According to www.whitehouse.gov, the government had about $2.1 trillion in receipts and $2.8 trillion in outlays (expenses) for 2013. Does this represent a surplus or a deficit? What was the ratio of the government's expenses to it's receipts for 2013? Express this as a decimal rounded to the thousandths place.
Answer:
The ratio of the government's expenses to it's receipts for 2013 is 1.3333333 trillion
Step-by-step explanation:
According to the given data we have the following:
Receipt=$2.1 trillion
Expenses=$2.8 trillion
Hence, it represent a decifit of $2.8 trillion-$2.1 trillion=$0.7 trillion
Therefore, to calculate the the ratio of the government's expenses to it's receipts for 2013 we would have to use the following formula:
ratio of the government's expenses to it's receipts=$2.8 trillion/$2.1 trillion
ratio of the government's expenses to it's receipts=1.3333333 trillion
The ratio of the government's expenses to it's receipts for 2013 is 1.3333333 trillion
Consider the line y=-9x+5.
Find the equation of the line that is parallel to this line and passes through the point (7, 2).
Find the equation of the line that is perpendicular to this line and passes through the point (7, 2).
Step-by-step explanation:
1) if the point A(7;2) and the given line is in slope-interception form, then the required parallel line has the same slope, its equation can be written as: y=-9x+C, where C - unknown number;
2) to calculate the C it is needed to substitute the A(7;2) into the required equation of the parallel line:
2=-9*7+C; ⇒ C=65.
3) the parallel line is: y=-9x+65.
4) if the point A(7;2) and the given line is in slope-interception form, then the slope of the perpendicular line is: (-1)/(-9)=1/9, and the required equation of the perpendicular line can be written as:
y=1/9 *x+C, where C - unknown number;
5) to calculate the C it is enough to substitute the A(7;2) into the required equation of the parallel line:
2=1/9 *7+C; ⇒ C=11/9;
6) the perpendicular line is:
\(y=\frac{1}{9} x+\frac{11}{9}.\)
a company has offices in 3 different cities and a total of 480 workers. there are 90 workers in new york and 130 workers are in san diego. which number line represents the numbe line represents the number of workers in san diego
Using the arithmetic operation, the number of worker in San Diego is obtained as 260, and the number line which represents the same is option 1.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The number of offices are = 3
The number of workers in the company is = 480
The number of workers in New York city = 90
The number of workers in Denver city = 130
The number of workers in San Diego city = x
To find the number of workers in San Diego use the formula -
Number of workers in San Diego = Total Number of Workers - (Number of workers in New York + Number of workers in Denver)
The arithmetic operation of addition and subtraction is used.
Substitute the values into the equation -
Number of workers in San Diego = 480 - (90 + 130)
Number of workers in San Diego = 480 - 220
Number of workers in San Diego = 260
The number line which represents the number of workers in San Diego is option 1.
Therefore, the number of workers in 260.
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A company has offices in 3 different cities and a total of 480 workers. There are 90 workers in New York and 130 workers are in Denver. Which number line represents the number line represents the number of workers in San Diego?
I do not understand this, can anyone help me out?
Answer:
the Answer what have to be the fist bc c is the only on that is not with a ,g or b
Step-by-step explanation:
11. Brent is making a wooden display case for his baseball collection. He has 24 balls
from American League games and 30 balls from National League games. He
wants to display the same number of baseballs in each row and does not want
to put American League baseballs in the same row as National League baseballs.
How many rows will Brent need in the display case to put the greatest number of
baseballs possible in each row!
Answer:
9 rows
Step-by-step explanation:
Find the GFC(greatest common factor) -
24 =2*2*2*3
30= 2*3*5
Each row will have 6 balls = 24+30= 54
= 54/6=9
Answer:
9 rows
Step-by-step explanation:
solve In 2010, the percentage of assisted living residents who had both heart disease and depression was 9%, the percentage with only heart disease was 25%, and the percentage with either condition was 48%. What percentage of assisted living residents had only depression
Answer:
The percentage of assisted living residents had only depression
P(D) =0.32
Step-by-step explanation:
Explanation:-
Given the percentage of assisted living residents who had both heart disease and depression was 9%
Let The event 'H' be the event of heart disease and 'D' be the event of depression
P(H ∩D) = 9% =0.09
The percentage with only heart disease was 25%
P(H) = 0.25
The percentage with either condition was 48%.
