calculate the size of angle x​

"The sum of two numbers is 20" can be translated mathematically into the equation:

x + y = 20.

"... and their difference is 10" can be translated mathematically as:

x - y = 10

We can now find the two unknown numbers, x and y, because we now have a system of two equations in two unknowns, x and y. We'll use the Addition-Subtraction Method, also know as the Elimination Method, to solve this system of equations for x and y by first eliminating one of the variables, y, by adding the second equation to the first equation to get a third equation in just one unknown, x, as follows:

Adding the two equations will eliminate the variable y:

x + y = 20

x - y = 10

-----------

2x + 0 = 30

2x = 30

(2x)/2 = 30/2

(2/2)x = 15

(1)x = 15

x = 15

Now, substitute x = 15 back into one of the two original equations. Let's use the equation showing the sum of x and y as follows (Note: We could have used the other equation instead):

x + y = 20

15 + y = 20

15 - 15 + y = 20 - 15

0 + y = 5

y = 5

CHECK:

In order for x = 15 and y = 5 to be the solution to our original system of two linear equations in two unknowns, x and y, this pair of numbers must satisfy BOTH equations as follows:

x + y = 20 x - y = 10

15 + 5 = 20 15 - 5 = 10

20 = 20 10 = 10

Therefore, x = 15 and y = 5 is indeed the solution to our original system of two linear equations in two unknowns, x and y, and the product of the two numbers x = 15 and y = 5 is:

xy = 15(5)

xy = 75

So we would expect both spinners to land on blue once, approximately.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. The closer the probability is to 1, the more likely the event is to occur, while the closer it is to 0, the less likely it is to occur.

Here,

To solve this problem, we can use the multiplication rule of probability, which states that the probability of two independent events A and B occurring together is equal to the product of their individual probabilities:

P(A and B) = P(A) × P(B)

In this case, we want to find the number of times both spinners land on blue, which is equivalent to the probability that spinner A lands on blue (0.5) multiplied by the probability that spinner B lands on blue (0.4), because the events are assumed to be independent. Therefore:

P(both blue) = P(A blue) × P(B blue) = 0.5 × 0.4 = 0.2

This means that the probability of both spinners landing on blue is 0.2, or 20%.

To estimate the number of times both spinners land on blue out of a certain number of trials, we can use the expected value of a binomial distribution, which is given by:

E(X) = n × p

where X is the random variable representing the number of successes (in this case, both spinners landing on blue), n is the number of trials, and p is the probability of success (0.2 in this case).

We are given that the number of times both spinners land on red is 84, which is equivalent to the number of trials minus the number of times both spinners land on blue. Let's denote the number of trials as n. Then we have:

n - 84 = number of times both spinners land on blue

Substituting the values we have found, we get:

n - 84 = 0.2n

Simplifying and solving for n, we get:

0.8n = 84

n = 105

Therefore, the estimated number of times both spinners land on blue out of 105 trials is: number of times both spinners land on blue

= 0.2 × 105 - 84 ≈ 1

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

Answer:

lesser x= -10.32

greater x= -3.68

Step-by-step explanation:

[tex] - 7 + \sqrt{11} = - 3.68[/tex]

[tex] - 7 - \sqrt{11} = - 10.32[/tex]

Answer:

Lesser x: -10.31 Greater X:-3.68

Step-by-step explanation:

Answer:

54 degrees

Step-by-step explanation:

The total degree of a triangle is 180. Since it is a right angle, one of the angles is 90 degrees. The equation is, 36+90+x=180. You should then get 54 degrees.

Answer:

0-6 de correct answer okay.

At x→ -3 the value of the limit of function g(x) does not exist because the left-hand limit and right-hand limit are not equal an option second is correct.

A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.

We have a graph of function g(x)

[tex]\rm \lim_{x \to a}g(x)[/tex]

Let's check at x = -3

Finding the left-hand limit and right-hand limit.

[tex]\rm \lim_{x \to -3^{-1}}g(x) = -2[/tex]

[tex]\rm \lim_{x \to -3^{+1}}g(x) = -4[/tex]

Since the left-hand limit and right-hand limit are not equal then at x = -3 the limit does not exist.

Thus, at x→ -3 the value of the limit of function g(x) does not exist because the left-hand limit and right-hand limit are not equal an option second is correct.

Learn more about the limit here:

brainly.com/question/8533149

#SPJ2

Answer:

Step-by-step explanation:

As,

[tex] {(ax)}^{2} = a \times a \times x \times x[/tex]

Hence,

[tex] {(2x)}^{2} [/tex]

= 2×2×x×x

[tex] = 4 {x}^{2} (ans)(without \: brackets)[/tex]

Answer:

The answer for A is A- 3.75

And the answer for B is B- 16

∠1 and ∠2 are equal angles as the lie on same side of transversal, are on parallel lines and are corresponding to each other

thank you

Answer:

B

Step-by-step explanation:

Answer:

x is 5

Step-by-step explanation:

Answer:

d. 0.303

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.

Subtraction between normal variables:

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

In this question:

We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.

Distribution of the difference between Sean's and Evan's income:

Sean has mean 225, Evan 240. So

[tex]\mu = 225 - 240 = -15[/tex]

Sean's standard deviation is of 25, Evan's of 15. So

[tex]\sigma = \sqrt{25^2+15^2} = 29.15[/tex]

Probability that Sean will have a greater income than Evan in a randomly selected week:

Probability of the subtraction being greater than 0, which is 1 subtracted by the pvalue of Z when X = 0. So

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

[tex]Z = \frac{0 - (-15)}{29.15}[/tex]

[tex]Z = 0.51[/tex]

[tex]Z = 0.51[/tex] has a pvalue of 0.695

1 - 0.695 = 0.305.

Closest to 0.303, option d.

Answer:

First option is correct

Answer:

Look at explanation

Step-by-step explanation:

For a) It is TRUE

For b) it is TRUE

For c) it is FALSE

Hope this helps!! :)

Answer:

okay, the answer to this question is listed below;

for a it says that half pupils choose maths.

And as you can see the results in the circle that it is true.

for the question c it says most pupils choose science that PE, as you can see the the circle that PE is a little more than science, so this Answer is false

Answer:

1/4

Step-by-step explanation:

1/2 x 1/2 = 1/4

Answer:

im sorry

i still dont know the answer tho

Answer:

0.82

Step-by-step explanation:

100 has 2 zeros so you move the decimal 2 places to the left.

82.

8.2

0.82

Answer:

0.82

Step-by-step explanation:

Decimals are out of 100, this fraction, 82/100, is also out of one hundred; this makes the question much easier to solve.  Just take the numerator and put it as a decimal, so in this case, the numerator is 82. We take that numerator and make it a decimal: 0.82.

Answer:

In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units such as square centimteres, square feet, square inches, etc.

Answer:

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.

Step-by-step explanation:

Answer:

SA = 2(Area of Trapezoid) + 2(Area of Rectangle) + Area of Base + Area of Top

SA = 2 ( 10cm + 6cm)(7cm) + 2(16cm x 8cm) + (16cm x 10cm) + (16cm x 8cm)

                        2

SA = 112 cm2 + 256 cm2 + 160 cm2 + 128 cm2

SA = 656 cm2 wrapping paper you need

Answer:

ST = 4

Step-by-step explanation:

A segment joining the midpoints of 2 sides of a triangle is half the length of the third side.

ST = [tex]\frac{1}{2}[/tex] PQ substitute values

- 32 + 9x = [tex]\frac{1}{2}[/tex] (- 5x + 28) ← multiply both sides by 2 to clear the fraction

- 64 + 18x = - 5x + 28 (add 5x to both sides )

- 64 + 23x = 28 ( add 64 to both sides )

23x = 92 ( divide both sides by 23 )

x = 4

Then

ST = - 32 + 9x = - 32 + 9(4) = - 32 + 36 = 4

Answer:

20.5 , 30.4 , 5.3

Step-by-step explanation:

SOHCAHTOA

sinθ = opposite / hypotenuse

cosθ = adjacent / hypotenuse

tanθ = opposite / adjacent

10. tan64° = 42 / x ; x = 42 / tan64° ; x = 20.48476872

12. sin54° = BD / 20 ; BD = 20 * sin54° ; BD = 16.18033989 ;

     tan28° = BD / DC ; DC = BD / tan28° ; DC = 30.43079344

13. tan51° = JL / 14 ; JL = 14 * tan51° ; JL = 17.28856019 ;

     cos72° = KL / JL ; KL = JL * cos72° ; KL = 5.342458907

Answer:

A = 846 in²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ( d₁ and d₂ are the diagonals ) , then

A = [tex]\frac{1}{2}[/tex] × 36 × 47 = 18 × 47 = 846 in²

Answer:

846

Step-by-step explanation:

area of a rhombus is [tex]\frac{pq}{2}[/tex]  where p and q are the two diagonals ..

so [tex]A=\frac{36*47}{2}[/tex]

A=846

3 feet in a yard... 12x3 = 36...... 36+36+36 =108 inches

108 divided by 6 is 18 bracelets

Answer:

Answer:

A. 6%

Step-by-step explanation:

The is no step by step explanation sadly

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Before _After_ diff ___rank

72 ______ 59 __13 __ 2

74 _______ 72 _ 2 __ 7

62 _____ 89 __ - 27 _ 1

74 _______ 67 __ 7 __4

78 ______ 81 __ - 3 __ 6

88 ______ 92 __ - 4 __5

71 _______ 81 __ - 10 __3

Ranking the data:

27, 13, 10, 7, 4, 3, 2

Observation 5 :

Before = 78 ; After = 81

Difference ; 78 - 81 - 3

Observation 5 = Rank 6

Ranks with negative difference, T = 6 + 5 + 3 + 1 = 12

Ranks with negative difference T+ = (2 + 7 + 4) = 13

Angle F should be 46 degrees

Answer:

5/64

Step-by-step explanation:

numerators 1 time 5 is 5 and denominators 8 times 8 is 64;  5/64