Consider the equations y = VI and y
32 – 1.
The system of equations is equal at approximately

Answer:

0.0158 = 1.58% probability that all of them are under 18.

Step-by-step explanation:

Probability of independent events:

If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B \cap C) = P(A)P(B)P(C)[/tex]

The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.

This means that [tex]P(A) = 0.235, P(B) = 0.258, P(C) = 0.26[/tex]

If one person is selected from each city, what is the probability that all of them are under 18?

Since the three people are independent:

[tex]P(A \cap B \cap C) = 0.235*0.258*0.26 = 0.0158[/tex]

0.0158 = 1.58% probability that all of them are under 18.

Answer:

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.5, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 1.9 feet.

This is the p-value of Z when X = 1.9. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.9 - 2.5}{0.4}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a p-value of 0.0668

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Answer:

B. -3

Step-by-step explanation:

Answer:

The  weight that separate the top 8% by 5.2605 and the weight that separate bottom 8% by 5.1195.

Step-by-step explanation:

We are given that

Mean,[tex]\mu=5.19[/tex]

Standard deviation,[tex]\sigma=0.05[/tex]

We have to find the two weights that separate the top 8% and the bottom 8%.

Let x1 and x2 the two weights that separate the top 8% and the bottom 8%.

Z-value for p-value =0.08 =[tex]-1.41[/tex]

For 8% bottom

[tex]Z=\frac{x_1-\mu}{\sigma}=-1.41[/tex]

[tex]\frac{x_1-5.19}{0.05}=-1.41[/tex]

[tex]x_1-5.19=-1.41\times 0.05[/tex]

[tex]x_1=-1.41\times 0.05+5.19[/tex]

[tex]x_1=5.1195[/tex]

For 8% top

p-Value=1-0.08=0.92

Z- value=1.41

Now,

[tex]\frac{x_2-5.19}{0.05}=1.41[/tex]

[tex]x_2-5.19=1.41\times 0.05[/tex]

[tex]x_2=1.41\times 0.05+5.19[/tex]

[tex]x_2=5.2605[/tex]

(x1,x2)=(5.1195,5.2605)

You'll need 2 more lines to complete this two column proof.

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

Line 4

For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

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

Line 5

The statement is what you want to prove since this is the last line.

So the statement is [tex]p || q[/tex]

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

Answer:

ai) 5pi

aii) 4.5pi

aiii) 4.1pi

b) 4pi

Step-by-step explanation:

a) Area of a circle is given by pi×r^2.

The average rate of change of the area of a circle from r=b to r=a is (pi×b^2-pi×a^2)/(b-a).

Let's simplify this.

Factor pi from the terms in the numerator:

pi(b^2-a^2)/(b-a)

Factor the difference of squares in the numerator:

pi(b-a)(b+a)/(b-a)

"Cancel" common factor (b-a):

pi(b+a).

So let's write a conclusive statement about what we just came up with:

The average rate of change of the area of a circle from r=b to r=a is pi(b+a).

i) from 2 to 3 the average rate of change is pi(2+3)=5pi.

ii) from 2 to 2.5 the average rate of change is pi(2+2.5)=4.5pi.

from 2 to 2.1 the average rate of change is pi(2+2.1)=4.1pi.

b) It looks like a good guess at the instantaneous rate of change is 4pi following what the average rate of change of the area approached in parts i) through iii) as we got closer to making the other number 2.

Let's confirm by differentiating and then plugging in 2 for r.

A=pi×r^2

A'=pi×2r

At r=2, we have A'=pi×2(2)=4pi. It has been confirmed.

Answer:

A. -¾ + 0 = -¾

B. -¾ - ¾ = -(¾ + ¾)

C. ¾ - ¾ = ¾ + (-¾)

E. -¾ + ¾ = ¾ + (-¾)

F. -¾ + ¾ = 0

Step-by-step explanation:

Let's check each equation to determine whether they are true or false.

If what we have in the both sides are equal, then the equation is true, if they're not, them it is false.

✔️-¾ + 0 = -¾

Add everything on your left together

-¾ = -¾ (TRUE)

✔️-¾ - ¾ = -(¾ + ¾)

Add everything on both sides together respectively

(-3 - 3)/4 = -(3 + 3)/4

-6/4 = -6/4 (TRUE)

✔️¾ - ¾ = ¾ + (-¾)

0 = ¾ - ¾ (+ × - = -)

0 = 0 (TRUE)

✔️-¾ + ¾ = ¾ - (-¾)

0 = ¾ + ¾ (- × - = +)

0 = 6/4 (FALSE)

✔️-¾ + ¾ = ¾ + (-¾)

0 = ¾ - ¾ (+ × - = -)

0 = 0 (TRUE)

✔️-¾ + ¾ = 0

0 = 0 (TRUE)

Answer:

The measure of the smallest angle is 30º

Step-by-step explanation:

Let the angles be:

[tex]x \to[/tex] the first angle (the smallest)

[tex]y \to[/tex] the second angle

[tex]z \to[/tex] the third angle

So, we have:

[tex]y = 2x[/tex]

[tex]z=x + 60[/tex]

Required

Find x

The angles in a triangle is:

[tex]x + y +z = 180[/tex]

Substitute values for y and z

[tex]x + 2x +x + 60 = 180[/tex]

[tex]4x + 60 = 180[/tex]

Collect like terms

[tex]4x = 180-60[/tex]

[tex]4x = 120[/tex]

Divide by 4

[tex]x = 30[/tex]

Answer:

12x2 – 75 = 3 (2x+5)(2x – 5)

Step-by-step explanation:

Answer:

Line 3

Step-by-step explanation:

→ Calculate gradient

[tex]\frac{6-3}{4-2} =1.5[/tex]

Answer:

Line 3

Step-by-step explanation:

(0,0) & ( 4 , 6)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{6-0}{4-0}\\\\=\frac{6}{4}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]

Answer: Is reinforced with other material

Step-by-step explanation:

The options are:

A is expensive to build.

B usually cracks under heavy weights.

C looks like any other road.

D is reinforced with other material.

The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.

Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.

Answer:

a. 8.95

b. it is

c. yes it belongs

d. males are 2.574 taller than females on average.

Step-by-step explanation:

GIven the regression outpuit that we have in this question, the value of the t test statistics for the shoe size can be solved as

a. test statistic = 1.164/0.13

t test = 8.95

b. the regression coefficient of shoe size is 1.164, this is statistically significant

c. Yes the variable shoe size does belong to the model.

d. The regression coefficient of gender shows that on the average, while holding other variables constant, males are 2.574 inches taller than the their female counterparts.

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Answer:

B

Step-by-step explanation:

because

Answer:

12

Step-by-step explanation:

First lets list all the factors of these numbers

72: 1,2 3,4,6,8,9,12,18,24,36,72

84: 1 , 2 , 3 ,4 , 6 , 7 , 12 , 14 ,  21 , 28 , 42 , 84

Now lets find the biggest number that is a factor of both 84 and 72  

as we can see the highest number that is the factor of both 84 and 72 is 12

12 is the hcf

Answer:

RM 1200 kalau ada gambar cuba insert

Answer:

The correct answer is =6.

Step-by-step explanation:

Solution,

Given;

11−17=49

or,11n-17=49

or,11−17+17=49+17

or,11=66

or,n=66/11

#n=6

HOPE IT HELPED♥︎

Step-by-step explanation:

Given that,

The mass of a patient = 70 kg

A 70kg patient has approximately 8 pints of blood.

The patient donates 470mL of blood.

We know that,

1 pint = 568 mL

8 pints = 4544 mL

Required fraction,

[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]

So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].

Answer:

.

Step-by-step explanation:

.

Answer: just had this problem! X = 11

Finding the line of best fit is something a Machine Learning Model would do.

This particular ML model is called "Linear Regressor" or "Linear Regression Model". Look it up and there are definitely calculators for it, as it is relatively simple.

You can also, if you know how to use ML libraries and code, use Python to determine the value of [tex]b[/tex].

Hope this helps.

Answer:

y = 5/4 x - 23/4

Step-by-step explanation:

4x + 5y = 31

5y = - 4x +31

y = -4/5 x + 31/5

⊥ slope = 5/4

-7 = 5/4 (-1) + B

-28 = -5 + 4b

-23 = 4B

b = -23/4

Answer:

upper bound for the error, | Error |  ≤ 0.0032

Step-by-step explanation:

Given the data in the question;

[tex]e^{0.4[/tex] < e < 3

Using Taylor's Error bound formula

| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]

where m = [tex]| f^{N+1 }(x) |[/tex]

so we have

| Error |  ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]

| Error |  ≤ ( 0.125 ) 0.0256

| Error |  ≤ 0.0032

Therefore, upper bound for the error, | Error |  ≤ 0.0032

Answer:

The quadrilateral is a rhombus

Step-by-step explanation:

Given

[tex]A = (2, 8)[/tex]

[tex]B = (3, 11)[/tex]

[tex]C = (4, 8)[/tex]

[tex]D=(3, 5)[/tex]

Required

The true statement

Calculate slope (m) using

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Calculate distance using:

[tex]d= \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]

Calculate slope and distance AB

[tex]m_{AB} = \frac{11 - 8}{3 - 2}[/tex]

[tex]m_{AB} = \frac{3}{1}[/tex]

[tex]m_{AB} = 3[/tex] -- slope

[tex]d_{AB}= \sqrt{(3 - 2)^2 + (11 -8)^2}[/tex]

[tex]d_{AB}= \sqrt{10}[/tex] -- distance

Calculate slope and distance BC

[tex]m_{BC} = \frac{8 - 11}{4 - 3}[/tex]

