How many 3-digit numbers can be formed if repetition is
allowed?

Answer:

The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Step-by-step explanation:

Let the random variable X represent the time it takes to wash the dishes.

The random variable X is uniformly distributed with parameters a = 10 minutes and b = 15 minutes.

The probability density function of X is as follows:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

Compute the probability that washing dishes will take between 12 and 14 minutes as follows:

[tex]P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx[/tex]

                           [tex]=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333[/tex]

Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

ith 0 identical marbles permitted to be included in any of the jars, An expression can be developed to determine the total of marbles in jar arrangements, which is:

E = [(n+j -1)!]*{1/[(j-1)!]*[(n)!]}, where n = number of identical balls and j =number of distinct jars, the contents of all of which must sum to n for each marbles in j jars arrangement. With n = 7 and j = 4. E = 10!/(3!)(7!) = 120= number of ways 7 identical marbles can be distributed to 4 distinct jars such that up to 3 boxes may be empty and the maximum to any box is 7 balls.i think is the answer

Answer:

A type II error is failing to reject the hypothesis that μ is equal to 2800 when in fact, μ is less than 2800.

Step-by-step explanation:

A Type II error happens when a false null hypothesis is failed to be rejected.

The outcome (the sample) probability is still above the level of significance, so it is consider that the result can be due to chance (given that the null hypothesis is true) and there is no enough evidence to claim that the null hypothesis is false.

In this contest, a Type II error would be not rejecting the hypothesis that the mean lifetime of the light bulbs is 2800 hours, when in fact this is false: the mean lifetime is significantly lower than 2800 hours.

Answer:

Explanation:

F(2) means, value of function at x=2.

Here,you can see from the graph,from 0 to 4, it's a straight line and value of y is 2.

Hope this helps...

Good luck on your assignment....

Answer:

240cm³

Step-by-step explanation:

First, let's assume the entire shape is full rectangular prism without that has the middle being cut out.

What this means is that, to get the volume of the solid made out of clay, we would calculate the solid as a full rectangular prism, then find the volume of the assumed middle cut-out portion. Then find the difference between both.

Let's solve:

Find the volume of the rectangular prism assuming the solid is full:

Volume of prism = width (w) × height (h) × length (l)

w = 4cm

h = 7cm

l = 3+6+3 = 12cm

Volume of full solid = 4*7*12 = 336cm³

Next, find the volume of the assumed cut-out portion using same formula for volume of rectangular prism:

w = 4cm

h = 7-3 = 4cm

l = 6cm

Volume of assumed cut-out portion = 4*4*6 = 96cm³

Volume of solid made from clay = 336cm³ - 96cm³ = 240cm³

Answer:

h < 2

Step-by-step explanation:

Step 1: Distribute

10h + 40 < 60

Step 2: Subtract 40 on both sides

10h < 20

Step 3: Divide both sides by 10

h < 2

Answer:

speed of slower driver 30 mph

speed of faster driver = 55 mph

Step-by-step explanation:

let the speed of slower driver b x mph

given

One driver drives 25 mph faster than another driver does

Speed of faster driver = (x+25) mph

we know time = speed / distance

also in same time faster will travel more distance than the slower one.

thus

driver with speed  (x+25) mph would have traveled 165 miles

driver with speed  x mph would have traveled 90 miles

time for driver with speed  (x+25) mph = 165/(x+25)

time for driver with speed  x mph = 90/x

Given that

They start at the same time and after a certain amount of time, one driver has driven 90 miles, and the other driver has driven 165 miles.

\time for driver with speed  (x+25) mph =time for driver with speed  x mph

165/(x+25) = 90/x

165x = 90(x+25)

=> 165x = 90x + 2250

=> 165x -90x = 2250

=> 75x = 2250

=> x = 2250/75= 30

Thus, speed of slower driver 30 mph

speed of faster driver = 30+25 = 55 mph

Hey there! I'm happy to help!

PART A

Let's break down each terms in the expression to find the factors that make it up and see the greatest thing they all have in common

To break up the numbers, we keep on dividing it until there are only prime numbers left.

TERM #1

Three is a prime number, so there is no need to split it up.

3pf²= 3·p·f·f              

TERM #2

We have a negative coefficient here. First, let's ignore the negative sign and find all of the factors, which are just 7 and 3. One of them has to be negative and one has to be positive for it to be negative. It could be either way, and when comparing to other, we might want one to be negative or positive to match another part of the expression to find the greatest common factor. So, we will use the plus or minus sign ±, knowing that one must be positive and one must be negative.

