The cost of each ream of paper is $4.5 and that of DVD is $5.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
Given that,
The price for 17 reams of paper and 12 DVDs is $136.50.
And, the price for 8 reams of paper and 21 DVDs is $141.
Suppose the cost of each ream of paper be x.
And, the cost of each DVD be y.
THen, the following equations can be made for the two cases,
17x + 12y = 136.50 (1)
8x + 21y = 141 (2)
Solve these equations by multiplying equation (1) by 7 and (2) by 4 and then subtracting them as,
7(17x + 12y) - 4(8x + 21y) = 7 × 136.50 - 4 × 141
=> 87x = 391.5
=> x = 4.5
Substitute x = 4.5 in equation (1) to get,
17 × 4.5 + 12y = 136.50
=> 12y = 136.50 - 76.50
=> 12y = 60
=> y = 5
Hence, the cost of each ream of paper and each DVD are $4.5 and $5 respectively.
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The Rogers family and the Walker family each used their sprinklers last summer. The water output rate for the Rogers family's sprinkler was 30 L per hour. The
water output rate for the Walker family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 45 hours, resulting in a total
water output of 1150 L. How long was each sprinkler used?
Rogers family's sprinkler:
hours
Walker family's sprinkler: hours
The Rogers family's sprinkler worked for 25 hours and Walker family's sprinkler worked for 20 hours
The water output rate of Roger's family's sprinkler = 30 liter per hour
The water output rate of Walker family's sprinkler = 20liter per hour
Total number of hours combined = 45 hours
Consider the number of hours that Rogers family's sprinkler work = x
The number of hours that Rogers family's sprinkler work = y
Then the equation will be
x + y = 45
x = 45 -y
Total water output = 1150 liters
30x + 20y = 1150
Here we have to use substitution method
30(45-y) + 20y = 1150
1350 - 30y + 20y = 1150
1350 - 10y = 1150
10y = 1350 - 1150
10y = 200
y = 200/10
y = 20 hours
Then,
x = 45 - y
x = 45 - 20
x = 25 hours
Hence, the Rogers family's sprinkler worked for 25 hours and Walker family's sprinkler worked for 20 hours
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John has 96 filter to post around town.Last week he posted 1/4. This week he posted 1/6. How many filter has he not posted?
The answer of how many filter has he not posted is 60, using fraction.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
John has 96 fliers
He post 1/4 of fliers so 96*1/4=24
So left post will be 96-24 = 72
So post 1/6 of remaining so 72*1/6=12
72-12=60
Hence 60 many filter has he not been posted.
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In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were correctly positive, while for people without HIV, 98.5% of tests conducted were correctly negative. A clinic serving an at-risk population offers free HIV testing, believing that 15% of the patients may actually carry HIV. What's the probability that a patient testing negative is truly free of HIV?
The probability that a patient with a negative result is truly HIV-free is 0.999.
How to find the probability that the negative result is correct?To find the probability that confirms that the result of the HIV test is negative, we must take into account the information provided in the information and perform the following mathematical operation.
The probability that No HIV and test positive is:
P = 0.85 * 0.985
P = 0.8372
The probability that HIV and test negative is:
P = 0.15 * 0.003
P = 0.00045
The probability that No HIV and negative test of HIV and negative test is:
P = 0.00045 + 0.8372
P = 0.8377
P = (NOT HIV / Test)
P = 0.8372 / 0.8377
P = 0.999
According to the above, the probability that a patient with a negative result is truly HIV-free is 0.999.
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Directions: Select all the correct answers.
Identify the products that are less than the value represented by the model. The entire grid represents one whole.
2.7×0,2
0.23 x 0.4
1.5 x 0.6
O 1.85 x 0.3
O
0.75 × 1.1
O
O
The products that are less than the value represented by the model are
0.23 x 0.4 , 1.5 x 0.6 , 1.85 x 0.3.
From the question, we have
the model has a grid of size 10 *10 = 100
Out of 100, 75 are covered.
75 grid = 75/100 =0.75
The products that are less than the 0.75 are
0.23 x 0.4 , 1.5 x 0.6 , 1.85 x 0.3.
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
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Binomial distribution calculation
If n=8 and p=0.2, find P(x-2)
Enter at least 3 decimal places.
The binomial distribution in 3 decimal place value is 0.294
Binomial distribution:
Binomial probability distribution determines the probability of a discrete random variable that results from an experiment in which there are two possible independent outcomes and which is repeated n times.
The calculation formula is:
[tex]P(X) = \binom{n}{X} \cdot p^X \cdot (1-p)^{n-X}[/tex]
where
n is the number of trials,
p is the probability of success on a single trial, and
X is the number of successes.
