Write the equation of a line containing (3,-7) that is parallel to the line given by the equation -4x+8y=3

The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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Answer:

52

Step-by-step explanation:

There are 116,280 ways to divide 19 people into five groups containing 5, 1, 2, 4, and 7 people, respectively.

A group is a set of elements with a binary operation that combines any two elements to form a third element in such a way that four conditions called group axioms are satisfied, namely closure, associativity, identity, and invertibility. Groups are used in many areas of mathematics, physics, and other sciences as a way of describing symmetries and transformations.

In the given questions,

To find the number of ways to divide 19 people into five groups containing, respectively, 5, 1, 2, 4, and 7 people, we can use the multinomial coefficient formula.

The multinomial coefficient formula states that the number of ways to distribute n distinct objects into k distinct boxes, where the first box contains n1 objects, the second box contains n2 objects, and so on up to the kth box containing nk objects, is given by:

(n choose n1, n2, ..., nk) = n! / (n1! * n2! * ... * nk!)

where n = n1 + n2 + ... + nk.

In this problem, we have n = 19 and k = 5, with n1 = 5, n2 = 1, n3 = 2, n4 = 4, and n5 = 7. So we can plug these values into the formula:

(19 choose 5, 1, 2, 4, 7) = 19! / (5! * 1! * 2! * 4! * 7!)

Using a calculator or computer program, we can simplify this expression to find:

(19 choose 5, 1, 2, 4, 7) = 116,280

Therefore, there are 116,280 ways to divide 19 people into five groups containing 5, 1, 2, 4, and 7 people, respectively.

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Answer:

Here we only need to analyze the vertical motion of the ball.

First, because the ball is in the air, the only force acting on the ball will be the gravitational force (we are ignoring air resistance), then the acceleration of the ball is equal to the gravitational acceleration, so we have:

a(t) = -32 ft/s^2

where the negative sign is because this acceleration is downwards.

To get the velocity equation, we need to integrate over the time, so we get:

v(t) = (-32 ft/s^2)*t + V0

where V0 is the initial velocity of the ball. In this case, the initial velocity of the ball will be the velocity that the ball had when it was dropped, which should be the same as the velocity of the hot air ballon, so we have:

V0 = 12 ft/s

Then the velocity equation of the ball is:

v(t) = (-32 ft/s^2)*t + 12 ft/s

To get the position equation we integrate again:

p(t) = (1/2)*(-32 ft/s^2)*t^2 + (12 ft/s)*t + H0

Where H0 is the initial height. We know that the ball was released at the height of 1120 ft, then we have:

H0 = 1120 ft.

Then the position equation is:

p(t) = (-16 ft/s^2)*t^2 + (12 ft/s)*t + 1120ft

a)  How many seconds after its release will the ball strike the ground?

The ball will strike the ground when its position equation is equal to zero, then we need to solve:

p(t) = 0 ft = (-16 ft/s^2)*t^2 + (12 ft/s)*t + 1120ft

This is just a quadratic equation, the solutions are given by Bhaskara's formula, so the solutions for t are:

\(t = \frac{- 12ft/s \pm \sqrt{(12 ft/s)^2 - 4*(-16ft/s^2)*(1120 ft)} }{2*(-16ft/s^2)}\)

We can simplify that to get:

\(t = \frac{-12ft/s \pm 268ft/s}{-32ft/s^2}\)

So we have two solutions:

\(t = \frac{-12ft/s + 268ft/s}{-32ft/s^2} = -8s\)

\(t = \frac{-12ft/s - 268ft/s}{-32ft/s^2} = 8.75s\)

The negative solution does not make sense, then the correct solution is the positive one.

We can conclude that the ball will hit the ground after 8.75 seconds.

b)  At what velocity will it hit the ground?

We already know that the ball strikes the ground 8.75 seconds after it is released.

The velocity at it hits the ground is given by the velocity equation evaluated in that time:

v(8.75 s) = (-32 ft/s^2)*8.75s + 12 ft/s = -268 ft/s

Answer:

B

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , so

∠ c + 56° + 38° = 180°

∠ c + 94° = 180° ( subtract 94° from both sides )

∠ c = 86°

The expression that represents the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)

It is important to note that an expression simply refers to mathematical statements which have at least two terms which are then related by an operator. In this case, they contain either numbers, variables, or both.

In this case, since Hayden rode his bike 5 times and each time he biked a 3 mile path, a 2 mile path, and a 2 1/4 mile path. Then in this situation, the expression will be:

= 5 × (3 + 3 + 2 1/4)

In conclusion, the correct option is A.

