The age of first boy is 15 and age of second boy is 3.
Now, According to the question:
The x and y-axis are two important lines of the coordinate plane. The x-axis is a horizontal number line and the y-axis is a vertical number line. These two axes intersect perpendicularly to form the coordinate plane. The x-axis is also called the abscissa and the y-axis is called the ordinate.
"Information available from the question"
The sum of ages of two boys are 18.
Let x be the first boy
and, y be the second boy.
x +y = 18
(x +3) = 3(y+3)
Calculate the product or quotient
x + 3 = 3y + 9
x = 3y + 9 - 3
x = 3y + 6
Now,
3y + 6 + y = 18
Calculate the sum or difference:
4y + 6 = 18
4y = 18 - 6
4y = 12
y = 12/4
y = 3
So, For the value of x:
x + 3 = 18
x = 18 - 3
x = 15
Hence, The age of first boy is 15 and age of second boy is 3.
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what is the location of the center of a circle with diameter endpoints at (7,23) and (11,21)
I think "E" it's the most close answer for me
Solve the proportion.
8/2 = 48/b
b = ___
(Help please )
Step-by-step explanation:
8/2 = 48/b
4=48/b
b=48/4
b=12
Answer:
Step-by-step explanation:
8/2 = 48/b
b = 48×2/8
b = 12
The length of the smallest side of a right triangle is 16. The lengths of the other two sides are consecutive odd integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides
The smaller side of the triangle from missing sides is 63cm.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
According to Pythagorean theorem,
H^2=P^2+B^2
Where H=hypotenuse, B=base, P=Perpendicular
Given base=16
let perpendicular=x then hypotenuse=x+2 as The lengths of the other two sides are consecutive odd integers
Therefore, (x+2)^2=x^2+16^2
x^2+4+4x=256+x^2
x=63 and x+2=65
Hence,
The smaller side of the triangle from missing sides is 63cm.
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if beth makes an initial investment of $1,000, how much will it be worth after three years if her average return is 8.25 percent (compounded monthly
After 3 years, Beth's investment will be worth $1,281.216.
What is percentage ?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used.
The formula to calculate the future value of an investment is:
FV = PV * (1 + r/n)^(nt)
where:
PV = present value = $1,000
r = annual interest rate = 8.25%
n = number of compounding periods per year = 12 (monthly)
t = number of years = 3
FV = $1,000 * (1 + 0.0825/12)^(12 * 3)
Plugging in the values and using a calculator, we get:
FV = $1,000 * (1 + 0.0825/12)^(12 * 3) = $1,000 * (1.006866)^36 = $1,000 * 1.281216 = $1,281.216
So after 3 years, Beth's investment will be worth $1,281.216.
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the graduate management admission test (gmat) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. the average gmat score is (magoosh website). assume that gmat scores are bell-shaped with a standard deviation of . use the empirical rule to answer the following. a. what percentage of gmat scores are or higher (to decimal)? b. what percentage of gmat scores are or higher (to decimal)? c. what percentage of gmat scores are between and (to decimal)? d. what percentage of gmat scores are between and (to decimal)?
a. The percentage of GMAT scores is 647 or higher approximately 15.9%
b. The percentage of GMAT scores that are 747 or higher (to 1 decimal) is approximately 2.3%.
c. The percentage of GMAT scores between 447 and 547 is approximately 84.1%.
d. The percentage of GMAT scores between 347 and 647 (to 1 decimal) is approximately 98.0%.
a. The GMAT score of 647 is 100 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 647-547/100 = 1.
Using a standard normal table, we can find that the percentage of GMAT scores that are 647 or higher is approximately 15.9%.
b. The GMAT score of 747 is 200 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 747-547/100 = 2.
Using a standard normal table, we can find that the percentage of GMAT scores that are 747 or higher is approximately 2.3%.
c. The GMAT scores between 447 and 547 are 100 points below and 100 points above the average score of 547, respectively.
Using the standard deviation of 100, we can calculate the standard score (z-score) as (447-547)/100 = -1 and (547-547)/100 = 0.
Using a standard normal table, we can find that the percentage of GMAT scores that are between -1 and 0 is approximately 84.1%.
d. The GMAT scores between 347 and 647 are 200 points below and 100 points above the average score of 547, respectively.
Using the standard deviation of 100, we can calculate the standard score (z-score) as (347-547)/100 = -2 and (647-547)/100 = 1.
Using a standard normal table, we can find that the percentage of GMAT scores that are between -2 and 1 is approximately 98.0%.
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The complete question is -
The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100.
a. What percentage of GMAT scores are 647 or higher?
b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?
c. What percentage of GMAT scores are between 447 and 547 ?
d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?
Pleaasee help algebra
The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Rita the mentor has two independent exercise designs that she offers her clients: Plan An and Plan B. Every client does it is possible that either (not both). On Friday there were 5 clients who arranged A and 3 who arranged B. On Saturday there were 2 clients who arranged A and 6 who arranged B. Rita prepared her Friday clients for a sum of 10 hours and her Saturday clients for a sum of 10 hours.
The length of each Plan A workout is given as,
Rate = (5 + 2) / 10
Rate = 7 / 10
Rate = 0.70 per hour
The length of each Plan B workout is given as,
Rate = (3 + 6) / 10
Rate = 9 / 10
Rate = 0.90 per hour
The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.
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x/15 + 3/15 = -1/5
the solution is x =
Answer:
x = -6
Step-by-step explanation:
x/15 + 3/15 = -1/5
x/15 + 1/5 = -1/5
x/15 = -2/5
x = -6
Let's check
-6/15 + 3/15 = -1/5
-3/15 = -1/5
-1/5 = -1/5
So, x = -6 is the correct answer.
61°24` in radians
Please and thank you
well, we know there are 60 minutes in 1 degree, so 24' is 24/60 = 0.4°, so 61°24' is really 61.4°, now, we also know that there are 180° in π radians, so
[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 61.4&x \end{array}\implies \cfrac{180}{61.4}~~ = ~~\cfrac{\pi }{x} \\\\\\ 180x=61.4\pi \implies x=\cfrac{61.4\pi }{180}\implies x=\cfrac{307\pi }{900}\implies x\approx 1.07~radians[/tex]
Select the correct answer from each drop-down menu.
In which accounts does the business record the amounts, and where are these accounts assembled?
The business records related amounts in their respective accounts known as
____
accounts. All such accounts are assembled in a book or collection called the
____
.
The business records related amounts in their respective accounts known as ledger accounts.
All such accounts are assembled in a book or collection called the
ledger.
What is the general ledger?All the accounts, including assets, liabilities, equity, revenues, and expenses, that are required to adequately portray a company's financial operations are included in the General Ledger.
Financial statements like the balance sheet, income statement, and cash flow statement are created from the accounts in the general ledger and offer an overview of the company's financial situation.
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HELP!!! ASSIGNMENT DUE SOON
order from least to greatest
6. Calculate each percentage mentally.
a. What is 10% of 70?
b. What is 10% of 110?
c. What is 25% of 160?
d. What is 25% of 48?
e. What is 50% of 90?
f. What is 50% of 350?
g. What is 75% of 300?
h. What is 75% of 48?
please help
Answer
percentage= 100
a. 10% of 70
10/100 × 70 = 7
b. 10% of 110
10/100 × 110 = 11
c. 25% of 160
25/100× 160 = 40
d.25% of 48
25/100 × 48 = 12
e. 50% of 90
50/100 × 90 = 45
f. 50% of 350
50/ 100 × 350 = 175
g.75% of 300
75/100 × 300 = 225
h. 75% of 48
75/100 × 48 = 36
You have one x2-block and 2n x-blocks (where n is a positive whole number). How many 1-blocks do you need to form a square? What are the dimensions of the square? Express your answer in terms of n.
Answer:
If you have one x2-block and 2n x-blocks, you need to add (2n)^2 1-blocks to form a square. The dimensions of the square will be (x2-block + 2n x-blocks) x (x2-block + 2n x-blocks) = (2n+2) x (2n+2) = (2n + 2)^2.
If the cylinder has a radius of 13.4 centimeters and a height of 27 centimeters, what is the area of the cross section?
The area of the cylinder is 3, 399. 74 square centimeters
How to determine the area of the cylinderThe formula for calculating the area of a cylinder is expressed with the equation;
A = 2πrh + 2πr²
Given that the parameters are;
A is the area of a cylinderπ takes the value of 22/7 or 3.14h is the height of the cylinderr is the radius of the cylinderFrom the information given, we have that;
Radius, r = 13.4 centimeters
Height, h = 27 centimeters
Now, subsitute the values, we get;
Area = 2× 3.14 × 13. 4× 27 + 2× 3.14 × (13.4)²
expand the bracket
Area = 2272. 104 + 1127.64
Add the values
Area = 3, 399. 74 square centimeters
Hence, the value is 3, 399. 74 square centimeters
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a) You are going to roll two 6-sided dice and take their difference, referred to as D. What is VAR(D)? b) You are going to roll two 6-sided dice and add them together, referred to as A. What is VAR(A)?
The probability that the sum of the numbers on the dice facing up add up to 3 is 1/18 and VAR(A)= 1
Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.
probability = desired outcome / total outcomes
A 6-sided dice has numbers 1, 2, 3, 4, 5, 6 at each of the 6 sides.
