Answer: READ BELOW
Step-by-step explanation:
To divide decimals, you can follow these steps:
1. Move the decimal point in the divisor (the number you're dividing by) to the right, counting the number of places you move it.
2. Move the decimal point in the dividend (the number you're dividing into) the same number of places to the right.
3. Divide the numbers as if they were whole numbers.
4. Place the decimal point in the quotient (the result) the same number of places from the right as the number you counted when moving the decimal points in step 1 and 2.
For example:
To divide 12.5 by 2.5, you would move the decimal point in 2.5 two places to the right to get 25, and move the decimal point in 12.5 two places to the right to get 1250. Then divide 1250 by 25 to get 50. Finally, place the decimal point two places from the right in the quotient 50 to get the final answer of 0.50.
Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible
quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest
he earns during t = 0 to t = 1. Find the exact value of R.
Answer:
8%
Step-by-step explanation:
We can start solving the problem by using the formula for compound interest:
A =[tex]P(1+\frac{R}{n})^{nt}[/tex]
Where A is the final amount, P is the initial principal, R is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.
Given that the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. We can use this information to set up an equation as follows:
[tex]P(1+\frac{R}{4})^{2}[/tex] = [tex]1.0816*P(1+\frac{R}{4})[/tex]
We can simplify this equation by canceling out the P and the (1+R/4) on the right side:
[tex](1+\frac{R}{4})[/tex] = 1.0816
We can then solve for R:
[tex]\frac{R}{4}[/tex]=[tex]\sqrt{(1.0816)-1}[/tex]
R = [tex]4(\sqrt{(1.0816)-1)}[/tex]
R ≈ 0.08, is the exact value of R.
So, Mr. Saver's nominal interest rate is 8%.
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two-thirds times g times 10.
The mathematical expression, for the given statement is 20g/3
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is a statement, two-thirds times g times 10.
Converting into mathematical expression,
2/3 of g = 2g/3
And,
2/3 of g of 10
= 2g/3 × 10
= 20g / 3
Hence, the mathematical expression, for the given statement is 20g/3
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Estimate the area between the x-axis and the curve y = 2x' +1 on the interval (0, 2). Be sure to draw the correct picture for each approximation 5) Use a left hand approximation. a) Use 4 boxes b) Use 8 boxes
Using a left-hand approximation means that we will use the left endpoint of each interval to approximate the area under the curve.
a) Using 4 boxes:
The interval from 0 to 2 can be divided into 4 equal parts, so each part has a length of 0.5.
The height of each box will be the value of y at the left endpoint of each interval.
The area of each box can be calculated as follows:
For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.5 * 1 = 0.5.
For the second box, the left endpoint is (0.5, 2) and the height is 2(0.5) + 1 = 2.5. The area is 0.5 * 2.5 = 1.25.
For the third box, the left endpoint is (1, 3) and the height is 2(1) + 1 = 3. The area is 0.5 * 3 = 1.5.
For the fourth box, the left endpoint is (1.5, 4) and the height is 2(1.5) + 1 = 4.5. The area is 0.5 * 4.5 = 2.25.
The total area is the sum of the areas of all the boxes, so the total area is 0.5 + 1.25 + 1.5 + 2.25 = 5.
b) Using 8 boxes:
The interval from 0 to 2 can be divided into 8 equal parts, so each part has a length of 0.25.
The height of each box will be the value of y at the left endpoint of each interval.
The area of each box can be calculated as follows:
For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.25 * 1 = 0.25.
For the second box, the left endpoint is (0.25, 2.5) and the height is 2(0.25) + 1 = 2.5. The area is 0.25 * 2.5 = 0.625.
For the third box, the left endpoint is (0.5, 3) and the height is 2(0.5) + 1 = 3. The area is 0.25 * 3 = 0.75.
And so on, for all 8 boxes.
The total area is the sum of the areas of all the boxes, so the total area is 0.25 + 0.625 + 0.75 + ... + 3.375 = 5.125.
So, the area between the x-axis and the curve y = 2x + 1 on the interval (0, 2) can be approximated as 5 or 5.125 depending on the number of boxes used.
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From a point within a triangle, Segments are drawn to the vertices. A necessary.and sufficient condition that the three triangles formed have equal areas, is that the point be:
(A) such that the three angles formed each have a
measure of 120°
(B) the centre of the inscribed circle
(C) the centre of the circumscribed circle
(D) the intersection of the medians
Option D is the correct Answer. A necessary and sufficient condition that the three triangles formed have equal areas, is that the point be the intersection of the medians.
