LMNO is a parallelogram. If NM\ =\ x+32\ and\ OL=2x+22,\NM = x+32 and OL=2x+22, find the value of x and then find NM and OL

A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.

You will spend an average of $50 a week at this restaurant.

The 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5

An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.

Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >,,, and. has the connotation "7 is greater than" (or "is less than 7," when read left to right).

Given the incomplete expression

1 1/4 × 2 1/5 _ 5/6 × 2 1/5

We are to fill it with the necessary inequality sign

For the expression:

1 1/4 × 2 1/5 = 5/4 * 11/5

1 1/4 × 2 1/5 = 55/20

1 1/4 × 2 1/5 = 2 3/4

For the expression 5/6 × 2 1/5

5/6 × 2 1/5 = 5/6 * 11/5

5/6 × 2 1/5 = 55/30

5/6 × 2 1/5 = 1 25/30

Since 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5

The complete question is : Select the correct symbol to compare the expressions below.

1 1/4 × 2 1/5 _ 5/6 × 2 1/5

Symbols: <, >, =

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Answer: NO

Step-by-step explanation:

This is not a function, since there are multiple outputs for ONE input.

Answer:

no

Step-by-step explanation:

to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.

Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

According to the question given,

Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.

The formula of a confidence interval that we will be using for the solution will be,

p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]

In the above expression,

p = observed population.

n = sample size

[tex]z_{a}[/tex] = critical value of confidence interval

Now the given observations in question = 115

That result in success = 46

The resultant sample proportion = [tex]\frac{46}{115}[/tex]

⇒ 0.40 and it is for both success and failure

Here we can see that the answer for both parts will be identical.

The critical value of z at 90% confidence = 1.64

a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.402

b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.598

Confidence interval = 0.402 to 0.598

Therefore,

Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

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By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.

A percentage is a component of a total amount, and the three-step rule is used to relate the measurements.

The percentage of voters who select Candidate J is:

60% of x are voters are female

30% of (1 - x), who vote are male

If the total of these percentages is larger than 50% = 0.5, Candidate J will be elected; therefore:

0.6x + 0.3(1 - x) > 0.5

0.6x + 0.3 - 0.3x > 0.5

0.3x > 0.2

x > 2/3

x > 0.667

x > 67%

By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.

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The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.

We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.

V=pi*r^2*h/3  since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get

V=pi(h/2)^2*h/3 and if we simplify this,  we get

V=pi*(h^3)/12

Now we need to take the derivative of both sides with respect to t

dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt

= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get

40 = pi * 16^2/4*dh/dt

dh/dt = 40 * 4 / ( 256 * pi )

= 40/(256*pi) ft/min,

= 10/64

= 5/32 ft/min

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The balloon's vertical distance above the ground is 358.9 feet.

An angle is said to be that of depression when it is measured downwards with respect to the horizontal plane.

So that applying the appropriate trigonometric function to solve the question, we have;

Tan θ = Opposite side/ Adjacent side

But,

θ = 90 - 24

  = 66

θ = [tex]66^{o}[/tex]

Let the vertical distance of the balloon be represented by x.

Tan 66 = 806/ x

x = 806/ Tan 66

  = 806/ 2.246

  = 358.86

x = 358.9 feet

The balloon's vertical distance above the ground is 358.9 feet.

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The final answer of the problem is -0.75.

What is the order of operations?

The order of operations is also known as the hierarchy of operations. The order of operations tells us the order in which we should perform mathematical operations in order to get the correct result. The order of operations is usually represented by the acronym PEMDAS:

P: Parentheses first

E: Exponents (ie Powers and Square Roots, etc.)

MD: Multiplication and Division (left-to-right)

AS: Addition and Subtraction (left-to-right)

We have,

-1 - (-0.25)

Using the order of operations, we can solve this problem as follows:

Parentheses: The first step is to perform any calculations inside parentheses. In this case, there are no parentheses, so we can move on to the next step.

Exponents: There are no exponents in this problem, so we can move on to the next step.

Multiplication and Division: There is no multiplication or division in this problem, so we can move on to the next step.

Addition and Subtraction: Finally, we can perform addition and subtraction in the problem. We start from left to right, so we start with the first operation: -1 - (-0.25). To subtract a negative number, we can use the rule that subtracting a negative number is the same as adding a positive number.

Therefore, we have -1 + 0.25.

The final step is to simplify the expression by performing the addition: -1 + 0.25 = -0.75.

Therefore, the final result of the problem is -0.75.

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Answer:

Step-by-step explanation:

Explanation:

As you know, each electron that's part of an atom has its own unique set of four quantum numbers that describes its position and spin.

This means that looking for the number of unique sets of quantum numbers is equivalent to looking for the number of electrons that can occupy the third energy level.

As you know, the number of orbitals you get per energy level is given by the equation

no. of orbitals

=

n

2

, where

n

- the principal quantum number, the ones that gives the energy level.

So, if you're dealing with the third energy level, you can say that it will contain a total of

no. of orbitals

=

3

2

=

9

distinct orbitals.

Now, each orbital can contain a maximum of

2

electrons of opposite spins. This means that the third energy level will contain a maximum number of

no. of electron

=

9

⋅

2

=

18 e

−

So, if each electron is described by an unique set of quantum numbers, you can conclude that

18

sets of quantum numbers are possible for the third energy level.

ok maybe that will help!

The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24

Centroid is the point in a triangle where all the medians of the triangle intersects.

Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,

1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,

Therefore, 40°+y = 90°

y = 50°

x+y = 90°

x = 90°-50°

x = 40°

z = 180°-50° (linear pair)

z = 130°

2) we know that, the centroid divides the medians into 2:1

AY = 2YP

AY = 16

IY = TY/2

IY = 9

FG = GY+YF   (segment addition postulate)

GY = YF/2

GY = 10

FG = 10+20 = 30

PA = AY+YP  (segment addition postulate)

PA = 8+16

PA = 24

Hence. the measures are x, y and z are 40°, 50° and 130° and  AY = 16, IY = 9, FG = 30, AP = 24

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Answer: $2,275.94

Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:

41.09(55)

41.09 x 55

That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!

The six trigonometric functions at 11π/3 are as follows-

sin (11π/3) = -[tex]\sqrt{3}[/tex]/2

cos (11π/3) = 1/2

tan (11π/3) = -[tex]\sqrt{3}[/tex]

cot (11π/3) = -1/[tex]\sqrt{3}[/tex]

sec (11π/3) = 2

cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]

Let us evaluate the six trigonometric functions at 11π/3 as follows -

11π/3 can be written as (6π+5π)/3 = 2π + 5π/3.

a. sin (11π/3) = sin (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= sin (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, sin is negative in the 4th quadrant.

= -sin (π/3)

= -[tex]\sqrt{3}[/tex]/2

Hence, sin (11π/3) = -[tex]\sqrt{3}[/tex]/2

b. cos (11π/3) = cos (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= cos (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, cos is positive in the 4th quadrant.

= cos (π/3)

= 1/2

Hence, cos (11π/3) = 1/2

c. tan (11π/3) = tan (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= tan (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, tan is negative in the 4th quadrant.

= -tan (π/3)

= -[tex]\sqrt{3}[/tex]

Hence, tan (11π/3) = -[tex]\sqrt{3}[/tex]

d. cot (11π/3) = 1/ tan (11π/3)

Hence, cot (11π/3) = - 1/ [tex]\sqrt{3}[/tex]

e. sec (11π/3) = 1/ cos (11π/3)

Hence, sec (11π/3) = 2

f. cosec (11π/3) = 1/ sin (11π/3)

Hence, cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]

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Answer: 36.4

Step-by-step explanation:

Just convert the percentage to decimal and multiply.

70 x 0.52 = 36.4

At least means less than or equal to.

Fewest means the smallest number of boxes.

12 3/4 +x ≥ 29 5/8

x ≥ 16 7/8

The fewest number of boxes would be almost ≅ 42 boxes

Part A:

Let x denote the amount of fudge at the shop.

Helena prepares 12 3/4 pounds of fudge containing nuts.

