The current age of the older brother is 16 years while that of the girl is 13 years.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the girl age, y the younger brother age and z the older brother age. Hence:
x = y + 5
y = x - 5 (1)
Also:
z = x + 3 (2)
In two years time:
(y + 2)(z + 2) = 12(x + 2)
(x - 5 + 2)(x + 3 + 2) = 12(x + 2)
(x - 3)(x + 5) = 12(x + 2)
x² + 2x - 15 = 12x + 24
x² - 10x - 39 = 0
x = -3 and x = 13
Age must be positive, hence x = 13
z = x + 3 = 13 + 3 = 16 years
The current age of the older brother is 16 years while that of the girl is 13 years.
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Carl placed $3,700 in a savings account that compounds interest annually for a rate of 2%. How much will he have in the account for 10 years?
Carl will have $4514 in his account for 10 years
How to calculate the amount of money in carl account ?Carl place $3700 in a savings account, this means that the principal is $3700
The rate is 2%
= 2/100
= 0.02
The number of years is 10
Therefore the money that will be in the account for 10 years can be calculated as follows
3700(1 + 0.02¹⁰)
= 3700(1.02¹⁰)
= 3700(1.22)
= 4514
Hence after a period of 10 years Carl will have $4514 in his bank account
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Substitute the given values into the given formula and solve for the unknown variable. if necessary, round to one decimal place.
The solution for the unknown variable in I = PRT where I = 2160, P =24000 and R = 0.03 is 3
How to substitute the given values into the given formula and solve for the unknown variable?The given parameters are
I = PRT
Where
I = 2160, P =24000 and R = 0.03
Substitute I = 2160, P =24000 and R = 0.03 in the above equation I = PRT
2160 = 24000 * 0.03 * T
Evaluate the product
So, we have
2160 = 720 * T
Divide both sides by 720
T = 3
Hence, the solution for the unknown variable in I = PRT where I = 2160, P =24000 and R = 0.03 is 3
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how did researchers come up with 684 coins needed to collect all of the pennies from 1959 to 1997?
The researchers came up with this number by making a model with specific coins to determine the difficulty, in terms of the probability of getting this coin.
What was the researchers purpose?The researchers Shiyoung Lu and Steven Skiena wanted to know how probable it was to collect a complete set of pennies since 1959 until 1997. By the end of this study, they decided at least 684 coins must be collected to complete this mission.
Why did they come out with this answer?Firstly, they analyze the probability for getting one coin. From this, it was concluded the probabillity was lower for old coins. After this, they used the data collected from all the coins and created an equation. This equation or model led them to conclude the answer was 684 coins.
Note: This question is incomplete because the text it refers to is missing; here is the name of the text:
"The Probabilities of Pennies"
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PLEASE HELPME HERE please
The actual area of her office is 50 ft squared.
How to find the actual area of her office?The blueprint for Zahra's new office measures 4 cm long and 2 cm wide.
The scale for the blueprint is 6 cm to 15 ft.
let's convert the units using the scale
6 cm = 15 ft
4cm = ?
cross multiply
length = 4 × 15 / 6
length = 60 / 6 = 10 ft
6 cm = 15 ft
2 cm = ?
cross multiply
width = 2 × 15 / 6
width = 30 / 6 = 5 ft
Therefore,
area of the actual office = 10 × 5
area of the actual office = 50 ft²
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A certain number has exactly 8 factors, including 1 and itself. If two of these factors are 21 and 35, what is the number?
On January 1, 2021, Hoosier Company purchased $920,000 of 10% bonds at face value. The bond market value was $975,000 on December 31, 2021. Required: Prepare the appropriate journal entry on December 31, 2021, to properly value the bonds assuming the bonds are classified as: (If no entry is required for a transaction/event, select "No journal entry required" in the first account field.) Trading securities. Securities available-for-sale. Held-to-maturity securities.