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A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

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Answer:

a and e

Step-by-step explanation:

Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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Answer:

1672.50 = 37.75x + 1068.50

x = 16

There were 16 players brought to the tournament.

Step-by-step explanation:

y = mx + b

y= the total cost

m = cost of each meal

x = the number of players

b = cost of the bus

Plug in what you know and solve for x

1672.50 =  37.75x + 1068.50  Subtract 1068.50 from both sides.

604 = 37.75x  Divide both sides by 37.75

16 = x

Equation: 1068.50 + 37.75x =1,672.50

Answer: X= 16

If 1,672.50 is our total it will go behind the equal sign. 37.75x and 1068.50 must be added together to help us receive our total.

Our written equation should look like this

1068.50 + 37.75x =1,672.50

X is the number of players on the team.To find out we must first subtract the amount of money spent on the bus, from the total amount spent.

1,672.50-1068.50 is 604. This means our equation now looks like this

37.75x=604. The next and final step is to divide 37.75 into 604.

604/ 37.75 is 16. Which means that there are 16 players on the team.

I hope this helps & Good luck.

The odds against this happening are  48:25 . For this we have to know the meaning of probability.

I showed that out of  22100 possible deals, there are  3744 ways to get a pair and  52 ways of getting 3 of a kind that makes a total of  3796 ways to get a pair or 3 of a kind.

If we multiply this by  3! then we get  22776 possible permutations that result in 3 of a kind or in a pair.

To get the number of permutations of deals where the first two cards are a pair, we note that the first card could be any one of the  52 in the pack.

The second card must be one of the  3 remaining cards that pairs up with the first one and then there are  50 cards that could be selected for the third.

That makes a total of  52×3×50=7800 permutations.

\(\frac{7800}{22776} = \frac{27}{73}\)

The odds against this happening are  48:25

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The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer: 24 percent of 25 is 6.

Step-by-step explanation: The output of 24 percent of 25 is 6. To obtain this answer, we multiply 0.24 by 25.

9514 1404 393

Answer:

  3.5 inches

Step-by-step explanation:

The volume is given by the formula ...

  V = LWH

Filling in the given values, we can solve for the remaining dimension.

  26.46 in³ = (4.2 in)(W)(1.8 in)

  W = 26.46 in²/(7.56 in²) = 3.5 in

The width of the prism is 3.5 inches.

________________________________

Answer:

Explanation:

Multiply height and length of a rectangle then devide to the volume of rectangular prism.

Formula:

Solution:

To double check do the solution of finding volume of rectangular prism.

Formula:

________________________________

Answer:

you see

Step-by-step explanation:

By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.

solve the equation logₓ(64) + 5 = 2, we can follow these steps:

Step 1: Move the constant term to the other side of the equation:

logₓ(64) = 2 - 5

logₓ(64) = -3

Step 2: Rewrite the equation in exponential form:

x^(-3) = 64

Step 3: Rewrite 64 as a power of x:

x^(-3) = x^6

Step 4: Set the exponents equal to each other:

-3 = 6

The equation -3 = 6 is not true, which means there is no real solution to the given equation.

Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.

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Recall that

d/dx sech(x) = - sech(x) tanh(x)

d/dx tan⁻¹(x) = 1/(1 + x²)

Then by the chain rule,

dy/dx = - sech(x) tanh(x) / (1 + x²)

Answer:

Multiplication

Step-by-step explanation:

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The reason these triangles are similar is A. Angle-Angle similarity.

Angle-Angle similarity, also known as AA similarity, states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

In the figure that we are given, we see two angles that are similar as shown on the diagram. These angles are on the different triangles and yet are congruent which means that the triangles are similar.

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Answer:  -1, -32/40, 14/35

An 86% confidence interval for the difference in age to leave mother is -3.10091

What is confidence Interval?

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given, Gorilla Baby sample

x means x bar here so, \(x_{1}\) = 3.21

\(s_{1}\) = 0.81

\(n_{1}\) = 64

Human Baby sample

x means x bar here so, \(x_{2}\) = 19.1

\(s_{2}\) = 2.16

\(n_{2}\) = 200

Confidence interval needs t score

t score = 1.18

86% confidence interval = \(x_{1}\) - \(x_{2}\) ± tc \(\sqrt{s^{2} {1} / n_{2} + s^{2} {2} / n_{2}\)

= 3.21 - 19.1 ± 1.18 √0.81²/64 +2.16²/200

= 3.21 - 19.1 ± 1.18 √0.033

= -3.10091

An 86% confidence interval for the difference in age to leave mother is -3.10091

The detail question is here,

A study based on the Association primate Ebmarah looked at the average age a baby gorilla leaves it’s mother versus the average age the human baby leaves it’s mother . Naturally they are different , so we don’t want a hypothesis test. Instead, find an  86% confidence interval  for the difference in age to leave mother.

