A living room is two times as long and one and one-half times as wide as a bedroom. The amount of
carpet needed for the living room is how many times greater than the amount of carpet needed for the
bedroom?
1 1/2
2
3
3 1/2

Answer:

answer is 2.3 hope you get the answer

Answer:

[tex]\boxed{c = 5.7 units}[/tex]

Step-by-step explanation:

Using Pythagorean Theorem:

=> [tex]c^2 = a^2+b^2[/tex]

Where c is hypotenuse, a is base and b is perpendicular and ( a, b = 4)

=> [tex]c^2 = 4^2+4^2[/tex]

=> [tex]c^2 = 16+16[/tex]

=> [tex]c^2 = 32[/tex]

Taking sqrt on both sides

=> c = 5.7 units

Answer:

Step-by-step explanation:

Given,

Base ( b ) = 4 units

Perpendicular ( p ) = 4 units

Hypotenuse ( h ) = ?

Now,

Using Pythagoras theorem to find length of hypotenuse:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plugging the values

[tex] {h}^{2} = {4}^{2} + {4}^{2} [/tex]

Evaluate the power

[tex] {h}^{2} = 16 + 16[/tex]

Calculate the sum

[tex] {h}^{2} = 32[/tex]

[tex]h = \sqrt{32} [/tex]

[tex]h = 5.65 \: units[/tex]

Hope this helps..

Best regards !!

Answer:

70.5°

Step-by-step explanation:

22² = (20)²+(18)² - 2(20)(18) cos X

484 = 400 + 324 - 720 cos X

-240 = -720 cosx

1/3 = cos X

[tex]cos^{-1}(\frac{1}{3})[/tex] = X

X = 70.52877937

Answer:

1575 ft

Step-by-step explanation:

Convert 1/10 to decimal to make the math simpler.

1/10 = 0.1

Divide 3.5 by 0.1.

3.5/0.1 = 35

Multiply 35 by 45.

35 × 45 = 1575

The train will travel 1575 feet in 3.5 seconds.

The distance covered by the train in 3.5 seconds will be 1575 feet.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A train travels 45 feet in 1/10 in a second.

Then the speed will be

Speed = 45 / (1/10)

Speed = 45 x 10

Speed = 450 feet per second

The distance covered by the train in 3.5 seconds will be

Distance = 450 x 3.5

Distance = 1575 feet

More about the speed link is given below.

https://brainly.com/question/7359669

#SPJ2

Answer:

18

Step-by-step explanation:

Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.

Answer:

[tex]\Large \boxed{\sf \ \ 4\sqrt{a^2+b^2} \ \ }[/tex]

Step-by-step explanation:

Hello,

You can use Pythagoras in the 4 right triangles.

For one triangle it comes [tex]\sqrt{a^2+b^2}[/tex].

Then for the polygon it gives [tex]4\cdot \sqrt{a^2+b^2}[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: x = 6.32 or -0.32

Step-by-step explanation:

2x² - 6x + 10  = 0

No we divide the expression by 2 to make the coefficient of x² equals 1

We now have

x² - 3x + 5     = 0

Now we remove 5 to the other side of the equation

x² - 3x          = -5

we add to both side square of  half the coefficient of x which is 3

x² - 3x + ( ⁻³/₂)²  = -5 + (⁻³/₂)²

(x  -  ³/₂)²           = -5 + ⁹/₄

Resolve into fraction

(x  - ³/₂)²             = ⁻¹¹/4

Take the roots of the equation

 x - ³/₂               = √¹¹/₄

 x - ³/₂               = √11/₂

x                       = ³/₂ ± 3.32/₂

                         = 3+ 3.32 or 3 - 3.32

                         =  6.32 or - 0.32

Answer:

The probability is 1

Step-by-step explanation:

Given

Number of flips = 8

Outcomes = 8 heads

Required

Probability of getting a head in the next row

This problem can be attributed to experimental probability and it'll be solved using experimental probability formula, which goes as follows;

[tex]Probability = \frac{Number\ of\ Occurence}{Total\ Trials}[/tex]

Let [tex]P(Head)[/tex] represents the probability of getting a head in the next row;

[tex]P(Head)= \frac{Outcome\ of\ head}{Total\ Flips}[/tex]

[tex]P(Head)= \frac{8}{8}[/tex]

[tex]P(Head)= 1[/tex]

Hence, the probability of obtaining a head in the next flip is 1

Answer:

Convenience sampling.

Step-by-step explanation:

To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called convenience sampling.