Given,
Here we have the following values,
n = 8
p = 0.2
Here we need to find the value of p(X = 2)
Here we know the values of
number of trials = 8
probability of success = 0.2
And the number of success = 2
Then the binomial distribution is calculated by applying these values on the formulas, then we get,
[tex]P(2) = \frac{8!}{2!(8-2)!} \cdot 0.2^2 \cdot (1-0.2)^{8-2}[/tex]
When we evaluating the expression, we have
P(2) = 0.29360128
Therefore, the resulting value is P(2) = 0.29360128
When we round of t into 3 decimal places then we get the value 0.294.
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Translate to an equation and solve. Let x be the unknown number.15 is 5% of what number?
x=
Type an integer or a decimal
15 is 5% of 300. So 300 is the unknown number.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find 15 is 5% of what number
Let us convert 5% to decimal.
Divide 5 by 100
5/100=0.05
By given x is the number
0.05x=15
Divide both sides by 0.05
x=300
Hence, 300 is the unknown number.
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what is the factorization of the polynomial below 2x^2+20x+50
[tex]2x^2+20x+50[/tex]
[tex]2(x^2+10x+25)[/tex]
find two numbers than sum to 10 and multiply to 25:
5 + 5 = 10
5 * 5 = 25
so the factorization is:
[tex]2(x+5)(x+5)\\\\= 2(x+5)^2[/tex]
Help please this is pre calculus
Answer:
5pi/12
105 degrees
Step-by-step explanation:
I can help with the first 2 too many answers in one will get my answer deleted
7pi/12 x 180/pi
7x15=105
Hopes this helps please mark brainliest
Hello! Can someone please help me out? I would appreciate it a lot thank you. I will give brainly. Look at the photo
The radius and diameter for the given figure are.
What is diameter?
In pure mathematics, a diameter of a circle is any line phase that passes through the middle of the circle and whose endpoints lie on the circle. It can even be outlined because the longest chord of the circle.
Main body:
A) as radius given = 3yd
so diameter = 2r
diameter = 2*3
= 6 yd
B) diameter given = 92 in
as d = 2r
92 = 2r
r = 46 in
C) as radius given = 23 ft
so diameter = 2r
diameter = 2*23
= 46 ft
Hence the values are as follows.]
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please answer need to turn it in
If f(a)=2a+1 and g(a)=5(a-1) what is (f-g)(a) when a=2
the answer is zero
you should know how you read the question
Choose a value of k so that the relation below is not a function.
{(-2,8),(0,3),(k,1),(-4,7)}
Responses
2
5
-1
-2
Answer:
-2
Step-by-step explanation:
it cannot be a function if there are more than one of the same x’s
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The three angles of the triangles are ∠A= 60°, ∠B = 75° and ∠C = 45°.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
The ∠5y + ∠7y = 180
∠12y = 180
y = 180/12 = 15
Hence the ∠CBA = 75° AND ∠ACB = 45°.
Now ∠A + 75+45 = 180
∠A = 180-120 = 60°
Hence, the three angles of the triangles are ∠A= 60°, ∠B = 75° and ∠C = 45°.
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Ascending order 2 1/3 2.3 23.5% 25/9
Ascending order - least to greatest
Answer: 2.35%, 2.3, [tex]2\frac{1}{3}[/tex], [tex]\frac{25}{9}[/tex]
Explanation:
0.235 (23.5%) is the least
2.3 (the actual decimal in the entire group) is the second least
2.33 ([tex]2\frac{1}{3} =\frac{7}{9}[/tex] as an improper fraction and [tex]\frac{7}{9} = 2.33[/tex]is the third least
2.78 ([tex]\frac{25}{9}[/tex] is already an improper fraction. In decimal version, it is 2.78) is the greatest.
------------------------------------------------------------------------
Have a great day and God bless! :D
Help me figure this out please
Two polygons are similar if their respective sides have a constant ratio and their corresponding angles are congruent (in other words, if they are proportional).
What is polygons?Two polygons are similar if their respective sides have a constant ratio and their corresponding angles are congruent (in other words, if they are proportional).Two polygons that share the same shape but not the same size are said to be similar polygons. Congruent angles and proportional sides are present in similar polygons, as well as similar angles in dissimilar polygons.Rectangles have a lot in common. Rhombuses have a lot in common. Squares resemble each other. Similarity exists among all congruent polygons.Triangles are said to be comparable to one another if any two of their respective angles are identical to any two of their respective angles in another triangle.To learn more about Polygons refer to:
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The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled. Find a5, he amount of water left in the tub after 5 minutes.
================================================
Work Shown:
[tex]a_n = a_{n-1} - 12\\\\a_1 = a_{1-1} - 12\\\\a_1 = a_{0} - 12\\\\a_1 = 84 - 12\\\\a_1 = 72\\\\[/tex]
After 1 minute, there are 72 gallons of water left.
[tex]a_n = a_{n-1} - 12\\\\a_2 = a_{2-1} - 12\\\\a_2 = a_{1} - 12\\\\a_2 = 72 - 12\\\\a_2 = 60\\\\[/tex]
After 2 minutes, there are 60 gallons left.
[tex]a_n = a_{n-1} - 12\\\\a_3 = a_{3-1} - 12\\\\a_3 = a_{2} - 12\\\\a_3 = 60 - 12\\\\a_3 = 48\\\\[/tex]
After 3 minutes, there are 48 gallons left.
[tex]a_n = a_{n-1} - 12\\\\a_4 = a_{4-1} - 12\\\\a_4 = a_{3} - 12\\\\a_4 = 48 - 12\\\\a_4 = 36\\\\[/tex]
After 4 minutes, there are 36 gallons left.
[tex]a_n = a_{n-1} - 12\\\\a_5 = a_{5-1} - 12\\\\a_5 = a_{4} - 12\\\\a_5 = 36 - 12\\\\a_5 = \boldsymbol{24}\\\\[/tex]
After 5 minutes, there are 24 gallons left.
------------------------
Table of values
[tex]\begin{array}{|c|c|} \cline{1-2}n & a_n\\\cline{1-2}0 & 84\\\cline{1-2}1 & 72\\\cline{1-2}2 & 60\\\cline{1-2}3 & 48\\\cline{1-2}4 & 36\\\cline{1-2}5 & \boldsymbol{24}\\\cline{1-2}\end{array}[/tex]
can you help me please
Answer:
[tex]-2 > x[/tex]
Step-by-step explanation:
We can solve the given inequality like we'd solve a regular equation. The only problem we should be looking out for is division/multiplication by a negative number - doing so would result in flipping the direction the inequality sign is facing (i.e. dividing by -1 would change < to > and vice versa.)
[tex]3x + 7 > 4x + 9 \text{ // Subtract 3x}\\3x + 7 - 3x > 4x + 9 - 3x\\\to 7 > x + 9 \text{ // Subtract 9}\\7 - 9 > x + 9 - 9\\\to -2 > x[/tex]
3x + 7 > 4 x + 9
STEPS/SOLUTION3x + 7 > 4 x + 9
1ST STEP (SUBTRACT 7 BOTH SIDES)3x + 7 - 7 > 4 x + 9- 73x > 4x + 22ND STEP (SUBTRACT 4X BOTH SIDES)3x - 4x > 4x + 2 - 4x-x > 23RD STEP (DIVIDE BOTH SIDE BY THE SAME FACTOR, AND FLIP ALSO THE SIGN AS IT IS NEGATIVE)-x/-1 < 2/-1-1 ÷ -1 and 2 ÷ -1ANSWERx < -2caroline bought 3 eye shadows and 4 lipsticks and paid a total of 39.53 write an equation to represent this situation assuming each eye shadow cost 4.79 how much did caroline pay for each lipstick
ANSWER:
The equation used to represent the situation is 3x + 4y = 39.53, and Caroline spent 6.29 per lipstick.
EXPLANATION:
We will use x for eyeshadow and y for lipstick.
The equation would be: 3x + 4y = 39.53
3(4.79) + 4y = 39.53
14.37 + 4y = 39.53
14.37 - 14.37 + 4y = 39.53 - 14.37
4y = 25.16
4y / 4 = 25.16 / 4
y = 6.29
Check.
3x + 4y = 39.53
3(4.79) + 4(6.29) = 39.53
39.53 = 39.53
I hope this helps! :D
harry took a $7000 three year loan with APR of 8.15% what is the monthly payment?
Answer: set up a proportion 7000 /3 yrs an 8.15% over 100 then cross multiply Step-by-step explanation:
How do you solve these?
for given triangles ΔABC and ΔADC,
∠ABC ≅ ∠ADC
In this question, we have been given a quadrilateral ABCD with segment AC is the angle bisector of angle BAD.
We need to prove ∠ABC ≅ ∠ADC
AB ≅ AD ......................(Given)
∠BAC ≅ ∠DAC ......................(Given)
AC ≅ AC .....................(Common side)
ΔABC ≅ ΔADC ..................(SAS postulate of triangle congruence)
∠ABC ≅ ∠ADC .............(corresponding sides of congruent triangles)
Hence proved.
Therefore, for given triangles ∠ABC ≅ ∠ADC
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there are 15/16 bags of purple clay and 3/4 bags of yellow clay. each color will be divided into 3/16 pound bags. how many more bags if purple can she make them yellow?
Ice skaters are skating on a solidly frozen lake. Which of the following could possibly be the temperature of the lake
Answer:
Below 30⁰F or 0⁰C
Step-by-step explanation:
Water freezes at those temperatures
explain revolving credit and give one example, then explain non-revolving credit and give one example.
Answer:
Revolving credit, as its name suggests, is intended to be more flexible. As long as you adhere to your credit terms, you can use it for a range of purchases. Non-revolving credit frequently has lower interest rates and consistent repayment schedules because it is typically utilized for a specific purpose, like a car loan or student loan.
What is the answer to this question?
Answer:
45 degrees
Step-by-step explanation:
angle AXD is equal to BXD plus AXB
95-x=(X+20)+(X+30)
95-x=2x+50
+x. +x
95=3x+50
-50. -50
45=3x
/3. /3
15=x
Now fill in X for bxd
15+30
45
Hopes this helps please mark brainliest
Round off 324.7 to the nearest ones
Answer:
Rounded to the nearest 0.01 or the Hundredths Place. = 324.70
Step-by-step explanation:
find the perimeter 24 4
Answer:
56
Step-by-step explanation:
24x2+4x2
Simplify
48+8
Solve
56
The perimeter of the triangle is 10x^2-6x+1 and the side lengths are 5x+7 and 8x^2-4x.What is the length of the missing side?
Answer:
2x^2-7x-6
Step-by-step explanation:
P=A+B+C=10x^2-6x+1
A=5x+7
B=8x^2-4x
C=?
C=P-(A+B)= 10x^2-6x+1-(5x+7+8x^2-4x)
=10x^2-6x+1-(8x^2-6x+7)
=2x^2-7x-6
In a bicycle store, a $500 bicycle is marked, "Get a 30% discount." What is the sale
price of the bicycle?
Answer:
350
Step-by-step explanation:
1. Take 30% of 500
You can accomplish this by multiplying 500 by 0.3 to get 150
500 x 0.3 = 150
150 is 30% of 500
2. Subtract your findings (30%) from total price (500)
500 - 150 = 350
350 is the sale price with a 30% discount on a $500 bicycle
Answer:
$350
Step-by-step explanation:
You have to multiply 500 by 0.7 to find the discount price.
500*0.7=350
Estimate the sum of the lengths of ribbon.
7 One-eighth yards + 8.2 yards
Which statements are true about the estimate? Check all that pply.
7 One-eighth can be rounded to 7.
8.2 can be rounded to 8.
The estimated sum is 2 yards.
The estimated sum is 15 yards.
To find the sum, subtract 8 – 7.
Estimate the sum of the lengths of ribbon. 7 One-eighth yards + 8.2 yards or: 7 1/8 yards + 8.2 yards
Which statements are true about the estimate? Check all that apply.
7 One-eighth can be rounded to 7.
8.2 can be rounded to 8.
The estimated sum is 2 yards.
The estimated sum is 15 yards.
To find the sum, subtract 8 – 7.
The given quadrilateral ABCD is an isosceles trapezoid. Which choice is NOT true about ABCD?
A) 2x + 10 = 4x - 30
B) angle A+ angle B+ angle C+ angle D=180°
C) angle A+ angle B+ angle C+ angle D=360°
D) AB = CD
Solve for angle DAB.
A) 50°
B) 20°
C) 30°
D) 65°
Answer:
B) angle A+ angle B+ angle C+ angle D=180°A) 50°========================
GivenABCD is an isosceles trapezoidSolutionPart 1Choices:
A) 2x + 10 = 4x - 30
TRUE, as A and D are congruent anglesB) angle A+ angle B+ angle C+ angle D=180°
NOT true, as the sum of interior angles is 360° not 180°.C) angle A+ angle B+ angle C+ angle D=360°
TRUED) AB = CD
TRUE, as marked same.Part 2Find the value of x:
2x + 10 = 4x - 304x - 2x = 10 + 302x = 40x = 20Find the measure of angle DAB:
m∠DAB = 2*20 + 10 = 50°Correct choice is A.
Answer:
b) A + B + C + D = 180° a) 50°Step-by-step explanation:
1) Finding the incorrect option?
The incorrect statement is,
→ angle A+ angle B+ angle C+ angle D=180°
(Because, A + B + C + D = 360°)
Hence, option (b) is the answer.
2) Solving for angle DAB?
Forming the equation,
→ 2x + 10 = 4x - 30
Now the value of x will be,
→ 2x + 10 = 4x - 30
→ 2x - 4x = -30 - 10
→ -2x = -40
→ x = -40/-2
→ x = 40/2
→ [ x = 20° ]
Then value of angle DAB is,
→ A = 2x + 10
→ A = 2(20) + 10
→ A = 40 + 10
→ [ A = 50° ]
Hence, option (a) is correct.