To divide a triangle into three triangles of equal area is to find the centroid the point where the medians intersect. After determining the centroid point G below, construct the segments connecting the vertices to the centroid. The three triangles created are of equal area.
So from a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be the intersection of the medians of the triangle.
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Please help me with this question.
The measure of angle t is (d) 103 degrees
How to determine the measure of angle tFrom the question, we have the following parameters that can be used in our computation:
The triangle
Using the law of cosines, we have the following equation:
t² = x² + y² - 2xy * cos(T)
Substitute the known values in the above equation, so, we have the following representation
44² = 32² + 24² - 2 * 24 * 32 * cos(T)
Evaluate the products and exponents
1936 = 1600 - 1536 * cos(T)
So, we have
cos(T) = -336/1536
Divide
cos(T) = -0.21875
Take the arccos of both sides
T = 103
Hence, the angle is 103 degrees
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In ΔTUV, t = 820 inches, mm∠U=132° and mm∠V=25°. Find the length of u, to the nearest inch.
The measure of the length of u for the condition is 1560 inches (approx).
What are the laws of sines?The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.
Given ΔTUV
t = 820 inches
∠U = 132°
∠V = 25°
and ∠T = 180 - 132 - 25
∠T = 23°
so according to the law of sines
[tex]\frac{SinT}{t} = \frac{SinU}{u}= \frac{SinV}{v}[/tex]
so u = t*(SinU/SinT)
u = 820(Sin132/sin23)
u = 820(1.9019)
u = 1559.58 inches = 1560 inches (approx)
Hence the value of u is 1560 inches (approx).
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what is the answer to the question y^2+4y
The equation y^2+4y represents a parabola that is open upward. The general form of a quadratic function is y = ax^2 + bx + c.
In this case, the coefficient of the x^2 term is 1, the coefficient of the x term is 4, and the constant term is 0.
This equation can be factored as y(y+4) = 0.
This equation is satisfied by y = 0 and y = -4.
Therefore, the solutions of y^2+4y = 0 are y = 0 and y = -4.
let a denote the event thsat moe than 1000 wells are formed, let b donate the event that that the well failed, let c denote that less than 500 wells are formed. what so the probabilyt of b given a g
(a) The probability of a failure given there are more than 1,000 wells in a geological formation is 0.1001.
(b) The probability of a failure given there are fewer than 500 wells in a geological formation is 0.0852.
(a) We have to determine the probability of a failure given there are more than 1,000 wells in a geological formation.
P(B∣A) = Total number of failed wells more than 1000 wells/Total number of wells with 1000 failed wells
P(B∣A) = (180 + 443 + 60)/(1685 + 3733 + 1403)
P(B∣A) = 683/6821
P(B∣A) = 0.1001
(b) We have to determine the probability of a failure given there are fewer than 500 wells in a geological formation.
P(B∣C) = Number of failed well/Number of failed wells with total less that 500 wells
P(B∣C) = (2 + 14 + 44 + 3)/(28 + 363 + 309 + 39)
P(B∣C) = 63/739
P(B∣C) = 0.0852
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The complete question is:
Consider the well failure data in the table below. Let A denote the event that the geological formation of a well has more than 1000 wells, let B denote the event that a well failed, and let C denote the event that the geological formation of a well has fewer than 500 wells.
(a) What is the probability of a failure given there are more than 1,000 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣A)=
(b) What is the probability of a failure given there are fewer than 500 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣C)=
Students’ GPAs and scores on standardized tests (SATs and ACTs) are entered into a formula that calculates an “admissions index” score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state. In this context, what percentile does the top 12% represent?
The percentile of the top students will be 88%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state.
The percentile of the top student is given as,
⇒ 100% - 12%
⇒ 88%
The percentile of the top students will be 88%.
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A new sidewalk will be 4 feet wide, 140 feet long, and filled to a depth of 6 inches ( 0.5foot) with concrete. How many cubic yards of concrete are needed?
The required volume of concrete in cubic yards to make the sidewalk is 124.4444 yards³
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Dimensions of the side walk 4 ft. 140 and 6 feet.
