A team of 10 people swim equal portions of a 10 km relay. What distance does each person swim?

Answer:

No

Step-by-step explanation:

But as we've stated, these prime factorizations are unique, so this can't be right. Therefore 21≠a2 , so a≠√21 , meaning that our earlier assumption of √21 being rational turns out to be wrong, therefore √21 is irrational.

Answer: y=4x-4

Step-by-step explanation:

To find the equation fo the line parallel to the given line, we can use the given point to find the y-intercept. We know that the slope must stay the same because parallel lines NEVER touch or cross. This means that the slope MUST be the same.

y=4x+b

We can use the given point to find the y-intercept.

8=4(3)+b             [multiply]

8=12+b                [subtract both sides by 12]

b=-4

Now that we have found the y-intercept, we can complete the equation.

y=4x-4

Answer:

The response variable is the episodes of pain reported

Step-by-step explanation:

A response variable, also known as the dependent variable or explanatory variable, is the variable that is not under the direct control of the researcher, but whose value varies with the changing of the independent variable. The response variable is the focus of the experimental question.

In this example, the effect of the drug hydroxyurea is to be tested on sickle-cell patients, hence the drug used is the independent variable, because the experimenter can choose to give the subjects either hydroxyurea or a placebo, hence it is under the direct control of the experimenter. However, the result ( differences in episodes of pain) is a response to the administered drug or placebo.

Answer:

[tex]\huge\boxed{m = \frac{y-b}{x}}[/tex]

Step-by-step explanation:

In order to solve for [tex]y=mx+b[/tex] and we want to solve for [tex]m[/tex], we want to get m on one side of the equation.

[tex]y = mx+b[/tex]

Let’s subtract b from both sides.

[tex]y - b = mx[/tex]

Now we can divide both sides by x so we have m on one side of the equation.

[tex]\frac{y-b}{x} = m[/tex]

Hope this helped!

It looks like the system is supposed to be

[tex]\mathbf x'=\begin{bmatrix}0&-1\\2&3\end{bmatrix}\mathbf x+\begin{bmatrix}e^t\\e^{-t}\end{bmatrix}[/tex]

with the initial condition, [tex]\mathbf x(0)=\begin{bmatrix}5&4\end{bmatrix}^\top[/tex].

Compute the eigensystem for the coefficient matrix:

[tex]\begin{vmatrix}-\lambda&-1\\2&3-\lambda\end{vmatrix}=\lambda^2-3\lambda+2=(\lambda-1)(\lambda-2)=0[/tex]

[tex]\lambda_1=1\implies\begin{bmatrix}-1&-1\\2&2\end{vmatrix}\mathbf v_1=\mathbf 0\implies\mathbf v_1=\begin{bmatrix}1\\-1\end{bmatrix}[/tex]

[tex]\lambda=2\implies\begin{bmatrix}-2&-2\\2&1\end{bmatrix}\mathbf v_2=\mathbf 0\implies\mathbf v_2=\begin{bmatrix}1\\-2\end{bmatrix}[/tex]

So we have the characteristic solution,

[tex]\mathbf x_c=C_1e^{\lambda_1t}\mathbf v_1+C_2e^{\lambda_2t}\mathbf v_2[/tex]

[tex]\mathbf x_c=C_1e^t\begin{bmatrix}1\\-1\end{bmatrix}+C_2e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}[/tex]

For the non-homogeneous part, we can guess a particular solution of the form

[tex]\mathbf x_p=te^t\begin{bmatrix}a\\b\end{bmatrix}[/tex]

(We might have started with [tex]e^t[/tex] instead, but that is already accounted for in the first characteristic solution.)

Its derivative is

[tex]{\mathbf x_p}'=e^t\begin{bmatrix}a\\b\end{bmatrix}+te^t\begin{bmatrix}a\\b\end{bmatrix}=e^t\begin{bmatrix}at+a\\bt+b\end{bmatrix}[/tex]

Substitute [tex]\mathbf x_p[/tex] into the system and solve for [tex]a,b[/tex]:

[tex]e^t\begin{bmatrix}at+a\\bt+b\end{bmatrix}=te^t\begin{bmatrix}0&-1\\2&3\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}+e^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]

[tex]\begin{bmatrix}at+a\\bt+b\end{bmatrix}=\begin{bmatrix}-bt+1\\(2a+3b)t-1\end{bmatrix}[/tex]

[tex]\implies a=1,b=-1[/tex]

and so the particular solution is

[tex]\mathbf x_p=te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]

The general solution to the system is then

[tex]\mathbf x=\mathbf x_c+\mathbf x_p[/tex]

[tex]\mathbf x=C_1e^t\begin{bmatrix}1\\-1\end{bmatrix}+C_2e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}+te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]

Use the given initial conditions to solve for the remaining coefficients.

