The ratio 8:73 represents B: The ratio 8:73 represents the ratio of 6th grade football players to total athletes.
What is a ratio?It should be noted that ratio demonstrates how many times one number can fit into another number as they contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point to another data point.
In this case, the football players for 6rh grade is 8 and the total number of athletes is 73.
Therefore, the ratio that illustrates this is 8:73.
In conclusion, the correct option is B.
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Answer:
b
Step-by-step explanation:
i took the test and its right :)
In the first hour Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, the sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes. How many did they sell?
The number of cupcakes sold will be 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, in the first hour, Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, they sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes.
The number of cupcakes sold will be,
N = (1/3) + (3/8) +[(2-1/3-3/8)]+3
N = (1/3)+(3/8) + (7/24)
N = 96 / 24
N = 4
Therefore, the number of cupcakes sold will be 4.
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Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 20 years?
The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20
How to find the value of money?When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.
If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.
In 20 years therefore, the value of $100 would be:
Value in 20 years = Value today x (1 - inflation rate) ^ number of years
= 100 x (1 - 4%) ²⁰
= $44.20
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Larry's tuition for last semester was $5510. If he paid $6080 this semester, his tuition increased by
% (round to the nearest tenth of a percent).
His tuition was increased by 10.34%
What is meant by percentage?A quantity or ratio stated as a fraction of 100 is known as a % in mathematics (from the Latin per centum, "by a hundred").
The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian phrase per cento, which means "for a hundred," gradually shrank to become the symbol for "percent," which is now used globally. It finally vanished totally. The word "per" was frequently shortened to "p." Two circles and a horizontal line made up the "cento," which is how the contemporary "%" symbol is now represented.
Given, Larry's tuition for last semester was $5510
% increase= (6080-5510)/5510
=0.10344
=0.10344*100
=10.34%
His tuition was increased by 10.34%
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The perimeter of a triangle is 42 feet. One side of the triangle is one foot longer than the second side. The third side is five feet longer than the second side. Find the lengths of all three sides (in feet). (Enter your answers as a comma-separated list.)
Answer:
12 ft, 13 ft , 17 ft
Step-by-step explanation:
let x be the length of the second side , then
one side is x + 1
third side is x + 5
the perimeter P is the sum of the 3 sides, then
P = x + x + 1 + x + 5 ← collect like terms
P = 3x + 6
given P = 42 , then equating gives
3x + 6 = 42 ( subtract 6 from both sides )
3x = 36 ( divide both sides by 3 )
x = 12
x + 1 = 12 + 1 = 13
x + 5 = 12 + 5 = 17
the 3 sides are 12 ft, 13 ft , 17 ft
The function d(t)= 1/2t+2 represents the amount (in inches) of water in a rain barrel for six rainy days, where t is the time (in days) since the rainfall began.
a. Find the domain and range?
Graph the function.
b. Interpret the slope and interprets of the graph.
The slope is ____ So, the water amount in the rain barrel changes at a rate of ____ inch per day. The Y -intercept is ____ So, the amount of water in the rain barrel before the rain began was ____ inches. There is no t -intercept in this context.
A) the domain is:
D: [0, 6]
The range is:
B)
"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."
"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."
And the graph can be seen at the end.
How to find the domain and range?Here we have the linear equation:
d(t) = (1/2)*t + 2
This refers to the amount of water in a barrel for six rainy days, where t is the number of days.
So the domain goes between t = 0 and t = 6.
The range will go between:
d(0) = (1/2)*0 + 2 = 2
d(6) = (1/2)*6 + 2 = 3 + 2 = 5
So the domain is:
D: [0, 6]
The range is:
T: [2, 5]
b) The complete sentences are:
"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."
"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."
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3. Adam is 20 years younger than Brian. In two years Brian will be twice as old as
Adam is now. How old
are they now? Solve the problem using the elimination method.
Answer:
Here,
Let the age of Adam be x
and ,Brian be y
so,x=y+20.........eqn 1
and ,2(y+2)=x
or,2y+4=x......eqn 2
Now ,
subtracting eqn1 and eqn 2
so, x=y+20
x=2y+4
- - -
______________
0 = -y+16
so,y=16 and x=y+20 =16+20=36 .
so Adam is 36 years old and brian is 16.
