The amount of water after x minutes is equal in both pools.
What is a Linear equation in one variable?
A univariate linear equation is an equation of the form ax + b = 0, where a and b are two integers, x is a variable, and there is only one solution.
For example, 2x+3=8 is a linear equation in one variable.
The given equation is 5000 - 50x = 4800 - 30x.
solving for 'x',
5000 - 50x = 4800 - 30x
5000 - 4800 = 50x - 30x
200 = 20x
x = 200/20
x = 10
The amount of water after 10 minutes in Pool A will be = 5000 - 50(10)
= 5000 - 500
= 450 liters
The amount of water after 10 minutes in Pool B will be = 4800 - 30(10)
= 4800 - 300
= 450 liters.
Hence, the amount of water will be the same in both pools.
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What is the area of the shaded portion of the parallelogram? Dimensions are in centimeters.
The area of the shaded portion of the parallelogram is 35.43 centimeter square
The base of the parallelogram = 8 centimeter
The height of the parallelogram = 6 centimeter
The area of the parallelogram = Base × Height
= 8 × 6
= 48 centimeter square
The radius of the circle = 2 centimeter
The area of the circle = π × [tex]r^2[/tex]
= π × [tex]2^2[/tex]
= 12.57 centimeter square
The area of the shaded region = The area of the parallelogram - The area of the circle
Substitute the values in the equation
= 48 - 12.57
= 35.43 centimeter square
Hence, the area of the shaded portion of the parallelogram is 35.43 centimeter square
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h(x)=x²+3x-2; 12-h(7)
How would I input 12-h(7) in place of x to solve this function?
Solve for 12 - h(7)
First find h(7)
h(7) = 7^2+3(7)-2
h(7) = 49 + 21 - 2
h(7) = 68
12 - 68 = - 56
12 - h(7) = -56.
I'm not sure if the question wants h(-56) as well, but just plug that in.
H(-56)=2966
hope this helps :)
x-1
3
If-
A) 2
B) 4
C) 9
D) 10
F.
= k and k = 3, what is the value of x ?
Answer:
D
Step-by-step explanation:
Multiply both sides by 3
x − 1 = 9
Add 1 to both sides
x = 10
Find the geometric mean between 2 and 19. Write your answer in radical form or round to the nearest tenth, if
necessary.
Answer: 6.2
Step-by-step explanation:
Geometric Mean = √( 2 x 19 ) = 2√38 = 6.1644
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12. What is the remaining credit after 81 minutes of calls?Calling Time In MinutesRemaining Credit In Dollars$
The remaining credit after 81 minutes of calls is $17.04.
Given that, the remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Let x be the number of minutes and y be the number of dollars.
According to question, the ordered pair is
(44, 22.96) and (68, 19.12)
The point slope form is (y-y1)=m(x-x1)
Slope = (y2-y1)/(x2-x1)
= (19.12-22.96)/(68-44)
= -3.84/24
m= -0.16
Put m= -0.16 and (x1, y1)=(44, 22.96), we get
(y-22.96)=-0.16(x-44)
When x=81
y-22.96=-0.16(81-44)
⇒ y-22.96=-0.16×37
⇒ y-22.96=-0.16×37
⇒ y-22.96=-5.92
⇒ y=-5.92+22.96
⇒ y=17.04
Therefore, the remaining credit after 81 minutes of calls is $17.04.
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What is an equation of the line that passes through the points (-2,7) and (-8,4)
Answer: y = (1/2)x + 8
Step-by-step explanation:
Slope: (4-7)/(-8--2) = (-3)/(-6) = 1/2
y = (1/2)x + b
7 = (1/2)-2 + b
7 = -1 + b
8 = b
y = (1/2)x + 8
a lottery consists of selecting 5 numbers out of 45 numbers. you win $10 if exactly three of your 5 numbers are matched to the winning numbers chosen. what is the probability of winning the $10? round your answer to six decimal places.
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
first number: 1/25 chance because we only want 1 out of the 25 possibilities.Second number: 1/24 because 1 number was already taken out.Third: 1/23Fourth: 1/22Fifth: 1/21Sixth: 1/20The chance of all of these events happening right after another is 1/25 x 1/24 x 1/23 x 1/22 x 1/21 x 1/20 = 1/127512000, or about 1 in a hundred million.learn more about probability click here:
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Find the diagonal of a rectangle with sides 7 in and 24 in
You can use the hypotenuse formula, e.g., from the Pythagorean theorem calculator, to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w², and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root: d = √ (l² + w²).