The event of rolling two fair 6-sided dice, which the numbers on the dice facing up add up to 3, is by having (1, 2) or (2, 1).
probability = desired outcome / total outcomes
probability = 2 / (6 x 6)
probability = 2 / 36
probability = 1/18
VAR(A)= 1
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The cost to produce bottled spring water is given by C(x) = 16x – 63 where x is the number of thousands of bottles. The total income (revenue) from the sale of these bottles is given by
C(x) = 16x – 63, where x is the number of thousands of bottles, gives the cost of producing bottled spring water.
The formula R(x) = - x2 + 326x – 7463 calculates the total amount (revenue) from the sale of these bottles.
How to determine?Bottles sold will yield the highest profit.
Profit maximization
Profit after selling 245 thousand bottles
C(x) = 16x – 63
R(x) = – x² + 326x – 7463.
Revenue – Cost = Profit
P(x) = R(x) – C (x)
= – x² + 326x – 7463 – (16x – 63) (16x – 63)
= – x² + 310x – 7400
Choice c)
Profit = x2 minus 310x minus 7400
P(x) = – x² + 310x – 7400
P’(x) = -2x + 310
P’(x) = 0 => -2x + 310 = 0 => x = 155
P’’(x) = - 2 < 0
As a result, profit is greatest at x = 155.
The highest profit will be generated if 155 bottles are sold.
Alternative b)
Profit maximization at x = 155
P(x) = – x² + 310x – 7400
= -(155)² + 310(155) – 7400
= Rs 16625
The highest possible profit is Rs 16625.
Alternative b)
Profit after selling 245 thousand bottles
X = 245
−(245)2 + 310(245) – 7400 = profit
= 8525
Alternative (a) Rs 8525
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What is the mathematical phrase for "Thrice a number more than 1?"
A. 2x+1
B. 1+2x
C. 3x+1
D. 1+3x
Answer:
C and D
Step-by-step explanation:
3x + 1 and 1 + 3x are the phrase for 'Thrice a number more than 1.
they can simplify to get the same answer.
se tienen 10 parlantes idénticos que emiten sonido simultáneamente y el nivel de intensidad medido en un punto es 100 db, ¿cuál es el nivel de intensidad del sonido que emite cada parlante?
The total sound level at the point is 100 dB (10 dB x 10 speakers).
The formula for calculating the sound level emitted by each speaker is 10 * log (100 / 10) = 10 dB. This means that each speaker emits a sound level of 10 dB.
To calculate this, we first need to understand the principle of the logarithmic addition of sound levels. The logarithmic addition of sound levels states that when two sound waves with different amplitudes overlap, the resulting amplitude is the sum of the logarithms of the individual amplitudes.
For example, let's say we have two sound waves with amplitudes of 10 dB and 20 dB. The resulting amplitude will be 10 * log (10 + 20) = 10 * log (30) = 10 dB + 20 dB = 30 dB.
Therefore, in our example, the 10 speakers each emit a sound level of 10 dB. This means that when all 10 speakers play simultaneously, the total sound level at the point is 100 dB (10 dB x 10 speakers).
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HELP ASAP WILL MARK THE BRAINLIEST
Answer:
Second choice : -3, 11, -45, 179
Step-by-step explanation:
First term: a₁ = - 3
Second term a₂ = -4a₁ -1 = (-4)(-3) - 1 = 12 - 1 = 11
There are only two options with 11 as the third term, Options 2 and 4 look the same but the fourth option has curly braces around the numbers making it a set rather than a sequence
If you wanted to be sure and compute the third term to see if it matches
a₃ = -4a₂ - 1 = -4(11)- 1 = -44 - 1 = -45
I need help with this one asap
Answer:
[tex]\frac{1}{4y^9}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]\frac{a^m}{a^n}[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex]
[tex]\frac{y^{-3} }{4y^{6} }[/tex]
= [tex]\frac{1}{4}[/tex] × [tex]\frac{y^{-3} }{y^6}[/tex]
= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6-(-3))} }[/tex]
= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6+3)} }[/tex]
= [tex]\frac{1}{4y^9}[/tex]
your Dad needed to get two matching gifts for his nephews, so he went to the store with $75 cash in his wallet. After buying the two gifts, now he has just $17 left over. How much did each gift cost?
Answer:
$29
Step-by-step explanation:
Since the gifts are matching, the cost of each gift be equal, say $x
Now, Total cash - cash leftover = cost of both gifts
which is, 75 - 17 = 2x
or $58 = 2x
Thus, x would be 58/2 = $29
Or each gift would cost $29
What's the value of x?
Answer:
52
Step-by-step explanation:
Using the exterior angle theorem, [tex]112+x=164 \implies x=52[/tex]
This paperweight is a hemisphere with a diameter of 7cm. The glass has a density of 3g/cm squared. Calculate the the mass of the paperweight.
