Answer:
Step-by-step explanation:
The simple interest formula is given by I = Prt, where P is the principal amount, r is the interest rate (per compounding period), and t is the time in years.
In this case, the interest rate is 5% per month, so we need to convert it to the equivalent annual interest rate, given by r = (0.05 x 12) = 0.6 (since there are 12 months in a year).
The time is 1.5 years, so t = 1.5.
So, the simple interest is:
I = Prt = 1000 x 0.6 x 1.5 = 900
The future value of the investment is the principal amount plus the interest earned, given by:
Future value = P + I = 1000 + 900 = 1900
So, the future value of the investment is $1900.
Answer: the future value of the simple interest investment, where 5% interest is paid monthly for 1.5 years on $1000, is $18074.06.
Step-by-step explanation:
To determine the future value of a simple interest investment, we need to calculate the interest earned over the investment period and add it to the original investment amount. Here's a step-by-step explanation for calculating the future value of a simple interest investment with a 5% interest rate paid monthly for 1.5 years on $1000:
Step 1: Convert the annual interest rate to a monthly rate.
Since the interest rate is 5% per year and the interest payments are made monthly, we need to convert the annual interest rate to a monthly interest rate. We can do this by dividing the annual interest rate by 12:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 5% / 12 = 0.05 / 12 = 0.00417
Step 2: Calculate the interest payment for each month.
For each month, we can calculate the interest payment by multiplying the monthly interest rate by the current balance:
Interest payment = Monthly interest rate * Current balance
Let's calculate the interest payment for the first month:
Interest payment = 0.00417 * $1000 = $4.17
Step 3: Add the interest payment to the current balance to get the new balance.
After each interest payment, we can add it to the current balance to get the new balance:
New balance = Current balance + Interest payment
New balance = $1000 + $4.17 = $1004.17
Step 4: Repeat the steps for each month.
We can repeat steps 2 and 3 for each of the 12 months in the first year and then for the 6 months in the second year.
Step 5: Add up the final balance.
After all 18 interest payments have been made, the final balance will be the sum of all the new balances:
Final balance = $1004.17 + $1004.17 + ... + $1004.17 (18 times) = $1004.17 * 18 = $18074.06
So, the future value of the simple interest investment, where 5% interest is paid monthly for 1.5 years on $1000, is $18074.06.
The histogram shows the ages of cars sold at a car auction. What percent of the cars was less than 20 years old or more than 40 years old?.
By the analysis of histogram , 40% percent of the cars was less than 20 years old or more than 40 years old.
The histogram may be seen here. Each column lists the age range at the bottom and the number of automobiles in that age group on the left.
The number of vehicles in the first two columns from the left (age 0-9 and 10-19) and the last two columns (age > 40) must be added together to determine the percentage of vehicles with less than 20 years or more than 40 years of age (age 40-49 and 50-59).
The total number of requested vehicles is equal to 8 that is (3 + 2 + 0 + 3).
The total number of automobiles must now be determined (by adding the cars in each column): 3 + 2 + 8 + 4 + 0 + 3 = 20
The ratio of the number of automobiles of the specified age to the total number of cars must then be calculated and converted into a percentage.
[tex]\frac{8}{20}[/tex][tex]= 0.40 = 40%[/tex]
40% percent of the cars was less than 20 years old or more than 40 years old.
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What is the sum of the following temeratures? -10°C; 24 °C; -12°C;8°C; -1 °C
The sum of the given temperature measures as required is; -9°C.
What is the value of the addition of the give temperatures;It follows from the task content that the sum of the given temperature measures is to be determined.
Since the given temperatures are; -10°C; 24 °C; -12°C; 8°C; -1 °C.
Therefore, the sum of the temperatures can be determined as follows;
-10°C + 24 °C + -12°C + 8°C + -1 °C
= 9°C.
Ultimately, the sum of the given temperatures is; 9°C.
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How many solutions does the following system of equations have?
There is No solution the system of Equation have.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Slope of Red line = Rise/ Run = 2/3
Slope of Blue line = Rise/ Run = 4/6 = 2/3
As, the two lines have the same slope and hence must be parallel, there are only two options: either they are separate lines, in which case there are no solutions, or they are the same exact line, in which case there are an endless number of solutions.
There are no answers since the two lines must be different since they are parallel and share the same slope but have separate y-intercepts.
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please help!!!! i need help pls
The volumes of the objects are;
1) 252 in^3
2) 850 cm^3
3) 90 cm^3
4) 936 feet^3
5) 168 cm^3
6) 125 m^3
How do we find volume of a cube?The volume of a cube can be found by using the formula:
V = s^3
where V is the volume and s is the length of one side of the cube. In other words, the volume of a cube is equal to the length of one side of the cube raised to the power of 3.
1) Volume = 7 * 9 * 4 = 252 in^3
2) Volume = 50 * 17 = 850 cm^3
3) Volume = 30 * 3 = 90 cm^3
4) Volume = 6 * 12 * 13 = 936 feet^3
5) Volume = 56 * 3 = 168 cm^3
6) Volume = 5^3 = 125 m^3
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A line passes through the points ( – 8,9) and ( – 2, – 9). Write its equation in slope-intercept form.
The slope-intercept form of the equation of the given line which passes through the points ( – 8,9) and ( – 2, – 9) is:
y = -3x - 15
What is meant by slope-intercept form of the line equation?
The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis) are known, the slope-intercept formula can be used to determine the equation of a line. The equation of a line is the equation that each point on the line fulfils.
Given the line passes through the points (– 8,9) and ( – 2, – 9).
When only two points on the line are given, the equation of the line is:
y - y₁ = m ( x - x₁)
m = slope = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] = (-9 - 9)/ ( -2 -(-8)) = -18/ 6 = -3
Substituting,
y - 9 = -3 ( x - ( -8))
y - 9 = -3x -24
y = -3x - 15
Therefore the slope-intercept form of the equation of the given line is:
y = -3x - 15
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If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
1) csc Θ = undefined
Answer:
that these angles are inclusive of 0° and 360° because the question states that 0° ≤ Θ ≤ 360°.
Step-by-step explanation:
If csc Θ is undefined, that means that the sine of the angle is zero, because csc Θ is the reciprocal of the sine function, and division by zero is undefined.
So we need to find all the angles where sin Θ = 0.
The sine function is equal to zero at multiples of 180 degrees, so the solutions to sin Θ = 0 are:
Θ = 0°, 180°, 360°
Note that these angles are inclusive of 0° and 360° because the question states that 0° ≤ Θ ≤ 360°.
Please help! 100 POINTS!!!!
Answer:
Answer is B.
[9 9]
[-3 2]
example: 3+6=9 9+0=9
5+ -8= -3 -2+4= 2
Branly please
Given the following historical demand and forecast, calculate the Tracking Signal in Week 3:
Week 1 Demand: 50 Forecast: 49
Week 2 Demand: 54 Forecast: 56
Week 3 Demand: 58 Forecast: 60
The Tracking Signal in Week 3 is -1.8.
The Tracking Signal in Week 3 can be calculated by using the following formula:
Tracking Signal = (Sum of Forecast Errors) / (Mean Absolute Deviation)
First, we need to calculate the forecast errors for each week:
Week 1 Forecast Error = Actual Demand - Forecast = 50 - 49 = 1
Week 2 Forecast Error = Actual Demand - Forecast = 54 - 56 = -2
Week 3 Forecast Error = Actual Demand - Forecast = 58 - 60 = -2
Next, we need to calculate the Mean Absolute Deviation (MAD):
MAD = (|1| + |-2| + |-2|) / 3 = (1 + 2 + 2) / 3 = 5 / 3 = 1.67
Finally, we can calculate the Tracking Signal:
Tracking Signal = (1 + -2 + -2) / 1.67 = -3 / 1.67 = -1.8
Therefore, the Tracking Signal in Week 3 is -1.8.
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let a (x)=3x^3-4x^2+x, and b(x)=x^2+2
Divide polynomials with remainders
a(x) = b(x) * (3x² - 10x + 21) + (8x - 8)
Polynomial Division with RemaindersTo divide the polynomial a(x) by b(x), we can use long division as follows:
3x - 6
-------------------
x² + 2 | 3x² - 4x² + x
- (3x³ + 0x²)
---------------
-4x² + x
- (-4x² - 8)
-------------
8x - 8
Therefore, the quotient is 3x - 6, and the remainder is 8x - 8.
We can write the result of the division as:a(x) = b(x) * (3x - 6) + (8x - 8)
Alternatively, we can use synthetic division to get the same result:-2 | 3 -4 1 0
| -6 20 -42
|-------------
| 3 -10 21 -42
The numbers on the bottom row represent the coefficients of the quotient, which are 3, -10, 21. The last number on the bottom row, -42, is the remainder. Therefore, the quotient is:
3x² - 10x + 21
And the remainder is:8x - 8
We can write the same result as before:a(x) = b(x) * (3x² - 10x + 21) + (8x - 8)
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Javier is standing at a distance from a flagpole. He sights the bottom of the flagpole at a 4°
angle of depression and the top of the flagpole at a 25°
angle of elevation. If Javier is 6 feet tall, what is the total height, to the nearest foot, of the flagpole?
Answer: To find the height of the flagpole, we can use the fact that the angles of depression and elevation are complementary angles, meaning that they add up to 90°.
Let's call the height of the flagpole "h". Then, we have:
h - 6 = h * tan(4°) (the height difference between Javier and the bottom of the flagpole)
and
h = 6 + h * tan(25°) (the height of the top of the flagpole as seen by Javier).
By substituting the first equation into the second, we can find h:
h = 6 + h * tan(25°)
h = 6 + h / tan(65°)
h * tan(65°) = 6 + h
h * tan(65°) - h = 6
h = 6 / (tan(65°) - 1)
Using a calculator, we find that h = approximately 43.3 feet. Rounding to the nearest foot, the height of the flagpole is 43 feet.
Step-by-step explanation:
2x − 5y + 3x = 8
3x − y + 4z=7
x+3y + 2x = -3
Answer:=3
Step-by-step explanation: For 2x-5y=3 substitute
what is the greatest common factor of 14 and 46
Answer: 2
Step-by-step explanation:
List all the factors:
14:
1 x 14
2 x 7
46:
1 x 46
2 x 23
Two is the only greatest number that can go into both 46 and 14.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure.
Maria uses a coordinate grid to display the following mathematical equation = 8√ 5 (5 + 2√5)
The term "mathematical expression"Mathematical expression is defined. A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like add, subtract, multiplying, divisions, exponentiation, and other as-yet-unlearned operations and functions.
How should a mathematical expression be written?Mathematical operators like addition, negation, multiplication, and division are used to create expressions in writing. The mathematical equivalent of an English phrase is a correctly arranged set of mathematical characters that expresses a coherent idea.
Here, Points are,
⇒ (1, 3) (5, 7) (5, 5) (8, 9) (8, 3 ) (1, 3)
Clearly, It make pentagon.
And, Area of pentagon = 1/4 √5 (5 + 2√5) a²
Here, The side of pentagon = √ (7 - 3)² + (5 - 1)²
= √4² + 4²
= √32
= 4√2
Thus, Area of figure = 1/4 √5 (5 + 2√5) a²
= 1/4 √5 (5 + 2√5) (4√2)²
= 8√ 5 (5 + 2√5)
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Answer:Maria uses a coordinate grid to display the following mathematical equation = 8√ 5 (5 + 2√5)
The term "mathematical expression"
Mathematical expression is defined. A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like add, subtract, multiplying, divisions, exponentiation, and other as-yet-unlearned operations and functions.
How should a mathematical expression be written?
Mathematical operators like addition, negation, multiplication, and division are used to create expressions in writing. The mathematical equivalent of an English phrase is a correctly arranged set of mathematical characters that expresses a coherent idea.
Here, Points are,
⇒ (1, 3) (5, 7) (5, 5) (8, 9) (8, 3 ) (1, 3)
Clearly, It make pentagon.
And, Area of pentagon = 1/4 √5 (5 + 2√5) a²
Here, The side of pentagon = √ (7 - 3)² + (5 - 1)²
= √4² + 4²
= √32
= 4√2
Thus, Area of figure = 1/4 √5 (5 + 2√5) a²
= 1/4 √5 (5 + 2√5) (4√2)²
= 8√ 5 (5 + 2√5)
Step-by-step explanation:
Marcus is 30 years younger than his mother. In 5 years, Marcus' age will be 1/4 of his mother's age. Find Marcus' mother's current age
Marcus is 30 years younger than his mother. Marcus' mother's current age is 35 years old.
To find Marcus' mother's current age, we need to use a system of equations.
Let:
x = Marcus' current age
y = his mother's current age.
We can write two equations based on the information given:
x = y - 30 (Marcus is 30 years younger than his mother)
x + 5 = 1/4(y + 5) (In 5 years, Marcus' age will be 1/4 of his mother's age)
Now we can substitute the first equation into the second equation and solve for y:
y - 30 + 5 = 1/4(y + 5)
y - 25 = 1/4y + 5/4
(3/4) y = 105/4
y = 105/3 = 35
So Marcus' mother's current age is 35 years old.
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Which events are mutually exclusive?
A double ferris wheel is pictured below. A large rotating arm with diameter 20 is centered 14 meters off the ground, and completes one rotation every 11 minutes. At the end of each side of the large arm is a smaller wheel with diameter 6 meters, which completes one rotation about its center every 6 minutes.
If you board the ferris wheel at point P at time t = 0, and each wheel rotates in the direction shown by the arrows, find an equation for your height, H above ground after t minutes.
This equation reflects the passenger's height above the ground after t minutes: H = 14 + 3 + (10)sin(2πt/11) + (3)sin(2πt/6).
What is equation?An equation in mathematics is a statement that two mathematical expressions are equal. Equations are used to represent mathematical relationships and to describe the behavior of systems or processes. An equation typically consists of two sides, separated by an equal sign (=). On one side of the equal sign is the expression representing what is known or given, and on the other side is the expression representing what is being found or sought. Equations can be used to model real-world situations, to describe the behavior of mathematical functions, to solve problems, and to make predictions. They are an important tool in many areas of mathematics and science, including algebra, calculus, physics, and engineering.
Here,
The height of a passenger on a double Ferris wheel can be calculated by considering the combined effect of two rotations: the rotation of the large arm and the rotation of the smaller wheel.
Let's call the length of the small arm as x, which is equal to half of the diameter of the small wheel, i.e. x = 3.
At time t = 0, the passenger is at point P, which is x meters above the ground. As the large arm rotates, the height of the passenger will change according to the formula:
H = 14 + x + (20/2)sin(2πt/11)
Where H is the height above the ground after t minutes, and (20/2) is half of the diameter of the large arm.
Additionally, as the small wheel rotates, the height of the passenger will change according to the formula:
H = H + (3)sin(2πt/6)
So, combining both the effects, the height of the passenger on the Ferris wheel can be expressed as:
H = 14 + 3 + (10)sin(2πt/11) + (3)sin(2πt/6)
This equation represents the height of the passenger above the ground after t minutes: H = 14 + 3 + (10)sin(2πt/11) + (3)sin(2πt/6).
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5. The table shows the number of pounds, x, of coffee ordered and the total price, y, in dollars, of each order. X 5 6 7 10 y $35 $42 $49 $70 Which best represents the units for the rate of change (rise over run) in the table? a.dollars. b.dollars per pound. c.pounds b.pounds per dollar
The table shows the number of pounds, x, of coffee ordered and the total price, y, in dollars, of each order. X 5 6 7 10 y $35 $42 $49 $70 Which best represents the units for the rate of change (rise over run) in the table? a.dollars. b.dollars per pound. c.pounds b.pounds per dollar
To find the units for the rate of change (rise over run), we need to determine the change in y (rise) divided by the change in x (run) for any two points in the table.
Let's choose the first and last points in the table, (5, $35) and (10, $70), respectively. The change in y is $70 - $35 = $35, and the change in x is 10 - 5 = 5. So the rate of change (rise over run) is:
rise/run = $35/5 = $7
Therefore, the best representation for the units of the rate of change is dollars per pound, as the rate of change indicates how much the price changes for every pound of coffee ordered. So the answer is (b) dollars per pound.
A sphere has a surface area of 100cm^2. Calculate the volume of the sphere
The radius of the sphere is 2.82 cm. Then the volume of the sphere will be 94.05 cubic cm.
What is the volume of the sphere?Let r be the radius of the sphere. Then the volume of the sphere will be given as,
V = 4/3 πr³ cubic units
The surface area of the sphere is 100 square cm. Then the radius of the sphere is given as,
100 = 4πr²
r = 2.82 cm
Then the volume of the sphere is given as,
V = 4/3 x π x 2.82³
V = 1.33 x 3.14 x 22.465
V = 94.05 cubic cm
The volume of the sphere will be 94.05 cubic cm.
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does any1 know the answer to this?
Answer:
Check below under ‘explanation’
Step-by-step explanation:
5 Units up means every point will move 5 units in the upward direction along the y- axis. Therefore the x- coordinates of every point will remain the same and only their y-coordinates will change:
Q’ = [tex](-8, -4)[/tex]
R’ = [tex](-2, -4)[/tex]
S’ = [tex](-2, 4)[/tex]
T’ = [tex](-8, 4)[/tex]
If the angles of a triangle are in the ration of 3 : 4 : 5, find them.
Answer:
the angles of the triangle are 45 degrees, 60 degrees, and 75 degrees, and they are in the ratio of 3 : 4 : 5.
Step-by-step explanation:
Let's denote the angles of the triangle as 3x, 4x, and 5x, where x is a constant.
Since the sum of the angles of a triangle is 180 degrees, we can write the following equation:
3x + 4x + 5x = 180
Simplifying this equation, we get:
12x = 180
Dividing both sides by 12, we get:
x = 15
Therefore, the angles of the triangle are:
3x = 3(15) = 45 degrees
4x = 4(15) = 60 degrees
5x = 5(15) = 75 degrees
So the angles of the triangle are 45 degrees, 60 degrees, and 75 degrees, and they are in the ratio of 3 : 4 : 5.
