independent vectors this means that:
c+d=0------------(1)
and c-d=0 i.e c=d-----------(2)
and from equation (1) using equation (2) we have:
2c=0
i.e. c=0
and similarly by equation (2) we have:
d=0
Hence, we are proved with the result.
We get that the vectors {u+v,u-v} is linearly independent.
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x-interecpt of 2x−y+6 = 0.
Answer:
x- intercept = - 3
Step-by-step explanation:
to find the x- intercept , where the line crosses the x- axis, let y = 0 in the equation and solve for x
2x - 0 + 6 = 0
2x + 6 = 0 ( subtract 6 from both sides )
2x = - 6 ( divide both sides by 2 )
x = - 3 ← x- intercept
Find the x of the triangle
Let the yellow dot equal to y In the diagram I drawn. NOW I WILL USE THE REASON SUM ANGLES OF A TRIANGLE 43°+57°+ YELLOW DOT=180°
[tex]43 + 57 + y = 180 \\ 100 + y = 180 \\ y = 180 - 100 \\ y = 80[/tex]
THE YELLOW DOT FROM THE TRIANGLE ON THE RIGHT IS EQUAL TO THE DOT ON THE TRIANGLE ON THELEFT SIDE BY VERTICAL OPPOSITE
[tex]x + x + y = 180 \\ 2x + 80 = 180 \\ 2x = 180 - 80 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]
x=50°
HOPE THIS HELPS.
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Mrs. harris is a librarian at eastside library. in examining a random sample of the library's book collection, she found the following. 661 books had no damage, 78 books had minor damage, and 26 books had major damage. based on this sample, how many of the 73,500 books in the collection should mrs. harris expect to have minor damage? round your answer to the nearest whole number. do not round any intermediate calculations.
The number of minor damaged books in 73500 book collection is 8,673 books.
Given that, 661 books had no damage, 78 books had minor damage, and 26 books had major damage.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the minor damaged books be x.
Now, 78 : 661 :: x : 73,500
⇒ 661x = 73500 × 78
⇒ 661x = 57,33,000
⇒ x = 57,33,000 ÷ 661
⇒ x = 8,673.22
≈ 8,673
Therefore, the number of minor damaged books in 73500 book collection is 8,673 books.
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a chess board is made using the ratio of square length to king's height, 3.5 inches to 4.5 inches. if a chess board is made with a king's height of 2.25 inches, what is the length of the square? 4.05 inches 2 inches 1.8 inches 1.75 inches
If the chess board is made with the height of the king the length of the square is going to be 1.75 inches
What is ratio?This is the term that is used to refer to the relationship that is in existence between two independent amounts.
The ratio is given as
3. 5 = 4.5 inches
? = 2.25
The unknown that we are to solve for here would be the value of the height of the king. This is to be gotten when we have to use the cross multiplication
2.25 * 3.5 = 4.5?
7.875 = 4.5?
divide through by 4.5
? = 7.875 / 4.5
= 1.75
Hence the length of the square is 1.75 inches.
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12.7÷787.47 what the answer
Answer:0.01612759851
Step-by-step explanation:
hope this helps
Answer:
0.016127598511689 or just 0.02
Step-by-step explanation:
R is directly proportional to T. If R = 60 when T = 10, Calculate the value of R when T = 7
Answer:
R = 42
Step-by-step explanation:
given R is directly proportional to T , then the equation relating them is
R = kT ← k is the constant of proportion
to find k use the condition R = 60 when T = 10
60 = 10k ( divide both sides by 10 )
6 = k
R = 6T ← equation of proportion
when T = 7 , then
R = 6 × 7 = 42
what’s the least common denominator of 5/7 and 4/5
Answer: It's 35
Step-by-step explanation:5 and 7 both go into 35
b) Write down the output y in terms of x.
Input
X
+4
+3
Output
y
6
For the given equation, the inequality is y > 14
What is an inequality in mathematics?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
x + 2×7 = y
=> y = x + 14
Here, y > x.
So, y > 14
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the floor of an elevator was 30feet above ground level.it travels down 10 feet below ground level. what distance has the elevators floor traveled?
Help Fast PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
40 feet
Step-by-step explanation:
-10 -30
Domenica is creating a banner to hang outside her business. Her design is shown below. It is composed of a square and two equal right triangles, one on either side of he square.
Take into account that the figure at the center is a square. Its area is given by:
A1 = (8 ft)² = 64 ft²
To the area of the other two triangles, first determine the length of the below side of the triangle, as follow:
20 ft - 8 ft = 12 ft
12 ft is the length of the two sides. Due to both triangles are equal, the length of their sides is:
12 ft/2 = 6 ft
Then, the area of the triangles is:
A2 = (6 ft)(8 ft)/2 = 48 ft/2 = 24 ft
Hence, the total area of the figure is:
AT = A1 + A2 + A2
AT = 64 ft² + 24 ft² + 24 ft² = 112 ft²
The toal area of the figure is 112 ft²
Water boils at different temperatures at different elevations. The boiling temperature of water is 212F at sea level (0 feet) but drops about 1.72F for every 1,000 feet of elevation. Write a formula for the boiling point at a given elevation. Then solve the formula for the elevation when the boiling point for water is 190F.
Answer:
Step-by-step explanation:
Can you please send a pic of the leason
a researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. under what conditions can that sample mean be treated as a value from a population having a normal distribution? question content area bottom part 1 select all that apply. a. the researcher collects more than 30 samples. b. if the population of grade-point averages has a normal distribution. c. if the population of statistics students has a normal distribution.
An sample mean can be thought to be the worth from populace having a typical dissemination when both or both of these circumstances is met:
1) The populace from which the example is being taken is Regularly circulated. So for this situation, if the number of inhabitants in grade-point midpoints is regularly circulated, the example mean would be treated as a worth from a populace having a typical dissemination
2) The example size is more prominent than 30. On the off chance that we don't know about the populace, yet the example size is more prominent than 30, the example mean can be considered as a worth from a populace having a typical conveyance.
If the 20th term is -40 and your 28th term is -73, what will be the first term
Answer:
The first term will be 38.375
Step-by-step explanation:
aₙ = a₁ + (n - 1) * d
a₂₀ = -40
a₂₈ = -73
-40 = a₁ + 19d
-73 = a₁ + 27d
When we have two similar equations with two unknowns, we can subtract them to get an answer.
-40 = a₁ + 19d --> -40 = a₁ + 19d
-(-73 = a₁ + 27d) --> 73 = -a₁ - 27d
-------------------------------------------------
33 = -8d
Solve for d by dividing by -8
d = -4.125
Now plug d into one of the original equations to solve for a₁
-40 = a₁ + 19(-4.125)
-40 = a₁ - 78.375
a₁ = 38.375
Write an equation of the line that passes through (-2, 5) and (-4, -5)
Answer: 5x + 15 = y
Step-by-step explanation:
mx+b = y
find rise over run
(y_2-y_1)/(x_2-x_1) = m
(-5-5)/(-4+2)
simplify
-10/-2
10/2
5 = m
plug in a point and find b
5(-2) + b = 5
-10 + b = 5
b = 15
5x + 15 = y
Question 2 of 10
Find f(3) if f(x)=x^3+2x²-x-1
IN THE PLACE OF X PLUG IN 3 AND SIMPLIFY
[tex]f(3) = ({3})^{3} + 2( {3})^{2} - (3) - 1 \\ f(3) = 27 + 2(9) - 3 - 1 \\ f(3) = 27 + 18 - 4 \\ f(3) = 45 - 4 \\ f(3) = 41[/tex]
ATTACHED IS THE SOLUTION.
Help please:):)
Create a table of data for two different linear functions. The table should use that same values of x for both functions. Based on your table, will the graph of these two functions intersect? Explain your answer
A table of data for two different linear functions using the same values of x for both functions is shown below:
x | y=2x+7 y=-x+4 -3 | 2(-3)+7=-6+7=1| -(-3)+4=3+4=7 -2 | 2(-2)+7=-4+7=3|-(-2)+4=2+4=6 -1 | 2(-1)+7=-2+7=5|-(-1)+4=1+4=5 0 | 2(0)+7=0+7=7 |-(0)+4=0+4=4 1 | 2(1)+7=2+7+9 |-(1)+4=-1+4=3 2 | 2(2)+7=4+7=11|-(2)+4=-2+4=2 3 | 2(3)+7=6+7=13|-(3)+4=-3+4=1 From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5. Therefore, the graph of the two functions will intersect at (1, 5)
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If m<4 =105, what if m<5
The angle 4 is 105°. From alternative interior angle the angle 5 is 105°.
Given that,
In the picture we can see,
The angle 4 is 105°.
We have to find the angle 5.
The parallel lines,
If a transversal divides two straight lines,
When the two alternate angles are equal, two straight lines become parallel.
The two straight lines are parallel if the pair of internal angles on the same side of traversals is supplementary.
The two straight lines are parallel if the pair of corresponding angles is equal.
The alternative interior angle are always equal.
The angle 4=angle 5
105°=angle 5
The angle 5 =105°.
Therefore, The angle 5 is 105°.
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y = -2x - 6
y = 2x+10
I WILL USE SUBSTITUTION TO SOLVE THE PROBLEM BY EQUATING -2X-6 TO 2X+10 SINCE THEY ARE BOTH EQUAL TO Y
WILL USE SUBSTITUTION TO SOLVE THE PROBLEM BY EQUATING -2X-6 TO 2X+10 SINCE THEY ARE BOTH EQUAL TO Y[tex] - 2x - 6 = 2x + 10 \\ - 2x - 2x = 10 + 6 \\ - 4x = 16 \\ \frac{ - 4x}{ - 4} = \frac{16}{ - 4} \\ x = - 4[/tex]
USE ANY OF THE EQUATIONS TO FIND THE VALUE OF Y YOU WILL GET THE SAME ANSWER
[tex]y = -2 ( - 4) - 6 \\ y = 8 - 6 \\ y = 2[/tex]
ATTACHED IS THE SOLUTION
Answer:
Simplifying
y = -2x + -6
Reorder the terms:
y = -6 + -2x
Solving
y = -6 + -2x
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Simplifying
y = -6 + -2x
-----------------------------
Simplifying
y = 2x + 10
Reorder the terms:
y = 10 + 2x
Solving
y = 10 + 2x
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Simplifying
y = 10 + 2x
find the number of subsets of 38,76,152,304
The number of subsets of {38,76,152,304} are 32.
