Mr. Hernandez combines 1 gallon of orange juice, 3 pints of pineapple juice, and 2 quarts of lemon‐lime soda to make punch for a party. He allows 2 cups of punch for each guest. Will there be enough punch to serve all 14 guests? How much, if any, punch will be left?

The coefficients and add the Exponents of the variables,correct answer is option a) x^10y^5.

To simplify the expression (3x^4y^2)(-2x^6y^3),

we need to multiply the coefficients and add the exponents of the variables.

The coefficient is 3 * (-2) = -6.

For the variable x, we multiply the exponents: x^4 * x^6 = x^(4+6) = x^10.

For the variable y, we multiply the exponents: y^2 * y^3 = y^(2+3) = y^5.

Putting it all together, the simplified expression is -6x^10y^5.

Therefore, the correct answer is option a) x^10y^5.

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To simplify the expression (3x4y2)(-2x6y3), multiply the coefficients and add the exponents of the variables. The simplified expression is -6x10y5.

To simplify the expression (3x4y2)(-2x6y3), we multiply the coefficients (numbers in front) and combine the variables with the same base by adding their exponents. So, (-2)(3) equals -6, x4+6 equals x10, and y2+3 equals y5. Therefore, the simplified expression is -6x10y5, which corresponds to option (d).

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Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(1, -1) and B(4, 3)

The distance between them is

\( |AB| = \sqrt{ ({1 - 4})^{2} + ({ - 1 - 3})^{2} } \\ = \sqrt{( { - 3})^{2} + ({ - 4})^{2} } \\ = \sqrt{9 + 16} \\ = \sqrt{25} \: \: \: \: \: \: \: \: \\ = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \)

We have the final answer as

Hope this helps you

Answer:

-6 is the x-coordinate value

Step-by-step explanation:

Mathematically, slope can be calculated as;

m = (y2-y1)/(x2-x1)

For the value of the slope to be undefined, it means that we are actually dividing by zero

For us to be dividing by zero, it actually means that there is no change in the x-value

The unchanging x-value is what has caused us to have an undefined slope value

Since line k and line g are parallel, their slopes are equal and the slope of k is undefined too

So the x-coordinates of the other points that lie on the line that we used in calculating the slope is -6

The graph of a proportional relationship is a line through the origin or a ray whose endpoint is the origin

3. No because it's a line that doesn't go through the origin

4. Yes because it's a line through the origin

5. Yes because 1/3 = 2/6 = 3/9 = 4/12

6. No because 4/2 isn't equal to 8/5

7. Draw a graph just like 4., but change the y-axis

8. a. Let the equation be y = ax. 27 = 3a. a = 9. Therefore the equation is y = 9x.

8. b. 9

8. c. 9 * 5 = 45

9. a. The car travels 25 (> 18) miles per gallon of gasoline.

9. b. 25 * 8 - 18 * 8 = 7 * 8 = 56

The correct equation is p - 53 = 118.

⇒ p - 53 = 118

Therefore, the correct equation is p - 53 = 118.

Answer:

Step-by-step explanation:

H

The speed of the man's shadow's tip at a distance of 10 feet from the light's base is given by dy/dt = 10 ft/s.

AB is equal to 15 feet in height.

Man's height in CD is 6 feet.

From the diagram attached, if BE = y, we may use the ratio of related triangles to obtain,

15/y = 6/(y - x) (y - x)

to obtain, cross-multiply;

15(y - x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

To get, multiply both sides by 3.

3y = 5x

separating the two sides according to t provides;

dy = dt + dx = 3.

(5/3)(dx/dt dy/dt)

putting yields for dx/dt at 6 ft/s;

dy/dt = (5/3)(6) (6)

dy/dt equals 10 ft/s

One of the many real-world applications of trigonometry is the study of heights and distance. The terms height and distance are frequently used while discussing the applications of trigonometry.

The following ideas are incorporated in the trigonometry application for height and distance:

Measurement of the separation between two heavenly bodies

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Answer:

See Attached

Step-by-step explanation:

See Attached for proof of RHS = LHS

Using functions, solution to the equation in this case is x = 7/8.

Functions are the central idea of calculus in mathematics. The functions are special types of relations. In mathematics, a function is described as a rule that provides a distinct outcome for each input x. A mapping or transformation in mathematics usually represents a function. These operations are frequently denoted by letters like f, g, and h.

The domain is known as the set of all possible values that can be passed into a function while it is specified. The term "range" refers to the whole set of values that the function's output is capable of producing. The co-domain is the set of values that might be a function's outputs.

The solution for the function is x = 7/8.

The corresponding graph for the function is attached.

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Answer:

Vertical asymptote: x=0

Horizontal asymptote: no horizontal asymptote

Using the concepts of horizontal and vertical asymptotes, the rational function has a no horizontal asymptote and vertical asymptotes (x = 0).