6.2 X ( -2.7) thats the qeustion
Answer:
Hi !!!
Step-by-step explanation:
6.2×(-2.7)
=-16.74
= -1.674×10¹
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Would the reaction rate on graph B of Model 2 ever reach a maximum level? Justify your answer.
By applying the concept of rate of a reaction, The graph B never saturates because the enzyme is always in excess.
What is the enzyme substrate reaction?
The enzyme is called a catalyst as it has an active site where the substrate can bind and convert into the product. Here in the graph the enzyme is amylase, and its substrate is starch. When there is an excess of enzymes in the solution, they can convert it into a product till substrates are available. If the substrate runs out, the reaction will come stop.
As per the concept of rate of a reaction, The graph B never saturates as the enzyme in the reaction is always in excess. These excess enzymes present will convert the starch into simple glucose molecules. Hence, there will be no upper limit, as both are in abundance.
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each week, between $30$ and $50$ students show up for an archery class run by betty and wilma. usually the students break up into groups of equal size for target practice. however, this week, betty noticed that she could not break the students up into multiple groups of equal size. wilma noticed that if she and betty both joined the students in practicing, they still could not break the archers up into groups of equal size. how many students showed up to the archery class this week?
This week 41 students showed up to the archery class that cannot be broken into multiple groups of equal sizes.
Prime numbers are numbers that cannot be divisible by any other numbers besides 1 and itself. Between 30 and 50, there are 4 prime numbers, which are 31, 37, 41, and 43. So, these prime numbers cannot be divided into equal sizes of multiple groups. But by adding 2 (If Betty and Wilma join the students) in 31, 37, and 43 we get composite numbers that can be divided into multiple groups of equal sizes.
So, 41 students showed up to the archery class this week and as 41 is a prime number, Betty and Wilma could not break the archers up into groups of equal size, and even if Betty and Wilma joined the students there will be 43 archers which even is a prime number and thus cannot be divided.
41 is the only possible number of students between 30 and 50 which cannot be broken into groups of equal sizes even if Betty and Wilma join the archers.
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what is the mean of 10,4,2,4
Answer:
5
Step-by-step explanation:
10+4+2+4=20
20/4=5
The mean is five.
Answer:
Mean = 5
Step-by-step explanation:
Mean = ( Sum of Data Points ) / ( Number of Data Points )
Sum of Data Points = 10 + 4 + 2 + 4 = 20
Number of Data Points = 4
Mean = 20 / 4 = 5
Glad to Help
What fraction is equivalent to the decimal and percent below? Enter your
answer in simplest form, using the slash (/) as the fraction bar.
Fraction Decimal Percent
?
0.33
33.3%
Answer:
Step-by-step explanation:
1 / 3
Reason being: 100 / 3 = 33.333333333
Lat week, Lia old 20 hand-engraved watch band, earning a total profit of $105. 0. She plan to make 50 engraved watch band to ell at the community art fair. If he ell all 50 watch band, how much profit can Lia expect to earn?
$
If Lisa sells 50 watch bands, she gets a profit of $262.50.
A unitary method is defined.
Mathematicians use the unitary method to solve problems by first determining the value of a single unit, or 1, (by dividing), and then determining the necessary value by multiplying the value of the single unit.
We must first ascertain the cost of one watch band.
To determine this, we simply divide $105 by 20, which equals $5.25.
We can divide $5.25 by 50 because she sells all 50 watchbands.
50 multiplied by $5.25 equals $262.50.
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While shopping with her husband (see practice e), Mrs. Garantua
bought 2 garden hoses (one to use as a neclace and the other to
use a leash for her pet whatchamacallit) and 2 giant flowerpots
(both to use as summer hats). If the hoses cost $30 each, and
the bill for all the items (hoses and flowerpots combined) was
$96, how much did each flowerpot cost?
Answer:
$18
Step-by-step explanation:
She bought 2 garden hoses which both cost $30, so she already spent $60. The subtract 60 from 90, and get $36 left. Divide that by 2 because she buys 2 flower pots, and you arrive at the answer of $18 per flower pot.
Rewrite in simplest terms: -5(-6k-6)-(-9k-10)−5(−6k−6)−(−9k−10)
help please n ty
The value of the expression -5(-6k-6)-(-9k-10) in simplest terms is 39k + 40
What is an algebraic expression?An algebraic expression can be described as an expression that is made up of terms, variables, coefficients, factors and constants.
These expressions are also known to be composed of certain mathematical operations, such as;
SubtractionDivisionMultiplicationBracketAdditionParenthesesWe have the expression;
-5(-6k-6)-(-9k-10)
expand the bracket
-5(-6k - 6) + 9k + 10
collect like terms
30k + 30 + 9k + 10
Add the like terms
39k + 40
Hence, the value is 39k + 40
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A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer:
$2825,32
Step-by-step explanation:
Value of the car after 1 year
$3000 * 3% = 3000 * 0.03 = 90
3000 - 90 = $2910
Value of the car after 2 year
$2910 * 3% = 2910 * 0.03 = 87.3
2910 - 87.3 = $2912,7
Value of the car after 3 year
$2912,7 * 3% = 2912,7 * 0.03 = 87.381
2912,7 - 87.381 = $2825,319
"Round to the nearest cent"
$2825,32
standard automobile license plates in a country display 3 numbers, followed by 2 letters, followed by 2 numbers. how many different standard plates are possible in this system? (assume repetitions of letters and numbers are allowed.) there are different standard plates possible in this system.
The system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
Define the term permutation?The number of potential arrangements for a given set is assessed mathematical terms, but this procedure is referred to as permutation. The arrangement's order is essential when using permutations.For the stated data;
Standard car license plates in a nation typically have 3 digits, 2 letters, and 2 numbers.
There are total 9 digits (0 - 9).
There are total 26 letter (A - Z)
Repetitions of letters and numbers given allowed.
Thus, numbers and the letters ca be arranged as;
1st place = 9 ways.
2nd place = 9 ways.
3nd place = 9 ways.
4th place = 26 ways.
6th place = 26 ways.
7th place = 9 ways.
8th place = 9 ways.
Total ways = 9×9×9×26×26×9×9
Total ways = 39917124
Thus, the system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
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A person invests 4500 dollars in a bank. the bank pays 7% interest compounded annually. to the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14900 dollars?
Answer:
A = Ao * (1+ i)^n amount Ao invested for n yrs at i/yr
14900 = 4500 (1.07)^n
3.311 = (1.07)^n
log 3.311 = n log 1.07 = n* .0294
n = log 3.311 / .0294 = .52 / .0294 = 17.6 yrs
Check:
Money will double about very 70 / 7 = 10 yrs
At 10 yrs around 9000 return
At 20 yrs 18,000 return - result appears reasonable
Need help please look at picture
Answer:
the three dots represent 'therefore'
Step-by-step explanation:
as shown in picture uploaded ^^
help meeeeeeeeeeeeeeeeee please
Answer:
x + x + 2 = x + 3
2x + 2 = x + 3
x = 1
x + 2 = 3
x + 3 = 4
so what is 9/4 divided by 6/5
Answer:
45/20
Step-by-step explanation:
Answer:
9/4 divided by 6/5 is 15/8
Step-by-step explanation:
9/4 ÷ 6/5 turns into 9/4 × 5/6 which is the reciprocal
9/4 × 5/6 = 45/24
Divide the numerator and denominator by 3 to get 15/8
15/8 is in its simplest form
What is the slope of the line created by this equation?
Round your answer out to two decimal places
6x + 7y = 5
Answer:
-0.86
Step-by-step explanation:
What is the slope of the line created by this equation? Round your answer out to two decimal places. 6x + 7y = 5
_____________________________________________
Slope intercept form solves for y:
y = mx + b when m = slope and b = y-intercept
First, solve for y:
6x + 7y = 5
subtract 6x from both sides:
6x + 7y - 6x = 5 - 6x
7y = 5 - 6x
divide both sides by 7:
7y/7 = (5 - 6x)/7
y = 5/7 - 6/7x
rearrange right side:
y = - 6/7x + 5/7
Back to the equation: y = mx + b when m = slope and b = y-intercept
your slope is -6/7
in decimal form, rounded to two digits: -0.86
how many ways are there to put $4$ balls into $3$ boxes, given that the balls are not distinguished and neither are the boxes?
