The sum of two numbers is -25. One number is 101 less than the other. Find the numbers

Answer:

x = -1.875

Step-by-step explanation:

-2 (5x + 8) = 14 + 6x

-10x - 16 = 14 + 6x

-16x = 30

x = 30/-16

x = -1.875

Therefore, we have proven the vertical angles theorem by using congruency properties.

The intersection of two straight lines produces two sets of linear pairs with congruent angles, according to this theorem. Moreover, it indicates that the neighboring angles created by the junction of these two lines are supplementary, or 180 degrees.

Here,

THEOREM:

According to the Vertical Angles Theorem, two crossing lines' opposing (vertical) angles must be equivalent.

THE ISSUE:

Show that ∠1 ≅∠3 and ∠2 ≅ ∠4

PROOF:

(1) A straight line measures 180 degrees; m∠1 + m∠2 = 180°

(2)  m∠3 + m∠2 = 180°; the length of a straight line is 180.

(3) Since the sum of the two left-hand sides of the equation equals 180 degrees, the transitive principle of equality holds that   m∠1 + m∠2 = m∠3 + m∠2       

(4) m∠1 = m∠3       which demonstrates the equality's subtraction property ( m∠2 is subtracted from both sides).

Definition of congruent angles: (5) ∠1 ≅ ∠3 

Likewise, for ∠2 ≅∠4:

(1)   m∠3 + m∠2 = 180°  a straight line has a 180° length.

(2) m∠3 + m∠4 = 180°  a straight line has a 180° length.

(3) Since both of the equation's left-hand sides add up to 180 degrees, the expression   m∠3 + m∠2 = m∠3 + m∠4        / transitive property of equivalence.

(4)  m∠2 = m∠4    , demonstrating the equivalence of subtraction (m∠3 is subtracted from both sides).

// definition of congruent angle , ∠2 ≅ ∠4      

We have therefore established the theorem.

Therefore, we have proven the vertical angles theorem by using congruency properties.

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Correlation Coefficient between the given variables is 0.0023

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

Correlation Value of the coefficient is always between -1 and +1. If the correlation coefficient value is positive, the two variables have a similar and same relationship. Otherwise, it shows how the two variables are different.

The Pearson correlation coefficient is the result of dividing the covariance of two variables by the sum of their standard deviations. It is typically displayed as ρ(rho).

The correlation coefficient can be determined using the formula if the two variables being discussed are x and y.

Formula for Correlation Coefficient:

r×{[n∑x∧2-(∑x)∧2][n∑y∧2-(∑y)∧2]}=n(∑xy)-∑x×∑y.

From given data:

∑x=3.95+4.18+7.5+6.19+6.35+7.23+7.98+8.15=51.53

∑y=16.12+15.75+21.45+20.08+22.60+21.95+26.42+28.38=172.75

∑x²=[tex]3.95^{2}+4.18^{2}+7.5^{2}+6.19^{2}+6.35^{2}+7.23^{2}+7.98^{2}+8.15^{2}=350.3393[/tex]

∑y²=[tex]16.12^{2}+15.75^{2}+21.45^{2}+20.08^{2}+22.60^{2}+21.95^{2}+26.42^{2}+28.38^{2}=3867.2291[/tex]

∑xy=[tex]3.95\cdot16.12+4.18\cdot15.75+7.5\cdot21.45+6.19\cdot20.08+6.35\cdot22.6+7.23\cdot21.95+7.98\cdot26.42+8.15\cdot28.38=1159.0163[/tex]

By substituting in formula:

[tex]r=\frac{8*1159.0163-51.53*172.75}{(8*350.3393-51.53^2)(8*3867.2291-172.75^2)}=\frac{370.3229}{147.3735*1095.2703}[/tex]

r=0.00229=0.0023

Correlation Coefficient between the given variables is 0.0023

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The correlation coefficient between the following variables is  0.76.

A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another. When two variables rise or decrease simultaneously, there is a positive correlation; when there is a negative correlation, one variable increases as the other falls.

We know the coefficient of correlation is [tex]r = \frac{\sum{XY}}{\sum{X^{2}Y^2}}[/tex].