There are two kinds of asymptotes that can be found. Horizontal asymptotes are found by definition of limit and vertical asymptotes are so by finding the roots of the denominator.

f(x)=2x^2-4/x^2-7x-8

For the Horizontal asymptote

f(x)=2x²-4/x²-7x-8

Taking x² common;

f(x)=2x²-4/x²-7x-8 (x²/x²)

f(x)= (2-4/ x² )/ (1-7/x -8/x²)

Hence, There is no horizontal asymptote

For Vertical asymptotes;

x²-7x-8 = 0

x = 0

There is vertical asymptotes: x = 0

Using the concepts of horizontal and vertical asymptotes, the rational function has a no horizontal asymptote and vertical asymptotes (x = 0).

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Valve guides can be measured for roundness and diameter using a micrometer or a bore gauge. Both of these tools are commonly used in the automotive industry to measure the dimensions of engine parts such as valve guides.

A micrometer is a precision measuring tool that uses a calibrated screw to measure the diameter of an object with high accuracy. It can be used to measure the diameter of the valve guide at different points along its length to check for roundness. A bore gauge, also known as an inside micrometer, is a specialized tool used to measure the inside diameter of a cylinder, such as the bore of an engine block or the valve guide. It consists of a probe that is inserted into the cylinder and expands to take a measurement. A bore gauge is particularly useful for measuring the internal dimensions of complex shapes like valve guides, which can have irregular or non-circular profiles. Both micrometers and bore gauges come in various sizes and types, and the specific tool used will depend on the size and shape of the valve guide being measured.

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Social scientists gather data from samples instead of populations because c. populations are often too large to test.

Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.

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Answer:

10= hikers 160= pounds carried in items or gear X divided by P = amount of pounds of items each hiker carries.

x=10 P=160

Step-by-step explanation:

i cant see part B

Expressions can be represented as equations or inequalities

(a) Long hike

The hiker's weight is given as:

\(\mathbf{Weight =160}\)

The hiker is embarking on a long hike, the recommended weight (x) of the backpack is calculated as:

\(\mathbf{x = 20\% \times 160}\)

\(\mathbf{x = 32}\)

The hiker's backpack weighs 15 lb.

So, the inequality that represents the additional weight is:

\(\mathbf{p + 15 \le 32}\)

Subtract 15 from both sides

\(\mathbf{p \le 32 - 15}\)

\(\mathbf{p \le 17}\)

(b) Day hike

The hiker's weight is given as:

\(\mathbf{Weight =180}\)

The hiker is embarking on a day hike (i.e. short hike), the recommended weight (x) is calculated as:

\(\mathbf{x = 15\% \times 180}\)

\(\mathbf{x = 27}\)

The hiker's backpack weighs 7.5 lb.

So, the additional weight the hiker can add is represented as:

\(\mathbf{p + 7.5 = 27}\)

Subtract 7.5 from both sides

\(\mathbf{p = 27 - 7.5}\)

\(\mathbf{p = 19.5}\)

Hence, the hiker can add additional 19.5 pounds

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Answer:

a.4×10 raised to power minus 5

b.5×10 raised to power minus 5

c.6×10 raised to power minus 6

d.8×10 raised to power minus 10

Answer:

do you mean scientific notation, I think they are already in standard form.

Step-by-step explanation:

A. 4 x 10^-5, count how many zeros before the number 4, and do the same with the rest.

B. 5 x 10^-5

C. 6 x 10^-6

D. 8 x 10^-10

If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .

In the question ,

it is given that ,

total numbers of car in the parking lot = 200 cars

number of white cars = 50

number of red cars = 30

number of silver cars = 20

let the number of green cars be "x" ,

So , the number of green cars possible = 200 - 100 = 100

that means x ≤ 100 .

So , P(green) = x/200

Option(a)

p = 0.2 ,

So , x/200 = 0.2

x = 40

Option(b)

p = 0.1 ,

So , x/200 = 0.1

x = 20

Option(c)

p = 0.6 ,

So , x/200 = 0.6

x = 120

Option(d)

p = 0.5 ,

So , x/200 = 0.5

x = 100 ,

We can see that only option(c) gives the number of green cars as 120 , which is not possible .

Therefore , If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .

The given question is incomplete , the complete question

In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green ?

(a) 0.2

(b) 0.1

(c) 0.6

(d) 0.5

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Answer:

2122.64 in^2

Step-by-step explanation:

Use the formula for the area of a circle: A=πr^2

The radius will be half the width of the cloth so 52÷2=26

26^2=676

Multiply by π given as 3.14

676×3.14=2122.64 square inches.

The symbol (carat) ^ is used to indicate an exponent when the keyboard doesn't have superscript.

Answer:

B

Step-by-step explanation:

2,122.64 in2

Answer: 16 gallons

Step-by-step explanation:

Since we are given the information that 1/4 of the gas is left, it simply means that (1 - 1/4) = 3/4 has been used.

The tank was filled and this was 12 gallons of gas.

Let the gas that the tank hold be represented by x. Therefore,

3/4 of x = 12

3/4 × x = 12

0.75x = 12

x = 12/0.75

x = 16

The tank holds 16 gallons of gas.

Answer:

5 meters

Step-by-step explanation:

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Answer:

H

Step-by-step explanation:

ST is similar to EF and WR is similar to CD.

Hope it helps.

Answer:

\(x^{3}\)

Step-by-step explanation:

multiply x by x

\(x^{2}\) · \(x\)

Multiply \(x^{2}\)    by \(x\)    by adding the exponents.

Raise  \(x\) to the power of  1

\(x^{2}\) · \(x^{1}\)

Use the power rule \(a^{m} a^{n} = a^{m+n}\) to combine exponents.

\(x^{2+1}\)

add 2 and 1

\(x^{3}\)

Answer

it can also be x^3...........

1.The two sides of the triangle that form the right angles. Are always the two shortest lengths given - Legs

2.The sides that's opposite the right angle. The length of this is always greater than the length of either leg.- Hypotenuse.

3. The triangle that contains a right angle(90°) - Right triangle.

4.In a right triangle the sum of the squares of the lengths of the legs equals the square of the lengths of the hypotenuse. - Pythagorean Theorem.

What is a right triangle?

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The decimal number that lies between 0.7 and 0.8, has three digits to the right of the decimal point, and whose sum of the digits is 24 is 7.98.

A decimal number is a number that has a fractional part represented by a decimal point. The digits to the right of the decimal point represent values that are smaller than 1.

In this problem, we are given that the decimal number has three digits to the right of the decimal point and that its sum of the digits is 24. Let's call the decimal number x. We can write an equation to represent the sum of the digits:

x = a + b/10 + c/100

Where a, b, and c are the digits of x.

We know that 0.7 < x < 0.8 and that the sum of the digits of x is 24, so we can write two more equations:

0.7 < a + b/10 + c/100 < 0.8

a + b + c = 24

By solving these three equations, we can find the decimal number x.

We know that a must be 7 because 0.7 < x < 0.8, so a = 7. We also know that b + c = 24 - 7 = 17. Now we need to find two digits b and c such that b + c = 17 and b/10 + c/100 is between 0 and 0.1.

The largest value of b that still satisfies this condition is 9. This means that

=> c = 17 - 9 = 8.

Therefore, the decimal number

=> x = 7 + 9/10 + 8/100 = 7.98.

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Answer:

No, It is a Partial Variation.

Step-by-step explanation:

Direct Variation: y = mx

Partial Variation: y = mx + k

The negation of the following statements are a. R: Ron did not go to school. b. S: A triangle does not have 3 sides. c. T: x ≠ 9 d. U: 20 is not a multiple of 3.

It's vital to know the opposite of a particular mathematical statement from time to time in mathematics. This practice is known as "negating" a claim. Remember that if a claim is true, then the negation must be false.

The negation of the following statements is:

a. R: Ron did not go to school.

b. S: A triangle does not have 3 sides.

c. T: x ≠ 9

d. U: 20 is not a multiple of 3.

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Answer:

240

hope this helps and pls give brainliest!

Answer:

The least common multiple (LCM) of 16, 30, and 40 is 240.

(Hope this helps! Btw, I answered first. Brainliest please!! :D)

All of the claims about the multiple regression output are correct. The first independent variable (X1) was a continuous-scale quantitative variable, whereas the second variable (X2) was coded 0 if Yes and 1 if No.

Multiple regression is an effective statistical approach for analyzing the associations between multiple independent variables and a single dependent variable. Multiple regression has numerous uses in the social sciences, and recent research used it to analyze the connection between two independent factors and a single dependent variable.

Finally, the total model is statistically significant, the slope coefficient for variable X1 is considerably different from zero, and the model explains almost 63% of the variance in the dependent variable.

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Answer:

when x = -3; y = -22/7

when x = 0;  y = -13/7

when x = 3;  y = -4/7

y = 3/7x - 13/7

x = 7/3y + 13/3

Step-by-step explanation:

x = -3;    3(-3) - 7y = 13; -9 - 7y = 13; -7y = 22; y = -22/7

x = 0;     3(0) -7y = 13; -7y = 13; y = -13/7

x = 3;     3(3) -7y = 13; 9 - 7y = 13; -7y = 4; y = -4/7

SOLVE FOR Y: 3x - 7y = 13; -7y = -3x + 13; y = 3/7x - 13/7

SOLVE FOR X: 3x - 7y = 13; 3x = 7y + 13; x = 7/3y + 13/3

The answer is (b) The system has no solution when a = 3.

We can use row reduction to determine the solution(s) of the system of linear equations for any value of a. The augmented matrix is:

\begin{bmatrix}

1 & 0 & 0 & 5 \

0 & 0 & 0 & 1 \

a & 1 & 2 & 6

\end{bmatrix}

First, we can use row operations to put the matrix in row echelon form:

\begin{bmatrix}

1 & 0 & 0 & 5 \

0 & 1 & 2 & 6-a \

0 & 0 & 0 & 1

\end{bmatrix}

Now we can see that the system has a unique solution if and only if the third row corresponds to the equation 0x + 0y + 0z = 1, which is never true, so we can conclude that the system has no solution when a is any number. Therefore, the answer is (b) The system has no solution when a = 3.

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