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A father is 30years older than his son. In 12years, the man will be three times as old as his son. Find their present ages.
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Let the present age of the son be x years
Then father's age will be (x+30) years
Given after 12 years father will be three times as old as his son
Therefore,
(x+12)3=x+30+12
3x+36=x+42
3x−x=42−36
2x=6
x=3
x+30=3+30=33
So, the present age of son is 3 years and present age of the father is 33 years
36. During rehearsal for the Founders' Day choir
program, the director, Mrs. Mazurek, tried 3 different
configurations, each using all the choir members at the
rehearsal. One configuration was to have only rows of
12, one was to have only rows of 15, and one was to
have only rows of 20. None of these configurations
worked because for each, the last row had 1 person
less than the other rows. What was the least of the
possible numbers of choir members at the rehearsal?
The LCM stands for the least common multiple. The least of the possible number of choir members at the rehearsal is 59.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
Given the configurations of choir members at the rehearsal, which are,
One configuration was to have only rows of 12, One was to have only rows of 15, And one was to have only rows of 20.Now, it takes the LCM of 12, 15, and 20, then the LCM will be 60, But since None of these configurations worked because for each, the last row had 1 person less than the other rows. The number of members was 1 less than the LCM.
Hence, the least of the possible number of choir members at the rehearsal is 59.
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3. There are 90 boxes to be shipped. The shipping clerk takes a sample of 9 boxes to estimate the total weight. The dot plot below shows the weights of the sample. 8. ++ 22 24 26 28 Box Weights (02) What is the median weight in the sample?
Let f(x)=√9x and g(x) = x + 7.
What’s the smallest number that is in the domain of fog
f(g(x))
√9(x+7)√9x+63The smallest no for the domain is -63 as square root of a negative no not possible.
For -63
√-63+630Answer:
x = -7
Step-by-step explanation:
[tex]\begin{aligned}f \circ g=f[g(x)] & = \sqrt{9(x+7)}\\& = \sqrt{9}\sqrt{x+7}\\ & = 3\sqrt{x+7}\end{aligned}[/tex]
Domain = input values (x-values)
As we cannot square root a negative number, the domain is:
x ≥ -7 → [-7, ∞)
Therefore, the smallest number that is in the domain of [tex]f \circ g[/tex] is -7
given f (x) = -4x + 4, solve for x when f (x) = 0
Answer:
x = 1
Step-by-step explanation:
Given:
f(x) = -4x + 4f(x) = 0We are asked to solve for x when the function is equal to zero.
We should have: 0 = -4x + 4
Solve
1. Subtract 4 from both sides
0 - 4 = -4x + 4 - 4
-4 = -4x
2. Divide both sides by -4
-4 ÷ -4 = -4x ÷ 4
1 = x
What is the hardest math eqaution you can find that is impossible but is not super long and is typeable? (Giving 100 points)
Solve It... Brainlist Too Pls For I Can Get To Next Level
I Have Stumbled Across This, Lol
A navigator marks three locations on a satellite map as shown. If the distance from Serravalle to San Marino is 982 miles, and the distance from Chiesanuova to San Marino is 833 miles, then how far is Chiesanuova from Serravalle?
In a satellite map of San Marino, Serravalle, and Chiesanuova in which navigation of three locations in the obtuse angle of San Marino 113.23 degrees, three points are located inside the yellow mark border
A.
2,300 miles
B.
1,518 miles
C.
1,233 miles
D.
1,052 miles
E.
998 miles
Answer:
1518 miles
Step-by-step explanation:
What does the line in a scatter plot mean?
Answer:
the line represents the average slope in which the dots line up. in other words, it shows where most of the options/solutions are on the plot
Step-by-step explanation:
nice pfp
Calculate the area of a regular octagon with the side length of 9 feet
Answer:
A ≈ 391.1 feet
formula to find the area of an octagon is shown below
[tex]area = 2(1 + \sqrt{2} )a { }^{2} [/tex]
Algebra 2 pls help!!! why do you only reflect one “side” of a parabola when defining its inverse?
This is why because
Parabola is symmetric on both sides of vertexThe x coordinate of vertex is the axis of symmetry for parabola.So reflection of only one side helps us in shifting the domain and range to its inverseFind the factors of function f. Based on the factors, which statement is true about the graph of function f? A. The graph crosses the x-axis at the point . B. The graph crosses the x-axis at the point . C. The graph crosses the x-axis at the point . D. The graph crosses the x-axis at the point .
The option (D) the graph crosses the x-axis at the point (2, 0) is correct because the graph crosses x-axis at points (0, 0), (5, 0), (-2, 0), and (2, 0).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The correct question is in the picture please refer to the attached picture.
We have a function:
f(x) = x⁴ - 5x³ - 4x² + 20x
By using factorization method:
[tex]\rm f(x) =x\left(x^3-5x^2-4x+20\right)[/tex]
[tex]\rm f(x) =x\left(x-5\right)\left(x+2\right)\left(x-2\right)[/tex]
By using zero product rule:
x = 0
x = 5
x = -2
x = 2
The graph crosses the x-axis at points (0, 0), (5, 0), (-2, 0), and (2, 0)
Thus, the option (D) the graph crosses the x-axis at the point (2, 0) is correct because the graph crosses the x-axis at points (0, 0), (5, 0), (-2, 0), and (2, 0).
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Answer: Edmentum/plato.
Step-by-step explanation:
what is the measure of angle f
Answer:
What is the context, at least give a figure
so techinichly not a question from school but I'm having trouble mathing out a personal question so I'm reading a thing where a guy spends 10000 years in another dimmention and 30 years pass on earth and I'm wondering how many days pass in the other dimension in one earth day
Answer:
uh it depends on the book or movie your watching in interstellar on one f the planets 1 minute was like a year on earth I’m not sure if time is different on the moon from the earth
Step-by-step explanation:
Answer: lwugga bird gang
Step-by-step explanation:
One marble is randomly drawn and then replaced from a jar containing two white marbles and one
black marble. A second marble is drawn. What is the probability of drawing a white and then a
black?
Answer:
1/3.
Step-by-step explanation:
Prob(Drawing white marble) = 2/3
Prob(Drawing a black marble on second draw ) = 1/2
So:
Prob(Drawing a white then a red marble) = 2/3 * 1/2
= 2/6
= 1/3.
Mike is adding 145 and 237. his work is shown. how can mike find the sum?
Answer:the answer is 352
Step-by-step explanation: mike can find the sum by adding the two numbers 145+237=352 to make it simpler you can start by adding the hundreds then the tens and then the ones.
Which expression is equivalent
Answer:
Option D
Step-by-step explanation:
All the parameters in the brackets will be raised to the power of 4.This means
[tex]( {4}^{4} \times ( {h}^{7} ) ^{4} \times ({k}^{2} ) ^{4} [/tex]
[tex] = 256 \times {h}^{28} \times {k}^{8} [/tex]
[tex] = 256 {h}^{28} {k}^{8} [/tex]
Match the graph to the correct inequality
X≥-3
X<-3
X≤ 3
X> -3
Answer: x ≥ -3
Step-by-step explanation:
Since the circle is "shaded" and it points to the right of -3. It will be read as greater than or equal to negative three.
Write an equation and find how much longer it would take to fly against the wind than
with it between New York and Los Angeles if the wind speed increases to 150 miles per
hour and the airspeed of the jet is 525 miles per hour. Round to the nearest hundredth.
The time taken by the jet will be equal to 6.58 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Assume that the distance between New York and Los Angeles is 2468 miles.The speed of wind is 150 miles per hour.The speed of the jet is 525 miles per hour.The time taken by the jet will be calculated as:-
Average speed = 525 - 150 = 375 miles per hour.
The time is taken to cover the distance of 2468 miles will be:-
Time = 2468 / 375 = 6.58 hours.
Therefore time taken by the jet will be equal to 6.58 hours.
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the largest of these five squares has side length 27 units, and each additional square's side length is 2/3 as large as the one before. What is the perimeter and area of the entire shape?