Convenience sampling can be defined as a sampling method which involves the researcher selecting or collecting data that is easily available or choosing the individuals who are easiest to reach in a population. It is a type of non-probability method of sampling where the first or easiest available data source is being used by the researcher without other requirements.

In this scenario, to gather information on customer satisfaction, the researcher went to the store most likely situated in a shopping mall to collect data from six (6) customers in each stores.

Some of the advantages of convenience sampling are low cost, data are collected quickly, lesser rules etc.

Answer:

23/20        

Step by step Explanation

Answer:

Step-by-step explanation:

[tex]2-\frac{3}{4}-1\frac{1}{10}=x\\x=2-\frac{3}{4}-\frac{11}{10}\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\x=\frac{2}{1}-\frac{3}{4}-\frac{11}{10}\\1,\:4,\:10\\\mathrm{Prime\:factorization\:of\:} ;\\1=1\\4=2\times \:2\\10=2\cdot \:5\\\mathrm{Multiply\:the\:numbers:}\:2\times \:2\times \:5=20\\Adjust\: fractions\: based\: on\: their\: LCM ;\\\frac{2}{1}=\frac{2\times \:20}{1\times \:20}=\frac{40}{20}\\\\\frac{3}{4}=\frac{3\times \:5}{4\times \:5}=\frac{15}{20}\\[/tex]

[tex]\frac{11}{10}=\frac{11\times \:2}{10\times \:2}=\frac{22}{20}\\\mathrm{Since\:the\:denominators\:are\:equal,\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\\mathrm{Subtract\:the\:numbers:}\:40-15-22=3\\\\x=\frac{3}{20}[/tex]

Answer:

[tex]Perimeter = 14 + 7\sqrt{2}[/tex]

Step-by-step explanation:

Given:

Area of the square = 49 in²

Required

Determine the perimeter of the one of the congruent triangles

First, we'll determine the length of the square;

[tex]Area = Length * Length[/tex]

Substitute 49 for Area

[tex]49 = Length * Length[/tex]

[tex]49 = Length^2[/tex]

Take Square root of both sides

[tex]7 = Length[/tex]

[tex]Length = 7[/tex]

When the square is divided into two equal triangles through the diameter;

2 sides of the square remains and the diagonal of the square forms the hypotenuse of the triangle;

Calculating the diagonal, we have;

[tex]Hypotenuse^2 = Length^2 + Length^2[/tex] -- Pythagoras Theorem

[tex]Hypotenuse^2 = 7^2 + 7^2[/tex]

[tex]Hypotenuse^2 = 2(7^2)[/tex]

Take square root of both sides

[tex]Hypotenuse = \sqrt{2} * \sqrt{7^2}[/tex]

[tex]Hypotenuse = \sqrt{2} * 7[/tex]

[tex]Hypotenuse = 7\sqrt{2}[/tex]

The perimeter of one of the triangles is the sum of the 2 Lengths and the Hypotenuse

[tex]Perimeter = Length + Length + Hypotenuse[/tex]

[tex]Perimeter = 7 + 7 + 7\sqrt{2}[/tex]

[tex]Perimeter = 14 + 7\sqrt{2}[/tex]

Answer:

y=-3/4x+2

Step-by-step explanation:

Add +3x both sides.

Divide each side by -4

-8/-4=2

Slope = -3/4

Y-intercept= 2

Correct expression of B(t) is;

B(t) = 5.0 + 0.25 sin(2πt/5.7)

Answer:

B'(t) = (5π/57)cos(2πt/5.7)

Step-by-step explanation:

We are given;

B(t) = 5.0 + 0.25 sin(2πt/5.7)

Now the rate of change of the brightness after t days is simply the derivative of B(t)

Thus;

B'(t) = 0 + [{0.25 cos(2πt/5.7)} × (2π/5.7)]

This leads to;

B'(t) = (0.5π/5.7)cos (2πt/5.7)

Simplifying this further gives;

B'(t) = (5π/57)cos(2πt/5.7)

Answer:

C) |-9| != |9|

Step-by-step explanation:

The definition of absolute value is simply the non-negative value of the argument without regards to the sign.  With this in mind, let's walk through these options.

A) -2/2 < 3 ==> -1 < 3 which is True

B) |-1| >= 0 ==> 1 >= 0 which is True since 1 is > 0

C) |-9| != |9| ==> 9 != 9 which is False since 9 == 9

D) -7 <= -5  which is True since -7 is < -5

Cheers

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer:

The probability is 0.28

Step-by-step explanation:

Here, we want to calculate the probability that the ball bearing randomly selected has a diameter greater then 4.4 mm

I.e P(X> 4.4)

P(X>4.4) = (4.75-4.4)/(4.75-3.5) = 0.35/1.25 = 0.28

Answer:

C. μ = 3.60

Step-by-step explanation:

Two tables have been attached to this response.

One of the tables contains the given data and distribution with two columns: Houses Sold and Probability

The other table contains the analysis of the data with additional columns: Frequency and Fx

=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,

When the number of houses sold = 0

F = P(0) x Total number of houses sold

F = 0.24 x 28 = 6.72

When the number of houses sold = 1

F = P(1) x Total number of houses sold

F = 0.01 x 28 = 0.28

=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,

When the number of houses sold = 0

Fx = F * x

F = 6.72 x 0 = 0

Now to get the mean, μ we use the relation;

μ = ∑Fx / ∑F

Where;

∑Fx = summation of the items in the Fx column = 100.8

∑F = summation of the items in the Frequency column = 28

μ = 100.8 / 28

μ = 3.60

Therefore, the mean of the given probability distribution is 3.60

The mean of the discrete probability distribution is given by:

C. μ = 3.60

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:

[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]

Hence option C is correct.

More can be learned about the mean of discrete distributions at https://brainly.com/question/24855677

Explanation:

The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.

A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.

Answer: B.) Circumcenter

Step-by-step explanation:

Answer:

The variables X and Y are dependent.

Step-by-step explanation:

The variable X denotes number of face cards . That is it can take values,

X = {0, 1, 2 }

Compute the probability for all he values of X as follows:

P [X = 0] = P (None of the 12 card is chosen in either draw)

              = (40/52)×(39/51)

              = 1560/2652

              = 0.5882

P [X = 1] = P (One of the card is face card is selected)

              = 2×(40/52)×(12/51)

              = 960/2652

              = 0.3619

P [X = 2] = P (Two of the 12 card is chosen in the draw)

              = (12/52)×(11/51)

              = 132/2652

              = 0.0498

The variable Y denotes number of cards numbered 10 . Thus, it can take values:

Y = {0, 1, 2 }

P [Y = 0] = P (None of the 4 card is chosen in either draw)

              = (48/52)×(47/51)

              = 2256/2652

              = 0.8507

P [Y = 1] = P (One of the 4 card is chosen in either draw)

              = 2×(4/52)×(48/51)

              = 384/2652

              = 0.1448

P [Y = 2] = P (Two of the 4 card is chosen in the draw)

              = (4/52)×(3/51)

              = 12/2652

              = 0.0045

Now compute the probability of (X and Y).

P [X = 0 and Y = 0] = P(None of the 16 card is chosen in either draw)

                              = (36/52)×(35/51)

                              = 1260/2652

                              = 0.4751

The variables X and Y are independent if,

P [X = 0 and Y = 0]  = P [X = 0] × P [Y = 0]

                               =  P [X = 0] × P [Y = 0]

                               = 0.8507 × 0.5882

                               = 0.5204

The two values are not equal.

Hence, the variables X and Y are not independent.

Answer:

C = $6050

Equation:

To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:

[tex]3500+150(S)=C[/tex]

3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.

Solving the equation

To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.

[tex]3500+150(17)=C[/tex]

150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.

Our answer is: C = $6050

Answer:

Type I error: Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.

Type II error: Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.

Step-by-step explanation:

We are given the following hypothesis below;

Let p = proportion of people who write with their left hand

Null Hypothesis, [tex]H_0[/tex] : p = 0.18      {means that the proportion of people who write with their left hand is equal to 0.18}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.18      {means that the proportion of people who write with their left hand is different from 0.18}

Type I error states that we would reject the null hypothesis given the fact that the null hypothesis was actually true. Or in other words, the probability of rejecting a true hypothesis.

So, according to our question, Type I error is to Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.

Type II error states that we would accept the null hypothesis given the fact that the null hypothesis was actually false. Or in other words, the probability of accepting a false hypothesis.

So, according to our question, Type II error is Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.

Answer: 11x + 30

Step-by-step explanation: Algebraic expression is a way of use letters to express relationships between algarisms.