-21p²2f= ±7·±3 (must be opposite operations) ·p·p·f

TERM #3

6pf= 2·3·p·f

TERM #4

Since 42 is made up of 3 prime factors (2,3,7), one of them or all three must be negative, because two negatives would make it positive. We will use the plus-minus sign again on all three because it could be just one is negative or all three are, but we don't know. We can use these later to find the greatest common factor when matching.

-42p²= ±2·±3·±7·p·p

Now, let's pull out all of our factors and see the greatest thing all four terms have in common

TERM 1: 3·p·f·f  

TERM 2: ±7·±3·p·p·f     (7 and 3 must end up opposite signs)

TERM 3: 2·3·p·f

TERM 4: ±2·±3·±7·p·p   (one or three of the coefficients will be negative)

Let's first look at the numbers they share. All of them have a three. We will rewrite Term 2 as -7·3·p·p·f afterwards because 3 must be positive to match. With term four, the 3 has to positive so not all three can be negative, so that means that either the 2 or 7 has to be negative, but in the end we they will make a -14 so it does not matter which one because.

Now, with variables. All of them have one p, so we will keep this.

Almost all had an f except the fourth, so this cannot be part of the GCF.

So, all the terms have 3p in common. Let's take the 3p out of each term and see what we have left. In term 4 we will combine our ±7 and ±2 to be -14 because one has to be negative.

TERM 1: f·f

TERM 2: -7·p·f

TERM 3: 2·f

TERM 4: -14·p

The way we will write this is we will put 3p outside parentheses and put what is left of all of our terms on the inside of the parentheses.

3p(f·f+-7·p·f+2·f-14·p)

We simplify these new terms.

3p(f²-7pf+2f-14p)

Now we combine like terms.

3p(f²-7pf-14p)

If you used the distributive property to undo the parentheses you could end up with our original expression.

PART B

Completely factoring means the equation is factored enough that you cannot factor anymore. The only things we have left to factor more are the terms inside the parentheses. Although there won't be something common between all of them, one might have pairs with one and not another, and this can still be factored out, and this can be put into (a+b)(a+c). Let's find what we have in common with the three terms in the parentheses.

TERM 1: f·f

TERM 2: -7·p·f

TERM 3: 2· -7·p (I just put 7 as negative and 2 as positive already for matching)

Term 1 and 2 have an f in common.

Terms 2 and 3 have a -7p in common.

So, we see that the f and the -7p are what can be factored out among all of the terms, so let's take it out of all of them and see what is left.

Term 1: f

Term 2: nothing left here

Term 3: 2

So, this means that all we have left is f+2. If we multiply that by f-7p we will have what was in the parentheses in our answer from Part A, and we cannot simplify this any further. This means that our parentheses from Part A= (f-7p)(f+2). This shows that (f-7p) is multiplied by (f+2)

Don't forget the GCF 3p; that's still outside the parentheses!

Therefore, the answer here is 3p(f-7p)(f+2).

Have a wonderful day! :D

Answer:

101

Step-by-step explanation:

We are given that

r(t)=[tex]<t^2,1-t,4t>[/tex]

We have to find the derivative of r(t).a(t) at t=2

a(2)=<7,-3,7> and a'(2)=<3,2,4>

We know that

[tex]\frac{d(uv)}{dx}=u'v+v'u[/tex]

Using the formula

[tex]\frac{d(r(t)\cdot at(t))}{dt}=r'(t)\cdot a(t)+r(t)\cdot a'(t)[/tex]

[tex]\frac{d(r(t)\cdot at(t))}{dt}=<2t,-1,4>\cdot a(t)+<t^2,1-t,4t>\cdot a'(t)[/tex]

Substitute t=2

[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot a(2)+<4,-1,8>\cdot a'(2)[/tex]

[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot <7,-3,7>+<4,-1,8>\cdot <3,2,4>[/tex]

[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=28+3+28+12-2+32=101[/tex]

The derivation of the equation will be "101".

Given expression is:

r(t) = 〈t², 1 - t, 4t〉

Let,

a(2) = <7, -3, 7>

a'(2) = <3, 2, 4>

As we know,

→ [tex]\frac{d(uv)}{dx}[/tex] = u'v + v'u

By using the formula, the derivation will be:

→ [tex]\frac{d(r(t).at(t))}{dt}[/tex] = r'(t).a(t) + r(t).a'(t)

                  = <2t, -1, 4>.a(t) + <t², 1 - t, 4t>.a'(t)

By substituting "t = 2", we get

                  =  <4, -1, 4>.a(2) + <4, -1, 8>. a'(2)

                  = <4, -1, 4>.<7, -3, 7> + <4, -1, 8>.<3, 2, 4>

                  = 28 + 3 + 28 + 12 - 2 + 32

                  = 101

Thus the response above is appropriate.

Find out more information about derivatives here:

https://brainly.com/question/22068446

Answer:

V= 452.39cm³ (to 2 d.p. )

S.A. = 326.73cm² (to 2 d.p. )

Step-by-step explanation:

Vcylinder = π r² h = π (4)² (9) = 144 π = 452.3893421cm³ = 452.39cm³ (to 2 d.p. )

S.A. cylinder = 2π r h + 2π r² = 2π (4)(9) + 2π (4)² = 104π = 326.725636cm² = 326.73cm² (to 2 d.p. )

Answer:

In that year approximately 2114 thousand people visited the park.

Step-by-step explanation:

Since the expression [tex]y(x) = -7.5*x^2 + 103*x + 2142[/tex] models the number of visitors in the park, where x represents the number of years after 2007 and 2021 is 14 years after that, then we need to find "y" for that as shown below.

[tex]y(14) = -7.5*(14)^2 + 103*14 + 2142\\y(14) = -7.5*196 + 1442 + 2142\\y(14) = -1470 + 3584\\y(14) = 2114[/tex]

In that year approximately 2114 thousand people visited the park.

Answer:

The population under consideration in the data set are all the adults in the United States.

Step-by-step explanation:

Sampling

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

The population of interest are all the residents of New York State.

In this question:

Sample of 765 adults in the United states.

So the population under consideration in the data set are all the adults in the United States.

Answer:

x=-2

Step-by-step explanation:

2 times -2=-4+3=-1

Answer:

  54

Step-by-step explanation:

  [tex](\sqrt{6} + \sqrt{24})^2=(\sqrt{6}+2\sqrt{6})^2\\\\=(3\sqrt{6})^2=(3^2)(6)=\boxed{54}[/tex]

Answer:

14    -50    -29    -541

Step-by-step explanation:

8-3=5-1=4+5=9-8=1+13=14-64=-50+21=-29-512=-541  

i got this by looking up sequence pattern finder in google and clicking on the second option then inserting the numbers you gave hope this helps

Answer:

The solutions are the roots of the quadratic. They are found where the graph crosses the x-axis.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A standard normal probability distribution is a normal distribution that has a mean of zero and a standard deviation of 1.

Answer:

a^x/y=1              x: 0

Step-by-step explanation: w.k.t,        a^0=1( any variable raised to 0 is 1)

                                    so, here the exponent is x/y which should have been 0 so that answer was 1.

Answer:

Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.

Step-by-step explanation:

Given the vertices of a triangle as: A(3, 5), B(− 1, 5), and C(3,− 6)

Since A and B are on the same y-coordinate, we have that:

AB = 3-(-1)=4 Units

Since A and C are on the same x-coordinate, we have that:

AC=5-(-6)=11 Units

Next, we determine the distance BC using the distance formula.

Given: B(− 1, 5), and C(3,− 6)

[tex]BC=\sqrt{(3-(-1))^2+(-6-5)^2}\\= \sqrt{(4)^2+(-11)^2}=\sqrt{137}$ Units[/tex]

Therefore:

Perimeter of the Triangle

[tex]= 4+11+\sqrt{137}\\ =15+\sqrt{137}$ Units\\=26.7 Units[/tex]

On plotting the triangle, it forms a right triangle such that the:

Base = 4 Units

Height = 11 Units

Therefore:

Area of a triangle [tex]=\dfrac12 *Base*Height[/tex]

Therefore:

Area of the Triangle = 0.5 X 4 X 11

=22 Square Units.

Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.

Answer:

The required matrix is[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Step-by-step explanation:

Matrix of rotation:

[tex]P = \left[\begin{array}{ccc}cos\pi/4&-sin\pi/4\\sin\pi/4&cos\pi/4\end{array}\right][/tex]

[tex]P = \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

x' + iy' = (x + iy)(cosθ + isinθ)

x' = x cosθ - ysinθ

y' = x sinθ + ycosθ

In matrix form:

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos\theta&-sin\theta\\sin \theta&cos\theta\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

The matrix stretches by 1.8 on the x axis and 0.7 on the y axis

i.e. x' = 1.8x

y' = 0.7y

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

[tex]Q = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right][/tex]

According to the question, the result is rotated by pi/3 clockwise radians

[tex]R = \left[\begin{array}{ccc}cos(-\pi/3)& -sin(-\pi/3)\\-sin(\pi/3)&cos(\pi/3)\end{array}\right][/tex]

[tex]R = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right][/tex]

To get the matrix A, we would multiply matrices R, Q and P together.

[tex]A = RQP = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right] \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Answer:

  (1, 2), (-2, -1)

Step-by-step explanation:

We can choose x = 1 and find y:

  y = 2/1 = 2

  (x, y) = (1, 2)

We can choose x = -2 and find y:

  y = 2/(-2) = -1

  (x, y) = (-2, -1)

Using the percentage concept, it is found that 51% of 10th graders surveyed preferred robotics, hence option B is correct.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, we have that 33% out of 65% of the students are 7th graders who preferred robotics, hence the percentage is given by:

[tex]P = \frac{33}{65} \times 100\% = 51%[/tex]

Which means that option B is correct.

More can be learned about percentages at https://brainly.com/question/14398287

#SPJ1

Answer:

It's A. 61% The dude above me is wrong.

Step-by-step explanation:

I just took the test

Answer:

40 ml of 73% solution required and 80 ml of 13% solution

Step-by-step explanation:

Let x = amt of 58% solution

It say's the amt of the resulting mixture is to be 120 ml, therefore

(120-x) = amt of 13% solution

A typical mixture equation

0.73x + 0.13(120-x) = 0.33(120)

0.73x + 15.6 - 0.13x = 39.6

0.6x=24

x=40 ml of 73% solution required

and

120 - 40 =80 ml of 13% solution

Answer/Step-by-step explanation:

Let's highlight the dimensions of the bedroom and living room using the information given in the question:

==>Squared Bedroom dimensions:

Side length = w = x ft

Area = x*x = x²

==>Rectangular living room dimensions:

width = side length of the squared bedroom = x

length = (x + 9) ft

Area = L*W = x*(x+9) = x² + 9x

Now let's match each given expression with what they represent:

==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"

As we have shown in the dimensions of the squared bedroom above.

==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room

==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"

i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.

==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".

i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x

Answer:

There are a total of 840 possible different teams

Step-by-step explanation:

Given

Number of boys = 6

Number of girls = 8

Required

How many ways can 4 boys and 5 girls be chosen

The keyword in the question is chosen;

This implies that, we're dealing with combination

And since there's no condition attached to the selection;

The boys can be chosen in [tex]^6C_4[/tex] ways

The girls can be chosen in [tex]^8C_5[/tex] ways

Hence;

[tex]Total\ Selection = ^6C_4 * ^8C_5[/tex]

Using the combination formula;

[tex]^nCr = \frac{n!}{(n-r)!r!}[/tex]

The expression becomes

[tex]Total\ Selection = \frac{6!}{(6-4)!4!} * \frac{8!}{(8-5)!5!}[/tex]

[tex]Total\ Selection = \frac{6!}{2!4!} * \frac{8!}{3!5!}[/tex]

[tex]Total\ Selection = \frac{6 * 5* 4!}{2!4!} * \frac{8 * 7 * 6 * 5!}{3!5!}[/tex]

[tex]Total\ Selection = \frac{6 * 5}{2!} * \frac{8 * 7 * 6}{3!}[/tex]

[tex]Total\ Selection = \frac{6 * 5}{2*1} * \frac{8 * 7 * 6}{3*2*1}[/tex]

[tex]Total\ Selection = \frac{30}{2} * \frac{336}{6}[/tex]

[tex]Total\ Selection =15 * 56[/tex]

[tex]Total\ Selection =840[/tex]

Hence, there are a total of 840 possible different teams

Answer: -64

Step-by-step explanation: Since we know that -4 x -4 is a positive, it equals 16, then a positive plus a negative equals a negative, so 16 x -4 equals -64

Answer:

-64

Step-by-step explanation:

-4 • -4 • -4

-4*-4 = 16

16*-4

-64

Answer:

Answer is given below with explanations.

Step-by-step explanation:

Answer is option 1) 85 : 51

[tex]given \: that \: \\ triangle \: SPT \: is \: similar \: to \: triangle \: QPR \\ corresponding \: sides \: of \: similar \: \\ triangles \: are \: in \: proportion \\ then \: \\ \frac{SP}{ QP} = \frac{PT }{ PR} \\ \frac{3x}{3x + 24} = \frac{51}{85} \\ taking \: reciprocal \: on \: both \: sides \\ \frac{3x + 24}{3x} = \frac{85}{51} [/tex]

Option 1 is correct.

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

It appears to be a parallelogram. But without actual numerical data, I don't think it's possible to prove this or not. I could be missing something though.