Given y = x² + 3x - 2, find y when x = -2​

The smallest number of eggs that could have been in the box is 1134

The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:

Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:

n ≡ 1 (mod 2)

n ≡ 1 (mod 3)

n ≡ 1 (mod 4)

n ≡ 1 (mod 5)

n ≡ 1 (mod 6)

n ≡ 0 (mod 7)

For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.

Plugging these values into the formula and simplifying modulo 5040, we get:

n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040

n = (−8946) mod 5040

n = (−3906) mod 5040

n = 1134 mod 5040

Therefore, the smallest number of eggs that could have been in the box is 1134

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In order to make one more kit with the remaining parts, you would need 1 more people marker and 1 more die using mathematical operations

Let's analyze the number of parts available and the requirements for each kit. To make a kit, you need 6 people markers, 3 six-sided dice, and 7 teleporter markers. From the available parts, you have 287 people markers, 143 six-sided dice, and 341 teleporter markers.

We can determine the maximum number of kits you can make by dividing the available quantity of each part by the number required per kit. For the people markers, you have enough to make 287 / 6 = 47 kits. For the six-sided dice, you have enough to make 143 / 3 = 47 kits as well. Finally, for the teleporter markers, you have enough to make 341 / 7 = 48 kits.

After making the maximum number of kits, you will have some remaining parts. To determine if you can make one more kit, you need to identify the part(s) for which you have the least availability. In this case, the limiting factor is the people marker, as you have only 287 available. Therefore, to make one more kit, you would need 1 more people marker. Additionally, since you have 143 six-sided dice available, you also need 1 more die to match the requirement. Therefore, the answer is A. 1 more people marker and 1 more die.

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Answer:

_______the answer is Y=X+1___________

Given the following 25 sample observations:

5.3, 6.1, 6.7, 6.8, 6.9, 7.2, 7.6, 7.9, 8.1, 8.9, 9.0, 9.2, 9.4, 9.7, 10.1, 10.4, 10.6, 10.8, 11.3, 11.4, 12.0, 12.1, 12.3, 12.5, 13.2.

Let Y1, Y2,...,Yn be the order statistics for this sample.

A) The interval (Y9, Y16) could serve as a distribution-free estimate of the median, m, of the population.

Find the confidence coefficient of this interval.

The sample size is 25, thus the median is Y(13), where Y is the order statistics of the sample.

So the interval (Y(9), Y(16)) is a 75% confidence interval for the median, m, of the population.

The confidence coefficient of this interval is 0.75.

B) The interval (Y3, Y10) could serve as the confidence interval for a proportion.

Determine this confidence interval and, using a binomial distribution chart, determine the confidence coefficient of this interval.

To calculate the confidence interval for a proportion, we need to calculate the sample proportion, P and use that to calculate the interval limits.

The sample proportion, P = (number of success)/(sample size)

P = (number of success)/(25)

P = (7/25)

= 0.28

So the confidence interval for the proportion is given by:

p ± z √((p(1 - p)) / n)p ± z √((0.28(0.72)) / 25)p ± z √(0.02016 / 25)p ± z (0.1421)

The interval (Y3, Y10) contains 8 observations out of 25.

Thus, the sample proportion is:

P = 8/25

= 0.32

Using a binomial distribution chart, we find the z-value that corresponds to a cumulative area of 0.975 is 1.96.

Hence the 95% confidence interval for the proportion is:

p ± z √((p(1 - p)) / n)

0.32 ± 1.96 √((0.32(0.68)) / 25)0.32 ± 0.1421

The confidence interval is (0.1779, 0.4621) and the confidence coefficient is 0.95.

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Answer:

v=2

Step-by-step explanation:

add five to the other side and: -8v=(-21+5)

divide -16 by -8: v= -16/-8

v=2

Answer:

17

Step-by-step explanation:

t^2 + m^2 = 64

(t+m)^2 = 98

(t+m)^2 = t^2 +2tm+ m^2

==>

t^2 +2tm+ m^2 = 98

t^2+m^2+2tm=98

64+ 2tm=98

2tm = 98 -64

2tm=34

tm= 34/2

tm = 17

The length of the diagonal of the parallelogram is 10 cm using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

In the question, we observe that the diagonal of the parallelogram will form a right-angled triangle with the adjacent side of length 8cm and 6cm.

thus by Pythagoras rule;

the length of the diagonal = √(6² + 8²) cm

the length of the diagonal = √(36 + 64) cm

the length of the diagonal = √100 cm

the length of the diagonal = 10 cm

In conclusion, by proper application of Pythagoras rule we have derived the length of the diagonal of the parallelogram to be 10 cm.

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\(denote \: by \: s \: the \: cost \: of \: a \: sweatshirt \\ denote \: by \: t \: the \: cost \: of \: a \: t \: shirt\)

\(3t + 7s = 240.5 \\ 6t + 5s = 220\)

\( - 6t - 14s = - 481 \\ 6t + 5s = 220\)

\( - 9s = - 261 \\ s = \frac{ - 261}{ - 9} = 29 \: dollars\)

\(3t + 7(29) = 240.5 \\ \)

3t + 203 = 240.5

3t = 37.5

t = 12.5 dollars

When the loaded die is rolled, the probability of getting a 1, 2, 4, 5, or 6 is 1/9 each, while the probability of getting a 3 is 5/9.

If a 3 is five times more likely to appear than each of the other five numbers on the die, we can assign the following probabilities to each outcome:

\(P(1) = P(2) = P(4) = P(5) = P(6) = x\) (some common probability)

\(P(3) = 5x\)

Since the sum of the probabilities for all possible outcomes must be equal to 1, we have:

\(P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = x + x + 5x + x + x + x = 9x = 1\)

Solving for x, we get:

\(x = 1/9\)

Therefore, the probabilities for each outcome are:

\(P(1) = P(2) = P(4) = P(5) = P(6) = 1/9\\P(3) = 5/9\)

So when the loaded die is rolled, the probability of getting a 1, 2, 4, 5, or 6 is 1/9 each, while the probability of getting a 3 is 5/9.

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The sum of all the internal angle is \($180^{\circ}$\).

The sum of all the internal angle is \($180^{\circ}$\).

\($$\angle A+\angle B+\angle C=180^{\circ}$$\)

1. 34 and 88

\(34+88+\angle C=180 \\\)

\(122+\angle C=180 \\\)

\(\angle C=180-122 \\\)

\(\angle C=58^{\circ}\)

2. 45 and 90

\(45+90+\angle C=180 \\\)

\(135+\angle C=180 \\\)

\(\angle C=180-135 \\\)

\(\angle C=45^{\circ}\)

3. 10 and 102

\(10+102+\angle C=180 \\\)

\(112+\angle C=180\)

\(\angle C=180-112 \\\)

\(\angle C=68^{\circ}\)

4. \($\boldsymbol{x}$\)and 50

\(x+50+\angle C=180 \\\)

\(\angle C=180-50-x \\\)

\(\angle C=(130-x)^{\circ}\)

The complete question is,

Find the measure of the third angle of a triangle given the measures of two angles.

1. 34 and 88

2. 45 and 90

3. 10 and 102

4. x and 50

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Answer:

(0, 2)

(1, 3)

(2, 4)

a. The probability that X is greater than 500 is approximately 0.368.

b. The conditional probability that X is greater than 1000 is approximately 0.368.

a. To compute Pr[X > 500), we use the cumulative distribution function (CDF) of the exponential distribution, which is:

F(x) = 1 - e^(-x/B)

Plugging in B = 500 and x = 500, we get:

Pr[X > 500) = 1 - F(500) = 1 - (1 - e^(-500/500)) = e^(-1) ≈ 0.368

Therefore, the probability that X is greater than 500 is approximately 0.368.

b. To compute Pr[X > 1000 | X > 500), we use the definition of conditional probability:

Pr[X > 1000 | X > 500) = Pr[(X > 1000) ∩ (X > 500)] / Pr[X > 500)

Since X is a continuous random variable, we can rewrite the probability of the intersection using the minimum of X:

Pr[(X > 1000) ∩ (X > 500)] = Pr[X > max(1000, 500)] = Pr[X > 1000]

Plugging in B = 500 into the CDF, we have:

Pr[X > 1000] = 1 - F(1000) = 1 - (1 - e^(-1000/500)) = e^(-2) ≈ 0.135

We already know from part a that Pr[X > 500) = e^(-1) ≈ 0.368.

