If I gallon = 4 quarts, how many gallons are equal to 108 quarts? Explain Your Answer.​

Answer: 8 1/3

Step-by-step explanation: Convert 3/4 to 9/12 then subtract, and simplify.

Answer:

8 and 1/3

Step-by-step explanation:

First, let's subtract the whole numbers:

16 - 8 = 8

Then, find the lowest common multiple of the two denominators, 4 and 12. In this case, 12 is the lowest common multiple. To turn 4ths into 12ths:

4 x 3 is 12, and 3 x 3 is 9

Now, subtract the two fractions:

9/12 - 5/12 = 4/12 = 1/3

That gives us a final answer of 8 and 1/3. Hope this helped!

Given :

The half-life of carbon 14 is 5,730 years.

To Find :

How much would be left of an original 50- gram sample after 2, 292 years.

Solution :

We know, rate law for first order reaction is given by :

\([A] = [A_o]e^{-kt}\)   ...1)

Here, \(A_o\) is initial amount and \(A\) is final amount.

And \(k = \dfrac{ln\ 2}{t_{0.5}}\)

Putting value of half time in above equation, we get :

\(k = \dfrac{ln\ 2}{5730}\\\\k = 1.21\times10^{-4} \ /s\)

Putting value of k in equation 1) , we get :

\([A] = 50\times e^{-1.21\times 10^{-4}\times 2292} = 37.89\ gm\\\\\)

Hence, this is the required solution.

Answer: i have zero clue lol

The general solution is y(t) = C₁e^(α₁t) + C₂e^(α₂t) + 81 + www, where C₁ and C₂ are arbitrary constants and α₁ and α₂ are the roots of the characteristic equation.

To find the general solution, we first need to solve the associated homogeneous equation, which is obtained by setting the nonhomogeneous term equal to zero: 50y'' + 4y' - 80y - 90 = 0. This equation has the form ay'' + by' + cy = 0, where a = 50, b = 4, and c = -80. The characteristic equation is obtained by assuming a solution of the form y(t) = e^(αt), where α is an unknown constant. Substituting this into the homogeneous equation gives the characteristic equation: 50α² + 4α - 80 = 0.

Solving this quadratic equation for α gives us two distinct roots, α₁ and α₂. Let's denote the particular solution p(t) = 81 + www as a separate term. The general solution of the nonhomogeneous equation is then given by y(t) = C₁e^(α₁t) + C₂e^(α₂t) + p(t), where C₁ and C₂ are arbitrary constants determined by initial conditions or additional constraints. Note that we avoid using the letters d, D, e, E, i, or I as arbitrary constants to avoid confusion with commonly used mathematical symbols. This general solution incorporates both the homogeneous solutions (C₁e^(α₁t) and C₂e^(α₂t)) and the particular solution p(t), providing a complete solution to the nonhomogeneous equation.

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If the storage container can hold 896 wooden cube blocks with edge length of 1/4 ft , then the volume of the container is 14 ft³ .

The shape of the storage container is rectangular prism ,

the number of cube blocks that the container can hold is = 896 wooden cube ,

the edge length of each cube is = 1/4 ft ,

we know that the volume of cube is = (edge length)³ ,

So , the volume of the container is = 896 × (1/4)³ ,

= 896 × (1/64) ,

On simplifying ,

we get ,

= 14 .

Therefore , the volume of the cube is 14 ft³ .

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The equation of the tangent plane to the surface at the point (4, -4, -144) is -8x + 64y - z - 256 = 0.

To find the equation of the tangent plane to the surface at the point (4, -4, -144), we need to find the partial derivatives of z with respect to x and y at that point:

∂z/∂x = 2x + 4y

∂z/∂y = 4x - 12y

Substituting x=4 and y=-4 into these expressions, we get:

∂z/∂x = 2(4) + 4(-4) = -8

∂z/∂y = 4(4) - 12(-4) = 64

So the normal vector to the tangent plane at the point (4, -4, -144) is <∂z/∂x, ∂z/∂y, -1> = <-8, 64, -1>. Therefore, the equation of the tangent plane is:

-8(x - 4) + 64(y + 4) - (z + 144) = 0

Simplifying this equation, we get:

-8x + 64y - z - 256 = 0

So the equation of the tangent plane to the surface at the point (4, -4, -144) is -8x + 64y - z - 256 = 0.

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Answer:

76 km/h

Step-by-step explanation:

19 km / 15 minutes = 76 km / 60 minutes ( i just multiplied by 4/4).

60 min = 1 hr, so the speed in km/h = 76 km/h

hope this helps! <3

1. The Bayesian form of the simple linear regression model is: y = β0 + β1 * x + ε.

where y is the dependent variable, x is the independent variable, β0 is the intercept, β1 is the slope, and ε is the error term.

2. The joint likelihood depends on the likelihood function, the prior distributions, and the data.

The Bayesian form of the simple linear regression model and explain what the joint likelihood depends on for this model.
The Bayesian form of the simple linear regression model involves updating our beliefs about the parameters of the model (slope and intercept) based on the observed data.

