Find the difference between the starting and ending values:
72 - 60 = 12
Divide that difference by the starting value:
12 ÷ 60 = 0.2
Convert that to a percent:
0.2 = 20%
The number of teachers increased by 20%.
The key is to divide the difference by the original number, not the ending number.
The area of a rectangular pool is 6² − 11 + 3.
Part A
Factor 6² − 11 + 3 to determine the dimensions (length and width) of the rectangular pool.
Understand & Think: What are you being asked or told to do _________________
What information do you know? _________________
Do & Answer: Factor the trinomial to determine the expressions that give the dimensions (length and width) of the rectangular pool.
Show all work and use the algebra skills
What are your factors? What do your factors mean? __________________________________________________________
Show how you would check your factors are correct here:
The dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.
What is Area of Rectangle?The area of Rectangle is length times of width.
Area of rectangular pool = 6x² − 11x + 3
To factor the trinomial, we need to find two binomials that multiply together to give the trinomial 6x² − 11x + 3.
We use product-sum method of factoring to find the two binomials.
We need to find two numbers that multiply to 6 (the coefficient of the x² term) and add to -11 (the coefficient of the x term).
6x² − 11x + 3
6x² −2x-9x + 3
(2x − 1)(3x − 3)
Hence, the dimensions of the rectangular pool are (2x − 1) and (3x − 3). The length of the pool is 3x − 3 and the width of the pool is 2x − 1.
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a can cottons 4 cups of pineapple juice the can of juice costs 2.56 what is the unit in dollars per fluid ounce
0.08$/fl. Ounce
The first step in finding the unit price of a can of pineapple juice in dollars per fluid ounce is to determine the volume of juice contained in the can. If a can holds 4 cups of juice, then we need to convert that volume to fluid ounces. One cup is equal to 8 fluid ounces, so 4 cups is equal to 32 fluid ounces.
Next, we need to determine the price of the juice in dollars per fluid ounce. We are told that the can costs 2.56 dollars, so we need to divide that cost by the number of fluid ounces in the can to find the unit price.
So, the unit price of the juice in dollars per fluid ounce is:
2.56 / 32 = 0.08 dollars per fluid ounce
So, for each fluid ounce of pineapple juice, the cost is 0.08 dollars. This is the unit price of the juice in dollars per fluid ounce. It is important to note that this unit price is only valid for this specific can of juice and may not be the same for other sizes or brands of pineapple juice.
In conclusion, the unit price of a can of pineapple juice containing 4 cups or 32 fluid ounces, and costing 2.56 dollars, is 0.08 dollars per fluid ounce.
Change 0.7 to fraction
Answer:
7/10
Step-by-step explanation:
Here ya go!
A function is shown below.
f(x) = 3x - 7
What is the value of f(-3)?
Answer:
Step-by-step explanation:
Put ' - 3' whre 'x' is and compute the answer
f(-3) = 3 (-3) - 7
= -9 - 7 = - 16
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The percentage of decrease is 20%
How to find the missing percentage?First, if we have an initial value A, and we increase it by x (a percentage in decimal form) then the new value will be:
A' = A*(1 + x)
Whle a decrease is written as:
A' = A*(1 - x)
In this case we have an increase of the 25%, it is written as:
A' = A*(1 + 0.25)
A' = A*1.25
IF we pass the factor to the other side, will get:
(1/1.25)*A' = A
(0.8)*A' = A
Now we want to write the coefficient on the left in the form (1 - x)
We will get:
0.8 = 1 - 0.2
0.2 is the percentage (in decimal form) decreased from A' to get A. Then the answer is 20%.
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is this relationship proportional 4/5 = 15/20
Answer:no
Step-by-step explanation:
if it was then it supposed to be like 4*20=5*15 which is not right equation
How many ways can grant arrange 3 of his 10 plants on a window leadge
Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.
Determine the number of the waysTo find the answer, we need to use the formula for permutations:
Permutations = n! / (n-r)!