Choosing the best bank for a new savings account
The major criteria to be considered when going for a bank to have a new savings account registered with them are as follows:
Low interest rates on my savingsFriendly customer serviceOnline banking site usability platform.Why low interest rate makes a criterion for choosing the bank to bank with.As an entrepreneur, finding a good bank to open a savings account with might be much tedious to do. However, I have live to understand that banks with low interest rate are a better catch if I am considering a good saving lifestyles. I cannot stand a banking system that charges me unnecessarily all the time all in the name of fee or the other, which results to reducing my money in their system.
That being said, discovering a bank which has welcoming and helping customer service is also an important factor to be considered when choosing to right banking system.
In conclusion, it can be deduced that a bank with which does not deduct one's money anyhow all in the name of interest is worth having a savings account with.
Complete question:
What are the conditions to be considered in choosing the best bank for a new savings account?
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consider the ellipse given by x^2+xy+2y^2=7. Find the y-coordinate(s) of all points where the ellipse has a vertical tangent line.
The ellipse given by x^2+xy+2y^2=7. The y-coordinate(s) of all points are -11.3, 11.2, -5.665, 5.585 where the ellipse has a vertical tangent line.
Define differentiation.Differentiation is the process of determining a function's derivative. Differentiating algebraic functions, trigonometric functions, and exponential functions are the three fundamental derivatives.
Given,
Ellipse given,
x²+ xy + y ² = 7
Differentiating:
dy/dx
x²+ xy + y² = 7
d/dx(x² + xy + y²) = d/dx(7)
2x + 1y + x dy/dx + 2y dy/dx = 0
dy/dx = 2x + y/ x + 2y
dy/dx = 0
2x + y = 0
x + 2y = 0
Now, we have 2 equations,
x² + xy + y² = 0
y = -2x
Solving equations by substitution method,
x² + x(-2x) + (-2x)² = 7
x² - 2x² + 4x² = 7
3x² = 7
x = ±√21/3
Using y = -2x
Points are:
( -2√21/3 , √21/3) and (2√21/3 , -√21/3)
±√21/3 = ±1.528
x² + xy + y² = 7 [-11.3, 11.2, -5.665, 5.585]}
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Consider the two points F(-9,0) and G(9,0) as the foci of an ellipse. The length of the major axis is 36. Give the equation of the ellipse.
well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]
[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]
Check the picture below.
the artist was hired to decorate 40 in 3 hours he completed 3/8 of the pots at that rate how long will it take the artist to decorate 25 clay pots?
The artist will take 5 hours to decorate 25 clay pots.
Given,
Number of pots to be decorated in 3 hours =40
Number of pots he decorated in 3 hours =[tex]\frac{3}{8}*40=3*5=15[/tex]
So, the artist took 3 hours to decorate 15 pots instead of 40 pots.
It means to decorate 1 pot he took time=[tex]\frac{Total time}{Number of pots decorated} =\frac{3}{15} =\frac{1}{15} hour[/tex]
So, to decorate 25 pots he need time,
[tex]time=\frac{1}{5}*25= 5 hours[/tex]
Thus, the artist need 5 hours to decorate 25 clay pots.
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Calculate ending inventory and COGS using FIFO and LIFO methods for ABC Inc.
On April 1, 2022 the balance in inventory is 220 units at $50 each
April 5, 2022 purchased 100 units at $60 each
Purchased 50 units at $45 each on April 10, 2022
Sold 300 units at $80 each on April 16, 2022
Sold 20 units at $95 each on April 25, 2022
Purchased 200 units at $40 each on April 30, 2022
The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:
FIFO LIFO
Ending inventory $10,250 $12,800
Cost of goods sold $17,000 $14,450
How does FIFO differ from LIFO?FIFO, which means First-in, First-out, computes the cost of goods sold based on the assumption that the physical flow of goods sold depends on the earlier inventory in stock.
FIFO can be applied under both the perpetual and periodic inventory systems, unlike LIFO.
LIFO means Last-in, First-out, and as a cost flow assumption assigns the cost of goods sold based on the latest inventory purchases.
LIFO cannot be used under the perpetual inventory system.
Date Activities Units Unit Rate Total Cost
April 1 Beginning inventory 220 $50 $11,000
April 5 Purchases 100 $60 6,000
April 10 Purchases 50 $45 2,250
April 16 Sales -300 $80
April 25 Sales -20 $95
April 30 Purchases 200 $40 8,000
Total 570 $27,250
Units sold 320
Ending inventory 250
FIFO:
Ending Inventory = $10,250 (200 x $40 + 50 x $45)
Cost of goods sold = $17,000 ($27,250 - $10,250)
LIFO:
Ending Inventory = $12,800 (220 x $50 + 30 x $60)
Cost of goods sold = $14,450 ($27,250 - $12,800)
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What is the function rule for the line?
f (x) = 2x - 4
f(x)=-4x - 2
f(x) = 4x - 2
f (x)= -2x + 4
Answer: f (x)= -2x + 4
Identify potential outliers, if any, for the given data. The normal annual precipitation (in inches) is given below for 21 different U.S. cities.
32.4 29.4 34.6 65.3 22.1 31.8 16.6 28.2 36.2 59.4 24.3 47.2 45.6 9.2 27.1 18.9 13.6 31.4 24.2 12.3 35.4
A. none
B. 65.3
C. 9.2; 12.3
D. 9.2; 59.4; 65.3
E. 59.4; 65.3
The potential outliers, given the normal annual precipitation in the different U.S. cities are E. 59.4; 65.3.
What are outliers?Outliers in a data distribution are values or data points that are far from the other points in the data. These can be statistically significant when they distort measures of central tendency such as mean.
In this case, the potential outliers in the normal annual precipitation 59.4 and 65.3 because they are far from the highest annual precipitation (before them) of 47.2 inches. 9.2 inches is quite low but it is close to 12.3 inches and 13.6 inches and so is not an outlier.
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What is the sum?
3
+
x+3x+3x+3
X
2
LoWatts Ltd makes light bulbs that are identical in size
They have regular orders from company A for 120 light bulbs and from Company B for 168 light bulbs.
LoWatts Ltd uses one size of box to supply both company A and company B. Each box used contains the same number of light bulbs and is full.
The number of boxes used is as few as possible
How many light bulbs does each box hold?
Using the greatest common factor, the number of light bulbs in each box is 24.
What is the greatest common factor?The greatest common factor (GCF) is the number that can divide two or more numbers without a remainder.
The GCF is a divisor that divides dividends evenly, leaving only quotients without remainders.
For instance, the greatest common factor of 120, 168, and even 288 is 24.
Using this GCF implies that 24 can divide 120, 168, and 288 without leaving any remainders.
Company A Company B Total
Total orders for light bulbs 120 168 288
Greatest common factor of 24 24 24
Number of boxes delivered 5 7 12
Thus, with the greatest common factor as 24 light bulbs in each box, Company A will be supplied 5 boxes, while Company B will be supplied with 7 boxes.
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A park found him spray 20 gallons of water in one half an hour then was turned off for a while when it was turned back on it's break 30 gallons and 347 hours explain how you think I found and sprayed water at the same rate both times it was on
The rate of spray at both times is 40 gallons/hour and it is the same.
What is the rate of change?
How quickly something changes over time is referred to as its rate of change, or ROC. Thus, it is the acceleration or deceleration of changes (i.e., the rate) rather than the magnitude of individual changes.
We have,
spray 20 gallons of water in 1/2 hour.
30 gallons and 3/4 hours (it's not 347 hours).
We simply calculate the rate for one hour:
1/2 hour = 20 gallons
3/4 hours = 30 gallons
Then for 1 hour,
1 hour = 20 * 2 = 40 gallons
1 hour = 30 * 4/3 = 40 gallons
Hence, the rate of spray at both times is 40 gallons/hour and it is the same.
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Sara sold a coin for $3, and its value increases by 2% each year after it is sold. Find the value of the coin in 8 years. Then write an exponential growth
function for this problem. After that, graph the function and state the domain and range. Finally, state what the y-intercept represents.
By using the concept of growth, it can be calculated that
Value of coin in 8 years is $3.52
[tex]3(\frac{51}{50})^x[/tex] is the required exponential function
Domain of the function is all positive real number
Range is [tex](0, \infty)[/tex]
y- intercept is 3
This means initial value of the coin is $3
What is growth?
Growth is the exponential increase in the value of the product at a certain rate over a certain period of time
Here, concept of growth has been used
Present value of the coin = $3
Rate = 2%
Time = 8 years
Future value =
[tex]3(1 + \frac{2}{100})^8\\\\3(1 + \frac{1}{50})^8 \\\\3(\frac{51}{50})^8[/tex]
= $3.52
If the time is x years, the given exponential function is
y =
[tex]3(1 + \frac{1}{50})^x\\\\3(\frac{51}{50})^x[/tex]
This is the required exponential function.
Since x represents time here, then x has to be positive
Domain of the function is all positive real number
Now
As [tex]x\rightarrow \infty[/tex], [tex]f(x) \rightarrow \infty[/tex]
As [tex]x\rightarrow -\infty[/tex], [tex]f(x) \rightarrow 0[/tex]
Range is [tex](0, \infty)[/tex]
For y- intercept, x = 0
Putting x = 0, we get y = 3
y- intercept is 3
This means initial value of the coin is $3
The graph of the function has been attached here
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how many different outcomes are possible when flipping a coin and rolling a die
The total possible outcome when a coin is flipped and a die is rolled is 12
What is Probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total possible outcomes.
For example if a coin is flipped, a coin only has two faces, this means that it will have 2 Total possible outcome. When a die is rolled, a die has 6 faces which means that it will Total outcome of 6. When both a coin is flipped and a die is rolled the total possible outcome is 6×2 = 12 outcomes.
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What is the greatest integer solution 5 - 3m > -10
Answer:
4
Step-by-step explanation:
5-3m>-10
-5. -5
-3m>-15
/-3. /-3
m<5
so 4 is the highest integer since 4 is less than 5
Hopes this helps please mark brainliest
What is an equation of the line that passes through the points (4, -2)(4,−2) and (8, 3)(8,3)
The equation of line passing through points (4,−2) and (8, 3) is 4y - 5x + 28 = 0
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given pair of points are (4,−2) and (8, 3).
The equation of line passing through two points (x₁, y₁) and (x₂, y₂) is given as,
y = ((x - x₁) / (x₁ - x₂)) (y₁ - y₂) + y₁
Substitute the respective values to get the equation of line as,
y = ((x - 4 ) / (4 - 8)) (-2 - 3) + (-2)
y = ((x - 4 ) / 4) × 5 - 2
4(y + 2) = 5(x - 4)
4y - 5x + 28 = 0
Hence, the equation of line for the given points is 4y - 5x + 28 = 0.
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For the following image, find the volume:
6 in
4 in
6 ft
The required volume of the given shape is given as 432 cubic feet.
Given that,
A 3-dimensional shape with a hexagonal profile is given with dimension,
a = 6 in, H = 6 in and h = 4 in as shown in figure.
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
The volume of the given shape is,
Volume = 6/2[ah] × H
Substitute the value in the above expression,
Volume = 3 [4×6] × 6
Volume = 432 cubic feet,
Thus, the required volume of the given shape is given as 432 cubic feet.
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Write the number in two other forms (fraction, decimal, or percent) 355%
Answer:3.55 , 71/20
Step-by-step explanation:
Need help solving this problem, please and thank you
The table below shows the cost of downloading songs from a website. \text{Number of Songs}Number of Songs \text{Total Cost}Total Cost 1313 \$9.36$9.36 1717 \$12.24$12.24 1919 \$13.68$13.68 What is the constant of proportionality between the total cost and the number of songs?
The constant of proportionality between the total cost and the number of songs is 0.72.
