What is 3x+8x=13+31?

Answer:

Sample space = 36

P(sum of 6) = 5/36

Step-by-step explanation:

Number of faces on a dice = 6

The sample space, for a toss of 2 dice ; (Number of faces)^number of dice

Sample space = 6^2 = 6*6 = 36

Sum of numbers appearing on the dice = 6

The sum of 6 from the roll of two dice has 5 different outcomes ; Hence, required outcome = 5

Total possible outcomes = sample space = 36

Probability, P = required outcome / Total possible outcomes

P = 5 / 36

Probabilities are used to determine the chances of events

The given parameters are:

[tex]n=6[/tex] --- the faces of a six-sided die

[tex]r = 2[/tex] -- the number of dice

(a) The number of sample points

This is calculated as:

[tex]Sample = n^r[/tex]

So, we have:

[tex]Sample = 6^2[/tex]

Evaluate the exponent

[tex]Sample = 36[/tex]

Hence, the number of sample points is 36

(b) The probability that the sum of 6

See attachment for the sample space of the sum of two dice.

From the sample space, there are 5 outcomes where the sum is 6.

So, the probability is:

[tex]Pr = \frac{5}{36}[/tex] --- where 36 represents the number of sample points

Divide 5 by 36

[tex]Pr = 0.1389[/tex]

Hence, the probability that the sum of the numbers appearing on the dice is equal to 6 is 0.1389

Read more about probabilities at:

https://brainly.com/question/10707698

Answer:

A. More students prefer Model A1 calculators than the Model C3 calculators.

Answer:

[tex]Given:[/tex] Δ ABC ≈ ΔDEF

[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²

⇒ 34/A(ΔDEF)=9²/(13.5)²

⇒34/A(ΔDEF)=81/182.25

⇒A(ΔDEF)=34×182.25/81

⇒Area of ΔDEF=76.5 cm²

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Hope it helps...

Have a great day!!!

Answer:

[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]

Step-by-step explanation:

The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.

Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.

Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.

Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:

[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]

Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.

[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]

14. largest 9510

15. smallest 1000000

16. n+6=22 —> n=22-6 —>n = 16

17. Add : 204 + 38429= 38633

...

Calculate Energy Cost by Appliance

Answer:

4

Step-by-step explanation:

We want the cubed root of 64  

(64)^(1/3)  

(4*4*4) ^ (1/3)  

4  

Unless this is 3 * sqrt(64)  

then it would be  

3 sqrt(8*8)  

3 (8)  

24

Answer:

1st degree

Step-by-step explanation:

You look at the largest exponet, right here, there are none so it would be 1st degree.

Answer:

1

Step-by-step explanation:

The degree of an expression with multiple exponents is the highest exponent in it. In this expression, there is no expression, so the answer will be 1 because there is no exponent and every variable and number has an invisible 1 as its exponent.

Hope this helps.

Answer:

Muhammad lives 8 km away from the school.

Hita lives 4 km away from the school.

Step-by-step explanation:

First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.

Answer:

Step-by-step explanation:

Answer:

3/8 x 5/8= 15/64

Step-by-step explanation:

Answer:

The correct answer is "76.98%".

Step-by-step explanation:

According to the question,

⇒ [tex]P(34000<x<46000) = P[\frac{34000-40000}{5000} <\frac{x- \mu}{\sigma} <\frac{46000-40000}{5000} ][/tex]

                                       [tex]=P(-1.2<z<1.2)[/tex]

                                       [tex]=P(z<1.2)-P(z<-1.2)[/tex]

                                       [tex]=0.8849-0.1151[/tex]

                                       [tex]=0.7698[/tex]

or,

                                       [tex]=76.98[/tex]%

9514 1404 393

Answer:

  (-3, 3)

Step-by-step explanation:

The blanks are trying to lead you through the process of finding the point of interest.

__

The horizontal distance from T to S is 9 . (or -9, if you prefer)

The ratio you're trying to divide the line into is the ratio that goes in this blank:

Multiply the horizontal distance by 2/3 . (9×2/3 = 6)

Move 6 units left from point T.

The vertical distance from T to S is 6 .