Mathematically, the total amount of fudge on Monday will be

12 3/4 +x

Of this amount of fudge  there are at least 29 5/8 pounds of fudge containing nuts at the fudge shop on Monday

12 3/4 +x ≥ 29 5/8

Part B:

The inequality can be solved

12 3/4 +x ≥ 29 5/8

x ≥ 29 5/8- 12 3/4

x ≥  29- 12     5/8- 3/4    

The whole numbers are subtracted and the fractions are solved separately to avoid long calculations.

x ≥  17  (5-6)/8

x ≥  17 - 1/8

x ≥  (136-1)/8

x ≥  (135)/8

x ≥  16 7/8

Part C :

To find the number of boxes we divide the equal number of pounds .

12 3/4 + 29 5/8

12 + 29   3/4 + 5/8

41  11/8

42 3/8

The fewest number of boxes would be almost ≅ 42 boxes

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The mean and standard deviation of the sampling distribution include the following: C. mean = 64, standard deviation = 2.5.

In Mathematics and statistics, the Central Limit Theorem states that the sampling distribution of means would always be normally distributed, as long as the sample size is large enough.

This ultimately implies that, the sampling distribution of means would always be normally distributed as the sample size gets larger in accordance with the Central Limit Theorem.

Mathematically, the standard deviation of a sampling distribution can be calculated by using this mathematical expression:

Standard deviation, σy = σ/√n

Where:

Substituting the given parameters into the formula, we have;

Standard deviation, σy = 10/√16

Standard deviation, σy = 10/4

Standard deviation, σy = 2.5.

In conclusion, the mean of an original population is expected to be equal to the mean of the sampling distribution of means i.e 64.

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Answer:

864

Step-by-step explanation:

The model predicts that the net discharge will be -0.8 + 1.2 cos(24) billions of cubic feet from t = 0 to t = 12.

The net amount of water discharged from the Poudre river from t = 0 to t = 12 can be found using the Fundamental Theorem of Calculus, which states that the net change in a function over an interval is equal to the function evaluated at the endpoints of the interval minus the function evaluated at the beginning of the interval.

In this case, the net discharge from t = 0 to t = 12 can be calculated as follows:

Net discharge = F(12) - F(0)

= (1.5 + 1.2 cos(212)) - (1.5 + 1.2 cos(20))

= 1.5 + 1.2 cos(24) - 1.5 - 1.2

= -0.8 + 1.2 cos(24)

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Eric typed 15 words more than Dae per minute.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

To find the amount of words typed in 1 minute for both;

Dae = 333/9

Dae = 27 words per minute

Eric = 252/6

Eric = 42 words per minute

Therefore 42 - 27 = 15 words per minute

Eric typed 15 more words per minute.

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The information needs to be divided into class intervals in order to make a histogram. Following that, make a tally to display the frequency (or relative frequency) of the data within each interval.

Histogram Illustration

135  137   136  137  138  139

140  139   137  140  142  146

148  145    139  140  142  143

144   143   141  139   137  138

139   136   133   134  132  132

Her weight should be a histogram.

Answer

131.5-133.5

133.5-135.5

135.5-137.5

137.5-139.5

139.5-141.5

141.5-143.5

143.5-145.5

145.5-147.5

147.5-149.5

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The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5

To test hypotheses using proportions, the following requirements are necessary:

np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.

The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.

This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.

Hence, the correct answer would be an option (A).

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A) Yes, X is a binomial random variable because all of the requirements for a binomial distribution have been established

B) The mean and standard deviation are respectively; 1.2 and 0.6

C) The probability given as P(X ≥ 2) is 0.34464

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula of binomial probability distribution is;

P(X = x) = nCr * p^(x) * (1 - p)^(n - x)

where;

p = probability of "success"

n = number of trials, or the sample size

x = the number of "successes" in the probability we are trying to calculate.

A) We are told that 6 friends each buy one 12-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.

Probability of success; p = 1/5

Number of events; n = 6 which is the random variable being binomial random variable:

There are two types of accomplishments: successes and failures.

Candies are unrelated to one another.

There is a set number of buddies available.

In addition, the chance of success is fixed.

Because all of the requirements for a binomial distribution have been established, then it is a binomial probability distribution.

B) The formula for the mean here is;

μ = np

Plugging in the relevant values gives;

μ = 6(1/5) = 1.2

Formula for the standard deviation is;

σ = √(np(1 - p))

Thus;

σ = √(6 * 1/5)(1 - (1/5)))

σ = 0.6

C) The probability P(X ≥ 2) calculated with online binomial probability calculator gives;

P(X ≥ 2) = 0.34464

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The p-value for the z-distribution table is 0.4854.

What is  z-distribution?

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.

Given that the z statistic to be 2.19 standard deviation above the population mean.

2.19 can be written as 2.1 + 0.09

Z₂.₁₉ = Z₂.₁₊₀.₀₉ =  0.4854

Therefore p-value is  0.4854.

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The reasons that complete the statements are:

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

Triangles = RST, and TUR

From the question, we have the following given parameters

∠SRT ≅ ∠UTR

This means that

Statement 2: ∠SRT ≅ ∠UTR ------ Given

At this point, we have

RS ≅ TU --- Congruent side (S)

∠SRT ≅ ∠UTR ------ Congruent angle (A)

RT ≅ TR --- Congruent side (S)

When these congruent sides and angles are combined, we have

SAS congruence property

The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent

Hence, the additional information on the congruency of the triangles are Given and SAS congruence property

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The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by  

Here we have

A (-12, 2) and B(-6, 2)

B (-6, 2) and C(-6, -4)

C (-6, -4) and D(6, 2)

D (6, 2) and E(6, 4)

E (6, 4) and F(-12, 4)  

Here we will find the distance between given points to find the point which has 6 units between them.

As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]

For Option A

A (-12, 2) and B(-6, 2)

Distance = √(-6 + 12)² + (2 - 2)²

= √[(6)² + (0)²] = √36 = 6

For Option B

For  B (-6, 2) and C(-6, -4)

Distance = √(-6 - (-6))² + ( - 4 - 2)²

= √[(0)² + (-6)²] = √36 = 6  

For Option C

For C (-6, -4) and D(6, 2)

Distance =√(6 - (-6))² + (2 - (-4))²

= √(12)² + (6)² = √180 = 6√5

For Option D

For D (6, 2) and E(6, 4)

Distance = √(4 - 2)² + ( 6 - 6)²

= √[(2)² + (0)²] = √4 = 2      

For Option E

For E (6, 4) and F(-12, 4)  

Distance = √(-12 - 6)² + (4 - 4)²

= √[(18)² + (0)²] = √18² = 18

Therefore,

The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

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The value of x in the problem is 0

Given that PQR is a straight line

In this problem PQ+QR=PR

The value of PQ is 9

The value of QR is not given but given an equation 2x+3

And QR is x+12

So PQ+QR=PR

9+2x+3=x+12

12+2x=x+12

2x-x=12-12

x=0

Therefore, the value of x in the problem is 0

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The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.

Straight line equation is y = a + bx.

The normal equations are

∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :

The values are calculated using the following table

x y x²             x⋅y

58 62 3364 3596

47 51 2209 2397

84 88 7056 7392

62 66 3844 4092

57 61 3249 3477

72 76 5184 5472

69 73 4761 5037

hence :

∑x = 449

∑y = 477

∑x² = 29667

∑x⋅y = 31463

Substituting these values in the normal equations

7a+449b=477

449a+29667b=31463

Solving these two equations using Elimination method,

7a+449b=477

and 449a+29667b=31463

7a+449b=477→(1)

449a+29667b=31463→(2)

equation(1)×449

⇒3143a+201601b=214173

equation(2)×7

⇒3143a+207669b=220241

Substracting

⇒-6068b = -6068

⇒6068b = 6068

⇒b = 1

Putting b = 1 in equation (1), we have

7a+449(1) = 477

⇒7a = 477  - 449

⇒7a = 28 or a  = 4.

Now Estimate y for x=50

y = a + bx , we get

y = 4 + 1×50

y = 4 + 50

y = 54

At x equals 50 we get the value of y as 54 .

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The number of hours it will take the student to complete the project is 5 / 6 hours.

A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate,  the time it will take the student to complete the project can be calculated as follows:

Therefore,

let

x = time it will take the student to complete the project

Hence

if 4 / 5 x = 2 / 3 hours

x = ? hours

cross multiply

Therefore,

number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x

number of hours to complete the whole math project = 2 / 3 x × 5 / 4x

number of hours to complete the whole math project = 10x / 12x

number of hours to complete the whole math project = 10 / 12

number of hours to complete the whole math project = 5 / 6 hours

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