What is the constant of proportionality?The constant of proportionality is the ratio that supplies the variable cost per unit of each song.
Other names for the constant of proportionality include:
SlopeUnit rateConstant rateConstant ratioRate of changeConstant of variation.Determining the constant of proportionality can help us formulate the total cost equation as y = 0.72x.
Number of Songs Total Cost Unit Cost
13 $9.36 $0.72 ($9.36/13)
17 $12.24 $0.72 ($12.24/17)
19 $13.68 $0.72 ($13.68/19)
Check:
y = 0.72x
y = 0.72(13)
y = $9.36
Thus, the constant of proportionality is 0.72, showing that a downloaded song costs $0.72 each.
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What is the domain and range of the graph in set notation
The required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).
Range, it is the set of values that come out to an outcome for certain mathematical operations.
Here,
A graph of the function is shown,
and the graph of the function is defined from -∞ to ∞, so the domain of the function is (-∞, ∞).
Also, the function has a value of the y-axis from -3 to ∞, and the range of the function is (-3, ∞).
Thus, the required domain of the function shown is (-∞, ∞) and the range is (-3, ∞).
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Arianys runs a farm stand that sells grapes
and apples. Each pound of grapes sells for
$3.75 and each pound of apples sells for
$4. Arianys made $251.75 from selling a
total of 64 pounds of grapes and apples.
Determine the number of pounds of
grapes sold and the number of pounds of
apples sold.
The number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
According to the question,
We have the following information:
Cost of 1 pound of grapes = $3.75
Cost of 1 pound of apples = $4
Total cost made by selling = $251.75
And the weight of the apples and grapes sold = 64
Now, let's take the weight of grapes to be x pounds and the weight of apples to be y pounds.
So, we have:
x+y = 64
x = 64-y ....(1)
3.75x+4y = 251.75
Putting the value of x in this equation:
3.75(64-y)+4y = 251.75
3.75*64-3.75y+4y = 251.75
240+0.25y = 251.75
0.25y = 251.75-240
0.25y = 11.75
y = 11.75/0.25
y = 47 pounds
Now, putting this value of y in equation 1:
x = 64-y
x = 64-47
x = 17 pounds
Hence, the number of pounds of grapes sold is 17 pounds and the number of pounds of apples sold is 47 pounds.
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2n²×5 work out 6th term of this sequence
The 6th term of this sequence is 360
How to determine the 6th term of this sequenceFrom the question, we have the following parameters that can be used in our computation:
Sequence representation = 2n² × 5
This means that
nth term = 2n² × 5
So, we have
f(n) = 2n² × 5
For the 6th term, the value of n is 6
i.e. n = 6
Substitute the known values in the above equation, so, we have the following representation
f(6) = 2(6)² × 5
Evaluate
f(6) = 360
Hence, the 6th term s 360
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|y + 4| < 1
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
A solution to this inequality |y + 4| < 1 in as an interval is: A. −5 < y < –3.
What is an inequality?An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Less than or equal to (≤).Greater than (>).Less than (<).Adding -1 to both sides of the inequality, we have:
|y + 4| + (-1) < 1 + (-1)
|y + 4| - 1 < 0
Evaluating the absolute value function, we have the following:
y + 4 < ±1
For the positive interval, we have:
y < -4 + 1
y < -3
For the negative interval, we have:
y < -4 - 1
y < -5
Finally, we would express the solution to this inequality as an interval as follows:
-5 < y < -3.
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Complete Question:
What is a solution to this inequality |y + 4| < 1?
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
2x=9 what is the value of x
Answer:
The answer is x=4.5
Step-by-step explanation:
I hope this helps
Classify the following number: 5√2. Choose all that apply.
Answer:
Real, Irrational
Step-by-step explanation:
5sqrt2 is NOT:
Natural (1,2,3...)
Whole (0,1,2,3...)
Integer (...-3,-2,-1,0,1,2,3...)
Rational (can be written like a ratio)
Imaginary (have the number i in it.)
It IS Irrational, will have neverending decimal with no repeating pattern.
5sqrt2 = 7.0710678119...
It IS REAL and IRRATIONAL.