The proposal during the Constitutional Convention that created a House proportionate to population along with a Senate in which all states were represented equally was called

Answer:

The Answer is A

Step-by-step explanation:

I'm 100% right.

If it is assumed that all 52 5 poker hands are equally likely, the probability of being dealt a flush is 0.001981

Flush means all 5 cards are of the same suit.

Now, we need to select one suit out of 4 which can be done in ⁴C₁ ways.

Now, when the suit is selected, we have to select 5 cards from that specific suit. This can be done in ¹³C₅ ways

In the game of poker, there are ⁵²C₅ possible hands.

So, the probability of a flush is given by:

              P = (⁴C₁ × ¹³C₅)/⁵²C₅

              P = (4 × 1287)/2598960

              P = 5148/2598960

              P = 0.001981 or 1.981 × 10⁻³ or 0.1981 %

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Answer:

Option A

Step-by-step explanation:

2(6 - 2y) = -1(4y - 9)

Distribute;

12 - 4y = -4y + 9

Add 4y to both sides;

12 ≠ 9

No solution

Answer: look at the explanation

Step-by-step explanation:

It goes down by 40%

For part (a), we can use Cauchy's Integral Formula which states that for a function f(z) that is analytic inside and on a simple closed contour C, and a point a inside C, we have:   The value of the integral is 2πi i0^(m+1).


f^(m)(a) = (1/2πi) ∮ C f(z)/(z-a)^(m+1) dz

where f^(m)(a) denotes the m-th derivative of f evaluated at a, and the integral is taken counterclockwise around C.

In our case, we have f(z) = 1, which is analytic everywhere, and C is the circle {izl = r} with counterclockwise orientation. So we can write:

iizml dz = i(1/2πi) ∮ {izl = r} 1/(z-i0) dz

where i0 is any point inside the circle, and the integral is taken counterclockwise around the circle.

Using Cauchy's Integral Formula with a = i0 and m = 0, we get:

iizml dz = i

So the value of the integral is just i.

For part (b), we need to evaluate the derivative of the integral, which is:

d/dz (iizml) = -m iizm-1

Using Cauchy's Integral Formula with a = i0 and m = 1, we get:

iizmlldzl = i(-m) (1/2πi) ∮ {izl = r} z^(m-1)/(z-i0)^2 dz

Note that the only difference from part (a) is the z^(m-1) term in the integral. We can simplify this using the Residue Theorem, which states that for a function f(z) that has a pole of order k at z = a, we have:

Res[f(z), a] = (1/(k-1)!) lim[z->a] d^(k-1)/dz^(k-1) [(z-a)^k f(z)]

In our case, the integral has a simple pole at z = i0, so we have:

Res[z^(m-1)/(z-i0)^2, i0] = lim[z->i0] d/dz [(z-i0)^2 z^(m-1)] = i0^m

Therefore, we can write:

iizmlldzl = -2πi Res[z^(m-1)/(z-i0)^2, i0] = -2πi i0^m

Note that the minus sign comes from the fact that the residue is negative. So the value of the integral is -2πi i0^m.

For part (c), we need to evaluate the integral of z^m around the same circle. Again, we can use Cauchy's Integral Formula with a = i0 and m = -1, which gives:

izm dz = (1/2πi) ∮ {izl = r} z^(m+1)/(z-i0) dz

Using the Residue Theorem, we can find the residue at z = i0, which is:

Res[z^(m+1)/(z-i0), i0] = lim[z->i0] z^(m+1) = i0^(m+1)

Therefore, we can write:

izm dz = 2πi Res[z^(m+1)/(z-i0), i0] = 2πi i0^(m+1).

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Part a) The slope of the hypotenuse of triangle ABC is Mab = -1.5

Part b) The coordinates of point R are (4,-7)

Part a

The formula to calculate the slope between two points is equal to

m = y2- y1 / x2 - x1

The hypotenuse of triangle ABC is the segment AB

A(-6, 8) and B(-2, 2)

substituting the values, we have:

mab = -3/2

Part b)

triangle ABC and triangle QRS are similar which means that the ratio of its corresponding sides is proportional, the slope of its corresponding sides are congruent and its corresponding interior angles are congruent too.

so mQR = Mab

mQR = -3/2

we have

3/2 = y + 4/ x - 2

Q(2, -4) and R( x,y )

We have said that Triangle ABC and triangle QRS are the same orientation

so

The x-coordinate of R must be positive

The y-coordinate of R must be negative

Plot points A,B and Q to understand

therefore

----> -3 = y+ 4  ----> y-7

----> 2 = x- 2   ----> x = 4

The coordinates of point R are (4,-7)

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#complete question:

Triangle ABC and triangle QRS are similar and are the same orientation. The endpoints of the hypotenuse of triangle ABC are A(-6, 8) and B(-2, 2). The hypotenuse of triangle QRS is on the same line as the hypotenuse of triangle ABC and is one-half the length of AB.

What is the slope of the hypotenuse of triangle ABC? __________________

What are the coordinates of the hypotenuse of triangle QRS? Q(2, -4) and R( _, _ )

Answer:

$100

Step-by-step explanation:

20%+30% = 50% off

50/100 = 1/2

200*1/2 = $100

To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If there is only one equation with more than one parameter, then the number of the solution will be infinite.

If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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Answer:

3/4 is equivalent to 6/7

Hey there!

Equivalent fractions have the same value. Here are some fractions that are equivalent to 6/7:

\(\frac{6}{7} =\frac{12}{14} =\frac{18}{21} =\frac{24}{28} ...\)

Hope it helps. Please let me know if you have any questions.

~An excited gal

\(MagicalNature\) here to help

Answer:

5/4

Step-by-step explanation:

(y₂ - y₁) / (x₂ - x₁)

(4,9) (-8, -6)

plug in

(-6 - 9) / (-8 - 4)

solve within parentheses

-15/-12

simplify

5/4

what is the slope of points (4,9) (-8,-6)

Answer:

5/4

Volume=80cubic feet

Length×Width×Height =80cubic feet

Base area×Height =80cubic feet

25square feet×Height =80cubic feet

Height =80÷25

=3.2feet

The height of the rectangular prism is 3.2 feet.

To determine the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet,

The volume of a rectangular prism, that is V = lwh, where l is the length, w is the width, and h is the height of the prism.

Given:

Volume (V) = 80 cubic feet

Base area (A) = 25 square feet

We know that the base area is equal to the product of the length and width:

A = lw.

Calculate the length (l) and width (w) from the given base area:

We know that A = lw, and A = 25 square feet.

If we assume the length to be greater than the width, we can express the base area as lw = 25.

We need to find two factors of 25 that have a difference as small as possible. The factors of 25 are 1, 5, and 25.

We can choose l = 5 feet and w = 5 feet.

V = lwh.

80 = 5 * 5 * h

Divide both sides of the equation by 25:

80/25 = h.

h = 16/5 = 3.2 feet.

Therefore, the height of the rectangular prism is 3.2 feet.

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The conjugate base of the weak acid hc2h3o2 (acetic acid) can be determined by removing a proton (H+) from the acid molecule. The formula for the conjugate base is C2H3O2- (acetate ion).

The formula for acetic acid (hc2h3o2) suggests that it consists of the elements hydrogen (H), carbon (C), and oxygen (O). To determine the formula of its conjugate base, we remove a proton (H+) from the acid molecule. Removing a proton results in the formation of an anion, which has a negative charge to maintain overall charge neutrality.

The removal of a proton from hc2h3o2 leads to the formation of the acetate ion, which has a formula of C2H3O2-. The C2H3O2- ion is referred to as the conjugate base of acetic acid.

In summary, the formula for the conjugate base of the weak acid hc2h3o2 (acetic acid) is C2H3O2- (acetate ion).

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The value of the area is πab which is enclosed by the ellipse with the equation (x²/a²) + (y²/b²) = 1.

To find the area enclosed by the ellipse with the equation (x²/a²) + (y²/b²) = 1.

To find the area of this ellipse, use the formula A = πab, where A is the area, a is the semi-major axis, and b is the semi-minor axis.

First, identify the values of a and b from the given equation.
In the equation (x²/a²) + (y²/b²) = 1, a² is the coefficient of x², and b² is the coefficient of y².

Now, calculate the area using the formula A = πab.
Plug the values of a and b into the formula and multiply them with π to find the area.

So, the area enclosed by the ellipse (x²/a²) + (y²/b²) = 1 is A = πab.

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The average increase in first-year GPA per one-point increase in ACT score is different for MSU students than it is for UM students.

Null hypothesis (H0): The relationship between ACT scores and GPA is the same for both UM and MSU students. The average increase in first-year GPA per one-point increase in ACT score is the same for both UM and MSU students.

Alternative hypothesis (Ha): The relationship between ACT scores and GPA is different for MSU students than it is for UM students. The average increase in first-year GPA per one-point increase in ACT score is different for MSU students than it is for UM students.

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Given:

If AB = 0,

Then it is not necessary that A=0 or B=0

To prove this, we consider an example:

Let n=m = p =2

Then AB is given as:

Clearly AB= 0 but A,B not equals to zero.

Hence, the given statement is not true.

Hence, the answer is false.

Answer:

Step-by-step explanation:

Cost before tax = $78 + $32 = $110

Tax = 8.5% of $110 = 0.085 x $110 = $9.35   (\(8.5\%=\frac{8.5}{100} =0.085\))

Total cost = $110 + $9.35 = $119.35

Answer:

rate of change

Step-by-step explanation:

Answer:

"rise over run" or "rate of change"

Step-by-step explanation:

"Slope" itself is "rise over run", or how quickly the line moves up or down relative to the x-axis as the value of x changes.

A gradient is really just another name for slope, not a description OF a slope.

Answer:

The height of the building that casts a shadow of 78m meters is 39m

Step-by-step explanation:

Let height be represented by H and the shadow is S

as they are directly proportional

H \(\alpha\) s

H=KS   ( where K is a proportionality constant)

H=2.5m , S= 5m

On substituting in the equation

2.5 = K*5

K= 0.5

Now the equation becomes

H = 0.5*S

Height when shadow is 78m

H= 0.5*78

H= 39m

Step-by-step explanation:

\(\huge\bold\purple{ 0.316 }\)

Answer:  0.31690140845=(rounded thousandths) 0.317 or

0.32 (rounded hundredths)

Step-by-step explanation: i think if you are dividing 11.25 into 35.5

Answer:

y > x - 2.

2*y + x < 4

The correct option is the third one.

Step-by-step explanation:

First let's find the red shaded part.

We can see that the shade is above the line, then we will have something like:

y > a*x + b

where a*x + b is the equation for the line.

a is the slope, and b is the y-intercept.

In the graph, we can see that the line intercepts the y-axis at y = -2, then we have:

b = -2

To find the slope we need two points of the line, we can use the points (0, -2) and (2, 0)

We know that for a line that passes through the points (x1, y1) and (x2, y2) the slope is:

a = (y2 - y1)/(x2 - x1)

Then for this line, the slope will be:

a = (0 - (-2))/(2 - 0) = 2/2 = 1

Then the equation for this line is:

1*x - 2

And the inequality is:

y > x - 2.

Now for the blue one, the shaded part is below the line, then we will have:

y < a*x + b

In this case, the y-intercept is y = 2.

And we can see that this line passes through the points (0, 2) and (4, 0)

Then the slope is:

a = (0 - 2)/(4 - 0) = -2/4 = -1/2

Then this inequality is:

y < (-1/2)*x + 2

If we rewrite this as the ones shown in the options, we have:

y < (-1/2)*x + 2

2*y < -x + 2*2

2*y + x < 4

Then the two inequalities are:

y > x - 2.

2*y + x < 4

Then the correct option is the third one:

The system of linear inequalities y > x - 2 and x + 2y < 4 is represented by the graph

Inequality is an expression that shows the non equal comparison of two or more numbers and variables

Given the inequalities  y > x - 2 and x + 2y < 4, plotting the two inequalities using the geogebra online graphing tool.

The solution of the inequality on the graph is the very dark region.

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Answer:

Question 1

Total number of marbles = 5 + 7 + 8 = 20

(a)

(b)

(c)

Question 2

(a)

(b)

(c)

Answer:

It's not 2. It would be 2 (5/48)

Step-by-step explanation:

Because 4*2=8/5

8/5 transfers to 24/15

Then 24/15-14/15 = 10/15

But wait... Nope... 2 doesn't work lol

I did some3 other math and I found it to be 2 (5/48)..?

The slope of both functions remains the same, there is no effect of the value of k on a slope.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The given functions are :

f(x) = 2x + 5

g(x) = ( 2x + 5) -3

From the graph of both functions,

Let us consider two pairs of coordinates to find the slope,

For f(x)

(0,5) and ( -2, 1)

The slope of f(x)

m= ( 1- 5) / (-2 -0)

m= 2

For g(x) at (0,2) and (-1, 0) slope of g(x),

m = ( 0-2) / (-1-0)

m = 2

The slope remains unaffected.

y-intercept of f(x) , put x = 0

⇒ y = 5

y-intercept of g(x) , put x = 0

y =(0+ 5) -3

y = 2

Change in the value of y-intercept due to the value of k = -3.

Therefore, for the given function f(x) = 2x + 5 and g(x) = ( 2x + 5) -3, the effects of the value of k on slope and y-intercept are as follows:

The slope of both functions remains the same, there is no effect of the value of k on a slope.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The graph is attached.

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The probability that a simple random sample of 35 students will spend an average amount between 600 and 700 dollars is approximately 0.6579, or 65.79%.

To find the probability that a sample of 35 students will spend an average of between 600 and 700 dollars, we need to standardize the sample mean using the formula:

z = (x - μ) / (σ / √(n))

where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values given in the problem, we get:

z₁ = (600 - 650) / (120 / √(35)) = -1.51

z₂ = (700 - 650) / (120 / √(35)) = 1.51

We now need to find the area under the standard normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find that the area between -1.51 and 1.51 is approximately 0.6579 or 65.79%

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Answer:

I use 2 mainly from bath and body.

Step-by-step explanation:

Pretty as a peach, and warm vanilla sugar

Answer: x=-3    y=7.

Step-by-step explanation:

\(\displaystyle\\\left \{ {{6x+4y=10\ \ \ \ \ (1)} \atop {12x+y=-29\ \ \ \ (2)}} \right.\\ We\ multiply\ both\ sides\ of\ equation\ (1)\ by\ -2:\\\left \{ {{(-2)*6x+(-2)*4y=(-2)*10} \atop {12x+y=-29}} \right. \\\\\left \{ {{-12x-8y=-20} \atop {12x+y=-29}} \right. \\\)\(We\ summarize\ equations\ (1)\ and\ (2):\\-7y=-49\\-7*y=-7*7\\Divide\ both\ sides\ of\ the\ equation\ by\ -7:\\y=7.\\We\ substitute\ the\ value\ of\ y\ into \ equation\ (1):\\6x+4*7=10\\6x+28=10\\6x+28-28=10-28\\6x=-18\\6*x=6*(-3)\\Divide\ both\ sides\ of\ the\ equation\ by\ 6:\\x=-3.\)