Evaluate the expression.
3 (x + y), x = 5 and y = 2

Answer:

A: Area

Step-by-step explanation:

The area is 6^2=36 and 36 is a perfect square.

Answer:

Step-by-step explanation:

convert either gram into kg or kg into gram

lets convert kg into g

1 kg=1000g

20kg=1000*24g

=20000g

450/20000*100%

450/200%

2.25%

first convert 450 g to kg = 0.45 kg

Now 0.45 kg as a. percentage of 20 kg = 0.45/20×100= 2.25%

Answer:

1, 2, 4, 8, 16, 32, 64

Step-by-step explanation:

1, 2, 4, 8, 16, 32, 64

Answer:

Step-by-step explanation:

The y-intercept is -3/4 and the x-intercept is -1/2.

Given, 4y + 6x = -3

To express this equation in terms of y as a function of x, we need to convert this into slope-intercept form. Let us see how to do it:

4y + 6x = -3

Subtracting 6x on both sides,

we get 4y = -6x - 3

Dividing by 4 on both sides,

we get y = (-6/4)x - (3/4)

Therefore, the equation in slope-intercept form is y = (-3/2)x - (3/4). Slope of the given equation:

y = (-3/2)x - (3/4)

The equation is in the form y = mx + b, where m is the slope of the line. Therefore, the slope of the given equation is -3/2. Y-intercept of the given equation:

y = (-3/2)x - (3/4)

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we need to set

x = 0.y = (-3/2)x - (3/4)y = (-3/2)(0) - (3/4)y = 0 - (3/4)y = -3/4

Therefore, the y-intercept is -3/4.

X-intercept of the given equation. To find the x-intercept, we need to set

y = 0.y = (-3/2)x - (3/4)0 = (-3/2)x - (3/4)(3/2)x = -3/4x = -3/4 × 2/3x = -1/2

The x-intercept is -1/2.

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

if anyone got the question asking between stations b and d instead of j and k the answer is 6

Step-by-step explanation:

6

Answer:

8.9

Step-by-step explanation:

Answer:

A. 1 cup of chocolate chips

B. 1/4 cup of granulated sugar

C. 1 and 5/8 cups of all purpose flour

Step-by-step explanation:

Divide all by 2

The number of bears living in the area after 17 years is; 22555

We are given the function;

f(t) = 103/(1 + 26e^(-0.31t))

Where f(t) is a function that models the number of bears living in the area after t period of years.

Thus, to find the number of bears living in the area after 17 years, we will just substitute 17 for t in the given function to get;

f(17) = 103/(1 + 26e^(-0.31*17))

f(17) = 103/0.00456653759

f(17) ≈ 22555 bears

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Using mathematical operations we can conclude that Jada drinks 8/15 liters of water.

So, liters of water Jada drinks:

We know that,

The container holds 4/5 liters of water.

Jada drinks 2/3 liters of water.

Now, liters of water Jada drinks is:

4/5 × 2/3

4×2/5×3

8/15

Therefore, using mathematical operations we can conclude that Jada drinks 8/15 liters of water.

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Answer:

I think it's this 62.13 in↑3.

I hope it's right!

The probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.

Bayes' theorem is used to update probabilities of a hypothesis or an event in light of new data or evidence. It is used to calculate the conditional probability of an event based on prior knowledge of the conditions that might be relevant to the event.In the given problem, we have to find the probability that the response indicated that the dog is small-sized given that they enjoyed the treat.

The probability that the dog is small-sized given that they enjoyed the treat is the conditional probability P(S|T), where S is the event that the dog is small-sized and T is the event that they enjoyed the treat. To find the value of P(S|T), we will use Bayes' theorem. Bayes' theorem states that P(S|T) = P(T|S) * P(S) / P(T) where P(T|S) is the probability that they enjoyed the treat given that the dog is small-sized, P(S) is the prior probability that the dog is small-sized, and P(T) is the probability that they enjoyed the treat.

P(S) = 3/7P(T|S) = 2/3P(T) = (2/3 * 3/7) + (1/4 * 4/7) = 18/84 + 4/28 = 1/3

(adding the probabilities of T given S and T given L)Therefore, P(S|T) = (2/3 * 3/7) / (1/3) = 2/7 = 0.285714...Rounding off to the nearest millionth, the probability is 0.286. Therefore, the probability that the response indicated that the dog is small-sized given that they enjoyed the treat is 0.286 (or 2/7) in fraction in the lowest terms.

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The gradient field of the function f(x,y,z)=ln√2 x2 + 3 y2 + 2 z2 is a vector-valued function that encodes information about the maximum rate of change of the output variable with respect to its input variables.

When computing this gradient field, the partial derivatives of the output variable with respect to each input variable are computed. Specifically, in this function, the partial derivatives would be the derivatives of the natural logarithm of the square root of 2x2 + 3y2 + 2z2 with respect to x, y, and z. These derivatives represent the rate of change of the output as any one of the three inputs change.

The final result is a vector whose components encode the slope of the output variable at each point in 3-dimensional space—in other words, a vector field. This gradient field is an essential tool for understanding the behavior of the function being studied, as it allows for visualizing how the output of the function changes as any of the input variables are changed.

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Answer:

Tank A

Step-by-step explanation:

Got it right on Kahn

The y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

When the line touches the y-axis, it forms a y-intercept.

Find the y when x = 0 to find these.

When the line touches the x-axis, the position for the y-intercept will look like (0,y).

So, have the given quadratic function:

y = x² + 2x − 8

Now, plot the given quadratic function on the graph:

(Refer to the graph attached below)

As we can see that the y-intercept is -4.