[tex]\mathbf x(0)=\begin{bmatrix}5\\4\end{bmatrix}[/tex]

[tex]\implies\begin{bmatrix}5\\4\end{bmatrix}=C_1\begin{bmatrix}1\\-1\end{bmatrix}+C_2\begin{bmatrix}1\\-2\end{bmatrix}[/tex]

[tex]\implies C_1=14,C_2=-9[/tex]

Then the solution to the initial value problem is

[tex]\mathbf x=14e^t\begin{bmatrix}1\\-1\end{bmatrix}-9e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}+te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]

[tex]\mathbf x=\begin{bmatrix}14e^t-9e^{2t}+te^t\\-14e^t-18e^{2t}-te^t\end{bmatrix}[/tex]

Answer:

210

Step-by-step explanation:

We can get 10% of 300 by doing 300 / 10 which is 30. 70 / 10 is 7, so we need 7 lots of 10% to work out 70%. Therefore, 30 * 7 students said that their favourite colour was blue, which is 210.

Answer:

210

Step-by-step explanation:

So 70% OF 300 students said their favorite color was blue

OF means multiply and 70% is equal to .70 so,

.70 x 300 = the number of students that said their favorite color was blue

                =210

So, the number of students that said their favorite color was blue is 210 students. :)

Answer:

18/40

Step-by-step explanation:

You multiply the denominator by 2 and the numerator by 2 to get 18/40

Answer:

x=w/(56+r)

Step-by-step explanation:

19x+rx=-37x+w

19x+rx+37x=w

x(19+37+r)=w

x(56+r)=w

x=w/(56+r)

if anything is unclear, ask freely.

Answer:

Step-by-step explanation:

[tex]3 - (-3) + 7 - 4 =\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:\\\\\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a\\\\-\left(-3\right)=+3\\\\=3+3+7-4\\\\3+3=6\\\\=6+7-4\\\\6+7=13\\\\=13-4\\\\13-4\\=9[/tex]

Answer:

the blanks are in this order the top two are 5 and 8

then (-,+,+)

then (-,-,+)

then (+,+,+)

last (+,-,+)

Step-by-step explanation:

Answer:

The actual triangle is larger

Step-by-step explanation:

Given

[tex]Scale = Actual Triangle : Drawing[/tex]

[tex]Scale = 30 : 1[/tex]

[tex]Jorge = 101[/tex]

Required

Determine which is bigger

The answer to this question can be extracted from the given scale.

The question says: the scale from the actual triangle to the drawing is 30 : 1.

This implies that;

If Jorge's drawing is 101, then the actual length is 30 * 101 =3030

Since, 3030 > 30, then

We cam conclude that the actual triangle is bigger

Answer:

Step-by-step explanation:

(9-6)/2 = 3/2 = 1.5

(-8-3)/2 = -11/2 = -5.5

(1.5, -5,5)

Answer:

[tex]15[/tex] inches

Step-by-step explanation:

Let the width be x.

Length = [tex]6+x[/tex]

Perimeter = Length + Length + Breadth + Breadth

Perimeter = [tex](6+x)+(6+x)+x+x=48[/tex]

[tex]6+x+6+x+x+x=48[/tex]

[tex]4x+12=48[/tex]

Subtract 12 from both sides:

[tex]4x+12-12=48-12[/tex]

[tex]4x=36[/tex]

Divide both sides by 4:

[tex]\frac{4x}{4}=\frac{36}{4}[/tex]

[tex]x=9[/tex] (Width)

Length = [tex]9+6=15[/tex] inches.

Answer:

l = 15 inches

Step-by-step explanation:

l = w + 6

p = 2l + 2w

substitute l into equation p

48 = 2(w + 6) + 2w

distribute the 2 into the parentheses

48 = 2w + 12 + 2w

combine like terms

48 = 4w + 12

subtract 12 from both sides

36 = 4w

divide by 4

9 = w

plug w into equation l

(9) + 6 = 15

l = 15 inches

Factor the x out first:

x(6x^2 - 7x - 5) = 0

Then factor the quadratic expression in the parenthesis:

x(2x + 1)(3x - 5) = 0

x = -1/2, 0, 5/3

Answer:60+1260+13 isnt equivalent

Step-by-step explanation:

Answer:14in 3

Step-by-step explanation:

Answer:

4.24

Step-by-step explanation:

Answer:

18.29

Step-by-step explanation:

hope this helped

Answer:

Listening

Step-by-step explanation:

The others are good qualities too, but first you need to listen to other people and have them listen to you. It's one of the first steps of communicating well with other people.

Answer:

The probability of having two boys = 25%

Step-by-step explanation:

The ordered sample space for two kids is given as S =  {bb, bg, gb, gg},

where bb = two boys, bg = a boy and a girl, gb = a girl and a boy, and gg = two girls, in that particular order.

bb occurs 1/4 times

and 1/4 = 0.25 or 25%

Calculating the probability of having two boys is given as the probability of having a boy multiplied by the probability of having a boy

= 0.5 x 0.5

= 0.25

= 25%

This agrees with the ordered sample space given above.

Answer: The answers to the questions by 10 of the friends

Step-by-step explanation:

The options to the question are:

a. The answers to the questions by the parents of 10 of the friends.

b. The results of a national poll of 1800 students in the same age group as the child.

c. The answers to the questions by 10 of the friends.

d. The answers to the questions by 10 people from the parents office.

From the question, we are informed that a concerned parent wants to determine the amount of time spent on the phone by her child's friends. The sample that is likely to bias the results of the study by reporting less than the actual time is the answers to the questions by 10 of the friends.

This is because since the questions are being asked from her friends, there'll be bias as the friends won't want to give the exact time used on phone, hence, they'll hold back some information.

Answer:

Luke, -32 < 36

Step-by-step explanation:

The two cards drawn by Sofia has values of -8 and 4 respectively. The product of her cards = -8 × 4 = -32. (Negative × positive = (negative)

The two cards drawn by Luke has values of -6 and -6 respectively. The product of his cards = -6 × -6 = 36 (negative × negative = positive).

36 greater than -32.

Luke had the largest product because -32 < 36.

Answer:

The answer is 57.

Step-by-step explanation:

You have to substitute w = 2 into the expression :

[tex]8 {w}^{2} + 8w + 9[/tex]

[tex]let \: w = 2[/tex]

[tex]8 {(2)}^{2} + 8(2) + 9[/tex]

[tex] = 32 + 16 + 9[/tex]

[tex] = 57[/tex]

Answer:

57

Step-by-step explanation:

[tex]8*2^{2}+8*2+9\\8*4+16+9\\32+16+9\\48+9\\57[/tex]

Answer:

B' is at (2.76,-4.9)

Equation of CC' is 11.38x+4.55y= -31.86

or at its slope-intercept form:

y= (-11.38x - 31.86)/4.55

Step-by-step explanation:

Answer:

c best shows the best relationship

Answer: 169.2 per acre are produced if a field is in the top 25%.

Step-by-step explanation:

Given:  The mean rain-fed corn yield of harvested fields are normally  distributed, produce 147.2 bushels per acre with a standard deviation of 33 bushels per acre.

Let X denote the mean rain-fed corn yield of harvested fields.

Let x denotes the number of bushels per acre are produced if a field is in the top 25%.

Top 25% on a density curve means , (100-25%)i.e. 75% area lies below x.

I.e.

[tex]P(X<x)=P(\dfrac{X-\mu}{\sigma}<\dfrac{x-147.2}{33})=0.75\\\\\Rightarrow\ P(Z<\dfrac{x-147.2}{33})=0.75\ \ [Z=\dfrac{X-\mu}{\sigma}][/tex].

Z-score for p-value of 0.75 (one tailed)=0.67 [By z-table]

Then, [tex]\dfrac{x-147.2}{33}=0.6744[/tex]

[tex]\Rightarrow\ {x-147.2}=33\times0.67\\\\\Rightarrow\ {x-147.2}=22.11\\\\\Rightarrow\ {x}=22.11+147.2=169.31[/tex]

Here approx value is 169.2 (from options).

So, 169.2 per acre are produced if a field is in the top 25%.

Answer:

A. 85

Step-by-step explanation:

Since DE and XY are parallel, this means that the given angle and angle x are alternate Angles. According to the law of alternate Angles, this means that they are equal. It also makes sense as the angle x is the same angle as the angle directly opposite angle 85. This is because they are on the same line across parallel lines. This also means they are equal because vertically opposite angles are always equal.

Therefore x =85

Hope this helped!

lol.Sorry I have to hurry up so my hand writing is bad i hope u can read it.