The four angles, in degrees, of quadrilateral ABCD are
angle A = (x² – 105)
angle B = (x² – 65)
angle C = (470 – 30x)
angle D=(510-30x)
Show that ABCD is a trapezium.
Show clear algebraic working.

Answer:

x=44

y=32

Step-by-step explanation:

Given numbers x and y:

y=x-12

x+y+7=83

x+x-12+7=83

2x=88

x=44

y=32

Answer

[tex]2 + 2 = 4[/tex]

Answer:

4

Step-by-step explanation:

2+2

4

hope it helps. Nice time

The  interval containing the middle-most 86% of sample mean in the interval notation is  is (196.4, 203.5)

The 50 +/- 86/2 percentile will make up the center 86% of the sample means' distribution.

The 86th percentile's z-score is 1.08

sample mean population mean = 200

standard deviation from mean = 19

sample size = 33.

Standard error (SE) is equal to 19 / sqrt(33) = 3.3077.

86th percentile x can be located using the formula z = (x - population mean)/sample error.

1.08 = (x - 200)/3.3077

x = 3.3077* 1.08 + 200 = 203.57

that is the interval's upper bound.

it is 3.5721 over the population mean (203.57 - 200).

Due to the symmetry of the normal distribution, the interval's bottom bound will be 1.66 standard deviations below the population mean (200 - 3.572 = 196.428).

then the interval is (196.4, 203.5).

To learn more about mean

brainly.com/question/17514579

#SPJ4

The length of the Zambezi river is 838 × 10⁵ or 83.8 × 10⁶ or 8.38 × 10

What is scientific notation?

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

For example, 750,000,000 can be written in scientific notation as 7.5 ✕ 10⁸.

The length of the Zambezi river 83,800,000 feet.

Rewrite 83,800,000:

83,800,000 = 838 × 100000

83,800,000 = 838 × 10⁵ [Since the number of zeros is 5]

Multiply and divide 10:

83,800,000 = 838 × 10⁵ × (10/10)

83,800,000 = (838/10) × 10⁵ × 10

83,800,000 = 83.8 × 10⁵ × 10

83,800,000 = 83.8 × 10⁶

Multiply and divide 10:

83,800,000 = 83.8 × 10⁶ × (10/10)

83,800,000 = (83.8/10) × 10⁶ × 10

83,800,000 = 8.38 × 10⁷

To learn more about  scientific notation, click on below link:

https://brainly.com/question/18073768

#SPJ1

For the given scatter plot of the data, the wrong with the conclusion was shown by option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect.

As given in the question,

Based on the class data of quiz3,

Teacher made scatterplot to represent the linear relation between amount of study time and quiz score

Pattern form was linear.

Using which correlation coefficient was computed to r = 0.8.

From the data scatterplot as it was linear the more time students study the good will the score.

Therefore, from the information of scatterplot option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect answer.

learn more about scatterplot here

brainly.com/question/29366075

#SPJ4

The y-intercept is 21 and the x-intercept is -21/8 for the equation -8x +y = 21.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given the equation is -8x + y = 21. The x and y-intercepts will be calculated as below,

For the y-intercept substitute, the value x=0 in the equation,

-8x + y  = 21

0 + y = 21

y = 21

For the x-intercept substitute the value of y=0 in the equation,

-8x + y  = 21

-8x = 21

x = -21 / 8

To know more about coordinate geometry follow

https://brainly.com/question/29927851

#SPJ1

Answer:

[tex]27x^6y^6[/tex]

Step-by-step explanation:

The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex].  So,

[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].

Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex].  So,

[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]

 For recording the angular velocity we will use

     angular velocity, ω = dθ /dt

Angular velocity:

Angular velocity is a vector quantity, expressed as the angular velocity or rotational speed of an object and the rate of change of angular displacement that specifies the axis about which the object rotates. The amount of change in a particle's angular displacement over time is called its angular velocity. The trajectory of the angular velocity vector is usually perpendicular to the plane of rotation in the direction given by the right-hand rule.

