Solve the initial value problem:
y''' - y' = 0 ; y(0) =2 , y'(0) = 3 , y''(0) = -1

This statement is false because the sample variance is always greater than or equal to the sample standard deviation.

Variance and standard deviation are both measures of variability or dispersion within a dataset. The sample variance is defined as the average of the squared differences between each data point and the mean of the dataset. On the other hand, the sample standard deviation is the square root of the variance.

Since variance involves squaring the differences, it accounts for the spread of the dataset more effectively than the standard deviation. As a result, the sample variance tends to be larger than or equal to the sample standard deviation.

Mathematically, this relationship can be expressed as follows:

Sample Variance = [tex]\[\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}\][/tex]

Sample Standard Deviation = [tex]\[\sqrt{\frac{{\sum_{i=1}^{n} (x_i - \overline{x})^2}}{{n - 1}}}\][/tex]

Where x represents each data point, [tex]\(\overline{x}\)[/tex] represents the mean, and n is the sample size.

Therefore, it is not possible for the sample variance to be smaller than the sample standard deviation.

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Answer:

c maybe

Step-by-step explanation:

4n(6n+2m)

24n²+8mn

Answer: C, 24n²+8mn

Step-by-step explanation:

So because 4n is on the outside of the bracket, you have to times everything on the inside of the bracket by 4n.

So, you do:

4n×6n=24n² (4×6=24 and n×n=n²)

4n×2m=8mn (4×2=8 and n×m=mn)

Then you add 24n² to 8mn like this:

24n²+8mn

Hope this helps :)

Answer:

12 miles

tep-by-step explanation:

1 inch  is 4 miles  4 times 3 inches ls 12

Answer:

answer is 16

good day mate

Ответ:​

Объяснение:

Probability of an event happening = Number of ways it can happen / Total number of outcomes

Number of ways it can happen: 1 (there is only 1 group with french team in it)

Total number of outcomes: 4 (there are 4 groups)

So the probability = 1/4

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Вероятность возникновения события = Количество способов которыми это может произойти / Общее количество исходов

Количество способов которыми это может произойти: 1 (есть только 1 группа с французской командой в ней)

Общее количество исходов: 4 (есть 4 группы)

Таким образом вероятность = 1/4

Я надеюсь, что это было полезно ^^

Answer:

2/5

Step-by-step explanation:

Since 4 out of 10 students are juniors, you can express this with the fraction 4/10. 4/10 can then be simplified to 2/5.

Answer:

x ≈ 5.1

Step-by-step explanation:

Using the sine ratio in the right triangle

sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{12}[/tex] ( multiply both sides by 12 )

12 × sin25° = x , that is

x≈ 5.1 ( to the nearest tenth )

Answer: V = 891 feet cubed

Step-by-step explanation:

Answer: R = 12*9 = 108*7.5 = 810ft

T = 12*9*1.5 = 162/2 = 81 ft

810+81 = 891ft^3

Step-by-step explanation:

Give other person brainiest.

if x+y=19

and

x-y=1

now solve it by adding the equations together

x+x , y+[-y] and 19+1

2x=20

x=10, y=9

Answer:

I think they charge a flat rate of $8 for a vehicle and $3 per person on top of that.

Step-by-step explanation:

There could be a multitude of rules, but let's try to find a simple one.

I would start by assuming that the park charges a fee for a vehicle and then for each person. Let's name those:

a - flat fee for a vehicle

b - fee per person

then a car with x people in it would be charged

a + bx

Let's see if the fees fit this assumption:

for x = 2

a + b*2 = $14

for x = 4

a + b*4 = $20

for x = 8

a + b*8 = $32

If so, we can subtract the second equation from the first and get

a + b*4 - a - b*2 = $20 - $14

b*2 = $6

b = 3$

a + b*2 = $14

a + $3*2 = a + $6 = $14

a = $8

so the first 2 equations gave us a = $8 and b = $3.

Let's see if these values fit the 3rd equation

a + b*8 = $32

$8 + $3*8 = $32

$8 + $24 = $32

$32 = $32

It fits!

That tells us that the rule is indeed very likely.

Answer:

1/3

Step-by-step explanation:

15/(15+18+12)=15/45=1/3

Answer:

Solution in photo

(a) If A is an invertible matrix, then A is an invertible matrix. - True

Explanation:

If A is invertible, then A has an inverse matrix A^(-1).

(b) If A is an invertible matrix, then A+ A is an invertible matrix. - False

Explanation:

A+ A = 2A is invertible if and only if A is invertible.

Therefore, this statement is false.

(c)

If A and B are n x n matrices, such that AB is invertible, then it follows that B is invertible. - False

Explanation:

Even if AB is invertible, it is not always true that B is invertible.

For instance, if A = [1 0], B = [0 1],

then AB = [0 1] which is invertible, but B is not invertible.

(d)

If A and B are n x n invertible matrices, then it follows that A - B must be an invertible matrix. - False

Explanation:

If A = [2 0], B = [0 1], then both A and B are invertible, but A - B = [2 -1] is not invertible.

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The value of dw/dt is  [tex]e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]

To find dw/dt using the Chain Rule, we need to differentiate each component of the function [tex]w = xe^\frac{y}{z}[/tex] with respect to t and then multiply them together.

Given:

[tex]w = xe^\frac{y}{z}[/tex]

x = t⁷

y = 6 - t

z = 4 + 9t

Let's find dw/dt step by step:

x = t⁷

Taking the derivative of x with respect to t:

dx/dt = 7t⁶

y = 6 - t

Taking the derivative of y with respect to t:

dy/dt = -1

z = 4 + 9t

Taking the derivative of z with respect to t:

dz/dt = 9

[tex]w = xe^\frac{y}{z}[/tex]

Taking the derivative of w with respect to x:

[tex]\frac{dw}{dx} =e^\frac{y}{z}[/tex]

[tex]w = xe^\frac{y}{z}[/tex]

Taking the derivative of w with respect to y:

[tex]\frac{dw}{dy} = (\frac{x}{z} )e^\frac{y}{z}[/tex]

[tex]w = xe^\frac{y}{z}[/tex]

Taking the derivative of w with respect to z:

[tex]\frac{dw}{dz} = (\frac{-xy}{z^2} )e^\frac{y}{z}[/tex]

Apply the Chain Rule to find dw/dt:

dw/dt = (dw/dx)(dx/dt) + (dw/dy)(dy/dt) + (dw/dz)(dz/dt)

Substituting the derivatives we found earlier:

dw/dt [tex]= (e^\frac{y}{z})(7t^6) + (\frac{x}{z} )e^\frac{y}{z}(-1) + (\frac{-xy}{z^2} )e^\frac{y}{z}(9)[/tex]

dw/dt [tex]= e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]

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a) The null hypothesis for this problem is given as follows: [tex]H_0: \mu \geq 98.3[/tex]

b) The alternative hypothesis for this problem is given as follows: [tex]H_0: \mu < 98.3[/tex]

The claim for this problem is given as follows:

"The mean body temperature of healthy animals is less than 98.3°F.".

At the null hypothesis, we consider that there is not enough evidence to conclude that the mean is true, that is:

[tex]H_0: \mu \geq 98.3[/tex]

At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is true, that is:

[tex]H_0: \mu < 98.3[/tex]

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Answer:

2/13

Step-by-step explanation:

P(Red,Blue) = 4/14 × 7/13

simplified it becomes 2/13

Answer: k= 10,-3 j=10,-8 L=5,-9 please give me the brainliest if you want to

Step-by-step explanation:

Given:

The shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.

Radius of the circle = 3 cm

To find:

The area of the sector in terms of π.

Solution:

The area of a circle is

[tex]A=\pi r^2[/tex]

Substituting [tex]r=3[/tex], we get

[tex]A=\pi (3)^2[/tex]

[tex]A=9\pi[/tex]

It is given that the shaded sector above covers [tex]\dfrac{1}{3}[/tex] of the circle.

The area of shaded sector [tex]=\dfrac{1}{3}A[/tex]

                                             [tex]=\dfrac{1}{3}(9\pi)[/tex]

                                             [tex]=3\pi[/tex]

Therefore, the area of shaded sector is 3π sq. cm.

The probabilities using Binomial Expansion is

A) P(X = 4) = C(160, 4)  p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾

B) P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾

C) P(X = 2) = C(160, 2)  p² (1 - p)⁽¹⁶⁰⁻²⁾

D) P(X = 1) = C(160, 1)  p¹ (1 - p)⁽¹⁶⁰⁻¹⁾

E) P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾

To determine the theoretical probability of the five possible combinations between females and males in the 160 families, we can use the binomial expansion formula:

P(X = k) = C(n, k) [tex]p^k(1-p)^{n-k}[/tex]

Where:

C(n, k) is the binomial coefficient, calculated as n! / (k! * (n - k)!).

p is the probability of success

(1 - p) is the probability of failure.

Let's calculate the probabilities for each combination:

A) 4 males, 0 females:

P(X = 4) = C(160, 4)  p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾

B) 3 males, 1 female:

P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾

C) 2 males, 2 females:

P(X = 2) = C(160, 2)  p² (1 - p)⁽¹⁶⁰⁻²⁾

D) 1 male, 3 females:

P(X = 1) = C(160, 1)  p¹ (1 - p)⁽¹⁶⁰⁻¹⁾

E) 0 males, 4 females:

P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾

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Step-by-step explanation:

1

A student made 6 bows from 12 yards of ribbon. How many bows can be made from 3

2

yards of ribbon?

2

D A bag of almonds weighs 1-pounds.

Answer:

32 degrees.

Step-by-step explanation:

Answer:

Sorry, I was on my phone. Its (2,3)

Step-by-step explanation:

Answer:

(2,3) is the answer

Step-by-step explanation:

The researcher can conclude that there is a statistically significant difference in the mean number of complaints between people living on the West Coast and those living in the Northeast.

To determine if there are geographical differences in how much people complain between the Northeast and the West Coast, we can conduct a hypothesis test.

Null hypothesis (H0): There is no difference in the mean number of complaints between the Northeast and the West Coast.

Alternative hypothesis (H1): There is a difference in the mean number of complaints between the Northeast and the West Coast.

Given the sample statistics, we can perform a two-sample independent t-test to compare the means of the two groups.

Let's calculate the test statistic and compare it to the critical value at a significance level of α = 0.05.

The West Coast sample has a mean (x1) of 9.5 and a standard deviation (s1) of 2.8, with a sample size (n1) of 20.

The Northeast sample has a mean (x2) of 15.5 and a standard deviation (s2) of 3.8, with a sample size (n2) of 20.

Using the formula for the pooled standard deviation (sp), we can calculate the test statistic (t):

sp = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

t = (x1 - x2) / (sp * sqrt(1/n1 + 1/n2))

Calculating the test statistic:

sp = sqrt(((19 * 2.8^2) + (19 * 3.8^2)) / (20 + 20 - 2)) ≈ 3.273

t = (9.5 - 15.5) / (3.273 * sqrt(1/20 + 1/20)) ≈ -4.63

Using a t-table or a statistical calculator, we can find the critical value for a two-tailed t-test with α = 0.05 and degrees of freedom (df) = n1 + n2 - 2 = 38. The critical value is approximately ±2.024.

Since the absolute value of the test statistic (4.63) is greater than the critical value (2.024), we reject the null hypothesis.

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Step-by-step explanation:

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