Multiply the vertical distance by 2/3 . (6×2/3 = 4)

Move 4 units up from point T.

__

Point T is (3, -1) so 6 left and 4 up is (3, -1) +(-6, 4) = (3-6, -1+4) = (-3, 3). The point that is 2/3 of the way from T to S is (-3, 3).

Answer:

x = -3  or x = 3  or x = 6

Step-by-step explanation:

x3 – 6x2 – 9x + 54 = 0

There is no common factor to factor out. There are 4 terms. We try factoring by grouping. Factor a common factor out of the first two terms. Factor a common factor out of the last two terms.

x^2(x - 6) - 9(x - 6) = 0

x - 6 is a common factor, so we factor it out.

(x^2 - 9)(x - 6) = 0

x^2 - 9 is the difference of 2 squares, so we factor it.

(x + 3)(x - 3)(x - 6) = 0

x + 3 = 0  or  x - 3 = 0  or x - 6 = 0

x = -3  or x = 3  or x = 6

Answer:

x=6     x=3   x=-3

Step-by-step explanation:

x^3 – 6x^2 – 9x + 54 = 0

Factor by grouping

x^3 – 6x^2     – 9x + 54 = 0

x^2(x-6)    -9(x-6 ) =0

Factor out x-6

(x-6)(x^2 -9) =0

Notice x^2 -9 is the difference of squares

(x-6)(x-3)(x+3) = 0

Using the zero product property

x-6 =0    x-3 =0   x+3 =0

x=6     x=3   x=-3

Answer:

c=cost of one chair rental

t=cost of one table rental

8c+3t=42

2c+5t=53

multiply the second equation, each term on both sides, by -4

8c+3t=42

-8c-20t=-212

add the two equations

-17t=-170

divide both sides by -17

t=$10 to rent one table

substitute t=10 into either original equation

2c+5(10)=53

2c+50=53

2c=3

c=$1.50 to rent one chair

Answer:

0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.

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.

n instances of a normal variable:

For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

Sum of normal variables:

When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.

Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.

This means that:

[tex]\mu_A = 10000*50 = 500000[/tex]

[tex]s_A = 1000\sqrt{50} = 7071[/tex]

Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.

This means that:

[tex]\mu_B = 20000*50 = 1000000[/tex]

[tex]s_B = 2000\sqrt{50} = 14142[/tex]

Distribution of the total of the 100 claims:

[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]

[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]

Find the probability the total of the 100 claims exceeds 1,530,000.

This is 1 subtracted by the p-value of Z when X = 1530000. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]

[tex]Z = 1.9[/tex]

[tex]Z = 1.9[/tex] has a p-value of 0.9713

1 - 0.9713 = 0.0287

0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.

Answer:

15

Step-by-step explanation:

By order of operations, multiplication and division are done first, then the addition and subtraction. Remember, multiplication and division have the same precedence, as does addition and subtraction.

21*6 = 126

126/7 = 18

18 + 12 = 30

30 - 15 = 15

Answer:

15

Step-by-step explanation:

21 × 6 ÷ 7 + 12 - 15​

= 126 ÷ 7 + 12 - 15

= 18 + 12 - 15

= 30 - 15

= 15

Answer:

the answer could be B i think cause that makes total sense

This question is incomplete, the complete question is;

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

What proportion of the students scored at least 23 points on this test, rounded to five decimal places?

Answer:

proportion of the students that scored at least 23 points on this test is 0.30850

Step-by-step explanation:

Given the data in the question;

mean μ = 22

standard deviation σ = 2

since test closely followed a Normal Distribution

let

Z = x-μ / σ      { standard normal random variable ]

Now, proportion of the students that scored at least 23 points on this test.

P( x ≥ 23 ) = P( (x-μ / σ) ≥  ( 23-22 / 2 )

= P( Z ≥ 1/2 )

= P( Z ≥ 0.5 )

= 1 - P( Z < 0.5 )

Now, from z table

{ we have P( Z < 0.5 ) = 0.6915 }

= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850

P( x ≥ 23 ) = 0.30850

Therefore, proportion of the students that scored at least 23 points on this test is 0.30850

Answer:

x=8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

they have the same intercepts

Answer:

Step-by-step explanation:

684 dollars

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is translated a units right and b units up, the new point is at A'(x + a, y + b).