[tex]m_{BC} = \frac{- 3}{1}[/tex]

[tex]m_{BC} = -3[/tex] -- slope

[tex]d_{BC} = \sqrt{(4-3)^2+(8-11)^2[/tex]

[tex]d_{BC} = \sqrt{10}[/tex] --- distance

Calculate slope CD

[tex]m_{CD} = \frac{5 - 8}{3 - 4}[/tex]

[tex]m_{CD} = \frac{- 3}{- 1}[/tex]

[tex]m_{CD} = 3[/tex] -- slope

[tex]d_{CD} = \sqrt{(3-4)^2+(5-8)^2}[/tex]

[tex]d_{CD} = \sqrt{10}[/tex] -- distance

Calculate slope DA

[tex]m_{DA} = \frac{8 - 5}{2 - 3}[/tex]

[tex]m_{DA} = \frac{3}{- 1}[/tex]

[tex]m_{DA} = -3[/tex] -- slope

[tex]d_{DA} = \sqrt{(2-3)^2 + (8-5)^2}[/tex]

[tex]d_{DA} = \sqrt{10}[/tex]

From the computations above, we can see that all 4 sides are equal, i.e. [tex]\sqrt{10}[/tex]

And the slope of adjacent sides are negative reciprocal, i.e.

[tex]m_{AB} = 3[/tex]  and [tex]m_{CD} = -3[/tex]

[tex]m_{CD} = 3[/tex] and [tex]m_{DA} = -3[/tex]

The quadrilateral is a rhombus

Answer:

1) x = 2

Step-by-step explanation:

Hope it helps. I'll try to solve the second one too

9514 1404 393

Answer:

Step-by-step explanation:

1. Substitution can work for this.

  2x +3(4x -5) = 13

  14x = 28 . . . . . add 15

  x = 2 . . . . . . . divide by 14

__

2. The equation z=6 eliminates all but the 1st and 3rd choices. Using that value in the first equation gives ...

  x + y + 6 = 5

  x + y = -1

Only the 3rd choice satisfies this equation.

  (x, y, z) = (-5, 4, 6)

Hi there!  

»»————-　★　————-««

I believe your answer is:  

{7, -5, (2/3), 5.79}

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{\underline{\textbf{Some Examples of Rational Numbers Are...}}}}\\\\\rightarrow \text{Integers}\\\\\rightarrow \text{Perfect Squares}\\\\\rightarrow \text{Terminating Decimals}\\\\\rightarrow \text{Recurring Decimals}[/tex]

⸻⸻⸻⸻

⸻⸻⸻⸻

The rational numbers are {7, -5, (2/3), 5.79}.

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

a) [tex]P(Adult)=\frac{73}{249}=0.2932=29.32%[/tex]

b) [tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]

c) [tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]

d) [tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]

e) [tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]

f) [tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the number of adults in the survey and divide them into the number of people in the survey by using the following formula>

[tex]P=\frac{desired}{possible}[/tex]

In this case we have a total of 17+43+13 adults which gives us 73 adults and a total of 249 people surveyed so we get:

[tex]P(Adults)=\frac{73}{249}=0.2932=29.32%[/tex]

b)

The same principle works for part b

there are: 40+34+17=91 people who likes chocolate ice cream the best so the probability is:

[tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]

c)

when it comes to the or statement, we can use the following formula:

P(A or B) = P(A) + P(B) - P( A and B)

In this case:

[tex]P(Adult)=\frac{73}{249}[/tex]

[tex]P(Vanilla)=\frac{10+10+43}{249}=\frac{63}{249}[/tex]

[tex]P(AdultandVanilla)=\frac{43}{249}[/tex]

so:

[tex]P(AdultorVanilla)=\frac{73}{249}+\frac{63}{249}-\frac{43}{249}[/tex]

[tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]

d)

Is a child and likes vanilla the best.

In the table we can see that 10 children like vanilla so the probability is:

[tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]

e)

Likes strawberry the best, GIVEN that the person is a child.

In this case we can make use of the following formula:

[tex]P(B/A)=\frac{P(AandB)}{P(A)}[/tex]

so we can get the desired probabilities. First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]

Then, we know there are 40+10+44=94 children, so the probability for the person being a child is:

[tex]P(Child)=\frac{94}{249}[/tex]

Therefore:

[tex]P(Strawberry/Child)=\frac{\frac{44}{249}}{\frac{94}{249}}[/tex]

[tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]

f)

The same works for the probability of the person being a child given that the person likes strawberry the best.

First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]

Then, we know there are 44+38+13 persons like strawberry, so the probability for the person liking strawberry is:

[tex]P(Child)=\frac{95}{249}[/tex]

Therefore:

[tex]P(Child/Strawberry)=\frac{\frac{44}{249}}{\frac{95}{249}}[/tex]

[tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]