finding the slope graphically

Answer:

1.2 pounds of chicken per serving.

Step-by-step explanation:

4 and 4/5 of pounds of chicken for serving of 4.

We can also write this as 4.8 pounds of chicken.

To find how much pound of chicken will be needed for a single serving we have to divide 4.8 by 4.

\( \frac{4.8}{4} = 1.2 \: pounds \: of \: chicken\)

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The two tanks differ in terms of Filling rates and initial volumes.

We can work with the equation for tank A, which represents a linear relationship between the volume of liquid in the tank (y) and the time it has been filling (x).

The equation y = 75x + 110 tells us that the tank A is filling at a constant rate of 75 units per minute, starting with an initial volume of 110 units.

To analyze the data for tank B, we would need to know the volumes of the tank at different times as it is being filled.

If the relationship for tank B is also linear, we could find the equation that represents it by using two points from the table and the slope-intercept form of a linear equation (y = mx + b). Once we have both equations, we can compare them to see how the two tanks differ in terms of filling rates and initial volumes.

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Answer:

-22

Step-by-step explanation:

When numbers are placed closed like that, and have a parenthesis, you will multiply.

11(-2) = 11 * -2 = -22

-22 is your answer.

~

Answer:

\(\Huge \boxed{-22}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

\(11(-2)\)

Multiplying,

\(\Longrightarrow \ \ 11*-2\)

\(\Longrightarrow \ \ -22\)

\(\rule[225]{225}{2}\)

Reason:

We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,

2x+10 = 0

2x = -10

x = -10/2

x = -5

Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

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Answer: 165 miles

Step-by-step explanation: In order to figure out the answer, you must do 55 x 3 because he drove for 3 hours at 55 mph so you could break it up and go 50 x 3 to equal 150 and 5 x 3 to equal 15 and add those to get 165.

Answer:

The answer is 165miles

Step-by-step explanation:

\(distance = speed \times time\)

d=55×3

d=165 miles

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer:

  x ≈ 2.09590327429

Step-by-step explanation:

You want the solution to 3^x = 10 using logarithms.

Taking logarithms of both sides of the given equation, we have ...

  x·log(3) = log(10)

Dividing by the coefficient of x gives ...

  x = log(10)/log(3)

  x ≈ 2.09590327429

__

Additional comment

If the logarithm to the base 10 is used, then this becomes ...

  x = 1/log₁₀(3)

The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.

For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.

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The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).

Taking the log of both sides, we get:

log(3^x) = log(10)

Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:

x * log(3) = log(10)

Next, we can divide both sides of the equation by log(3) to isolate the variable x:

x = log(10) / log(3)

Using a calculator, we can evaluate the right side of the equation:

x ≈ 1.46497

Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.

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Answer:

Step-by-step explanation:

Since the viewing angle between the star and Planet B is 19 degrees, we can use trigonometry to find the distances from Planet A to Planet B. Let's call these distances x and y, where x is the distance to the closer position of Planet B and y is the distance to the farther position of Planet B, as shown in the figure.

Using the Law of Cosines for the triangles with sides 65, x, and 45 (for the closer position) and 65, y, and 45 (for the farther position), we can write:

x^2 = 65^2 + 45^2 - 26545*cos(19) ≈ 2374.6

y^2 = 65^2 + 45^2 - 26545*cos(161) ≈ 10864.6

Taking the square roots of both sides, we get:

x ≈ 48.7 and y ≈ 104.2

Therefore, the possible distances from Planet A to Planet B are approximately 48.7 million miles (for the closer position of Planet B) and 104.2 million miles (for the farther position of Planet B), rounded to the nearest tenth.

Answer:

20:9

Step-by-step explanation:

Here we will simplify the ratio to 40:18 for you and show you how we did it.

To simplify the ratio 40:18, we find the greatest common divisor of 40 and 18, and then we divide 40 and 18 by the greatest common divisor.

The greatest common divisor that you can use to simplify 40:18 is 2. This means the answer to ratio 40:18 simplified is:

20:9

The value of x is 6.

What is system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations in mathematics. For instance, the system of three equations 3x + 2y - z = 1, 2x - 2y + 4z = -2, -x + y - z = 0 has the three variables x, y, and z.

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

Graphically, a system of linear equations that has no solution indicates two parallel lines-that is, two lines that have the same slope but different y-intercepts.

To have the same slope, the x-and y-coefficient must be the same.

To get from -2/3 to -8 you multiply by 12, so multiply  -1/2x by 12 as well to yield 6x.

Because the other x-coefficient is a, it must be that a = 6  and (D) is correct.

Note that, even though it is more work, you could also write each equation in slope-intercept form and set the slopes equal to each other to solve for a.

Hence, the value of x is 6.

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Let x and y be the two numbers

x + y = 72 ------------------------------(1)

x - y = 4 ----------------------------------(2)

Add equation (1) and equation (2)

2x = 76

Divide both-side of the equation by 2

x = 38

substitute x = 38 into equation (1) and then solve for y

38 + y = 72

subtract 38 from both-side of the equation

y = 72 - 38

y = 34

The two numbers are 34 and 38

Given the measure of an angle in degrees.

We need to convert it to radians.

The measure of the angle in degrees = 45

Convert to radians as follows:

So, the answer will be option B. π/4

Answer:

0.999945 = 99.9945% probability that at least two of the alarms are triggered.

Step-by-step explanation:

For each alarm, there are only two possible outcomes. Either it is triggered, or it is not. The probability of an alarm being triggered is independent of any other alarm, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A home security system is designed to have a 90% reliability rate.

This means that \(p = 0.9\)

Suppose that 6 home equipped with this system experience an attempted burglary.

This means that \(n = 6\)

Find the probability that at least two of the alarms are triggered.

This is:

\(P(X \geq 2) = 1 - P(X < 2)\)

In which

\(P(X < 2) = P(X = 0) + P(X = 1)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{6,0}.(0.9)^{0}.(0.1)^{6} = 0.000001\)

\(P(X = 1) = C_{6,1}.(0.9)^{1}.(0.1)^{5} = 0.000054\)

\(P(X < 2) = P(X = 0) + P(X = 1) = 0.000001 + 0.000054 = 0.000055\)

Then

\(P(X \geq 2) = 1 - P(X < 2) = 1 - 0.000055 = 0.999945\)

0.999945 = 99.9945% probability that at least two of the alarms are triggered.

Answer:

Step-by-step explanation:

The probability of the stone landing in the center of the red circle is 0.16.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Given that, the scoring area consists of four concentric circles on the ice with radii of 3 inches, 2 feet, 3 feet, and 4 feet.

To calculate the probability of the stone landing in the center of the red, white, or blue circle, we must first calculate the area of each circle.

The area of the red circle = π× (3 inches)²= 28.27 in²

The area of the white circle = π× (2 feet)² = 50.27 ft²

The area of the blue circle = π× (3 feet)² = 113.09 ft²

Now, we can calculate the probability of the stone landing in the center of the red, white, or blue circle.

The probability of the stone landing in the center of the red circle = 28.27 in² / (28.27 in² + 50.27 ft² + 113.09 ft²) = 0.16

The probability of the stone landing in the center of the white circle = 50.27 ft² / (28.27 in² + 50.27 ft² + 113.09 ft²) = 0.27

The probability of the stone landing in the center of the blue circle = 113.09 ft² / (28.27 in² + 50.27 ft² + 113.09 ft²) = 0.57

Therefore, the probability of the stone landing in the center of the red circle is 0.16.

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Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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The 1st digit is 1 out of 10 numbers

The 2nd digit is 1 out of 9 numbers

The 3rd digit is 1 out of 8 numbers

The 4th digit is 1 out of 1 numbers.

Total combinations are 10 x 9 x 8 x 7 = 5040

Since the combination 7654 is one out of the total the probability would be 1/5040

Answer:

a)to find mean

(sum the scores, divide by the number of scores) that is

( 2+ 2 + 0 + 5 +1 +, 4,+ 1, + 3, + 0,+ 0+ , 1, +4, + 4, + 0,+ 1, + 4, +3,+ 4, + 2,+ 1, +0)/21

= 42/21

= 2

b)

median means order the scores numerically then you choose the score in the middle and that is 2

c)sum of squared deviations is done by take difference between each score and the mean, square the result That is

Summation (xbar - x)²

add the final answer is 56

d)variance is gotten by taking sum of squared deviations, divide by (n-1))=

Summation (xbar - x)²/n-1

=2.8

e)standard deviation is square root of variance)= √V = 1.6

140.55 pounds will be sold approximately each week at the optimal price of $0.67/lb.

To find the price elasticity of demand for bananas at $0.20/lb, we need to use the formula:

According to the given data:

E(p) = -p(q'/q(p))

where q' is the derivative of q(p) with respect to p.

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(0.20) = -0.20(q'(0.20)/q(0.20))

= \(-0.20(-225e^(1.5(5-0.20)) / 100e^(1.5(5-0.20)))\)

= 2.70

Therefore, the price elasticity of demand for bananas at $0.20/lb is 2.70.

To find the price elasticity of demand for bananas at $1/lb, we can use the same formula:

E(p) = -p(q'/q(p))

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(1) = -1(q'(1)/q(1))

= \(-1(-225e^(1.5(5-1)) / 100e^(1.5(5-1)))\)

= 0.68

Therefore, the price elasticity of demand for bananas at $1/lb is 0.68.

To find the price that maximizes revenue, we need to find the value of p that makes revenue, R(p), maximum.

Revenue is given by:

R(p) = pq(p)

= \(p100e^(1.5(5-p))\)

To maximize revenue, we need to find the critical point of R(p) by taking its derivative and setting it equal to zero:

\(R'(p) = 100e^(1.5(5-p)) - 150pe^(1.5(5-p)) = 0\)

Simplifying this expression, we get:

\(2e^(1.5(5-p)) - 3pe^(1.5(5-p)) = 0\)

2 = 3p

p = 2/3

Therefore, the price that maximizes revenue is $0.67/lb.

To find the maximum revenue per week, we can plug this price back into the revenue equation:

\(R(2/3) = (2/3)*100e^(1.5(5-2/3))\)

= $167.56

Therefore, the maximum revenue per week is $167.56.

To find how many pounds will be sold each week at the optimal price of $0.67/lb, we can plug this price back into the demand equation:

\(q(2/3) = 100e^(1.5(5-2/3))\)

= 140.55

Therefore, approximately 140.55 pounds will be sold each week at the optimal price of $0.67/lb.

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The parametric equations are mathematically given as

(x(t), y(t), z(t))= (2-4t, 1-t, t)

Generally, To express the parametric point from A (2,1,0) to B(-2,0,1) in parametric form, we can use the following equation:

P(t) = (2-4t, 1-t, t)

To find the parametric equations for a point moving from A to B, we can use the following formula:

x = x₁ + t(x₂ - x1)

y = y₁ + t(y₂ - y₁)

z = z₁ + t(z₂ - z₁)

Where (x₁, y₁, z₁) is the starting point (A), (x₂, y₂, z₂) is the ending point (B), and t is a parameter that varies from 0 to 1.

Using this formula, the parametric equations for a point moving from A (2,1,0) to B(-2,0,1) are:

x = 2 + t(-2 - 2)

= 2 - 4t

y = 1 + t(0 - 1)

= 1 - t

z = 0 + t(1 - 0)

= t

These equations describe the motion of a point that starts at A, moves along the line segment from A to B, and arrives at B when t = 1.

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The complete Question was found

Find parametric equations for the line. (Use the parameter t.)

The line through points A (2,1,0) to B(-2,0,1)

(x(t), y(t), z(t))= \((\square)\)

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

Blue shirts: \(\frac{1}{6}\)×\(12=2\)

White shirts: \(\frac{2}{3}\)×\(12=8\)

∴ there are 2 students(12-2-8=2) wearing a different shirt.

Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)

Solving :

\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)

Step 2: Subtracting 10 on both sides :

\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)

We get ,

\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)

Step 3: Dividing both sides by 5 :

\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)

On cancelling , we get :

\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.

A proportion describes two ratios equated to each other.

Proportion is a fractional value that compares one value or quantity to another.

The profits for the second year of operation = $170,500

Let the profits for the first year of operation = x

Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)

Using equations, 5.76x = $170,500

x = $29,600 ($170,500  ÷ 5.76)

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Answer:

9

Step-by-step explanation:

      - Plug the values into the distance formula.

√(x2 - x1)² + (y2 - y1)²

√[2 - (-7)]² + [-8 - (-8)]²

√(9)² + (0)²

√81

= 9