The total area is 1289.41 units².
The total perimeter is 281.32 units.
What is the total area and perimeter?The first step is to determine the side lengths of the other squares:
Length of the second square = 2/3 x 27 = 18 Length of the third square = 2/3 x18 = 12 Length of the fourth square = 2/3 x 12 = 8Length of the fifth square = 2/3 x 8 = 5.33Area of a square = length²
Perimeter of a square = 4 x length
Area of the first square = 27² = 729 Area of the second square = 18² = 324Area of the first square = 12² = 144 Area of the first square = 8² = 64Area of the first square = 5.33² = 28.41Total area = sum of the areas of the 5 squares = 1289.41 units²
Perimeter of the first square = 4 x 27 = 108 unitsPerimeter of the second square = 4 x 18 = 72Perimeter of the third square = 4 x 12 = 48 Perimeter of the fourth square = 4 x 8 = 32 Perimeter of the fifth square = 4 x 5.33 = 21.32Total perimeter = 281.32 units
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Answer:
PERIMETER: 584/3, AREA: 11605/9
Step-by-step explanation:
PERIMETER: The side lengths form a geometric series with a = 27, and r = 2/3. Along the bottom we see all five lengths, and those same lengths are seen along the top. The sum of these lengths is 27+18+12+8+16/3=211/3.
We can also calculate this as the sum of the geometric series:
27 (1 - (2 / 3) ^ 5)/ 1 - (2 / 3) = 27(1 - 32 / 243)/ (1 / 3) = 81 x 211/243 = 211/3
We see these lengths twice, once along the bottom and once as horizontal segments on the top. We also add the left side of 27. The vertical segments on the right must also have a total length of 27, since they cover the same ground as the left side.
The total perimeter: 2 x 211/3 + 2 x 27 = 584/3
AREA: 27^2 + 18^2 + 12^2 + 8^2 + (16/3)^2 = 11605/9
In a computer game, you can win, draw or lose.
Kiran plays two games against Afua.
The probability that Kiran will win any game against Afua is 0.6.
The probability that Kiran will draw any game against Afua is 0.3.
Work out the probability that Kiran will win at least one game.
thanks
Answer:
0.3??? sorry I'm just as confused
22. Solve 7x - 9 = 28+ 4(x - 1).
X=-3
X=3
x = 11
X=-11
Answer:
[tex]x = 11[/tex]
Step-by-step explanation:
[tex]7x - 9 = 28 + 4(x - 1) \\ 7x - 9 = 28 + 4x - 4 \\ 7x - 4x = 28 - 4 + 9 \\ 3x = 33 \\ \\ x = \frac{33}{3} \\ \\ x = 11[/tex]
Answer:
c) x = 11
Step-by-step explanation:
Given equation: 7x - 9 = 28 + 4(x - 1)
Steps:
1. Distribute 4 through the parentheses:
7x - 9 = 28 + 4(x) + 4(-1)
7x - 9 = 28 + 4x - 4 [simplify]
7x - 9 = 24 + 4x
2. Subtract 4x from both sides:
7x - 4x - 9 = 24 + 4x - 4x
3x - 9 = 24
3. Add 9 to both sides:
3x - 9 + 9 = 24 + 9
3x = 33
4. Divide both sides by 3:
3x ÷ 3 = 33 ÷ 3
x = 11
5. Check your work:
7x - 9 = 28 + 4(x - 1) [substitute 11 for x]
7(11) - 9 = 28 + 4(11 - 1) [simplify]
77 - 9 = 28 + 4(10) [simplify]
68 = 28 + 40 [add]
68 = 68 ✔
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Hey! Could someone help me with this question as quick as possible? Hope everyone is having a great day/night.
Answer:
The y-intercept is 4.
Step-by-step explanation:
The point lies on the coordinate (0,4) meaning it is the y intercept. Hope this helps! :)
There are 12 teams, each representing a different country, in a women’s olympic basketball tournament. in how many ways is it possible for the gold, silver, and bronze medals to be awarded? use the formula for permutations to find your answer. 220 440 1,320 1,728
The number of ways it is possible for the gold, silver, and bronze medals to be awarded is 1320 ways
Permutation and CombinationPermutation are related to arrangement and combination has to do with selection.
If there are 12 teams, each representing a different country and the possible awards are gold, silver, and bronze medals, the number of ways they can be selected is given as:
12P3 = 12!/(12-3)!
12P3 = 12!/9!
12P3 = 12 * 11 * 10
12P3 = 1320 ways
Hence the number of ways it is possible for the gold, silver, and bronze medals to be awarded is 1320 ways
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Karla and Jeremy have cicular pool with a diameter of 14 feet. what is the circumference of the pool? Use 3.14 = 22/7
Answer:
43.96 feet
Step-by-step explanation:
The formula for the circumference of a pool is π*diameter or 2*π*radius.
Therefore, since the diameter is 14, 14*3.14= 43.96
Nat has 2 episodes filmed for her new series. She plans
on filming 6 more episodes per month. Write a linear
equation that could represent this
if the bowl contains 5 red marbles 7 blue marbles and 8 white marbles what is the probability you will draw a red marble when you pick one out?
5/20
15/20
7/20
2/5
Answer:
[tex]\displaystyle \frac{5}{20}[/tex]
Step-by-step explanation:
We will put the number of wanted outcomes over the number of possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possibly outcomes}} =\frac{\text{red marbles}}{\text{number of all marbles in the bowl}}=\frac{5}{5+7+8} =\frac{5}{20}[/tex]
Subtract the additive inverse of −5/8 from the multiplicative identity.
Answer:
-1.25 or -10/8
Step-by-step explanation:
the additive inverse of a number is the number that would make it zero when added
ex. the inverse of 5 is -5 because 5+(-5)=0
so the inverse of -5/8 is 5/8 because -5/8+5/8=0. The question said to subtract the additive inverse.
-5/8-(5/8)=
-5/8-5/8=
-10/8 or -1.25
Select the correct answer.
Which function is a linear function?
OA 1-3xy
OB. y+7=5x
OC. ³+4=y
OD. 9(x²-y)=3
OE y-x³=8
Answer:
linear equation is the equation having degree 1 like ax+by=c so option B is correct ..
y+7=5x will be treated as the linear function. Thus, option B is correct.
What is a linear function?Any formula with one or two variables and no exponents is said to be linear. On the coordinate plane, this property depicts a straight line. In order to maintain the same function's linear illness, extra variables in a function must be constant.
y+7=5x
This equation can be written in a proper form:
y=5x-7
As this equation does not have any power therefore this will be treated as a linear function.
Therefore, option B is correct.
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What is the volume of a cone with a height of 27 cm
and a radius of 13 cml? Round your answer to the
nearest tenth.
Answer:
i dont now..............................
Step-by-step explanation:
What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The
diagram is not drawn to scale.
O11 ft
011√2 ft
011-√√3 ft
0 22 ft
Answer:
The answer is 22 if it it has 30 degree and 60 degree for other angles
The answer is [tex]11\sqrt{2}[/tex] if it is a 45-45-90 case
Step-by-step explanation:
anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board. two students will be selected, and they will alternate attending the school board meetings. all five students are equally well qualified, so the school superintendent decides to draw names at random. what is the probability he will choose debbie and esther as the two representatives? enter your answer as a fraction in simplest terms.
Probability that he will choose debbie and esther as the two representatives is 1/20 .
What is the meaning of Probability ?Probability is the stream in mathematics in which likeliness of an event to happen is studied.
The range of probability lies between 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.
It is given that anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board.
two students will be selected, and they will alternate attending the school board meetings.
all five students are equally well qualified, so the school superintendent decides to draw names at random.
probability he will choose debbie and esther as the two representatives = ?
Probability of chosing debbie is 1/5
Probability of choosing Esther is also 1/5
Either of them if chosen first the probability is 1/5
and the either of them chosen second the probability is 1/4
Probability that he will choose debbie and esther as the two representatives = (1/5)*(1/4) = 1/20 .
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