To solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
What is integers ?
Integers are a set of whole numbers that include both positive and negative numbers, as well as zero. Integers can be represented on a number line that extends infinitely in both directions.
To solve problems with integers, you need to understand the basic operations such as addition, subtraction, multiplication, and division. You also need to know the rules and properties of integers, such as the commutative, associative, and distributive properties, as well as the rules for adding, subtracting, multiplying, and dividing positive and negative integers.
When solving a problem with integers, you should first identify which operation you need to perform first based on the order of operations. This order is typically remembered with the acronym PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). Once you have identified the operation, you can use the appropriate mathematical technique to solve the problem.
Therefore, to solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
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The Boy Scout troop raised money
in a fundraiser. They donated $400 to
the food bank and half of the remaining
amount to the animal shelter. Malik and
Jacob wrote equations to represent y, the
amount of money donated to the animal
shelter based on x, the total money raised.
MALIK
*-400
2
y=.
JACOB
y=-400
Which equation is correct? Explain.
The equation deduced by Malik is the correct equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Given that, the Boy Scout troop raised money in a fundraiser. they donated $400 to the food bank and half of the remaining amount to the animal shelter, they both represented the amount donated for the animal shelter :-
Malik: y = (x-400) / 2
Jacob: y = x/2 - 400
So, if we consider y as the money donated for the animal shelter and x is the total-raised money,
Therefore, according to the question,
$400 donated to food bank, then the left amount = x-400
Half of the money donated to the animal shelter based = (x-400) / 2
Therefore, the equation will be:-
y = (x-400) / 2
Hence, the equation deduced by Malik is the correct equation.
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5. Mrs. Walsh conducted a survey of the most popular after-school snack in the
middle school. Of the 400 students surveyed, 70 preferred muffins, 70 preferred
pretzels, 50 preferred fruit, 50 preferred yogurt, 80 preferred cheese and crackers,
and 80 preferred granola bars. Select all of the sections of a circle graph that each
represent of the entire circle.
muffins
Opretzels
fruit
yogurt
cheese and crackers
granola bars
06-1
All of the sections of a circle graph that each represent 1/8 of the entire circle include the following:
C. fruit.
D. yogurt.
What is a circle graph?In Mathematics, a circle graph is sometimes referred to as a pie chart and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.
Since there were 400 students surveyed, their preference can be calculated as follows:
Muffins = 70/400
Pretzels = 70/400
Fruit = 80/400 = 1/8
Yogurt = 80/400 = 1/8
Cheese and crackers = 80/400 = 1/5
Granola bars = 80/400 = 1/5.
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Anthony is younger than Kadeesha. Their ages are consecutive integers. Find Anthony's age if the sum of the square of Anthony's age and 2 times Kadeesha's age is 82.
Answer:
8 yo
Step-by-step explanation:
A = age of Anthony
K = age of Kadeesha
Formulate equations based on the information given:
K = A + 1
A² + 2K = 82
Solve the simultaneous equations by substitution:
A² + 2(A + 1) = 82
A² + 2A + 2 = 82
A² + 2A - 80 = 0
(A + 10)(A - 8) = 0
A + 10 = 0 → A = -10
A - 8 = 0 → A = 8
Anthony can't be -10yo, so he is 8yo
Kadeesha is, therefore, 9yo
which two ratios represent quantities that are proportional A 7/10 and 10/10 B 20/28 and 15/18 C 18/48 and 21/56 D 3/5 and 13/10
The answer is C) 18/48 and 21/56.
Step-by-step explanation:Two ratios are proportional if they have the same ratio when simplified to lowest terms.
A) 7/10 and 10/10 cannot be proportional because 7/10 cannot be simplified further, while 10/10 simplifies to 1/1.
B) To simplify the first ratio, we can divide both the numerator and denominator by 4, giving us 5/7. To simplify the second ratio, we can divide both the numerator and denominator by 3, giving us 5/6. Since these simplified ratios are not equal, the two ratios are not proportional.
C) To simplify the first ratio, we can divide both the numerator and denominator by 6, giving us 3/8. To simplify the second ratio, we can divide both the numerator and denominator by 7, giving us 3/8. Since these simplified ratios are equal, the two ratios are proportional.
D) To simplify the first ratio, we can multiply both the numerator and denominator by 2, giving us 6/10, which simplifies to 3/5. The second ratio is already in simplified form. Since these simplified ratios are not equal, the two ratios are not proportional.
