Please help me extra points for 1 math question. Please help before my time is up. Five times a number, added to -3, is 37. Find that number.

Answer:

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

And replacing we got:

[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]

And we can use one of the points in order to find the intercept like this:

[tex] -3= \frac{2}{3} (-3) +b[/tex]

[tex] b =-3 +2=-1[/tex]

And the equation would be given by:

[tex] y= \frac{2}{3}x -1[/tex]

Step-by-step explanation:

We want an equation given by:

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

where m i the slope and b the intercept

We have the following two points given:

[tex] (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)[/tex]

We can find the slope with this formula:

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

And replacing we got:

[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]

And we can use one of the points in order to find the intercept like this:

[tex] -3= \frac{2}{3} (-3) +b[/tex]

[tex] b =-3 +2=-1[/tex]

And the equation would be given by:

[tex] y= \frac{2}{3}x -1[/tex]

Answer:

72°

Step-by-step explanation:

This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°

Answer:

A

Step-by-step explanation:

Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)

The total angle of triange is 180°

So 180-72-72=36°

Answer:

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Step-by-step explanation:

From the given information;

the probability of getting returned p = 0.1

If eight rings are sold today, what is the probability that fewer than three will be returned;

According to binomial distribution

Binomial distribution is the probability of success or failure of an outcome of an experiment under observation which is usually repeated several trials. Binomial experiments are random experiment with fixed number of repeated experiment. If we cannot predict before head, the outcome of an experiment , the experiment is called a random experiment.

So , using binomial distribution to determine the probability that fewer than three will be returned;

i.e

[tex]P(X<3) =[/tex] [tex]\sum_{x=0}^{2}\binom{8}{x}(0.1)^{x}(1-0.1)^{8-x}[/tex]

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

[tex]\frac{1}{\lambda} =6[/tex]

[tex]\lambda = \frac{1}{6}[/tex]

a) The required probability is

[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]

The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated

[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]

c)  

Let [tex]X_r[/tex] denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]

ii) The average time that the battery is expected to last is calculated

[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]

Answer:

0.45

Step-by-step explanation:

9/20 is the same as 0.45

Answer:

0.45

Step-by-step explanation:

9/20= 9*5/20*5= 45/100= 0.45

Answer:

The expected value of the random variable with the given probability distribution = 12 .52

Step-by-step explanation:

Given data

 x    :   0         1            5       10     1000

p(x)  :  0.33  0.32   0.24     0.10    0.01

The expected value of the given random variable of given probability distribution

E(X)  =  ∑ x p ( X = x)

E(X)  =  0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01

E (X)  =  12.52

Answer:

The percentage of the employee will experience a lost-time accident in both years is 0.0%

Step-by-step explanation:

Let A denote events that employees suffered lost-time accidents during the last year

Let B denote events that employees suffered lost-time accidents during the current year

P(A) = 5% = 0.05

P(B) = 4% = 0.04

P(B | A) = 15% = 0.15

(a) P (A ∩ B) = P(B | A) × P(A)

= 0.15 × 0.05

= 0.0075

= 0.0 (1 decimal place)

The probability that an employee will experience a lost- time accident in both years is 0.0

Answer:

A) The probability that a randomly selected medical student who took the test had a total score that was less than 484 = 0.06178

B) The probability that a randomly selected study participant's response was between 504 and 516 = 0.29019

C) The probability that a randomly selected study participant's response was more than 528 = 0.00357

D) Option D is correct.

Only the event in (c) is unusual as its probability is less than 0.05.

Step-by-step explanation:

The b and c parts of the question are not complete.

B) Find the probability that a randomly selected study participant's response was between 504 and 516

C) Find the probability that a randomly selected study participant's response was more than 528.

D) Identify any unusual event amongst the three events in A, B and C. Explain the reasoning.

a) None.

b) Events A and B.

C) Event A

D) Event C

Solution

This is a normal distribution problem with

Mean = μ = 500

Standard deviation = σ = 10.4

A) Probability that a randomly selected medical student who took the test had a total score that was less than 484 = P(x < 484)

We first normalize or standardize 484

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (484 - 500)/10.4 = - 1.54

To determine the required probability

P(x < 484) = P(z < -1.54)

We'll use data from the normal distribution table for these probabilities

P(x < 484) = P(z < -1.54) = 0.06178

B) Probability that a randomly selected study participant's response was between 504 and 516 = P(504 ≤ x ≤ 516)

We normalize or standardize 504 and 516

For 504

z = (x - μ)/σ = (504 - 500)/10.4 = 0.38

For 516

z = (x - μ)/σ = (516 - 500)/10.4 = 1.54

To determine the required probability

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

We'll use data from the normal distribution table for these probabilities

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

= P(z ≤ 1.54) - P(z ≤ 0.38)

= 0.93822 - 0.64803

= 0.29019

C) Probability that a randomly selected study participant's response was more than 528 = P(x > 528)

We first normalize or standardize 528

z = (x - μ)/σ = (528 - 500)/10.4 = 2.69

To determine the required probability

P(x > 528) = P(z > 2.69)

We'll use data from the normal distribution table for these probabilities

PP(x > 528) = P(z > 2.69) = 1 - P(z ≤ 2.69)

= 1 - 0.99643

= 0.00357

D) Only the event in (c) is unusual as its probability is less than 0.05.

Hope this Helps!!!

Answer:

  24

Step-by-step explanation:

Let t represent the volume of the tank in gallons. Then we have ...

  (1/8)t + 15 = (3/4)t . . . . . . . . . . . adding 15 gallons fills the tank to 3/4

  15 = (6/8 -1/8)t = (5/8)t . . . . . . . subtract 1/8t

  15(8/5) = (8/5)(5/8)t . . . . . . . . . multiply by 8/5 (the inverse of 5/8)

  24 = t

The tank holds 24 gallons.