If a point A(x, y) is reflected across the line y = -x, the new point is at A'(-y, -x).

If a point A(x, y) is rotated counterclockwise by 270 degrees, the new point is at A'(y, -x).

Let us assume that triangle ABC has vertices at A(-6, -1), B(-3, -3) and C(-1, -2).

If it is moved 5 units to the right and 2 units up, the new point is at A'(-1, 1), B'(1, -1) and C'(3, 0). If it is reflected across the line y = -x, the vertices are at A"(-1, 1), B"(1, -1) and C"(0, -3). If it is then rotated counterclockwise about the origin by 270°, the new point is at A'"(-1, -1), B"'(1, 1), C"'(3, 0)

Answer:

His least score for him in the fourth paper has to be 76.

Step-by-step explanation:

Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:

(70 x 4) - (68 x 3) = X

280 - 204 = X

76 = X

Therefore, his least score for him in the fourth paper has to be 76.

Answer:

AC = 377.19

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 5 = 33/AC

AC tan 5 = 33

AC = 33/ tan 5

AC = 377.19

Answer:

B

Step-by-step explanation:

$3 per gallon

that is the procedure above

Answer:

17 : 27

Step-by-step explanation:

x=3

y=5

4(3)+5 : 6(5)-3

= 12+5 : 30-3

= 17 : 27

Answer:

[tex]|F'H'| = 2 * |FH|[/tex]

Step-by-step explanation:

Given

[tex]E = (0,1)[/tex]             [tex]E' = (-1,2)[/tex]

[tex]F = (1,1)[/tex]             [tex]F' = (1,2)[/tex]

[tex]G = (2,0)[/tex]             [tex]G' =(3,0)[/tex]

[tex]H = (0,0)[/tex]            [tex]H' = (-1,0)[/tex]

[tex](x,y) = (1,0)[/tex] -- center

[tex]k = 2[/tex] --- scale factor

See comment for proper format of question

Required

Compare FH to F'H'

From the question, we understand that the scale of dilation from EFGH to E'F'G'H is 2;

Irrespective of the center of dilation, the distance between corresponding segment will maintain the scale of dilation.

i.e.

[tex]|F'H'| = k * |FH|[/tex]

[tex]|F'H'| = 2 * |FH|[/tex]

To prove this;

Calculate distance of segments FH and F'H' using:

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

Given that:

[tex]F = (1,1)[/tex]             [tex]F' = (1,2)[/tex]

[tex]H = (0,0)[/tex]            [tex]H' = (-1,0)[/tex]

We have:

[tex]FH = \sqrt{(1- 0)^2 + (1- 0)^2}[/tex]

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

[tex]FH = \sqrt{1 + 1}[/tex]

[tex]FH = \sqrt{2}[/tex]

Similarly;

[tex]F'H' = \sqrt{(1 --1)^2 + (2 -0)^2}[/tex]

[tex]F'H' = \sqrt{(2)^2 + (2)^2}[/tex]

Distribute

[tex]F'H' = \sqrt{(2)^2(1 +1)}[/tex]

[tex]F'H' = \sqrt{(2)^2*2}[/tex]

Split

[tex]F'H' = \sqrt{(2)^2} *\sqrt{2}[/tex]

[tex]F'H' = 2 *\sqrt{2}[/tex]

[tex]F'H' = 2\sqrt{2}[/tex]

Recall that:

[tex]|F'H'| = 2 * |FH|[/tex]

So, we have:

[tex]2\sqrt 2 = 2 * \sqrt 2[/tex]

[tex]2\sqrt 2 = 2\sqrt 2[/tex] --- true

Hence, the dilation relationship between FH and F'H' is::

[tex]|F'H'| = 2 * |FH|[/tex]

Answer:NOTT !!  A segment in the image has the same length as its corresponding segment in the pre-image.

Step-by-step explanation:

AS IN THE PICTURE...........