Which of the following is the equation of the ellipse with a vertical major axis, center at (–4, 6), a = 5, and b = 2?

quantity x minus 4 end quantity squared over 25 plus quantity y plus 6 end quantity squared over 4 equals 1
quantity x plus 4 end quantity squared over 25 plus quantity y minus 6 end quantity squared over 4 equals 1
quantity y minus 6 end quantity squared over 25 plus quantity x plus 4 end quantity squared over 4 equals 1
quantity y plus 6 end quantity squared over 25 plus quantity x minus 4 end quantity squared over 4 equals 1

Answer:

31 and 73

Step-by-step explanation:

Writing this is variable form,

x+y = 104

x-y = 42

If we use the process of elimination and add the system of equations together;

2x = 146

x = 73

Substituting that back in;

x - y = 42

(73) - y = 42

y = 31

Answer:

\(a=73 \text{ and } b=31\)

Step-by-step explanation:

\(a+b=104 --- (1)\\a-b=42 ---(2)\\\)

Add (1) and (2), we get

\(2a=104+42\\a=\dfrac{146}{2}\\=73\)

\(73-b=42\\-b=42-73\\b=31\)

Step-by-step explanation:

this chart is a life saver!

If function has points (1/2,0) and (6,0) then \(g(x)=2x^{2} -13x+6\\\)

Given x-intercepts at (1/2,0)(6,0) and we have to find the function g(x)

If the x-intercepts lie at (1/2,0)(6,0) then the function has roots of 6 and 1/2. Function is a relationship between variables having value of y for each value of x. Value of x is domain and value of y is known as codomain.

If we insert x=6 or x=1/2 into the equation of g(x) we will obtain 0 as under:

g(6)=0

In order to get 0 the equation will be x-6.

In order to get 0 for root the equation will be x-1/2.

but x-1/2 does not appear in any of these but its multiples can be there :

\(2(x-1/2)=2x-1\)

Therefore the function will be as under:

\(g(x)=(x-6)(2x-1)\)

\(g(x)=2x^{2} -x-12x+6\)

\(g(x)=2x^{2} -13x+6\)

Hence the function g(x) is \(g(x)=2x^{2} -13x+6\).

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\(2^{100} = 16^{25} =32^{20} =1024^{10}\)

P/s: \(2^{100} = 2^{4.25} =16^{25}\) ......

ok done. Thank to me :>

Answer:

b 205

Step-by-step explanation:

would be the closest answer.

Hope this hlepsss!

there are 70 simple random samples of size 4 that can be selected from a population of size 8. Your answer is 70.by using combination concept

There are 70 simple random samples of size 4 that can be selected from a population of size 8.
To determine how many simple random samples of size 4 can be selected from a population of size 8, we can use the combination formula, which is:

C(n, k) = n! / (k!(n-k)!)

where C(n, k) is the number of combinations, n is the total population size, and k is the sample size.

In this case, n = 8 and k = 4. Plugging the values into the formula:

By following function

C(8, 4) = 8! / (4!(8-4)!)

C(8, 4) = 8! / (4!4!)

C(8, 4) = (8×7×6×5) / (4×3×2×1)

C(8, 4) = 1680 / 24

C(8, 4) = 70

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a.) W=31.9J

b.) Normal force=0

c.) Gravitational force = 0

We apply the definition of "work by a constant force" in the first three part  and in the fourth part, we total the results. The work performed by the overall (net) force is equal to the sum of the separate forces' respective amounts of work.

Work by a constant force is defined as W=FΔrcosθ.

Work, in general, is the result of force and the displacement it produces. W = FX is the formula used to express how much work a force has produced. Here, x is the body's displacement as a result of the force F. The dot product informs us that only the force that causes displacement is taken into account when calculating the work done.

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The force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

According to the question,

We have the following information:

The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. And when m=8kg and d=5meters then F=100 Newtons.

Now, let's take the constant for this case to be k.

We have the following expression:

F = km/\(d^{2}\)

Putting the values in this expression to find the value of k:

100 = 8k/(5*5)

Using the cross multiplication method:

2500 = 8k

k = 2500/8

k = 312.5

Now, we have the following value of F:

F = 312.5*2/15*15

F = 625/225

F = 2.78 Newton

Hence, the force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

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Let, x and y denotes the number of coin Deniel and Edwin had first. Then we have:

x + y = 500 .....(i)

Since Daniel spent 3/7 of his coins means he has 4/7 of his coins remaining and Edwin had spent its 7 coins so he has y-7 coins are remaining. Also given the ratio of the number of coins remaining is 3:2. Hence,

(4x/7):(y-7)  = 3:2

=> 8x/7 = 3y - 21

=> 8x/7 = 3( 500-x) - 21

=> 8x/7 = 1500 - 3x - 21

=> 29x = 1479*7

=> x = 357

So, the number of coins Daniel had at first is 357 coins.

Since Daniel’s remaining amount after spending some coins was 4/7 of its all coins and we know Daniel’s all coins were 20 cents coins. Hence, the money Daniel had in the end:Amount = (4/7)*357*0.20Amount = 40.8$

(a) The number of coins Daniel had at first:357

(b). The money Daniel had in the end:$40.8

Answer: Daniel had 134 coins at first.

All of Daniel's coins were 20-cent coins, he would have had 134 * 20 cents = $26.80 in the end.

Step-by-step explanation:

Let's solve the problem step by step:

(a) Let's assume Daniel had x coins at first. Edwin would have had 500 - x coins since they had a total of 500 coins.

After Daniel spent 3/7 of his coins, he would have (1 - 3/7)x = 4/7x coins left.

Edwin spent 7 coins, so he would have had (500 - x) - 7 = 493 - x coins left.

According to the given ratio, we have the equation:

(4/7x) / (493 - x) = 3/2

Cross-multiplying, we get:

2(4/7x) = 3(493 - x)

Simplifying, we have:

8/7x = 1479 - 3x

Combining like terms, we get:

11x = 1479

Dividing by 11, we find:

x = 1479/11 = 134

Therefore, Daniel had 134 coins at first.

(b) Since all of Daniel's coins were 20-cent coins, he would have had 134 * 20 cents = $26.80 in the end.

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Answer:

x = -20

Step-by-step explanation:

2.5(x - 4) = -60

~Distribute left side

2.5x - 10 = -60

~Add 10 to both sides

2.5x = -50

~Divide 2.5 to both sides

x = -20

Best of Luck!

Answer:

5:2

It actually it is!

look female  5          male    2

                          5  :   2

female to male

(5)         (2)

5 to 2

Step-by-step explanation:

Do you get it now?

Pls consider giving my answer Brainliest! It would mean and help a lot! ; )

Answer:

5:2

Step-by-step explanation:

The answer is 5:2 because:

1) Since there are 2 male teachers for every 5 female teachers, the ratio has to be 5:2 because they did not give us any specific numbers.

For example, if they 10 female teachers, then there would be 4 male teachers. The ratio for this example would be 10:4

Hope this helps! :D

Answer:

You are correct

rise: go down 2 which is -2

run: to right 3 which is 3

so the slope is -2/3

Answer:

i think its 3/2 and -3/2.

Step-by-step explanation:i

at the top it says 2 can be eliminated, aka , its asking which are the WRONG answers.

the correct answer is -2/3 and 2/3. this is because when you move up and left, (positive direction) it goes up 2, and left 3. now lets turn this around to check the other. -2/3 goes down 2 and right 3. so if you look the way its going in the negative direction (down, right) it goes down 2 and to the right 3.

Answer:

Step-by-step explanation: To find out what grade Sally needs to earn on her fifth and last math test to achieve a 90 average, we  use the following steps:

Step 1: Add the total points Sally has received: 80 + 82 + 92 + 98 = 352.

Sally has taken 4 tests so far.

Step 2: Find the total marks required for a 90 average on 5 tests: 90 x 5 = 450.

Step 3: Find the score Sally needs to achieve on her fifth test by subtracting the points earned  from the total required points: 450 - 352 = 98.

Therefore, Sally needs to earn a grade of 98 on her 5th and last test to achieve a 90 average on all five tests this semester.

Answer:

1st one, A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x be the number.

Sum of 4 and the number: x+4

250 is the frequency of the Q1 class.

Find the middle score (Q2):

Middle Score (Q2) is calculated as L + [(N/2 - CF) / f] * w

Where

L = lower limit of the middle score class, which equals 30

N is equal to 1,000 students in total.

CF = 450, which is the cumulative frequency of the middle-score class.

300 is the middle score class frequency, or f.

10 is the middle scoring class's width, or w.

Middle Score (Q2) =30 + 1.67 = 31.67

Identify the lower quartile (Q1):

Q1 equals L plus [(N/4 - CF) / f]*w

Where L is the Q1 class's lower border and equals 20

N is equal to 1,000 students in total.

CF = 200, which is the cumulative frequency of the Q1 class before it.

250 is the frequency of the Q1 class.

W = the Q1 class's width, which is 10

Q1 =  20 + 2 = 22

The lower quartile is 22

Establish the upper quartile (Q3):

Q3 is equal to L + [(3N/4 - CF) / f] * w

where L is the lower limit of the Q3 class, and 30

N is equal to 1,000 students in total.

CF = 450, which is the cumulative frequency of the Q3 class.

The upper quartile stands at 450.

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One thousand students took a mathematics examination, which consisted of two papers. Each paper was marked out of 50. Table A gives the distribution of marks for Paper 1, and Table B is the corresponding cumulative frequency table. Find the median, lower quartile (Q1), and upper quartile (Q3) marks for Paper 1.

Table A (Paper 1 Marks Distribution):

Marks Range Frequency

0-9 50

10-19 150

20-29 250

30-39 300

40-49 200

50 50

Table B (Cumulative Frequency):

Marks Range Cumulative Frequency

0-9 50

10-19 200

20-29 450

30-39 750

40-49 950

50 1000

Answer:

3

Step-by-step explanation:

3x3=9

21/9= 3

Answer:

(x,y)→(x+7,y)

Step-by-step explanation:

Cuz the point isn't moving up or down so the y is the same and x+7 cuz the point moved 7 units to the right so its position changed in the x-axis.

Im reallyyyy bad at explanations but hope this helped:)

The conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

To find the conditional probability that the size of the family is less than 6 given that it is at least 3, we need to use the formula for conditional probability.

Let's denote A as the event that the size of the family is less than 6, and B as the event that the size of the family is at least 3.

The conditional probability of A given B, denoted as P(A|B), is calculated as follows:

P(A|B) = P(A and B) / P(B)

First, we need to find P(B), the probability that the size of the family is at least 3. Since the family is selected at random, we can assume that all possible family sizes have an equal chance of being selected.

Let's assume the total number of possible family sizes is n. The probability of selecting a family with at least 3 members is the sum of the probabilities of selecting a family with exactly 3 members, exactly 4 members, and exactly 5 members.

P(B) = P(3) + P(4) + P(5)

Next, we need to find P(A and B), the probability that the size of the family is both less than 6 and at least 3. Since any family size less than 6 is also at least 3, P(A and B) will be the same as P(B).

Finally, we can substitute the values into the formula for conditional probability:

P(A|B) = P(A and B) / P(B) = P(B) / P(B) = 1

Therefore, the conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

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In this case, the nurse should perform a complete physical exam to determine the cause of the patient’s symptoms. The nurse should also assess the patient's vital signs, including heart rate, blood pressure, and temperature.

Once the assessment is completed, the nurse should immediately initiate fluid resuscitation to prevent dehydration and hypovolemic shock. The nurse should also administer pain medication as ordered and elevate the head of the bed to relieve abdominal distention.In this case, the patient is exhibiting symptoms of dehydration, including vomiting and minimal intake, which may result in hypovolemic shock. The patient is also experiencing severe abdominal distention and pain, which may indicate a gastrointestinal obstruction or perforation. These symptoms can be life-threatening and require immediate intervention by the nurse. Therefore, the nurse should perform a complete physical examination to determine the cause of the patient's symptoms. This examination should include a detailed abdominal assessment, such as auscultation for bowel sounds, palpation for tenderness and rigidity, and percussion for the presence of ascites. The nurse should also assess the patient's vital signs, including heart rate, blood pressure, and temperature. The nurse should also monitor the patient's urine output to ensure adequate fluid replacement and to detect any signs of renal failure. The nurse should administer pain medication as ordered and elevate the head of the bed to relieve abdominal distention.

In conclusion, the nurse should perform a complete physical exam to determine the cause of the patient’s symptoms. The nurse should also assess the patient's vital signs, including heart rate, blood pressure, and temperature. Once the assessment is completed, the nurse should immediately initiate fluid resuscitation to prevent dehydration and hypovolemic shock. The nurse should also administer pain medication as ordered and elevate the head of the bed to relieve abdominal distention.

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a. Find v' (18). The given function is v(t) = (t-19)². We have to find v'(18). Now, we will differentiate the given function with respect to t.

Thus, we have to apply the chain rule of differentiation.

v(t) = (t-19)²v'(t) = 2(t-19) * (d/dt)(t-19).

By using the power rule, we can say that(d/dt)(t-19) = 1v'(t) = 2(t-19)So, v'(18) = 2(18 - 19) = -2 m/s (meters per second).

b. Interpret the physical meaning of this quantity.

v'(18) is the instantaneous rate of change in the car's speed at t = 18.

When the car is 18 seconds away from the stop sign, its speed is changing at the rate of 2 m/s per second.

The negative sign indicates that the car is slowing down.

So, the car is moving with a speed of 2 m/s at t = 18 and it is decreasing at the rate of 2 m/s per second.

Hence, option (C) is the correct answer.

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Answer:

part a: 840 if she withdrew the first month down to 730 and the rate it decreases is 110 then it is 840

part b: 110every month she withdraws 55 dollars because 55 plus 55 is 110

so every 2 months she would have withdrawn 110 dollars

Step-by-step explanation:

In Bitcoin, when a merchant waits for n confirmation of a payment transaction before providing the product, there is a risk of a double-spend attack. In this situation, the network is aware of a branch crediting the merchant, which has n blocks on top of the one in which the fork started.

      By simulating m as a negative binomial variable, P(m) = (m + n - 1m)pnqm can be used to more precisely compute this probability for a given value of m.

           The attacker, on the other hand, has a branch with only m additional blocks. If we assume the honest network and the attacker have a proportion of p and q of the total network hash power, respectively, the probability of the attacker catching up when he is currently z blocks behind is given by az = paz+1 + qaz−1, where a is a constant.

          To calculate the probability more accurately, we can model m as a negative binomial variable.

          This is the number of successes (blocks found by the attacker) before n failures (blocks found by the honest network), with a probability q of success.

          The probability for a given value m is then given by P(m) = (m + n - 1m)pnqm.

         Thus, when dealing with a double-spend attack in Bitcoin, the probability that the attacker will be able to catch up is given by az = paz+1 + qaz−1, where a is a constant.

              This probability can be more accurately calculated by modeling m as a negative binomial variable, with the probability for a given value m given by P(m) = (m + n - 1m)pnqm.

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Answer:

x = {- 8, 2}

Step-by-step explanation:

Since, B is between line AC.

\(\therefore AB + BC = AC\\

\therefore x^2 - 3x + 9x = 16\\

\therefore x^2 - 3x + 9x - 16=0\\

\therefore x^2 + 6x - 16=0\\

\therefore x^2 + 8x - 2x- 16=0\\

\therefore x(x +8) - 2(x + 8)=0\\

\therefore (x+8)(x-2)=0\\

\therefore x + 8 = 0\: or \: x-2=0\\

\therefore x = - 8 \:or\: x = 2\\

\huge \orange {\boxed {\therefore x = \{-8,\: 2\}}} \)

Answer:

tanΘ = \(\frac{4}{3}\)

Step-by-step explanation:

tanΘ = \(\frac{opposite}{adjacent}\)

the opposite side requires to be found.

let the opposite side be x then using Pythagoras' identity in the right triangle

x² + 12² = 20²

x² + 144 = 400 ( subtract 144 from both sides )

x² = 256 ( take square root of both sides )

x = \(\sqrt{256}\) = 16

then

tanΘ = \(\frac{16}{12}\) = \(\frac{4}{3}\)