Where:
- n is the total number of items
- r is the number of items to be arranged
- ! means factorial (e.g. 5! = 5 x 4 x 3 x 2 x 1)
In this case:
- n = 10 (the total number of plants)
- r = 3 (the number of plants to be arranged on the window ledge)
Plugging these values into the formula, we get:
Permutations = 10! / (10-3)! = 10! / 7! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1) = (10 x 9 x 8) / 1 = 720
Therefore, Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.
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A
65°
B
Reflex Angle B =
degrees.
The solution is, B = 245, is a Reflex Angle., when it is given that A=65.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
We know that, a ray is a line that continues on forever inn one direction with a point at it's start.
here, we have,
A = 65°
now, B is a Reflex Angle ,
so, we know that Reflex Angle means the angle with value >180 to <270.
now, we get,
B = 180 + 65
= 245
Hence, The solution is, B = 245, is a Reflex Angle.
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please help with this
Answer:
1. S = 20w + 100
2. M = -400w + 3,500
Step-by-step explanation:
1. Since Mateo is starting with a balance of $100, we can set this as our constant term (the 'b' in y = mx + b). Every week, he earns $20, so we can set this as the coefficient on the variable w (which represents how many weeks have passed).
2. Emily is spending money in this situation, so the coefficient on w is negative, as the amount of money she has left is getting smaller. The exact amount that she spends each week is $400, so the negative of that is going to be the coefficient of w in the equation. We can set the constant term in this equation to $3500, as Emily starts with that much money when no weeks have passed (when w = 0).
Solve for x show proofs urgentttt
The value of the length, x is 5√3
How to determine the value of the length, xFrom the question, we have the following parameters that can be used in our computation:
Rise = 11
Length = x
Hypotenuse = 14
The value of the length , x is calculated as
x^2 = Hypotenuse^2 - Rise^2
Substitute the known values in the above equation, so, we have the following representation
x^2 = 14^2 - 11^2
So, we have
x^2 = 75
Take the square root of bpth sides and evaluate
x = 5√3
Hence, the value of x is 5√3
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what is the answer to this
The value of x is 15√2
The value of the side y is 30
How to determine the length of the sidesThe sum of angles in a rectangle is 360 degrees
To determine the value of the variable, x
Let's use the trigonometric identity, cosine
cos = adjacent/hypotenuse
substitute the values
cos 45 = 15/x
Find the value
1/√2 = 15/x
cross multiply
x = 15√2
For y, we have;
sin 45 = y/15√2
1/√2 = y/15√2
Make y subject
y= 15√2 /√2
y = 60/2
y = 30
Hence, the values are 30 and 15√2
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You have 2 different savings accounts. For Account A, the simple interest earned after 21 months is $9. 45. For ulo, l le interest rate is 3. 6% for Account A and 2. 4% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer
The principal for Account A is $150, and we do not have enough information to find the principal for Account B. Account A earned the most interest the first month because it has a higher monthly interest rate.
About interest ratesThe principal for Account A can be found using the formula for simple interest:
I = Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Rearranging the formula to solve for P, we get P = I / (rt).
For Account A, the interest is $9.45, the interest rate is 3.6%, or 0.036, and the time is 21 months, or 1.75 years.
Plugging these values into the formula, we get:
P = $9.45 / (0.036 × 1.75) = $150
So the principal for Account A is $150.
For Account B, we do not have enough information to find the principal. We know the interest rate, but we do not know the interest or the time.
To determine which account earned the most interest the first month, we can compare the monthly interest rates.
The monthly interest rate for Account A is 3.6% / 12 = 0.3%, and the monthly interest rate for Account B is 2.4% / 12 = 0.2%.
Since the monthly interest rate for Account A is higher, it earned the most interest the first month.
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what is the mass to the nearest tenth of a gram of 3.50 moles of sodium metal?
Answer:
The mass of 3.5 moles of Ca (Sodium) is 140 g to two significant figures.
If a least-squares regression line fits the data well, what characteristics should the residual plot exhibit? Sketch a well-labeled example
x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
[tex]y=b_1x+b_0[/tex]
There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.
Given a collection of pairs (x,y) of numbers, there is a line [tex]y=b_1x+b_0[/tex] that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.
[tex]b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)[/tex]
x' is the mean of all the x-values, y' is the mean of all the y-values, and n is the number of pairs in the data set.
[tex]y=b_1x+b_0[/tex]
specifying the least squares regression line is called the least squares regression equation.
Example,
Find the least squares regression line for the five-point data set
x = 2 2 6 8 10
y= 0 1 2 3 3.
compute the table,
x y x2 xy
2 0 4 0
2 1 4 2
6 2 36 12
8 3 64 24
10 3 100 30
28 9 208 68 (sum)
[tex]S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125[/tex]
The regression line is y=0.34375x-0.125
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find the probability of three or fewer heads on four flips of a fair coin. enter the answer to four decimal places.
The probability of getting three or fewer heads on four flips of a fair coin is 0.75.
The fair coin is flipped four times. The sample space can be found as follows,
There will be 4 trial and each trial can have two outcomes so the total number of outcomes is 2x2x2x2.
Total possible outcomes are 16.
Now, the number of favorable outcomes when there will be 3 or less heads will be 6 because there has to be 3 heads in four position and that too without repetition.
So, the probability of event is,
P = Total favorable event/Total possible events
P(of three or fewer heads on four flips of a fair coin) = 6/8
So, probability of three or fewer heads on four flips of a fair coin is 0.75.
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Solve the system of equations below. Show work.
2x+y=10
3x-y=5
The solution to the simultaneous equation given is (3, 4)
Solving system of equationGiven the system of equation below
2x+y=10
3x-y=5
From equation 2, the value of y is expressed as:
y = 3x - 5
Substitute the result into equation to have:
2x + 3x - 5 = 10
5x - 5 = 10
5x = 15
x = 3
Since y = 3x - 5
y = 3(3) - 5
y = 4
Hence the solution to the system of equation is (3, 4)
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Triangle abc is reflected over the line y = x to produce triangle a'b'c'. What will be the coordinates of a'?.
The coordinates of A' in triangle A'B'C' which was produced after reflection with condition y =x is equal to option d. ( 1, 2).
Graph is attached.
Triangle A'B'C' is produced after reflection of the triangle ABC over the line y = x.
From the graph we have ,
Coordinates of A is ( 2 , 1)
Coordinates of B is (-1, 4)
Coordinates of C is ( 0, -2)
Condition of reflection of triangle ABC over the line y = x.
x-coordinates replace by y and y replace by x.
Coordinates of triangle A'B'C' are
Coordinates of A' is ( 1, 2)
Coordinates of B' is (4, -1 )
Coordinates of C' is ( -2, 0 )
Therefore, if the coordinates of point A in triangle ABC are (2, 1), the coordinates of point A' in triangle A'B'C' would be option d. (1, 2).
The above question is not complete , the complete question is:
Triangle ABC is reflected over the line y = x to produce triangle A'B'C'. What will be the coordinates of A'? Graph is attached.
a. (2,−1) b. (−2,−1) c. (2,1) d. (1,2)
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Kirill purchased 20 cows, pigs and chickens for $3,447. If cows cost $750 each,
pigs cost $60 each, and chickens cost $3 each, and he bought two more chickens than
pigs, how many of each animal did he purchase?
Explanation on how to do this please?
Answer:
Step-by-step explanation:
i don't know
you sell small candles for 14$ and large candles for 16$ at the warehouse. At the warehouse, you pay x dollars for small candles and y dollars for large candles after one month you sold 45 small candles and 68 large candles at a store. A write and simplify and expression. B if you buy the candles at the warehouse for 5$ for small candles and 7$ for large candles what is the profit after your month of selling at the store?. Thank you so much
Solve.
√9 = + [?]
Enter the number that goes in the green box.
Enter
Answer:
3
Step-by-step explanation:
the square root basically means ___ multiplied by ___ equals the number in the square root, in this case being 9. the +/- symbol means that -3 multiplied by -3 equals positive 9 and positive 3 multiplied by positive 3 equals positive 9
A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 18% are pennies and 36% are dimes. There are 2 more nickels than pennies. How much money does the bag contain?
Answer: $4.20
Step-by-step explanation:
The bag contains $4.20. We know that 18% of the coins are pennies and 36% are dimes. There are 50 coins total, so 18% of 50 is 9 pennies and 36% of 50 is 18 dimes. Since there are 2 more nickels than pennies, there must be 11 nickels. 9 pennies plus 11 nickels plus 18 dimes equals 38 coins. To calculate the total amount of money, we multiply 38 by the value of each type of coin: 9 pennies x $0.01 = $0.09, 11 nickels x $0.05 = $0.55, and 18 dimes x $0.10 = $1.80. Adding these together, we get $0.09 + $0.55 + $1.80 = $2.44. Therefore, the bag contains $4.20.
Answer: There are 9 pennies, 18 dimes, and 11 nickels and 12 quarters
so in total, the bag has $11.2
Step-by-step explanation:
18% of 50 = 9
36% of 50 = 18
Mona bought 556.9 ounces of sugar, and she spilled 18.5 ounces of it on the floor. How much is left?
Answer: i think it is 538.4
Step-by-step explanation:
PLEASE HELP ME ASAP WHAT IS THE VALUE OF X IN THE QUADRILATERAL
From the sum of the interior angles, it is possible to find x=70°.
Quadrilaterals
There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square, all angles are 90° and all sides present the same value.
The sum of the interior angles of a quadrilateral is equal to 360°.
The question gives a trapezoid and its respective angles. Thus,
x+85+150+55= 360
x+140+150=360
x+290=360
x=360-290
x=70°
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Answer:
b) 70°
Step-by-step explanation:
We know that,
→ The sum of all interior angles in a quadrilateral is 360°.
Now we have to,
→ Find the required value of x.
Forming the equation,
→ 85° + 150° + 55° + x = 360°
Then the value of x will be,
→ 85° + 150° + 55° + x = 360°
→ 290° + x = 360°
→ x = 360° - 290°
→ [ x = 70° ]
Hence, the value of x is 70°.
two lines that form a right angle at their point of intersection
Two lines that form a right angle at their point of intersection are perpendicular to each other.
The negative reciprocal is equal to the slope of the perpendicular lines. A transversal line is a line that is perpendicular to two parallel lines. Equal pairs of alternate angles and matching angles are created in the case of the transversal line.
When two lines intersect at a right angle, they are perpendicular to each other. The junction is referred to as the point of perpendicularity. The perpendicular lines form a 90-degree angle, and they can be used to create a coordinate system or used in geometric constructions. Such lines are called perpendicular lines.
Correct Question :
Two lines that form a right angle at their point of intersection are called what?
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What is 90 degree F in C?
90 degrees Fahrenheit is equal to approximately 32.2 degrees Celsius using conversion formula method.
To convert Fahrenheit to Celsius, the following formula can be used:
Celsius = (Fahrenheit - 32) x 5/9
Plugging in 90 degrees Fahrenheit, we get:
Celsius = (90 - 32) x 5/9
Celsius = 58 x 5/9
Celsius = 290/9
Celsius ≈ 32.2
Therefore, 90 degrees Fahrenheit is approximately 32.2 degrees Celsius.
Fahrenheit is a temperature measurement system developed by the German physicist Daniel Gabriel Fahrenheit in 1724.
