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The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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A graph of four points with integer coordinates that are each 3 units away from (2, 3) is shown in the image attached below.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N).

Where:

In order to write an equation that models the four points with integer coordinates that are each 3 units away from (2, 3), we would have to apply a set of translation to f(x) by 3 units:

A (5, 3)

B (-1, 3)

C (2, 6)

D (2, 0)

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Answer:

6v+8

Step-by-step explanation:

you multiply the equation in parantheses by 2

Answer:

=8+6v

all you had to do was simply the expression

Answer:

-2

Step-by-step explanation:

Answer: The equation for the graph is x = -4.

Based on the given information that AD is congruent to BC and AC is congruent to BD, we can prove that ED is congruent to EC.

To prove that ED is congruent to EC, we will use the concept of triangle congruence. We know that AD is congruent to BC (given) and AC is congruent to BD (given).

Now, let's consider triangle ACD and triangle BDC. According to the given information, we have AD ≅ BC and AC ≅ BD.

By the Side-Side-Side (SSS) congruence criterion, if the corresponding sides of two triangles are congruent, then the triangles are congruent.

Therefore, triangle ACD is congruent to triangle BDC.

Now, let's focus on segment DE. Since triangle ACD is congruent to triangle BDC, the corresponding parts of congruent triangles are congruent. Therefore, segment ED is congruent to segment EC.

Hence, we have proved that ED is congruent to EC using the given information about the congruence of AD with BC and AC with BD.

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Answer:

a ) 7a + 12

b) b - 15

Step-by-step explanation:

a)2a+5a +8+8

= 7a + 12

b) b - 7 - 8

= b-15

The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

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The height of the cylinder is 3.6 inches.

We know that the volume of a cylinder of radius R and height H is:

V = pi*R²*H

where pi = 3.14

We know that the radius is R = 5in and the volume is 284.7 inches cubed, replacing that in the formula above we will get:

284.7 in³= 3.14*(5 in)²*H

Solving that for H we will get:

H= (284.7 in³)/ 3.14*(5 in)²

H = 3.6 inches.

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Answer:

\(x=2y+6\)

Step-by-step explanation:

So we have the system:

\(-x+2y=-6\\3x+y=8\)

If we isolate the x-variable in the first equation:

\(-x+2y=-6\)

Subtract 2y from both sides:

\(-x=-6-2y\)

Divide both sides by -1:

\(x=2y+6\)

Therefore, we would substitute the above into the second equation:

\(3x+y=8\\3(2y+6)+y=8\)

The answer is 2y+6

Further notes:

To solve for the system, distribute:

\(6y+18+y=8\)

Simplify:

\(7y+18=8\)

Subtract:

\(7y=-10\)

Divide:

\(y=-10/7\approx-1.4286\)

Now, substitute this value back into the isolated equation:

\(x=2(-10/7)+6\\x=-20/7+42/7\\x=22/7\approx3.1429\)

Step-by-step explanation:

Start by solving the equation for x (☓)

\( - x + 2y = 6 \\ \: \: \: \: \: 3 + y = 8\)

\(x = 6 + 2y\)

\(3(6 + 2y) + y = 8\)

\(y = - \frac{10}{7} \)

\(x = 6 + 2 \times ( - \frac{10}{7} )\)

\(x = \frac{22}{7} \)

\( (\frac{22}{7} . - \frac{10}{7} )\)

\((x.y) \: \: ( \frac{22}{7} . - \frac{10}{7} )\)

Answer:A. (9, –36)

Step-by-step explanation:

A. (9, –36)

Answer: 2√5, -2√5

Step-by-step explanation:

To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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Answer:

5) 119 degrees

6) 25 degrees

7) 45 degrees

8) 115 degrees.

Answer:

Answer: The measure of ∠CBD is 36°. The length of segment CD is 6 cm.

The trigonometric function gives the ratio of different sides of a right-angle triangle. The length of the segment CD will be equal to 12cm (60/5).

The trigonometric function gives the ratio of different sides of a right-angle triangle.

\(\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\\)

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1.   For a regular pentagon, the measure of an internal angle is equal to 108°, therefore, the measure of ∠ABD is 108°.

2.   Since the line CB is bisecting ∠ABD, therefore, the measure of the ∠CBD is 54°.

3.   The length of the segment CD will be equal to the length of a side of the pentagon, therefore, the length of the segment CD will be equal to 12cm (60/5).

4.   The trigonometric ratio that can be used to compare BC to CD using ∠CBD is Tangent.

5.   The approximate length of BC can be determined as,

Tan(54°)=CD/BC

BC = CD/Tan(54°)

BC = 8.719 cm

6.    The approximate length of BD can be determined using the Pythgorus theorem,

BD² = CD² + BC²

BD = 10.5835 cm

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Answer: 4x-6=-46

4x-6=-46

Answer:

c = 72

a = 51

b = 57

x = 28

Step-by-step explanation:

2x+1 + 2x-5 = 108

4x -4 = 108

4x = 112

x = 28

(2(28)-5)= 51

(2(28)+1) = 57

Answer:

Step-by-step explanation:

yes

The correct probability that a 60% free-throw shooter will miss her next free throw is 0.064, or 6.4%.

If a free-throw shooter has a 60% success rate, it means she makes 60% of her free throws, which translates to missing 40% of her free throws.

To find the probability of missing the next free throw, we need to multiply the probability of missing for each independent event.

Assuming each free throw attempt is independent, the probability of missing the next free throw would be:

Probability of missing \(= 0.4 \times 0.4 \times 0.4 = 0.064\)

Therefore, the correct probability that a 60% free-throw shooter will miss her next free throw is 0.064, or 6.4%.

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Answer:

Yes

Step-by-step explanation:

I think its yes.I think It's Yes.

So, Lana gave away 26.32% of he Pokemon cards  to her little brother.

To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.

In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:

(125 / 475) * 100 = 0.2632 * 100 = 26.32%.

Lana gave away 26.32% of her Pokemon cards to her little brother.

Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:

Percentage given away

= (Cards given away / Total cards) * 100

= (125 / 475) * 100

= 26.32%.

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Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

The main difference between X1 and x1 is that X1 is a random variable and x1 is a specific numerical value.

In mathematics, variables are often used to represent different values, and the difference between uppercase and lowercase letters is often used to distinguish between different types of variables. X1 is a random variable, which represents a value that can take on different values depending on the outcome of an experiment or a probability distribution. x1, on the other hand, is a specific numerical value, which represents a fixed value that is known or can be determined. In short, X1 refers to a variable whose value is uncertain and x1 refers to a specific value of that variable.

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To solve for the Marshallian demands x1(p1, p2, m) and x2(p1, p2, m) in the consumer problem with utility function U(x1, x2) = min{x1, ax2}, we need to maximize the utility subject to the budget constraint p1x1 + p2x2 ≤ m, where p1 and p2 are the prices of goods 1 and 2 respectively, and m is the consumer's income.

To find the Marshallian demands, we need to solve the consumer's optimization problem. The objective is to maximize the utility function U(x1, x2) = min{x1, ax2} subject to the budget constraint p1x1 + p2x2 ≤ m.

The first step is to set up the Lagrangian function:

L(x1, x2, λ) = min{x1, ax2} + λ(m - p1x1 - p2x2)

Next, we take the first-order conditions by differentiating the Lagrangian with respect to x1, x2, and λ, and setting the derivatives equal to zero. This will give us the equations for the optimal values of x1, x2, and the Lagrange multiplier λ.

By solving these equations, we can find the specific values for x1(p1, p2, m) and x2(p1, p2, m) that maximize the utility function while satisfying the budget constraint. The resulting demands will depend on the prices (p1, p2) and the consumer's income (m).

Note that the specific calculations involved in solving the optimization problem can be quite involved and may require further mathematical manipulation.

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Thus the expression is 0.15x.

Given,

A reasonable tip for some is 15% of the subtotal.

We need to write an expression that would represent how much tip you should leave if x represented the subtotal.

Let the quantity be 100.

5% of 100 = 5/100 x 100 = 5

10% of 100 = 10/100 x 100 = 10

50% of 100 = 50/100 x 100 = 50

We have,

Subtotal = x

Tip = 15%

Write the expression for 15% of x

15% of x

= 15/100 x (x)

= 0.15x

Thus the expression is 0.15x.

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Answer:

x= +8 or -8

Step-by-step explanation:

x=  -b±\(\sqrt{b^2-4ac}\) /2a

x=−0±\(\sqrt{0^2 negative4(1)( negative 64)}\) /√2(1)

x=−0±0\(\sqrt{256}\)/√2

x=−0±256−−−√2

x=−0±162

x=16/2 x=−16/2

x=8

x=−8

Answer:

B)

Step-by-step explanation:

This is hope i got it and it may or may not be helpful 10 divide by 430

Rui Feng invested approximately $45,644.91.

To find the original amount invested by Rui Feng, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal amount (the original investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Given that Rui Feng received $5,800 as interest at the end of 3 years, we can calculate the final amount:

A = P + I

A = P + $5,800

Using the formula for compound interest and rearranging the equation, we can solve for the principal amount (P)

P = A - $5,800

Substituting the values into the formula, we have:

P = $5,800 / (1 + 0.04/2)^(2*3)

P = $45,644.91 (rounded to two decimal places)

Therefore, Rui Feng invested approximately $45,644.91 originally.

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