A particular shade of orange paint has 2 cups of yellow paint for every 3 cups of red paint.According to the double number line, how many cups of red paint are required to make three batches

Answer:

-50

Step-by-step explanation:

7 - (7 * 11 - 1) ÷ 2 - (5)² + 6

7 - (77 - 1) ÷ 2 - 25 + 6

7 - (76) ÷ 2 - 25 + 6

7 - 38 - 25 + 6

-31 - 19

-50

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-Chetan K

B. \( - 50\) ✅

Step-by-step explanation:

\(7 - \frac{7 \times 11 - 1}{2} - ({5})^{2} + 6 \\ = 7 - \frac{77 - 1}{2} - 25 + 6 \\ = 13 - 25 - \frac{76}{2} \\ = - 12 - 38 \\ = - 50\)

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a)  The direction in which you should walk to descend fastest is: (-12, -16)

b) The slope of your path is: -88

c) The direction of the greatest increase in temperature at the point (−2, 2) is: (-4, 4)

The maximum rate of change is: 4√2

d) The direction of the greatest decrease is: (4, -4).

The most negative rate of change is: 4√2

(a) The equation on the surface is:

z = 15 - (3x² + 2y²)

The gradient of this surface will be the partial derivatives of the equation. Thus:

Gradient of the surface z:

∇z = (-6x, -4y)

Since you are standing above the point (2,4), then the direction to descend fastest is:

∇z(2,4) = (-6(2), -4(4))

∇z(2,4) = (-12, -16)

That gives us the direction to descend fastest is in the direction.

(b) If you start to move in the direction (-12, -16) above, then slope of your path (rate of descent) is given by the dot product expressed as:

Slope = ∇z(2,4) · (-12, -16)

= (2)(-12) + (4)(-16)

= -24 - 64

= -88

(c) We want to find the direction of the greatest increase in temperature at the point (−2,2).

Thus, the gradient of T(x,y) is given by:

∇T = (2x, 2y).

The direction is:

∇T(-2, 2) = (2(-2), 2(2))

∇T(-2,2) = (-4, 4)

The maximum rate of change is:

∇T(-2,2) = √((-4)² + 4²)

= √(16 + 16)

= √(32)

= 4√2

(d) The direction of the greatest decrease is:

(-∇T(-2, 2)) = (-(-4), -4)

= (4, -4).

The most negative rate of change is:

∇T(-2, 2) = √(4² + (-4)²)

= √(16 + 16)

= √(32)

= 4√2

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Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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Answer:

8

Step-by-step explanation:

If you do the math with the area to find out the perimeter, and you will find the largest one to be the poster with the area of 144 , and the smaller one to be the one with the area of 100

Answer:

Length= squre root of area

Length of big poster = squre root of 144

=12

Length of small poster=squre root of 100

=10

The perimeter = 4*length

Big poster perimeter=4*12=48

Small poster perimeter =4*10=40

The difference= 48 - 40 = 8

It is bigger by 8

Answer:

575%

Step-by-step explanation:

Convert the fraction to a decimal, then multiply by 100

.

Answer:

5

Step-by-step explanation:

(5-2)^2 + (7-3)^2 = radius^2

radius=√25

radius=5

Answer:  4 2/3

Step-by-step explanation:

14/3 is an improper fraction. Let's take the numerator and divide it by the denominator.

Divide 14 by 3. The quotient digit is 4.

Multiply the quotient digit 4 by the divisor 3.

Subtract 12 from 14.

The result of 14 divided by 3 is 4 with a remainder of 2.

Thus, 14/3 as a mixed number can be written as 4 2/3.

14/3 as it can't further cut out.

Because in a mixed number it is 4 2/3. This can be expressed as a fraction by multiplying the whole number (4) by the denominator (3) and adding it to the numerator (2), giving a fraction of 14/3.

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If the standard deviation of sales is equal to some value, we can calculate the variance by squaring the standard deviation.

to answer the question, we need to understand the relationship between standard deviation and variance. the variance is the average of the   square   d differences from the mean, while the standard deviation is the square root of the variance.

in the concert sales dataset (containing sample data), the standard deviation of sales is equal to question 22select one: a. square of the mean sales value b. square of the variance of sales c. square root of the mean of sales d. square root of the variance of sales

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Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

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ANSWER

EXPLANATION

We want to find the expression that best represents the measure of the interior angle of a regular polygon with n sides.

