9514 1404 393
Answer:
72
Step-by-step explanation:
h(4) = 4^3 -2·4 = 64 -8 = 56
g(4) = 3·4 +4 = 16
Then the sum is ...
(h+g)(4) = h(4) + g(4) = 56 +16
(h+g)(4) = 72
P(A)=[tex]\frac{9}{20}[/tex],P(B)=[tex]\frac{3}{5}[/tex],P(A∩B)=[tex]\frac{27}{100}[/tex] ,P(A∪B)=?
The value of the probability P(A∪B) is 39/50
How to determine the probability?The given parameters are:
P(A)= 9/20
P(B) = 3/5
P(A∩B) = 27/100
To calculate the probability P(A∪B), we make use of the following equation
P(A∪B) = P(A) + P(B) - P(A∩B)
So, we have:
P(A∪B) = 9/20 + 3/5 - 27/100
Evaluate the expression
P(A∪B) = 78/100
Simplify
P(A∪B) = 39/50
Hence, the value of the probability P(A∪B) is 39/50
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Please please help me dayson is covering a package in the shape of a rectangular prism with wrapping paper. the package is 50 centimeters by 20 centimeters by 18 centimeters. he has 1 square meter of wrapping paper. can he completely cover the package with wrapping paper? complete the explanation to show your answer. dayson has 1 m2 of wrapping paper, which is cm2. the package has a surface area of cm2. does dayson have enough paper? enter yes or no.
The package has a surface area of 4520cm². The area of the package is less than the area of the wrapping paper. So, dayson can cover the package with the wrapping paper.
According to the question,
The first step is to determine the surface area of the package.
Total surface area of a cuboid = 2 (l w + w h + l h)
where:
• l = length
• w = width
• h = height
2[(50 x 20) + (50 x 18) + (20 x 18)] = 4520cm²
The second step is to convert 1 square meter to cm
1m² = 100 cm²
100 x 100 = 10,000
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Select the correct location on the proof.
Given: TriangleXYZ with altitude h
Prove: x^2 = z^2 + y^2 - 2yz cos(X)
The first error in the proof is the fourth reason
What are mathematical proofs?Mathematical proofs are statements or collections of statements that are used to prove or disprove a statement, proof or theory
How to determine the first error in the proof?To determine the first error in the proof, we simply read through the statements and the given reason
From the table in the question, we have the following conclusions
Statement 1 is correct because the given parameter is the triangle XYZ with altitude hStatement 2 is correct because it represents the definition of cosine and sineWhen the equations in statement 2 are cross multiplied, they give the equations in statement 3 (by the multiplication operation). This means that statement 2 is correctThe reason at statement 4 is incorrect. This is so because x^ = h^2 + (y - r)^2 as used in statement 4 represents the Pythagoras theorem and not the substitution property of equalityHence, the first error in the proof is the fourth reason
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D= [xlx is a whole number}
E = {xlx is a perfect square between 1 and 9)
F = (xlx is an even number greater than or equal to 2 and less than 9]
Which of the following is D n F?
O (4, 6).
O (2, 4, 6)
O (2,4,6,8)
O (2)
Answer: C: [tex]D\cap F = \{2, 4, 6, 8\}[/tex]
Step-by-step explanation:
Let's first find the specific numbers that are in sets D and F.
[tex]D=\{0,1,2,\ldots\}[/tex], as D has all whole numbers.
[tex]F=\{2,4,6,8\}[/tex], as all of these numbers are even, greater than or equal to two, and less than nine.
Since all the numbers in F are whole numbers, all of them would be in D. Hence, the intersection of both would just be {2, 4, 6, 8}.
[tex]D\cap F = \{2, 4, 6, 8\}[/tex]
Which of the following sets of ordered pairs represents a function
A.{-8,14) , (-7,-12) , (-6,-10) ,( -5,-8)}
B. {(-4,-14) , (-9,-12) , (-6,-10), (-9,-8)}
C {(8,-2) , (9,-1),(10,2),(8,-10)}
D. { (-8,-6) , (-5,-3) , (-2,0),(-2,3)}
Answer: A
Step-by-step explanation:
Each value of x maps onto only one value of y.
I am a 3 digit positive number. The sum of my digits is 18. My middle digit is the product of -2 and -4. My first digit is 3^2.
Hi! ⋇
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The first digit of this number is 3², which is 9.
The Number is : 9xx
________
The second digit is: -2·(-4)=8.
The Number is : 98x.
________
The sum of all the digits is 18. This gives us an equation that we can solve in terms of x!
[tex]\multimap\sf{9+8+x=18}[/tex] (x is the digit we are looking for)
Now it takes a little arithmetic to find x :)
[tex]\multimap\sf{17+x=18}[/tex]. Just subtract 17 from both sides to find x!
[tex]\multimap\sf{x=1}[/tex]. And Now, can you see the number!
It's 981, of course :)
Hope this made sense to you!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\large\it{\overbrace{Calligrxphy}}[/tex]
Which statements about the system are true? Select two options.
y = y equals StartFraction 1 over 3 EndFraction x minus 4.x – 4
3y – x = –7
Answer:
no solution
Step-by-step explanation:
y = (1/3)x - 4
3y - x = -7
put the first equation into the second
3(1/3)x - (3)4 - x = -7
x - 12 - x = -7
-12 = -7 can never be true so this is no solution
Can someone help me please
Answer: B. [tex]12log(x)-4log(y)[/tex]
Step-by-step explanation:
Properties of logs:
[tex]log_{a} (\frac{B}{C} )=log_{A}B-log_{A} C[/tex]
[tex]logA^B = BlogA[/tex]
So, [tex]log\frac{x^{12} }{y^4} =logx^{12} -logy^4 =12log(x)-4log(y)[/tex]
It would be 12 log x - 4 log y (B)
A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 54.50 and a standard deviation of 9. If 67.66% of his students received grades of C or above, what is the minimum score of those students receiving a grade of at least a C
Students who receive a grade of at least a C must have a minimum score of 50.38.
Calculation of the minimum scoreWe may assume that the cut-off will be below 67.66 % because that percentage is more than 50%.
To get the value of 67.66 - 50 = 17.66, we must search in a regular normal table.
Hence, A z value of 0.458 will cause that value to occur.
Next, increase the standard deviation of 9 by 0.458.
The result is 4.122.
This indicates that the threshold for a student earning a C or higher is the mean minus 4.122.
So, the final result is 54.50-4.122 = 50.38.
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How many roots does the polynomial….
Answer:
(a) 3
Step-by-step explanation:
The fundamental theorem of algebra tells you a polynomial has a number of roots equal to its degree.
RootsThe degree of a polynomial is the largest exponent of the variable. Here, the degree is 3. That means there are three roots.
In general, the roots of a polynomial with real coefficients will be real or pairs of complex roots. The attached graph shows the roots of this cubic function are all real (and irrational).
HELP ASAP PLEASE
Select the correct answer. Figure 1 has been transformed to produce figure 2. Which notation describes this transformation?
Figure 1 was translated using the rule (x', y') ⇒ (x -9, y + 2) to produce figure 2.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.
Translation is the movement of a point either up, down, left or right on the coordinate plane.
Figure 1 was translated 9 units left and 2 units up using the rule (x', y') ⇒ (x -9, y + 2) to produce figure 2.
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Given g of x equals cube root of the quantity x plus 6, on what interval is the function negative? (–∞, –6) (–∞, 6) (–6, ∞) (6, ∞)
The interval where the function is negative is (–∞, –6)
How to determine the negative interval?The function is given as:
[tex]f(x) = \sqrt[3]{x + 6}[/tex]
Set the radicand to less than 0
x + 6 < 0
Subtract 6 from both sides
x < -6
Rewrite as an interval notation.
(–∞, –6)
Hence, the interval where the function is negative is (–∞, –6)
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Find the slope of the line on the graph.write your answer as a fraction or a whole number, not a mixed number
Answer:
slope = [tex]-\frac{1}{2}[/tex] if it were in an
Step-by-step explanation:
the graph is a negative and will therefore have a negative slope. to find the slope, pick a point on the graph and find the [tex]\frac{rise}{run}[/tex].
for instance, start with the point (0,1). Then go down 1 and left 2 to get to the next point on the graph (2,0). 1 is the "rise" and 2 is the "run" hence -1/2 being the slope.
you could also use the slope formula: [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
point 1: (0,1) (x₁ ,y₁)
point 2: (2,0) (x₂ , y₂)
[tex]\frac{0-1}{2-0} =-\frac{1}{2}[/tex]
how many 'words' can be made from the name ESTABROK with no restrictions
The number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.
How to determine the number of waysGiven the word:
ESTABROK
Then n = 8
p = 6
The formula for permutation without restrictions
P = n! ( n - p + 1)!
P = 8! ( 8 - 6 + 1) !
P = 8! (8 - 7)!
P = 8! (1)!
P = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 × 1
P = 40, 320 ways
Thus, the number of ways in which the name 'ESTABROK' can be made with no restrictions is 40, 320 ways.
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What is the slope of the line through parentheses two, three parentheses and parentheses -3, four parentheses?
The Slope of the line :
[tex]m=-\frac{1}{5} \approx-0.2[/tex]
What is slope?Using small, whole integer coordinates, it is simple to manually determine a line's slope. The formula becomes more effective if the coordinates are given greater or decimal values.