We know the volume of the rectangular cuboid side walk will be given by
V= 4×140×6
=3360 ft³
Thus the volume of concrete that will be required to make the side walk is 3360 ft³
In yards³ we know
1 cubic foot= 0.037037 yards cube
∴ 3360ft³=124.4444 yards³
Hence, The required volume of concrete in cubic yards to make the sidewalk is 124.4444 yards³
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HELPP PLS FAST MATH MATH MATH
The answer to each part is given above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the functions as follows -
p(x) = - 5x + 5
q(x) = - 4x - 2
We can write -
(p о q)(5) = (- 5x + 5)(- 4x - 2)
(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2)
(p о q)(5) = 20x² + 10 - 20x - 10
(p о q)(5) = 20x² - 20x
(p о q)(5) = 20 x 25 - 20 x 5
(p о q)(5) = 500 - 100
(p о q)(5) = 400
(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2) = (q о p)(5) = 400
(q о p)(5) = 400
Therefore, the answer to each part is given above.
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The numeral preceding 100000 base 2
One less than the given number is known as preceding number whereas one more than the given number is the succeeding number.
The logics followed in order to find them:
Base numbers work exactly the same as base 10 numbers (the ones we use on a daily basis).
Take for example, in a decimal system, we have 10 digits available:
0,1,2,3,4,5,6,7,8,9.
When counting, when we get to the 9, we start over again, but writing a 1 to the left.
0,1,2,3,4,5,6,7,8,9,10,11,12....20,21,22,23....,90,91,92,93,94,95,96,97,98,99,10
When reaching 99, we have no more digits to use, so we start the count again and go from 99 to 100.
The same works with any other base number, take for example the base 7 number.
When counting in base 7, we only have 7 digits available: (0,1,2,3,4,5,6) So when 0_{7},each the digit 6, we go immediately to 10, like this:
It went from 6 to 10 and from 16 to 20. This is because in base 7, there is no digits from 7 to 9, so we have directly to 20.
So, if working with decimal numbers, the previous value for 640 would be 639, but notice that in base 7,
There is no such thing as the digit 9, so the greatest digit we can use there 6,
Therefore, the previous value for the number would be. The next number would be because the 1 does exist for a base 7 system.
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Complete question :-
What is the numeral preceding and succeeding each of the following.
A) 640 base 7
B) 100000 base 2
C) 555 base 6
D) 100 base 5
E) 10000 base 4
F) 405 base 6
Lucas earns R875,00 in five working days how much would he earn in 12 working days,at the same rate
Answer:
Below
Step-by-step explanation:
12/5 * 875 = R 2 100 000
to see how this works, set up a ratio
5 is to 875 000 as 12 is to x
5 / 875 000 = 12/x
x = 12/5 * 875 000
Answer:
R210,000
Step-by-step explanation:
875,00 : 5 days
x :12 days
cross multiply:
87500*12 = 1050000
5*x = 5x
divide:
1050000/5 = 210000
Christine received a $1500 bonus. She decided to invest it in a 5-year certificate of deposit (CD) with an annual interest rate of 1.44% compounded annually. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) (b) Assuming no withdrawals are made, how much money is in Christine's account after 5 years? How much interest is earned on Christine's investment after 5 years? X S
a) Assuming Christine makes no withdrawals, her $1,500 investment in a 5-year certificate of deposit with an annual interest rate of 1.44% compounded annually, will be worth (future value of) $1,611.16 after 5 years.
b) The total interest earned on Christine's investment after 5 years is $111.16.
What is the future value?The future value represents the compounded present value.
The future value can be computed using an online finance calculator.
N (# of periods) = 5 years
I/Y (Interest per year) = 1.44%
PV (Present Value) = $1,500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $1,611.16
Total Interest = $111.16
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find f(g(1)) if f(x)=4x and g(x)=2x+5
Evaluating the composition of functions in x = 1 gives:
f(g(1)) = 28
How to find the composition of functions?Here we have the two functions:
f(x) = 4x
g(x) = 2x + 5
And we want to find to find the composition f(g(x)), we will get:
f(g(x)) = 4*g(x)
Replacing g(x) there we will get:
f(g(x)) = 4*(2x + 5)
= 8x + 20
Now we can evaluate that in x = 1, then we will get:
f(g(1)) = 8*1 + 20 = 28
That is what we wanted to find.
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seven less than the product of 3 and a number is equal to 8 use the variable y for the unknown number
Answer:
y = 5
Step-by-step explanation:
3y - 7 = 8 Add 7 to both sides
3y - 7 + 7 = 8 + 7
3y = 15 Divide both sides by 3
y = 5
One-fourth of the animals at the shelter are cats. If there are 660 animals at the shelter how many are cats?
Answer:
165 of the animals at the shelter are cats.
Step-by-step explanation:
If one-fourth of the animals at the shelter are cats and there are 660 animals at the shelter, to get the number of cats you divide the total number of animals by the percentage of cats.
660 / 4 = 165
What is the value of x in 2(5^x) =14?
A. log 7 - log 5
B. log 5/log 7
C. log 2
D. log 7/log 5
Help pls I’m in the test rn..
Answer: it would be B:log 5/log 7
Step-by-step explanation:
Interpret the slope.
f(x)=4+x
The slope is
Therefore , the solution of the given problem of slope comes out to be
line's equation is y =.1333 x + 1.55.
What is meant by slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).If you look at the line from left to right, a line that is moving up will have a positive slope and a line that is moving down will have a negative slope.
Here,
Given : f(x) =4 +x
The line's "intercept" of the y-axis marks the location of the y-intercept. It also makes sense because a player with a 25 cm heel to toe measurement is about 1.55 metres tall. This is most likely.
Any line has the equation y=mx+b (m=slope, b=y-intercept).
Finding two spots on this line where it crosses will reveal the slope of the line. I'll use the numbers (25.5, 1.6) and (26.25,1.7).
=> (y(2)-y(1)) / (x(2)-x(1))
=> m 1.7 - 1.6 / 26.25 - 25.5
=>.1/.75 =.13333 is the formula to calculate the slope.
At roughly 1.55m, this line crosses the y-intercept.
This line's equation is y =.1333 x + 1.55.
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In Exercises 15-18, each linear equation is in the form y= mx + b. Identify m and b.
15. y = 52 +8
16. y=-2x - 6
Find the most important variable in the problem.
A bag of marbles is full with 20 marbles, 12 of which are yellow. How many
are not yellow?
• A. the number of marbles that are not yellow
B: the number of yellow marbles
• C. the total number of marbles
There are 20 marbles, and 12 of them are yellow; therefore, the number of yellow marbles does not equal the number of marbles, nor does the number of yellow marbles equal the number of yellow marbles because they are yellow.
What might possibly be the smallest amount of marbles in the bag *?I There can only be 31 marbles in the bag, since 30 marbles is the most number that each person can have equitably, plus one extra marble. As a result, the first response is A. Since 60 is divisible by 2, 3, and 5, plus 1 (leaving 1 remaining), 61 might also be a conceivable number of marbles in the bag.
How do you calculate the likelihood of a ball?The likelihood of selecting a ball from a bag is calculated by dividing the total number of balls by the quantity of that color. As a result, the likelihood of a red ball in the first case is 3/9, or 1/3. The likelihood of selecting a second ball if that ball is now eliminated is 2/8 or 1/4.
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Rahul is 1.45 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
If Rahul is 1.45 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. the height of the tree is 9.43m.
How to find the height?Let x represent the height
x /1.45 = 31.55 -26.7
Cross multiply
x = 31.55 × 1.45 / 4.85
x = 45.7475 /4.85
x = 9.43
Therefore the height is 9.43.
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Solve ◇ABC if A - 90º, B = 44°, and c = 17. 12pt v Paragraph
The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .
What is a Triangle ?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The properties of a Triangle are :
Three sides and three angles make up a triangle.A triangle's total angles are always 180 degrees.A triangle's outside angles are always a sum of 360 degrees.The total of the parallel interior and exterior angles is additional.The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.
In triangle ΔABC
∠B = 44° and ∠C = 17°
So, The sum of angles of a triangle is 180°
Therefore,
∠A + ∠B + ∠C = 180°
⇒∠A + 44° + 17° = 180°
⇒∠A = 180° - 61°
⇒∠A = 119°
The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .
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King Arthur had 30 3030 gold coins and 43 4343 silver coins in his pocket. How many coins did he have in all?
Answer:
737373
Step-by-step explanation:
You just add them together? Am I missing something?
Pete's Plumbing charges 25x + 50 dollars for x hours of work. Plugged Pipes charges 50x + 75
dollars for the same number of hours.
a. Write an expression in simplest form to represent how much more Plugged Pipes costs
than Pete's Plumbing for x hours of work.
b. If they each work for 2 hours, how much more expensive is Plugged Pipes?