Total Moment of Inertia:

The total moment of inertia is the sum of the moments of inertia of the mass elements in the body.

Unlike mass, which is a constant for a given body, the moment of inertia depends on the location of the center of rotation. In general, the moment of inertia is calculated by using integral calculus.

Thin cylindrical shell open at both ends, radius r, mass m.

This formula assumes that the thickness of the shell is negligible. This is a special case of a thick-walled cylindrical tube with r1=r2. A point mass m at the end of a rod of length r has the same moment of inertia and the value r is called the radius of gyration.

Learn more about Angular velocity:

https://brainly.com/question/29557272

#SPJ4

Answer:

4

Step-by-step explanation:

***Your question is asking for f(4) - f(2)***
If so, this is the answer:

[tex]f(4) = 2\cdot4 + 3 = 11\\\\f(2) = 2\cdot 2 + 3 = 7\\\\f(4) - f(2) = 11 - 7 = 4[/tex]

The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

To learn more about the isosceles triangles, visit:

https://brainly.com/question/1475130

#SPJ1

The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

To learn more about the isosceles triangles, visit:

brainly.com/question/1475130

#SPJ1

The expression which represents the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).

It follows from the task content that the expression which represents the nth term of the given sequence, in terms of variable, n be determined.

According to the task content, the first term, a of the sequence is; 1.

Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.

Consequently, the required expression is an arithmetic sequence which can be modelled by;

T (n) = a + d (n - 1)

Since the constant common difference of consecutive terms in the sequence is; 7,

Therefore, the expression for the nth term of the expression is;

nth = 1 + 7(n -1)

On this note, the required expression which represents the nth term of the arithmetic sequence in discuss is; T (n) = 1 + 7 (n -1).

Read more on arithmetic sequence;

https://brainly.com/question/22972770

#SPJ1

Answer:

x=5

Step-by-step explanation:

If p and q are parallel, then the two angles in question should be equal to one another.

So,

(3x+15)°=(8x-10)°

(3x+15)°+10°=(8x-10)°+10°

(3x+25)°=(8x)°

(3x+25)°-(3x)°=(8x)°-(3x)°

25°=5x°

5=x

So, the two angles should be (8(5)-10)° and (3(5)+15)°.  Both of these expressions equal 30°.  This makes sense, as the illustration shows that the two angles are acute.

The given expression can be simplified to get the value as 19. The correct option is (A).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

[tex](12b - 2^{c}) /\sqrt[3]{a}[/tex]

Substitute a = 64, b = 9 and c = 5 to obtain the value as below,

⇒ (12 × 9 - 2⁵)/∛64

⇒ (108 - 32)/4

⇒ 76/4

⇒ 19

Hence, the value of the given expression is obtained as 19.

To know more about algebraic expression click on,

brainly.com/question/953809

#SPJ1

The image of the complete problem is attached here.

Answer:

listed below

Step-by-step explanation:

5.) x=77 and y=63

6.)y=60 and x= 1230

7.)y=65 and x=92

8.)y=69 and x=175

The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

The population propose will match the pattern mean's proposal. The population trendy deviation divided by the rectangle root of the sample length yields the same results as the standard deviation of the distribution of the sample means, also known as the same old mistakes of the proposed (n).

The general sample recommends factors to be included in the pattern mean calculation.

The population suggest is calculated using the sum of all values within the population denoted with the aid of the summation of X divided by the number of values in the population that is denoted with the aid of N. The population suggest is the mean or average of all values within the given population.

Therefore,

The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

Learn more about Population mean visit :

brainly.com/question/19538277

#SPJ4

a) No, it is not possible. A Type I error is rejecting the null hypothesis when it is in fact true.

b)Yes, it is possible. A Type II error is not rejecting the null hypothesis when it is in fact false.

A false positive conclusion in statistics is known as a Type I error, and a false negative conclusion is known as a Type II error.

The significance level, or alpha, determines the likelihood of a Type I error, whereas beta determines the likelihood of a Type II error. These dangers can be reduced by carefully designing the layout of your study.

If your results show statistical significance, that means they are very unlikely to occur if the null hypothesis is true. In this case, you would reject your null hypothesis. But sometimes, this may actually be a Type I error.

If your findings do not show statistical significance, they have a high chance of occurring if the null hypothesis is true. Therefore, you fail to reject your null hypothesis. But sometimes, this may be a Type II error.

To learn more about hypothesis testing visit: brainly.com/question/17099835

#SPJ4

The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.

When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.

This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.

Given that triangle AXY is similar to triangle ABC, it means that:

m<A = m<A

m<X = m<B

m<Y = m<C

AX/AB = AY/AC = XY/BC

To find the length of AB, we could use the following expression derived from the ratios stated above:

AX/AB = AY/AC

Cross multiply:

(AB) * (AY) = (AX) * (AC)

Divide both sides by AY

(AB) * (AY) / AY = (AX) * (AC) / AY

AB = AX * AC/AY

The expression to use is: A. AB = AX * AC/AY

Learn more about similar triangles on:

https://brainly.com/question/14285697

#SPJ1

Answer:

Step-by-step explanation:

Given the conditional statement ~p → q, the statement logically equivalent is ~q → p.

Answer:

The prime factors are 3 and 3

The correlation of the rates of return between x and y is the closest to = 0.4

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect.

Calculation for the correlation of the returns,

Using this formula,

Covariance of the returns = Correlation coefficient between the returns*Stock returns standard deviation*Mod T Stock returns standard deviation

The sample standard deviations of the rates of return for stock x and stock y were 0.20 and 0.12

The sample covariance between the returns of x and y is 0.0096.

Let plug in the formula

Covariance of the returns = Correlation * (0.20) * (0.12)

0.0096 = Correlation * (0.20) * (0.12)

0.0096 = Correlation * 0.024

0.0096 / 0.024 = Correlation

0.4 = Correlation

Correlation = 0.4

Therefore,

The correlation of the rates of return between x and y is the closest = 0.4

To learn more about Correlation visit :

brainly.com/question/29587264

#SPJ4

The required relation as a set of ordered pairs is (C) {(–2,4), (0,0), (2,4)}.

A set of ordered pairs is any pair of components that appear in a specific sequence and are wrapped in brackets.

If there are two elements, "a" and "b," then the two distinct pairings are "(a, b)" (b, a).

A is referred to as the first element and B is referred to as the second element in an ordered pair (a, b).

A pair of numbers in a particular order is known as an ordered pair.

The ordered pairings (1, 2) and (-4, 12) are two examples.

It matters which of the two numbers comes first: (2, 1) and (1, 2) are not the same thing (2, 1).

So, an arrow in a relationship travels from -2 to 4, 0 to 0, and 2 to 4.

Consequently, by virtue of ordered pairs.

The ordered pairings are obtained:

(-2, 4)

(0, 0)

(2, 4)

Hence, the pairs are (-2, 4), (0, 0), and (-2). (2, 4)

Therefore, the required relation as a set of ordered pairs is (C)  {(–2, 4), (0, 0), (2, 4)}.

Know more about Ordered pairs in the set here:

https://brainly.com/question/20348140

#SPJ1

Correct question:
Write the relation as a set of ordered pairs.

A relation. An arrow goes from negative 2 to 4, 0 to 0, 2 to 4.

a. ordered pairs: {(4, –2), (0, 0), (2, 4)}

b. ordered pairs: {(–2, 4), (0, 0), (4, 2)}

c. ordered pairs: {(–2, 4), (0, 0), (2, 4)}

d. ordered pairs: {(4, –2), (0, 0), (4, 2)}

Please select the best answer from the choices provided

A

B

C

D

Answer: 2 170 kilograms [kg] of Salt fit into 1 cubic meter. 135.46867 pounds [lbs] of Salt fit into 1 cubic foot. Salt weighs 2.17 gram per cubic centimeter or 2 170 kilogram per cubic meter, i.e. density of salt is equal to 2 170 kg/m³; at 20°C (68°F or 293.15K) at standard atmospheric pressure . In Imperial or US customary measurement system, the density is equal to 135.469 pound per cubic foot [lb/ft³], or 1.254 ounce per cubic inch [oz/inch³] .

Step-by-step explanation:

Answer:

The number of degrees Celsius goes down 6 every week. (-6)

Step-by-step explanation:

If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).

The equation will look something like this:

w ÷ t = c

Fitting the numbers into this equation will look something like this:

2 ÷ -12 = -6

Every week, it changed -6 degrees Celsius.

Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.

a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.

b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.

c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.

d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.

For more questions like Probability click the link below:

https://brainly.com/question/29251004

#SPJ4

The cosecant of the angle is 0.2

From the question, we have the following parameters that can be used in our computation:

(5,-12)

This means that

(x, y) = (5,-12)

The csc(θ) is calculated as

csc(θ) = 1/x

Substitute the known values in the above equation, so, we have the following representation

csc(θ) = 1/5

Evaluate

csc(θ) = 0.2

Hence, the value of csc(θ) is 0.2

Read more about unit circle at

brainly.com/question/20691579

#SPJ1

The standard deviation of Y is 432.

                (Y = 75X - 100)

The formula of the standard deviation is :

                           SD(Y) = SD(75X - 100)

Substituting the value of SD(X) and SD(100) in the above expression.

SD(Y) = 75SD(X) - SD(100)

SD(Y) = 75 SD(X) - 0

SD(Y) = 75 × 5.76

SD(Y) = 432

Hence, the standard deviation of Y is 432.

Read more about standard deviation:

https://brainly.com/question/22920224

#SPJ4

The decimal equivalent of the relative frequency, rounded to the closest tenth, is 1.

The proportion of outcomes when a certain event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Thirty male college students at random were chosen.

The following table lists their heights in inches. These heights are 12 44 70 73 68 66 73 70 23 23 64 74 and 68 69 70 71 73.

Therefore, the frequency of any height value in the data set is just its count. A value's relative frequency is simply the ratio of its corresponding frequency to  the total frequency.

So, the frequency table is

Height(xi) Frequency(fi) Relative frequency

66                  3                        3/30=0.1

67                  3                                3/30=0.1

68                 4                                 4/30=0.13

69                3                                3/30=0.1

70               2                                2/30=0.06

71                  4                                4/30=0.13

72                 2                                 2/30=0.06

73                  6                                 6/30=0.2

74                 3                                 3/30=0.1

Total    30                                1

the frequency distribution for the data is given above.

The relative frequency as decimals, rounded to the nearest tenth is 1

To know more about frequency distribution click :

brainly.com/question/16891663

#SPJ1

Answer:

2.5

Step-by-step explanation:

Step-by-step explanation:

Given

Shelf Width = 3ft 9in

Copies = 18

Required

Determine the width of each book

This is calculated by dividing the shelf width by the number of copies.

Width = Shelf Width ÷ Copies

Width = (3 ft 9in) ÷ (18)

[Convert with to inches]

Width = (3 * 12 + 9) ÷ (18)

Width = (36 + 9) ÷ (18)

Width = 45 ÷ 18

Width = 2.5 inches

Part a: Probability Americans drink coffee or drink tea = 0.50.

Part b: Conditional probability: 2/3.

Part a: Probability, Americans drink coffee or drink tea.

P(C∪T) = P(C) + P(T) - P(C∩T)

P(C∪T) = 0.40 + 0.30 - 0.20

P(C∪T) = 0.50

Part b: They are more likely to consume coffee if they also drink tea.

P(C | T) = P(C∩T)/P(T)

P(C | T) = 0.20/0.30

P(C | T) = 0.20/0.30

P(C | T) = 2/3

Thus, the conditional probability they drink coffee given that they drink tea is 2/3.

To know more about the conditional probability, here

https://brainly.com/question/23382435

#SPJ1