Let the age of Maisie be x
From the first statement, Ellie is six years older than Maisie implying:
[tex]\text{Ellie's age = x + 6}[/tex]From the second statement, Zoe is twice as old as Eli implying:
[tex]\text{Zoe's age = 2(x+6)}[/tex]From the last statement, the sum of their ages is 50 implying:
[tex]x\text{ + x + 6 + }2(x\text{ + 6) = 50}[/tex]Solving for x:
We open the bracket and collect like terms
[tex]\begin{gathered} x+x\text{ + }6\text{ + 2x + 12 = 50} \\ x\text{ + x + 2x + 6 + 12 = 50} \\ 4x\text{ + 18 = 50} \\ 4x\text{ = 50 - 18} \\ 4x\text{ = 32 } \\ \text{Divide both sides by 4} \\ \frac{4x}{4}\text{ = }\frac{32}{4} \\ x\text{ = 8} \end{gathered}[/tex]Hence, Zoe's age is:
[tex]\begin{gathered} =2(x\text{ + 6)} \\ =\text{ 2(8+6)} \\ =\text{ 2 }\times\text{ 14} \\ =\text{ 28} \end{gathered}[/tex]Answer:
Zoe's age = 28
What situation cannot be represented by the equation x + 10 = 45?
A. Nicholas rode his bike 45 miles last week. He rode 10 miles on Tuesday and the rest of the miles on Wednesday. What is x, the number of miles Nicholas rode his bike on Wednesday?
B. Two players scored a total of 45 points in a game. One player scored 10 points. What is x, the number of points scored by the other player?
C. Marissa spent $45 on a hat and a shirt. The hat cost $10. What is x, the cost of the shirt in dollars?
D. There are 45 students in a group. There are also 10 adults in the group. What is x, the total number of students and adults in the group?
in triangle ABC , angle A = 30 degrees and angle C = 35 degrees. what is angle B degrees?
Answer:
115°
Step-by-step explanation:
The sum of the three angles in a triangle is always 180°
m∠A + m∠B + m∠C = 180°
m∠B = 180 - m∠A - m∠C
m∠B = 180 - 30 - 35 = 115
Jacob is preparing a monthly budget. His net pay is $1, 350 every two weeks, and his monthly rent is $936. What percentage
of his monthly budget should Jacob allocate for rent?
The percentage of monthly budget should Jacob allocate for rent is 27.7%.
What is termed as the percentage?A percentage is a ratio with the second term being 100. Percentage refers to parts per hundred. The term is derived from the Latin word per centum, that also means "per hundred." In mathematics, the symbol% stands for percent.For the given question;
Jacob's two week earning is $1,350.
Jacob's one week earning will be $1,350/2 = $675.
Considering there are 5 weeks in a months.
Jacob's one month earning will be $675×5 = $3,375.
The total monthly rent = $936.
Let 'x' be the percentage Jacob pay for the rent.
Then,
x% of 3,375 = 936
Simplifying the expression.
3,375x/100 = 936
x = 93,600/3,375
x = 27.7 %
Thus, the percentage of monthly budget should Jacob allocate for rent is 27.7%.
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Ollie borrowed $5000 for 3 years at a compound interest rate of 10%.
How much did Ollie pay back?
Answer: Assuming interest rate is yearly, Ollie would have to pay back 6, 655 dollars :)
Step-by-step explanation:
The formula for compound interest is
Y = P(1 + r/m)^mt, with P being the initial deposit (5000), r being the interest rate (0.10), m being the amount of times it is compounded per year (1), and t being the number of years (3).
What is the slope of a line perpendicular to the line whose equation is 2x+3y=24
simplify
please help asap love you if u do ;)
The slope of the line perpendicular to the line whose equation 2x+3y= 24 is 3/2
The equation of the line is
2x+3y = 24
The standard form of the linear equation is
Ax + By = C
Where A, B and C are the integers
By comparing the standard form of the linear equation with the given equation
A = 2
B = 3
C = 24
The slope of the equation in standard form m = - A/B
Substitute the values in the equation
The slope of the equation in standard form m = -2/3
Slope of a line perpendicular to the line = -1/m
= -1/(-2/3)
= 3/2
Hence, the slope of the line perpendicular to the line whose equation 2x+3y= 24 is 3/2
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simplify the expression . express using positive exponents.
The simplified expression of (5x⁶y²)³ is 125[tex]x^{18}y^{6}[/tex] which is expressed using the positive exponents.
What exactly is a positive exponent?A positive exponent indicates that the base should be multiplied by that many.
Give a good illustration of a positive exponent.For instance, 10 should be multiplied by 10x10x10, or 1000, if the number is 103. The variable x should be multiplied by itself nine times if the variable is x raised to 9.
What does "simplifying exponent" mean?It is possible to simplify exponents by putting exponent-containing algebraic formulas into a simpler form that prevents further simplification.
The given expression is (5x⁶y²)³
Simplifying it further we get,
(5x⁶y²)³ = 125[tex]x^{18}y^{6}[/tex]
Therefore, the simplified expression of (5x⁶y²)³ is 125[tex]x^{18}y^{6}[/tex] which is expressed using the positive exponents.
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Question is down below, match the answer choices with the units.
whichWe define:
• A = original area = 100 sq units,
,• A' = dilated area.
If we dilate a trapezoid in a scale factor k, the area scales as:
[tex]A\rightarrow A^{\prime}=k^2\cdot A\text{.}[/tex]Using the area A = 100 sq units, we have:
[tex]\begin{gathered} A^{\prime}=k^2\cdot100\text{ sq units,} \\ k^2=\frac{A^{\prime}}{100\text{ sq units}}, \\ k=\sqrt[]{\frac{A^{\prime}}{100\text{ sq units}}}\text{.} \end{gathered}[/tex]This formula gives as the scale factor k for witch we must dilate the trapezoid to have an area A'.
1) For A' = 6400 sq units, we have:
[tex]k=\sqrt[]{\frac{6400\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{64}=8.[/tex]2) For A' = 100 sq units, we have:
[tex]k=\sqrt[]{\frac{100\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{1}=1.[/tex]3) For A' = 25 sq units, we have:
[tex]k=\sqrt[]{\frac{25\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{\frac{1}{4}}=\frac{1}{2}.[/tex]4) For A' = 900 sq units, we have:
[tex]k=\sqrt[]{\frac{900\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{9}=3.[/tex]Answers
• 8
,• 1
,• 1/2
,• 3
11. Tom borrowed some money from his father seven months ago. Every month,
he pays back $400 to his father. Currently, he owes $2,500.
a) How much will he owe his father three months from now?
b) How much money did he borrow from his father?
In three months, he will owe his father $2500 less $1200, or $1300.
One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
Tom's payment for 7 months is 400 * 7 = $2800.
He borrowed $5300 ($2500 plus $2800).
His monthly payment for three months is 400*3.
In three months, he will owe his father $2500 less $1200, or $1300.
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Graphing proportional relationships
Answer:
hello fríend nose inglus
Which number is a MULTIPLE of both 12 and 24?
A: 6
B: 24
C: 12
D: 8
E: 2
Answer:B - 24
Step-by-step explanation:
12 x 2 = 24
24 x 1 = 24
–8(y-7)=2y+6Simplify your answer as much as possible
You have the following equation:
-8(y -7) = 2y + 6
In order to solve for y, proceed as follow:
-8(y -7) = 2y + 6 expand the factor right side
-8y + 56 = 2y + 6 subtract 2y and subtract 56 both sides
-8y - 2y = 6 - 56 simplify
-10y = -50 divide by -10 both sides
y = -50/(-10)
y = 5
Hence, the value of y is 5
1 point
Which graph represents the solution x > 3?
Graph 1 represents the solution x > 3.
In Graph 1, the line is highlighted from point 3 with a white dot which is used to assert that all the values from 3 to positive infinity but 3 would not be considered. The highlighted side is toward the positive side.
In Graph 2, the line is highlighted from point 3 with a white dot which is used to assert that all the values from 3 to negative infinity but 3 would not be considered. The highlighted side is toward the negative side.
In Graph 3, the line is highlighted from point 3 with a black dot which is used to assert that all the values from 3 to positive infinity and 3 would be considered as well. The highlighted side is toward the positive side.
In Graph 4, the line is highlighted from point 3 with a black dot which is used to assert that all the values from 3 to negative infinity and 3 would be considered as well. The highlighted side is toward the negative side.
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write each expression as a product
(2x+y)^2-(x-2y)^2
Answer:3x^ - 3y^ + 8xy (^ is ^2 !!)
Step-by-step explanation:
(2x+y)^ - (x-2y)^(2x+y)(2x+y) - (x-2y)(x-2y)4x^ + 2xy + 2xy + y^ - x^ + 2xy + 2xy - 4y^
in new york state, the mean salary for high school teachers in 2017 was $81,410 with a standard deviation of $9,500. only alaska’s mean salary was higher! assume new york’s state salaries follow a normal distribution.
The percentage of New Yorks state teachers that earn between $7000 and $75000 is 13.63%.
What will the percentage be?Let the salary of the teachers be represented as x.
Mean = $81410
Standard deviation = $9500
In this case, the probability for normal distribution will be used. This is illustrated as P(a < Z < b).
where a = lower number.
b = higher number
Therefore, the probability of earning the amount will be:
P(70000 < X < 75000)
= P[(70000 - 81410/9500) < Z < (75000 - 81410/9500)
= P(-1.20 < Z < -0.67)
Using the z table to look for the value
= 0.8849 - 0.7486
= 0.1363
= 13.63%.