For this question:

Units digit = x

Tens digit = 10(x + 3)

The number in question is:

10(x + 3) + x

10x + 30 + x

To simplify, add, subtract, multipy or divide similar terms:

As x is of the first order:

10x + x + 30

11x + 30

The simplified algebraic expression is 11x + 30

Answer:

It's 12 and 43

Step-by-step explanation:

A square is a plane shape with equal length of sides, while a right triangle is a triangle that has one of its angles to be [tex]90^{o}[/tex]. Thus, the areas of the smaller squares could be:

A. 12 and 43

A square has equal length of sides, so that its area is given as:

Area of a square = length x length

                            = [tex]l^{2}[/tex]

For the largest square its area = 55 [tex]units^{2}[/tex], so that:

Area = [tex]l^{2}[/tex]

⇒ 55 = [tex]l^{2}[/tex]

l = [tex]\sqrt{55}[/tex]

Now applying the Pythagoras theorem to the right triangle, we have:

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

where hypotenuse = [tex]\sqrt{55}[/tex]

([tex]\sqrt{55}[/tex][tex])^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex] = 55

Therefore, the addition of the areas of the smaller squares should be equal to that of the largest square.

Thus from the theorem above, the areas of the smaller squares could be 12 and 43.

i.e 12 + 43 = 55

Visit: https://brainly.com/question/18440758

Before we can find any of the three items mentioned, we need the height. The diameter is 10, so the radius is 5. A right triangle with hypotenuse 13 and leg 5 forms. The height is h. Use the pythaogrean theorem to solve for h

5^2+h^2 = 13^2

25+h^2 = 169

h^2 = 169-25

h^2 = 144

h = sqrt(144)

h = 12

The height is 12. We now have enough info to find the volume, the lateral area and surface area.

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

Volume

V = (1/3)*pi*r^2*h

V = (1/3)*3.14*5^2*12

V = 314 cubic cm

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

Lateral Area

LA = pi*r*L

LA = 3.14*5*13

LA = 204.1 square cm

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

Surface Area

SA = 2*pi*r + pi*r*L .... note how we add on the lateral area to the bottom circular area

SA = 2*3.14*5 + 3.14*5*13

SA = 235.5 square cm

Answer:

   sqrt( 146)

Step-by-step explanation:

To find the distance, we use the following formula

d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)

    sqrt( ( -9-2) ^2 + ( 0-5) ^2)

  sqrt( ( -11) ^2 + ( -5) ^2)

   sqrt( 121+25)

   sqrt( 146)

Answer:

Step-by-step explanation:

The happiest used in a test in statistics are the null and the alternative hypothesis. The null hypothesis is usually the default statement while the alternative hypothesis is thevopposite of the null hypothesis.

In this case study, the null hypothesis is u1 = u2: the average mean time it takes to accelerate to 30 miles per hour for car 1 is the same as that for car 2.

The alternative hypothesis is u1 > u2: the mean time it takes to accelerate to 30 miles per hour is greater than that for car 2 thus car 1 is slower to accelerate as it takes more time.

Answer: Required number of ways =  1715

Step-by-step explanation:

Given, there are 45 balloons: 15 are blue; 20 are green; 10 are red.

3 balloons are selected for the float.

Number of combinations to select r things out of n things : [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

So, the number of ways to select 3 ballons such that they are the same color = (Ways to select all blue ) x (Ways to select all green ) x (Ways to select all red)

[tex]^{15}C_3+^{20}C_3+^{10}C_3\\\\=\dfrac{15!}{12!\times3!}+\dfrac{20!}{17!\times3!}+\dfrac{10!}{7!\times3!}\\\\=\dfrac{15\times14\times13}{6}+\dfrac{20\times19\times18}{6}+\dfrac{10\times9\times8}{6}\\\\=455+1140+120\\\\=1715[/tex]

Hence, Required number of ways =  1715

Answer:

work is pictured and shown

Answer:

Infinitely many solutions.

Step-by-step explanation:

To solve the system of equation using the substitution method, the problem has already given us a solution for x:

x = -4y - 9

Using this, we can plug that into the first equation and solve for y:

3x + 12y = -27

3(-4y - 9) + 12y = -27

-12y - 27 + 12y = -27

-27 = -27

The fact that our solution indicate -27 = -27 means that these two equations have infinitely many solutions for the value y.  This simply means that no matter what we put in for y, the statement will always be true.

Notice that these two equations are in fact the same equation:

x = -4y - 9 ==> x + 4y = -9 ==> 3x + 12y = -27

Since these two equations are the same, then there are infinitely many solutions.

I'm not sure quite what they want for the form in terms of y, but let's solve for y since they already solved for x:

x = -4y - 9

x + 9 = -4y

y = (-1 / 4) (x + 9)

Cheers.