Answer:
a. To find out how much more expensive Plugged Pipes is than Pete's Plumbing, we need to subtract Pete's Plumbing's cost from Plugged Pipes' cost. The expression for the difference in cost is:
(50x + 75) - (25x + 50) = 25x + 25
This is the simplified form of the expression that represents the difference in cost.
b. If they each work for 2 hours, we can substitute x = 2 into the expressions for their costs and compare the results:
Plugged Pipes: 50(2) + 75 = 125 dollars
Pete's Plumbing: 25(2) + 50 = 100 dollars
So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.
Step-by-step explanation:
Sure, here is a step-by-step explanation of how to find the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work:
Start with the expression for the cost of Plugged Pipes: 50x + 75Subtract the expression for the cost of Pete's Plumbing: 25x + 50To do this, we need to distribute the subtraction (-) sign to the x and the constant terms: (50x + 75) - (25x + 50)Next, we'll combine like terms: 50x - 25x + 75 - 50 = 25x + 25The final expression, 25x + 25, represents the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work.To find out how much more expensive Plugged Pipes is for 2 hours of work we can substitute x = 2 into the expression for their costs and compare the results:
Plugged Pipes: 50(2) + 75 = 125 dollars
Pete's Plumbing: 25(2) + 50 = 100 dollars
So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.
Suppose you take a random sample of size 25 from a population with mean of 120 and a standard deviation of 15. Your sample has a mean of 115 and a standard deviation of 13.8. Which of the following has a mean of 120 and a standard deviation of 3?answer choicesthe distribution of the populationthe distribution of the sample datathe sampling distribution of the sample mean.the sampling distribution of the population mean.No important distribution related to this situation has the given mean and standard deviation.
After taking the random sample, the following has the mean sample of (c) the sampling distribution of the sample mean.
A random sample is a group of people chosen at random, all with the same probability, from a larger group of people as mentionedinstatistics. It makes sure that the results you get from your sample should be close to what you would have gotten if you measured the entire population.
All units in the population have an equal chance of being chosen using the simplest random sample. Sampling should completely eliminate any signs of bias. Every person in the big population set has the same chance of being chosen because the people who make up the subset of the bigger group are selected at random.
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The flooring will cost $2 per square foot. How much would it cost Suzie to lay this flooring so it fully covers the floor of room?
Answer:
To find out how much it would cost Suzie to lay the flooring so it fully covers the floor of room, you need to know the area of the room's floor and the cost per square foot of the flooring.
If the flooring will cost $2 per square foot, and if the area of the room's floor is x square feet. Then the total cost will be $2x.
Without knowing the area of the room's floor, it is impossible to determine the cost of the flooring.
In art class students are mixing black and white paint to make gray paint. Hai mixes 6 cups of black and 5 cups of white.Arianna mixes 6 cups of black and 1 cup of white paint. Whose gray will be darker?
36÷9643 what is the solution and answer
Answer:
0.0037
Step-by-step explanation:
Because 36/9643 cannot be simplified down any further, the only other way to describe it is as a decimal which is ~0.0037.
2. Sarah and James are selling hot dogs and
hamburgers at the State Fair. Sarah sold 4 hot
dogs and 7 hamburgers for a total of $68. James sold 7 hot dogs and 3 hamburgers foratotal of
$67. How much do the hot dog and hamburger
cost?
Step-by-step explanation:
115 its rhe reuth i rhibk lol
Answer:
To find the cost of a hot dog and hamburger, we can set up a system of equations based on the information given. For example, let x be the cost of a hot dog and y be the cost of a hamburger. Then we have:
4x + 7y = 68 (equation 1)
7x + 3y = 67 (equation 2)
We can use substitution or elimination methods to solve the system of equations.
Substitution method:
Solve equation 1 for y in terms of x: y = (68 - 4x)/7
Substitute this expression into equation 2: 7x + 3((68 - 4x)/7) = 67
Simplifying and solving for x: 7x + 3(68 - 4x)/7 = 67
7x + 204 - 12x = 469
-5x = -401
x = 80
Substitute x = 80 back into equation 1: 4(80) + 7y = 68
320 + 7y = 68
7y = -252
y = -36
Therefore, the cost of a hot dog is $80, and the price of a hamburger is $-36 (which is not possible, it could be a typo or mistake in the given information)
Step-by-step explanation:
