According to the given information, the sum of the calories of a bag of popcorn and a juice box is 518. Taking x as the number of calories of a bag of popcorn and y as the number of calories of a juice box, we have that:
[tex]x+y=518[/tex]Then, 2 bags of popcorn (it means 2x) and 6 juice boxes (it means 6y) have a total of 1456 calories, this is:
[tex]2x+6y=1456[/tex]Use this system of equations and solve the problem, this way:
Solve the first equation for x:
[tex]x=518-y[/tex]Use this expression and replace for x in the second equation:
[tex]\begin{gathered} 2(518-y)+6y=1456 \\ 1036-2y+6y=1456 \\ 4y=1456-1036 \\ y=\frac{420}{4} \\ y=105 \end{gathered}[/tex]Use this value to find the value of x:
[tex]x=518-105=413[/tex]It means that there are 413 calories in each bag of popcorn and 105 calories in each juice box.
Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
I am a product of three different prime numbers, my largest factor is 13. I am between 185 and 200 who am I ?
The product of three different prime numbers that has largest factor is 13 and is between 185 and 200 is 195.
What are prime numbers?It should be noted that prime numbers are the numbers that can be divisible by only 1 and itself. They include 2, 3, 5, 7, 11, 13, etc.
It should be noted that the information illustrated that the prime numbers are 3, 5 and 13. The multiplication will be:
= 3 × 5 × 13
= 195
The number is between 185 and 200.
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How do you write 0.083 as a fraction?
Answer: 83/1000 should be the answer
Step-by-step explanation:
0.083 goes to the thousandths place. Which would mean the denominator would be 1000, and in the hundredths and thousandths place it says 83, so the numerator would be 83. Resulting in the answer, 83/100.
The solution of the expression 0.083 in form of fraction is,
⇒ 83/1000
We have to given that,
Write a number 0.083 as a fraction.
Here, The number is,
⇒ 0.083
⇒ 0.083 x 1000 / 1000
⇒ 83/1000
Therefore, The solution of the expression 0.083 in form of fraction is,
⇒ 83/1000
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Mia used a pattern to create figures with building blocks. The first three figures are shown.
Figure 1
Mia needs
Assuming the building pattern continued, how many blocks would be needed to build the 6th figure?
Figure 2
AX blocks to build the 6th figure.
Figure 3
Answer:
I think the answer would be 33
Can someone help me with this geometry question?
4/5 is the probability that jack will win at least 30 points in a throw.
What do we mean by probability?The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.The probability is determined by dividing the total number of outcomes by the total number of potential events.Odds and probability are two different concepts.Calculating odds involves dividing the probability of an event by the probability that it won't happen.So, the probability formula:
P = favourable events/Total number of eventsFavorable events: (At least 30 points) ⇒ 30 + 40 + 50Total events: (Sum of all points) ⇒ 150Now, insert values in the formula as follows:
P = favourable events/Total number of eventsP = 120/150P = 12/15P = 4/5Therefore, 4/5 is the probability that jack will win at least 30 points in a throw.
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In the figure, m/RPZ= 95 and TU || RQ || VW. Find the measure of angle UZP.
The measure of the corresponding angle; ∠UZP = 95°.
What is defined as the term corresponding angle?The definition of corresponding angles states that when two parallel lines intersect with a third, the angles that take up its same relative position at every intersection are said to be corresponding angles to one another. The statement "If a line intersects parallel lines, therefore the corresponding angles with in two intersection regions are congruent" is true either way, based on the corresponding angles theorem.For the given question;
Lines TU || RQ || VW are parallel.
The measure of the ∠RPZ= 95.
Thus, from the diagram,
∠UZP = ∠RPZ= 95
As both angles are corresponding angle so equal.
Therefore, the measure of the ∠UZP = 95°.
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Harlan is preparing a dip for a party the recipe calls for 4 cups of sour cream and three packages of onion soup mix he doesn’t want to prepare that my street decides to use only 2 cups of sour cream and one and a half packages of onion soup mix is this a proportional relationship
Yes!, This is a proportional relationship.
A proportional relationship means that the ratios of two variables are equal.
According to the question, the requirements of the recipe are
Number of cups of sour cream required be x1 = 4
Number of packages of onion soup mix required be y1 = 3
Used products by Harlan,
Cups used by Harlan of sour cream be x2 = 2
Packages of onion soup mix used by Harlan be y2 = 1.5
As we can see that,
x1/x2 = y1/y2
4/2 = 3/1.5
2 = 2
L.H.S = R.H.S ( ratio is same)
Therefore, we conclude that the above case is a proportional relationship.
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h(1) = -2
h(2) = 1
h(n) = h(n-2) + h(n-1)
Answer:
h(1)=h(1-2)+h(1-1)
h(1)=h(-1)+h(0)
h(-1)-h(-1)=0
h(0)=h(0)
Find the contrapositive and determine if it is true or false.
Statement : Obtuse angles are not right angles.
The contrapositive statement is If an angle is a right angle, then is not an obtuse angle True. Option B
What is a contrapositive statement?
A contrapositive statement can be defined as a theorem created by contradicting the hypothesis and conclusion of a statement.
It involves exchanging both the hypothesis and conclusion of a given conditional statement and then negating both hypothesis and conclusion.
It is a combination of an inverse and converse statements.
The hypothesis and conclusion are interchanged or switched.
A contrapositive statement is written as;
a b is equivalent to b ~a
Given the statement;
Obtuse angles are not right angles.
The contrapositive statement is :
If an angle is a right angle, then is not an obtuse angle
Thus, the contrapositive statement is true
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Which inequality is represented by the number line below?
The inequality that is represented by the number line is C. x ≤ 7.
What is an inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line. A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.
It should be noted that from the number line, we can see that the arrow starts from -7 and then moves backwards. This shows that it's x ≤ 7.
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What is the volume of this rectangular prism? 1/4 cm 1/2 cm 1/3 cm
The formula of the volume of a rectangular prism
[tex]V=l\times w\times h[/tex]we substitute the values given
l=length= 1/3cm
w=width=1/2cm
h=height=1/4cm
[tex]V=\frac{1}{3}\times\frac{1}{2}\times\frac{1}{4}=\frac{1}{24}cm^3[/tex]A candy company developed a new consumer product that is expected to earn $3,000 in profit each year if consumer demand is low, $19,000 per
year if consumer demand is moderate, and $31,000 per year if consumer demand is high. The probability of low, moderate, and high demand is
35%, 45%, and 20%, respectively. Determine the expected monetary value (EMV) for the new product.
The most appropriate choice for probability and profit will be given by:
Expected monetary value is $15800
What is probability and profit?
Probability of an event is the chance of occurance of that event.
Probability can be obtained by Number of favourable outcomes divided by the total number of outcomes
Probability varies from 0 to 1.
If the selling price of an item is more than its cost price, difference between the selling price and the cost price gives the profit.
Profit if consumer demand is low = $3000
Profit if consumer demand is moderate = $19000
Profit if consumer demand is high = $31000
Probability of low demand = 35%
Probability of moderate demand = 45%
Probability of high demand = 20%
Expected monetary value = $([tex]3000 \times \frac{35}{100}+19000 \times \frac{45}{100}+ 31000 \times \frac{20}{100}\\[/tex])
= $([tex]1050 + 8550+6200[/tex])
= $[tex]15800[/tex]
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fing the square root of 225 with process class 5
The Square root of 225 is 15
What is division ?The act of repeatedly subtracting is called division. It functions in the opposite way to how multiplication works. Forming equal groups is how it is described. When dividing numbers, we split a larger number into smaller ones so that the product of the multiplication of those smaller numbers equals the larger number that was divided. As an illustration, 4 2 = 2. This knowledge can be expressed as the multiplication 2 x 2 = 4.