Answer:
Step-by-step explanation:
think that there are 15 ways ... call the boxes A, B, and C.
You could put all four b***s into either box A, or box B, or box C ---> 3 ways.
You could put three ball into one box and the other ball into another box:
-- 3 into A, 1 into B, 0 into C; or 3 into A, 0 into B, 1 into C; or 1 into A, 3 into B, 0 into C; or 1 into A, 0 into B, 3 into C; or 0 into A, 3 into B, 1 into C; or 0 into A, 1 into B, 3 into C ---> 6 ways
You could put two balls into one box and the other two balls into another box:
-- 2 into A, 2 into B, 0 into C; or 2 into A, 0 into B, 2 into C; or 0 into A, 2 into B, 2 into C ---> 3 ways.
You could put two b***s into one box and one ball into each of the other two boxes:
-- There are three boxes that could get the two b***s ---> 3 ways
Total: 3 + 6 + 3 + 3 = 15 ways.
Keilantra read 16 1/2 pages in 3/4 of an hour. If she continues reading at the same rate, how many pages will she read in an hour?
Answer: Around 40 pages
Step-by-step explanation: Im not sure if this is the answer but from what I can do this would be the answer
Answer:
she will read 22 pages :)
Step-by-step explanation:
Convert 3/4 of an hour into minutes - 60 x 3/4 = 45so kellantra is reading 16.5 pages every 45 minutes kellantra has 15 minutes left before an hour has passed, so divide 16.5 by 3 to work how how much she reads in 1/4 of an hour 16.5/3 = 5.5 pages per 1/4 houradd your values: 16.5 + 5.5 = 22 pages!a manufacturer wants to increase the absorption capacity of a sponge. based on past data, the average sponge could absorb 3.5 ounces. after the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. what is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
Reject a null hypothesis because computed t is higher than 2.821 is the decision rule.
Define the term hypothesis?The hypothesis is a succinct statement of the researcher's estimate of the findings of the study, that may or may not be confirmed by the results, in such a scientific experiment or survey. The scientific method's fundamental step is hypothesis testing.A statistical hypothesis known as a null hypothesis asserts because no statistical significance can be found in a collection of provided observations.For the given question;
Test hypothesis:
H₀; μ = 3.5
Upper tailed test:
Hₐ; μ > 3.5
Significance value; α = 10.
Then, degree of freedom.
Df = α - 1
Df = 10 - 1
Df = 9
The critical value;
t(₀.₀₁, ₉) = 2.821
Rejection region;
Rejected H₀ for t > 2.821
Thus, reject a null hypothesis because computed t is higher than 2.821 is the decision rule for the absorption amount of the sponge.
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Line g has an equation of y= 1 3 x–1. Parallel to line g is line h, which passes through the point (10,2). What is the equation of line h?
need answer ASAP
Work out the 3rd term.
in the
geometric sequence
generated by 5n
The third term in the sequence generated by 5n is 15.
According to the question,
We have the following information:
The sequence is given by the formula 5n.
In this case, n represents the number of the term.
(Note that the sequence generated by this formula can not be a geometric sequence because the common ratio of these terms is not the same.)
So, we have to find the 3rd term of this sequence. Then, we will find the value of this sequence by putting the value of n as 3.
So, we have the following expression:
5*3
15
Hence, the third term in the sequence generated by 5n is 15.
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This shows a figure.
What is the measure of angle n?
65\degree65°
70\degree70°
110\degree110°
115\degree115°
To find the value of n we first have to find the value of angle m. because we know the sum of angle m and angle n would be equal to 180 degrees as they both lie on a straight line. to find angle m we have to use the angle sum property of a triangle which says the sum of all the internal angles of a triangle is equal to 180 degrees.
so using the angle sum property,
65+45+m = 180
m= 180-65-45
m=70
now we know m is 70 degrees
for n,
m+n = 180 -(i)
putting m=70 in equation (i)
70 + n = 180
n = 180-70 = 110 degree
nine out of ten student prefer math class over lunch. how many student do not prefer math if 200student were asked
Answer:
Step-by-step explanation:
20? lol