The general formula for finding the total angle in a regular n sided polygon is given as:

Therefore, to find the measure of each interior angle of the polygon, we have to divide the total angle by the number of sides.

That is:

Hence, that is the expression that best represents the measure in degrees of the interior angle of a regular polygon having n sides.

Answer:

-1/5

Step-by-step explanation:

3/5 is greater than 2/5, so your answer goes into the negatives

Answer:-1/5

Step-by-step explanation:

2/5-3/5

(2-3)/5

-1/5

The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.

We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:

x = (9 mi/h) * (0.25 h) = 2.25 mi

y = (8 mi/h) * (0.25 h) = 2 mi

The distance between the two people is given by:

\(d = sqrt(x^2 + y^2)\)

Taking the derivative with respect to time t, we get:

\(d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))\)

Substituting the values we found earlier, we get:

\(d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h\)

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As a fraction, length of the 15 rods = 8 4/7 feet

As decimal, length = 8.57 feet

initial length pipes = 4 feet

Dividing the length of the pipe into 7:

length of 15 of those rods:

The main difference between everyday logic and mathematical logic is that everyday logic is based on general observations and opinions, while mathematical logic is based on precise statements and facts.

Differences:
- Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.
- Everyday logic is often used to make decisions or solve problems in daily life, while mathematical logic is used to solve complex mathematical problems.
- Everyday logic can be subjective and influenced by personal beliefs or experiences, while mathematical logic is objective and follows a set of universally accepted principles.

Similarities:
- Both everyday logic and mathematical logic use reasoning to draw conclusions.
- Both everyday logic and mathematical logic rely on evidence and facts to support their conclusions.
- Both everyday logic and mathematical logic can be used to solve problems and make decisions.

In conclusion, while everyday logic and mathematical logic have some similarities in terms of their use of reasoning and evidence, they differ in their approach and application. Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.

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The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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The verified statemeent are:

Let's verify the given statements using suitable integers:

1. Subtraction is not associative:

Let's choose integers a = 2, b = 3, and c = 4.

(a - b) - c = (2 - 3) - 4 = -1 - 4 = -5

a - (b - c) = 2 - (3 - 4) = 2 - (-1) = 2 + 1 = 3

Since (-5) is not equal to 3, we can conclude that subtraction is not associative.

2. Multiplication is associative:

Let's choose integers a = 2, b = 3, and c = 4.

(a * b) * c = (2 * 3) * 4 = 6 * 4 = 24

a * (b * c) = 2 * (3 * 4) = 2 * 12 = 24

Since 24 is equal to 24, we can conclude that multiplication is associative.

3. Division is not closed:

Let's choose integers a = 4 and b = 2.

a / b = 4 / 2 = 2

However, if we choose a = 4 and b = 0, then the division is not defined because we cannot divide by zero.

4. Multiplication is distributive over subtraction:

Let's choose integers a = 2, b = 3, and c = 4.

a * (b - c) = 2 * (3 - 4) = 2 * (-1) = -2

(a * b) - (a * c) = (2 * 3) - (2 * 4) = 6 - 8 = -2

Since -2 is equal to -2, we can conclude that multiplication is distributive over subtraction.

5. Product of an odd number of negative integers is a negative integer:

Let's choose three negative integers: a = -2, b = -3, and c = -4.

a * b * c = (-2) * (-3) * (-4) = 24

Since 24 is a positive integer, the statement is not true.

The product of an odd number of negative integers is a positive integer.

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Answer:

The distance between boat A and boat B will be 7.2 units apart.

What is the distance between two points?

It is the measure of distance between the two points and is known as length. The length is measured in meters generally. Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

A marina is looking like a direction framework. Boat An is moored at (3.1, −1) and Boat B is moored at (−4.1, −1).

Then the distance between the points (3.1, −1) and (−4.1, −1) will be given as,

D² = (-1 + 1)² + (3.1 + 4.1)²

D² = (7.2)²

D = 7.2 units

The distance between boat A and boat B will be 7.2 units apart.