The value of bonds assuming the bonds are classified as: (If no entry is required for a transaction/event, select "No journal entry required" in the first account field.) is Dr.$ [tex]$55,000[/tex] and Cr. $ [tex]55,000[/tex]
We are required to Prepare the appropriate journal entry on December 31, 2018, to properly value the bonds assuming the bonds are classified as
1. Trading securities.
2. Securities available for sale.
3. Held-to-maturity securities
For Dec 31,2021: For valuation of the bonds are classified as Trading securities (975,000-920,000) is Dr.$ [tex]$55,000[/tex] and Cr. $ [tex]55,000[/tex]
For Dec 31,2021: For valuation of the bonds are classified as Securities available for sale (975,000-920,000) is Dr.$ [tex]$55,000[/tex] and Cr. $ [tex]55,000[/tex]
For Dec 31,2021: No journal entry required as this is held to maturity.
Bonds: The term "bond market" refers to all debt securities trades and issuance, and it is also used interchangeably with the terms "debt market," "fixed-income market," and "credit market." Bonds are frequently issued by governments to raise money for debt repayment and infrastructure development.
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Solve. m/5=4 Responses 4/5 5/4 9 20
Answer: m=20
Step-by-step explanation:
Isolate m by multiplying 5 on both sides. m= 4*5 => m=20
the soil for house plants consists of 12 percent water.if someone wants to plants flower that need 28 percent water in the soil, how many litters of water they need to add to 5 kg of soil?
1.111 liters of water must be added to 5 kilograms of soil.
How much water we need to add in a soil sample
According to the statement, water percentage is equal to the ratio of water mass divided by the total mass of water and dust and multiplied by 100. Then, the initial and final percentages are defined below:
Initial percentage
y / 5 = 0.12 (1)
Final percentage
(y + x) / (5 + x) = 0.28 (2)
Then, we need to resolve the resulting system of linear equations:
y = 0.6 (1)
y + x = 1.4 + 0.28 · x
0.72 · x = 1.4 - y
x = 1.944 - 1.389 · y
x = 1.111
We need to add 1.111 kilograms of water. If the density of a kilogram per liter, the volume required in liters is:
V = (1.111 kg) / (1 kg / L)
V = 1.111 L
1.111 liters of water must be added to 5 kilograms of soil.
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Help answer ANY of these questions please!
BD bisects
R
А.
9x
(8x + 3)º
D
Step-by-step explanation:
9x°+(8x+3)=180°
17x°+3=180°
17x°=180°-3°
17x°=177°
x=177/17
x=10.41
When Akiko rides her bike to school, she travels 1 mi for every 6 min. Does this ratio mean that it takes Akiko 6 min to get to school? Explain
Answer: No
Step-by-step explanation:
Answer: no
Step-by-step explanation: because it says 1 mile for every 6 minutes not it takes Akiko 1 mile in 6 minutes to get to school
I will mark brainliest, answer choices are:
Quadrant I
Quadrant 2
Quadrant 3
Quadrant 4
A"(0,2)
A"(1,-2)
Answer:
ok..I think it Is C or B! not 100% sure tho..
help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
A square classroom is 5 to the power of 2 ft wide. The classroom has an area of
Answer:625 ft
Step-by-step explanation:
What is the order from least to greatest 9/7, 0.1, 1/4, 40% help
The order from the least to the greatest is 0.1, 1/4, 40%, 9/7.
What is the order?The numbers given are in improper fraction, decimals, proper fraction and percentage.
Improper fraction is a fraction in which the numerator is greater in value than the denominator. Proper fraction is a fraction in which the numerator is less in value than the denominator. A decimal is a number that consists of integers and non-integers separated by a decimal point. Percentage is the fraction of an amount expressed as a number out of 100.
For ease, all the numbers would be converted to percentages :
9/7 x 100 = 128.57%
0.1 = 10%
1/4 x 100 = 25%
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Solve for g.
