3w^2-12w=-12
use quadratic formula to solve

he distance between the foci of an ellipse with major axis length 10 units and minor axis length 6 units is 8 units.

Let's assume the length of the major axis is 2a and the length of the minor axis is 2b.

The distance between the foci, represented by 2c, can be calculated using the equation c² = a² - b².

Let's say the length of the major axis is 10 units (2a = 10) and the length of the minor axis is 6 units (2b = 6).

Substituting these values into the equation, we have:
c² = (10/2)² - (6/2)²
c² = 5² - 3²
c² = 25 - 9
c² = 16

Taking the square root of both sides to find c, we have:
c = √16
c = 4

Therefore, the distance between the foci of the ellipse is 2c = 2(4) = 8 units.

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Answer:

Y+3=-4(x+4) is correct answer

The number οf triangles that can be fοrmed is C(5,3)C(10,3) = 10120 = 1200.

In mathematics, cοmbinatiοns refer tο the number οf ways yοu can chοοse a specific number οf items frοm a larger set οf items, where the οrder in which yοu chοοse the items dοes nοt matter.

1. a) 9!/7! = 9*8 = 72

b) The questiοn seems tο be incοmplete. Please prοvide additiοnal infοrmatiοn.

c) P stands fοr permutatiοn, which is the number οf ways tο arrange οbjects in a specific οrder. A Stands fοr cοmbinatiοn, which is the number οf ways tο select οbjects withοut regard tο their οrder.

2. a) There are 6 ways tο chοοse οne apple frοm the basket.

b) There are 6 ways tο chοοse οne apple and 9 ways tο chοοse οne pear, sο there are 6*9 = 54 ways tο chοοse οne apple and οne pear.

c) There are 15 ways tο chοοse either οne apple οr οne pear (6 apples + 9 pears - 0 cοmmοn fruits).

d) There are 698 = 432 ways tο chοοse οne fruit οf οne variety and twο fruits οf anοther variety.

3. a) There are 6 subjects tο be studied and exactly οne lessοn is planned fοr each subject. Therefοre, there are 6! = 720 ways tο make a list οf lessοns fοr this day.

b) There are 6 chοices fοr the first digit, 5 chοices fοr the secοnd digit, 4 chοices fοr the third digit, and 3 chοices fοr the fοurth digit. Therefοre, there are 654*3 = 360 different fοur-digit numbers that can be fοrmed frοm the given digits.

c) There are 8 peοple and we need tο chοοse a cοmmittee οf 4 peοple. Therefοre, there are C(8,4) = 70 ways tο chοοse a cοmmittee οf fοur peοple.

3. Let n be the number οf members in the aerοbics grοup. Each member can shake hands with n-1 οther members. Since each handshake invοlves twο peοple, the tοtal number οf handshakes is n(n-1)/2. We are given that this tοtal is 66, sο we can sοlve fοr n as fοllοws:

\($ \frac{n(n-1)}{2} = 66\)

\(n(n-1) = 132\)

\(n^2 - n - 132 = 0\)

\((n-12)(n+11) = 0\)

Since n must be positive, the only possible value is n=12. Therefore, there are 12 members in the aerobics group.

4. There are 5 points on line a and 10 points on line b. Any three points on different lines can form a triangle, as long as they are not collinear.

Therefore, the number of triangles that can be formed is C(5,3)C(10,3) = 10120 = 1200.

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The probability that a woman is having one child of each sex is 0.2548.

The probability of having two children of the same gender (either both girls or both boys) can be calculated by multiplying the probability of having a girl or a boy is (which is 1/2 or 0.5) by itself twice, as each child is independent of the other:

0.5 × 0.5 = 0.25 (probability of having either two girls or two boys)

Since the total probability of having two girls or two boys is 0.5048 as given in the question, the probability of having one child of each sex is: 0.5048 - 0.25 = 0.2548.

Therefore, the probability that a woman with two children has one child of each sex is 0.2548

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

y=5x+2

Step-by-step explanation:

This would be the equation for this graph but the answer would be five. :)

Hope this helps!

Answer:

it is y=2+8

Step-by-step explanation:

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

The equation in slope intercept form is x =4 .

Given:

x = -5

x + 5 = 0

here slope m = ∞.

line equation passes through (4,-3) with m = ∞

-3 = 1/0(4) + c

4 + c = 0

c = -4.

y = (1/0)x - 4

x - 4 = 0

x = 4.

Therefore the equation in slope intercept form is x =4 .

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The function represents the difference h(x) is x^2+7x.

You know that the area of Rectangle A is given by

\(f(x) = 4x^2 + 6x\)

And the area of Rectangle B is given by

\(g(x) = 3x^2 - x\)

Therefore, to find the function representing the difference, you need to subtract the functions f(x) and g(x).

The way in which two things are being compared is not the same or the fact of not being the same.

Then, you get this function h(x)

\(h(x)=f(x)-g(x)\\h(x)=4x^2 + 6x-(3x^2 - x)\\h(x)=4x^2+6x-3x^2+x\\h(x)=x^2+7x\)

Therefore the function represents the difference h(x) is x^2+7x.

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Answer: D

Step-by-step explanation:

Answer:

y = -√(x - 6)

Step-by-step explanation:

The first choice on the left

y = -√(x - 6)

The larger x gets

the more negative y becomes

Rational functions are functions written as fractions. The correct function is \(y=-\sqrt{x-6}\)

Rational functions are functions written as fractions.

According to the question, we are to select the function for which as y tends to minus infinity, x will tend to positive infinity.

For the function \(y=-\sqrt{x-6}\)

Substitute y = -∞ into the equation

\(-\infty=-\sqrt{x-6}\\\sqrt{x-6} = \infty\\x-6=\infty\\x=\infty+6\\x=\infty\)

Hence the correct function is \(y=-\sqrt{x-6}\)

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Answer: y = 12x + 27

Step-by-step explanation:

The slope represents the money he is saving per day (12), and the y intercept represents the money he has already saved (27)

Answer:

17

Step-by-step explanation:

ZBAM= 90

90=4x+22

90 minus 22= 68

68=4x

68 divided by 4=17

The predicted year when the population of dolphins reaches 0 is 99 years after 2003, which is in the year 2102 (rounded to the nearest whole number).

a) The equation that models the population, P(t), of dolphins at any time t years after 2003 can be found using the slope-intercept form of a linear equation.

First, we need to find the slope (m) of the line. The slope is determined by the change in population divided by the change in time.

Using the given information, the change in population is 70 - 81 = -11, and the change in time is 2016 - 2003 = 13. Therefore, the slope (m) is -11/13.

Next, we need to find the y-intercept (b) of the line. The y-intercept is the population at the starting time (t = 0).

Given that the population in 2003 is 81, the y-intercept (b) is 81.

Thus, the equation that models the population of dolphins is P(t) = (-11/13)t + 81.

b) To predict the population of dolphins in the year 2027, we need to find the value of P(t) when t = 2027 - 2003 = 24.

Substituting t = 24 into the equation P(t) = (-11/13)t + 81, we get P(24) = (-11/13)(24) + 81 = 70.

Therefore, the predicted population of dolphins in the year 2027 is 70 (rounded to the nearest whole number).

c) To predict in what year the population reaches 0, we need to find the value of t when P(t) = 0.

Setting P(t) = 0 in the equation P(t) = (-11/13)t + 81 and solving for t, we get (-11/13)t + 81 = 0.

Simplifying the equation, we have (-11/13)t = -81. Multiplying both sides by -13/11, we obtain t = 99.

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Answer:

12

Step-by-step explanation:

Answer:

14 jackets

Step-by-step explanation:

20 plastic bottles=1 fleece jacket

280 plastic bottles=?

(280×1)÷20

=14

Answer:

volume

Step-by-step explanation:

Victoria should use volume measurement to determine how much sand she should buy.

The solution of the equation 4 sin 2θ-3 /cosθ=0 for 0≤θ<2π are: π/2 and 3π/2.

To write the equation in terms of a single angle θ, we can use the following trigonometric identities:

sin(2θ) = 2sin(θ)cos(θ)

cos(θ) = 1 / sec(θ)

Now let's rewrite the equation: 4sin(2θ) - (3/cos(θ)) = 0

Using the identities: 4(2sin(θ)cos(θ)) - (3 / (1/sec(θ))) = 0

Simplifying further: 8sin(θ)cos(θ) - 3sec(θ) = 0

Multiplying both sides by sec(θ) to eliminate the denominator:  8sin(θ)cos(θ)sec(θ) - 3 = 0

Since sec(θ) = 1/cos(θ), we can rewrite the equation as:  8sin(θ)cos²(θ) - 3cos(θ) = 0

Now we can solve the equation: cos(θ)(8sin(θ)cos(θ) - 3) = 0.

Either cos(θ) = 0 or 8sin(θ)cos(θ) - 3 = 0

1. When cos(θ) = 0:

θ = π/2 or θ = 3π/2

2. When 8sin(θ)cos(θ) - 3 = 0:

8sin(θ)cos(θ) = 3

Using the identity 2sin(θ)cos(θ) = sin(2θ):  

4sin(2θ) = 3

sin(2θ) = 3/4 , This equation does not satisfy the condition 0 ≤ θ < 2π.

Therefore, the solutions to the equation 4sin(2θ) - (3/cos(θ)) = 0, for 0 ≤ θ < 2π, are: θ = π/2, 3π/2

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Answer:

x = 13

Step-by-step explanation:

As given , the triangle is right angle . So we can use

Pythagoras theorem

       ⇒  a² = b² + c²

            a² = (12)² + (5)²

           a² = 144 + 25

          a² = 169

           After taking square root

            a = 13

    So  

         x = 13

The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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Answer:

Step-by-step explanation:

Answer:

850

Step-by-step explanation:

500 times 0.7 plus 500

Answer:

take out x+60 and = x+54 cross multiply for starters

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

59 feet per second.

Step-by-step explanation:

Firstly, we need to convert miles into feet and hours into seconds.

We know that there are 5280 feet in a mile.

To convert hours into seconds we multiply how many minutes are in an hour by how many seconds there are in a minute (60x60) to get 3600.

We multiply 5280 by 40 to get 211200 feet per hour

Because of the word "PER" we know that this is a divison problem.

211200 divided by 3600 is 58.66 repeating. Rounded to the nearest whole number makes it 59 feet per second.

Using a significance level of 0.05, we can conclude that fails to reject the null hypothesis. There is not sufficient evidence to support the claim that the proportion of urban gardens visited by native bees is different than 25%. The correct option is d).

Based on the given information, Sarah has calculated a p-value of 0.178 and is using a significance level of 0.05. The p-value is a measure of the strength of evidence against the null hypothesis. In hypothesis testing, if the p-value is less than the chosen significance level (0.05 in this case), it suggests that the observed data is statistically significant and provides evidence to reject the null hypothesis.

On the other hand, if the p-value is greater than the significance level, it indicates that the observed data is not statistically significant, and there is insufficient evidence to reject the null hypothesis.

In this scenario, since the p-value (0.178) is greater than the significance level (0.05), the best conclusion is to "Fail to reject the null hypothesis." This means that there is not sufficient evidence to support the claim that the proportion of urban gardens visited by native bees is different than 25%. The data collected does not provide strong enough evidence to conclude that there has been a significant change in the proportion over the five-year period.

Therefore, the correct answer is D. "Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the proportion of urban gardens visited by native bees is different than 25%."

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Answer:

\(2\frac{11}{12} +5 \frac{1}{2} + 3\frac{3}{8}\) (write them out and convert them all into mixed fractions)

\(\frac{35}{12} + \frac{11}{2} + \frac{27}{8}\) (find the LCD aka least common denominator)

\(\frac{70}{24} + \frac{132}{24} + \frac{81}{24}\) (add all numerators together)

\(\frac{283}{24}\)  (this is improper, so you need to convert back to mixed by dividing)

\(11\frac{19}{24}\) (this is your answer)

Answer:

You didn't provide any choices or options to pick from but here are the possible answers is:

- Encourage the use of the incentive spirometer every 2 hours

-Instruct to splint incision when coughing and deep breathing.

-Reposition the client every 2 hours

-Assist with early ambulation.

Step-by-step explanation:

Hope I could help!

In the plan of care to prevent postoperative atelectasis, interventions should not include the use of tobacco products or exposure to secondhand smoke.

The nurse should include several interventions in the plan of care to prevent postoperative atelectasis, but there are specific interventions that should not be included. Atelectasis is the partial or complete collapse of the lung, and preventing it is crucial after surgery. Here are some interventions that should be included:

Incentive Spirometry: The nurse should encourage the client to use an incentive spirometer to promote deep breathing and lung expansion.

Early Ambulation: Encouraging the client to get out of bed and walk as soon as possible after surgery helps improve lung function.

Pain Management: Adequate pain control measures should be in place to ensure the client can take deep breaths without discomfort.

Coughing and Deep Breathing Exercises: The nurse should teach and encourage the client to perform regular coughing and deep breathing exercises to clear the airways and prevent mucus buildup.

Positioning: Proper positioning, such as elevating the head of the bed, can aid lung expansion.

What should not be included in the plan of care is the use of tobacco products or exposure to secondhand smoke, as smoking and smoke exposure are detrimental to lung health and can worsen atelectasis. These should be strictly avoided to prevent postoperative complications.

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Mine is not heating up I don't know about others