What is subset?If every element of set A is also an element of set B, then set B is a superset of set A and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another. If every element in a set A is also an element in a set B, then the set A is a subset of the set B. The set A is therefore contained within the set B. A⊂B is used to represent the subset connection.
Given Data
Set = {38,76,152,304}
When there are "n" elements in a set, there are 2ⁿ subsets of that set, and there are 2ⁿ subsets of that subset.
Here,
n = 5
Equating in formula:
= 2⁵
= 32
The number of subsets of {38,76,152,304} are 32.
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Leah can run 720 yards in 4.5 minutes. How many yards can she run in 2 minutes at the same rate?
A. 350
B. 320
C. 160
D. 110
How Many Positive Integer Pairs (x,y) satisfy 4x+12y=640
The number of positive Integer Pairs (x,y) that satisfy 4x+12y=640 is 160
How to determine the value?To determine whether the function is above or below the x-axis, we must examine the graph of the function relative to the x-axis as shown below:
When a function is above the x-axis, it is positive. When a function is below the x-axis, it is considered negative. The function is described in the context of this issue as follows:
Given that both x and y have exponents of 1, this function is linear. The values above the line on the function are the ordered pairings. The values of x for which the function is positive are provided by: For integer integers, that is, numbers without decimal places, from the graph of the function given at the conclusion of the answer 0 ≤ x ≤ 160.
The number is 160.
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D is directly proportional to x. D=36 when x=5. Work out the value of D when x=8
Step-by-step explanation:
D is directly proportional to x. D=36 when x=5. Work out the value of D when x=8.
Because they are directly proportional:
x/D = x/D
5/36 = 8/D
multiply both sides by D:
D(5/36) = D(8/D)
5D/36 = 8
multiply both sides by 36:
36(5D/36) = 8 * 36
5D = 288
divide both sides by 5:
5D/5 = 288/5
D = 288/5
or D = 57.6
How many vehicles does the dealership sell for each 1000 spent on advertising
a long distance runners distance ran in miles varries direclty with the time in minutes. the runner ran 2 miles in 14 minutes.how long would it take the runner to go 9 miles ?
Answer:
Answer down below!
Step-by-step explanation:
If you know that he ran 2 miles in 14 minutes, you can also say he ran 1 mile in 7, because he is running in 7 minute increments
Let's go up together! (The numbers express how many miles have been run!)
7 minutes14 minutes 21 minutes28 minutes35 minutes42 minutes49 minutes56 minutes63 minutesSo in 63 minutes, the runner will have ran 9 miles!
what is the answer to this question?
Answer:
A
Step-by-step explanation:
Proportions can be any number so other statements can't be always true
Answer:
A. Class X has a greater proportion of boys than Class Y
Step-by-step explanation:
- Before choosing any objective, first relate the two proportions.
Multiply class Y by 2:
[tex]{ \rm{y = 2(4 : 5)}} \\ { \rm{y= 8:10}}[/tex]
- So it can be related with class X as the ratios have a common proportion of girls; 10
[tex]{ \rm{x= 9:{ \green{10}}}} \\ { \rm{y = 8:{ \green{10}}}}[/tex]
- By observation, we see that class X has a greater number of boys than in class Y
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: ...creed}}}[/tex]
Find the midpoint M of the line segment joining the points S = (4,-2) and T = (-6,2).
To find the midpoint of the given line segment, we need to find the mean of the x coordinates and the y coordinates of the given points:
[tex]\begin{gathered} x=\frac{4+(-6)}{2}=-\frac{2}{2}=-1 \\ y=\frac{-2+2}{2}=0 \end{gathered}[/tex]It means that the midpoint is M = (-1,0).
Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain
A compound interest that pays 5% interest compounded daily is preferable. This is so even though the interest rates on the two accounts are equal, the 5% interest compounded daily account is used more frequently.
What is difference between simple interest and compound interest ?Interest is the cost of borrowing money, such as the sum added to a loan debt. It is also possible to classify the rate paid for holding money on deposit, such as in the case of a certificate of deposit. The two ways to calculate interest are simple interest and compound interest.
On the principal, or original loan amount, of a loan, simple interest is calculated.
Since compound interest is calculated using both the principal and the accrued interest from previous periods, it is frequently referred to as "interest on interest".
If interest is computed on a compound basis rather than a simple basis, the amount of interest that must be paid on a loan can vary significantly. Positively speaking, the magic of compounding may be a powerful tool for wealth growth and can work in your favor when it comes to your assets.
Simple interest and compound interest are fundamental financial concepts, but understanding them thoroughly may enable you to make better choices when applying for a loan or making investments.
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