The selling price of each cup of lemon juice is 3/2 times as much as the selling price of a cup of apple juice. For every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. He earns $12 more from apple juice than from lemon juice. How much does Mr Tan earn altogether?

The triangles which are right triangles as required to be determined in the task content are; Choice A; Triangle 1 and Choice D; Triangle 4.

Recall; the Pythagorean theorem only holds for right triangles.

Therefore, for a triangle to be a right triangle; the square of its longest side must be equal to the sum of squares of its two other sides.

Therefore;

Triangle 1 is a right triangle because; (√106)² = 9² + 5²; 106 = 106.

Triangle 2 is not a right triangle because; (√39)² ≠ 2² + 6²; 39 ≠ 40.

Triangle 3 is not a right triangle because; (√179)² ≠ 6² + 12²; 179 ≠ 180.

Triangle 4 is a right triangle because; (√73)² = 3² + 8²; 73 = 73.

Ultimately, the correct choices are; Choices A ana D.

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The length of the tarp with an area of 200 square meters is 40 meters.

The area of a rectangle is expressed as;

Area = length × width

Given that;

When a rectangular tarp has an area of 200 square meters and a width of 5 meters, we can use the above formula to find the length of the tarp.

Plug these values into the formula and solve for the length:

Area = length × width

200 = Length x 5

To solve for Length, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 5:

200/5 = Length

This simplifies to:

40 = L

L = 40

Therefore, the rectangular tarp is 5 meters wide and 40 meters long.

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Answer:

To simplify the expression, we need to distribute the negative sign to all the terms inside the parentheses, and then combine like terms.

Starting with:

(5x^4-4x^3-2x^2+x-19)-(x^4+5x^3+8x^2+x+5)

Distribute the negative sign inside the parentheses:

5x^4 - 4x^3 - 2x^2 + x - 19 - x^4 - 5x^3 - 8x^2 - x - 5

Now we can combine like terms:

(5x^4 - x^4) + (-4x^3 - 5x^3) + (-2x^2 - 8x^2) + (x - x) + (-19 - 5)

Simplifying further:

4x^4 - 9x^3 - 10x^2 - 24

Therefore, the simplified expression is:

4x^4 - 9x^3 - 10x^2 - 24.

The solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3.

To solve the trigonometric equation sin 2x=−√3/2 on the interval [0,2π), we need to find the values of x that satisfy the equation. We can do this by using the inverse sine function and the periodicity of the sine function.

First, let's find the general solution of the equation:
sin 2x=−√3/2
2x= sin⁻¹(−√3/2) + 2πn or 2x= π - sin⁻¹(−√3/2) + 2πn, where n is an integer
2x= -π/3 + 2πn or 2x= 4π/3 + 2πn
x= -π/6 + πn or x= 2π/3 + πn

Now, we need to find the values of x that are in the interval [0,2π). We can do this by plugging in different values of n until we find all the solutions in the interval.

For x= -π/6 + πn:
When n=0, x= -π/6 (not in the interval)
When n=1, x= 5π/6 (in the interval)
When n=2, x= 11π/6 (in the interval)
When n=3, x= 17π/6 (not in the interval)

For x= 2π/3 + πn:
When n=0, x= 2π/3 (in the interval)
When n=1, x= 5π/3 (in the interval)
When n=2, x= 8π/3 (not in the interval)

Therefore, the solutions of the equation on the interval [0,2π) are x= 5π/6, 11π/6, 2π/3, and 5π/3. These are the exact form answers. If we want to round them to two decimal places, we get x= 2.62, 5.24, 1.05, and 3.14.

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Answer:

The price of per ounce of strawberries is $ 0.25.

Step-by-step explanation:

Pounds to ounce conversion:

As we know that,

 One pound = 16 Ounce

Since, Jill bought a pound of strawberries for $4

It means that,

Price of 16 Ounces of strawberries = $ 4

So taht,  Price of one ounce of strawberries

Hence, the price of per ounce of strawberries is $ 0.25.