Given that :Square root of 225
225 = 3 × 75
225 = 3 × 3 ×25
225 = 3 ×3 × 5 ×5
225 = 3² × 5²
225 = (3 × 5)²
225 = 15²
√225 = 15
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How many feet of chain fence are necessary to
enclose a dog pen that is square and has an area of
144 square feet?
Answer:
48 feet
Step-by-step explanation:
Areas of a square is the length times the width. In a square the length and width are the same number because all the sides of a square have the same length.
12 x 12 = 144, so each side of the pen is 12 feet. We want to find the perimeter (the distance around the square). 4(12) = 48
Customers are charge a late fee of 20% of their bill . This person is a week late on a bill of 200$ what should we charge for late fee
Answer:
Step-by-step explanation:
20$
f the gradient of a line is 3, what is the gradient of the line which is perpendicular to A
Answer:
-1/3
Step-by-step explanation:
gradients of perpendicular lines= m1 × m2=-1
hence , 3 × m2 = -1
m2 -1/3
Please help I’ll mark you as brainliest if correct!!
The sequences are :
a. 2 , 16 , 18 , 54 , 162 is Geometric progression
Three terms : 486, 1458, 4374.
b. 1, 6 , 11, 16, 21 is arithmetic progression
Next three terms 26, 31., 36..
What is geometric progression?In a geometric progression, each element following the first is created by multiplying it by a number known as the common ratio, which is represented by the symbol r.You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).The terms in the sequence that result if the same number is added to or removed from each term of an A.P. are also in an A.P. with the same common difference.To learn more about : Progression
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You deposit $200 in an account earning 2% interest compounded annually. How much will you have in the account in 20 years?
Answer:
221
Step-by-step explanation:
Interest goes up 5 dollar each year
Marked
Price
$320.00
Rate of
Discount
20%
Discount
Sale Price
$
$
(Simplify your answers. Type whole numbers or decimals.)
Answer: 64 is the answer
Step-by-step explanation:
I had a question like this and got it right! Hope this the correct answer for you!
well, we know that the regular price is 320 bucks, but is discounted by 20% so
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 320}}{\left( \cfrac{20}{100} \right)320}\implies 64~\hfill \underset{\textit{discount price}}{\stackrel{320~~ - ~~64}{\text{\LARGE 256}}}[/tex]
To rent a certain meeting room, a college charges a reservation fee of $19 and an additional fee of $6 per hour. The chemistry club wants to spend at most $67
on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
By estimating the linear inequality, the possible numbers of hours the chemistry club could rent the meeting room exists 9 hours.
What is meant by Linear inequalities?In mathematics, an expression with uneven sides is referred to as an inequality. When a relationship leads to a non-equal comparison between two expressions or two numbers, it is referred to as an inequality in mathematics.
In this case, the equal sign "=" is replaced with any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol ().
Strict inequalities are denoted by the symbols "" and ">," whereas slack inequalities are denoted by "" and "". A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.
To rent a certain meeting room, a college charges a reservation fee of $19 - 16 and an additional fee of $6 per hour. The chemistry club wants to spend at most $67 - 70
Given that, college charges a reservation fee of $19 and an additional fee of $6 per hour.
The chemistry club wants to spend at most $67.
To estimate the possible numbers of hours the chemistry club could rent the meeting room:
The governing inequality is
19 + 6t < 67
The solution is
t < (67-19)/6
simplifying the above equation, we get
t = 8 hours.
Therefore, the value of t = 8 hours.
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Which calculation correctly uses prime factorization to write in simplest form?
What is the sign of (-2)³? What is the sign of (-3)²? Justify your answers.
Based on the given bases with powers, the sign of (-2)³ is negative.
The sign of (-3)² can be found to be positive.
The justification for the signs can be found below.
How to find the sign?When multiplying two negative numbers, the result would be a positive number. When multiplying positive number by a negative number, the result would be negative.
(-2)³ is the same as -2 x -2 x -2 which is:
= -2 x -2 x -2
= 4 x -2
= -8
4 became positive but then became negative when multiplied by another -2.