3g + 3 = 9
g=
Answer:g=2
3g+3-3=9-3
3g=6
3g/3=6/3
g=2
Step-by-step explanation:
there you go
[tex] \bf \implies g \: = 2[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow3g + 3 = 9[/tex]
[tex]\bf \longrightarrow3g = 9 - 3[/tex]
[tex]\bf \longrightarrow3g = 6[/tex]
[tex]\bf \longrightarrow g = \bf\frac{ \cancel{6}}{\cancel{3}}2[/tex]
[tex]\bf \longrightarrow g = 2[/tex]
One year is approximately 526000 minutes. Calculate, correct to the nearest whole number, the average number of times his eyes will blink per minute
Answer:
10520000 approximately I think
the formula v = x can be used to find the volume of a cube where x repersents the lenth of each edge of the cube
what is the volume of a cube with edges of lenth x=4 feet enter the answer as a whole number or decimal the box below
Answer:
64
Step-by-step explanation:
Formula is V = x³
For x = 4 feet
V =4³ = 4 x 4 x 4 = 64 cubic feet
If f(x) = x^3, write a new function, g (x), that applies the following transformations
A reflection across the x-axis
A vertical stretch by a factor of 4
A reflection across the y-axis
A horizontal compression by a factor of 1/5
Your answer must begin with " g (x)= "
The function g(x) that represents the required transformations of f(x) = x³ are;
A reflection across the x–axis;
g(x) = -(x³)A vertical stretch by a factor of 4;
g(x) = 4•f(x)A reflection across the y–axis;
g(x) = (-x)³A horizontal compression by a factor of 1/5;
g(x) = (x/5)³How can the required transformation of f(x) be obtained?The function g(x) that represents the reflection of f(x) across the x–axis is presented as follows;
g(x) = -f(x)
Therefore, we have;
f(x) = x³
Which gives;
g(x) = -(x³)The function, g(x) that represents a vertical stretch of a function f(x) by a factor of c, is presented as follows;
g(x) = c•f(x)
Where c = 4, we have;
g(x) = 4•f(x)
Therefore;
g(x) = 4•x³The function g(x) that represents a reflection across the y–axis is presented as follows;
g(x) = f(-x)
Therefore;
g(x) = (-x)³The function, g(x), that represents the horizontal compression of f(x) by a factor of c is presented as follows;
g(x) = f((1/c)•x)
Which gives;
g(x) = ((1/5)•x)³ = (x/5)³
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Jennifer purchased a flower on Monday that was 4 2/3 inches tall. By Friday, the flower was 6 1/4 inches tall. How many inches did the flower grow between Monday and Friday?
A. 25/4
B. 11
C. 2
D. 19/12
The library has 28 science fiction books. Each shelf holds 5 books,
how many ways can you place books on the shelf?
With Combination, There are the 98280 ways by which we place books on the shelf.
According to the statement
We have to find that the number of ways can by which place books on the shelf.
So, For this purpose, we know that the
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
From the given information:
The library has 28 science fiction books. Each shelf holds 5 books
Then
apply the combination,
Then
C(n,r) = C(28,5)
after solving it become
C(28,5) = 28! /(5!(28-5)!)
And
C(28,5) = 28! /(5!(23)!)
Then after rearranging the terms and solving the value becomes
C(28,5) = 98280.
So, With Combination, There are the 98280 ways by which we place books on the shelf.
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Isn't -4(-2)=8.
It should be r = 8 + 58=66?
r = 66
Natasha has a job putting letters in envelopes to b mailed. In 1 hour she puts 42 letters in envelopes. which equation best represents y, the total number of letters Natasha puts in envelopes in x hours if she continues at this rate?
The equation which best represents the total number of letters Natasha puts in envelopes in x hours is y = 42x.
Given,
Number of letters Natasha puts in envelopes = 42 letters in 1 hour
Total number of letters Natasha puts in envelopes in x hours = y
We have to find the equation which best represents y:
Here,
Natasha puts 42 letters in 1hour
So, in x hour Natasha can put 42 × X letters.
That is,
y = 42 × x
y = 42x
Therefore, the equation which best represents the total number of letters Natasha puts in envelopes in x hours is y = 42x.