The model can be represented as:
y = β0 + β1 * x + ε

Where y is the dependent variable, β0 is the intercept, β1 is the slope, x is the independent variable, and ε is the error term.
In the Bayesian approach, we assign prior distributions to the model parameters, β0 and β1, and update these priors using the observed data to obtain posterior distributions.
The joint likelihood for the Bayesian simple linear regression model depends on three components:
The likelihood function:

This represents the probability of observing the data given the model parameters.

For a simple linear regression model, the likelihood function is typically based on the assumption that the errors (ε) follow a normal distribution with mean 0 and variance \(\sigma^2.\)
The prior distributions:

These represent our beliefs about the model parameters (β0 and β1) before observing the data.

Common choices for priors include normal or uniform distributions.
The data:

The observed values of the dependent variable (y) and the independent variable (x) are used to update the prior distributions and obtain the posterior distributions for the model parameters.

The Bayesian form of the simple linear regression model involves updating our beliefs about the model parameters (intercept and slope) using prior distributions and observed data.

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(–6,2) is the possible coordinates of point D if ΔDEF is congruent to ΔABC.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Shapes are congruent if you can turn one into the other by moving, rotating or flipping.

We can use this symbol  to show that two things are congruent.

Two triangles are congruent if and only if all the corresponding legs are congruent.

The only point that makes the corresponding legs to be congruent is

(–6,2)

because we can match these two triangles by flipping the red one two times and moving it into the blue one.

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89.09% of books will weigh 11 pounds or more, then the number of books will be 129.

The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.

The weights of books in a bookcase are normally distributed with a mean of 11.6 pounds and a standard deviation of 1.3 pounds. There are 136 books on the bookshelf.

Then the z-score when the books will weigh 11 pounds or more will be

\(z= \frac{11-13.5}{2.3} \\\\z= -1.0869\)

Then the probability will be

\(P(x > 11) = 1-P(x < 11 ) = 0.8909\)

89.09% of books will weigh 11 pounds or more, then the number of the books will be

=145 × 0.8909

=129.1805 ≈ 129

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Answer:

W.

Step-by-step explanation:

Because it's a cubic function which means it has to be a function because it literally has function in it.

Answer:

30

Step-by-step explanation:

Use the fundamental counting principal.

There are 6 possible outcomes on one spinner and 5 possible outcomes on the other spinner. Multiply the possible outcomes together to get the total possible outcomes.

6 x 5 = 30

Answer:

D

Step-by-step explanation:

Factor
this is how is should be
x + 2 = 0
=> x = -2
x - 3 = 0
=> x = + 3

Given:

Alexandra bought a television set for $724 in Boston.

The sales tax rate was 6.25% of the purchase price.

So, the sales tax =

The total cost =

So, the answer will be The total cost = 769.25

Answer:

To find the principal amount, you can use the formula for continuously compounded interest:

A = Pe^(rt)

where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.

Substituting in the given values:

1,433,785.18 = P * e^(0.054 * 12)

To find P, we can divide both sides by e^(0.054 * 12)

P = 1,433,785.18 / e^(0.054 * 12)

We can say that in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem.

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Other complex mathematical strategies were known to the Babylonians. For example, in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem long before Pythagoras.

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Answer:

they both ate the same amount

QUESTION REPHRASED:

Dana ate 60% of a 50 g chocolate bar and Neel ate 40% of a 75 g chocolate bar.

Who ate more pure chocolate?

Step-by-step explanation:

60% of 50g is 30g

40% of 75g is also 30g

They both ate the same amount of chocolate.

The ratio of two numbers that has no dimensions is what is known as a percentage. It may be used to determine how much one number exceeds another when comparing two figures, or it is used to compare the two statistics to a uniform grid.

Dana ate 50 grams of a 60% chocolate bar

= 50 * 60 / 100

= 30 grams

Neel ate 75 grams of a 40% chocolate bar

= 75 * 40 / 100

= 30 grams

As both Dana and Neel have eaten an equal amount of chocolate which is 30 grams.

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Answer:

$109+$281=x when x=391

so that means a laptop equals $391 dollars

Answer:

Horizontal : y = 7

Vertical: x = -2 and x = 2.

Step-by-step explanation:

I am assming this is (7x^2 - 1)/(x^2 - 4)

If we do the division we get 7 + 27/(x^2 - 4)

So the horizontal asymptote is y = 7.

Find the vertical asymptotes:

These occr when the denominator = 0, so:

x^2 - 4 = 0

x^2 = 4

x = 2 or -2.

So they are x = -2 and x = 2.

The effect  of adding k on the graph of f(x) will shift the curve upward by k units on the xy-plane.

Given the parent function of the given graph expressed as  f(x) = 2x^2 + 4.

If this function is represented as f(x)+k, the addition of the constant "k" shows hat the  function f(x) has been shifted vertically upwards by a factors of 'k'

Hence the effect  of adding k on the graph of f(x) will shift the curve upward by k units on the xy-plane.

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The function f has the property injective. (D)

An injective function is also known as a one-to-one function, which means that for every unique output, there is a unique input.

In this case, the function f maps the single element in the domain {1} to the single element in the codomain {1}, and there is only one possible output for the single input, so it is injective.

It does not have the properties of being increasing, decreasing, strictly increasing, strictly decreasing, or surjective because the function is a constant function mapping the single element in its domain to the single element in its codomain.

As a result, it does not change in value and cannot be classified as increasing or decreasing. Additionally, it is not surjective because the codomain contains one element that is not mapped to by the function.

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Your answer to this question would be A.

(Aka) 401.92 in sq 2

Answer:

a ;)

this answer was to short so i had to add stuff.

Answer:

Can i be brainlest i neeed it

Answer:

translated up 4 units and s(t)= 22.5t + 775

Step-by-step explanation:

first one count spaces between lines. second one add the t's together and the numbers to get final answers

Answer: 12

Step-by-step explanation:

The value of h'(1) is 4.

We must differentiate the function h(x) = 5f(x) - 4g(x) + 3x2 - 2 and evaluate it at x = 1 in order to determine the value of h'(1).

First, let's use the information provided to calculate the derivatives of f(x) and g(x):

Given that, f'(1) equals 2, and g'(1) equals 3, let's break down h(x) into its individual terms:

The following is the derivative of 5f(x) with respect to x: h(x) = 5f(x) - 4g(x) + 3x2 - 2

In a similar vein, the derivative of 4g(x) with respect to x is as follows:

(4g(x))' = 4g'(x) = 4g'(1) = 4 * 3 = 12

The subsidiary of 3x^2 regarding x is:

(3x2)' = 6x The derivative of the constant term -2 is zero because it does not involve x.

Now, let's add the derivatives of each term to get h'(x):

h'(x) = (5f(x))' - (4g(x))' + (3x2)' + 0 = 10-12 + 6x + 0 = 6x - 2 Ultimately, we must evaluate h'(x) when x is one:

The value of h'(1) is 4, since h'(1) = 6(1) - 2 = 6 - 2 = 4.

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Step-by-step explanation:

Let's find the difference between 7508 and the other numbers.

A. 5706 - 7508 = -1802

B. 6993 - 7508 = -515

C. 8108 - 7508 = 600

D. 8522 - 7508 = 1014

E. 1050 - 7508 = -6458

If we do not take +ve / -ve into account,

the closest number to 7508 = the smallest difference

which in this case, is B, 6993.

Answer:

B. 6993

Step-by-step explanation:

hope this helps :)

A basis for the subspace of R4 consisting of all vectors perpendicular to v is [-7/9, 1, 0, 0], [-2/9, 0, 1, 0], [1/3, 0, 0, 1].

We can find a basis for the subspace of R4 consisting of all vectors perpendicular to v by solving the homogeneous system of linear equations Ax = 0, where A is the matrix whose rows are the components of v and x is a column vector in R4.

The augmented matrix [A|0] is:

| 9 7 2 -3 | 0 |

||

||

||

||

We can row reduce the augmented matrix using elementary row operations to get it in reduced row echelon form.

| 1 7/9 2/9 -1/3 | 0 |

||

||

||

||

We can write the solution as a parametric vector form:

x1 = -7/9s - 2/9t + 1/3u

x2 = s

x3 = t

x4 = u

where s, t, and u are arbitrary constants.

Therefore, a basis for the subspace of R4 consisting of all vectors perpendicular to v is:

[-7/9, 1, 0, 0], [-2/9, 0, 1, 0], [1/3, 0, 0, 1]

These vectors are linearly independent and span the subspace of R4 perpendicular to v.

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The height of ball which is droped from 2m and rises to 75% after third bounce is equals to the 0.843 meters.

If an object is thrown from high and has a bouncing feature, each bouncing is less than the initial height until it stops. Each bounce reduces the growth rate until it reaches zero. In order to calculate the height of each bounce, so we can estimate what percentage the object will reach after each bounce. If we get the percentage of each bounce, we can easily determine the height of each bounce. We have, a ball is droped from 2 meters and bounce up to 75%. That is height of first bounce is determined by using percentage, height is 2 m × 75% = 2 m×0.75 = 1.5 m

In second bounce, height is 1.5 m × 75%

= 1.5 m×0.75 = 1.12 m

In third bounce, 1.12 m× 75%

= 1.12 m×0.75 = 0.843 m

The height the ball reaches on its third bounce is 0.843 m.

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Complete question :

A ball is dropped from a height of 2 meters and rises up by 75% of its height on each bounce. How high would the third bounce be?

The normal probability plot determines a normal distribution

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the centre of the range.

Normal distributions are symmetric, uni-modal, and asymptotic, and the mean, median, and mode are all equal

A data set (when graphed) must follow a bell-shaped symmetrical curve centered around the mean

Given data ,

Let the normal distribution be represented as N

Now , the normal probability is P

A normal probability plot, also known as a "normal plot," plots sorted data against values chosen to resemble a straight line in the final image if the data are roughly normally distributed.

Divergences from normalcy are shown by deviations from a straight line.

A straight, diagonal line means that you have normally distributed data. If the line is skewed to the left or right, it means that you do not have normally distributed data.

Hence , the normal probability plot determines a normal distribution

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