(-3)² is 3 x 3:
= 3 x 3
= 9
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Find the length of AC¯¯¯¯¯¯¯¯A. 33.13B. 377.19C. 378.63D. 2.89
The trigonometry ratios are
[tex]\begin{gathered} SinD=\frac{AK}{KD} \\ \\ tanD=\frac{AK}{AD} \\ \\ tanK=\frac{AD}{AK} \\ \\ cosK=\frac{AD}{KD} \end{gathered}[/tex]AD = 31
AK = 24
Since we do not have the length of KD, then
The value of sinD and cosK are wrong
Let us find tanD and tanK to check which one is right
[tex]tanD=\frac{24}{31}[/tex]But the given value is 31/24, then tanD is wrong
[tex]tanK=\frac{31}{24}[/tex]It is the same with the given value
The correct option is C
(2x+1)(3x+2)=6xsquare+7x+2
Factorization of the given equation : 6x² + 7x +2 is equal to
(2x +1 ) ( 3x +2 ).
As given in the question,
Given equation is
6x² + 7x +2
Using the sum and the product pattern we get
Product of extreme terms is 6 × 2=12
Factors of 12 are 1, 2, 3, 4, 6,12
4 ×3=12(product of extreme terms)
4 +3 = 7(middle term)
Factorize the equation by splitting middle term
6x² +7x +2
=6x²+ 4x +3x +2
=2x( 3x+2)+1(3x+2)
=(2x+1)(3x+2)
Therefore, factorization of the given equation : 6x² + 7x +2 is equal to
(2x +1 ) ( 3x +2 ).
The complete question is :
Factorize the given equation : 6x² + 7x +2 .
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The value of the 1 digit in 13,089 is how much greater that the value of the digit one in 30,124
For 13,089 - the value of the digit 1 is ten thousand or 10,000
For 30,124 - the value of the digit 1 is one hundred or 100
Therefore:
[tex]\frac{10000}{100}=100[/tex]Answer: the value of the digit 1 in 13,089 is 100 times greater than the value of the digit 1 in 30,124
What is the net salary for someone with a gross of $150 000 a year if they must pay a tax of 30%?
Gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
As given in the question,
Gross salary of an individual is $150 000 a year
Percentage of tax on gross salary =30%
Amount of tax is equal to
= 30% of $150 000
= (30/100)× 150 000
= $45000
Net salary per year
= $(150 000 - 45000)
= $105000
Net salary per month
= $(105000/12)
= $8750
Therefore, gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
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What’s the correct answer answer asap for brainlist
Answer:
answer a
Step-by-step explanation:
spongy bone in the center
A school event requires 4 adults for every 35 kids. 12 adults are available. How many kids can attend?
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
therefore
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
So the answer is 105
4. In a school of 120 students, 41 studied Maths, 48 studied Chemistry and 42 studied Physics, 16 studied both Chemistry and Maths, 14 studied Maths and Physics, 18 studied Chemistry and Physics and 9 studied all the three subjects. Find how many of them studied:
(i) Exactly one subject.
(ii) At least one subject.
(iii) None of the subjects
Answer:
i) 62
ii) 92
iii) 28
Step-by-step explanation:
i) 19+23+20
=62
ii) 23+9+9+7+19+5+20
=92
iii) 120-23-9-9-7-19-5-20
or
120-92
=28
You invested $28,000 in two accounts paying 3% and 6% annual interest, respectively. If the total interest earned for
the year was $1590, how much was invested at each rate?
The amount invested at 3% is $
The mount invested at 6% is $
Answer: 6000 at 3% and 22000 at 6%
Step-by-step explanation:
x + y = 28,000
0.3x + 0.6y = 1500
multiply everything in the first equation by 0.3 since we want to be able to eliminate the variable x from both equations.
0.3x +0.3y = 840 then subtract second equation to just get one variable
0.3x + 0.6y =1500
-0.3y = -660
y = 22000
28000 - 22000 = 6000 which is x
So 6000 is invested at 3% and 22000 is at invested at 6%