Because all horizontal lines have the same y-coordinates, it is important to note that all of them have a gradient of zero. In the slope formula's numerator, this will produce a zero. A vertical line, on the other hand, will have an arbitrary slope because the x-coordinates are constant. When applying the formula, this will lead to a division by zero error.
slope = (y₂ - y₁) / (x₂ - x₁)
Using the two points P=(2,3) and Q=(-3,4) as your input, determine the slope.
P=(x1,y1) and Q=(x2,y2) are two points on a line, and the slope of that line is given by :
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
we have that:
[tex]x_{1}=2, y_{1}=3, x_{2}=-3, y_{2}=4[/tex]
Fill in the blanks in the slope calculation,
[tex]m=\frac{(4)-(3)}{(-3)-(2)}\\\\=\frac{1}{-5}\\\\=-\frac{1}{5}[/tex]
Reaction: the slope of the line is =[tex]m=-\frac{1}{5} \approx-0.2[/tex]
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Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Finding Function Values for Elements of the Domain”Below is an example of one.
——————————————————————
Example :
For the problem below find the range for the given.
Given: b(x) = -2x + 12, find the range of b for the domain {-3, 5, 9}.
——————————————————————
2. Answer each question and write a brief step by step process on how you got the answer to each of your questions.
This question is asking to create 5 of your own questions, so here are mine with the process on how I got each:
Question 1: Given c(x) = 8x + 32, find the range of c for the domain {1, 3, 5}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by 8, and adding by 32.
c(1) = 8(1) + 32 = 8 + 32 = 40
c(3) = 8(3) + 32 = 24 + 32 = 56
c(5) = 8(5) + 32 = 40 + 32 = 72
Range: {40, 56, 72}
Question 2: Given d(x) = x - 7, find the range of d for the domain {-2, 3}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, and subtracting 7.
d(-2) = -2 - 7 = -9
d(3) = 3 - 7 = -4
Range: {-9. -4}
Question 3: Given f(x) = 7x + 738, find the range of f for the domain {1.5, 11}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by 7, and adding 738.
f(1.5) = 7(1.5) + 738 = 10.5 + 738 = 748.5
f(11) = 7(11) + 738 = 77 + 738 = 815
Range: {748.5, 815}
Question 4: Given g(x) = -2804x + 7268, find the range of g for the domain {50, 75, 256}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by -2804, and adding 7268.
g(50) = -2804(50) + 7268 = -140200 + 7268 = -132932
g(75) = -2804(75) + 7268 = -210300 + 7268 = -203032
g(256) = -2804(256) + 7268 = -717824 + 7268 = -710556
Range: {-132932, -203032, -710556}
Question 5: Given h(x) = -3x - 4, find the range of h for the domain {1, 2, 3}.
Answer w/ Process:
For each equation, I am plugging in each domain value for x in the function, multiplying by -3, and subtracting by 4.
h(1) = -3(1) - 4 = -3 - 4 = -7
h(2) = -3(2) - 4 = -6 - 4 = -10
h(3) - -3(3) - 4 = -9 - 4 = -13
Range: {-13, -10, -7}
b(-3)
-2(-3)+126+1218b(5)
-2(5)+12-10+122b(9)
-2(9)+12-18+12-6Range
{-6,2,18}Rest questions
#1
k(x)=2x²-5
Find the range of k for domain {1,2,6}
#2
h(x)=9x³
Find the range of h for domain {9,0,8}
#3
o(x)=6x-7
find the range of o for domain {0,1,9}
#4
p(x)=23x²-5x
Find the range of p for domain {3,4,8}
Find the inverse of the function.
y = 2x^2 -4
Answer:The inverse of the function y = 2x^2 –4 is;. y = √(x +4)/2To find the inverse of the function;We must first solve for x in the equation as follows;y = 2x² - 4y + 4 = 2x²x² = (y +4)/2x = √ (y +4)/2By swapping x and y; we then have;y = √(x +4)/2
Four pounds of apples cost $5 How much would 10 pounds o apples cost?
Answer:
Step-by-step explanation:
plus all of them 5times 10
Can someone please help us
180-180=100
2+3=5
100÷5= 20
x = 20
Answer:
[tex]5x+80=180[/tex]
I hope this helps and that you can give a brainliest!
Step-by-step explanation:
This is a straight line which is always 180°.
Here there are 3 angles adding up to the total 180°.
So the initial equation is [tex]3x+80+2x =180[/tex].
But there are coefficients that share the same variable.
So by simplifying the equation, you end up with:
[tex]5x+80=180[/tex]
Find the odds against hitting the ball if you have made 3 out of 19 attempts
We conclude that the odds of hitting the ball are 0.158
How to find the odds?
The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.
Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:
P = 3/19 = 0.158
We conclude that the odds of hitting the ball are 0.158
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what is x
x =x=x, equals
^\circ
∘
degrees
A tub contains red, green, blue and white counters. 5% of the counters are red, with an equal number of blue and white counters. The ratio of red to green counters is 3: 7. There is 20 more green than red counters. What is the probability of picking a red or blue counter?
