2. a. Determine the Cartesian equation of the plane with intercepts at P(-1,0,0), (0,1,0), and R(0,0,-3). b. Give the vector and parametric equations of the line from part b.

To satisfy both conditions, (a) x being a multiple of 7 and (b) x^2 being less than 500, there are 14 values of x.

Condition (a) states that x must be a multiple of 7. Since there are infinitely many multiples of 7, the range of x satisfying this condition is (-∞, ∞), which means any real number can satisfy this condition.

Condition (b) states that x^2 must be less than 500. To find the range of x that satisfies this condition, we take the square root of both sides, which gives us -√500 < x < √500. Simplifying further, we get -22.36 < x < 22.36.

To find the intersection of the ranges satisfying both conditions, we consider the common values within the two ranges. The range satisfying both conditions is (-22, 22), inclusive. Since x can be positive or negative, there are 22 positive values and 22 negative values, giving a total of 44 values that satisfy both conditions. However, we need to account for the zero value, which is also a multiple of 7 and has its square less than 500. Hence, including zero, there are a total of 45 values of x that satisfy both conditions.

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The expected number of empty bins when tossing n balls into n bins, with each toss being independent and equally likely, can be determined using the concept of probability.

Let's define the probability that a specific bin remains empty after n tosses as P(empty). Since each ball has n choices, there are n^n possible ways to distribute the balls. To find the probability that a specific bin is empty, we can consider the situation where balls can be tossed into the remaining n-1 bins, resulting in (n-1)^n possible distributions. Therefore, P(empty) = ((n-1)^n) / (n^n).

Now, to calculate the expected number of empty bins, we can use the concept of linearity of expectation. The expected value of the sum of random variables is equal to the sum of the expected values of the individual random variables. In this case, the random variables represent the empty status of each bin (1 if empty, 0 if not).

The expected number of empty bins is the sum of the probabilities of each bin being empty, which is n * P(empty). So, the expected number of empty bins = n * (((n-1)^n) / (n^n)).

Using this formula, you can determine the expected number of empty bins when n balls are tossed into n bins independently and with equal likelihood.

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Answer: 10 I think

Step-by-step explanation: Jill sold half and you dont know how much it is you know that now she has 36, but before she bought 16 so 36 - 16 = 20 but she sold half

Answer:10 magazines

Step-by-step explanation:

36-16/2=m

20/2=m

10=m. m=magazine

According to elementary algebra, time t has values of 3 and 1 seconds, respectively.

Polynomial equations are those created by combining variables, exponents, and coefficients. The higher exponent, known as the degree of the equation, might have several exponents.

A polynomial expression equal to 0 is the basis of a polynomial equation. For instance, since 3x² - 5 is a polynomial expression, 3x² - 5 = 0 is a polynomial equation.

Quadratic equations are two-variable, degree-two polynomial equations of the form f(x) = \(ax^{2}\) + bx + c = 0 and with the variables a, b, c, and R R and a = 0.

With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x).

Knowing that h = 15 m, we can enter that number into the equation to find t:

15 = 20t - \(5t^{2}\)   Let's set the equation equal to 0 to solve

-\(5t^{2}\) + 20t - 15 = 0 Let's factor out a -5 to simplify the equation

-5(t2 - 4t + 3) = 0  0/-5 is still 0

\(t^{2}\) - 4t + 3 = 0   Let's find factors for this solution

(t -3)(t - 1) = 0   We have 2 solutions for this equation

t = 3, t = 1

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Answer:

B.

Step-by-step explanation:

6x3=18

18x4=72

3x3=9

9x2=18

72=18=90

Answer:

'n' will represent the number 5.

Step-by-step explanation:

\(9n \: + 2 = 47 \\ 9n \: = 47 - 2 \\ 9n \: = 45 \\ n \: = 45 \div 9 \\ n \: = 5\)

Answer:

-29, -34, -39

Step-by-step explanation:

the numbers are going down by five each time.

-24-5=-29

-29-5=-34

-34-5=-39

Hope this helps!

Answer:

-29

Step-by-step explanation:

because -14 and -19 is minus 5

you can use the formula for the volume of a rectangular prism to solve for one of the dimensions of the prism (either the length, width, or height).

What is a rectangular prism?

A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a box or a cuboid. A rectangular prism has three dimensions: length, width, and height.

To find the base area of a rectangular prism when given the volume, you can use the formula for the volume of a rectangular prism and the formula for the base area of a pyramid.

The volume of a rectangular prism is given by the formula V = lwh,

where V is the volume, l is the length, w is the width, and h is the height.

The base area of a pyramid is given by the formula B = A/h,

where B is the base area, A is the total surface area of the pyramid, and h is the height of the pyramid.

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Answer:

-4/7

Step-by-step explanation:

(1/2) ÷ (-7/8)

Multiply 1/2 by the reciprocal of -7/8

(1/2) * (-8/7)

-4/7

Hope this helps.

Answer:

it would be 8^12

Step-by-step explanation:

when exponents are dividing eachother and the bases are the same it would be like

\( \frac{ {x}^{3} }{x} \)

so it would turn into x^3-1 then the answer would be x^2

Using the fact that vertical angles are congruent we obtain the value of x = 2.

To calculate the value of x in this scenario, we can use the fact that vertical angles are congruent, meaning they have equal measures.

Provided that ∠e and ∠f are vertical angles, we have:

m∠e = m∠f

Substituting the provided measures, we have:

9x + 12 = 3x + 24

Now we can solve this equation for x.

First, let's isolate the variable terms by subtracting 3x from both sides:

9x - 3x + 12 = 3x - 3x + 24

Simplifying:

6x + 12 = 24

Next, we'll isolate the constant term by subtracting 12 from both sides:

6x + 12 - 12 = 24 - 12

Simplifying:

6x = 12

Finally, to solve for x, we divide both sides by 6:

(6x)/6 = 12/6

Simplifying:

x = 2

Therefore, the value of x is 2.

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Answer:

4

Step-by-step explanation:

answer is 5*0.8=4 yards of fabric

Answer:

4 yards

Step-by-step explanation:

He need 4/5 yards to make 5 shirts. Multiply the two to find your answer

4/5 * 5 = 4

He will need 4 yards of fabric to make 5 shirts.

Answer:

C

Step-by-step explanation:

5 x 3 = 15 and 15 x 2 = 30 ft

Answer:

$112 = $16 x

Step-by-step explanation:

Answer: 3 Jars

Step-by-step explanation:

Given

A batch of peanut butter cookies requires \(\frac{3}{4}\) of a jar

For 3 batches of Cookies, No of Jars required

\(\Rightarrow 3\times \dfrac{3}{4}=\dfrac{9}{4}\\\\\Rightarrow \dfrac{9}{4}=2+\dfrac{1}{4}\)

That is 2 complete Jar and one-fourth of third. In totality, it would be 3

jars.

Symmetric and asymmetric cryptography are both used to secure data, with symmetric algorithms being faster and better suited for bulk data encryption while asymmetric algorithms provide an additional layer of security and are better suited for smaller data sets.

Symmetric cryptographic algorithms use the same key to encrypt and decrypt data, while asymmetric cryptographic algorithms use different keys to encrypt and decrypt data. Symmetric algorithms are generally faster than asymmetric algorithms, making them more suitable for bulk data encryption. Additionally, symmetric algorithms are not vulnerable to man-in-the-middle attacks.

Asymmetric algorithms, on the other hand, are more secure than symmetric algorithms since they require two different keys to encrypt and decrypt data. This makes them more difficult to break, as an attacker would need to obtain both keys. Asymmetric algorithms are also more suitable for smaller amounts of data, such as digital signatures, where the security of the data is more important than speed. However, asymmetric algorithms are vulnerable to man-in-the-middle attacks and other types of attacks that target the keys used to encrypt and decrypt data.

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Answer:

hypotenuse

Step-by-step explanation:

The side opposite the right angle has a special name - hypotenuse

The other two sides of the right triangle are called legs

The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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Answer:191.80 lbs

Step-by-step explanation:

Answer:

190

Step-by-step explanation:

I need brainliest cutie

Answer:

C

Step-by-step explanation:

Comment.

D is definitely incorrect. If you want to be formal about it, use the distributive property. The common factor in both terms is ∛(6c). So what you are left with ∛(6c) ( 5 + 7) or

∛(6c)(12) or the answer is C

Answer: 12 ∛(6c)

A z-score of 1 indicates that the observed number of girls is 1 standard deviation above the expected number. In general, a z-score greater than 2 or less than -2 is considered unusual. In this case, the z-score of 1 does not suggest a significantly high number of girls, as it is within the typical range of outcomes.

The Range Rule of Thumb states that for a normal distribution, the range is approximately four times the standard deviation. To determine whether 6 girls in 8 births is a significantly high number of girls, we need to calculate the expected number of girls based on the probability of having a girl or a boy. Assuming a 50/50 chance of having a girl or a boy, we would expect 4 girls in 8 births.

Using the Range Rule of Thumb, we can calculate the standard deviation as range/4. In this case, the range is 6-0=6, so the standard deviation is 6/4=1.5.

To determine if 6 girls in 8 births is significantly high, we can calculate the z-score using the formula:

z = (observed value - expected value) / standard deviation

In this case, the observed value is 6 and the expected value is 4.

z = (6-4) / 1.5 = 1.33

Looking up this z-score in a standard normal distribution table, we see that the probability of getting a z-score of 1.33 or higher is 0.0918, or about 9%. This means that 6 girls in 8 births is not significantly high, as it falls within the normal range of variation.
Using the Range Rule of Thumb, we can determine whether 6 girls in 8 births is a significantly high number of girls. The Range Rule of Thumb is used to estimate the standard deviation (SD) of a sample, which can be helpful in determining if an observation is unusual.

First, calculate the expected proportion of girls using the assumption that there is a 50% chance of having a girl (0.5). Multiply this by the total number of births (8) to find the expected number of girls: 0.5 x 8 = 4.

Next, find the range by subtracting the minimum possible number of girls (0) from the maximum possible number of girls (8): 8 - 0 = 8.

Now, apply the Range Rule of Thumb to estimate the standard deviation (SD): SD = Range / 4 = 8 / 4 = 2.

Calculate the z-score to see how many standard deviations the observed number of girls (6) is from the expected number (4): z-score = (6 - 4) / 2 = 1.

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Answer:

3/9

Step-by-step explanation:

2/6 divided by 2 = 1/3

So, 2/6 times 2 = 2/9

PLS MARK BRAINLIEST...thx

Answer:

c) 27.9

Step-by-step explanation:

Since MN is the midsegment ,

MN = (AB + CD)/2

21.1 = (AB + 14.3)/2

21.1*2 = AB + 14.2

AB = 42.2 - 14.2

AB = 27.9

Answer:

C

Step-by-step explanation:

the midsegment is equal to half the sum of the parallel bases, that is

\(\frac{1}{2}\) (AB + CD) = MN ( substitute values )

\(\frac{1}{2}\) (AB + 14.3) = 21.1 ( multiply both sides by 2 to clear the fraction )

AB + 14.3 = 42.2 ( subtract 14.3 from both sides )

AB = 27.9 cm

Answer:

The diameter of a sphere is twice its radius. Therefore, if the diameter of the sphere is 36, the radius of the sphere is 18 (half of 36).

The volume of a sphere is given by the formula V = (4/3)πr^3, where π is approximately 3.14159 and r is the radius of the sphere.

Substituting the value of the radius, we get:

V = (4/3) × π × 18^3

= (4/3) × π × 5832

≈ 9733.78 cubic units

Therefore, the volume of the sphere with a diameter of 36 is approximately 9733.78 cubic units.

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Answer:

Yes

Step-by-step explanation:

boys to girls is  3 to 4 or 3:4

girls to boys is 4 to 3 or 4:3

-------------------------------------------------------------------

The genders are mixed up but the ratios are the SAME or EQUIVALENT.

-------------------------------------------------------------------

boys 3

girls 4

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\(enjoyyourday\)

Answer:

4

Step-by-step explanation:

u divide 14 by 2 and then subtract 3

hope this helps!

These values of h and k are specific to the given system of equations and may not apply to other systems.

(a) The system has no solution when h = 16.
(b) The system has a unique solution for any value of h ≠ 16.
(c) The system has many solutions when h = 16.

To determine the values of h and k that result in different solutions for the given system of equations, let's analyze the coefficient matrix of the system:
```
2   4
8   h
```
(a) To have no solution, the coefficient matrix must be inconsistent. This occurs when the determinant of the matrix is zero. In this case, the determinant is 2h - 32. So, to have no solution, we need 2h - 32 = 0. Solving this equation, we find h = 16. Therefore, the system has no solution when h = 16.

(b) To have a unique solution, the coefficient matrix must be consistent and have a non-zero determinant. This means that 2h - 32 ≠ 0. Since the determinant of the coefficient matrix is 2h - 32, we can conclude that the system has a unique solution for any value of h such that h ≠ 16.
(c) To have many solutions, the coefficient matrix must be consistent and have a determinant of zero. In this case, we need 2h - 32 = 0, which gives us h = 16. Therefore, the system has many solutions when h = 16.

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