Answer:

7 Units

Step-by-step explanation:

Answer:

y = 300x + 100

Step-by-step explanation:

y = mx + c

the line intersects the y axis at 100, so c = 100

m = difference between y-coordinates / difference between x-coordinates

m = (400-100)/(1-0) = 300/1 = 300

y = 300x + 100

Answer: A is definitely the correct answer

Answer:

No

Step-by-step explanation:

Average amount of shampoo in a shampoo bottle: 16oz

16oz x 10 = 160oz = about 1.25 gallons

1.25 \(\neq\) 3

Answer:

If the bottles are greater than 38.4 oz then the total volume would be greater than 3 gallons.

If the bottles are less than 38.4 oz the total volume would be less than 3 gallons.

Step-by-step explanation:

Needs more info, specifically what size shampoo bottles.

We can still figure out some info from what is given though...

let's convert to ounces since most shampoo bottles are ounces not gallons...

3 gallons=384 ounces

figure out what size bottle would exactly equal 384 oz when there are 10 bottles...

10x=384

x=38.4

If the bottles are greater than 38.4 oz then the total volume would be greater than 3 gallons.

If the bottles are less than 38.4 oz the total volume would be less than 3 gallons.

Monthly payment before deferral: $345.09. Balance after deferral: $67,901.53. Monthly payment after deferral: $380.57. Monthly payment to pay off debt within 25 years from graduation: $421.63.

To calculate the monthly payment for a student loan, we can use the loan amortization formula.

Monthly payment calculation:

We can use the formula for calculating the monthly payment on an amortizing loan:

PMT = (P * r) / (1 - (1 + r)^(-n))

where PMT is the monthly payment, P is the loan amount, r is the monthly interest rate, and n is the total number of payments.

Given:

P = $62,100 (loan amount)

r = 4.6% per year / 12 months = 0.046/12 (monthly interest rate)

n = 25 years * 12 months = 300 (total number of payments)

Substituting these values into the formula, we can calculate the monthly payment:

PMT = (62,100 * (0.046/12)) / (1 - (1 + (0.046/12))^(-300))

Balance after deferral period:

To calculate the balance after the deferral period of 2 years, we need to calculate the interest accrued during that period and add it to the original loan amount:

Interest accrued during deferral = P * r * deferral period (in years)

New balance = P + Interest accrued during deferral

New monthly payment after deferral period:

To calculate the new monthly payment after the deferral period, we can use the same formula as before, but with the new balance and the remaining number of payments:

New PMT = (New balance * r) / (1 - (1 + r)^(-n))

Monthly payment to pay off the debt within 25 years from graduation:

To calculate the monthly payment to pay off the debt within 25 years from graduation, we need to adjust the remaining number of payments:

Remaining number of payments = 25 years * 12 months - deferral period

Then we can use the same formula as before to calculate the monthly payment.

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Answer:

1 its an obvious answer cause 1+4=5

The solution to the systems of equations graphically is (2, 4)

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

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

Disagree ΔABC ≅ ΔDEC by ASA butt by SAS

Step-by-step explanation:

point C is the midpoint of (A/E), C is also the midpoint of (B/D )

BC = CD   and AC = CE

∠BCA = ∠ECD

ΔABC ≅ ΔDEC by SAS not by ASA

Answer:

Step-by-step explanation:

the line given is

\(x + 3y = 6\\3y = -x + 6\\y = \frac{-1}{3} (x) + 2\\\)

parallel lines have the same slope

\(y = \frac{-1}{3} (x) + b\\3 = \frac{-1}{3}(5) + b\\\frac{9}{3} = \frac{-5}{3} + b\\ b = \frac{14}{3}\\\)

\(y = \frac{-1}{3} (x) + \frac{14}{3}\)

The equation of line passes through the point (5, 3) will be;

⇒ y = - x/3 + 14/3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (5, 3).

And, The parallel line is,

⇒ x + 3y = 6

⇒ y = - x/3 + 2

Now,

Since, The equation of line passes through the point (5, 3).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

⇒ y = - x/3 + 2

⇒ m = dy/dx = - 1/3

⇒ m = - 1/3

Thus, The equation of line with slope - 1/3 is,

⇒ y - 3 = - 1/3 (x - 5)

⇒ y - 3 = - 1/3 (x - 5)

⇒ y - 3 = - x/3 + 5/3

⇒ y = - x/3 + 5/3 + 3

⇒ y = - x/3 + 14/3

Therefore, The equation of line passes through the point (5, 3) will be;

⇒ y = - x/3 + 14/3

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Answer:

lol ok

have a good day :)

Step-by-step explanation:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.