Therefore, the answer is C) 18/48 and 21/56.the price of petrol increased from R12,58 per litre to R13,28 per litre. Determine the percentage increase in the price
Therefore, the percentage increase in the price of petrol is approximately 5.57%.
What percentages were converted?One tenth of any amount is represented by the relative number 10% in the image. Since one percent (1%) represents the one tenth of something, 100 percent (100%) denotes the entire thing, and 200 percent (200%) denotes twice the amount indicated. percentage. Mathematical percentile is a similar subject.
To find the percentage increase in the price of petrol, we can use the formula:
percentage increase = (new value - old value) / old value x 100%
Here, the old value is R12.58 per litre, and the new value is R13.28 per litre. Substituting these values into the formula, we get:
percentage increase = (13.28 - 12.58) / 12.58 x 100%
percentage increase = 0.70 / 12.58 x 100%
percentage increase = 0.0557 x 100%
percentage increase = 5.57%
Therefore, the percentage increase in the price of petrol is approximately 5.57%.
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The driver fueled his car before departing from Jeffrey's Bay. His tanks capacity is 28litres. Calculate how much he will pay for fuel if he fills up the tank to half of its capacity, and the price of fuel was R17, 98 per litre
The total cost of the driver to fill the fuel is given by A = $ 251.72
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the total cost of the driver to fill the fuel be A
Now , the value of A is
Let the total capacity of the fuel tank be = 28 Liters
Now , the driver fills half the tank
So , the amount of fuel to be filled = 28 / 2 = 14 Liters
Now , the cost of fuel per Liter = $ 17.98
And , the total cost of the driver to fill the fuel A = amount of fuel to be filled x cost of fuel per Liter
On simplifying the equation , we get
The total cost of the driver to fill the fuel A = 14 x $ 17.98
The total cost of the driver to fill the fuel A = $ 251.72
Hence , the equation is A = $ 251.72
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) The zeros of the function y = (x + 2)2 - 25 are
1)-2 and 5
2)-3 and 7
3)-5 and 2
4)-7 and 3
The zeros ( roots ) of the function y = (x + 2)^2 - 25 are x = 3 and x = -7.
What are the zeros ( roots ) of the given function?Given the function in the question;
y = ( x + 2 )² - 25
To find the zeros of the function, simply means find the values of x in the function y = ( x + 2 )² - 25, when y equals zero.
Equat the function to 0
(x + 2)^2 - 25 = 0
Adding 25 to both sides, we get:
(x + 2)^2 - 25 + 25 = 0 + 25
(x + 2)^2 = 25
Taking the square root of both sides, we get:
x + 2 = ±√25
x + 2 = +5
Solving for x, we get:
x = -2 + 5 = 3
or x = -2 - 5 = -7
Therefore, the zeros of the function are 3 and -7.
Option 4) -7 and 3 is the correct answer.
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Simplify [tex]\frac{cos^2a}{sin(a)-1}[/tex]
The simplified form is [tex]-(sina + 1)[/tex].
What is Trigonometry?One of the most significant areas of mathematics, trigonometry has a wide range of applications. Trigonometry is a discipline of mathematics that primarily focuses on the analysis of how a right-angle triangle's sides and angles relate to one another.
Given the function:
[tex]\frac{cos^2a}{sina - 1}[/tex]
Simplifying by using conjugate multiplication:
[tex]\frac{cos^2a \times (sina + 1)}{sina - 1 \times (sina + 1)}[/tex]
[tex]= \frac{cos^2a \times (sina + 1)}{sin^2a - 1^2}[/tex]
using [tex]sin^2a + cos^2a = 1[/tex]
[tex]= \frac{cos^2a \times (sina + 1)}{-cos^2a}[/tex]
[tex]= -(sina + 1)[/tex]
Hence, the simplified form is [tex]-(sina + 1)[/tex].
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7pt= ? QT ANSWER QUICK AND SHOW WORK
Answer:
7pts=4.20332
i think
Step-by-step explanation:
Terrell drove at a speed of 48 miles per hour for 21 hours. How far did he travel?
b) Work out the size of angle
answer in degrees (°).
56°
X
x. Give your
59°
77°
Check the picture below.
Where would a person experience the least atmospheric pressure?
A. An altitude exactly at sea level
B. An altitude of 1 km below sea level
C. An altitude of 7 km above sea level
D. An altitude of 1 km above sea level
Answer: The atmospheric pressure decreases with altitude. This is because as we move higher above the earth's surface, there is less air above us and therefore less weight pushing down on us. Therefore, the correct answer is:
C. An altitude of 7 km above sea level
At an altitude of 7 km above sea level, a person would experience the least atmospheric pressure because they would be furthest from the earth's surface and there would be very little air above them. This is why the air pressure in the Earth's upper atmosphere is much lower than at the surface of the Earth.
Step-by-step explanation:
What is the area of this trapezoid
Enter your answer in the box
Answer:
322 ft^2
Step-by-step explanation:
((a+c)*v )/2 35+11 *14 /2
Please help:)))))))))))
Option C is correct, x=-1/12y² represents the equation of the parabola.
What is Conic section?A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane
The given curve represents a parabola
A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
it's a sideway parabola (expressed as x=......) plus it does not have any x<0 as you can see in the graph,
so x must be always positive for every value of y
Hence, option C is correct, x=-1/12y² represents the equation of the parabola.
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Suppose you have an outstanding balance of $400 on your credit card, which has a 15%
APR. You have carefully considered your budget and decided that you can afford to pay
$75 per month until the balance is paid in full. You have also decided that you will not
make any additional purchases using the card.
4
Assuming that the card compounds daily, what will the balance be after the first payment
at the end of the first month?
Answer:
The first step is to calculate the daily interest rate. We can do this by dividing the annual percentage rate (APR) by 365 (the number of days in a year):
Daily interest rate = 15% / 365 = 0.00041096
Next, we need to calculate the interest that accrues on the outstanding balance for the first month. Since there are 30 days in a typical month, we can multiply the daily interest rate by the outstanding balance and the number of days in the month:
Interest for first month = 0.00041096 × $400 × 30 = $4.93
This means that the outstanding balance after the first payment will be:
$400 + $4.93 - $75 = $329.93
So the balance after the first payment will be $329.93.
Reference the table above to solve this question.
Air pressure decreases during a storm. The difference between the normal air pressure 'n' and the air pressure during the 1935 Florida Keys hurricane was greater than 121 millibars.
Write an inequality that could be used to find the normal air pressure in the Florida Keys before the hurricane?
Answer:
Step-by-step explanation:
Let's assume that the normal air pressure in the Florida Keys before the hurricane is represented by the variable 'p'. The inequality that could be used to find 'p' based on the given information is:
p - 121 > n
This inequality states that the difference between the normal air pressure 'p' and the air pressure during the hurricane ('n') is greater than 121 millibars. By rearranging this inequality, we can solve for 'p':
p > n + 121
Therefore, the normal air pressure in the Florida Keys before the hurricane was greater than the air pressure during the hurricane plus 121 millibars.
1 and 3/8 as the Sum of two fractions answer is
Answer:
Step-by-step explanation:
45
A plan for a house includes a rectangular room with an area of 80 square feet and a perimeter of 36 feet. What are the length and width of the room
Answer:
Let's call the length of the rectangular room "L" and the width "W". We know that the area (A) of the room is 80 square feet, so:
A = L x W
We also know that the perimeter (P) of the room is 36 feet. The formula for the perimeter of a rectangle is:
P = 2L + 2W
We can use the fact that P = 36 to solve for one of the variables in terms of the other. Solving for W, we get:
W = (36 - 2L) / 2
Now we can substitute this expression for W into the formula for the area:
A = L x ((36 - 2L) / 2)
Simplifying, we get:
80 = (L x (36 - 2L)) / 2
Multiplying both sides by 2, we get:
160 = L x (36 - 2L)
Expanding the right side, we get:
160 = 36L - 2L^2
Rearranging and simplifying, we get a quadratic equation:
2L^2 - 36L + 160 = 0
We can solve this quadratic equation using the quadratic formula:
L = [36 ± sqrt(36^2 - 4(2)(160))] / (2(2))
Simplifying, we get:
L = [36 ± sqrt(576)] / 4
L = [36 ± 24] / 4
L = 15 or L = 5
Since the length cannot be smaller than the width, we can disregard the solution L = 5. Therefore, the length of the rectangular room is 15 feet, and the width can be found using the formula we derived earlier:
W = (36 - 2L) / 2 = (36 - 2(15)) / 2 = 3
So the length of the room is 15 feet and the width is 3 feet.
A company sells doughnuts. They incur a fixed cost of $25,000 for rent, insurance, and other expenses. It costs $0.25 to produce each doughnut. Let x = number of doughnut produced. Find the Variable cost.
The variable cost for x doughnuts produced is 0.25x.
What is variable cost?
Costs that vary according on how much of an item or service a company produces are known as variable costs.
The fixed cost for the company is $25,000, which is a constant amount that does not depend on the number of doughnuts produced. The variable cost, on the other hand, is the cost that varies with the number of doughnuts produced.
Since it costs $0.25 to produce each doughnut, the variable cost for x doughnuts can be calculated as 0.25x.
Therefore, the variable cost for x doughnuts produced is 0.25x.
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17 buckets are filled with water the line plot below shows the amount of water in gallons that each bucket contains what is the total amount that have more than one quart of water?
The total amount of water in buckets that contain more than one quart is 39 gallons.
What is amount?Amount is a noun that refers to a quantity or number of something. It can also be used to refer to a sum of money. Amount is commonly used in mathematics, banking, and accounting to represent a specific quantity or monetary figure. Amounts are often expressed as a whole number, fraction, or decimal. Amounts can be expressed in various ways, such as in dollars, euros, pounds, or other forms of currency. Amount is also used to describe the size or extent of something, such as an amount of time or effort.
According to the line plot, buckets with numbers 1, 2, 3, 4, 6, 8, 12, 14, 15, and 17 all contain more than one quart of water, for a total of 39 gallons. Bucket 5 has one quart exactly, and the other buckets contain less than one quart.
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The total amount of water in buckets that contain more than one quart is 39 gallons.
What is amount?Amount is a noun that refers to a quantity or number of something. It can also be used to refer to a sum of money. Amount is commonly used in mathematics, banking, and accounting to represent a specific quantity or monetary figure. Amounts are often expressed as a whole number, fraction, or decimal. Amounts can be expressed in various ways, such as in dollars, euros, pounds, or other forms of currency. Amount is also used to describe the size or extent of something, such as an amount of time or effort.
According to the line plot, buckets with numbers 1, 2, 3, 4, 6, 8, 12, 14, 15, and 17 all contain more than one quart of water, for a total of 39 gallons. Bucket 5 has one quart exactly, and the other buckets contain less than one quart.
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3x^2+42x+72
Student 1 Student 2
(X+2)(x+12). 3(x+2)(x+12)
Which answer is the correct answer?
What was wrong with that is incorrect? Explain what they did wrong.
What important note can you make about factoring that you’ve learned from mistakes made on this problem?
Student 1's answer is the correct answer: (x+2)(x+12).
What is expressionAn expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
What is expression and equation?Expression is a mathematical phrase which combines, numbers, variables and operators to show the value of something. An equation is a mathematical statement wherein two expressions are set equal to each other.
Student 2's answer, 3(x+2)(x+12), is incorrect because they multiplied the factors by 3, which is not necessary and changes the value of the expression.
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8.2 A sum of R45 360 has to be shared among three people. Divide the money between Ayanda, (4 Zipho and Palesa according to the ratio of 4:3:2
Answer:
Ayanda will receive R20,160, Zipho will receive R15,120, and Palesa will receive R10,080.
Step-by-step explanation:
We can use the ratio of 4:3:2 to find the total number of parts:
4 + 3 + 2 = 9
This means that the money will be divided into 9 equal parts, and Ayanda will get 4 parts, Zipho will get 3 parts, and Palesa will get 2 parts.
To find the value of one part, we divide the total amount by 9:
45,360 / 9 = 5,040
Therefore, one part is worth R5,040.
Now we can find the amount of money each person will receive by multiplying their respective parts by the value of one part:
Ayanda: 4 parts × R5,040/part = R20,160
Zipho: 3 parts × R5,040/part = R15,120
Palesa: 2 parts × R5,040/part = R10,080
Therefore, Ayanda will receive R20,160, Zipho will receive R15,120, and Palesa will receive R10,080.
When writing 7–√979 as 7n7n, which statement is true about the value of n?
[tex](\sqrt[9]{7} = 7^{1/9}[/tex] is true about the value of n in polynomial.
What is a polynomial, simply put?
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.
the value of n is 1/9 because ([tex](\sqrt[9]{7} )^{9}[/tex] = 7¹
and ( [tex](7^{1/9})^{9}[/tex] = 7¹
[tex](\sqrt[9]{7} = 7^{1/9}[/tex]
is correct option .
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Which of the following equations represents a linear function?
x = 3
y equals one half times x minus 5
y equals three fourths times x squared
3x − 6 = 4
The equations that represent a linear functions are:
x = 3y = 1/2x - 53x − 6 = 4How to determine the linear functionsFrom the question, we have the following parameters that can be used in our computation:
The list of options
As a general rule
Linear functions are functions with a degree of 1
Using the above as a guide, we have the following equations with a degree of 1:
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Please help!!! See imagine bellow!!!
Answer:
onomatopoeia
Step-by-step explanation:
65% of the people in Missouri pass the driver’s test on the first attempt. A group of 5 people took the test. What is the probability that less than 3 in the group pass their driver's tests in their first attempt?
Round your answer to three decimal places.
Remember: 65% = 0.65.
Answer:
Step-by-step explanation:
This problem involves a binomial distribution where the probability of success (passing on the first attempt) is 0.65, and the probability of failure (not passing on the first attempt) is 0.35. We want to find the probability that less than 3 out of 5 people pass on their first attempt.
We can use the binomial probability formula to calculate this:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
Where X is the number of people who pass on their first attempt.
P(X = 0) = (5 choose 0) * 0.65^0 * 0.35^5 = 0.0024
P(X = 1) = (5 choose 1) * 0.65^1 * 0.35^4 = 0.0289
P(X = 2) = (5 choose 2) * 0.65^2 * 0.35^3 = 0.1323
So,
P(X < 3) = 0.0024 + 0.0289 + 0.1323 = 0.1636
Therefore, the probability that less than 3 out of 5 people pass their driver's tests on the first attempt is approximately 0.164, rounded to three decimal places.
Cloey has a shop that sells video games. On Friday,Her shop sells 3,878 video games. On Saturday,she sells 8,999video games. On Sunday,she sells____ video games. Use the total of video games from Friday and Saturday to solve the question.
Answer:
6,000 Video Games
Step-by-step explanation:
To find out how many video games Cloey sold on Sunday, we need to add the number of video games she sold on Friday and Saturday and then subtract that total from the total number of video games she sold over the three days:
Total number of video games sold on Friday and Saturday = 3,878 + 8,999 = 12,877
Total number of video games sold over the three days = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday)
We know that the total number of video games sold over the three days is the sum of the number sold on Friday and Saturday plus the number sold on Sunday. We can rearrange this equation to solve for the number sold on Sunday:
Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday
Substituting in the values we know, we get:
Number sold on Sunday = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday) - (number sold on Friday) - (number sold on Saturday)
Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday
Number sold on Sunday = (3,878 + 8,999 + X) - 12,877
Number sold on Sunday = X - 0
Simplifying this expression, we get:
Number sold on Sunday = 6,000
Therefore, Cloey sold 6,000 video games on Sunday.
The triangles are similar.
What is the value of x?
Enter your answer in the box
x = ?
Answer:
x = 12
Step-by-step explanation:
96 / 24 = 4, 28/ 7 = 4, assuming that it dilated by 4, so use 4 to multiply 25, 4 x 25 = 100 so 6x+28 = 100 then plug it in 6(12) + 28 = 100., 100 = 100
To check use a^2 + b^2 = c^2
28^2 + 96^2 = (6(12)+28)^2
784 + 9216 = (72+28)^2
784 + 9216 = 100^2
784 + 9216 = 10000
10000 = 10000
How much money should be deposited today in an account that earns 8.5% compounded monthly so that it will accumulate to $9000 in three years?
The amount of money that should be deposited is
Answer:
$6981
Step-by-step explanation:
If you put $6981 in a deposit and your interest rate is 8.5% monthly it will give you $2,019.62 which then means your total will be $9,000.62
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Find the center and radius of the circle represented by the equation below.
x^2+y^2-8x-20y+52=0
Answer:
Step-by-step explanation:
To find the center and radius of the circle represented by the equation:
x^2 + y^2 - 8x - 20y + 52 = 0
We can start by completing the square for both x and y terms as follows:
(x^2 - 8x) + (y^2 - 20y) + 52 = 0
(x^2 - 8x + 16) + (y^2 - 20y + 100) + 52 = 16 + 100
(x - 4)^2 + (y - 10)^2 = 64
Thus, the equation can be rewritten in the standard form of the circle as:
(x - 4)^2 + (y - 10)^2 = 8^2
Therefore, the center of the circle is (4, 10), and its radius is 8 units.
Step-by-step explanation:
x² + y² - 8x - 20y + 52 = 0
the standard circle equation is
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle, and r is the radius.
now, we need to find the squared terms in the original equation.
x² and y² are clearly from the (x - h)² and (y - k)².
and then
(x - h)² = x² - 2hx + h²
-2hx = -8x
2h = 8
h = 4
(y - k)² = y² - 2ky + k²
-2ky = -20y
2k = 20
k = 10
h² + k² = 16 + 100 = 116
116 - r² = 52
r² = 64
r = 8
so, the center is (4, 10), the radius is 8.