What is the mean of this set 0,3,6,9,11,13,14
Answer:
8
Step-by-step explanation:
0+3+6+9+11+13+14 = 56
56/7 = 8
Does anyone have the answers to the first part of UNIT 3 Polynomials and Factoring LESSON 9 Polynomials and Factoring Unit Test Connexus
A polynomial is an expression consisting of variables and coefficients and factoring is the process of breaking down a polynomial into simpler units
A polynomial is an expression consisting of variables and coefficients, which are combined using only addition, subtraction, and multiplication. For example, 3x^2 + 2x - 1 is a polynomial, where x is the variable, 3 and 2 are coefficients, and ^2 and ^1 are exponents.
Factoring is the process of breaking down a polynomial into simpler units, which can be multiplied together to obtain the original polynomial. The simplest units are usually linear expressions, which have the form ax + b, where a and b are coefficients. For example, the polynomial 3x^2 + 2x - 1 can be factored into (3x - 1)(x + 1) by identifying two linear expressions that when multiplied together produce the original polynomial.
Factoring is an important tool in algebra, as it can help to simplify expressions, solve equations, and identify the roots of a polynomial.
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A week before a state election, a random sample of voters from City J and a random sample of voters from City K were taken. Of the 100 voters selected from City J, 65 indicated they were supporting a certain candidate for state senate. Of the 125 voters selected from City K, 75 indicated they were supporting the same candidate. Which of the following is the correct combined proportion, Pc, for the difference in population proportions for the two cities (J minus K) in their support for the candidate?
The proper combined percentage, Pc, for the disparity in population proportions between the two cities' support for the candidate (J minus K) is: 0.65−0.60 / √(0.62) (0.38) (1/100 + 1/125)
What is meant by proportion?An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls). If two ratios or fractions are equivalent, it can be shown using the proportion formula. By dividing the supplied values, we may determine the value that is missing. You may write the percentage formula as a: A and d are the extreme terms, and b and c are the mean terms, according to the formula b::c: d = a/b = c/d.An equation in which two ratios are made equal is known as a percentage.Therefore, the correct answer is 0.65−0.60 / √(0.62) (0.38) (1/100 + 1/125)
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base area 42 m height 8 m
Where may you be going with this?
A sidewalk in the shape of two triangles, a rectangle, and a square was built around the edge of a building shown. What’s is the area of the sidewalk in square feet
Answer:144
Step-by-step explanation:
Help me find the measurements please.
Charlie reads quickly. He reads
1
3
7
1
7
3
1, start fraction, 3, divided by, 7, end fraction pages every
2
3
3
2
start fraction, 2, divided by, 3, end fraction minutes. Charlie reads at a constant rate.
Charlie reads [tex]2\frac{1}{7}[/tex] pages per minute.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Charlie reads [tex]1\frac{3}{7}[/tex] pages every [tex]\frac{2}{3}[/tex] minute.
Therefore, His unit rate can be obtained by dividing the number of pages by the amount of time which is,
= [tex]\frac{1\frac{3}{7}}{\frac{2}{3}}[/tex] pages per minute.
= (10/7)×(3/2) pages per minute.
= 30/14 pages per minute.
= 15/7 pages per minute.
= [tex]2\frac{1}{7}[/tex] pages per minute.
Q. Charlie reads quickly he reads [tex]1\frac{3}{7}[/tex] pages every [tex]\frac{2}{3}[/tex] minute, His unit rate of page per minute would be?
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What is a 2 sample z-test?
Answer:
Two-Sample Z-Test. The Two-Sample Z-test is used to compare the means of two samples to see if it is feasible that they come from the same population. The null hypothesis is: the population means are equal.
Step-by-step explanation:
have a nice day.
Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
If 1 gallon equals 4 quarts then Lorraine can fill total 8 jars.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars.
First, we need to convert the 2.5 gallons of tomatoes to quarts.
As, 1 gallon = 4 quarts then
2.5 gallons = 2.5 x 4 = 10 quarts.
Now, number of quarts per jar
= 10 quarts / 1.25 quarts/jar
= 8 jars.
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pls help fast..Special Triangle Segments
.. 1.Find the value of the variable given the triangles are similar. Answer the additional questions. Show all work. Name the property you used in your problem.
Answer: (Give brainliest)
a = 4.5
type of segment = Angle Bisector
property = property of XT/WY = XY/WZ
Step-by-step explanation: