What is the distance between these two points?
(2,0) and (2,−5)

The  original two-digit number is 11 * 10 + 3 = 113.

Let us correspond to the original two-digit number as "10x + y," with x and y showing the tens and units digits, respectively.

We know from the first piece of information:

x + y = 14

According to the second piece of information:

2(10x + y) + 10y + x = 222

When we simplify this equation, we get:

20x + 22y = 202

We get 10x + 11y = 101 by dividing both sides by 2.

We now have two equations with two variables that can be solved by substitution or elimination. For example, in the first equation, we can solve for x and then substitute into the second equation:

x = 14 - y\s10(14 - y) + 11y = 101

When we simplify this equation, we get: y = 3

Putting y = 3 back into the first equation yields: x = 11.

The  original two-digit number is 11 * 10 + 3 = 113.

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A car traveling at 60 miles per hour will travel distance of 66 feet before the driver reacts to an obstacle.

To convert miles per hour to feet per second, we need to multiply by the conversion factor of 1.4667 (since 1 mile = 5280 feet and 1 hour = 3600 seconds, 5280/3600 = 1.4667).

Therefore, a car traveling at 60 miles per hour is traveling at 88 feet per second.

Using the given reaction time of 3/4 of a second, the distance traveled before the driver reacts is:

distance = rate x time = 88 feet/second x 3/4 second = 66 feet

Hence,

A car traveling at 60 miles per hour will travel a distance of 66 feet before the driver reacts to an obstacle.

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Answer:

maximum score = 92

Step-by-step explanation:

the maximum score is the largest value in the data set.

maximum score = 92

Answer:

  height = 2/5h

Step-by-step explanation:

You want the height of a frustum if the volume of the frustum is 98/125 times the volume of the original cone, which was of height h.

Let h' represent the height of the part of the cone that is removed to leave the frustum. Then its volume (v') is ...

  v' = (volume of large cone)(1 - 98/125) = v·(27/125)

The scale factor between h' and h is ...

  (h'/h)³ = v'/v = 27/125

  h'/h = ∛(27/125) = 3/5

The height of the frustum in terms of the height of the original cone is ...

  frustum height = (height of large cone) - (height of small cone)

  frustum height = h - (3/5)h

  frustum height = 2/5h

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The exponential function for the given table will be y=0.01(2)ˣ where x=positive integer.

What exactly are exponential functions?

An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.

Growth that is exponential

The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.

Now,

as given in the table initial value = 0.01

and it is increasing into multiples of 2ˣ where x=positive integer

Then for the value of y for any value of x will be

y=0.01(2)ˣ where x=positive integer

Hence,

           The exponential function for the given table will be y=0.01(2)ˣ.

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The relationship between and in terms of equation is linear model

In statistics, linear relationships are often studied as they provide a simple way to model data. However, not all relationships between variables can be accurately represented using a linear model. In such cases, transforming the variables can sometimes reveal a nonlinear relationship.

When we say we have found a linear relationship between two variables, it means that one variable can be expressed as a linear function of the other.

If we have two variables x and y, a linear relationship between them would be of the form y = mx + b, where m is the slope of the line and b is the y-intercept. This means that as x increases or decreases, y changes in a straight-line fashion.

To find the nonlinear relationship between the original variables, we need to invert the transformation. In this case, we can express y in terms of x by using the inverse of the transformation we applied. Let's say we applied a transformation of the form y' = log(y) and x' = log(x), then we can invert this transformation by taking the exponential of both sides of the equation, giving us

=> [tex]y = e{y'}[/tex] and [tex]x = e^{(x').}[/tex]

Using these equations, we can express the linear model in terms of the original variables as

=> [tex]y = e^{(mx' + b)}[/tex]

Therefore, the relationship between y and x in terms of e and the rounded numerical value is given by

=> [tex]y = e^{(mx' + b)}[/tex]

where m and b are the slope and intercept of the linear model.

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The total cost of the item would be [tex]$115[/tex].The original price of oranges purchased by Mr. S Ralph can be calculated by subtracting the sales tax from the total cost.

Sales tax is calculated as a percentage of the original price. In this case, the sales tax is 15%, meaning that the original price can be found by dividing the total cost (which includes the sales tax) by 1.15.To calculate the original price of the oranges, divide the total cost of $165.31 by 1.15. This gives us a total of $143.87. Thus, the original price of the oranges purchased by Mr. S Ralph is $143.87 without the sales tax included.Sales tax is a form of taxation imposed by governments on goods and services. Generally, for the majority of goods and services, the sales tax is calculated as a percentage of the original price. This means that the total cost of the goods or services can be calculated by adding the percentage of sales tax to the original price.For example, if an item costs $100, and the sales tax rate is 15%, the total cost of the item would be calculated by multiplying the original price by 1.15 (100% + 15% = 115%). The total cost of the item would be [tex]$115[/tex].

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Answer:

To solve the system of equations graphically, you can plot the two lines on a coordinate plane and find the point where they intersect, which represents the solution to the system.

First, let's start by rewriting the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the first equation:

3x + y = 15

y = -3x + 15

For the second equation:

3x - 4y = 0

y = (3/4)x

Next, we can plot these two lines on a coordinate plane by using any two points on each line and connecting them with a straight line.

Once the lines are plotted, we can find the point where they intersect, which represents the solution to the system. In this case, the solution is (2, 9), meaning that at x = 2 and y = 9, both equations are satisfied.

So, the solution to the system of equations is (2, 9), which means that the two lines intersect at the point (2, 9).

The two statements that justifies step three and four in the congruency proof are;

Reason 3: SSS Congruency Postulate

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

The two column proof is as follows;

Statement 1: AB ≅ AD, BC ≅ DC

Reason 1: Given

Statement 2: AC ≅ AC

Reason 2: Reflexive Property of Congruence

Statement 3: ΔABC ≅ ΔADC

Reason 3: SSS Congruency Postulate

Statement 4: ∠ABC ≅ ∠ADC

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

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Answer:

P (of red ball) = 1 - ( 310 + 25 ) = 1 - (3 + 410 ) = 1 - 710 = 10 - 710 P (of red ball) = 310 No. of black balls = 20total no. of balls 25 = 20total balls

Step-by-step explanation:therya goo

Answer:

48

Step-by-step explanation:

If the ratio is 3:4, we can just divide 35 by 3.

Then we get 12, and to get the red balls we can multiply by 4 because that is the ratio

4*12= 48

there are 48 red balls

Ivan would expect to make $43.67 in profit if he had 50 customers.

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

Expected Profit = 1.45 • Customers – 28.83.

If Ivan had 50 customers, using the least squares regression equation, the expected profit would be:

Expected Profit = 1.45 * 50 - 28.83

So, we have

Expected Profit = 72.5 - 28.83

Evaluate the difference

Expected Profit = 43.67

Hence, the expected profit is $43.67

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Complete question

Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.

The least squares regression equation is:

Expected Profit = 1.45 * Customers - 28.83.

How much profit would Ivan expect to make if he had 50 customers?

The unknown sides of the figure are

< KNL = 89.85 degrees

< KJL = 50 degrees

< JKM = 40 degrees

< JML = 80 degrees

A rhombus has it's interior angles equal to 360 degrees and the opposites and angels are equal

hence angle MLK = MJK = 100 degrees

< JML = < JKL = say x

2x + 2(100) = 360

2x = 360 - 200

2x = 160

x = 80

< MJL + < KJL = MJK adjacent angles

50 + < KJL = 100

< KJL = 50 degrees

The sides of a rhombus are equal

JM = KL =  15.6

ML = JK = 15.6

Given that NK = 12 and NL = 10, using cosine rule we solve for < KNL

cos < KNL = (15.6² - 12² - 10²) / -2 * 12 * 10

cos < KNL = 1/375

< KNL = arc cos (1/375)

< KNL = 89.85

< JKM + < JKL +  <JNK = 180 sum of angles on a triangle

<JNK = 180 - 89.85 = 90.15

< JKM + 50 + 90.15 = 180

< JKM = 180 - 50 - 90.15

< JKM = 39.85 approximately 40

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This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.

The interest rate in this situation is 19% compounded monthly. This means that each month, the interest rate is applied to the total balance. The formula to calculate the amount of interest owed is:Interest Owed = Balance x (Interest Rate/12) .In this case, the formula would be:Interest Owed = 16,783 x (0.19/12).This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.

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Answer:

y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal

Step-by-step explanation:

-5(y + 0.2) = 25  Distribute the -5

-5(y) + -5(0.2) = 25   Adding a negative is the same as subtracting a positive

-5y - 1 = 25   add 1 to both sides

-5y - 1 + 1 = 25 + 1

-5y = 26  Divide both sides by -5

[tex]\frac{-5y}{-5}[/tex] = [tex]\frac{26}{-5}[/tex]

y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal

Answer: To solve the equation -5(y + 0.2) = 25, we need to isolate y by performing the following steps:

Distribute the -5 to the expression inside the parenthesis:

-5 * y - 5 * 0.2 = 25

-5y - 1 = 25

Add 1 to both sides of the equation to isolate -5y on one side:

-5y - 1 + 1 = 25 + 1

-5y = 26

Divide both sides of the equation by -5 to find y:

(-5y) / -5 = 26 / -5

y = -5.2

So, the solution to the equation -5(y + 0.2) = 25 is y = -5.2.

Step-by-step explanation:

Both the quantity of candy bars and bags of chips sold are Melanie sold five bags of chips and eighteen candy bars (5 + 13).

A product that has been sold has been exchanged for cash. You'll notice a "Sold" sign appear in the front yard of the house across the street whenever new neighbours purchase it.

In addition to being a noun, the verb sell has three different tenses: simple present, simple past, and past participle. I'll sell my current vehicle and purchase a new one. She is distributing water bottles at the football game. My old college textbooks were all sold on the internet yesterday.

Let x be the number of bags of chips sold, then the number of candy bars sold would be x + 13.

The total revenue from the sales of the bags of chips would be $1.25 * x and the total revenue from the sales of the candy bars would be $1.50 * (x + 13).

Since the total revenue was $33.25, we can set up an equation:

$1.25x + $1.50(x + 13) = $33.25

Expanding and simplifying the right side:

$1.25x + $1.50x + $19.50 = $33.25

Combining like terms:

$2.75x + $19.50 = $33.25

Subtracting $19.50 from both sides:

$2.75x = $33.25 - $19.50 = $13.75

Dividing both sides by $2.75:

x = $13.75 / $2.75 = 5

So Melanie sold 5 bags of chips and 5 + 13 = 18 candy bars.

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Answer: it will take both the kids 5 hours

Step-by-step explanation: 45+5x5=50   5+9x5=5

9 times 5 is 45 in 5 hours Isaiah will have completed 5 pages and he started at 45 so in 5 hours Brenna will have completed 45 pages and she started at 5

The probability using the fair spinner to get P less than 4 is 3/8.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The total sections = 8.

The probability of less than 4 is:

P(less than 4) = Number of outcomes less than 4/ Total sections

P(less than 4) = 3/8

Hence, the probability using the fair spinner to get P less than 4 is 3/8.

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Answer: ITS 0.25!

Step-by-step explanation: i took the test

The equation is [tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

What is meant by zeroes of polynomials?

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.

It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.

It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.

So, the equation is [tex]y=a(x-1)^{2} (x-3)^{3}[/tex].

We will substitute x=2 and y= 87 in the above equation.

[tex]87=a(2-3)^{3} \\a=-87[/tex]

Therefore now the equation will be:

[tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

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In a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.

To calculate the test performance of the screening test in a primary care setting with a 15% baseline cervical cancer prevalence,

we can use the same sensitivity and specificity values obtained in the study, but apply them to a different population.

Given that the prevalence of cervical cancer is 15%, the number of true positives (TP) and false negatives (FN) in the screened population would be:

TP = Prevalence x Sensitivity x Number screened

TP = 0.15 x 0.91 x 3300

TP = 449.19, rounded to 449.

FN = Number with disease - TP

FN = 0.15 x 3300 - 449

FN = 26.5, rounded to 27.

Similarly, the number of true negatives (TN) and false positives (FP) in the screened population would be:

TN = (1 - Prevalence) x Specificity x Number screened

TN = 0.85 x 0.85 x 3300

TN = 2382.75, rounded to 2383.

FP = Number without disease - TN

FP = 0.85 x 3300 - 2383

FP = 396.5, rounded to 397.

Using these values, we can construct the following 2x2 contingency table for the primary care setting:

Actual condition:-

Test outcome       Positive (P)                          Negative (N)

Disease (D)       True positive (TP = 449)         False negative (FN = 27)

No disease (ND) False positive (FP = 397)  True negative (TN = 2383)

Using this contingency table, we can calculate the following test performance measures:

Sensitivity = TP / (TP + FN) = 449 / (449 + 27) = 0.943, or 94.3%.

Specificity = TN / (FP + TN) = 2383 / (397 + 2383) = 0.857, or 85.7%.

Positive predictive value (PPV) = TP / (TP + FP) = 449 / (449 + 397) = 0.531, or 53.1%.

Negative predictive value (NPV) = TN / (FN + TN) = 2383 / (27 + 2383) = 0.988, or 98.8%.

Therefore, in a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.

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The correct answer to this statistical problem is (c) uncertain, because there are other variables at play and correlation does not equal causation.

In this scenario, we're looking at the sales of Ben and Jerry's ice cream before and after the advertisement was introduced. The sales increased by 30% for the following three months after the advertisement. So, does this mean that the advertisement was effective? The answer is not as straightforward as a simple "yes" or "no."

Option (c) acknowledges that there are other variables at play and that correlation does not equal causation.

This is the most accurate answer because it recognizes that while the increase in sales may be related to the advertisement, it's impossible to say for sure whether the advertisement was the cause of the increase in sales.

There could be other factors, such as the weather or a change in consumer preferences, that also contributed to the increase in sales.

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Answer: 19

Step-by-step explanation: 15 x 19 = 285ft^2

The percent increase of the population in the past 10 years is 12.5%.

Percent​ increase is simply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.

It is expressed as;

C = ((x₂ - x₁) / x₁)100%

Where x₁ is initial value and x₂ is new value

Given that;

Plug in the given values into the above equation and simplify.

C = ((x₂ - x₁) / x₁) × 100%

C = (( 9000 - 8000 ) / 8000) × 100%

C = ( 1000 / 8000) × 100%

C = 0.125 × 100%

C = 12.5%

Therefore, the percent increase is 12.5.

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Answer:

The possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Step-by-step explanation:

The coefficient of x² in the expansion of (2 - x)(3 + bx)³ can be found by expanding the brackets.  

Expand the cubed part by using the (a + b)³ formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Therefore:

[tex]\begin{aligned}(3 + bx)^3 &= (3)^3 + 3(3)^2(bx) + 3(3)(bx)^2 + (bx)^3\\&= 27 + 27bx + 9b^2x^2 + b^3x^3\end{aligned}[/tex]

So:

[tex](2-x)(3 + bx)^3 = (2-x)(27 + 27bx + 9b^2x^2 + b^3x^3)[/tex]

To find the coefficient of the term in x², multiply the constant in the first parentheses by the coefficient of the term in x² in the second parentheses and add this to the product of the coefficient of the term in x in the first parentheses and the coefficient of the term in x in the second parentheses:

[tex](\bold{2}-x)(27 + 27bx + \bold{9b^2}x^2 + b^3x^3)\\\phantom{.}\underbrace{\uparrow \qquad \qquad\qquad\qquad\;\uparrow}\\ \phantom{wlwww}\text{multiply}[/tex]

[tex](2-x)(27 + \bold{27b}x + 9b^2x^2 + b^3x^3)\\\phantom{bbb..}\underbrace{\uparrow \qquad \quad\;\uparrow}\\ \phantom{ww.w}\text{multiply}[/tex]

Therefore, the expression for the coefficient of x² is:

[tex]2 \cdot 9b^2 + (-1) \cdot 27b[/tex]

Since the coefficient of x² in the expansion is 45, set the expression to 45 and solve for b:

[tex]\begin{aligned}2 \cdot 9b^2+(-1) \cdot 27b&=45\\18b^2-27b&=45\\18b^2-27b-45&=0\\9(2b^2-3b-5)&=0\\2b^2-3b-5&=0\\2b^2-5b+2b-5&=0\\b(2b-5)+1(2b-5)&=0\\(b+1)(2b-5)&=0\\\\ \implies b+1&=0 \implies b=-1\\ \implies 2b-5&=0 \implies b=\dfrac{5}{2}\end{aligned}[/tex]

Therefore the possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

A graph of the system of linear equations y = -2x + 2 and y = -2x + 1 is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines have the same slope and are parallel.

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Answer:|x-1|-2

Step-by-step explanation: see picture below!

Rounding this to the nearest cent, the total amount that was wanted to be saved is $64.29.

To solve this problem, we can set up a proportion using the given information. Let x be the total amount that was wanted to be saved.

We know that the amount saved ($45) is 70% of the total amount that was wanted to be saved. Therefore, we can write:

45 = 0.7x

To solve for x, we can divide both sides by 0.7:

x = 45 ÷ 0.7

x = 64.28571429

The answer to the problem is $64.29, rounded to the nearest cent. This means that the total amount that was wanted to be saved was $64.29, and 70% of this amount is equal to the amount that was actually saved ($45). To check our work, we can multiply 64.29 by 0.7 to see if it equals 45. When we do this, we get:

64.29 x 0.7 = 45.003, which rounds to $45, so our answer is correct.

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Answers:

===========================================

Work Shown:

[tex]15 \text{ m} = (15 \text{ m})*\frac{100 \text{ cm}}{1 \text{ m}} = 1500 \text{ cm}\\\\\\1.6 \text{ km} = (1.6 \text{ km})*\frac{1000 \text{ m}}{1 \text{ km}}*\frac{100 \text{ cm}}{1 \text{ m}} = 160,000 \text{ cm}\\\\\\467 \text{ mm} = (467 \text{ mm})*\frac{1 \text{ cm}}{10 \text{ mm}} = 46.7 \text{ cm}[/tex]

Each conversion fraction is set up to cancel out any unit that isn't "centimeters".

Side notes:

Answer: E

Step-by-step explanation:

The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.

The length of the third side of ALMN is 20 units.

If AGHI and ALMN are similar, then their corresponding sides are proportional.

Let's call the length of the third side of ALMN "x". We can set up the proportion using the two sides of AGHI and ALMN that we know:

10/8 = 15/12 = x/16

To find x, we can cross-multiply and simplify:

15 × 16 = 12x

240 = 12x

x = 240/12

x = 20

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