P(H∪D) = 48%=0.48
By addition theorem on probability
\(P(H UD) = P(H) +P(D) - P(H n D)\)
\(0.48 = 0.25 + P(D) -0.09\)
P(D) = 0.48 -0.16
P(D) = 0.32
The percentage of assisted living residents had only depression
P(D) =0.32
Find the exact surface area of a sphere with a diameter of 13cm
Answer:
A = 530.929158457
Answer:
Area = 706.8583471
Explanation:
The used law to measure the surface area of the sphere is
\(area \: = 4\pi \: {r}^{2} \)
Where (r) is the radius. The radius is half the diameter, so it will be half 13 which is equal to 7.5. By using this law:
\(4\pi \: {7.5}^{2} = 706.8583471\)
If you like my explanation please give me 5 stars.What will be the result of substituting 2 for x in both expressions below?
+4
x+6-x-2
O Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
O Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
O One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
Equivalent Algebraic expressions:Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expressionns.
Given the algebraic expressions,
\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)
Substituting 2 for x in the first expression gives:
(1/2 × 2) + 4
1 + 4
5
Substituting 2 for x in the second expression gives:
2 + 6 - (1/2 ×2) - 2
8 - 1 - 2
8 - 3
5
Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
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How many gallons of paint are required to paint one side of a block wall of the following dimensions: 6'x172'? The paint being used will cover 200ft2 per gallon. 2. Compute the gallons of sealer required to seal a floor 120' x250'. The sealer being used will cover 175 ft2 per gallon. 3. If a concrete column is 20" in diameter and 18'-3" in height, how many cubic yards of concrete would be needed to fill the form? Round off to the next largest cubic yard. 4. What is the circumfrence of a circle with a diameter of 12'-5"?
The Values for rectangle type wall and circle will be gallons of paint that are required to paint one side of a block wall =5.16 gallon, the gallons of sealer required to seal a floor=4.22 gallon and circumference of circle≈39 feet.
What exactly is a rectangle?
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
For example, if one side of a rectangle is 20 cm long, the opposing side is similarly 20 cm long.
A rectangle has two diagonals that intersect. Both diagonals are the same length
P = 2 (Length + Width) is the perimeter.
Rectangle Area=Length*Breadth
Now,
1. Given Length of wall=172 feet and breadth =6 feet then area=172*6=1032
square feet and The paint being used will cover 200 square ft per gallon.
so, gallons of paint that are required to paint one side of a block wall
=1032/200=5.16 gallon
2. Length=250 feet, breadth=120 feet then perimeter=2*370=740 feet
paint used to seal 175 feet floor=1 gallon
then the gallons of sealer required to seal a floor 120' x250'=740/175=4.22 gallon
3. Incomplete question.
4.diameter=12feet 5inch=149 inch
circumference of circle=π*diameter=3.14*149≈39 feet
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what is 9.7 times 8.6
Answer:
83.42
Step-by-step explanation:
Answer:
83.42
Step-by-step explanation:
x = 9.7 x 8.6
= 83.42
Find the equation to the line
The equation of the line is y = 2/3x + 1
How to determine the equation of the line?The graph represents the given parameter
From the graph, we have the following points that can be used in our computation:
(x, y) = (0, 1) and (3, 3)
The equation of the line is then calculated using the following equation
y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁
Where
(x, y) = (0, 1) and (3, 3)
Substitute the known values in the above equation, so, we have the following representation
y = (3 - 1)/(3 - 0) * (x - 0) + 1
Evaluate
y = 2/3 (x - 0) + 1
So, we have
y = 2/3x + 1
Hence, the line equation is y = 2/3x + 1
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Which expression is equivalent to 1/3(9x + 12) + 4x + 6?
A: 7x + 18
B7x + 10
C:13x x +6
D:13x + 18
The expression is equivalent to 1/3(9x + 12) + 4x + 6 will be 7x + 10. Then the correct option is B.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 1/3(9x + 12) + 4x + 6
Simplify the expression, then we have
⇒ 1/3(9x + 12) + 4x + 6
⇒ 3x + 4 + 4x + 6
⇒ 7x + 10
The expression is equivalent to 1/3(9x + 12) + 4x + 6 will be 7x + 10. Then the correct option is B.
