Write the prime factorization of 10.

Answer:

25

Step-by-step explanation:

Given the model:

y=−3.5x+400

Number of children in amusement park = y

Temperature = x

On a certain day:

Temperature = 90°F

Number of children in park = 60

Using the model :

The predicted number of children in park when temperature is 90°F would be :

y = - 3.5(90) + 400

y = - 315 + 400

y = 85

Model prediction = 85 children

Actual figure = 60

Residual :

|Actual - predicted | = |60 - 85| = 25 children

The ball travels the farthest when the toss angle is 45 degrees. At this angle, the horizontal and vertical components of the ball's initial velocity are balanced, maximizing the projectile's range.

This occurs because the horizontal distance covered by the ball is determined by the initial velocity in that direction, while the vertical distance is affected by the gravitational force pulling the ball downward.

When the toss angle is less than 45 degrees (e.g., 15 or 30 degrees), the vertical component of the initial velocity increases, causing the ball to spend more time in the air and resulting in a shorter horizontal distance traveled. On the other hand, when the toss angle exceeds 45 degrees (e.g., 60 degrees), the vertical component of the initial velocity decreases, leading to a more rapid descent and again reducing the overall range.

Therefore, a toss angle of 45 degrees provides the optimal balance between the horizontal and vertical components of the ball's velocity, allowing it to cover the greatest distance when thrown from ground level.

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To find the local and absolute minima and maxima for the given functions over the interval (-∞, ∞), we need to analyze their derivatives.

Let's begin with the first function:

y = x^2 + 4x + 5

Step 1: Find the derivative of y with respect to x.

y' = 2x + 4

Step 2: Set y' = 0 and solve for x to find critical points.

2x + 4 = 0

2x = -4

x = -2

Step 3: Classify the critical point.

Since the derivative is a linear function, there is only one critical point. In this case, it's a minimum since the coefficient of x^2 (2) is positive.

Step 4: Determine the values of y at the critical point and at ±∞.

To find the y-value at x = -2:

y = (-2)^2 + 4(-2) + 5

y = 4 - 8 + 5

y = 1

As x approaches -∞ or ∞, y approaches ∞. Therefore, there is no absolute minimum or maximum.

Hence, for the function y = x^2 + 4x + 5, there is a local minimum at (-2, 1), and no absolute minimum or maximum.

Moving on to the second function:

y = x^3 - 12x

Step 1: Find the derivative of y with respect to x.

y' = 3x^2 - 12

Step 2: Set y' = 0 and solve for x to find critical points.

3x^2 - 12 = 0

3x^2 = 12

x^2 = 4

x = ±2

Step 3: Classify the critical points.

Since the derivative is a quadratic function and the coefficient of x^2 (3) is positive, we have a local minimum at x = -2 and a local maximum at x = 2.

Step 4: Determine the values of y at the critical points and at ±∞.

For x = -2:

y = (-2)^3 - 12(-2)

y = -8 + 24

y = 16

For x = 2:

y = (2)^3 - 12(2)

y = 8 - 24

y = -16

As x approaches -∞ or ∞, y approaches -∞. Therefore, there is no absolute minimum or maximum.

Therefore, for the function y = x^3 - 12x, there is a local minimum at (-2, 16), a local maximum at (2, -16), and no absolute minimum or maximum.

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The equation of the new function will be g(x) = x² – 6. Then the correct option is A.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line.

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

where a is the leading coefficient.

The function is given below.

f(x) = x²

If you vertically shift this function down 6 units.

Then the equation of the new function will be

If the value of k is negative, then the function get shifted downwards.

Then the new function will be

g(x) = x² – 6

Then the correct option is A.

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The predicted outcome of the game, or the strategy profile played in the game, would then depend on the remaining strategies.

1. A strategy is considered strictly dominant for a player if it always leads to a higher payoff than any other strategy, regardless of the choices made by the other player. In this game, for player 1 to have a strictly dominant strategy, the payoff for strategy U must be strictly higher than the payoffs for strategies M and D, regardless of the choices made by player 2.

2. For player 2 to have a strictly dominant strategy, the payoff for strategy R must be strictly higher than the payoffs for strategies L and any other possible strategy that player 2 can choose.

3. To determine if any player has a strictly dominant strategy, we need to compare the payoffs for each strategy for both players. In this specific example, using the given values (a=2, b=3, c=4, x=5, y=5, z=2, and w=3),

4. The order in which strategies are deleted does matter when using iterative deletion of weakly dominated strategies. In the given example, when we delete the weakly dominated strategy M for player 1, we are left with a 2x2 game.

(c) In the original game of part (4), when we note that U is a weakly dominated strategy for player 1, we can look for a strategy that weakly dominates it. By comparing the payoffs, we can determine the weakly dominant strategy.

(d) After deleting U and noting that L is weakly dominated for player 2, we can delete it as well. The predicted outcome of the game, or the strategy profile played in the game, would then depend on the remaining strategies.

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Answer:

Step-by-step explanation:

Its C. a-6

Answer:

c

Step-by-step explanation:

on edg2020

Answer:

x = 9

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle is

Parallel to the third side

then the 2 angles are same- side interior angles and sum to 180° , that is

16x - 33 + 8x - 3 = 180

24x - 36 = 180 ( add 36 to both sides )

24x = 216 ( divide both sides by 24 )

x = 9

DSA is only used for signature purposes but RSA is used for cryptographic purposes.

But somehow DSA uses discrete logarithms for Encryption and in RSA long-term calculations are used which is more secure as compared to DSA.

Now while signing messages with DSA leads to a more time and more memory-consuming process because at every point the message is signed. So the verification of signatures gets complicated.

But in the case of RSA, the calculations are high, but they consume less memory and less need for verification. Because of large calculations, RSA is much slower than DSA.

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Tom can paint the room alone in 12 hours.

Let's assume that the work required to paint the room is equivalent to 1 unit of work. If John can paint the room alone in 6 hours, his work rate per hour is 1/6.

Similarly, if John and Tom together can paint the room in 4 hours, their combined work rate per hour is 1/4. Let x be Tom's work rate per hour.

Then, we can set up the following equation:1/6 + x = 1/4

To solve for x, we can simplify the equation as follows:

Multiplying both sides by 12 (the LCM of 6 and 4) yields:2 + 12x = 3Solving for x gives:12x = 1x = 1/12Therefore, Tom's work rate per hour is 1/12, which means he can paint the room alone in 12 hours.

Summary:Tom can paint the room alone in 12 hours

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Answer:

5

Step-by-step explanation:

1) origin point is (0;0);

2) the required distance is:

\(d=\sqrt{(-3-0)^2+(4-0)^2} =5.\)

The solution to this system of linear equations y - x = 6 and y + x = -10 is (-8, -2).

y - x = 6

⇒y = x + 6

y + x = -10

⇒y = - x - 10

Since both equations are equal to y, equate them.

x + 6 = - x - 10

x + x = - 10 - 6

2x = - 16

Divide both sides by 2

x = -8

Put the value of x in either of the equations

y - x = 6

y - (-8) = 6

y + 8 = 6

y = 6 - 8

y = - 2

Therefore, the solution to the system of linear equations is (-8, -2).

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Answer:

B

Step-by-step explanation:

The value of C, which represents the upper control limit (UCL) for the X-bar chart in the process of filling baby formula into bottles, is approximately 3.40552. This means that any average amount of baby formula above this limit may indicate a process out of control and require investigation.

To determine the value of C in this scenario, we need to use the formula for the control chart limits for an X-bar chart. The control limits for an X-bar chart with sample size n can be calculated using the following formula:

Upper Control Limit (UCL) = mean + A2 * R

Lower Control Limit (LCL) = mean - A2 * R

In this case:

The target value for the baby formula is 3 ounces.

The average amount of baby formula placed in the bottles is 2.941 ounces (mean).

The sample size is 200 bottles.

The standard deviation of the amounts is 0.1 ounce.

To calculate the value of C, we need to determine the value of A2, which depends on the sample size. The value of A2 can be found in statistical tables or calculated using statistical software. For a sample size of 200, A2 is typically 2.574.

Using the formula for the control limits, we can calculate the upper and lower control limits:

UCL = mean + A2 * R

= 2.941 + 2.574 * 0.18

= 2.941 + 0.46452

= 3.40552

LCL = mean - A2 * R

= 2.941 - 2.574 * 0.18

= 2.941 - 0.46452

= 2.47648

The value of C is the value of the upper control limit (UCL) in this case, which is approximately 3.40552.

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An equation is formed of two equal expressions. The equation that has solutions of m=–5 and m=9 is (m+5)(m-9)=0.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it is given that the solution of m is -5 and 9. Therefore, the equation which will represent the solution of m as -5 and 9 is

(m+5)(m-9)=0

Hence, the equation that has solutions of m=–5 and m=9 is (m+5)(m-9)=0.

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Answer:

The degree is 4

Let me know if it helped :)

Answer:

Step-by-step explanation:

FRaction form:   49/4

Decimal form:    12.25

Mixed Number:   12 1/4

Answer:

34cm

Step-by-step explanation:

2+1+8+3+8+3+2+7

The correct answer is n=4:)

Answer:

n= 4

Step-by-step explanation:

Answer:

13.3

Step-by-step explanation:

Therefore, the value of x in the circle with center O is x = 7.

A circle is a geometric shape consisting of all points that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius. A circle is a two-dimensional shape, and it is often represented by the symbol "O" or "⭕". The circumference of a circle is the distance around its edge or boundary.

Here,

If AB and BC are chords of a circle with center O, then we can use the intersecting chords theorem to find the value of x. According to the intersecting chords theorem, if two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. That is,

AB * BD = CB * BD

where BD is the length of the segment of chord AC that is inside the circle.

We can rearrange this equation to get:

AB * BD - CB * BD = 0

Factorizing BD from both terms, we get:

BD * (AB - CB) = 0

Since BD cannot be zero (as it is a positive length), we have:

AB - CB = 0

Substituting the given values, we get:

(4x-1) - (3x+6) = 0

Simplifying this equation, we get:

x - 7 = 0

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The 1st Quartile germination rate is 92%, the 1st Quartile germination rate represents the threshold below which 25% of the germination rates fall.

To determine this, we need to arrange the germination rates in ascending order and find the value that corresponds to the 25th percentile.

In this case, we have a packet of 160 seeds with 95% germination rate. To find the 1st Quartile germination rate, we need to consider the germination rates of the remaining 5% of seeds that did not germinate.

Since 92% is the claimed germination rate mentioned on the seed packet, we can assume that the 5% of seeds that did not germinate fall below this claimed rate. Therefore, the 1st Quartile germination rate is 92%.

The 1st Quartile, also known as the lower quartile or 25th percentile, divides a dataset into four equal parts. It represents the threshold below which 25% of the data points fall.

In this scenario, we have a packet of 160 seeds with a 95% germination rate. This means that 95% of the seeds successfully germinated. To find the 1st Quartile germination rate, we need to consider the remaining 5% of seeds that did not germinate.

Since the information on the seed packet claims a germination rate of 92%, we can assume that the 5% of seeds that did not germinate fall below this claimed rate.

As a result, the 1st Quartile germination rate is 92%. This indicates that 25% of the seeds in the packet had a germination rate below 92% while the remaining 75% had a germination rate equal to or higher than 92%.

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AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

B.

Step-by-step explanation:

A. For model log(y) only:

Answer: 23.5325

B. For model log(x) only:

Answer: 0.9592

C. For model log(y) and log(x):

Answer: 3.2000

A more detailed explanation of the answer.

For the given question, suppose a slope of 3.2 is obtained for a model fitted to log-transformed data. The task is to calculate the back-transformed slope for each of the following models.

A. For model log(y) only:
Backtransformed slope = exp(3.2) - 1
1. Calculate exp(3.2) = 24.53253
2. Subtract 1: 24.53253 - 1 = 23.53253
Answer: 23.5325 (rounded to 4 decimal places)

B. For model log(x) only:
Backtransformed slope = 1 - exp(-3.2)
1. Calculate exp(-3.2) = 0.04076
2. Subtract from 1: 1 - 0.04076 = 0.95924
Answer: 0.9592 (rounded to 4 decimal places)

C. For model log(y) and log(x):
Backtransformed slope = 3.2
Answer: 3.2000 (rounded to 4 decimal places)

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The prime factorization of 27 is \(3^3\) and the simplified radical form of the square root of 27 is 3√3.

Prime factorization is the method of finding the prime numbers that duplicate together to provide a composite number.

For case, the prime factorization of 27 is 3 x 3 x 3. This can be since 3 could be a prime number and 3 x 3 x 3 = 27.

Streamlining radicals includes finding the best frame of a square root or 3d shape root expression.

For illustration, the square root of 27 can be simplified as follows:

√27 = √(3 x 3 x 3) = √3 x √3 x √3 = 3√3

Typically the best frame since 3 may be a prime number and cannot be disentangled advance.

So also, the 3d shape root of 27 can be disentangled as takes after:

∛27 = ∛(3 x 3 x 3) = 3∛3

Once more, typically the best shape since 3 may be a prime number and cannot be disentangled encourage. 

Therefore, the prime factorization of 27 is \(3^3\) and the simplified radical form of the square root of 27 is 3√3.

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Answer:

$46

Step-by-step explanation:

Given that :

The expression : 2m+ 10c ( amount made from selling muffins and C cakes.)

This means cost per muffin is 2 and cost per cake is 10

Hence, amount made from selling 3 muffins and 4 cakes ;

2(3) + 10(4)

$6 + $40

= $46

Answer:

X is equal to 1.2

Step-by-step explanation:

6/5 equals 1.2

i don't have to sound rude but can i have brainliest please i need 4 more :')

Answer:

12.56km

Step-by-step explanation:

Circumference of circle=2pi r

Set pi=3.14

2xpix2=12.56km