help please! find the value of y​

e follSOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the general equation of an ellipse

STEP 2: Identify the parameters

the length of the major axis is 2a

the length of the minor axis is 2b

STEP 3: Get the equation of the ellipse

STEP 4: Pick the nearest equation from the options,

Hence, the equation of the ellipse in the image is given as:

OPTION A

There are 20 ways to select president, 19 ways to select vice-president, 18 ways to select treasurer.

In this case, the task is to select a president, a vice-president, and a treasurer from the math club, and no member can hold more than one office. There are 20 choices for the president, since there are 20 members in the club and each member is eligible to be president. There are then 19 choices for the vice-president, since the president cannot also be the vice-president. Finally, there are 18 choices for the treasurer, since the president and vice-president cannot also be the treasurer.

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Using the sum of angles in a triangle to determine the value of x in the cyclic quadrilateral, the value of x is 74°

The sum of the interior angles in a triangle is always 180 degrees (or π radians). This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

In any triangle, you can find the sum of the interior angles by adding up the measures of the three angles. Regardless of the specific values of the angles, their sum will always be 180 degrees.

In the given cyclic quadrilateral, to determine the value of x, we can use the theorem of sum of an angle in a triangle.

Since x is at opposite to the right-angle and angle p is given as 16 degrees;

x + 16 + 90 = 180

reason: sum of angles in a triangle = 180

x + 106 = 180

x = 180 - 106

x = 74°

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Answer:

Triangle P' Q' R' is half the size of the original triangle.

-The scale factor is probably 1/3.

Part B: P'(1, −2), Q'(0, 3), and R'(−1, 0).

Part C: No, the triangles are not congruent. If the second triangle didn't have a dilation, and instead have a reflection of the first triangle, then it would be congruent.

Step-by-step explanation:

:)

Answer:

To graph a system of linear inequalities, you will need to graph each inequality separately on the same set of axes. Here is the general process for graphing a linear inequality:

Begin by plotting the inequality's equation in standard form: Ax + By > C (or < C, or = C).

Determine the values of x and y that make the inequality true. To do this, set each side of the inequality equal to zero and solve for x and y. For example, if the inequality is 2x + 3y > 6, you would set 2x + 3y = 0 and solve for x and y.

Graph the line that represents the equation.

Determine the direction of the inequality by looking at the inequality symbol. If the symbol is ">," the line will be shaded above it. If the symbol is "<," the line will be shaded below it. If the symbol is "≥," the line will be shaded above it, including the line itself. If the symbol is "≤," the line will be shaded below it, including the line itself.

Repeat the process for each additional inequality in the system.

The solution to the system of inequalities is the area where all of the shaded regions overlap. This is the region where all of the inequalities are simultaneously true.

Here is an example of how to graph a system of linear inequalities:

Suppose we want to graph the following system of inequalities:

2x + 3y > 6

-x + 2y < 4

To graph the first inequality, we set 2x + 3y = 0 and solve for x and y. This gives us x = -(3/2)y. We can then plot this line on a graph.

Next, we determine the direction of the inequality by looking at the inequality symbol. In this case, the symbol is ">," so we shade the area above the line.

To graph the second inequality, we set -x + 2y = 0 and solve for x and y. This gives us x = (1/2)y. We can then plot this line on the same graph.

Next, we determine the direction of the inequality by looking at the inequality symbol. In this case, the symbol is "<," so we shade the area below the line.

The solution to the system of inequalities is the area where the shaded regions overlap. This is the region where both inequalities are simultaneously true.

The statement 2 is true i.e. He  is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be root multiplicities or complex.

Understanding the fundamental theorem of algebra, the number of roots of a polynomial equation must be equal to the degree of the equation. While been given any polynomial in factored form, we must expand the parentheses to find the highest-degree term.

For the equation  provided, simplified form could be x⁵ + 2x² = 0, and as looking at this polynomial and graphing it, it is evident that the total roots or solutions is equal to the highest exponent of the term x which is 5. Hence, Josh makes an incorrect statement.

The multiplicity of a root is the number of occurrences of the said root in the entire complete factorization of the polynomial, as by the means of the fundamental theorem of algebra. The root multiplicities are thus the repeated roots as involved in the full factorization process of a single equation of a polynomial.

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The correct question is:

Josh graphs a system of equations to determine the roots of the polynomial equation x⁵ = -2x²  . From the graph, he determines that there are two solutions to the equation. Which statement is true?

100 mph going there, 50 coming back

The area of triangle BMN is 124.7 square centimeter.

Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.

Analysis:

AB = AC = BC = 50cm

AH = AC/2 = 50/2 = 25cm

From Δ ABH, using Pythagoras theorem to find BH.

\((BH)^{2}\) = \((AB)^{2}\) - \((AH)^{2}\)

\((BH)^{2}\) = \(50^{2}\) - \(25^{2}\)

\((BH)^{2}\) = 2500 - 625

\((BH)^{2}\) = 1875

BH = \(\sqrt{1875}\) = 43.3cm

ΔBMN and BHC are similar,

so, BM/BH = MN/HC

BM/43.3 = 12/25

25BM = 12 X 43.3

BM = 519.6/25 = 20.78cm

Area of ΔBMN

= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter

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Given

Answer

Which is triangle 2

The other transformations are given, (x, y) → (-3x, y), (x, y) → (3x, y - 1), and (x, y) → (-x, 3y), do not preserve distances and angles, and therefore do not preserve congruence.

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

A transformation that results in an image that is congruent to its pre-image is a rigid transformation, which means that it preserves distances and angles.

The only rigid transformations are translations, reflections, and rotations.

Out of the four transformations given, the transformation that is a reflection across the y-axis, (x, y) → (-x, y), will result in an image that is congruent to its pre-image.

This is because a reflection across the y-axis preserves distances and angles, and therefore preserves congruence.

Hence, The other transformations are given, (x, y) → (-3x, y), (x, y) → (3x, y - 1), and (x, y) → (-x, 3y), do not preserve distances and angles, and therefore do not preserve congruence.

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Therefore, After 20 minutes, there are approximately 11.9 kg (rounded to one decimal place) of salt in the tank.

To solve this problem, we need to consider the rate of change of the amount of salt in the tank over time.

(a) Let's denote the amount of salt in the tank after t minutes as y (in kg). We can set up a differential equation to represent the rate of change of salt:

dy/dt = (rate of salt in) - (rate of salt out)

The rate of salt in is given by the concentration of salt in the incoming water (0 kg/L) multiplied by the rate at which water enters the tank (90 L/min). Therefore, the rate of salt in is 0 kg/L * 90 L/min = 0 kg/min.

The rate of salt out is given by the concentration of salt in the tank (y kg/9000 L) multiplied by the rate at which water leaves the tank (90 L/min). Therefore, the rate of salt out is (y/9000) kg/min.

Setting up the differential equation:

dy/dt = 0 - (y/9000)

dy/dt + (1/9000)y = 0

This is a first-order linear homogeneous differential equation. We can solve it by separation of variables:

dy/y = -(1/9000)dt

Integrating both sides:

ln|y| = -(1/9000)t + C

Solving for y:

y = Ce^(-t/9000)

To find the particular solution, we need an initial condition. We know that at t = 0, y = 12 kg (the initial amount of salt in the tank). Substituting these values into the equation:

12 = Ce^(0/9000)

12 = Ce^0

12 = C

Therefore, the particular solution is:

y = 12e^(-t/9000)

(b) To find the amount of salt in the tank after 20 minutes, we substitute t = 20 into the particular solution:

y = 12e^(-20/9000)

y ≈ 11.8767 kg (rounded to one decimal place)

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\((1 - 5i)(5 + 6i) \\ = 5 + 6i - 25i - 30 {i}^{2} \\ = 5 - 19i + 30 \\ = 35 - 19i\)

I hope I helped you^_^

Answer:

35-19i

Step-by-step explanation:

(1-5i)(5+6i)

5-25i+6i-30i^2 where i^2=-1

5-25i+6i-30(-1)

5-19i+30

5+30-19i

35-19i

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The average speed that would allow arriving at school on time is equal to 24.32 miles per hour if school starts in 37 minutes.

The speed that is required to arrive on time can be determined by the following formula;

s = d ÷ t

Here d represents the distance and t represents the time

As the school starts in 37 minutes and the distance is 15 miles, substituting these values in the equation;

s = (15/37) miles per minute

As 1 hour = 60 minutes; multiply by 60 to find the speed in miles per hour as follows;

s = 15/37 × 60

s = 900/37

s = 24.32 miles per hour

Therefore, the average speed that would allow arriving at school on time is calculated to be 24.32 miles per hour.

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Answer:

\(\frac{1}{2}\)x-4

Step-by-step explanation:

Answer:

1/2 (x)-4

Step-by-step explanation:

Hopes this helps

The 95% confidence interval for the proportion of all Californians who considered moving out of state is (0.504, 0.530). We can be 95% confident that the true proportion of all Californians who considered moving out of state lies between 50.4% and 53.0%.

The UC Berkeley Institute of Governmental Studies conducted a poll in 2019 with 4,527 respondents in California, where 51.7% of them reported considering moving out of the state. The objective is to calculate a 95% confidence interval for the proportion of all Californians who considered moving out of state, given the sample size and proportion.

B. The formula to calculate the confidence interval for a proportion is:

CI = p^ ± z* √[(p^(1-p^))/n]

Where p^ is the sample proportion, n is the sample size, and z* is the critical value of the standard normal distribution for the desired confidence level. For a 95% confidence level, z* = 1.96.

Substituting the given values into the formula, we get:

CI = 0.517 ± 1.96 * √[(0.517*(1-0.517))/4527]

CI = 0.517 ± 0.013

The 95% confidence interval for the proportion of all Californians who considered moving out of state is (0.504, 0.530). Therefore, we can be 95% confident that the true proportion of all Californians who considered moving out of state lies between 50.4% and 53.0%.

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the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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Answer:

5 minutes per mile

Step-by-step explanation:

15 divided by 3 = 5

This expression represents the same value as log2(3) but uses base 10 logarithms instead.

To rewrite log2(3) using the change of base formula, follow these steps:

1. Identify the given base, which is 2, and the argument, which is 3.

2. Choose a new base for the logarithm. Common choices are base 10 (common logarithm) or base e (natural logarithm). Let's use base 10 for this example.

3. Apply the change of base formula, which states: log_b(a) = log_c(a) / log_c(b), where b is the original base, a is the argument, and c is the new base.

So, to rewrite log2(3) using the change of base formula with base 10, you would get:

log2(3) = log10(3) / log10(2)

This expression represents the same value as log2(3) but uses base 10 logarithms instead.

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The even integers are 10,12 and 14.

Concept:  An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Let x,x+2,x+4 be the least, middle and greatest integer respectively.

According to the question,

15< x+x+2+x+4< 21

(3x+6)/2> 15      and    (3x+6)/2< 21

30< 3x+6                      3x+6> 42

24<3x                            3x<36

8<x                                x>12

x=10

x+2=12

x+4=14

Hence, The even integers are 10,12 and 14.

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Each member of the club needs to pay £ 4.895 to cover the cost of hiring the buses.

A youth club's 143 members and eight leaders ride a bus to a bowling alley.

The buses for hire by the beezer bus company hold 32 passengers each.

The cost of each bus to hire is £140.

There are eight leaders and 143 members.

Therefore, there are a total of 143 + 8 = 151 passengers.

So, the number of buses required will be:

= 151 / 32 =  4.7 ≈ 5 buses

Therefore, the cost of hiring 5 buses will be:

= 5 × £140 = £ 700

As the eight leaders will not ay.

Therefore, the amount each member needs to pay is:

= £ 700 / 143

= £ 4.895

Each member of the club needs to pay £ 4.895 to cover the cost of the buses.

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a. The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes.

b. The probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20

What is Probability?

Probability is a field of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of inaccuracy in study by using probability.

a. The mean of the sampling distribution of the difference in sample means, xF - xM, is equal to the difference of the population means, μF - μM = 8.8 - 7.3 = 1.5 minutes.

where σF and σM are the standard deviations of the populations of female and male students, respectively, and nF and nM are the sample sizes of female and male students, respectively.

\(Standard\ Deviation = \sqrt{3.3^2/8 + 2.9^2/8} \\\\Standard\ Deviation = \sqrt{{2.75} }\\\\Standard\ Deviation = 1.65\ minutes\)

So, the mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes, respectively.

b. The probability of getting a difference in sample means xF - xM that is less than 0 can be found using a standard normal distribution table. First, we need to standardize the difference in sample means xF - xM by subtracting the mean and dividing by the standard deviation:

z = (xF - xM - (μF - μM)) / standard deviation

z = (0 - 1.5) / 1.65 = -0.91

Looking up -0.91 in a standard normal distribution table, we find that the probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

So, there is a 20% probability of getting a difference in sample means xF - xM that is less than 0.

Hence, The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes and probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

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To count the number of subsets of a set with k elements, we use the recurrence relation sk+1 = 2sk with the initial condition s0 = 1.

For your initial condition, consider a set with 0 elements, which has only one subset - the empty set. Thus, S(0) = 1. Using the recurrence relation and initial condition, you can compute the cardinality of the power set for any set of size k.

To count the number of subsets of a set with k elements, we can set up a recurrence relation.

Let sk be the cardinality of the power set of a set with k elements. When we add one more element to the set, we have two options for each subset: either include the new element or don't include it.

This means that the number of subsets of the set with k+1 elements is twice the number of subsets of the set with k elements. Therefore, we have the recurrence relation: sk+1 = 2sk.

Our initial condition is the number of subsets of an empty set, which is 1 (since the empty set itself is a subset). So s0 = 1.

In this course, when working with counting activities and sets, you can set up a recurrence relation to count the number of subsets of a set with k elements. Let S(k) represent the cardinality of the power set of a set of size k.

When you add one more element to the set, you essentially double the number of possible subsets, as each existing subset can either include or exclude the new element.

Therefore, the recurrence relation can be expressed as:

S(k) = 2 * S(k-1)

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In triangle ΔABC angle m∠A = 38.68°

An angle is the space between of the point of intersection of two rays meeting at a common vertex.

Since we have triangle ΔABC and m∠B = 90 and the ratio BC/AC = 0.625. We desire to find angle A, we proceed as follows.

In  ΔABC, since m∠B = 90, this implies that ΔABC is a right-angled triangle.

Also, the ratio BC/AC = cosC

Since BC/AC = 0.625

⇒ cosC = 0.625

Taking inverse cosine of both sides, we have

C = cos⁻¹(0.625)

= 51.318°

≅ 51.32°

Also in ΔABC

m∠A + m∠B + m∠C = 180°  (sum of angles in a triangle)

So, m∠A = 180° - m∠B - m∠C

= 180° - 90° - 51.32°

= 90° - 51.32°

= 38.68°

So, angle m∠A = 38.68°

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The length of the shortest straight  is approximately 28.01 ft.

What is the right triangle?

A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".

To find the length of the shortest straight beam,we can use the Pythagorean theorem.

Let's denote the length of the beam as L and  a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.

Using the Pythagorean theorem,

\(L^2 = (28 ft)^2 + (1 ft)^2\)

Simplifying the equation:

\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)

\(L = \sqrt{785}ft\)

Calculating the value of L:

L ≈ 28.01 ft

Therefore, the length of the shortest straight beam  is approximately 28.01 ft.

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The proportion of observations that are 45 or less is 130/130 = 1.000 (rounded to 3 decimal places).

a. The number of observations that are more than 35 but no more than 45 is 120.b. To find out the proportion of the observations that are 45 or less, we need to first determine the total number of observations,

which is given by the last cumulative frequency value, i.e., 130. So, out of 130 observations, how many are 45 or less?

We can subtract the cumulative frequency value of the interval 45 < x ≤ 55 from the total number of observations as shown below:

130 - 130 = 0

This means that there are no observations greater than 55. Therefore, the proportion of observations that are 45 or less is 130/130 = 1.000 (rounded to 3 decimal places).

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Answer:

Step-by-step explanation:

12

Solution:

Give the sequence:

The common difference is the difference between two consecutive terms.

Thus, the common diffrence is evaluated as

Thus, from the explicit formula,

The explicit form is evaluated to be

The recursive form is evaluated as

Answer:

Four percent

Step-by-step explanation:

Answer:

Total area of board = 36x² + 324 + 216x

Step-by-step explanation:

Given:

Side of square = x + 3

Total number of square = 6 x 6 = 36

Area of each square = Side x Side

Area of each square = (x + 3)²

Area of each square = x² + 9 + 6x

Total area of board = 36[Area of each square]

Total area of board = 36[x² + 9 + 6x]

Total area of board = 36x² + 324 + 216x

\(\text{To get the total surface area, all we have to do is multiply } 18 \text{ by } 12, \text{which gets us}\)\($18\cdot12 = \boxed{216\text{ ft}^2}\).

\(\text{So, our answer is } \boxed{216\text{ ft}^2}.\)

Larry needs 216 square feet of carpeting for her rectangular living room.

To find the amount of carpeting Larry needs, we need to calculate the area of her rectangular living room. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the living room is 18 feet and the width is 12 feet.

So, the area of the living room is:

Area = Length * Width

Area = 18 feet * 12 feet

Area = 216 square feet

Therefore, Larry needs 216 square feet of carpeting for her living room.

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