Therefore, the y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

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If a line with slope 4 has one point of intersection with the quadratic function y = x² + 2x − 8, what is the y-intercept of the line?

a. -4

b. 10

c.-10

d. 4

e. -8

Answer:

It's a Binomial

Step-by-step explanation:

Answer:

Equation is y = 3

Step-by-step explanation:

\((x_1, y_1) = ( -2, 3) \ , \ (x_2, y_2) = (8, 3 )\)

\(Slope,m = \frac{y_2 - y_1}{x_2-x_1} = \frac{3-3}{8 -- 2} = 0\)

\(Equation : (y - y_1) = m (x - x_1)\)

               \(y - 3 = 0 (x -- 2)\\y - 3 = 0\\y = 3\)

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

The lowest common multiple 3 and 4 is 12.

Step-by-step explanation:

The total multiples of both 3 and 4 between 1 - 100 are 100/12 = 8 4/12 i.e. 8.

Thus, the answer is option (c) 97 mph.

An outlier is a value that lies significantly away from the rest of the values in the dataset. For a given dataset, we can determine outliers using z-scores.According to the problem statement, the mean speed of the fastballs thrown by major league baseball pitchers is 87 mph, and the standard deviation is 3 mph. To determine which speed is an outlier, we need to find its corresponding z-score.z = (x - μ) / σHere, x is the speed we want to test, μ is the mean speed, and σ is the standard deviation of speeds.Using the formula above, we can calculate the z-scores for each speed given in the options:a. z = (84 - 87) / 3 = -1b. z = (92 - 87) / 3 = 1.67c. z = (97 - 87) / 3 = 3.33d. z = (81 - 87) / 3 = -2Since a z-score of ±2 or higher is generally considered an outlier, the speeds of 97 mph and 81 mph are classified as outliers. Thus, the answer is option (c) 97 mph.

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The value of the given integral \(\( \int_{-2}^{3} x(x+2) d x \)\)    is\($$\int_{-2}^{3} x(x+2) d x = \int_{-2}^{3} (x^2+2x) d x = 11 + 25 = \boxed{36}$$\) Thus, the answer is 36.

The integral can be solved using the distributive property and the power rule of integration. We start by expanding the integrand as follows:\($$\int_{-2}^{3} x(x+2) d x = \int_{-2}^{3} (x^2+2x) d x$$\)

Using the power rule of integration, we can integrate the integrand term by term. Applying the power rule of integration to the first term, we get\($$\int_{-2}^{3} x^2 d x = \frac{x^3}{3}\bigg|_{-2}^{3} = \frac{3^3}{3} - \frac{(-2)^3}{3} = 11$$\)

Applying the power rule of integration to the second term, we get\($$\int_{-2}^{3} 2x d x = x^2\bigg|_{-2}^{3} = 3^2 - (-2)^2 = 5^2 = 25$$\)

Therefore, the value of the given integral is\($$\int_{-2}^{3} x(x+2) d x = \int_{-2}^{3} (x^2+2x) d x = 11 + 25 = \boxed{36}$$\)

Thus, the answer is 36.

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The value of x is 13.

Given,

Q is the midpoint of P and R.

PR = 9x - 31 and QR = 43

We need to find the value of x.

We have,

<------9x - 31-------------->

P_______Q_______R

                  <-----43------>

Since Q is the midpoint of P and R.

PQ = QR = PR/2

Now,

QR = PR/2

43 = (9x - 31) / 2

Multiplying 2 on both sides

43 x 2 = 9x - 31

86 = 9x - 31

Adding 31 on both sides

86 + 31 = 9x - 31 + 31

117 = 9x

Dividing by 9 into both sides

117/9 = 9x/9

13 = x

x = 13

Thus the value of x is 13.

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Answer:

\(\left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}\)

Given endpoints of the diameter of the circle:

To find the center of the circle, substitute the given endpoints into the midpoint formula:

\(\begin{aligned} \implies \textsf{Midpoint} & =\left(\dfrac{0+7}{2},\dfrac{-4-3}{2}\right)\\& =\left(\dfrac{7}{2},-\dfrac{7}{2}\right)\end{aligned}\)

\(\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Substitute the found center and one of the given points (0, -4) into the equation and solve for r²:

\(\implies \left(0-\dfrac{7}{2}\right)^2+\left(-4-\left(-\dfrac{7}{2}\right)\right)^2=r^2\)

\(\implies \left(-\dfrac{7}{2}\right)^2+\left(-\dfrac{1}{2}\right)^2=r^2\)

\(\implies \dfrac{49}{4}+\dfrac{1}{4}=r^2\)

\(\implies \dfrac{50}{4}=r^2\)

\(\implies r^2=\dfrac{25}{2}\)

Therefore, the equation of the circle is:

\(\implies \left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}\)

The graph of the circle is attached.

Using the distance formula we can conclude that the measure of line AB is 64 units.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.

The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

So, the formula is:

d = √(x2-x1)² + (y2-y1)²

Now, insert values as follows:

d = √(x2-x1)² + (y2-y1)²

d = √(10-2)² + (1-9)²

d = √(8)² + (-8)²
d = √64+64

d = √128

d = 64 units

Therefore, using the distance formula we can conclude that the measure of line AB is 64 units.

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The type of statistical technique that is employed in future predictions of outcomes based on presented data is: C. linear regression.

Linear regression can be described as a statistical technique that is used to make future predictions using the regression equation of a line of best fit that models the relationship between variables Y and X.

Through the regression equation, outcomes of the future can be predicted. This statistical technique is known as: C. linear regression

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Answer:

- 3

Step-by-step explanation:

Calculate the gradient (slope) m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 5, - 2) and (x₂, y₂ ) = (- 3, - 8)

m = \(\frac{-8-(-2)}{-3-(-5)}\) = \(\frac{-8+2}{-3+5}\) = \(\frac{-6}{2}\) = - 3