The probability of picking a red counter is therefore; 8/25.
What is the probability of picking a red counter?Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;
x = (2/3)× 24 = 16 red.
The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.
The total number of counters is therefore; 40/0.8 = 50 counters.
The probability of picking a red counter is therefore; 16/50 = 8/25.
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Two poles of different heights are used for a climbing event and need to be secured to the ground using wires. The shorter pole is 6.0 m tall and the wire is secured 8.0 m from the base of the pole. If wire of the taller pole is 16.0 m long. Determine the height of the taller pole
Answer:
12.8 m.
Step-by-step explanation:
The length of the wire on the shorter pole (AC)
= √(6^2+8^2)
= √100
= 10 m.
The 2 triangles are similar so
10/16 = 8/x where x is height of taller pole.
10x = 128
x = 12.8m
PLLLLLEASE I NEED HELP SO BADLY PLEASE ASAP PLEASE PLEASE T_T
Answer:
[tex]x^2+7x-8-\frac{3}{x-7}[/tex]
Step-by-step explanation:
I think this question is a bit hard to explain by typing, so I'll add an image down below.
I used long division for this question, and the final answer is: [tex]x^2+7x-8-\frac{3}{x-7}[/tex]
El rio Lempa sirve de linea fronteriza entre Honduras y El Salvador, mide 300km
de largo. ¿Cuántos metros mide este rio?
Answer:
El río mide:
300000 metros.
Step-by-step explanation:
1 km = 1000 metros
300 km = 300 * 1000 = 300000 metros
...
Increase 320 mangoes by 5%
Answer:
336 mangoes
Step-by-step explanation:
If 320 mangoes = 100%
Increasing them by 5% means that we will need to work out 105%
32 mangoes = 10%
3.2 mangoes = 1%
336 mangoes = 105%
Our final answer is 336 mangoes
Hope this helped and have a good day
Part a: is the probability of hitting the black circle inside the target closer to 0 or 1? explain your answer and show your work. (5 points) part b: is the probability of hitting the white portion of the target closer to 0 or 1? explain your answer and show your work. (5 points)
The probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.
Given:
The square's length is 10 units.
The circle's diameter is equal to two units.
To Determine:
It is necessary to determine the probability that the target's white section and black circle will both be hit.
Solution:
The square's area is 10 x 10 or 100 units.
The shaded circle's area is given by πr² = 3.14 (1)² = 3.14 units.
The white area has a surface area of (100 - 3.14) = 96.86 units.
Probability of an event = The number of favorable events /Total number of events
The probability that it will occur in the shaded area = 3.14/100 = 0.0314 (The probability is close to 0).
The probability of hitting the white section is equal = 96.86/100= 0.9686.
(The probability is quite near to 1)
Hence, the probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.
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The graph shows the amount of money that Janice saves each week from her summer job. Which equation best represents the graph?
The equation which best represents the graph shows the amount of money that Janice saves each week from her summer job is option A which is y=200x.
Given a graph showing the amount of money that Janice saves each week from her summer job.
Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation and cubic equation.
Equation can be formed from any two points present on the graph with the help of following formula:
[tex](y-y_{1})=(y_{2} -y_{1} ) /(x_{2} -x_{1} )*(x-x_{1} )[/tex] where [tex](x_{1} ,y_{1} ),(x_{2} ,y_{2} )[/tex]are the points.
So,we have to find points first which are (6,1200),(7,1400)
Put the values in the formula:
(y-1200)=(1400-1200)/(7-1)*(x-1200)
y-1200=200/1(x-6)
y-1200=200(x-6)
y-1200=200x-1200
y=200x-1200+1200
y=200x
Hence the equation shows the amount of monet that Janice saves each week from her summer job is option A which is y=200x.
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What is the conditional probability that, when flipping a non-biased coin four times, there are at least two hs, given that the first flip is a h?
The conditional probability that, when flipping a non-biased coin four times, there are at least two heads, given that the first flip is a head, is 3/4.
Calculating the Conditional Probability:
Let us assume that getting a head in the first flip of coin is event B
Also, let us assume that getting a head in on of the remaining three flips is A
Then we have to find the probability of A given B, that is, P(A|B).
The formula for conditional probability is given as follows,
P(A|B) = P (A∩B) / P(B)
The probability of getting two heads, P(A∩B) = 3/8
The probability of getting head in the first flip, P(B) = 1/2
∴ P(A|B) = (3/8) / (1/2)
P(A|B) = 3/4
Thus, the conditional probability of getting at least two heads, given that the first flip is a head is 3/4.
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in 2019 there were 16 named storms, of which 8 grew into hurricanes and 5 were major. What fraction of hurricanes were major?