Therefore, the probability is 13.63%.
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in new york state, the mean salary for high school teachers in 2017 was $81,410 with a standard deviation of $9,500. only alaska’s mean salary was higher! assume new york’s state salaries follow a normal distribution. What is the percentage of New Yorks state teachers that earn between $7000 and $75000?
Use the following image to complete the sentences describing the ratio of spots to eyes.
A ladybug with 2 eyes and 6 spots.
A ladybug with 2 eyes and 6 spots.
There are 6 spots for every
eyes.
There are
spots for every 1 eye.
Using ratios, the sentences are completes as follows:
There are 6 spots for every 2 eyes.There are 3 spots for every 1 eye.What is the ratio between two amounts?The ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
Between two amounts b and a, the ratio is given by the division of b by a, as follows:
r = b/a.
This means that the ratio between two amounts is not commutative, meaning that the order of the amounts matters.
A ladybug with 2 eyes and 6 spots, hence the first sentence is given as follows:
There are 6 spots for every 2 eyes. (ratio is the number of eyes for 6 spots).
The number of spots per eye is the ratio of the number of spots and the number of eyes, as follows:
Spots per eye = 6 spots/2 eyes = 3 spots per 1 eye.
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The average temperatures across Washington, Texas, Oklahoma, New York, Missouri, Hawaii and Michigan are48°F, 65°F, 60°F, 45°F, 54°F, 64°F, 70°F, and 45°F respectively.Find the median
SOLUTION
Let's list the values first. These are
48, 65, 60, 45, 54, 64, 70 and 45
Now, we have to arrange these values from the smallest to the largest. Doing this we have
45, 45, 48, 54, 60, 64, 65, 70.
The median will be between the middle items which are 54 and 60. So we will find the median by the following way
[tex]\begin{gathered} \text{Median = }\frac{54+60_{}}{2} \\ \text{Median }\frac{114}{2} \\ \text{Median = 57} \end{gathered}[/tex]Therefore, the Median is 57°F
Daisy has two measuring jugs, A and B, which can hold a combined volume of
900 ml.
Daisy fills jug A with water. She then fills jug B by pouring in water from jug A.
After this, there is 500 ml of water remaining in jug A.
Work out the volume of each measuring jug.
Help please
Daisy has two measuring jugs, A and B. The volume of each measuring jug will be A and B will be 500 ml and 400 ml.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Daisy has two measuring jugs, A and B, that together have a capacity of 900 ml, A jug of water is filled by Daisy. Afterward, she transfers water from jug A into jug B. Following this, jug A has 500 ml of water left.
Total volume = volume in jug A + volume in Jug B
If there are 500 ml of water remaining in jug A.
900 ml = 500 ml + volume in Jug B
volume in Jug B = 900 - 500
volume in Jug B = 400 ml
Thus, Daisy has two measuring jugs, A and B. The volume of each measuring jug will be A and B will be 500 ml and 400 ml.
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Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10.
Rectangle C has length 30 and width 15,
B? If so, what is the scale factor?
a, Is Rectangle A a scaled copy a of Rectangle
b. Is Rectangle B a scaled copy of Rectangle
A? If so, what is the scale factor?
C. Explain how you know that Rectangle C is not a scaled copy a of Rectangle B.
d. Is Rectangle
A.a scaled copy of Rectangle
C? If so, what is the scale factor?
Answer:
A. Yes, Rectangle A is a scaled copy of rectangle B.
B. Yes, Rectangle B is a scaled copy of rectangle A.
C. No, Rectangle A is not a scaled copy of rectangle C.
Step-by-step explanation:
Rectangle A has dimensions 12x8 and Rectangle B has length 15x10.
We see that sides of A and B are proportional because
[tex]\frac{12}{15} = \frac{8}{10}[/tex]
So we say that since sides are proportional A and B are similar or scaled copy of each other.
Since A is smaller and B is bigger, a is 0.8 scaled copy of B. Similarly B has an enlargement scale factor = 1.25 Rectangle C has 30x15, not proportion with sides of A and B. Hence we find that C is neither a scaled copy of A nor B
Hope this helps! :))
the mean monthly electric bill for 59 residents of the local apartment complex is $65. what is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex?
In linear equation, the best point estimate of mean monthly electric bill is $65 .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.The sample mean is an unbiased estimate of the population mean μ.
Thus, the best point estimate of mean monthly electric bill is $65 .
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Write and Solve Equations in Context
A group of friends wants to go to the amusement park. They have $246.75 to spend
on parking and admission. Parking is $14, and tickets cost $33-25 per person,
including tax. Write and solve an equation which can be used to determine 2, the
number of people who can go to the amusement park.
Equation:
?
Answer: 2 =
Answer:
8 people
Step-by-step explanation:
117.50 - 5.50 = 112
112 ÷ 14.8 = 7.56756756757, but you round it up to 8, so the answer is 8 people.
scientific notation. 3{,}868{,}000{,}000
Answer:
3.868 * 10^9
Step-by-step explanation:
3868000000
=3.868 * 10^9
:]
need help btw the last two i guessed the last to boxes so yea
Answer:
Everything is right. No need to change anything.
Find the value of r in the equation below.X-17 = 12
Answer : x = 39
We are given the equation
x - 17 = 12
First, isolate the value of x
When you isolate the value of x, the figure 17 cross the equality sign and change to positive
x = 12 + 17
x = 39
Solve the system.
x - 5y + 4z=27
4x-3y-z-23
3x + 3y - 6z=-9
Answer:
Step-by-step explanation:
Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-5y+4z=27,4x-3y-z=23,3x+3y-6z=-9 Tiger Algebra Solver.
Write 72.4% as a decimal
Answer:
0.724
Step-by-step explanation:
percent means ' out of 100 ' , then
72.4% = [tex]\frac{72.4}{100}[/tex] = 0.724
Two ways to write k/3+16
The two ways to write the expression k/3+16 are 1/3k + 16 and (k + 48)/3
How to rewrite the expression?From the question, the expression is given as
k/3+16
Start by factoring 1/3 out of the first term
So, we have the following expression
1/3k + 16
The above is one of the ways of rewriting the expression
Another way is by taking the LCM
So,we have
k/3+16 = (k + 48)/3
Hence, the equivalent expressions are 1/3k + 16 and (k + 48)/3
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8. Un vendedor de bebidas en un conocido pueblo mágico analiza sus ventas en días festivos
y encuentra que si vende x bebidas en un día su utilidad (en pesos) está dada por.
y=-0.015x² +45x-2700
¿Cuál es la utilidad máxima por día festivo?
Answer: the maximum profit per holiday is 31050 pesos
Step-by-step explanation:
y=-0,015x²+45x-2700 (1)
It`s a quadratic equation like y=ax+bx+c
Therefore, the value of x at which y is maximal is:
[tex]\displaystyle\\x=\frac{-b}{2a} \\\\x=\frac{-45}{2(-0.015)} \\\\x=\frac{-45}{-0.03} \\\\x=\frac{45(100)}{0.03(100)}\\\\x=\frac{4500}{3} \\\\x=\frac{3(1500)}{3} \\\\x=1500[/tex]
Substitute the value of x into equation (1):
[tex]y=-0,015(1500^2)+45(1500)-2700\\\\y=-0.015(15*10^2)^2+67500-2700\\\\y=-0.015(15^2)(10^4)+64800\\\\y=-0,015*225*10^4+64800\\\\y=-150*225+64800\\\\y=-33750+64800\\\\y=31050 \ pesos[/tex]
Starting at sea level, a turtle descends at a constant rate to a depth of -yard relative to sea level in minute.
The turtle continues descending at this same rate.
What is the turtle's depth relative to sea level after the first minute?
Enter your answer as a simplified mixed number in the box
The turtle's depth relative to sea level after the first minute is 1.2 yards.
Given,
The depth where the turtle descends, d = -3/4 yards
The speed of turtle relative to sea level, t = 5/8 minutes.
We have to find the turtle's depth relative to sea level after the first minute.
The rate at which the turtle descends, r = d/t
r = d/t
r = (-3/4) / (5/8)
r = -3/4 × 8/5
r = -6/5 yards/minute
r = -1.2 yards/min
Now, the depth of turtle after the one minute, D = rt
Where, r = -1.2 yards/min and t = 1 min
Then,
D = -1.2 × 1 = -1.2 yards
That is,
The turtle's depth relative to sea level after the first minute is 1.2 yards
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Which term describes the red curve in the figure below?
A. Hyperbola
B. Ellipse
C. Circle
D. Parabola
Simplify three raised to the fourth power raised to the negative one power
one over three raised to the fourth power
one over three raised to the power of negative four
negative three raised to the fourth power
three raised to the power of the third power
The result of the given expression is one over three raised to the fourth power.
what is logarithmic equation ?
Logarithm , the exponent or power to which a base must be raised to yield a given number.
Simplifying exponential equation
Exponential equations are inverse of logarithmic equation. Exponential equation is expressed as y = ab^x
Given the expression below;
(3⁴)⁻¹ = 3⁻⁴
According to the law of indices
a^-n = 1/a^n
Using this law above, this will be expressed as;
(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴
Hence the result of the given expression is one over three raised to the fourth power
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