5. A candy company used 12 gallons of syrup to make 6 batches of candy. What is the rate of syrup per batch?​ (Please explain!)

D. mz1 = 45° and mz2 = 45 are complementary angles (mz1 + mz2 = 90°), but neither angle is obtuse (greater than 90°), so the guess is wrong. This is a counter-example to show.

A supplementary angle is an angle where the sum of two angles is 90 degrees. That is, if angle A and angle B are complementary, angle A measurement + angle B measurement = 90 degrees. Supplementary angles may be adjacent (having a common vertex and edge) or non-adjacent (having no common vertex or edge), but they always complement each other.

There are various kinds of angles to study.

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The amount that Roxanne should deposit at the beginning of each 3 months to accumulate $134,000 at 4% compounded quarterly for three years is $10,461.13.

The quarterly deposit can be computed using an online finance calculator with the following parameters.

The quarterly deposit shows the periodic investment that must be made to accumulate a future value of $134,000.

N (# of periods) = 12 quarters (3 x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

FV (Future Value) = $134,000

Results:

PMT (periodic deposits) = $10,461.13

Sum of all periodic deposits = $125,533.56

Total Interest = $8,466.44

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Length of fence = Circumference of the pool – width of the gate. Length of fence = 6.28x – 150 cm.

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Let x be the number of hamburgers sold, then the number of cheeseburgers sold can be represented as 2x. The total number of hamburgers and cheeseburgers sold is the sum of these two quantities, so we can write an equation:

x + 2x = 396

To solve for x, we can combine like terms on the left side of the equation:

3x = 396

Then we can divide both sides by 3 to get:

x = 132

So, the number of hamburgers sold on Saturday is 132.

Step-by-step explanation: 1 is in the ten thousand places and has a place value of 10,000. 3 is in the thousand's place and has a place value of 3,000. 5 is in the hundreds and has a place value of 500.

Answer:

it is undefined

Step-by-step explanation:

Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.

Answer:

undefined slope

Step-by-step explanation:

When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.

It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.

You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:

n = (1200 - 2550) ln / ln (1 - 0.05)

Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.

When we enter the values, we will get:

n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months

The motorcycle will take approximately 15.7 months to drop in value to less than £1200.

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Answer:

Step-by-step explanation:

X+X+X+Y+Y=

you simply count equal letters and add them x+x+x is 3x and y + y = 2y.

x + x + x + y + y =

3x + 2y

There are 34 ways by which  pairs of potential clients can be randomly chosen from pool or eight candidates.

We can be able to talk about the combination when the order of the selection is not seen as important as in the case that we have in the question here. We have been told that the pairs are to be chosen randomly.

As such we would have the use of the formula for combination as follows;

C = n!/r!( n - r)!

C = 8!/2!(8 - 2)!

C = 8 * 7 * 6!/2! 61

C = 8 * 7/ 2 * 1

C = 28

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Answer: 28%

Step-by-step explanation: First, we need to find how much she runs in total on Tuesday and Wednesday. So, we add 3 + 4 to get 7. With that, we need to determine how much 7 is from 25. So, it'd look like this:

7 * 100 / 25

700 / 25

=28

Therefore, she's done 28% of her goal (within the 2 days) I hope this helped!

Answer:

I think the other person who answered the question is right

Step-by-step explanation:

Answer:

Step-by-step explanation:

LHS = tanθ/secθ - 1 + tanθ/secθ + 1

Cross multiplication,

tanθ(1 - secθ) - tanθ(1 + secθ)/1 + sec^2θ

= tanθ(1 - secθ - 1 - secθ)/-tan^2θ

= -2secθ/-tanθ

= 2 x 1/cosθ / sinθ/cosθ

= 2cosecθ = RHS

Hence proved.

Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

the formula is written as x3 -10x = 100.

We continue testing for the value of x that is valid for x3 -10x = 100 via trial and error.

We've made multiple tries and have:

x = 5.4 (roughly) (approximately)

In x3 -10x = 100, replace x with 5.4.

5.4^3 -10 * 5.4 = 100

Evaluate

103.5 = 100

Approximate

100 = 100

Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given  equation problem.

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Comparing the maple tree and the pine tree growth information, the tree that grows faster is the pine tree.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,  b for maple is given as 1.5 and we calculate for pine using the data in the table. the equation is derived as follows

f(x) = a(b)ˣ

12 = a(b)¹

24 = a(b)²

dividing 24 = a(b)² by 12 = a(b)¹

b = 2

hence for pine tree the b is 2 which is greater than 1.5

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a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.

b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).

The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:

Area = base x height.

The base and the height for this problem are obtained counting the number of dots, hence:

Hence the area is given as follows:

Area = 4 x 6

Area = 24 units squared.

The shaded region is composed by a triangle with base 4 and height 3, hence:

Area shaded = 0.5 x 4 x 3 = 6 units squared.

(formula for the area of the triangle).

Meaning that the fraction is given as follows:

6/24 = 1/4.

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Therefore , the solution of the given problem of triangle comes out to be  base=4m,16 and height=8m,2m.

In a plane, any three points can be joined to form triangles, which have three sides and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

Given :

Triangle area = 16[tex]m^{2}[/tex]

Thus,

To find the possible base and height of the triangle.

The base can be given by 4 m,16

and height be = 8m or 2m

vice-versa

height = 4m ,16mand base =8m,2m

Therefore , the solution of the given problem of triangle comes out to be  base=4m,16 and height=8m,2m.

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Answer:

see below

Step-by-step explanation:

given that the area of the triangle is 16m² . We need to list all the possible lengths of its base and height. As we know that, the area of triangle is ,

ar(∆) = 1/2 * base* height

substitute the respective values,

16m² = 1/2* b * h

b*h = 32

now here we need to list out all the possible factors of 32 as ,

1 *32

2 *16

4*8

8*4

16 *2

32*1

therefore, all the possible lengths of heights and bases are ,

and we are done!

-Rishabh

Answer:

18 red balls, 3 blue balls, 6 yellow balls.

Step-by-step explanation:

a ratio helps us understand the relationship between two or more values (in this case three values). More specifically it tells us how much of one item is present, for every amount another item is also present.

In this example, the ratio of red:blue:yellow is given to be: 6:1:2, which means, for every 6 red balls, there is one blue ball and two yellow balls.

In some cases, a ratio can be simplified, similar to a fraction, by dividing each number by some common factor, but in this case, the ratio cannot be simplified any further.

Instead of directly trying to find how many red, yellow, or blue balls there are first, we can instead try solving for how many group of sixes are there in the total number of red balls. It helps to think of it this way, since for every group of six red balls there are, there is one blue ball and two yellow balls, which means we can just multiply this number by one and two to find the number of blue and yellow balls in their respective orders. For simplicity, let's assign this to the unknown "G".

Using this logic, we can set up the following equation:

[tex]6G+1G+2G=27[/tex]

For every group of six red balls... there is 6 red balls, 1 blue ball, and 2 yellow balls, adding all these together should give us the total number of balls, which was given to be 27 balls. Now we can just combine the stuff on the left into one term, by adding the coefficients.

[tex]9G=27[/tex]

Now divide by 9

[tex]G=3[/tex]

Now that we know the number of group of six red balls there are, we can multiply six, one, and two to find the red, blue, and yellow balls.

[tex]\text{red balls} = 3 * 6 = 18\\\\\text{blue balls} = 3 * 1 = 3\\\\\text{yellow balls} = 3 * 2 = 6[/tex]

and you can all this together, to double check, which gives us 27.

Answer:

18,3,6

Step-by-step explanation:

Given ,

To Find : The number of red,blue and yellow balls present in the bag

Let us take the variable as 'x' to represent the number of balls in the bag

When we Put the values in a equation,

6x+x+2x = 27

9x = 27

x = [tex]\frac{27}{9}[/tex]

x = 3

Hence the number of,

Red Balls = 6x = 6 x 3 = 18

Blue Balls = x = 3

Yellow Balls = 2x = 2 x 3 = 6

Answer: The ratio 18:26 simplified is 9:13.

Step-by-step explanation:

To simplify the ratio 18:26, we find the greatest common divisor of 18 and 26, and then we divide 18 and 26 by the greatest common divisor.

The greatest common divisor that you can use to simplify 18:26 is 2. Which means the answer to ratio 18:26 simplified is: 9:13

Answer:9/13

explanation: k12

a cubic function whose graph passes through the points (-3, 0), (1, 0), (4, 0), and (0,8) is: f(x) = - 2 (x + 3) (x - 1) (x - 4)

A cubic function is a function whose expression contains the cube of the x variable. A function is referred to as a cubic function if its formula is f(x) = ax³ + bx² + cx + d. a, b, c, and d can all be constants in this case, but make sure that a 0. The b, c, or d might all be zeros.

A cubic function has 3 roots.

Let, assume α, β and γ.

So, f(x) = K (x - α). (x - β). (x - γ)

f(x) is defined by values of x where f(x) = 0

0 = K (x - α). (x - β). (x - γ)

x = α, β, γ

The given cubic function graph is cutting x - axis at 3 points: (-3, 1 ,4)

Now, f(x) = K (x - (-3). (x - 1). (x - 4)

f(x) = K (x + 3) (x - 1) (x - 4)

Next, f(x) passes through point (0,8) which means:

f(0) = 8

so, 8 = K (0 + 3) (0 - 1) (0 - 4)

or, k = - 2

Now, f(x) = - 2 (x + 3) (x - 1) (x - 4)

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Greatest common factor (GCF) of 50 and 65 is 5.

We will first find the prime factorization of 50 and 65. After we will calculate the factors of 50 and 65 and find the biggest common factor number .

Step-1: Prime Factorization of 50

Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:

50 = 21 × 52

Step-2: Prime Factorization of 65

Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:

65 = 51 × 131

Step-3: Factors of 50

1, 2, 5, 10, 25

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 50 and 65. The biggest common factor number is the GCF number.

So the greatest common factor 50 and 65 is 5.

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Raffles are chance-based contests in which participants compete to win exciting prizes.

To participate, all you need is a ticket with a number on it. Following the sale of all tickets, a drawing is conducted during which a random selection of tickets is made. If you chance to have the winning ticket, congratulations! a lot of engagement.

Raffles elicit a great deal of interest and support because people enjoy playing games of chance, especially when they have the possibility to win a significant prize.

high income. Your organisation has a strong possibility of making some big money from ticket sales if engagement is high!

low price. A virtual free raffle can be found online! A virtual raffle is the most cost-effective type of fundraising because you won't need to print actual tickets, reserve a location for the drawing, or buy refreshments.

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Answer: y = -150x + 1800

Step-by-step explanation:

1. Find the linear slope of the line between two points.

(Change in Y)/(Change in X)

2. Write out an equation in point slope form.

(y-y1) = m(x-x1)

y-1800 = -150(x-0)

3. Simplify the equation and turn it into slope-intercept form.

y = -150x + 1800

The relative frequency table that summarizes the data is given by the image at the end of the answer.

The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.

Given:

The percentage of people interested in waterskiing

= 90/250 x 100

= 36%.

Thus, the percentage of people that was not interested in waterskiing is

=100-36

= 64%

Now, the percentages related to paddle boarding are :

Yes: 72/250 = 28.8%.

No: 18/250 = 7.2%.

Of those not interested in waterskiing, the percentages related to paddle boarding are

Yes: 112/250 = 44.8%.

No: (120 - 72)/250 = 19.2%.

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Answer: 448

Step-by-step explanation: Parallelogram formula base times height

Answer:

Step-by-step explanation:

the answer is 6

Therefore , as a result, we may state that the stated trapezoid angles x = 110°, which is the solution to the problem.

A trapezoid is a quadrilateral that has at least one connected pair of sides. It has the name trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. The trapezoid's base is made up of its parallel sides. A closed, flat shape having two neighboring sides and four successive sides is called a trapezoid. The parallel walls and base of the trapezoid are commonly referred as as the parallel sides and the legs, respectively.

Here,

Given : 110°

and 90°

To find the value of x ,

Thus,

The value of angle opposite to x :

=> 110° + y =180°

=>y =180°-110°

=>y = 70°

thus, x value is

=> x + 70° =180°

=> x =110°

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The solution to the product expression 4/3 * 5/3 is 20/9

From the question, we have the following parameters that can be used in our computation:

The product 4/3*5/3

To start with, we need to represent the statement as an expression

So, we have the following representation

4/3 * 5/3

Using a calculator, we multiply the numerator

So, we have the following representation

4/3 * 5/3 = 20/3 * 1/3

Using a calculator, we multiply the denominator

So, we have the following representation

4/3 * 5/3 = 20/9

Hence, the solution is 20/9

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The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.

A system of linear equations consists of two or more equations and looks for common answers.

1. Let us suppose small prints = x

Large prints = y

Total prints sold can be written as follows:

x + y = 52

The total cost of the prints can be written as follows:

50x + 75y = 2975

The system of equations is:

x + y = 52   . . . equation 1

50x + 75y = 2975 . . .equation 2

Using equation 1 we have:

x = 52 - y

Substituting the value of x in equation 2 we have:

50(52 - y) + 75y = 2975

2600 - 50y + 75y = 2975

25y = 2975 - 2600

25y = 375

y = 15

Now, substituting the value of y in equation 1 we have:

x + 15 = 52

x = 52 - 15

x = 37

Hence, the solution of the system of equations is y = 15 and x = 37.

2. Let us suppose the altitude = x.

The rising balloon can be thus written as:

40 +10x

The descending balloon can be written as:

165 - 15x

Solving the system of equations by substituting the value of x we get x= 5.

Hence, the altitude at which both the balloons are at the same height is 5m.

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The ratio of number of burgers without onions to the number of burgers with onions is 4:1.

The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.

Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;

ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)

                = 12/ 3

                = 4/ 1

The ratio of number of burgers without onions to burgers with onions = 4:1

Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.

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Answer:

-3/4

Step-by-step explanation:

y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.