Mark each of the following statements True or False by selecting an option from the dropdown list next to the statement. 1. The plane ( 4 x+2 y-3 z=4 ) and the line ( x=1+t, y=2+t, z=3+2 t ) do not meet. 2. The vectors u=⟨4,6,8⟩ and v=⟨−6,−9,x⟩ are parallel if, and only if, x=−12. 3. The cross product of u=⟨1,2,4⟩ and v=⟨4,3,2⟩ is orthogonal to w=⟨−9,−8,−8⟩.

Answer:

D

Step-by-step explanation:

The rate of change of the function that has a graph that passes

through the points (-1, 3) and (-2,-4) is slope and is equal to 7.

We have given two points  (-1, 3) and (-2,-4) .

Rate of change of graph is given by slope

Using slope formula , we get

      m = -4 - 3 / -2 - (-1)

      m = -7 / -2 + 1

      m = -7 / -1

       m = 7

Learn more about slope here :

https://brainly.com/question/17248198

#SPJ9

Answer:

A

Step-by-step explanation:

1A). 1² + 4²

= 1 + 16

= √17

B). 1² + 16²

= 1 + 256

= √256

= 16

C). 2² + 8²

4 + 64

= 68

= 2√16

D). 2² + 15²

= 4 + 225

= √299

Answer:

Step-by-step explanation:

Let the three numbers be a-d, a, a+d being a series in AP.

The sum of the three numbers is 24 = a-d+ a+ a+d = 3a

Thus a = 8.

Now a-d-1, a-2, a+d form a GP. It means, the common ratios should be equal or the middle term should be the Geometric Mean of the first and third terms, or

(a-d-1)(a+d) = (a-2)^2 or

(8-d-1)(8+d) = (8-2)^2, or

(7-d)(8+d) = 36, or

56 -8d +7d -d^2 = 36, or

56 -8d +7d -d^2 - 36 = 0, or

d^2 +d -20 = 0

(d+5)(d-4) = 0

Thus d = -5 or 4

So the AP is 13,8,3 or 4,8,12

Check: 13,8,3 in AP becomes (13–1), (8–2), 3 = 12, 6, 3 which is a GP with r = (1/2)

4,8,12 in AP becomes (4–1), (8–2), 12 = 3, 6, 12 which is a GP with r =2

Answer:

2.25

Step-by-step explanation:

k = 13.5 ÷ 6 = 11.25 ÷ 5 = 4.5 ÷ 2 =  2.25

Answer:

x = 5,-2

Step-by-step explanation:

Multiply the whole equation by 3(x+1) to get rid of the denominator.

\( \large{ \frac{x + 2}{3} \times 3(x + 1) = \frac{2(x + 2)}{x + 1} \times 3(x + 1)} \\ \large{(x + 2)(x + 1) = 2(x + 2) \times 3} \\ \large{ {x}^{2} + 3x + 2 = 6(x + 2)} \\ \large{ {x}^{2} + 3x + 2 = 6x + 12}\)

Then we solve the equation.

\( \large{ {x}^{2} + 3x + 2 - 6x - 12 = 0} \\ \large{ {x}^{2} - 3x - 10 = 0} \\ \large{(x - 5)(x + 2) = 0} \\ \large{x = 5, - 2}\)

Since we are also solving rational equation, make sure that x ≠ -1 for this problem. Because if x = -1, the denominator is 0 which is undefined. Since our solutions are x = 5,-2 and not -1. Therefore the answer is x = 5,-2

Answer:

88

Step-by-step explanation:

^9199eoijdfwieufhiqehgfb

The population of the country in 40 years later will be 387.1992905 million people. The result is obtained by using the equation of estimating the future population.

The future population can be estimated by the following equation:

P = P₀ × (1 + i)ⁿ

Where

If at a certain time, the population is 55 million people and the growth rate is 5% per year, what will the population be in 40 years later?

The estimation of the population in 40 years later:

P = P₀ × (1 + i)ⁿ

P = 55 million × (1 + 0.05)⁴⁰

P = 55 million × (1.05)⁴⁰

P = 55 million × 7.0399871

P = 387.1992905 million people

Hence, the population in 40 years later will be 387.1992905 million people.

Learn more about future population here:

brainly.com/question/29383337

#SPJ4

The percentage of undergraduate students who show almost no gain in learning in their first 2 years of college in the United States is a sample proportion with a null hypothesis (H0) and an alternate hypothesis (Ha) that we want to check. In this question, we are supposed to test whether we can reject H0 at a 1% significance level or not.

Step 1: Identify the Null Hypothesis and Alternate Hypothesis Let P be the population proportion of students who show no gain in learning in their first 2 years of college in the United States.H0: P = 0.45Ha: P < 0.45Step 2: Check for Independence and Sample Size Conditions We don't have any information on independence; however, we assume that the sample was randomly selected. Hence, the independence condition is met. Step 3: Calculate the Test StatisticUnder the null hypothesis, the sample proportion (p) is approximately equal to 0.45. We can use this fact to calculate the test statistic.Using the p-value approach: Z = (p - P) / sqrt(PQ/n)Z = (0.38 - 0.45) / sqrt(0.45*0.55/1500)Z = -5.39Using the critical value approach:Critical value = Zα, where α = 0.01Critical value = -2.33Step 4: Find the p-valueThe p-value is the probability of observing a test statistic at least as extreme as the one calculated in step 3 if the null hypothesis is true.Using a calculator, the p-value for Z = -5.39 is less than 0.0001 (approximately zero).

To know more about proportion visit:

https://brainly.com/question/31548894

#SPJ11

Answer:

5

Step-by-step explanation:

you divide 6/30=5

hope this helps

Answer:

The correct option is;

Both spreads are best described by the standard deviation

Step-by-step explanation:

The given information are;

,                                    College                       High School

High,                              20                               20

Low,                                6                                 3

Q₁,                                   8                                 5.5

Q₃,                                  18                                16

IQR,                                 10                                10.5

Median,                           14                                11

Mean,                              13.3                             11

σ,                                      5.2                             5.4

Checking for outliers, we have

College

Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7

Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33

For high school

Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25

Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75

Therefore, there are no outliers and the data is representative of the population

From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2

The difference between the low and the high is also approximately 3 standard deviations

Therefore the college spread is best described by the standard deviation

Similarly for the high school students, the IQR is approximately two standard deviations, the  difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4

Therefore the high school spread is also best described by the standard deviation.

Answer:

Both spreads are best described by the standard deviation

Step-by-step explanation:

The slope of the line that passes through (-4, 7) and (-6, 5) is 1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinate points are (-4, 7) and (-6, 5).

Now, slope m=(5-7)/(-6+4)

m=-2/(-2)

m=1

Substitute m=1 and (x, y)=(-4, 7) in y=mx+c, we get

7=1(-4)+c

c=11

Substitute m=1 and c=11 in y=mx+c, we get

y=x+11

Therefore, the slope of the line that passes through (-4, 7) and (-6, 5) is 1.

To learn more about the slope of a line visit:

https://brainly.com/question/14511992.

#SPJ1

let's firstly convert the mixed fractions to improper fractions and then subtract.

\(\stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}} ~\hfill \stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}~~ - ~~\cfrac{14}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~ - ~~(2)14}{6}}\implies \cfrac{51~~ - ~~28}{6}\implies \cfrac{23}{6}\implies {\LARGE \begin{array}{llll} 3\frac{5}{6} \end{array}}\)

Answer:

raw

Step-by-step explanation:

If a researcher has collected data and wishes to analyze them, the researcher must first create a data set using the Raw scores.

Answer:

the answer is 252

Step-by-step explanation:

7 x 8 x 9

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

     2

Step-by-step explanation:

BC = AD (opposite sides in parallelogram is equal)

x + 8 = 2x + 1

8 - 1 = 2x - x

7 = x

x = 7

BC = x + 8 = 7 + 8 = 15

Answer:The family will use 792 gallons of water in the new washing machine

Step-by-step explanation:

1440 X 0.55=792

100-45=55

Answer:

D) left a units, down b units

Step-by-step explanation:

Changes close to x, affect the horizontal, left/right movement (but sort of the opposite direction than you would expect.... + left move and - right move)

A number tacked on to the end of the equation moves the curve up or down as you would guess (+ up and - down)

Answer: The product of this equation, expressed as a mixed number is -3 17/20

Answer:

4 7/40

Step-by-step explanation:

brainliest? :)

Answer:

8

Step-by-step explanation:

11/22= 0.5 multiply 16 and 0.5 and you get 8

Answer: i might be wrong and i apologize if i am but i think its 15.125

Step-by-step explanation:

The binomial and Poisson distributions are two different types of discrete probability distributions. The binomial distribution is used when two possible outcomes exist for each event.

The Poisson distribution is used when the number of events occurring in a fixed period or area is counted. It is also known as a "rare events" distribution because it calculates the probability of a rare event occurring in a given period or area.

The main difference between the two distributions is that the binomial distribution is used when there are a fixed number of events or trials. In contrast, the Poisson distribution is used when the number of events is not fixed.
Another difference between the two distributions is that the binomial distribution assumes that the events are independent. In contrast, the Poisson distribution takes that the events occur randomly and independently of each other.

For example, if a company wants to calculate the probability of having a certain number of defects in a batch of products, they would use the Poisson distribution because defects are randomly occurring and independent of each other.
The binomial and Poisson distributions are discrete probability distributions used in statistics and probability theory. Both distributions are essential in various fields of study and have other properties that make them unique. The binomial distribution is used to model the probability of two possible outcomes.

In contrast, the Poisson distribution models the probability of rare events occurring in a fixed period or area.
For example, the binomial distribution can be used in medicine to calculate the probability of a patient responding to a specific treatment. The Poisson distribution can be used in finance to calculate the likelihood of a certain number of loan defaults occurring in a fixed period. Another difference between the two distributions is that the binomial distribution is used when the events are independent. In contrast, the Poisson distribution is used when the events occur randomly and independently.
The binomial and Poisson distributions are different discrete probability distributions used in various fields of study. The main differences between the two distributions are that the binomial distribution is used when there are a fixed number of events. In contrast, the Poisson distribution is used when the number of events is not fixed.

To know more about discrete probability distributions, visit :

brainly.com/question/12905194

#SPJ11

Answer:

0.8 or 0.80

Step-by-step explanation:

Step-by-step explanation:

ans is 2 nd option

first bracket multiply with 7 and second multiply with 2 multiply the sign also carefully.

In this problem

we have an exponential growth function of the form

where

a is the initial value -----> a=1 (one member)

b is the base of the exponential function

substitute the value of a

Find out the value of b

we know that

The membership of an online club is tripling every day

that means

For x=1

the value of y=3

substitute

therefore

The exponential equation

Find out the rate

b=1+r

3=1+r

r=2

r=200%

therefore

The function that models the situation is

where

x is the number of days

y is the number of membership

Answer:

40

Step-by-step explanation:

both angles are corresponding angles which means both are equal

i.e

4x-50 = 2x+30

4x-2x = 50+30

2x = 80

x = 80/2

therefore x = 40

keep smiling

5) We have to find the winner using the Copeland method.

In this method we compare each pair of candidates and see which one is preferred.

The candidate that wins is awarded one point.

If it is a tie, each one gets 1/2 points.

In this case, we have to consider the number of votes per column.

Then, we will have 4!/(2! * 2!) = 24/4 = 6 pairs.

We compare each pair:

-AB:

For the first column: A

For the second column: B

For the third column: A

For the fourth column: B

For the fifth column: B

For the sixth column: A

Then, for A we have 7 + 11 + 12 = 30.

For B we have 10 + 6 + 6 = 22.

Then A earns one point.

For the next pairs we repeat the process:

-AC:

We will directly count the votes for each candidate.

Votes for A: 11 + 6 + 12 = 29.

Votes for C: 7 + 10 + 6 = 23.

Then A earns another point.

-AD:

Votes for A: 7 + 12 = 19

Votes for D: 10 + 11 + 6 + 6 = 33

Then D earns one point.

-BC:

Votes for B: 10 + 6 + 6 + 12 = 34

Votes for C: 7 + 11 = 18

Then B earns one point.

-BD:

Votes for B: 10 + 6 + 12 = 28

Votes for D: 7 + 11 + 6 = 24

Then B earns another point.

-CD:

Votes for C: 7 + 10 +6 + 12 = 35

Votes for D: 10 + 6 = 16

Then C earns a point.

The total points are:

A: 2 points

B: 2 points

C: 1 point

D: 1 point

We have a tie between A and B.

We don't have a rule that is applied to break the tie, but we can look at the pair AB to see which one wins in that case. If we look A > B, so we can consider A to be the winner after the tie.

6) We have to apply the plurality method.

In this case we only look at the first choices.

Then, from the first column, C gets 7 votes.

From the second column, B gets 10 votes.

From the third column, D gets 12 votes.

From the fourth column, B gets another 6 votes.

From the fifth column, D gets another 6 votes.

From the sixth columns, A gets 12 votes.

Then, we can summarize as:

A = 12

B = 10 + 6 = 16

C = 7

D = 12 + 6 = 18

Then, D is the winner according to the plurality method.

Answer:

5) The Copeland's method gives a tie between A and B. We can break the tie comparing the pair (A,B), where A wins over B.

6) The plurality method gives D as the winner.

The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To know more about percentages visit

https://brainly.com/question/32197511

#SPJ11

The area of the domain enclosed by the curve with parametric equations x = tsin t, y = cost, t ∈ [0, 2π] is 2π + 2.

The parametric equations given are:

x = t sin t
y = cos t

To find the area of the domain enclosed by the curve, we can use the formula for the area of a region bounded by a curve given in parametric form:

A = ∫[a,b] y dx

where a and b are the limits of the parameter t that describe the domain of the curve.

In this case, we have:

a = 0
b = 2π

So, we need to compute:

A = ∫[0,2π] cos(t) (t sin(t)) dt

Using integration by parts with u = t and dv = sin(t) dt, we get:

A = [t cos(t)]|[0,2π] - ∫[0,2π] cos(t) dt + ∫[0,2π] sin(t) dt

The first integral evaluates to:

[t cos(t)]|[0,2π] = 2π

The second integral evaluates to:

∫[0,2π] cos(t) dt = [sin(t)]|[0,2π] = 0

The third integral evaluates to:

∫[0,2π] sin(t) dt = [-cos(t)]|[0,2π] = 2

Therefore, the area of the domain enclosed by the curve is:

A = 2π - 0 + 2 = 2π + 2

To learn more about parametric equations go to:

https://brainly.com/question/29275326

#SPJ11