Give your answer to 3 significant figures
WILL MARK BRAINLIEST!
Answer:
The answer assumes that the density of glass is 3 g/cm^3, not 3 g/cm^2.
The mass of the paperweight is 270 grams.
Step-by-step explanation:
Lets calculate the volume of a sphere having a radius of 3.5cm, and then divide that by 2 to get the volume of the hemisphere (half a sphere). The sphere has a diameter of 7cm (therefore, a radius of 3.5cm).
Vol (sphere) = (4/3)πr^3
Vol = (4/3)(3.14)(3.5cm)^3
Vol = 180 cm^3
Half of this (the hemisphere) will be 90 cm^3
We know the volume, and we know the density of glass (3 g/cm^3), so multiply the two to obtain the mass of the paperweight.
(90 cm^3)*(3g/cm^3) = 270 grams
Given the quadratic formula f(x)= 3x^2 - 2x + 5, calculate the average rate of change from x= -2 to x = 0.
The average rate of change from x = -2 to x = 0 of the function f(x) = 3x² - 2x + 5 is -8.
What is the average rate of change from x = -2 to x = 0?The average rate of change from -2 to 0 is;
f(0) - f(-2) / 0 - (-2)
Given the quadratic equation in question;
f(x) = 3x² - 2x + 5
Plug in the values;
[ ( 3(0)² - 2(0) + 5 ) - ( 3(-2)² - 2(-2) + 5 ) ]/ 0 - (-2)
[ ( 0 - 0 + 5 ) - ( 12 + 4 + 5 ) ]/ 0 - (-2)
[ 5 - 21 ] / 0 - (-2)
[ -16 ] / 2
-16/2
-8
Therefore, the average rate of change is -8.
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a circle with an area of `8\pi` square centimeters is dilated so that its image has an area of `32\pi` square centimeters. what is the scale factor of the dilation?
The scale factor of the dilation of the given object is 4.
The scale factor of dilation:
The scale factor of the dilation of an object is determined by taking the ratio of image length to the corresponding object length.
Dilation is the process of resizing or transforming an object. The transformation that makes the objects smaller or larger with the help of the given scale factor.
The basic formula to find the scale factor of a dilated is:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
[tex]SD=\frac{32cm^2}{4cm^2}[/tex]
SD=4
Thus, the scale factor of the dilation of the given object is 4.
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Precal problem is confusing please help me!
Use the graph off shown to find the x-values (if any) at which f is not continuous.
The graph shows that f is not continuous at x=-4 and x=4. This is because the graph does not have a continuous line at those points.
What is the graph ?A graph is a visual representation of data that uses dots, lines, or bars to show how different elements of a set of data are related. Graphs are typically used to show patterns or trends in data over time, or to compare different sets of data. Graphs can also be used to show the relationships between different variables.
At x=-4, there is a large gap between the left side and the right side of the graph. At x=4, the graph has a sharp corner, which shows that the graph is not continuous.
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Help me please
Thank you
Have a great day :)
. Ryan bought cans of soup on sale for $1.30 each and paid with a $20 bill. If he received at least $5 but no more than $10 back, which inequality represents c. the number of cans he purchased?
Answer:
[tex]5 \leqslant 20 - 1.3x < 10[/tex]
write a non-fruitful function draw triangle(someturtle, somesize) which makes a turtle draw an equilateral triangle.
A non-fruitful function which makes a turtle draw an equilateral triangle is given in the explanation.
Here is an example of a non-fruitful function in Python that takes a turtle object and a size as arguments and makes the turtle draw an equilateral triangle:
import turtle
def draw_triangle(some_turtle, some_size):
for i in range(3):
some_turtle.forward(some_size)
some_turtle.left(120)
# Create a turtle object
t = turtle.Turtle()
# Call function to draw an equilateral triangle of size 100
draw_triangle(t, 100)
# Hide turtle and exit the turtle window
turtle.done()
This function makes the turtle move forward by some_size units and turn left by 120 degrees three times, resulting in a triangle with three equal sides and three 60-degree angles.
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a student spends 3/4 of his money on tuition and 1/3 of what remains on books. if he has $50 dollars left, how much money did he start with?
Answer:
$75
Step-by-step explanation:
3/4 -tuition
4/4-3/4=1/4 1/3×1/4=1/12 -books
1/12+1/4=1/3 1-1/3= 2/3 -left which is equal to $50
2/=$50
1=
1×3/2×$50= $75
Identify the initial amount (a) and the decay factor (b) in the exponential function
y = 5 * 0.5^x
Answer: The initial amount (a) in the exponential function is 5, and the decay factor (b) is 0.5.
Step-by-step explanation: :D
