Find the length of segment JK with endpoints J(4, 8) and K(-1, -2). Leave the answer as a radical. Simplify if necessary

6 bowls can hold 16 tomatoes.

Given:

Total tomatoes: 16

Each bowl holds: 3 tomatoes

Explanation:

To find the number of bowls needed divide total tomatoes by tomatoes each bowl can hold.

Solve:

16 ÷ 3 = 5.333...

So, we need more than 5 bowls, [6 bowls] to hold the tomatoes.

Answer:

6 bowls

Step-by-step explanation:

So . .

Then . .

Reason. .

Because you must be able to hold all 16! Therefor you round!

Hope this helps!  

Answer:

Step-by-step explanation:

It is given that the area of a circle is 36.43cm² and we have to find the length of the radius.

So, first of we must know this formula :

⇒ πr² = Area(Circle)

Now, Substituting the given values in the formula :

⇒ 3.14 × r² = 36.43

⇒ r² = 36.43/3.14

⇒ r² = 11.60

⇒ r = √11.60

⇒ r = 3.40

Therefore,

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with area of circle that is 36.43 cm² . And we are asked to find the length of radius of circle rounded to two decimal points .

We know that ,

\( \qquad \quad \frak{Area_{(Circle)} = \pi r {}^{2} } \quad \bigstar\)

Where ,

Solution : -

According to question , area of Circle is equal to 36.43 . So ,

\( \longrightarrow \qquad \: \pi r {}^{2} = 36.43\)

Step 1 : Substituting value of π :

\( \longrightarrow \qquad \:3.14 \times r {}^{2} = 36.43\)

Step 2 : Transposing 3.14 to right side :

\( \longrightarrow \qquad \: r {}^{2} = \cancel{\dfrac{36.43}{3.14} }\)

On dividing 36.43 by 3.14 , We get :

\( \longrightarrow \qquad \: r {}^{2} = 11.60\)

Step 3 : For removing square from r , We are applying root on both sides :

\( \longrightarrow \qquad \: \sqrt{r {}^{ 2 }} = \sqrt{ 11.60}\)

We get :

\( \longrightarrow \qquad \:r = \sqrt{11.60} \)

Step 4 : Finding square root of 11.60 , We get :

\( \longrightarrow \qquad \: \purple{\underline{\boxed{\frak{r = 3.40 \: cm}}}} \)

The equation of the parabola formed by the plane that is parallel to a generating line of a double napped cone is y = (A/B)x^2 + (6/B)x + (9/B + K/B).

The equation of a double napped cone is given by:

\(Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Jz + K = 0\)

Where A, B, C, D, E, F, G, H, J and K are constants.

A plane that is parallel to a generating line of a double napped cone will intersect the cone at a single point, forming a parabola. The equation of a parabola can be written as:

y = ax^2 + bx + c

Where a, b, and c are constants.

We can find a, b and c by substituting the equation of the plane into the equation of the double napped cone.

For example, if the equation of the plane is x + y – z = 3 then we can substitute this into the equation of the double napped cone and solve for the coefficients a, b and c.

Substituting x + y – z = 3 into the equation of the double napped cone:

\(Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Jz + K = 0\)

We get:

\(Ax^2 + B(x + 3)^2 + C(-x - 3)^2 + K = 0\)

Expanding, we get:

\(Ax^2 + Bx^2 + 6Bx + 9B + Cx^2 - 6Cx - 9C + K = 0\)

Grouping terms and solving for a, b and c, we get:

a = A/B

b = 6/B

c = 9/B + K/B

Therefore, the equation of the parabola formed by the plane that is parallel to a generating line of a double napped cone is y = (A/B)x^2 + (6/B)x + (9/B + K/B).

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The midpoint of the segment with endpoints (9, 7, 3) and (5, 3, 2) is (7, 5, 2.5).

To find the distance between two points in three-dimensional space, we can use the formula:

Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\)

Let's calculate the distance between the points (9, 7, 3) and (5, 3, 2):

Distance = \(\sqrt{(5 - 9)^2 + (3 - 7)^2 + (2 - 3)^2}\)

= (\(\sqrt{(-4)^2 + (-4)^2 + (-1)^2}\)

= \(\sqrt{(16 + 16 + 1)}\)

= \(\sqrt{33}\)

≈ 5.7 (rounded to the nearest tenth)

Therefore, the distance between the points (9, 7, 3) and (5, 3, 2) is approximately 5.7.

To find the midpoint of the segment with these endpoints, we can use the midpoint formula:

Midpoint = \((x_1 + x_2) / 2, (y_1 + y_2) / 2, (z_1 + z_2) / 2)\)

Let's calculate the midpoint:

Midpoint = ((9 + 5) / 2, (7 + 3) / 2, (3 + 2) / 2)

= (14 / 2, 10 / 2, 5 / 2)

= (7, 5, 2.5)

Therefore, the midpoint of the segment with endpoints (9, 7, 3) and (5, 3, 2) is (7, 5, 2.5).

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The value of m = 4 satisfies the equation 9 raised to 2m divided by 9 raised to - 5 is equal to 9 raised to 13​.

Exponents are a type of mathematical notation used to describe repeated multiplication of a single integer. Exponents are sometimes referred to as powers or indexes. The exponent, which denotes how many times the base number should be multiplied by itself, is represented as a superscript to the right of the base number.

From the given statement the algebraic expression is:

\(9^{(2m)} / 9^{(-5)} = 9^{13}\)

Using the rule of exponents:

\(9^{(2m + 5)} = 9^{13}\)

2m + 5 = 13

2m = 8

m = 4

Hence, m = 4 is the value that satisfies the equation 9 raised to 2m divided by 9 raised to - 5 is equal to 9 raised to 13​.

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Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.

We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:

( 3, 4 ) and ( − 2, 1 )

We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.

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The profit for one small cake is approximately £0.3564.

To find the profit for one small cake, let's assign variables to represent the profits. Let's call the profit for one small cake "P_s," the profit for one medium cake "P_m," and the profit for one large cake "P_l."

Given information:

The ratio of small to medium to large cakes sold is 9:5:12.

The profit for one medium cake is three times the profit for one small cake.

The profit for one large cake is four times the profit for one small cake.

The total profit is £815.76.

We can set up equations based on the given information:

P_m = 3P_s (Profit for one medium cake is three times the profit for one small cake)

P_l = 4P_s (Profit for one large cake is four times the profit for one small cake)

Total profit = 286P_s + 286P_m + 286P_l = £815.76 (Total profit is the sum of profits for each cake sold)

Since we know the ratio of small, medium, and large cakes sold, we can express the number of each cake sold in terms of the ratio:

Let's assume the common ratio is "x," so we have:

Small cakes sold = 9x

Medium cakes sold = 5x

Large cakes sold = 12x

Now we can substitute these values into the total profit equation:

286P_s + 286P_m + 286P_l = £815.76

Substituting P_m = 3P_s and P_l = 4P_s:

286P_s + 286(3P_s) + 286(4P_s) = £815.76

Simplifying:

286P_s + 858P_s + 1144P_s = £815.76

2288P_s = £815.76

Dividing both sides by 2288:

P_s = £815.76 / 2288

P_s ≈ £0.3564

Therefore, the profit for one small cake is approximately £0.3564.

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The word "INFINITY" has eight letters. To find out the number of distinct permutations that can be made from the word "INFINITY," we will use the formula for permutation. The formula is:$$P(n,r) = \frac{n!}{(n-r)!}$$Where n is the total number of items and r is the number of items taken at a time.

Using the formula, we get:\($$P(8,8) = \frac{8!}{(8-8)!}$$$$P(8,8) = \frac{8!}{0!}$$$$P(8,8) = 8!$$$$P(8,8) = 40,320$$\). There are 40,320 distinct permutations that can be made from the letters of the word INFINITY. To find out the number of permutations that start with the letter Y, we will treat Y as a fixed letter at the beginning. Then we will find the number of permutations of the remaining seven letters.

This can be done using the same formula as before. But this time, we will use n = 7 and r = 7. The formula becomes:\($$P(7,7) = \frac{7!}{(7-7)!}$$$$P(7,7) = \frac{7!}{0!}$$$$P(7,7) = 7!$$$$P(7,7) = 5,040$$\). Therefore, there are 5,040 permutations that start with the letter Y.

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The probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Let's use the following notation:

P(TB) represents the probability that an adult has tuberculosis, which is given as 0.05.

P(POS|TB) represents the probability that the test is positive given that an adult has tuberculosis, which is given as 0.746.

P(NEG|TB) represents the probability that the test is negative given that an adult has tuberculosis, which is 1 - P(POS|TB) = 0.254.

We are asked to find the probability of an adult getting a NEG result and truly having tuberculosis, which can be calculated using Bayes' theorem as follows:

P(TB|NEG) = P(NEG|TB) * P(TB) / P(NEG)

We can calculate P(NEG) using the law of total probability, which considers the two possible cases for an adult: having tuberculosis (TB) or not having tuberculosis (TB').

