discrete or continuous ​

Answer:

The total amount of candles is 768.

Step-by-step explanation:

Why? If there are 32 boxes of candles and 24 candles are in each box you would have to multiply 32x24 which is = to 768 candles in each box.

Answer:

\((x - y)(x + y + 1)\)

Step-by-step explanation:

\(x(x + 1) - y(y + 1)\)

\(=> x^{2} + x - y^{2} - y\)

Lets re-arrange it.

\(=> x^{2} - y^{2} + x - y\)

Now , lets expand x² - y².

\(=> (x + y)(x - y) + (x - y)\)

Taking ( x - y ) common ,

\(=> (x - y)(x + y + 1)\)

Answer:

\(x(x + 1) - y(y + 1) \\ → {x}^{2} + x - {y}^{2} - y \\→( {x}^{2}- {y}^{2}) + (x - y) \\→ (x - y)(x + y) + (x - y) \\→ \boxed{ (x - y)(x + y + 1)}✓\)

Answer:

10

Step-by-step explanation:

i29 82hd 18su 7wh2isyu3 27wb liczba eieh2u 2i2jw

Answer:

see below

Step-by-step explanation:

f(x) = –(x + 6)(x + 2)

The function is increasing until it reaches the vertex, so it will increase until x=-4.  The function will decrease after the vertex, so after x = -4

increasing: -∞ < x < -4

decreasing : -4 < x < ∞

Answer:

The function is increasing for all real values of x where x is -2

Step-by-step explanation:

You can put your work in a graphing calculator

The probability of randomly selecting the chair and the ranking member is 1/105 or approximately 0.0095.

There are 15 members of the Senate Committee on Homeland Security and Governmental Affairs, two of whom are selected to serve as the committee chair and ranking member. Each member is equally likely to be chosen for either of these positions.

To begin, we must first determine the total number of ways two members can be selected from a committee of 15. This is calculated using the combination formula:

nCr = (n!)/((r!)(n-r)!)where n = 15 and r = 2.

Thus,

nC2 = (15!)/((2!)(15-2)!)

nC2 = (15x14)/(2x1)nC2

= 105

Now we must determine the probability of selecting one member to be the committee chair and the other to be the ranking member.

This is calculated as follows: P = 1/105 or approximately 0.0095. Hence, the probability of randomly selecting the chair and ranking member is 1/105 or approximately 0.0095.

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Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and  0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.

a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.

b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)

Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,

P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228

P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392

P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269

P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093

P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016

P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011

d) The mean and standard deviation of the distribution is given by:

mean = n*p = 5*0.256 = 1.28

standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995

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The equation is P = \(25cos(0.224t) + 50\), where P represents the percentage of the moon's surface visible and t is the number of days since the moon was full.

To determine an equation for the percentage of the moon's surface visible as a function of the number of days since the moon was full, we can use the cosine function \(P = Acos(Bt) + C\), where P represents the percentage visible, t is the number of days since full moon, A is the amplitude, B is the frequency, and C is the vertical shift.

Given that the maximum percentage visible is 50%, we know that C = 50. The period of the function is 28 days, so we can calculate B using the formula B = 2π/period = 0.224. The amplitude A can be calculated as half of the maximum percentage visible, or A = 25.

Therefore, the equation for the percentage of the moon's surface visible as a function of the number of days since full moon is P = 25cos(0.224t) + 50.

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Using the normal distribution, it is found that there is a 0.3156 = 31.56% probability that the sample proportion will be less than 14%.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The proportion and the sample size are given, respectively, by:

p = 0.15, n = 294

Hence the mean and the standard error are given, respectively, by:

The probability is the p-value of Z when X = 0.14, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.14 - 0.15}{0.0208}\)

Z = -0.48

Z = -0.48 has a p-value of 0.3156.

0.3156 = 31.56% probability that the sample proportion will be less than 14%.

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Answer:

D

Step-by-step explanation:

maybe this will help you .

Answer:

The closest answer would be C

Step-by-step explanation:

this is split in 1/4th meaning what is 306.63 divided by 1/4?

Answer:

\(\displaystyle \sin \theta = \frac{4}{5}\) if \(\displaystyle \cos\theta = -\frac{3}{5}\) and \(\theta\) is in the second quadrant.

Step-by-step explanation:

By the Pythagorean Trigonometric Identity:

\(\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1\) for all real \(\theta\) values.

In this question:

\(\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}\).

Therefore:

\(\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}\).

Note, that depending on \(\theta\), the sign \(\sin \theta\) can either be positive or negative. The sine of any angles above the \(x\) axis should be positive. That region includes the first quadrant, the positive \(y\)-axis, and the second quadrant.

According to this question, the \(\theta\) here is in the second quadrant of the cartesian plane, which is indeed above the \(x\)-axis. As a result, the sine of this

It was already found (using the Pythagorean Trigonometric Identity) that:

\(\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}\).

Take the positive square root of both sides to find the value of \(\sin \theta\):

\(\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}\).

the slope of the line is 4

Answer:

(-2,-2),(1,1),(3,-1),(2,-4),(2,2),(-1,-1),(-3,1),(-2,4),(-2,2),(-1,-1),(-3,1),(-2,4),(-2,-2),(1,-1),(3,-1),(2,-4)

Step-by-step explanation:

just multiply the y coordinate by -1

Answer:

just multiply the y coordinate by -1

Step-by-step explanation:

The correlation coefficient of -0.84 between the variables "impulsivity" and "hours spent viewing TV" indicates a strong relationship, suggesting that the more impulsive an individual is, the less time they spend viewing TV.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of -0.84 indicates a strong negative relationship between impulsivity and hours spent viewing TV.

The negative sign indicates an inverse relationship, meaning that as one variable (impulsivity) increases, the other variable (hours spent viewing TV) decreases.

The magnitude of -0.84 indicates a relatively strong relationship. Since the correlation coefficient is close to -1, it suggests that there is a strong tendency for individuals with higher levels of impulsivity to spend less time viewing TV.

Conversely, those with lower levels of impulsivity tend to spend more time watching TV.

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Therefore, the probability that at least half of them must wait for more than 10 minutes is approximately \(1.137 x 10^-13.\)

Additionally, using relevant terms from the question in the answer is helpful.

Explanation:Given that waiting times at a service counter in a pharmacy are exponentially distributed with a mean of 10 minutes, we are to approximate the probability that at least half of the 100 customers must wait for more than 10 minutes.P(X > 10) is the probability of a customer waiting for more than 10 minutes.\(P(X > 10) = 1 - P(X < 10)P(X < 10) = 1 - P(X > 10) = 1 - e^(-10/10) = 1 - e^-1 = 0.632\)

Therefore, \(P(X > 10) = 1 - 0.632 = 0.368\)Thus, P(at least 50 customers wait for more than 10 minutes) =

\(P(X > 10)50 = 0.368^50 = 1.137 x 10^-13.\)

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The general solution for the second differential equation is y = \(e^[(1/2)x^2 + C2] - 4\)

1. \(dy/dx = 2x/y\)

Step 1: Separate variables. To do this, multiply both sides by y and divide both sides by dx:
\(y dy = 2x dx\)

Step 2: Integrate both sides:
\(∫y dy = ∫2x dx\)

Step 3: Evaluate the integrals:
\((1/2)y^2 = x^2 + C1\), where C1 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
\(y^2 = 2x^2 + 2C1\\y = ±√(2x^2 + 2C1)\)

So, the general solution for the first differential equation is \(y = ±√(2x^2 + 2C1\)).

2. \(dy/dx = x(y+4)\)

Step 1: Separate variables. To do this, divide both sides by (y+4) and multiply both sides by dx:
\(dy / (y+4) = x dx\)

Step 2: Integrate both sides:
\(∫[1 / (y+4)] dy = ∫x dx\)

Step 3: Evaluate the integrals:
\(ln|y+4| = (1/2)x^2 + C2\), where C2 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
\(y+4 = e^[(1/2)x^2 + C2]\\y = e^[(1/2)x^2 + C2] - 4\)

So, the general solution for the second differential equation is y = \(e^[(1/2)x^2 + C2] - 4\)

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Answer:

p=14x+6

Step-by-step explanation:

p=2(l+b)

p=2(2x+5x+9-6)

p=2(7x+3)

p=14x+6

x = time goal

16% = .16

.16 x = 32

x = 32/.16 = ___________ minutes

Jesse' weekly reading time is an illustration of ratio and proportion.

Jesse' weekly reading time is 200 minutes

Represent the reading time with x.

16% of his weekly reading time is given as 32 minutes

This is represented using the following equation

\(16 \% \times x = 32\)

Express 16% as decimal

\(0.16\times x = 32\)

Divide both sides by 0.16

\(x = 32/0.16\)

\(x = 200\)

Hence, Jesse' weekly reading time is 200 minutes

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Answer:

19

Step-by-step explanation:

Answer:

Horizontal asymptote: y=2

Reflect over the y-axis because of the negative raise power of x.

Domain: (-∞,∞)

Range: (2, ∞)

Decreasing all through the function.

Step-by-step explanation:

To approach this problem, we need to remember some of the transformation rules for functions:

*f(x)+d vertical translation up d units

*af(x) vertical stretch when a>1

Therefore, for the following function:

Since the function h(x) is shifted 2 units up, then the asymptote of the original Euler function would translate 2 units up.

Horizontal asymptote: y=2

Reflect over the y-axis because of the negative raise power of x.

Domain: (-∞,∞)

Range: (2, ∞)

Decreasing all through the function.

The parabola has its vertex at (h, k), and the focus is located at (h + p, k). The directrix line is represented by the equation x = h - p.

The equation of a parabola with a given focus and directrix can be derived using the geometric definition of a parabola. Let's consider a parabola with a focus F and a directrix line d. The parabola is defined as the set of all points P such that the distance from P to the focus F is equal to the perpendicular distance from P to the directrix line d. The equation of the parabola can be expressed in terms of either x or y, depending on the orientation of the parabola.

To derive the equation, we can assume that the focus F is located at (h, k + p), where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus. Let's also assume that the directrix line is given by the equation y = k - p.

If we consider a generic point P(x, y) on the parabola, we can calculate the distance between P and the focus F using the distance formula:

√((x - h)² + (y - (k + p))²)

Similarly, we can calculate the perpendicular distance from P to the directrix line d, which is simply the difference in y-coordinates:

|y - (k - p)|

According to the definition of a parabola, these distances should be equal. Therefore, we can set up the equation:

√((x - h)² + (y - (k + p))^2) = |y - (k - p)

To simplify this equation, we square both sides to eliminate the square root:

(x - h)² + (y - (k + p))² = (y - (k - p))²

Expanding and simplifying, we get:

(x - h)² + (y - k - p)² = (y - k + p)²

Further simplifying, we obtain:

(x - h)² = 4p(y - k)

This is the equation of a parabola with its vertex at (h, k) and the focus at (h, k + p). The directrix line is given by the equation y = k - p.

Therefore, the equation of the parabola in x-equals form is:

(x - h)² = 4p(y - k)

Alternatively, if you prefer the y-equals form, you can rearrange the equation as follows:

y = (1/(4p))(x - h)² + k

In this form, the parabola has its vertex at (h, k), and the focus is located at (h + p, k). The directrix line is represented by the equation x = h - p.

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∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

3

Step-by-step explanation:

Angle 1 is a supplement of angle 2, and m angle 1 is 123 degrees. Angle 2 is a complement of angle 3. Find m angle 3.

Marta wins the game is rolling a sum of 6. However, it is important to note that the exact outcome that Marta needs to win the game depends on the specific conditions and probability of the game.

It is difficult to determine the exact outcome that Marta needs to win the game without additional information. However, we can make some assumptions and analyze the probability of each option.

If Marta has a lower probability of winning than Elena, then the outcome that Marta needs must have a lower probability than the probability of rolling an even number first and a number less than 3 second. The probability of rolling an even number first is 3/6 or 1/2, and the probability of rolling a number less than 3 second is 2/6 or 1/3. The product of these probabilities is 1/2 × 1/3 = 1/6, which is the probability of Elena winning the game.

Option 1: Rolling a sum of 7

The probability of rolling a sum of 7 is 6/36 or 1/6, which is higher than the probability of Elena winning the game. Therefore, this option is not possible.

Option 2: Rolling a sum of 6

The probability of rolling a sum of 6 is 5/36, which is lower than the probability of Elena winning the game. Therefore, this option is possible.

Option 3: Rolling a sum of 2 or a sum of 9

The probability of rolling a sum of 2 is 1/36 and the probability of rolling a sum of 9 is 4/36. The sum of these probabilities is 1/36 + 4/36 = 5/36, which is higher than the probability of Elena winning the game. Therefore, this option is not possible.

Option 4: Rolling a sum that is greater than 9

The probability of rolling a sum that is greater than 9 is 4/36 or 1/9, which is higher than the probability of Elena winning the game. Therefore, this option is not possible.

Option 5: Rolling a sum that is greater than 2 but less than 5

The only possible sums that satisfy this condition are 3 and 4. The probability of rolling a sum of 3 is 2/36 or 1/18, and the probability of rolling a sum of 4 is 3/36 or 1/12. The sum of these probabilities is 1/18 + 1/12 = 5/36, which is higher than the probability of Elena winning the game. Therefore, this option is not possible.

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Answer:

A. 2(8)+2(w)=26

B. 16+2w=26

Subtract 16 from both sides of the equation

2w=10

Divide both side by 2

The width is 5

Step-by-step explanation:

Answer:

The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours

The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours

since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Step-by-step explanation:

The given parameters are;

The elapsed time by which Ms. Croft missed the boat = 5 hours

The speed of the cruise ship = 528 mi/day

The speed of the speedboat = 100 miles in 2.5 hours

The speed of the helicopter = 90 mph

The time it would take Ms. Croft to arrive at the harbor = 3.5 hours

Therefore, we have;

The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph

The location of the cruise after the first 5 hours = 5 × 22 = 110 miles

The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph

By traveling with a speed boat

The time at which Ms. Croft will intercept the cruise ship is given by the following relation;

40 mph × t = 22 mph × t + 110 miles

Which gives;

40 mph × t - 22 mph × t = 110 miles

18 mph = 110 miles

t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours

By taking the helicopter, we have;

Upon arrival at the harbor, after 3.5 hours, we find

90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles

90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles

68 mph × t = 77 miles + 110 miles = 187 miles

t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours

The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours

Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Answer:

hmmmmmmmm

Step-by-step explanation:

yea i really dont know

Given:

Mark started reading on Saturday , and he is reading 40 pages per day.

Allen didn't start until Sunday , but he is still reading 45 pages a day.

To find:

How many days will it take Allen to catch up to Mark, and how many pages will they each have read?

Solution:

Let \(x\) represent the number of days Allen has been reading. Then the number of days Mark has been reading is \((x+1)\).

Mark is reading 40 pages per day. So, he will read \(40(x+1)\) pages.

Allen is reading 45 pages a day. So, he will read \(45x\) pages.

Allen catch up to Mark when they read equal number of pages.

\(40(x+1)=45x\)

\(40x+40=45x\)

\(40=45x-40x\)

\(40=5x\)

Divide both sides by 5.

\(\dfrac{40}{5}=\dfrac{5x}{5}\)

\(8=x\)

In 8 days Allen will catch up to Mark.

\(45x=45(8)\)

\(45x=360\)

Therefore, they each have read 360 pages.