Answer:

D: 13

I hope you understand, I am not that good at explaining. And I am not completely sure with my answer, but I think it's correct.

Answer:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Step-by-step explanation:

We want to simplify the following expression:

[tex] \frac{a^3 b^2}{a^{-1} b^{-3}}[/tex]

And we can rewrite this expression using this property for any number a:

[tex] a^{-1}= \frac{1}{a}[/tex]

And using this property we have:

[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]

And simplifying we got:

[tex] a^3 b^2 a b^3[/tex]

[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]

Answer:

D

Step-by-step explanation:

(eˣ − e⁻ˣ) / (eˣ + e⁻ˣ) = t

Multiply by eˣ/eˣ.

(e²ˣ − 1) / (e²ˣ + 1) = t

Solve for e²ˣ.

e²ˣ − 1 = (e²ˣ + 1) t

e²ˣ − 1 = e²ˣ t + t

e²ˣ = 1 + e²ˣ t + t

e²ˣ − e²ˣ t = 1 + t

e²ˣ (1 − t) = 1 + t

e²ˣ = (1 + t) / (1 − t)

Solve for x.

2x = ln[(1 + t) / (1 − t)]

x = ½ ln[(1 + t) / (1 − t)]

Use log rule.

x = ln(√[(1 + t) / (1 − t)])

Answer:

96

Step-by-step explanation:

Rectangle area:

(8)(10)=80

Triangle area:

(1/2)(4)(8)=16

Total area:

16+80=96

Answer:

[tex]96 {ft}^{2} [/tex]

Step-by-step explanation:

[tex]area = \frac{1}{2} (a + b)h \\ = \frac{1}{2} \times (10 + 14) \times 8 \\ = \frac{1}{2} \times 24 \times 8 \\ = 96 {ft}^{2} [/tex]

Answer:

35

Step-by-step explanation:

3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9

a+b=?

------

all numbers get cancelled apart from the first denominator and the last numerator:

1/2*a= 9

then

a+b= 18+17= 35

Answer:

the answer is E the number at the top tells you which position it falls under in the alphabet

The slope is zero. Slope formula is Y=mx+b and since B is 1.5 and it is a straight line, Y=mx+1.5. What plus 1.5 is 1.5? 0. Hope this helps.

Answer:

FALSE

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = [tex]x^2+7[/tex]

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = [tex]x^2+7[/tex]

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

Answer:

Yes

Step-by-step explanation:

the function that gives the alcohol level is:

[tex]A ( x ) = - 0.015 x^3 + 1.05 x[/tex]

where x is the number of hours.

we need to know if after 4 hours an average person is legally drunk, thus:

[tex]x=4[/tex]

and we substitute this in the function:

[tex]A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)[/tex]

solving these operations we obtain:

[tex]A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2[/tex]

[tex]A(4)=3.24[/tex]

the alcohol level after 4 hours is 3.24.

Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.

Answer:

B.

Step-by-step explanation:

In the attached file

Answer:

the Swiss Chalet had higher occupancy than its competitive set in 2019

Step-by-step explanation:

Answer:

x = -6

Step-by-step explanation:

-2/3x + 9 = 4/3x - 3

First we need to simplify to where we have x on one side and a constant (number not connected to a variable) on the other side.

Subtract 4/3x from both sides:

-2/3x + 9 - 4/3x = -3

-6/3x + 9 = -3

Now subtract 9 from both sides:

-6/3x + 9 - 9 = -3 - 9

-6/3x = -12

Now turn -6/3 into a whole number to make things more simple:

-6/3 = -2

-2x = -12

Now divide both sides by -2 to get x by itself

-2x/-2 = -12/-2

x = -6

Answer:

The correct answer will be "0.400 gm".

Step-by-step explanation:

The give values are:

Needs of hospital, N = 0.100 gm

Time, t = 10 days

Minimum amount of Xenon, N₀ = ?

As we know,

⇒  [tex]N(t)=N_{0} \ e^{-\lambda t}[/tex]

∴  Decay constant, λ = [tex]\frac{ln2}{t_{1/2}}[/tex]

                                λ = [tex]\frac{ln2}{5}[/tex]

On putting values, we get

⇒  [tex]0.100=N_{0} \ e^{-\frac{ln2}{5}}\times 10[/tex]

⇒  [tex]0.1=N_{0} \ e^{-2ln2} = N_{0} \ e^{-ln4}[/tex]

⇒  [tex]0.1=N_{0} \ e^{ln\frac{1}{4}}[/tex]

⇒  [tex]0.1=\frac{N_{0}}{4}[/tex]

⇒  [tex]N_{0}=0.1\times 4[/tex]

⇒  [tex]MX_{e}=0.400 \ gm[/tex]

Answer:

A) 50 km : 45 km : 65 km

B) 18:45:3

Step-by-step explanation:

A) 160 km in the ratio 10:9:13

10:9:3 ⇔ 50 km : 45 km : 65 km

B) 66 in the ratio 6:15:1

6:15:1  ⇔ 18:45:3

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]

Now, substitute the given values:

[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]

[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

Learn more about angle of elevation here:

https://brainly.com/question/31006775

#SPJ4

Answer:

C. can have more than one factor, each with several treatment groups.

Step-by-step explanation:

A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.

Completely randomized design has found application in agricultural and environmental researches.

Answer:

I think it is -2

Step-by-step explanation:

I think but I do not know

Answer:

x=-21

Step-by-step explanation:

x+12=-9

minus twelve on both sides

-9-12 equals -21

x=-21