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The equation below shows the relation between the temperature in degrees Celsius, C, and degrees Fahrenheit, F: F = 9/5C + 32
Which of the following formulas correctly solves for C?
A. C = 5F - 32/9
B. C = 5F/9 - 32
C. C = 9/5 (F - 32)
D. C = 5/9 (F - 32)
The formula that correctly solves for C is D. C = 5/9 (F - 32)
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
The given formula is,
F = 9/5C + 32
where Celsius is C, and degrees Fahrenheit is F
To solve for C let us isolate C to the one side and other terms to the other,
9/5 C = F - 32
Multiplying both side by 5/9 we get,
9/5 C *5/9 = 5/9* (F - 32)
or, C = 5/9 (F - 32)
which is the formula for C.
Thus, the formula that correctly solves for C is D. C = 5/9 (F - 32)
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Find the interest earned on a $30,000 deposit for six months at 1% interest, compounded continuously.
The interest earned on even a $30,000 deposit compounded monthly at 1% is $15150.75.
What exactly is compound interest?Compound interest is applied when the principal amount changes after the specified time period.
For example, if you give someone $500 at a 10% yearly interest rate, $500 is your principal amount. After one year, the interest will be $50, and the principle amount will indeed be $550; therefore, the interest for the following year will be $550, not $500.
According to the given data:P = P₀e^rt where r represents the annual interest rate as well as t represents the time period in years.
So,
P₀ = 30000
r = 1% = 0.01
t = 6 months = 0.5 year
So,
P = 30000e^0.01(0.5)
P = 30000 × 1.5050250835
P = $45150.752505
So, interest
I =45150.752505- 30000 = $15150.75
The interest earned on even a $30,000 deposit over six months at 1% compounded daily is $15150.75
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The first three terms of the geometric series are: x+5,x+1, and x.
Calculate the:
a)Value of x
b) common ration
c) limiting sum
Answer:
Step-by-step explanation:
x= -2
Graph the solution of the inequality on a number line. 3(x – 2) – (1 – x) > 2x – 7
The solution to the given inequality is x > 0. The graph of the solution to the inequality is shown below
Graphing Inequalities on a Number lineFrom the question, we are to determine the solution of the given inequality
The given inequality is
3(x – 2) – (1 – x) > 2x – 7
Solving the inequality
3(x – 2) – (1 – x) > 2x – 7
First, clear the parentheses by applying the distributive property
3x - 6 - 1 + x > 2x - 7
4x -7 > 2x - 7
Then,
4x - 2x > -7 + 7
2x > 0
x > 0/2
x > 0
Hence, the solution to the given inequality is x > 0. The graph of the solution to the inequality is shown below
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What is the domain and range of f(x)=24
Answer: Domain:(−∞,∞),{x|x∈R} Range:{y|y=24}
Answer:
y=
24
x
Step-by-step explanation:
y
=
24
x
if im not mistaken
A laptop computer has a regular price of $500 and is on sale for $330. What percent of the regular price is the savings?
Answer:
i belive its 34% becouse you are saveing 170 dollars
Since January 2000, the population of the city of Brownville has
grown according to the mathematical model y = 720,500(1.022)x, where x is the
number of years since January 2000. If this trend continues, use this model to
predict the year during which the population of Brownville will reach 1,548,800)
The population of the Bownville city reach 1,548,800 at nearly 2015
Given, Since January 2000,
The population of the city of Brownville has grown according to the mathematical model.
Y= 720,500(1.022) x
Where, X= number of years
To find: If this continues, predict the year during which population of Brownville will reach 1,548,800
Starting population = 720,500
Growth rate = 1.022
(720500) (1.022) x = 1,548,800
1.022x = 2.1496
Taking log on both sides
log1.022x = log2.1496
x log 1.022 = log 2.1496
x=log 1.022×2.1496
x=15
Therefore, nearly it takes 15 years to reach the population 1,548,800
Hence the population of the Bownville city reach 1,548,800 at nearly 2015.
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