Putting it all together, we have:

Pr[X > 1000 | X > 500) = Pr[X > 1000] / Pr[X > 500) = (e^(-2)) / (e^(-1)) = e^(-1) ≈ 0.368

This result shows that the conditional probability that X is greater than 1000, given that it is already greater than 500, is the same as the probability that X is greater than 500 on its own. In other words, knowledge of the fact that X is already greater than 500 does not change our prediction about whether it will be greater than 1000 or not.

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The number of communication channels, 1 channels would two people require.

To find number of communication channels, we use;

On the other hand, it might be a sign of the scope and intensity of the project communication management needed in huge projects and so-called megaprojects. This could, for example, entail allocating specific resources to project communication responsibilities in accordance to the number of available channels for communication. These factors may be especially important for teams working on sensitive projects and projects where information flow may be unclear or even fraudulent.

Number of potential communication channels = n x (n-1)/2

Given n = 2;

→ x = 2*(2 - 1)/2

    = 2*1/2

    = 1

The number of communication channels, 1 channels would two people require.

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Answer:

✓ 4 2/5 divided by 1 1/10= 4

Step-by-step explanation:

✓ Factor the numerator and denominator and cancel the common factors.

✓  Hopefully this helps you!

-Keira

When \(4\frac{2}{5}\)  is divided by \(1 \frac{1}{10}\)  we get the value 4.

Convert mixed numbers to improper fractions:

\(4\frac{2}{5}\) = (4 × 5 + 2) / 5 = 22/5

\(1 \frac{1}{10}\) = (1 × 10 + 1) / 10 = 11/10

Divide the two fractions:

(22/5) ÷ (11/10)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(22/5) × (10/11)

220/55

220/55 can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 5:

(220 ÷ 5) / (55 ÷ 5)

= 44/11

=4

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Answer:

the answer is $36.04

Step-by-step explanation:

34 dived into 100= 0.34 times 6 equals 2.04 34+2.04=36.04

Answer:

-1

Step-by-step explanation:

Following PEMDAS The answer equals to -1

*plssss make me brainlist*

Answer:

Let's simplify step-by-step.

5x2−3x−(5x2−3x+1)

Distribute the Negative Sign:

=5x2−3x+−1(5x2−3x+1)

=5x2+−3x+−1(5x2)+−1(−3x)+(−1)(1)

=5x2+−3x+−5x2+3x+−1

Combine Like Terms:

=5x2+−3x+−5x2+3x+−1

=(5x2+−5x2)+(−3x+3x)+(−1)

=−1

Step-by-step explanation:

Show your work

Answer:

Only one solution (x = 0)

Step-by-step explanation:

From the graph attached,

Parabola in the graph touches the origin.

It doesn't intersect the x-axis.

Therefore, There will be only one root or solution of the given function,

x = 0

The equation for line P such that the system has an infinite number of solutions is given as follows:

3) 2x + 2y = -2.

The first equation for the system of equations is given as follows:

x + y = -1.

A system of equations has an infinite number of solutions when the two equations are multiples.

Multiplying the equation by 2, we have that:

2x + 2y = -2.

Meaning that equation 3 is correct.

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The probability that have owned their current homes for at least one year is 78/212

Given that,

In the two-way frequency table below, a sample of 942 homeowners is grouped according to how many credit cards they have and how long they have owned their current homes. of the sample's homeowners who possess four or more credit cards

To find : The probability that homeowners have lived in their current residences for at least a year

Required Probability

=( Number of homeowners having four or more credit cards and have

owned their current homes for at least one year /

Number of homeowners having four or more credit cards )

= 58+ 20/134 + 58 + 20

= 78/212

Hence, The probability that have owned their current homes for at least one year is 78/212

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Given:

Base dimensions of a rectangular prism = 15 cm × x cm

The height of the prism = 8 cm

Volume of the prism = 600 cm.

To find:

The value of x.

Solution:

Base area of the prism is:

\(B=length\times width\)

\(B=15\times x\)

\(B=15x\)

Volume of the prism is:

\(V=Bh\)

Where, B is the base area and h is the height of the prism.

Putting \(V=600,B=15x,h=8\), we get

\(600=15x\times 8\)

\(600=(8)(15)x\)

\(\dfrac{600}{(8)(15)}=x\)

Therefore, the correct option is C.

Answer:

4

Step-by-step explanation:

We want xy=54=2*3^3 such that x is at least 2 and y is at least 5. Thus, the possible combinations (x,y) are (2,27), (3,18), (6,9), and (9,6). There are 4 such combinations.

Answer:

10 centimeters.

Step-by-step explanation:

First, we need to remember what's the formula to get the volume of a rectangular solid and a cube.

The volume of the first equals:

Volume = Length x Width x Height

While the volume of the cube is:

\(Volume = a^{3}\) where a is the edge.

We are given the measures of the rectangular solid so we can calculate its volume:

\(Volume= (20)(5)(10)=1000\) cubic cms.

Now, we know that  both the volume of the rectangular solid and the cube are the same so we will use this information to calculate the edge of the cube.

\(1000=a^3 \\\sqrt[3]{1000} =\sqrt[3]{a^3} \\10=a\)

Thus the length of an edge of the cube is 10 centimeters

Answer:

True

Step-by-step explanation:

True, because a polygon have all angles that are equal and all lengths are the same length.

Answer: newtons

Step-by-step explanation:

Answer:

I believe it is Newtons :)

Step-by-step explanation:

a) We have:

W = X1 - X2 + X3

So, E[W] = E[X1] - E[X2] + E[X3] (by linearity of expectation)

Using the given mean vector, we get:

E[W] = 1 - 0 + 2 = 3.

(b) We have:

Var(W) = Var(X1) + Var(X2) + Var(X3) - 2Cov(X1,X2) - 2Cov(X1,X3) + 2Cov(X2,X3) (by the formula for variance of a sum of random variables)

Using the given variance-covariance matrix, we get:

Var(W) = 1 + 1 + 1 - 2(0.5) - 2(0.5) + 2(0.5) = 1.

(c) Since W is a linear combination of normal random variables, it follows that W is also normally distributed. Therefore, we can standardize W and use the standard normal distribution to find P[W > 4]:

P[W > 4] = P[(W - 3)/sqrt(Var(W))] = P[Z > (4-3)/1] = P[Z > 1],

where Z is a standard normal random variable. Using a standard normal table or calculator, we get:

P[Z > 1] = 0.1587 (approx).

(d) We need to find P[W > U], where U = 2X1 - X2 + X3. Since W and U are linear combinations of normal random variables, it follows that W - U is also normally distributed. Therefore, we can standardize W - U and use the standard normal distribution to find P[W > U]:

P[W > U] = P[(W - U)/sqrt(Var(W - U))] = P[Z > (0 - E[W-U])/sqrt(Var(W-U))],

where Z is a standard normal random variable. To find E[W-U] and Var(W-U), we compute:

E[W-U] = E[W] - E[U] = 3 - 2(1) + 0 = 1,

Var(W-U) = Var(W) + Var(U) - 2Cov(W,U) = 1 + 4 + 2(0.5) - 2(1.5) = 1.

Substituting these values, we get:

P[W > U] = P[Z > -1/sqrt(1)] = P[Z > -1],

where Z is a standard normal random variable. Using a standard normal table or calculator, we get:

P[Z > -1] = P[Z < 1] = 0.8413 (approx).

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Answer:

$150

Step-by-step explanation:

The sale price is $120. We're looking for 80% of the original price, given this sale price.

\(120 = .8p\)

\(p = 150\)

Answer:

d > -2

Step-by-step explanation:

-2d-2 < 3d+8

3d+8 > -2d-2

3d + 2d > -2 -8

5d > -10

d > -2

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Answer:

C)9,5,1,3

a1=9

a2=a(2-1)-4= a1-4= 9-4=5

a3=a(3-1)-4= a2-4= 5-4=1

Hope this will help :-)