P(NEG) = P(NEG|TB) * P(TB) + P(NEG|TB') * P(TB')

= 0.254 * 0.05 + 0.7653 * 0.95

= 0.7352

Now we can substitute the values into Bayes' theorem:

P(TB|NEG) = 0.254 * 0.05 / 0.7352

= 0.01725

Therefore, the probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

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Answer:

positive correlation

Step-by-step explanation:

negative correlation is when the pattern is going down

no correlation is when there is no pattern and the dots r scattered just randomly

The coordinates of point X in Quadrant I for Y(-1,2) and Z(6,2) are (6,6).

In a 45°-45°-90° triangle, the two legs are congruent, and the hypotenuse is the square root of 2 times the length of each leg. Since the triangle has a right angle at Z, the length of ZY and ZX will be equal.

Given that Y is located at (-1,2) and Z is located at (6,2), we can determine the length of YZ by finding the horizontal distance between the two points. In this case, YZ has a length of 6 units.

Since the triangle is a 45°-45°-90° triangle, the lengths of the legs will be equal. Therefore, the length of ZX is also 6 units.

To find the coordinates of point X, we start at the y-coordinate of Z (which is 2) and move up by the length of ZX (which is 6 units). Since the triangle is in Quadrant I, the x-coordinate of X will be the same as Z (which is 6). Thus, the coordinates of X in Quadrant I for Y(-1,2) and Z(6,2) are (6,6).

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Answer:

its f

Step-by-step explanation:

Rule for 270° counterclockwise rotation: (x, y) → ( ‐ y, x )

Answer:

21cm

Step-by-step explanation:

3 plus 4 plus 6 is 13, meaning 13 shares

91 divided by 13 is 7

7 times 3 is 21

A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.

In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.

Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.

Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.

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Answer:

y = ax^2 + bx - c

Step-by-step explanation:

The product means multiply

The production cost(y) = computing components (a) * number of devices (x) +  product of labour (b) * number of devices (x) - savings on reusable material (c)

Therefore,

y = ax^2 + bx - c

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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The equation is:  119.98n - 89 = 2000n.

The cost of the phone is $89, and the plan costs $119.98 per month. Let the number of months be n. The total cost will be: Total cost = $89 + $119.98nThe total anytime minutes are 2000 per month. So in n months, the total anytime minutes will be:

Total anytime minutes = 2000n Equating the total cost and the total anytime minutes we have,$89 + $119.98n = 2000n

Simplifying,$119.98n - 2000n = -$89-$880.02n = -$89 Dividing by -880.02n = 0.101353We can round this to n ≈ 0.1, which means it will take approximately 0.1 months, or about 3 days to make up the cost of the phone with the savings from the plan.

The equation is: 119.98n - 89 = 2000n.

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Answer:

I think the answer is P(x>178)

Step-by-step explanation:

Answer: 0.16

Step-by-step explanation: Quizzed

The correct answers are:

B. 15°, 75°, 90°

E. 60°, 60°, 60°

what are interior angles ?
Interior angles are angles that are formed inside a closed figure, such as a polygon. In the case of a triangle, the interior angles are the three angles formed inside the triangle where its three sides intersect. The sum of the three interior angles of a triangle is always 180 degrees.

Steps to be followed:

In a triangle, the sum of the interior angles is always 180 degrees.

Let's use the variables a, b, and c to represent the three angles of a triangle. Then, we have the following formula:

a + b + c = 180

Let's take option A as an example. The sum of the angles is:

10 + 10 + 160 = 180
So the angles add up to 180 degrees. However, this does not guarantee that the angles could form a triangle. In fact, we can use the Law of Cosines to show that the side lengths of such a triangle would not satisfy the triangle inequality.

Option B has angles 15, 75, and 90 degrees. The sum of these angles is:

15 + 75 + 90 = 180 (they could form a triangle.)

Option E has angles 60, 60, and 60 degrees. The sum of these angles is:

60 + 60 + 60 = 180 (they could form an equilateral triangle.)

In options C and D, the sum of the angles is greater than 180 degrees, which is not possible for a triangle in Euclidean geometry.

Therefore, the correct options are B and E

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Answer:A B C

Step-by-step explanation:

The Laplace transform of \(e^{2t} * sin(t) is 1 / ((s - 2)(s^2 + 1))\).

Theorem 7.4.2 states that if F(s) = ℒ{f(t)} and G(s) = ℒ{g(t)}, then ℒ{f(t) * g(t)} = F(s) * G(s), where * denotes the convolution operation.

In this case, we want to evaluate the Laplace transform of the function \(e^{2t}\) * sin(t). Let's denote f(t) = \(e^{2t}\) and g(t) = sin(t).

The Laplace transform of f(t) is ℒ{f(t)} = F(s), and the Laplace transform of g(t) is ℒ{g(t)} = G(s).

To find ℒ{\(e^{2t}\) * sin(t)}, we need to find F(s) and G(s) and then apply the convolution property.

First, let's find F(s), the Laplace transform of f(t) = e^(2t):

ℒ{\(e^{2t}\)} = F(s)

∫[0,∞] \(e^{2t}\) \(e^{-st}\) dt = F(s)

∫[0,∞] \(e^{(2-s)t}\) dt = F(s)

Using the formula for the Laplace transform of \(e^{at}\), we have:

F(s) = 1 / (s - 2)

Next, let's find G(s), the Laplace transform of g(t) = sin(t):

ℒ{sin(t)} = G(s)

∫[0,∞] sin(t) e^(-st) dt = G(s)

Using the formula for the Laplace transform of sin(t), we have:

G(s) = 1 / (s² + 1)

Now, applying the convolution property, we have:

ℒ{e^(2t) * sin(t)} = F(s) * G(s)

= (1 / (s - 2)) * (1 / (s² + 1))

= 1 / ((s - 2)(s² + 1))

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Answer:

A

Step-by-step explanation:

Answer:

ecall that 6 + 6 + 6 = 6 × 3

Instead of adding 6 three times, you can multiply 6 by 3 and get 18, the same answer.

Similarly,

6 + 6 + 6 + 6 + 6 + 6 + 6 = 6 × 7 = 42

Still by the same token,

2 + 2 + 2 + 2 = 2 × 4

Answer:

See below for explanation since answer already provided along with question

Step-by-step explanation:

When adding binary numbers just add them as you would decimal numbers starting at the rightmost bit.

Note for bit addition

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0 with a carry of 1 which is added to the next left column

When subtracting bits

0 - 0 = 0
0 - 1 = 1 but requires a carry from the next left column

1 - 0 = 0

1 - 1 = 0

First 11011₂ + 10011₂
Add the right most bits 1 + 1 = 0 with a carry of 1

The next left column has 1 + 1 = 10 + 1 = 11 that means 1 with a carry of 1

The next left column has 0 + 0 = 0; add the carry to get 0 + 1 = 1; no carry

The next left column has 1 + 0 = 1; no carry

The left most column has 1 + 1 = 0 with a carry of 1 which is appended to the left most position

Reading from left to right this would be 1 0 1 1 1 0

(This is the same as adding two 2-digit numbers with a carry. For example, 74 + 82 = 156)

In long addition format:

 \(0 \quad 1 \quad 1 \quad 0 \quad 1 \quad 1\quad +\\0 \quad 1 \quad 0 \quad 0 \quad 1 \quad 1\quad \\---------\\1 \quad 0 \quad 1 \quad 1 \quad 1 \quad 0\quad\\---------\\\)

The leading zeros above are only for alignment and do not affect the values  . Note the addition result has 6 places whereas the items being added have only 5 places

Subtracting 1 1 1 0 1  will give

\(1 \quad 0 \quad 1 \quad 1 \quad 1 \quad 0 \quad -\\\quad 0 \quad 1 \quad 1 \quad 1 \quad 0 \quad 1\\---------\\\quad 0 \quad 1 \quad 0\quad 0\quad 0\quad 1\\---------\\\)

Here, starting at the right most column we get 0 - 1 = 1 which requires a carry from the next left column. So the bit in the next left column becomes 1 - 1 = 0 which makes that column  0 - 0 = 0

The next two columns on the left have both 1 so it is just 1 - 1 = 0 in both
In the next to last left column we have 0 - 1, this requires a carry from the left most column so it becomes 0 - 1 with carry = 10 - 1 = 1

Hope that was comprehensible

Answer:

35 hours

Step-by-step explanation:

As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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\(6=\frac{m}{8}\\x=48\)

Answer:

To plot (1,5), start at the origin (0,0) and move right 1 unit and up 5 units.

(1,5)

To plot (4,−1) , start at the origin (0,0) and move right 4 units and down 1

units.

(4,−1)

List the points below:

(1,5),(4,−1)

Step-by-step explanation:

Answer:

3 per month

12 divide by 4 is 3

The mean = 29

Look at the screenshot below for explanation and I hope this answers your question. Have a good day.