Answer:

0.25

Step-by-step explanation:

16 ounces = 1 pound

4.00 / 16 = 0.25

The values of m that will result in a repeated solution for 3x^(2)+4mx+m=0  are m = 0 and m = 3/4.

The given quadratic equation is 3x^(2)+4mx+m=0. In order to find the value(s) of m that will result in a repeated solution, we need to use the discriminant of the quadratic formula.

The discriminant of the quadratic formula is given by b^(2)-4ac, where a, b, and c are the coefficients of the quadratic equation.

In the given equation, a = 3, b = 4m, and c = m.

Plugging these values into the discriminant, we get:

(4m)^(2)-4(3)(m) = 16m^(2)-12m = 0

A repeated solution occurs when the discriminant is equal to 0. So, we need to solve the equation 16m^(2)-12m = 0 for m.

Factoring out a common factor of 4m, we get:

4m(4m-3) = 0

This gives us two possible values for m:

4m = 0 or 4m-3 = 0

Solving for m, we get:

m = 0 or m = 3/4

Therefore, the values of m that will result in a repeated solution for the given quadratic equation are m = 0 and m = 3/4.

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y = 2.50 / (1 + 15.80^−x)

You can use technology to approximate the given data with a logistic regression curve y = N/(1 + Ab^−x).

To do this, you'll need to calculate the parameters A, N, and b. To calculate A and N, you can use the values of y at the extremes of x. At x = 0, y = 3.0 and at x = 150, y = 9.9. So, A = (9.9 - 3.0) / (1 - 0.003^150) and N = 9.9 - A*0.003^150. Then, b can be calculated using the average of the logarithm of all x values. The final logistic regression curve will be:

y = 2.50 / (1 + 15.80^−x)

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Answer:

964 1/4m

Step-by-step explanation:

length x width x height

Answer:

964.25 is the volume

Step-by-step explanation:

To find the volume of a rectangular prism your going to do length times width times height.

Your length is 7 1/4m

Your height is 14m

Your width is 9 1/2m

So we are going to do 7 1/4 * 9 1/2 * 14

Which will give you 964.25

The supplementary angles are ∠GDF and ∠EDG, ∠CED and ∠BEC. The correct options are C and D.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complementary angles is 90 degrees.

The sum of the two angles ∠GDF and ∠EDG is equal to 180°. So these angles are supplementary to each other.

The sum of the two angles ∠CED and ∠BEC is equal to 180°. So these angles are supplementary to each other.

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To determine the base of a parallelogram, we can use the formula for the area of a parallelogram, which is A = b*h, where A is the area, b is the base, and h is the height.

We are given the height (h) and the area (A), so we can rearrange the formula to solve for the base (b):
b = A/h

Substituting the given values for A and h:
b = 15/6

Simplifying:
b = 2.5

Therefore, the base of the parallelogram is 2.5 feet.

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Answer:  2+n

Step-by-step explanation:

Tn=T1 + (n-1) d

3+(n-1)1

3+n-1

3-1+n

2+n

Option D, {5+(-1/3)+(-10)}+(2/3+7), would be easier to simplify if we use the commutative property.

What is the commutative property, and how can it be used to simplify expressions?

The commutative property is a property of addition and multiplication that allows us to change the order of the numbers being added or multiplied without changing the result.

That is, [tex]a + b = b + a[/tex] and [tex]a \times b = b \times a[/tex].

To simplify expressions, we can use the commutative property to rearrange the order of the terms in a way that makes the arithmetic easier to perform.

Find the expression:

We are given the expression -1/3-10+7+2/3+5, and we want to know which option would be easier to simplify using the commutative property.