Now, [tex]\sum{XY}[/tex] = (3.95)×(16.12) + (4.18)×(15.75) + (7.50)×(21.45) + (6.19)×(20.08)

+ (6.35)×(22.60) + (7.23)×(21.95) + (7.98)×(26.42) + (8.15)×(28.38).

[tex]\sum{XY} =[/tex] 1159.02.

[tex]\sum{X} =[/tex] 51.53.

[tex]\sum{X^2} =[/tex] 463.35.

[tex]\sum{Y} =[/tex] 172.75.

[tex]\sum{Y^2} =[/tex] 5047.015.

∴ [tex]r = \frac{\sum{XY}}{\sum{X^{2}Y^2}}[/tex].

= [tex]\frac{1159.02}{\sqrt{463.35\times 5057.015}}[/tex].

= 1159.02/1530.74.

= 0.76.

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Function notation, such as f(x) = 3x + 5, can be interpreted by plugging in different values for x and evaluating the resulting expression.

For example, if we plug in 2 for x, we get f(2) = 3(2) + 5 = 11. This means that the value of the function at x = 2 is 11. By plugging in different values for x, we can evaluate the function at any point on its domain.

A connection between two variables can be expressed using function notation. We are accustomed to writing straight-line equations in the form y = m x + c .

We can express this in function notation as f (x) = m x + c by substituting y with f (x).

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to estimate the average coffee intake of Coursera students, measured in cups of coffee. C) μ=0.55, σ=1 is not necessarily true.

Given that survey is of 1000 students so n = 1000, average is 0.55 cups per day  i.e. mean (x bar) = 0.55 and standard deviation is of 1 cup per day ,i.e. S.D (s) = 1 .

First, determine the mean. Step 2: Calculate the square of each data point's variance from the mean. Add the values from Step 2 in Step 3. Divide by the total number of data points in step 4.

Just because the sample statistics are these values doesn't mean the population values will be exactly equal to them, therefore it's not necessarily true μ=0.55, σ=1 .

C) μ=0.55, σ=1 is not necessarily true.

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The number of right-handed players in the local little league given its percentage is 28

Based on the given task content; the number of right-handed players there can be determined by solving the percentage of right-handed players.

Number of right-handed players = Percentage of right-handed players × Total number of players in the local little league

= 40% × 70

= 40/100 × 70

= 0.4 × 70

= 28

In conclusion, the total number of right-handed players is 28

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The perimeter of the rectangle is equal to 2(√90 + √40).

A coordinate plane is a 2D plane which 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.

The perimeter is defined as the sum of all the sides of the rectangle.

Given coordinates of the rectangle are (4, −3), (2, 3), (11, 6), and (13, 0). The length and width of the rectangle are calculated by the distance formula.

D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]

Here, D is the distance, and the  y₂ and y₁ are the coordinates.

L = √(13-4)² + 3² = √90

W = √ ( 4-2)² + (3 + 3)² = √40

The perimeter is,

P = 2(L + W)

Here, P is the perimeter and L is the length, and W is the width.

P = 2 (√90 +√ 40)

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X=77

y=77by 2

answer is complete

Answer:

7

Step-by-step explanation:

54 - 3 = 51

51 divided by 7 is 7 with 2 left over

The rate per student for the gym is given as $5.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The rent of gym for 30 students is $150.

And, for 70 students it is $350.

The rate of rent in both the cases can be found by taking the ratio as follows,

The unit cost in the first case = Total rent ÷ Number of students

                                                 =  150 ÷ 30 = $5  

And, the unit cost in the second case = 350 ÷ 70 = $5

Hence, the required rate is obtained as $5 per student for both the cases.

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An ordinary bend is a ringer molded bend that gives probabilities of irregular factors taken in a nonstop conveyance. The z score formula is used to standardize the random variables into a z score.

Using the z score formula and the z table, standardize the value of x and use it to denote the cellphone's lifetime in months.

The area under the probability density function curve in a given range is the probability that a continuous random variable fall within a given range. Because the value of a random variable must be in the sample space, the total area under the curve for any pdf is always 1.

A continuous probability distribution is the normal distribution. Probability is affected in multiple ways by this. 1 is the total area under the normal curve. A normal random variable X has a 0 chance of matching any given value.

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Full Question = A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable.

Answer:

Natalie arrives is Sheffield at 1:00 pm

Step-by-step explanation:

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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L1 (Ridge Regression) regularization is better than L2( Lasso regression). A regularization term two general types of regularization L1 and L2 regularization is added to solve the overfitting problem.

Let's use a linear regression formula for this explanation, y = mx + c

This is the simplest formula, so if there is only one feature, this is the formula. But in the real world, we rarely deal with just one feature. Most of the time we have multiple functions.

y = m₁ x₁ + m₂x₂ + ----+ mₙxₙ

To create simpler (sparse) models when the dataset has a large number of features, here are some of the regularization techniques used to correct overfitting and feature selection. A regression model that uses the L1 regularization method is called a Lasso regression. Lasso regression (least absolute shrinkage and selection operator) is Add "absolute size".

∑(Yᵢ ) - ∑Xᵢβⱼ)² + λ ∑|βⱼ|

Models using L2 are called ridge regression Ridge Regression adds the "squared magnitude" of the coefficients as a penalty term to the loss function. where the highlighted part represents the L2 regularization factor and the cost function

∑(Yᵢ - ∑Xᵢβⱼ )² + λ ∑β²

The L1 regularization is more robust than the L2 regularization for fairly obvious reasons. Since we take the weights squared, the cost of outliers present in the data increases exponentially. L1 regularization takes the absolute value of the weights, so the cost increases only linearly. Both L1 and L2 can add cost penalties depending on the complexity of the model, so when calculating the cost using the loss function, an auxiliary component called the regularization term adds complexity to the model. Added for segmentation.

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To find the original price of the T-shirt before the discount, we need to divide the discount by the percentage to find the discount amount, then add the discount amount to the sale price to find the original price. In this case, the discount was $10.50 * 30% = $<<10.5030.01=3.15>>3.15. So the original price of the T-shirt before the discount was $10.50 + $3.15 = $<<10.50+3.15=13.65>>13.65. Answer: \boxed{13.65}.

Answer:

$15.00

Step-by-step explanation:

The original price is x, an unknown.

x is 100% of the original price.

The discount was 30%.

100% - 30% = 70%

The discounted price was 70% of the original price.

70% of x is $10.50

0.7x = 10.5

x = 15

Answer: $15.00

The rent per unit will be $8,354.22 to have a Net Operating Income (NOI) of $100,000.

The net operating income (NOI) is the difference between the gross operating income and the operating expenses.

The net operating income excludes some fixed or period expenses.

                                                                                            Total

Rent per unit (per month) = $696.19 ($8,354.22/12)   $150,376

Vacancy Rate (5% of Potential Gross Income)                   7,519

Effective Gross Income                                                $142,857

Operating Expenses (30% of Effective Gross Income) 42,857

Net Operating Income (NOI)                                      $100,000

Number of Units 18

Gross operating income = net operating income + operating expenses

Operating expenses = 30% of effective gross income

Net operating income = 70% of effective gross income (100 - 30%)

= $100,000

Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)

Vacancy rate = 5% of potential gross income

Effective Gross Income = 95% (100 - 5)

Potential gross income = $150,376 ($142,857 ÷ 95%)

Number of units = 18

Rent per unit = $8,354.22 ($150,376/18)

Rent per month = $696.19 ($8,354.22 ÷ 12)

Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.

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Part 1) The rule of the translation is    (x,y) ------> (x+4,y+5) ,Part 2) B'(4,8) Part 3) C'(3,3)

Find out the rule of the translation

we know that

The transformation of the point A to A' is equal to

A(-4,1) ------> A'(0,6)

so

The rule of the translation is equal to

(x,y) ------> (x + a ,y + b)

(-4,1) ------> (-4 + a, 1 + b)

Find the value of a

-4 + a = 0 -----> a = 4

Find the value of b

1 + b = 6 -----> b = 5

substitute the values of a and b

(x,y) ------> (x+4,y+5)

That means -----> The translation is 4 units at right and 5 units up

Find out the coordinates of B'

Applying the rule of the translation

(x,y) ------> (x+4,y+5)

so

B(0,3) ------> B'(0+4,3+5)

B(0,3) ------> B'(4,8)

Find out the coordinates of C'

Applying the rule of the translation

(x,y) ------> (x+4,y+5)

so

C(-1,-2) ------> C'(-1+4,-2+5)

C(-1,-2) ------> C'(3,3)

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An equation in the form x = a , where a is a constant can never be a function.

What is a function?

A function is defined as a relation between a set of inputs having one output each.

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and codomain or range.

A function is generally denoted by f(x) where x is the input.

The general representation of a function is y = f(x).

According to the given question:

An equation is in the form x = a , where a is a constant.

This equation is a vertical line parallel to y axis. For a function a relation of y = f(x) is missing in the given equation since a is a constant.

Hence, x = a can never be a function.

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The average rate of change between interval 5 to 11 is 4.5.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Given

Average rate of change

= Change in output/ Change in input

= 45 - 18/ 11 -5

= 27/6

4.5

The average rate of change between interval 5 to 11 is 4.5.

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To find the formula for the nth term of a geometric sequence, we can use the formula:

a_n = a_1 * r^(n-1)

where a_1 is the first term of the sequence, r is the common ratio, and n is the position of the term.

In this case, the first term of the sequence is a_1 = 7 and the common ratio is r = (-21)/7 = -3. Plugging these values into the formula, we get:

a_n = 7 * (-3)^(n-1)

Therefore, the formula for the nth term of the geometric sequence is:

a_n = 7 * (-3)^(n-1)

Answer:

[tex]a_n=7\left(-3\right)^{n-1}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given geometric sequence:

To find the common ratio, divide a term by the previous term:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{63}{-21}=-3[/tex]

Substitute the found common ratio and given first term into the formula to create an equation for the nth term:

[tex]a_n=7\left(-3\right)^{n-1}[/tex]

Answer: y = 11 , x =3

Step-by-step explanation:

Since its an isosceles triangle , two angles or two side are equal.

So lets take 5y - 3 as one of the equal angles, so

5y-3+ 5y-3 + 76 = 180 (angles in a triangles should add up to 180)

10y - 6 + 76 = 180

10y = 180 - 70

10y =110

y = 110/10

y = 11

Now, since we found y we need to find x.

Lets us take 8x and 13x - 15 as the equal sides.

8x = 13x - 15

8x - 13x = -15

-5x = -15

x = -15 / -5

x = 3

so we found the values of x and y !

Answer:

Step-by-step explanation:

You want the values of x and y, given an isosceles triangle with congruent sides JK=8x and KL=13x-15, angle K=76°, and angle J=(5y-3)°.

  JK = KL

  8x = 13x -15

  15 = 5x . . . . . . add 15-8x

  3 = x . . . . . divide by 5

The sum of the angles in the triangle is 180°.

  2(∠J) +∠K = 180°

  2(5y -3) +76 = 180 . . . . substitute known values, divide by °

  10y +70 = 180 . . . . . . simplify

  y +7 = 18 . . . . . . . . divide by 10

  y = 11 . . . . . . . . . subtract 7

The values of x and y are 3 and 11, respectively.

The product of 0.123(overline) and 9 is equal to 149/142.

To multiply 0.123(overline) and 9, we can first rewrite 0.123(overline) as a fraction. To do this, we can express 0.123(overline) as a fraction with a denominator of 1000, which represents the number of thousandths that 0.123(overline) represents:

To find the product of 123/1000 and 9, we can use the distributive property:

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common factor, which is 7:

Therefore, the product of 0.123(overline) and 9 is equal to 149/142.

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The program can be broken down into four classes, each with a different percentage of instructions.

Program in math is a set of instructions or steps that are used to solve a problem. It is a systematic approach to problem-solving, using algorithms and data structures to store and manipulate data. Program in math can be used to solve a variety of problems, from simple arithmetic operations to complex calculations such as solving equations or finding the optimal solution for a game. Program in math helps us to make decisions, find patterns, and solve problems in an efficient and organized way.

Class A consists of 20% of the instructions,

Class B consists of 30%,

Class C consists of 20%  

Class D consists of 30%.

This breakdown allows for a better understanding of the program, making it easier to analyze and determine what needs to be done to improve it.

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The program can be broken down into four classes, each with a different percentage of instructions.

Program in math is a set of instructions or steps that are used to solve a problem. It is a systematic approach to problem-solving, using algorithms and data structures to store and manipulate data. Program in math can be used to solve a variety of problems, from simple arithmetic operations to complex calculations such as solving equations or finding the optimal solution for a game. Program in math helps us to make decisions, find patterns, and solve problems in an efficient and organized way.

Class A consists of 20% of the instructions,

Class B consists of 30%,

Class C consists of 20%  

Class D consists of 30%.

This breakdown allows for a better understanding of the program, making it easier to analyze and determine what needs to be done to improve it.

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Answer:

Step-by-step explanation:

a. To calculate the incremental income after taxes, we need to determine the incremental costs and revenues associated with extending credit to the new customers. The additional credit sales will generate $180,000 in revenue, but we need to subtract the expected uncollectible amount of 12% * $180,000 = $21,600. The net additional credit sales will be $180,000 - $21,600 = $158,400.

The production and marketing costs will be 72% * $180,000 = $129,600. The total incremental costs will be $129,600 + $16,200 (collection expense) = $145,800.

The incremental income before taxes will be $158,400 - $145,800 = $12,600. The income tax will be 34% * $12,600 = $4,284. The incremental income after taxes will be $12,600 - $4,284 = $8,316.

To calculate the return on incremental investment, we need to determine the incremental investment required to extend credit to the new customers. Since no additional investment in assets is required, the incremental investment will be equal to the incremental costs of $145,800. The return on incremental investment will be $8,316 / $145,800 = 5.7%.

Based on the return on incremental investment of 5.7%, the company should not extend credit to the new customers, as it is below the desired return of 10%.

b. If an additional investment in inventory is required to extend credit to the new customers, we will need to recalculate the incremental income after taking into account the additional investment. If the additional investment in inventory is $x, the incremental investment will be $145,800 + $x. The incremental income before taxes will be $158,400 - ($129,600 + $16,200 + $x) = $12,600 - $x. The income tax will be 34% * ($12,600 - $x) = $4,284 - $x * 0.34. The incremental income after taxes will be ($12,600 - $x) - ($4,284 - $x * 0.34) = $8,316 - $x * 0.34.

To determine whether credit should be extended, we need to compare the return on incremental investment to the desired return of 10%. The return on incremental investment will be ($8,316 - $x * 0.34) / ($145,800 + $x). Setting this equal to the desired return of 10% and solving for x, we find that the additional investment in inventory cannot exceed $24,764 for the company to meet its desired return. If the additional investment in inventory is less than or equal to $24,764, the company should extend credit to the new customers. If it is greater than $24,764, the company should not extend credit to the new customers.

Answer:

The correct answers are (x+3) . 2 and 2x+6.

In the first expression, (x+3) . 2, the parentheses indicate that x+3 should be treated as a single term and multiplied by 2. This is equivalent to 2(x+3).

In the second expression, 2x+6, the 2 is multiplied by x and the 3 from x+3, giving 2x+6, which is also equivalent to 2(x+3).

The other expressions are not equivalent because they do not properly distribute the multiplication. For example, in 2 . x+3, the 2 is only being multiplied by x, not x+3, and in 2x+5, the 2 is only being multiplied by x and not 3.

Answer:

  8/17

Step-by-step explanation:

You want the ratio of 32 mm to 6.8 cm, compared in mm.

The ratio of interest is ...

  (32 mm)/(6.8 cm) = (32 mm)/(68 mm) = (4·8)/(4·17) . . . . . mm cancels

  = 8/17

The ratio of ball diameters is 8/17.

Answer:

Step-by-step explanation:

Answer:

0, -12

Step-by-step explanation: