Give an example of a vector such that together with forms a basis of.

Answer: \(26.4\ \text{days}\)

Step-by-step explanation:

Given

Half life of radioactive substance is \(T_{\frac{1}{2}}=20\ \text{days}\)

Initial amount \(A_o=2\ \text{days}\)

Amount left at any time is given by

\(\Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}\)

It takes 26.4 days to reach 2 gm.

Answer:

A

Step-by-step explanation:

use the equation x=4+y/3 to find out.

8x + 2y = 24

2y = -8x + 24

y = -4x + 12.....so the slope is -4, and the y int is 12 or (0,12)

to find the x int, sub in 0 for y and solve for x....in either the original equation or the slope intercept equation

8x + 2y = 24

8x + 2(0) = 24

8x = 24

x = 24/8

x = 3.....so the x int is 3 or (3,0)

now plot ur intercepts (3,0) and (0,12)......now start at ur y int (0,12)...and since ur slope is -4, u come down 4 spaces, then to the right 1 space, then down 4, and to the right 1...keep doing this and u should cross the x axis at (3,0)

Answer:

Step-by-step explanation:

A)212

Therefore, probability solution is estimating this likelihood without additional data or analysis is inappropriate correct response is option a.

The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

Because of the skewed demographic distribution, the right response is (a).

We could use the normally distributed to compute probabilities because the length of adult American ladybirds is distributed normally with a known standard deviation. The normal distribution may not, however, correctly depict the distribution of ladybird lengths in the population due to the skewed population distribution.

Furthermore, even if the difference between the actual community mean and the assumed mean of 1 cm is tiny, the given size of the population of 440000 could result in a statistically significant outcome.

However, because the assumption of normality may not hold true, this does not imply that we can accurately determine the likelihood of a random ladybird in Raleigh being larger than 1.5 centimetres.

Therefore, estimating this likelihood without additional data or analysis is inappropriate.

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Mrs. Adam will use all the water if she camps alone in 24 days. Let's assume that Mr. Adam's water consumption rate per day is represented by "x",Mrs. Adam's water consumption rate per day is represented by "y".

We are given that Mr. Adam alone uses all the water in 12 days, so we can write the equation: 12x = 1 (representing all the water). When Mrs. Adam joins him, they use all the water in 8 days, so we can write the equation: 8(x + y) = 1. Now, we need to find the water consumption rate of Mrs. Adam when she camps alone. Let's represent it as "z". If Mrs. Adam camps alone, she will use all the water in "z" days, so we can write the equation: zy = 1. To find the value of "z", we can rearrange the equations and solve for it: 12x = 1. 8(x + y) = 1. Solving these equations, we can find the values of x and y, and then substitute them into the third equation to solve for z. After solving the equations, we find that x = 1/12 and y = 1/24. Substituting these values into the third equation: (1/24)z = 1. Simplifying the equation, we find: z = 24.

Therefore, Mrs. Adam will use all the water if she camps alone in 24 days.

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The correct option is (C) I and III only. Let's see how:

I. True. In a t-test for a single population mean, increasing the sample size (while everything else remains the same) changes the number of degrees of freedom used in the test. The degrees of freedom for a single population mean t-test is calculated as (sample size - 1), so when the sample size increases, the degrees of freedom also increase.

II. False. In a chi-square test for independence, increasing the sample size (while everything else remains the same) does not change the number of degrees of freedom used in the test. The degrees of freedom in a chi-square test for independence are calculated as (number of rows - 1) x (number of columns - 1), which is not affected by the sample size.

III. True. In a t-test for the slope of the population regression line, increasing the number of observations (while leaving everything else the same) changes the number of degrees of freedom used in the test. The degrees of freedom for a regression slope t-test is calculated as (number of observations - 2), so when the number of observations increases, the degrees of freedom also increase.

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Answer:

543.2 miles

Step-by-step explanation:

Input the given value of x into the equation and solve for y:

y = -67.9x + 679

y = -67.9(2) + 679

y = -135.8 + 679

y = 543.2

The total distance in miles after 2 hours is 543.2 miles.

Answer:

4 or -4

Step-by-step explanation:

The number on top (the numerator) is the absolute value of 8.  This is just asking the distance from 0.  8 is 8 units away from zero, but so is -8.

So the answer could be \(\frac{8}{2}\) or \(\frac{-8}{2}\), the answer simplified would be 4 or -4

Answer:

250

Step-by-step explanation:

150 divided by 3 is 50. Meaning you spend 50 minutes per class. 50 times 5 would be 250.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment.

An observational study is used in fields such as epidemiology, social sciences, psychology, and statistics to draw conclusions from a sample to a population where the independent variable is not under the researcher's control due to ethical concerns or logistical constraints.

Observational studies involve the study of participants who have had no forced change in their circumstances, i.e., no intervention.

Although participants' behavior may change while being observed, the goal of observational studies is to look into the 'natural' state of risk factors, diseases, or outcomes.

Observational studies are those in which researchers examine the impact of a risk factor, diagnostic test, treatment, or other intervention without attempting to change who is or is not exposed to it.

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The situation that probably does not have a lurking variable operating in some way is, option D: Neighborhoods with more station wagons tend to have more playgrounds. So, the correct option is, option D.

This is because it is unlikely that there is a hidden variable that is causing both the presence of station wagons and the presence of playgrounds. It is possible that neighborhoods with more families and children tend to have both more station wagons and more playgrounds, but this is not a hidden variable as it is already known and understood.

In contrast, the other options all involve relationships between variables that could be explained by a hidden variable.

For example, in option A, it is possible that the lurking variable is the weather, which affects both the sales of cold medication and the sales of ice cream.

Similarly, in option E, the lurking variable could be the overall economic health of the town, which affects both the number of teachers and the sales of floor wax and cat litter.

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The smallest resolution for this instrument is 1/256 inches.

This is also the instrument's uncertainty, as it represents the smallest measurable increment.

Let's first understand the terms mentioned:
Slide caliper:

A measuring instrument with a main scale and a vernier scale for taking precise measurements.
Divisions per inch:

The number of equal divisions on the main scale in one inch.
Vernier:

A short auxiliary scale that slides along the main scale, allowing for more precise readings.
Divisions per major division:

The number of equal divisions on the vernier scale that correspond to one division on the main scale.
Now, let's determine the smallest resolution and uncertainty for this instrument.
Calculate the main scale resolution
Main scale resolution = 1 inch / 32 divisions per inch = 1/32 inches
Calculate the vernier scale resolution
Vernier scale resolution = Main scale resolution / Vernier divisions per major division = (1/32 inches) / 8 = 1/256 inches.

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Answer:

around 82.45 cubic cm

Step-by-step explanation:

The formula for the volume of a sphere is (4/3) * pi * r^3.

Since the radius is 2.7, we can plug this into the formula to get (4/3) * pi * 19.683.

This simplifies to 26.244pi, which is around 82.45 cubic cm.

Answer:

x = 15/\(\sqrt{3}\) and y = 30/\(\sqrt{3}\)

Step-by-step explanation:

I just used this trick I remembered from Honors Geometry. I am now in Honors Algebra II w/ Trig. So this trick is what is used for 30-60-90 special right triangles

The best prediction for the number of times you will roll an even number when rolling a 6-sided die 42 times is 21.

When rolling a fair 6-sided die, each outcome (numbers 1 through 6) has an equal probability of occurring. In this case, we are interested in the number of times an even number appears when rolling the die 42 times.

Out of the 6 possible outcomes, half of them (numbers 2, 4, and 6) are even. Therefore, the probability of rolling an even number on a single roll is 3/6, or 1/2.

When rolling the die 42 times, the expected number of times an even number will appear can be calculated by multiplying the probability of rolling an even number on a single roll by the total number of rolls:

Expected number of even rolls = (Probability of rolling an even number) * (Number of rolls)

= (1/2) * 42

= 21

Therefore, the best prediction for the number of times you will roll an even number when rolling a 6-sided die 42 times is 21.

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Answer:

y = 1x + 3

Step-by-step explanation:

Slope (m) =

\( \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \)

Points: (0,3) & (-3,0)

\( \frac{3 - 0}{0 - ( - 3)} \)

\(m = \frac{3}{3} \)

m = 1

y = 1x + b

To find b:

3 = 1(0) + b

3 = b or b = 3

Final Answer: y = 1x + 3

Double Check:

3 = 1(0) + 3

3 = 3

0 = 1(-3) + 3

0 = - 3 + 3

0 = 0

Answer:

y = x + 3

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

Step-by-step explanation:

I won't be answering the question but i will explain how to do it.

So....

.1 is 1/10 of 1.

.3 is 3/10 of 1.

MEANING .1 is smaller than 3.

1/2 is SMALLER than 3/4.

1/2 is equal to 2/4.

.85 is EQUAL to 85/100 rounded up to 9/10 making it larger than numbers such as .79 and 1/2.

PLZ MARK BRAINLIEST!!!

This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Answer:

B. No solutions

Step-by-step explanation:

y= -3x + 9

3y = -9x + 9

Rewrite the first equation below. Then, divide both sides of the second equation by 3 and write it below the first equation.

y = -3x + 9

y = -3x + 3

Now look at the two equations. They are both written in the slope-intercept form, y = mx + b, where m = slope, and b = y-intercept. They have the same slope (m = -3) and different y-intercepts (9 and 3), so they are equations of two different lines, but since the slopes are the same, the lines are parallel. Since the lines never intersect, there is no solution.

Answer: No solutions

Answer:

B

Step-by-step explanation:

Khan

Answer:

\(3.844 * 10 ^ 5\)

Step-by-step explanation:

Scientific notation is of the form \(N * 10^a\). Where N is a number \(1 \leq N < 10\).

So in this case we need to move the decimal place to the left, in order to create such a number.

By moving the decimal place to the left we get: 3.84400

We moved the decimal to the left 5 times, so our value of \(a = 5\) and \(N = 3.84400\)

Therefore scientific notation is: \(3.844 * 10 ^ 5\)

Answer:

-40

Step-by-step explanation:

Let's input x into all of the slots.

\(-2^{2}+-7^{2}+19-6\)

Now, let's solve!

\(-4-49+19-6\)

\(-40\)

So, the answer is -40!

Therefore, one cherry pie costs $0.40 and one pumpkin pie costs $4.20.

To solve the problem, we can use a system of equations. Let's call the cost of one cherry pie "c" and the cost of one pumpkin pie "p".
From the information given, we know:
2c + 6p = 46 (from Jill's sales)
10c + 5p = 50 (from Shayna's sales)
We can simplify these equations by dividing both sides by their respective coefficients:
c + 3p = 23
2c + p = 5
Now we can solve for one of the variables. Let's solve for c using the second equation:
2c + p = 5
2c = 5 - p
c = (5 - p)/2
We can substitute this expression for c into the first equation:
c + 3p = 23
(5 - p)/2 + 3p = 23
5 - p + 6p = 46
5p = 21
p = 4.20
Now that we know p, we can use the expression we found for c to find its value:
c = (5 - p)/2
c = (5 - 4.20)/2
c = 0.40

Therefore, one cherry pie costs $0.40 and one pumpkin pie costs $4.20.

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The correct student's t- distribution requires knowing the degrees of freedom. The degrees of freedom are there for a sample of size n is B) n-1.

Distribution is described as the technique of having items to consumers. An instance of distribution is rice being shipped from Asia to the USA. The frequency of occurrence or quantity of lifestyles.

Distribution manner to spread the product for the duration of the market such that a big quantity of humans should purchase it. Distribution involves doing the following matters. An amazing delivery machine to take the goods into one-of-a-kind geographical regions.

Distribution is one of the four elements of the advertising and marketing mix. Distribution is the method of creating a service or product available for the consumer or enterprise user who needs it. this may be executed without delay through the manufacturer or service company or the usage of indirect channels with vendors or intermediaries.

Disclaimer: The question is incomplete. Please read below to find the missing content.

Question: To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

A) n

B) n-1

C) n+1

D) [X - μ / (s / n)]

The degrees of freedom depends on the number of parameters you are estimating.

8=

i-1

In student t distribution we estimate the population mean through sample mean and population standard deviation through sample standard deviation

So here both parameters depend on the sample mean i.e. we just calculate from a sample of size n so

Degrees of freedom for students t distribution is B) n-1

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The sample 79, 69, 72, 63, 70, 73, 66, 70,54,48 from a normal population with population mean u and population variance o2 the correct answer is (c) 66.4 ± 4.62.

To find the 95% confidence interval for the population mean (μ), we can use the t-distribution since the population standard deviation is unknown.

Given the sample: 79, 69, 72, 63, 70, 73, 66, 70, 54, 48

We first calculate the sample mean  and the sample standard deviation (s).

Sample mean  = (79 + 69 + 72 + 63 + 70 + 73 + 66 + 70 + 54 + 48) / 10 = 664 / 10 = 66.4

Next, we calculate the sample standard deviation (s). Since this is a sample, we use the b estimator for the standard deviation:

s = sqrt((∑(xi - )2) / (n - 1))

= sqrt((∑(79-66.4)2 + (69-66.4)2 + ... + (48-66.4)2) / (10 - 1))

≈ 8.62

Now, we can calculate the confidence interval using the formula:

Confidence Interval =  ± (t * (s / sqrt(n)))

Here, t is the critical value from the t-distribution with (n-1) degrees of freedom for a 95% confidence level. Since n = 10, the degrees of freedom is 9.

Looking up the critical value for a 95% confidence level and 9 degrees of freedom in the t-distribution table, we find t ≈ 2.262.

Substituting the values into the formula:

Confidence Interval = 66.4 ± (2.262 * (8.62 / sqrt(10)))

Calculating this expression, we get approximately:

Confidence Interval ≈ 66.4 ± 4.62

Therefore, the correct answer is (c) 66.4 ± 4.62.

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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Answer:

d) 0.25 divided by 0.42

Step-by-step explanation:

To find the percentage of students who passed the second test,given that they have already passed the first test, you can use the following formula:

\( \small\sf \: percentage \: who \: passed \: both \: tests = \frac{(percentage \: who \: passed \: both \: tests \: and \: first \: test) }{ (percentage \: who \: passed \: first \: test)} \\ \\ \)

Given that 25% of the class passed both tests and 42% of the class passed the first test,

percentage who passed both tests

→ (25%) / (42%)

→ 0.25/0.42

→ 0.595 or 59.5%

Therefore, 59.5% of the students who passed the first test also passed the second test.

Answer:

1.4 pounds

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation:

8x2.8 = 22.4

22.4/16 = 1.4 pound

Answer:

The slope is 3/4 and the y-intercept is -5.

Explanation:

The slope-intercept form of the equation of a line is given as;

where m represents the slope and b represents the y-intercept.

So if we're given the below equation;

To find the slope and y-intercept, all we need to do is to compare the given equation with the standard slope-intercept form of the equation of a line. So if we do that, we'll notice that;

So the slope of the line is 3/4 and the y-intercept is -5.

Answer:

x > 2

Step-by-step explanation:

To solve the inequality 56x - 13 > 113, you can start by isolating the variable on one side of the inequality. Subtract 113 from both sides:

56x - 113 > 0

Next, add 113 to both sides:

56x > 113

Finally, divide both sides by 56:

x > 2

So the solution is x > 2, meaning that x can be any value greater than 2.

Answer:

\(x > \dfrac{9}{4} \\\\\)

or

x > 2.25

This does not fit any of the provided answer choices. Either the inequality is copied wrong or the answer choices are copied wrong

Step-by-step explanation:

The inequality is 56x - 13 > 113

Add 13 to both sides:
56x - 13 + 13 = 113 + 13

56x > 126

Divide by 56 both sides
\(\dfrac{56x}{56} > \dfrac{126}{56}\)

Reducing the above fraction to lowest by dividing numerator and denominator by 14 to get:
\(x > \dfrac{126 \div 14}{56\div 14}\\\\x > \dfrac{9}{4}\)

None of your answer choices fit. So not sure whether the inequality given is incorrectly copied/pasted or the answer choices are.

The closest this comes to is x > 2 but the inequality will not be satisfied for any value of x between 2(excluded) and 2.25(included)

Answer:

92

Step-by-step explanation:

Answer:

52.5

Step-by-step explanation: