Make a conjecture about the next item in each sequence. 1, 4, 9, 16, 25

Answer:

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes

Given line

Perpendicular line is

Using given point (-6, 8), finding y-intercept

So the line is

To determine the number of solutions of the given equation, let's simplify it first:

(x^2 + 1)^2 + 2(x^2 + 1) - 3 = 0

Let's substitute a new variable, let's say u = x^2 + 1, to simplify the equation further:

u^2 + 2u - 3 = 0

Now, we have a quadratic equation in terms of u. To find the solutions for u, we can factorize the equation:

(u + 3)(u - 1) = 0

This equation will be true if either (u + 3) equals zero or (u - 1) equals zero.

For (u + 3) = 0, we have u = -3.

For (u - 1) = 0, we have u = 1.

Now, let's substitute back u = x^2 + 1:

For u = -3:

x^2 + 1 = -3

x^2 = -4

This equation has no real solutions because the square of any real number cannot be negative.

For u = 1:

x^2 + 1 = 1

x^2 = 0

This equation has a single solution: x = 0.

Therefore, the given equation has only one solution, x = 0.

The correct answer is A. 1.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

2

Step-by-step explanation:

simplify the equation to

[tex]2{x}^{2} + 2 + 2 {x}^{2} + 2 - 3 = 0[/tex]

simplify again by combining lIke terms to get

[tex]4 {x}^{2} + 1 = 0[/tex]

since x 2 can mean that x can be both a positive and negative number so there can be 2 solutions. they will both involve imaginary numbers because 4x 2 is guaranteed to be positive

Answer:

Heyhey!!! How ya doing?

Step-by-step explanation:

I can feel it on my skin

It's coming down on me

teardrops on my face

Water like misery

Let it wash away my sins

It's coming down on me

Answer:

add a photo please

Step-by-step explanation:

I cant solve it without knowing the choices

To find the center of the given equation, we need to rewrite it in the standard form of a circle equation, which is:

[tex]\sf\:(x - h)^2 + (y - k)^2 = r^2 \\[/tex]

where (h, k) represents the center coordinates of the circle and r represents the radius.

Given equation:

[tex]\sf\: x^2 + y^2 + 16y + 40 = 8x + 4y \\[/tex]

Rearranging the terms:

[tex]\sf\:x^2 - 8x + y^2 + 16y - 4y = -40 \\[/tex]

Completing the square for the x-terms:

[tex]\sf\: (x^2 - 8x + 16) + y^2 + 12y - 4y = -40 + 16 \\[/tex]

Completing the square for the y-terms:

[tex]\sf\: (x^2 - 8x + 16) + (y^2 + 12y + 36) = -40 + 16 + 36 \\[/tex]

Simplifying:

[tex] \sf\:(x - 4)^2 + (y + 6)^2 = 12 \\[/tex]

Comparing this with the standard form, we can see that the center of the circle is at (4, -6).

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

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Answer: center is 8,5

Step-by-step explanation: i dont have one

Answer:

That would be nice.

Step-by-step explanation:

If you could :)

Answer:

Step-by-step explanation:

(8x²-18x+10)/(x²+5)(x-3)

express the expression as a partial fraction:

(8x²-18x+10)/[(x^2+5)(x-3)] =A/x-3 +bx+c/x²+5

both denominator are equal , so require only work with the nominator

(8x²-18x+10)=(x²+5)A+(x-3)(bx+c)

8x²-18x+10= x²A+5A+bx²+cx-3bx-3c

combine like terms:

x²(A+b)+x(-3b+c)+5A-3c

(8x²-18x+10)

looking at the equation

A+b=8

-3b+c=-18

5A-3c=10

solve for A,b and c (system of equation)

A=2 , B=6, and C=0

substitute in the value of A, b and c

(8x²-18x+10)/[(x^2+5)(x-3)] =A/x-3 +(bx+c)/x²+5

(8x²-18x+10)/[(x^2+5)(x-3)] = 2/x-3 + (6x+0)/(x²+5)

(8x²-18x+10)/[(x^2+5)(x-3)] =

(4x+2)/[(x²+4)(x-2)]

(4x+2)/[(x²+4)(x-2)]= A/(x-2) + bx+c/(x²-2)

(4x+2)=a(x²-2)+(bx+c)(x-2)

follow the same step in the previous answer:

the answer is :

Answer:

Step-by-step explanation:

Answer: No Solutions

Step-by-step explanation: There are no values of x that make the equation true.

I hope this helps you out.

Answer:

[tex]\boxed {x = \frac{10}{c}}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]3(cx - 7) = 9[/tex]

-Divide [tex]9[/tex] by [tex]3[/tex]:

[tex]cx - 7 = \frac{9}{3}[/tex]

[tex]cx - 7 = 3[/tex]

-Add [tex]7[/tex] to both sides:

[tex]cx - 7 + 7 = 3 + 7[/tex]

[tex]cx = 10[/tex]

-Take [tex]c[/tex] and divide it on both sides:

[tex]\frac{cx}{c} = \frac{10}{c}[/tex]

[tex]\boxed {x = \frac{10}{c}}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]\frac{10}{c}[/tex].

Answer: 3 units to the left of three because the answer would be -3

Step-by-step-explanation: If we subtract 6 from 3, we get -3. Pretend these are dolars. So we have 3

How many dolars do you have left?

Well, we pay them the three we have, but then we owe them $3, because they still need $6 total.

We owe them 3 dolars, or we have -3 dollars.

Now let's just put a dot where -3 is on a number line.

Another way to look at this would be we started with 3 (blue dot) and we subtract 6, or move 6 to the left to get our red dot...which is -3

Either way you do it, -3 (which is the red dot) is your answer.

Answer:

3 units to the left of 3

Step-by-step explanation:

The random variable is the number of brown MOM's in a package of 50 MOM's. The given numbers are n = 50 and p = 0.13. The probabilities of exactly none, exactly 44, at least 43, and at most 45 MOM's being brown can be calculated using the binomial probability formula.

a) The random variable in this scenario is the number of brown MOM's in a package of 50 MOM's.

b) The given numbers with correct symbols are:

n = 50 (number of MOM's in the package)

p = 0.13 (proportion of brown MEM's)

c) This is a binomial experiment because the following conditions are met:

- There are only two outcomes for each MOM: brown or not brown.

- The number of MOM's is fixed at 50.

- The probability of selecting a brown MOM remains constant at 13% for each randomly selected MOM.

- The selection of one MOM being brown does not affect the probability of another MOM being brown.

d) The probability that exactly none of the MOM's are brown can be calculated using the binomial probability formula as P(X = 0) = C(50, 0) * (0.13)^0 * (1 - 0.13)^(50 - 0).

e) The probability that exactly 44 MOM's are brown can be calculated using the binomial probability formula as P(X = 44) = C(50, 44) * (0.13)^44 * (1 - 0.13)^(50 - 44).

f) The probability that at least 43 MOM's are brown can be calculated by summing the individual probabilities of having 43, 44, 45, ..., 50 MOM's brown. This can be calculated as P(X ≥ 43) = P(X = 43) + P(X = 44) + ... + P(X = 50).

g) The probability that at most 45 MOM's are brown can be calculated by summing the individual probabilities of having 0, 1, 2, ..., 45 MOM's brown. This can be calculated as P(X ≤ 45) = P(X = 0) + P(X = 1) + ... + P(X = 45).

By substituting the appropriate values into the binomial probability formula and performing the calculations, we can find the probabilities (d), (e), (f), and (g) to 4 decimal places.

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Complete question :

Physics students drop a ball from the top of a 100 foot high building and model its height as a function time with the equation h(t) = 100 - 16t^2.The height, h, is measured in feet and time, t, is measured is seconds.

Find the value of h(0). Include proper units. What does this output represent?

Answer:

Kindly check explanation

Step-by-step explanation:

The model given :

Height, h as a function of time :

h(t) = 100 - 16t^2

To find h(0): substitute 0 for t in the model defined ;

h(0) = 100 - 16(0)²

h(0) = 100 - 0

h(0) = 100

The output gives the height at which the ball was before it was dropped, it depicts the height when the travel time of the ball is 0

Answer:

-23/4 =c

Step-by-step explanation:

21+30=-4c+28​

Combine like terms

51 = -4c+28

Subtract 28 from each side

51 = -4c+28

Subtract 28 from each side

51-28 = -4c+28-28

23 = -4c

Divide each side by -4

23/-4 = -4c/-4

-23/4 =c

Answer: [tex]-\frac{23}{4}[/tex] or 5.75

Step-by-step explanation:

Step 1. Simplify 21 + 30 to 51

51 = −4c + 28

Step 2. Subtract 28 from both sides

51 - 28 = -4c

Step 3. Simplify 51 - 28 to 23

23 = -4c

Step 4. Divide both sides by -4

[tex]-\frac{23}{4}[/tex] = c

Step 5. Switch sides

c = [tex]-\frac{23}{4}[/tex]

Decimal Form Answer: -5.75

I hope this helps you out.

Answer:

Well, I can't see the graph but the y-intercept is the point on the line to where if you are on 0 either go up or down and the point the line is on is the y-intercept.

Answer:

.75

Step-by-step explanation:

trust meeeeee

Answer:.... if the doorbell rings the cat will jump into the mashed potatoes

Step-by-step explanation:

Literally what was that

Answer:

B.

Step-by-step explanation:

I just took the test.

Brainliest?

Answer:

C. 5x10^-10

Step-by-step explanation:

That equations answer is 5e-7, or 0.00000005, and C is equal to 0.000000005.

To find the population density in terms of people per square mile, we need to determine the area within a 15-mile radius and divide the population by that area.

To calculate the population density, we first need to find the area within a 15-mile radius. The formula for the area of a circle is A = πr², where A is the area and r is the radius. In this case, the radius is 15 miles.

Using the formula, we can find the area within the 15-mile radius:

A = π(15)² = 225π square miles

Next, we divide the given population of 40,000 by the area to find the population density:

Population density = 40,000 / (225π) people per square mile

To simplify the calculation, we can approximate the value of π to 3.14:

Population density ≈ 40,000 / (225 * 3.14) people per square mile

Simplifying further:

Population density ≈ 40,000 / 706.5 people per square mile

Using a calculator, we can find the approximate value:

Population density ≈ 56.7 people per square mile

Therefore, the population density within a 15-mile radius is approximately 56.7 people per square mile.

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The sample size required is 29.

To find the sample size, we need to use the concept of Acceptable Quality Level (AQL) and Lot Tolerance Percent Defective (LTPD) along with the consumer's risk and producer's risk.

The AQL is the maximum percentage of defective items that the company is willing to accept from the LSI manufacture department, which is specified as 6%. On the other hand, the LTPD is the maximum percentage of defective items that the assembly department is willing to accept, which is specified as 39%.

To calculate the sample size, we can use the formula for the sample size in attribute sampling plans:

n = ([tex]Z^{2}[/tex] * p * q) / [tex]E^{2}[/tex]

Where:

n = sample size

Z = Z-value corresponding to the desired level of confidence (for consumer's risk of 10% and producer's risk of 5%, we can use Z = 1.65)

p = expected proportion of defective items (maximum between AQL and LTPD)

q = 1 - p

E = precision or tolerable error (difference between AQL and LTPD)

In this case, we want to determine the sample size, assuming the worst-case scenario. Therefore, we choose p as the maximum between AQL and LTPD, which is 39%. Hence, q is 1 - p, which is 61%. The precision or tolerable error (E) is the difference between AQL and LTPD, which is 39% - 6% = 33%.

Substituting these values into the formula, we have:

n = ([tex]1.65^{2}[/tex] * 0.39 * 0.61) / ([tex]0.33^{2}[/tex])

n ≈ 28.74

Since the sample size should be a whole number, we round up to the nearest whole number.

Therefore, the sample size required is approximately 29.

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Step-by-step explanation:

number of boys=25

number of girls =16

ratio of boys to girl is 25:16

and the fraction is =25/16

Answer:

$.75

Step-by-step explanation:

9 ÷ 12 = 0.75

.75 × 12 = 9

Answer:

$4.80 per day

Step-by-step explanation:

We want the unit rate so take the dollar amount and divide by the number of days

$48/10

$4.80 per day

a) Based on the given data, we can conjecture that the set of dogs will have a larger mean, median, and standard deviation compared to the set of cats. This is because the weights of the dogs are generally higher and more spread out than the weights of the cats.

Dogs and cats typically have different average weights, with dogs being larger and heavier on average compared to cats. From the given data, the weights of the dogs range from 13 to 102 pounds, while the weights of the cats range from 4 to 22 pounds.

Considering the mean, the larger weights of the dogs will contribute to a higher mean compared to the weights of the cats. Since the mean is influenced by extreme values, the presence of larger dogs with weights such as 76 and 102 will tend to increase the mean for the dog set.

Moving on to the median, which represents the middle value of a dataset, the dogs are likely to have a larger median because their weights are generally higher. The median is less affected by extreme values, so even though there are a few heavier dogs, they won't significantly impact the overall position of the median for the dog set.

Lastly, the standard deviation measures the dispersion or spread of the data. Since the weights of the dogs exhibit a wider range, including both lighter and heavier dogs, the dog set is expected to have a larger standard deviation compared to the cat set, where the weights are more concentrated within a smaller range.

In summary, based on the general characteristics of dogs and cats, we can conjecture that the set of dogs will have a larger mean, median, and standard deviation compared to the set of cats, given the provided weights.

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The formula for the variance of the MLE estimator of β₀ is:

Var(β₀) = {σ²}{n} [ 1 + x²} / {∑{i=1}ⁿ (x_i - x²}

For the simple linear regression model, we have:

[tex]y_{i} = \beta_{0} + \beta _{1} x_{i} + epsilon_{i}[/tex]

where y(i) is the response variable, x (i) is the predictor variable, β₀ and β₁ are the intercept and slope parameters, and ∈(i) is the error term.

To find the variance of the MLE estimators of β₀ and β₁, we first need to derive the MLEs for these parameters:

β₁= {sum{i=1}ⁿ (xi - {x})(y_i - {y})}/{{i=1}ⁿ (x_i - {x})²}

β₀ = {y} -  β₁x

where x and y are the sample means of the predictor and response variables, respectively.

Next, we need to find the variances of these estimators. The formula for the variance of the MLE estimator of β₁ is:

$Var( β₁) = σ²∑{i=1}ⁿ (x_i - x²)

where , σ² is the variance of the error term.

And, the formula for the variance of the MLE estimator of β₀ is:

Var(β₀) = {σ²}{n} [ 1 + x²} / {∑{i=1}ⁿ (x_i - x²}

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Answer:

-8.4 to 8.4 and 12.6

Step-by-step explanation:

The answer fam is.... They are equivalent