The Celsius scale is widely used throughout the world for measuring temperature, and it is the standard unit of temperature used in most scientific research and international trade. In addition to measuring air temperature, Celsius is used to measure temperature in a variety of fields, including chemistry, biology, and engineering.
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The diameter of a circle is 24 cm. Find its area to the nearest whole number.
Answer:
Area = 452 cm²
Step-by-step explanation:
[tex] = \frac{\pi }{4} {d}^{2} [/tex]
[tex] = \frac{\pi}{4} {(24)}^{2} = 452.39 \: cm²[/tex]
which go's to which.................................
the matches are
-2(2x+5) ≤ -7(x+4) x<=-6
4x-3x-1 x<=-1
5(x-3)9(x+1) x>=-6
3(x-4)+5 2x-9 x>=-2
What is inequality?Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.
Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.
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The correct matching of the inequalities can be shown from the calculations below
What is inequality?
Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.
Using the principle of inequalities we have;
1) -2(2x + 5) ≤ - 7(x + 4)
-4x -10 ≤ -7x -28
-4x +7x ≤ -28 + 10
3x ≤ -18
x ≤ -6
2) 4x - 6/2 ≥ 3x - 1
4x - 6 ≥ 6x - 2
4x - 6x ≥ -2 + 6
-2x ≥ 4
x ≤ -2
3) 5(x - 3) ≤ 9(x + 1)
5x - 15 ≤ 9x + 9
5x - 9x ≤ 9 + 15
-4x ≤ 24
x ≥ -6
4) 3(x - 4) + 5 ≥ 2x - 9
3x - 12 + 5≥ 2x - 9
3x - 2x ≥ -9 + 12 -5
x ≥ -2
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What is the rate of change?
Answer:
Step-by-step explanation:
75%
3. Arianne is purchasing a new home. After making her down payment, she will need to obtain a mortgage for $90,000. Based on her credit score, she qualifies for a fixed rate 30-year mortgage with a 5% APR. Calculate her monthly payment, the amount of her first monthly payment that is an interest payment, the amount that is applied to the principal, and the new loan balance.
i have the answers i just need help on explaining how i got there, i’ve been working on it for over than 2hrs and can’t find it, please help
Arianne's monthly mortgage payment will be $536.82.
What is the monthly payment of Arianne?A mortgage payment is generally made up of components like principal, interest, taxes and insurance. The interest is the cost of borrowing money. The amount of interest one pay is determined by your interest rate and your loan balance.
To calculate Arianne's monthly mortgage payment, we can use the following formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
First, we need to calculate the monthly interest rate: i = APR / 12 = 5% / 12 = 0.004167
Next, we can substitute the values into the formula: The computation of our monthly payment goes as follows:
= $90,000 [ 0.004167(1 + 0.004167)^360 ] / [ (1 + 0.004167)^360 – 1 ]
= $536.82.
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Liz is buying a home for $426,000. She is making a 22% down payment and financing the rest with a 20-year loan at 5.25% interest.
What will her total payment for the home be? Round your answer to the nearest dollar.
Use a mortgage table to find the monthly mortgage payment per 1000 dollars borrowed.
$598,424
$600,306
$610,442
$631,057
In linear equation, $869,776 will her total payment for the home be .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
You have to use the number in the intersection of the row for 5.25% interest and the column for 20 years.
The number is $6.74.
That means that, for every $1,000 borrowed for 20 years at 5.25% interest you will pay $6.74 every month.
2. Amount borrowed
You will make a 22% down payment:
Thus the amount borrowed is $426,000 - $93,720 = $332,280
3. Monthly payment
Multiply the monthly payment per 1,000 by the amount borrowed divided by 1,000:
4. Total monthly payments:
Multiply the number of payments by the monthly payment.
Number of payments = 20 years × 12 payments /year = 240 payments.
5. Total payment for the home.
The total payment for the home will be the down payment plus the amount paid to the bank:
$322,280 + $537,496 = $869,776
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