Gorilla:

Sampled 64 babies

Stayed with mother on average 3.21 years

Standard deviation:  0.81

Human:

Sampled  200 babies

Stayed with mother on average 19.1 years

Standard deviation:  2.16

Matched  pairs  standard deviation :0.23

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Answer:

The value of k is -4 and the equation of the line is \(y =-\frac{1}{2}\cdot x +10\).

Step-by-step explanation:

The equation of the line is defined by the following formula:

\(y = m\cdot x + b\) (1)

Where:

\(x\) - Independent variable.

\(y\) - Dependent variable.

\(b\) - y-Intercept.

\(m\) - Slope.

In addition, the slope of the equation of the line (\(m\)) can be known from two distinct points:

\(m = \frac{y-y_{o}}{x-x_{o}}\) (2)

Where \(x_{o}\) and \(y_{o}\) are the coordinates of the reference point.

By applying (2) in (1), we derive the resulting expression:

\(y = \frac{y-y_{o}}{x-x_{o}}\cdot x + b\)

\(y\cdot (x-x_{o}) = (y-y_{o})\cdot x + b\cdot (x-x_{o})\)

\(x\cdot y -y\cdot x_{o} = x\cdot y -x\cdot y_{o}+b\cdot x -b\cdot x_{o}\)

\((b-y)\cdot x_{o} = b\cdot x -x\cdot y_{o}\)

\((b-y)\cdot x_{o} +x\cdot y_{o} = b\cdot x\) (3)

If we know that \(b = 10\), \(x = 2\), \(y = 9\), \(x_{o} = k+10\) and \(y_{o} = -2\cdot k -1\), then the value of \(k\) is:

\((10-9)\cdot (k+10)+2\cdot (-2\cdot k -1) = (10)\cdot (2)\)

\(k+10 -4\cdot k -2 = 20\)

\(-3\cdot k +8 = 20\)

\(-3\cdot k = 12\)

\(k = -4\)

The value of the slope is:

\(m = \frac{9-7}{2-6}\)

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

The equation of the line is \(y =-\frac{1}{2}\cdot x +10\).

Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.

A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.

Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:

Interest = Principal x Rate x Time

Interest = $2,500 x 0.15 x 1

Interest = $375

Thus, the total sum his friend will be required to pay Darrel is:

Total amount = Principal + Interest

Total amount = $2,500 + $375

Total amount = $2,875

Thus, the total amount his friend owes Darrel is $2,875.

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Answer:

Step-by-step explanation:

4(3x-5)^2+5=13

4(3x-5)^2+5-13=0

As  (a-b)^2=a^2-2ab+b^2

4((3x)^2-2(3x)(5)+(5)^2)-8=0

4(9x^2-30x+25)-8=0

36x^2-120x+100-8=0

36x^2-120x+92=0

using the Quadratic Formula where

a = 36, b = -120, and c = 92

x=(−bc± sqrt(b^2-4ac))/2a

x=(-(-120)±sqrt((−120)^2−4(36)(92))/2(36)

=120±sqrt(14400−13248−)/72

=120±sqrt(1152)/72

The discriminant b2−4ac>0

so, there are two real roots.

x=(120±24sqrt(2))/72

x=(120/72)±24sqrt(2)/72

implify fractions and/or signs:

x=5/3±sqrt(2)/3

hich becomes

x=2.13807

x=1.19526

The Solution:

Given:

Required:

Find the value of the investment after 5 years.

The Formula:

In this case,

Substitute:

Answer:

(a) $79,747.14

Find the number of months it will take the account to increase to more than $70,000

Solve for n in the equation below:

Answer:

13 months or more

Answer:

288 000

Step-by-step explanation:

Just multiply 30(boxes) x 10(boxes) x 24(bottles) x 20 (ounces) and you get how many ounces are in 1 pallet and since need 2 pallets, you multiply again by two and you 288 000

Answer:

1 : 45

Step-by-step explanation:

225 divided by 5 equals 45. You can now use this ratio to determine the number of people with different amounts of buses; when you change x from 1 to n, you would need to multiply 45 by n, and you will have your new ratio column in the table.

Hope this helps :)

The equation which models the relationship expressed in slope intercept form ls y = 45x

Expressing the equation in the form :

Slope, b = (900 - 225) / (20 - 5) = 45

Using any (x, y) points on the table given to find the value of c :

225 = 45(5) + c

225 = 225 + c

c = 0

Hence, the equation which models the relationship is y = 45x

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