Option D, {5+(-1/3)+(-10)}+(2/3+7), would be easier to simplify using the commutative property because we can group the terms that have like terms together. Specifically, we can group the negative terms together and the positive terms together:

{5+(-1/3)+(-10)}+(2/3+7) = {(5)+[(-1/3)+(-10)]}+{(2/3)+7}

Now we can simplify each group separately. For the first group, we can add the terms inside the brackets using the commutative property:

{-1/3+(-10)} = -10 - 1/3 = -31/3

For the second group, we can add the terms directly:

{2/3+7} = 2/3 + 21/3 = 23/3

Substituting these results back into the original expression, we get:

-1/3-10+7+2/3+5 = -31/3 + 23/3 + 5

Now we can add the terms directly to get:

-31/3 + 23/3 + 5 = -8/3 + 5 = 7/3

Therefore, the expression simplifies to 7/3.

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Standard form of the number 3.5 × 10⁷ is 35000000.

In the United States and countries using US conventions, the standard form is the usual way of writing numbers in decimal notation.

The standard form of a number is a way of writing the number in a form that follows certain rules. Any number that can be written as a decimal number.

Given number

3.5 × 10⁷

In standard form, digits are written left or right of decimal

number can be written as

= 35000000

Hence, 35000000 is standard form of the number 3.5 × 10⁷.

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The inequality is 3x + 2y ≥ 93 and the grade received is A for the test

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the number of multiply questions be x

Let the number of matching questions be y

Substituting the values in the equation , we get

3x + 2y ≥ 93

when x = 20 and y = 18

On simplifying the equation , we get

3 ( 20 ) + 2 ( 18 ) ≥ 93

60 + 36 ≥ 93

96 ≥ 93

Therefore , the student receives an A grade for the test

Hence , the inequality is true

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Answer:

Step-by-step explanation: g

A company establishes a sinking fund to pay a debt of $150,000 due in 4 years. The required payment at the beginning of each six-month period is $6,235.54.

The sinking fund payment will earn interest at a rate of 9% per year, compounded semi-annually. This means the effective interest rate per six-month period is [tex](1 + 0.09/2)^2 - 1 = 0.045 = 4.5%[/tex]

Using the formula for the future value of an annuity, [tex]FV = R[((1+r)^n - 1)/r][/tex], where r is the interest rate per period and n is the number of periods, we can calculate the required payment R as:

[tex]150,000 = R[((1+0.045)^8 - 1)/0.045][/tex]

R = 6,235.54

Therefore, the company needs to make payments of $6,235.54 at the beginning of each six-month period to accumulate enough money in the sinking fund to pay off the $150,000 debt in 4 years.

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Answer: Factors

Step-by-step explanation:

The probability that a person from the survey who has a tablet also has a laptop is 0.058, or approximately 5.8%.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We are given that 62% of respondents have a tablet and 30% have a laptop.

Let T represent the event of having a tablet and L represent the event of having a laptop.

Then, we know -

P(T) = 0.62

P(L) = 0.30

We are also given that 12% of respondents who have a laptop also have a tablet.

In other words, the probability of having a tablet given that a person has a laptop is -

P(T|L) = 0.12

We can use this conditional probability to find the probability that a person who has a tablet also has a laptop, denoted by P(L|T).

By Bayes' theorem, we have -

P(L|T) = P(T|L) × P(L) / P(T)

Substituting the values we know, we get -

P(L|T) = 0.12 × 0.30 / 0.62

Simplifying this expression, we get -

P(L|T) = 0.058

Therefore, the probability value is 0.058, or 5.8%.

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Answer: cos B-sin²A = cos²A-sin-B

Step-by-step explanation:

Answer: cos B-sin²A = cos²A-sin-B

Explanation:

Using the double angle identity, we can express the left side of the equation as:

cos(A + B).cos(A-B) = cos A.cos B - sin A.sin B

Now, using the Pythagorean identity, we can rewrite the right side of the equation as:

cos²A-sin-B = cos A.cos B - sin A.sin B

Hence, we can conclude that cos(A + B).cos(A-B) = cos B-sin²A = cos²A-sin-B

Answer: Read the step by step explanation for the answer.

