Simplify the expression:
– 10x + – 4 – 8 + 7x

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:

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

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:

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:

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

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Answer:

H0: p=0.85;

Ha: p>0.85

Step-by-step explanation:

What was being tested is that:

the coach wanted to know if the proportion of basketball players who are over 72 inches is more than 85%.

The null hypothesis which we are testing against would be that the proportion of basketball players who are over 72 inches is 85%.

H0: p=0.85;

Ha: p>0.85

Answer:

answer is 2.3 hope you get the answer

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:

69 meters

Step-by-step explanation:

Answer:

Please privately chat to us why you chose to cheat during online class, otherwise we will contact your parents and kick you out of our program for the reason stated.

Step-by-step explanation:

Please contact your Quantitive Reasoning teacher at her email, as stated in Google Classroom.

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:

[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

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:

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:

1. Pattern (rule) : y = x-6

2. Pattern (rule) : y=x^2+1

3. Pattern (rule)  : y = -3x

4. Pattern (rule) : y = 2x-2

5. Pattern (rule) : y = x^2

Step-by-step explanation:

Note: question number correspond to your order of questions.

1. Pattern (rule) : y = x-6

for missing parts, see attached table.

2. Pattern (rule) : y=x^2+1

3. Pattern (rule)  : y = -3x

4. Pattern (rule) : y = 2x-2

5. Pattern (rule) : y = x^2

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:

   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:

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:

The 90%  confidence level is  [tex]19.15< L < 20.85[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 64[/tex]

     The mean age is  [tex]\= x = 20 \ years[/tex]

      The standard deviation  is   [tex]\sigma = 4 \ years[/tex]

Generally  the degree of freedom for this data set is mathematically represented as

        [tex]df = n - 1[/tex]

substituting values

        [tex]df = 64 - 1[/tex]

        [tex]df = 63[/tex]

Given that the level of confidence is  90%  the significance level is mathematically evaluated as

          [tex]\alpha = 100 - 90[/tex]

         [tex]\alpha =[/tex]10 %  

         [tex]\alpha = 0.10[/tex]

Now   [tex]\frac{\alpha }{2} = \frac{0.10}{2} = 0.05[/tex]

Since we are considering a on tail experiment

The  critical value for half of  this significance level at the calculated  degree of freedom is obtained from the critical value table as

           [tex]t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669[/tex]

   The margin for error is mathematically represented as

          [tex]MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

substituting values  

          [tex]MOE = 1.699 * \frac{4 }{\sqrt{64} }[/tex]

         [tex]MOE = 0.85[/tex]

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

           [tex]\= x - MOE < L < \= x + E[/tex]

substituting values  

         [tex]20 - 0. 85 < L < 20 + 0.85[/tex]

         [tex]19.15< L < 20.85[/tex]

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: 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

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:

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

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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

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.

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer:

The standard error  S.E of the mean is 5

Step-by-step explanation:

From the given data;

Fifty students are enrolled in a Business Statistics class.

After he first examination, a random sample of 5 papers was selected.

Now; let consider a random sample of 5 papers was selected. with the following grades : 60, 75, 80, 70, and 90

The objective of this question is to determine the standard error of the mean

In order to achieve this ; we need to find the mean and the standard deviation from the given data.

TO start with the mean;

Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{n} \sum x_i[/tex]

Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{5} (60+75+80+70+90)[/tex]

Mean [tex]\overline X[/tex] = 0.2(375)

Mean [tex]\overline X[/tex] = 75

On the other hand; the standard deviation is :

[tex]s = \sqrt{\dfrac{1}{n-1}\sum(x_i - \overline X)^2}[/tex]

[tex]s = \sqrt{\dfrac{1}{5-1}((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}[/tex]

[tex]s = \sqrt{\dfrac{1}{4}(225+0+25+25+225 )}[/tex]

[tex]s = \sqrt{\dfrac{1}{4}(500 )}[/tex]

[tex]s = \sqrt{125}[/tex]

s = 11.18

Finally; the standard error  S.E of the mean is:

[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]

[tex]S.E = \dfrac{11.18}{\sqrt{5}}[/tex]

[tex]S.E = \dfrac{11.18}{2.236}[/tex]

[tex]S.E = 5[/tex]

The standard error  S.E of the mean is 5