Using a system of equations, it is found that Wilma is 50 years old and Yvonne is 10 years old.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Wilma's age.Variable y: Yvonne's age.Wilma is 5 times as old as yvonne, hence:
x = 5y.
In ten years, yvonne's age will be a third of wilma's age, hence:
[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]
Since x = 5y:
[tex]y + 10 = \frac{1}{3}(x + 10)[/tex]
[tex]y + 10 = \frac{1}{3}(5y + 10)[/tex]
3y + 30 = 5y + 10
2y = 20.
y = 10.
Then:
x = 5y = 5 x 10 = 50.
Wilma is 50 years old and Yvonne is 10 years old.
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A competition to catch the most rainbow trout on Lake Rainbow pitched the men against the ladies. 16 men and 12 women participated. Each participant had a total of 15 attempts before they retired from the competition. It was predicted that the men would have a 9% chance of catching a rainbow trout at each attempt. One participant's experience resulted in 3 successful catches. The probability that this participant was a woman is 40%. Find the probability that a participant successfully catches 3 rainbow trout, given that the participant was a woman.
The probability that a participant successfully catches 3 rainbow trout, given that the participant was a woman is 0.0042.
P(woman) = 12/28
= 3/7
P(men) = 16/28
= 4/7
P(3 trouts) = P(3 trout | women)*P(woman) + P(3 trout | men)*P(man)
= P(3 trout | women)*(3/7) + (15C3 * (0.09^3)*(1-0.09)^(15*3))*(4/7)
= P(3 trout | women)*(3/7) + (0.00476)*(4/7)
P(woman | 3 trout) = P(3 trout | women)*P(woman) / P(3 trouts)
{P(3 trout | women) = p}
p*(3/7) / (p*(3/7) + (0.00476)*(4/7)) = 0.40
p*(3/7)/0.40 = (p*(3/7) + (0.00476)*(4/7))
p*((3/7)/0.40 - (3/7)) = (0.00476)*(4/7)
p = [(0.00476)*(4/7)] / [((3/7)/0.40 - (3/7))]
= 0.0042
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3. What mathematical symbol is appropriate to use given the
word?
4. What word is appropriate to use given the symbol?
Answer:
X
Step-by-step explanation:
Can I add [tex]2\sqrt{3} + 5\sqrt{3}[/tex] further?
Yes, they can be added and simplified further. 2√3 + 5√3 = 7√3 .
Take √3 as common factor:
2√3 + 5√3
(2 + 5)√3
7√3
The two irrational numbers sums to form another irrational number 7√3 . In decimals that is 12.12435...
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Yes, The terms assigned above are alike so they can be added easily by simple algebric method where root number can be treated as a variable.
[tex]\qquad \sf \dashrightarrow \: 2 \sqrt{3} + 5 \sqrt{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: (2 + 5) \sqrt{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 7 \sqrt{3} [/tex]
Error Analysis Your classmate says that there is not enough information to determine whether the two triangles below are congruent. Is your classmate correct? Explain.
Answer:
Your classmate says that there is not enough information to determine whether the two triangles below are congruent. Is your classmate correct?
yes it is
The two triangles are congruent triangles by RHS theorem of congruent triangles
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔMLJ
Let the second triangle be represented as ΔLJK
Now , the measure of ∠MLJ = 90°
The measure of ∠LJK = 90°
The measure of side MJ = measure of side LK
So , the two sides of the triangles are similar and they have a common hypotenuse
Therefore , the triangles are congruent by right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Hence , the triangles are congruent
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Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates of A′ of the rotated quadrilateral A′B′C′D′?
Elias Rubio deposits three checks for $598.20, $2,274.26, and $3,248.79.
His cash consists of 75 one dollar bills, 78 five dollar bill., 83 ten-dollar
bills, 80 quarters, 32 dimes, 95 nickels, and. 5 pennies. He would like to
receive $40.00 in cash.
Based on the amount of cash that Elias Rubio brings, we can calculate that his total cash deposit is $1,323
How much did Elias deposit in cash?This can be found as:
= (75 x 1) + (78 x 5) + (83 x 10) + (80 x 0.25) + (32 x 0.10 or 10 cents) + (95 x 0.05 or 5 cents) + (5 x 0.01 or 1 cent)
Solving gives:
= 75 + 390 + 830 + 20 + 3.20 + 4.75 + 0.05
= $1,323
Remaining part of the question:
How much did he deposit in cash?
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Mike has 63 toys. 18 of them are new and 12 are his favorites, while 4 are new and favorites. Mike is giving away all the toys that are neither new nor favorites. How many toys does mike have? ASAp
Answer:34
Step-by-step explanation:
Giving away all that is not new or fav so 12 fav + 18 new + 4 which are new an favorite = 34
Answer:
22
Step-by-step explanation:
63 is the total
14 are new
8 are fav
14+8=22
Given a function f : a → b and a subset y ⊆ b, is f (f −1 (y)) = y always true? prove or give a counterexample
If the subset y is the empty set, then the statement is false. That is the counterexample.
Is the statement true?
We know that for an invertible function, we always have that:
[tex]f(x) = y\\f^{-1}(y) = x[/tex]
Now, the range of f(x) is the set b. This means that the domain of the inverse is the set b. Such that:
f^{-1} is defined on b→a
Now we want to work on a subset y ⊆ b.
And here comes the problem.
The empty set {∅} is a subset of ay other set. So, if y is the empty set, there are no elements where we can evaluate the inverse function. From that counterexample, we conclude that the statement is false.
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5(2x - 12) + 21 = 2x + 41
05
08
O 10
072
Answer:
x = 10
Step-by-step explanation:
5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side
10x - 60 + 21 = 2x + 41
10x - 39 = 2x + 41 ( subtract 2x from both sides )
8x - 39 = 41 ( add 39 to both sides )
8x = 80 ( divide both sides by 8 )
x = 10
Which of the following is equivalent to √?
O
2
√2
O 2√2
2+√√√2
Answer:
2 sqrt(2)
Step-by-step explanation:
To simplify a square root
sqrt(8)
sqrt(4*2)
sqrt(4) sqrt(2)
2 sqrt(2)
Answer:
2√2
Step-by-step explanation:
√8 =[tex]\sqrt{4 \times 2}[/tex]
= 2√2 (√4 = 2)
Hence, 2√2 is the required answer.
3. Choose the equation that correctly shows the Commutative Property of Multiplication. 5 × 1 3 = 1 3 ÷ 5 5 × 1 3 = 5 × 1 3 5 + 1 3 = 1 3 × 5
According to the commutative property of multiplication, changing the order of components has no effect on the product. The correct option is B.
What is the commutative property of multiplication?According to the commutative property of multiplication, changing the order of components has no effect on the product.
For example: 4 × 8 = 8 × 4 = 32
The equation that correctly shows the Commutative Property of Multiplication is,
5 × 1 3 = 5 × 1 3
Hence, the correct option is B.
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City worker drain a community pool that contains 403,920 gallons of water. The pump they use removes water at a rate of 40 cubic feet per minute. One cubic foot of water contains 7.48 gallons how long in hours will it take to remove all the water from the pool
Answer:
22.5 hours
Step-by-step explanation:
One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have
299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours
Which statement about proportional relationships is false?
A proportional relationship must graph as a line.
A graph of a proportional relationship must pass through (0, 0).
Each point (or pair) in a proportional relationship must share the same ratio.
O Each point (or pair) in a proportional relationship must share the same difference.
Mark this and return
Save and Exit
Next
Submit
Answer:
Each point (or pair) in a proportional relationship must share the same difference is the false statement.
Bilquis wants to ride her bicycle 47.6 miles this week. She has already ridden 8 miles. If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal?
If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal is 4.7
We have given that,
Bilquis wants to ride her bicycle 47.6 miles this week. She has already ridden 8 miles.
We have to determine that If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal.
Based on the given conditions, formulate: 8+4x=26
Rearrange unknown terms to the left side of the equation:4x=26-8
Calculate the sum or difference:4x=18
Divide both sides of the equation by the coefficient of the variable:4x/4=18/4
Calculate the product or quotient:x=18/4
We get the result:4.7
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Answer: The answer is 6.6
Step-by-step explanation:
2. Compare and contrast a function and its inverse. Represent your
answer in a table of values and in a mapping diagram.
The table of values for the comparison of a function and its inverse function is shown in the image attached below.
What is an inverse function?An inverse function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).
In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property to the table (see attachment), we have:
f(-6) = -10f⁻¹(-10) = -6f⁻¹(f(3)) = -9.Read more on inverse function here: https://brainly.com/question/15635761
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Solve the following inequalities and represent the solution on the number line.
d) 5x ≥ 15
e) 3(2x + 1) ≤ 15
d) 5x ≥ 15
Let's solve your inequality step-by-step.
5x≥15
Step 1: Divide both sides by 5.
[tex]\frac{5x}{5} \geq \frac{15}{5}[/tex]
[tex]x\geq 3[/tex]
(Attachment #1)
e) 3(2x + 1) ≤ 15
Let's solve your inequality step-by-step.
3(2x+1)≤15
Step 1: Simplify both sides of the inequality.
6x+3≤15
Step 2: Subtract 3 from both sides.
6x+3−3≤15−3
6x≤12
Step 3: Divide both sides by 6.
[tex]\frac{6x}{6} \leq \frac{12}{6}[/tex]
[tex]x\leq 2[/tex]
(Attachment #2)
25:50=4x:8. What is the value of X
Answer: X = 1
Step-by-step explanation:
25/50 = 4x/8
First, multiply both sides by 8, therefore, the 8 on the right side will be canceled out.
25*8/50 = 4x*8/8
25*8/50 = 4x
25*8 = 200
200 divided by 50 = 4
4 = 4x
After that, you just need to divide 4 on both sides, therefore, the 4 on the right side will cancel out.
4/4 = 4x/4
1 = x
X = 1
Hope I helped! :]
Dexter makes 40 cookies.
He eats 16 of the cookies and take the rest to school.
What percentage of the cookies does he take to school?
Given: cot = -0.59 in QII, find sin
The value of sin x in Q II is 0.86 .
What are Trigonometry ?This the field in Maths which deals with a right angled triangle and the other angles in the triangle.
It is given that cot = -0.59
cot x = cos x / sin x
Using online trigonometric calculator
sin x in Q II is 0.86 .
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Select the correct answer.
As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers. If the work is divided evenly, how many walls must each volunteer paint?
A.
24
B.
29
C.
34
D.
39
The 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers.
Total number of volunteers = 36
Number of walls = 864
The number of walls each volunteer paint can be expressed as a fraction:
= 864/36
= 24
Thus, the 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.
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Please help! To solve the equation 1.75n = 7 for n, what operation must be applied to both sides in order to isolate the variable n?
Answer:
C
Step-by-step explanation:
1.75n = 7 ( to isolate n divide both sides by 1.75 )
n = [tex]\frac{7}{1.75}[/tex] = 4
Answer:
c.) Divide by 1.75
Step-by-step explanation:
Given equation:
⇒ 1.75n = 7
Here the coefficient of n which is 1.75 needs to be removed. There is only one way of doing that - by dividing both sides by 1.75.
When done so:
⇒ 1.75n/1.75 = 7/1.75
⇒ n = 4
Solve the quadratic function by factoring.
y = 4x² 13x + 10
Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that
[tex](4)(10) = 40[/tex]
Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40
Now split 13x into 5x+8x and solve by grouping
[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]
Factor out the GCF in each quantity
[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]
Now group x+2 together
[tex](x+2)(4x+5)[/tex]
Finally, set each factor equal to 0 and solve for x
[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]
If the bearing of p from y is 048degrees what is the bearing of y from p
Step-by-step explanation:
see photo for detailed analysis
Using a standard deck of cards, find the probability of selecting a jack, replacing the card, and then selecting a king.
please explain
The probability of selecting a jack, replacing the card, and then selecting a king is 1/169
How to determine the probability?In a standard deck of cards, we have:
Total = 52
Jack = 4
King = 4
The probability of each is:
P(Jack) = 4/52
P(King) = 4/52
So, we have:
P = 4/52 * 4/52
Simplify
P = 1/13 * 1/13
Evaluate
P = 1/169
Hence, the probability is 1/169
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What is the greatest area of a rectangle with a perimeter of 60cm? What is the length and width of this rectangle?
The length and width of this rectangle are 15 cm respectively
How to determine the greatest area?The perimeter is given as:
Perimeter, P = 60
The greatest area is calculated as:
Greatest = (P/4)^2
Substitute 60 for P
Greatest = (60/4)^2
Evaluate the quotient
Greatest = 15^2
Evaluate the exponent
Greatest = 225 square centimeters
Hence, the greatest area is 225 square centimeters
How to determine the length and widthWe understand that the area is the greatest.
In such a scenario;
Length = Width
This means that:
Area =Length^2 =Width^2
So, we have:
Length^2 =Width^2 = 225
Take the square root
Length =Width = 15
Hence, the length and width of this rectangle are 15 cm respectively
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Dry concrete can be made by mixing sand, gravel and cement
in the ratio 1: 2: 3. If you want 1800 kg of dry concrete,
how much of each will you need? Give your answers in
kilograms (kg).
A ratio shows how many times one number contains another.
Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is
[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]
The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]
And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]
What is the ratio ?
A ratio is an ordered pair of numbers [tex]a[/tex] and [tex]b[/tex], written [tex]\frac{a}{b}[/tex] where [tex]b[/tex] does not equal [tex]0[/tex]. A proportion is an equation in which two ratios are set equal to each other.
Here the given ratio is [tex]1:2:3[/tex].
Here given that,
The dry concrete is [tex]1800kg[/tex].
And the multiplication of the ratio is [tex]1[/tex]×[tex]2[/tex]×[tex]3=6[/tex]
Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is
[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]
The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]
And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]
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In a factory, the chance that a certain machine works without overheating in the morning is 50%. if it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. what is the probability that on a given day it will work in the morning and overheat later on? a. 4% b. 3.75% c. 7.5% d. 3.5%
Answer: C. 7.5%
Solve as decimal
0.5*0.15=0.075
Move two decimal points over
0.075 -> 7.5
Change back to percent
7.5%
1
2 3
4
5
6
7
8
9 10
Which set of angle measures could be the measures of the interior angles of a triangle?
O 90°, 42°, and 58°
O 60°, 60°, and 60°
O 100°, 48°, and 42°
O 31°, 75°, and 70°
TIME REMAI
42:34
Answer:
1) -
2) +
3) -
4) +
Step-by-step explanation:
сумма внутренних углов треугольника не должна превышать 180 градусов
Karl’s math class is playing a number game. Each student is given a number card containing the numbers 1 to 6. The rules of the game are that each student must put a cross through two numbers on the card and hand it in to the teacher. The teacher has a bag containing six balls numbered 1 to 6. When all the number cards have been handed in the teacher draws out two balls from the bag. Every student who had chosen the same two numbers shown on the balls wins a prize. If there are 30 students in Karl’s class, how many students are likely to win a prize? Describe your reasoning
By finding the probability, we can expect that 2 out of the 30 students will win the prize.
How many of the 30 students will win the prize?
First, we should get the probability of winning this game.
Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.
Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:
p = 1/6
The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:
q = 1/5
The joint probability is then:
P = 2*(1/6)*(1/5) = 1/15.
Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.
Then the expected number of students that will win is equal to the probability times the total number of students:
(1/15)*30 = 2
So out of the 30 students, we can expect that 2 will win.
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Find all real numbers $a$ that satisfy \[\frac{1}{a^3 + 7} -7 = \frac{-a^3}{a^3 + 7}.\]
The real number of the given expression is a=-2.
Given that the expression is [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex]
Real numbers is known as the union of both rational and irrational numbers. Real numbers can be both positive or negative and are denoted by the symbol “R”.
To compute the value of a.
In the given expression multiply both sides with (a³+7) as
[tex]\frac{(a^3+7)}{a^3+7}-7=\frac{-a^3(a^3+7)}{a^3+7}[/tex]
Simplify the expression as,
1-7(a³+7)=-a³
Expand out terms of the left hand side
1-7a³-49=-a³
-7a³-48=-a³
Taking out minus common from both sides and cancel them
-(7a³+48)=-(a³)
7a³+48=a³
Add -a³-48 on both sides
7a³+48-a³-48=a³-a³-48
6a³=-48
Divide both sides with 6
(6÷6)a³=(-48÷6)
a³=-8
write -8 in the expansion form which is (-2)×(-2)×(-2)=-8
a³=(-2)³
From above it says that
a=-2
Hence, real number that satisfy [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex] is a=-2.
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