Step-by-step explanation:

We can prove this trigonometric identity using the product-to-sum and Pythagorean identities as follows:

Starting with the left-hand side (LHS):

cos(A + B).cos(A - B)

Using the product-to-sum identity:

= [cos A cos B - sin A sin B][cos A cos B + sin A sin B]

= cos²A cos²B - sin²A sin²B

Using the Pythagorean identity:

= cos²A(1 - sin²B) - sin²A(1 - cos²B)

= cos²A - cos²A sin²B - sin²A + sin²A cos²B

= cos²A - sin²A + sin²A cos²B - cos²A sin²B

Using the Pythagorean identity:

= cos²A - sin²A + sin²A(1 - sin²B) - cos²A sin²B

= cos²A - sin²A + sin²A - sin²A sin²B - cos²A sin²B

= cos²A - sin²A + sin²A cos²B - sin²B cos²A

= cos²A - sin²A + cos²A sin²B - sin²B cos²A

Using the Pythagorean identity:

= cos²A - sin²A + cos²A - sin²B

= 2cos²A - sin²A - sin²B

= cos²A + cos²A - sin²A - sin²B

= cos²A + sin²A cos²B - sin²B

= RHS

Therefore, we have shown that (b) cos(A + B).cos(A-B) = cos B-sin²A = cos²A-sin-B.

The simplified expression without parentheses is [tex]-8a^5b^7 + 18a^3b^5[/tex].

To rewrite the expression without parentheses and simplify it as much as possible, we need to distribute the term (-2a^(3)b) to each term inside the parentheses. This is done by multiplying the term outside the parentheses with each term inside the parentheses.

So, we have:
[tex](4a^2b^6-9b^4)(-2a^3b) = (4a^2b^6)(-2a^3b) - (9b^4)(-2a^3b)[/tex]

Next, we simplify the terms by combining like terms and using the rules of exponents:

[tex]= -8a^5b^7 + 18a^3b^5[/tex]

So, the simplified expression without parentheses is [tex]-8a^5b^7 + 18a^3b^5[/tex].

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2 divided by 4 and 3 divided by 6 where these number can be any numbers that have the same ratio as 1:2 and under 0-6 and not repeating them.

A number is a fundamental building block of mathematics. For a range of tasks, including measuring, counting, and indexing, numbers are utilised. There are different types of numbers depending on their characteristics, such as natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc. The basic integer arithmetic operations can be used to calculate the outcome number.

In the given question, we need to find two sets of three distinct numbers between 0 and 6 that have the same ratio.

One possible solution is:

2 divided by 4.

= 3 divided by 6

Here:

The ratio of the first set is 2:4 or 1:2. When we divide 2 by 4, we get 0.5.

The ratio of the second set is 3:6 or 1:2. When we divide 3 by 6, we also get 0.5.

Therefore, we have:

2 divided by 4.

= 0.5

3 divided by 6.

= 0.5

So, we can say:

2 divided by 4

= __ divided by __

where 3 and 6 can be any numbers that have the same ratio as 1:2.Similarly,

3 divided by 6

= __ divided by __

where 3 and 6 can be any numbers that have the same ratio as 1:2.

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Step-by-step explanation:

I think it might be A

I am not sure

The quadrilateral MNOP if MN=OP and MP=NO, then it must be square (option d).

First of all, since the opposite sides are equal in length (MN=OP and MP=NO), we know that MNOP is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel and equal in length.

If we were given additional information about the angles of the quadrilateral, we could determine whether MNOP is a rectangle or a rhombus.

Lastly, it is worth noting that MNOP cannot be a square, because a square is a special type of quadrilateral with all four sides equal in length and all four angles equal to 90 degrees.

In summary, based on the information given in the question, we can conclude that MNOP is a parallelogram, but we cannot determine whether it is a rectangle or a rhombus without additional information. We can also rule out the possibility that it is a square.

Hence the option (d) is correct.

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Complete Question:

Choose ALL answers that describe the quadrilateral MNOP if MN=OP and MP=NO?

a) Parallelogram

b) Rectangle

c) Rhombus

d) Square

e) Trapezoid

Answer:0.1

Step-by-step explanation:

0.1

a) The number of turning points of the function is 3.
b) The end behavior of the function is that as x approaches positive infinity.
c) The potential real zeros of the function are the factors of the constant term, 8. These are ±1, ±2, ±4, and ±8.
d) Using Descartes' Rule of Signs, there are 3 sign changes in the polynomial, so there can be 3 or 1 positive real zeros.
e) Using synthetic division and the potential real zeros, we can find that the rational zeros are -2 and 4.
f) The graph of the function is shown below with the turning points and zeros labeled.

The number of turning points of the function is 3. because the degree of the polynomial is 4 and the number of turning points is one less than the degree.

f(x) approaches positive infinity and as x approaches negative infinity, f(x) approaches negative infinity. This is because the leading coefficient is positive and the degree is even.

There are 2 sign changes in the polynomial with the x values replaced with -x, so there can be 2 or 0 negative real zeros.

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Answer: 515,783

Step-by-step explanation:  f(x)= a(1+r)^x      450,000(1+0.023)^6

Following are the measures of the angles given :∠ ABC = 180, ∠ BCD = 180, ∠ CDA = 270, ∠ DAB = 270.

What is parallel lines ?

Parallel lines are two or more lines that are always the same distance apart and never intersect, no matter how far they are extended.

Since AB is parallel to DC and AD is parallel to BC, we know that angles A and C are corresponding angles and angles B and D are also corresponding angles. Corresponding angles are congruent when two parallel lines are intersected by a transversal.

So, we have:

∠ A = ∠ C

∠ B = ∠ D

Given:

∠ D = 3x - 75

∠ B = x + 35

We can solve for x using the fact that the sum of the angles in a quadrilateral is 360 degrees:

∠ A + ∠ B + ∠ C + ∠ D = 360

Substituting the values we know, we get:

∠ A + (x + 35) + ∠ C + (3x - 75) = 360

Simplifying, we get:

4x - 40 = 360

4x = 400

x = 100

Now we can substitute x = 100 into the expressions for ∠ B and ∠ D to find their values:

∠ B = x + 35 = 100 + 35 = 135

∠ D = 3x - 75 = 3(100) - 75 = 225

Since angles A and C are corresponding angles, we know that:

∠ A = ∠ C = 180 - ∠ B = 180 - 135 = 45

Therefore, we have:

∠ ABC = ∠ A + ∠ B = 45 + 135 = 180

∠ BCD = ∠ B + ∠ C = 135 + 45 = 180

∠ CDA = ∠ C + ∠ D = 45 + 225 = 270

∠ DAB = ∠ D + ∠ A = 225 + 45 = 270\

So, we can see that angles ABC and BCD are straight angles (180 degrees) and angles CDA and DAB are reflex angles (more than 180 degrees).

Therefore, Following are the measures of the angles given :∠ ABC = 180, ∠ BCD = 180, ∠ CDA = 270, ∠ DAB = 270.

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The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).

To find the sum of the two polynomials, we need to add the coefficients of the like terms. Like terms are terms that have the same variable and exponent.

Step 1: Identify the like terms in the two polynomials.
- The like terms are 8x^(5) and 4x^(5), -5x^(3) and 0 (since there is no x^(3) term in the second polynomial), x^(2) and -6x^(2).

Step 2: Add the coefficients of the like terms.
- 8x^(5) + 4x^(5) = 12x^(5)
- -5x^(3) + 0 = -5x^(3)
- x^(2) + -6x^(2) = -5x^(2)

Step 3: Combine the terms to get the sum of the two polynomials.
- 12x^(5) + -5x^(3) + -5x^(2)

Step 4: Simplify the expression if possible.
- There are no like terms that can be combined, so the expression is already simplified.

The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).

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