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Suppose an online store has an item on sale for 10% off the original price. By what perceny does the store have to increase the price of the item in order to sell it for the original amount
The most appropriate choice of percentage will be given by-
The store have to increase the price of the item by \(11\frac{1}{9}\) % in order to sell it for the original amount.
What is Percentage?
Percentage is a ratio expressed as a percentage of 100.
Let the original price be x
Percentage decrease in price due to sale = 10%
Decrease in price due to sale = \(\frac{10}{100} \times x\)
= \(\frac{x}{10}\)
New price = (\(x - \frac{x}{10}\))
= \(\frac{10x-x} {10}\)
= \(\frac{9x}{10}\)
Now,
Increase in price from \(\frac{9x}{10}\) to \(x\) = \(\frac{x}{10}\)
Percentage by which the store have to increase the price of the item in order to sell it for the original amount =
\(\frac{\frac{x}{10} }{\frac{9x}{10} } \times 100\)
=\(\frac{x}{10} \times \frac{10}{9x} \times 100\)
= \(\frac{100}{9}\)
= \(11\frac{1}{9}\) %
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Find the median of the following
data set.
14,24,35,37,43,35,45,24,29,41,45,
37,19,45,44
Answer:
37,43,35 should be the answer to your game
Answer: 24
Step-by-step explanation: First of all because the number of data is 15 numbers, you know don't have to divide. Cross out the 1st and last numbers until you get to one number. I got 24
The sum of 4 twelves and 7 sixteens
Answer: 160
Step-by-step explanation:
So here they are telling you that there are 4 twelves, a.k.a 4 groups of 12. Which means that you have to multiply 4 x 12 = 48
Then there are 7 sixteens, a.k.a 7 groups of 16.
Which also means that you have to multiply 7 x 16 = 112
Add both numbers and there you have your answer!
I hope you found my answer helpful! :)
How many coupons can be generated
The number of coupon codes that can be generated is given as follows:
247,808 coupon codes.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
The codes are composed as follows:
Two letters -> each with 22 options, as letters can be repeated.Three digits -> each with 8 options, as digits can also be repeated.Thus the total number of codes is obtained as follows:
N = 22² x 8³
N = 247,808 coupon codes.
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Graph the solution to the following system of inequalities.
y>−3x8
y>_(−3x-4)
The graph of the system of inequalities y > 3x + 8 and y ≤ -4 - 3x is shown in the picture.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The system of inequalities:
y > 3x + 8
y ≤ -4 - 3x
The above inequalities represent the linear equation:
The graph is shown in the picture.
Thus, the graph of the system of inequalities y > 3x + 8 and y ≤ -4 - 3x is shown in the picture.
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The average daily balance of a credit card for the month of November was $700, and the unpaid balance at the end of the month was $1,400. If the annual percentage rate is 15.6% of the average daily balance, what is the total balance on the next billing date December 1? Round your answer to the nearest cent.
Answer:
Step-by-step explanation:
To calculate the total balance on the next billing date, we need to consider the average daily balance and the unpaid balance from the previous month.
Given:
Average daily balance for November = $700
Unpaid balance at the end of November = $1,400
Annual percentage rate (APR) = 15.6%
Step 1: Calculate the interest charged for the month of November.
Interest = (Average daily balance * APR * Number of days in the month) / 365
Number of days in November = 30
Interest = (700 * 0.156 * 30) / 365 = $36.44 (rounded to the nearest cent)
Step 2: Add the interest to the unpaid balance to get the total balance on December 1.
Total balance = Unpaid balance + Interest
Total balance = $1,400 + $36.44 = $1,436.44
Therefore, the total balance on the next billing date, December 1, is $1,436.44 (rounded to the nearest cent).
The total balance on the next billing date December 1 is $1,509.20.
What is an annual percentage rate?The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR).
Given,
The average daily balance of a credit card for November = is $700Unpaid balance at the end of the month = $1,400The annual percentage rate = 15.6%Then, the percentage rate for November = \(\sf\frac{15.6}{100}\) × 700
\(\sf = \$109.20\)
Balance on 1st December = unpaid balance at the end of November + percentage rate
\(\sf = $1400 +$109.20\)
\(\sf =\$1509.20\)
Therefore, the total balance on the next billing date December 1 is $1,509.20.
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Find the width, thank you!
length=3width-5
(2(x))+(2(3x-5)=46
2x+6x+10=46
8x=56
x=7
width=7 length=16
Answer:
w = 7
l = 3w-5
2l + 2w = 46
lets substitute the value of length
2(3w-5)+2w
6w-10+2w
6w+2w = 8w
8w-10 = 46
add 10 to both sides to cancel out the -10 on the left side.
8w = 56
56/8 = 7
w = 7
hope this helps and hope it is correct
Step-by-step explanation:
The weights of four similar packs of tomatoes are listed below.
Pack A: 2.456 pounds
Pack B: 2.457 pounds
Pack C: 2.454 pounds
Pack D: 2.459 pounds
Malcolm rounds the weights to the nearest hundredth pound. Which weight does
not round to 2.46 pounds?
A 2.456 pounds
B 2.457 pounds
C 2.454 pounds
D 2.459 pounds
Answer:
The weight that does not round to 2.46 pounds is C 2.454 pounds.
Step-by-step explanation:
Based on the given information, the weights of the four similar packs of tomatoes are as follows:
Pack A: 2.456 poundsPack B: 2.457 poundsPack C: 2.454 poundsPack D: 2.459 poundsMalcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:
Pack A: 2.46 poundsPack B: 2.46 poundsPack C: 2.45 poundsPack D: 2.46 poundsFrom the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.
Let V be the space spanned by the two functions cos(t) and sin(t). Find the matrix A of the linear transformation T(f(t))=f′′(t)+3f′(t)+7f(t) from V into itself with respect to the basis {cos(t),sin(t)}.
Answer: The matrix A of the linear transformation T(f(t)) = f''(t) + 3f'(t) + 7f(t) from the space spanned by the functions cos(t) and sin(t) into itself with respect to the basis {cos(t), sin(t)} can be found by computing the images of the basis vectors under T and expressing those images as linear combinations of the basis vectors.
We have:
T(cos(t)) = -cos(t)'' - 3cos(t)' - 7cos(t) = -cos(t) - 3(-sin(t)) - 7cos(t) = -8cos(t) - 3sin(t)
T(sin(t)) = -sin(t)'' - 3sin(t)' - 7sin(t) = -sin(t) - 3cos(t) - 7sin(t) = -8sin(t) + 3cos(t)
So, with respect to the basis {cos(t), sin(t)}, the matrix A is:
A = [ -8, -3; 3, -8 ]
This is the matrix representation of the linear transformation T with respect to the basis {cos(t), sin(t)}.
Step-by-step explanation:
Write the sentence as an equation.
106 more than the quantity 68 times y is the same as 36 decreased by y
Answer: 68y+106=36-y
Find the slope between the points (-3, -5) and (2, -5). Enter DNE if the slope between the points is undefined.
Answer: The slope is 0
Step-by-step explanation: The coordinates dont change from y=-5 to y=-5
Answer: 0
Step-by-step explanation:
The y value between the points isn't changing, so the slope is 0.
(y2-y1)/(x2-x1)=
(-5-(-5))/2-(-3)=
(-5+5)/2+3=
0/5=0
PLEASE HELP!
I need help solving these problems.
1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x
2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x
3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1
4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x
5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x
6. When we simplify cos x + sin xtan x, the result obtained is sec x
How do i simplify the trig identities?We can simplify the trig identities as follow:
1. Simplification of sec² x + tan² xsec² x
sec² x + tan² xsec² x = sec² x(1 + tan² x)
Recall
sec² x = 1 + tan² x
Thus,
sec² x(1 + tan² x) = sec² x × sec² x
sec² x(1 + tan² x) = sec⁴x
Therefore, the simplified is written as
sec² x + tan² xsec² x = sec⁴x
2. Simplification of (sec² x - 1) / sin² x
(sec² x - 1) / sin² x
Recall,
sec² x - 1 = tan² x
Thus,
(sec² x - 1) / sin² x = tan² x / sin² x
Recall
tan² x = sin² x / cos² x
Thus,
tan² x / sin² x = (sin² x / cos² x) / sin² x
tan² x / sin² x = 1/ cos² x
Recall
1/ cos² x = sec² x
Therefore, the simplified expression is written as:
(sec² x - 1) / sin² x = sec² x
3. Simplification of (1/sec² x) + (1/csc² x)
(1/sec² x) + (1/csc² x)
Recall
sec² x = 1/cos² x
Thus,
cos² x = 1/sec² x
Also,
csc² x = 1/sin² x
Thus,
sin² x = 1/csc² x
Therefore, we have
(1/sec² x) + (1/csc² x) = cos² x + sin² x
Recall
cos² x + sin² x = 1
Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:
(1/sec² x) + (1/csc² x) = 1
4. Simplification of (sec x / sin x) - (sin x / cos x)
(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x
Recall
sec x = 1/cos x
sinx sinx = sin² x
Thus,
(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x
(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x
Recall
1 - sin² x = cos² x
Thus, we have
[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x
[1 - sin² x] / sinx cos x = cos x / sin x
Recall
cos x / sin x = cot x
Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:
(sec x / sin x) - (sin x / cos x) = cot x
5. Simplification of (1 + sin x)(1 - sin x)
(1 + sin x)(1 - sin x)
Clear bracket
1 - sin x + sin x - sin² x
1 - sin² x
Recall
1 - sin² x = cos² x
Thus, we have
(1 + sin x)(1 - sin x) = cos² x
6. Simplification of cos x + sin xtan x
cos x + sin xtan x
Recall
tan x = sin x / cos x
cos x + sin xtan x = cos x + sin x (sin x / cos x)
cos x + sin xtan x = cos x + (sin² x / cos x)
cos x + sin xtan x = (cos² x + sin² x) / cos x
Recall
cos² x + sin² x = 1
cos x + sin xtan x = 1 / cos x
1/cos x = sec x
Thus,
cos x + sin xtan x = sec x
The simplified expression of cos x + sin xtan x is sec x
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least
$45
nough
What is the fewest number of full weeks Briyana
would have to work to have enough money?
Answer:
we don't have the full answer sry.
Step-by-step explanation:
Answer:
10 weeks
Step-by-step explanation:
A sphere and its dimension are shown in the diagram 15 inches
The measurement that is closest to the volume of the sphere is given as follows:
1,767.1 in³.
What is the volume of an sphere?The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:
\(V = \frac{4\pi r^3}{3}\)
From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:
r = 0.5 x 15
r = 7.5 units.
Then the volume of the sphere is given as follows:
V = 4/3 x π x 7.5³
V = 1,767.1 in³.
Missing InformationThe sphere is given by the image presented at the end of the answer.
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A car travels a distance of 112km at an average Speed of 70km/h. It then Travells Further for 60km at an average Speed of 50 km/hr. Calculate for the entire Journey of the total time taken.
The total time taken for the entire journey is 2.8 hours.
To calculate the total time taken for the entire journey, we can use the formula:
Time = Distance / Speed
For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:
Time1 = 112 km / 70 km/h = 1.6 hours
For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:
Time2 = 60 km / 50 km/h = 1.2 hours
To find the total time for the entire journey, we sum up the times for both parts:
Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours
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Geometry please answer quickly I will give brainliest
Answer:
20 +2x+1=7, hope this is the answer
In Joe's fish tank, there are 7 goldfish and 12 snails. How does the ratio 12:19 describe Joe's fish tank?
Answer:
honestly this was the only thing i was ever good at in math.
its kinda fun cuz its like puzzle solving.
Answer:
The ratio represents they are 12 snails for every 19 sea creatures in Joe's tank.
Step-by-step explanation:
In total, there are 19 sea creatures in the tank. And since there are 12 snails in the tank, the ratio represents that there are 12 snails for every 19 sea creatures in Joe's tank.
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Hope it helps!
Oreana's 150 g bag of trail mix is x% raisins. Brandon's 250 g bag of trail mix is y% raisins. They combine the two mixes together in one bowl.
Write an expression which shows how many grams of raisins are in the bowl
The expression which shows how many grams of raisins are in the bowl will be
(0.01x) * 150 + (0.01y) * 250
What is the expression that shows the raisin?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The expression which shows how many grams of raisins are in the bowl will be:
= (x% × 150) + (y% × 250)
= (0.01x) * 150 + (0.01y) * 250
This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.
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