of the students in barbara's class, 2/5 have a pet cat. of the students who have a cat, 3/4 also have a dog. what fraction of the students in barbara's class have both a cat and a dog? write your answer as a fraction or as a whole or mixed number.

Considering the expression of a line, the slope intercept form is y= -x+2.

A linear equation o line can be expressed in the form y = mx + b

where

This is known as the slope-intercept form. This form is one of the most common forms used to represent the equation of a line and can be used to find the equation of a line when given the slope of the straight line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis).

In this case, the line is x+y=2. Expressed in the form y = mx + b, you get:

y= 2 -x     or     y= -x +2

Finally,  x+y=2 in slope intercept form is y= -x+2.

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The vertex is (-5 , 5) , y-intercept is (0 , -20) and reflection of y-intercept across symmetry is (-10 , -20).  

What is parabola ?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

a curve made when a cone's surface collides with a plane that is perpendicular to a straight line: a curve created when a point moves in such a way that its separation from a fixed point equals its separation from a fixed line something with a bowl-like form.

Parabola, also known as an open curve or conic section, is formed when a right circular cone and a plane perpendicular to one of the cone's elements cross.

In the equation you provided, the corresponding values are:

a = -1

b = -10

c = -20

Plugging in the values to find the vertex yields:

- (-10)/(2*-1)

= 10/-2

= -5

This is the x-coordinate of the vertex

-x²-10x - 20

= -(-5)² - 10×(-5) - 20

= -25 +  50 - 20

= 5

∴The vertex is located at the point (-5 , 5)

The y-intercept when x = 0

-x² - 10x - 20

= -20

The y-intercept of the vertex at the point (0 , -20)

Since you have 2 points, look at the y-intercept and imagine a point reflected across the line of symmetry.

That point will be your last point, and is located at: (-10 , -20)

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Answer:

the answer is 46% which is option d.

Step-by-step explanation:

To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.

His total monthly debt payments are:

$2,500 (mortgage payment)

$250 (lease payment)

$500 (credit card payments)

$425 (speed boat payment)

Total Monthly Debt Payments = $2,500 + $250 + $500 + $425 = $3,675

His gross monthly income is his annual salary of $96,000 divided by 12 months which is $8,000

DTI = Total Monthly Debt Payments / Gross Monthly Income = $3,675 / $8,000 = 0.46 or 46%.

The value of Jim's DTI (debt-to-income) ratio is 40%.

Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.

Given that,

Annual salary = $96,000

Monthly income = 96000/12 = $8000

Total income per month = $8000 + $1,200 = $9,200

Monthly expenses = $2,500 + $250 + $500 +  $425

                               = $3675

DTI = 3675 / 9,200 = 0.399 = 39.9% ≈ 40%

Hence the DTI of Jim is 40%.

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Answer:

30 feet

Step-by-step explanation:

The scale factor is 1 inch = 3 feet

So 10 inches = 10 x 3 feet= 30 feet

Height of the lighthouse is 30 feet

The longest portion is 18 inches longer than the shortest portion.

What is algebraic equation ?

An algebraic equation is a mathematical statement that shows that two expressions are equal. It typically consists of a combination of numbers, variables and mathematical operations such as addition, subtraction, multiplication, and division.

We know that the ratio of the portions is 1:2:4, so we can use this ratio to find the length of each portion by dividing 42 inches by the sum of the ratio, 1+2+4 = 7.

So each portion is 42 inches / 7 = 6 inches.

The longest portion is 4 times the length of the shortest portion, which is 6 inches. So the longest portion is 4 * 6 inches = 24 inches.

24 - 6 = 18 inches ,

Therefore, the longest portion is 18 inches longer than the shortest portion.

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Answer:

Untuk mencari nilai x dari persamaan 4x+7x+141+85+x+27=360, pertama-tama kita harus menyederhanakan persamaan tersebut dengan menambahkan semua x yang ada di sisi kiri persamaan.

4x+7x+x = 12x

Selanjutnya, kita harus mengurangi semua bilangan yang ada di sisi kiri persamaan dari kedua sisi persamaan:

360 = 12x + 141 + 85 + 27

Setelah itu, kita harus mengurangi semua bilangan yang ada di sisi kanan persamaan dari kedua sisi persamaan:

360 - 253 = 12x

107 = 12x

Akhirnya, kita harus membagi 107 dengan 12 untuk mencari nilai x:

x = 8.9167

Jadi, nilai x dari persamaan tersebut adalah 8.9167.

It's worth noting that some steps are not needed to be done and the equation can be simplified by doing some operations at once like : (4x+7x+x+141+85+27=360) => (12x+253=360) => (12x=107) => (x=8.9167)

The requried, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

Null Hypothesis (H0): The mean height of five-year-old children in the city is not greater than 42.5 inches.

Alternative Hypothesis (Ha): The mean height of five-year-old children in the city is greater than 42.5 inches.

We will conduct a one-sample t-test since we have the sample mean and standard deviation.

Let's calculate the t-statistic and find the corresponding p-value.

The formula for the t-statistic is:

[tex]t=\dfrac{x-\mu}{s/\sqrt n}[/tex]

Where:

x  is the sample mean (44.1 inches),

μ is the population mean under the null hypothesis (42.5 inches),

s is the sample standard deviation (3.5 inches),

n is the sample size (40).

Let's calculate the t-statistic:

[tex]t=\dfrac{44.1-42.5}{3.5/\sqrt n}\\t=2.89[/tex]

Now, we need to locate the p-value associated with this t-statistic. The p-value is the probability of observing a t-statistic as extreme as the one calculated (or even more extreme) under the assumption that the null hypothesis is true.

The p-value can be looked up using a t-distribution table or calculated with statistical software. In this matter, since the t-statistic is quite large, the p-value will be very small.

Suppose the p-value is less than the significance level (α) chosen for the test (commonly 0.05). In that case, we reject the null hypothesis in favor of the alternative hypothesis. This means there is convincing evidence that the mean height of five-year-old children in this city is greater than 42.5 inches.

Conversely, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

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On solving the equation " [tex]2y + 3 = 13[/tex] " for y , we get the value of y is 5  .

What is an Equation ?

An Equation is defined as the mathematical statement which shows that the two mathematical expressions are equal .

the equation is given as : [tex]2y + 3 = 13[/tex] ;

In the given equation , we have to solve for y ;

Subtracting 3 from both sides ,

we get ;

⇒ [tex]2y+ 3 - 3 = 13 -3[/tex] ;

⇒ [tex]2y = 10[/tex] ;

dividing both sides by 2 ,

we get ;

⇒ [tex]y = \frac{10}{2}[/tex] ;

On simplifying ,

we get y = 5 .

Therefore , After solving for y , the value of y = 5 .

The given question is incomplete , the complete question is

How do you solve the problem 2y + 3 = 13 for y ?

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The coordinates of its midpoint M are (0,6)

A line is an infinitely long object with no width, depth, or curvature.

Given that a line segment has the endpoints B(0, 2) and C(0, 10).

We need to find the  coordinates of its midpoint M.

Midpoint=(0+0/2, 2+10/2)

Midpoint=(0, 12/2)

Midpoint=(0, 6)

The coordinates of its midpoint M are (0,6)

Hence, the coordinates of its midpoint M are (0,6)

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There is no association between the state and the amount of median debt for graduates.

To find the association between states and the median debt, you need to find the percentage of the graduates in the state that either have a median debt of less than $ 9, 000 or at least $ 9, 000.

The percentage of California University graduates with median debt less than $ 9, 000 is:

= 130 / 575

= 23 %

The percentage of New York University graduates with median debt less than $ 9, 000 is:

= 72 / 343

= 21 %

The percentage of California University graduates with median debt at least $ 9, 000 is:

= 445 / 575

= 77 %

The percentage of New York University graduates with median debt at least $ 9, 000 is:

= 271 / 343

= 79 %

The percentages are similar to each other which shows that being from either state does not mean that there will be an association between the state and the median debt.

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High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

We have to find from the given options which data outcome of the number of customers in line would best support opening another cash register.

The number of customer in the line having high mean with small standard deviation means deviation in data small and data cluster around mean. High mean I'm play high number of customer in line. This help to opening another cash register.

Hence, High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

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1. The  triangles, which are similar to ΔAED  are ΔAFE, ΔEFD, ΔECD, ΔABE

2.  The length of segment FA is, 32/3 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

A rectangle ABCD having triangles in it,

1.  ΔAED is a right angle triangle,

all the triangle which are right angle triangle will be similar to  ΔAED

So,  ΔAFE, ΔEFD, ΔECD, ΔABE are similar triangles

2. Now, consider ΔEFD

EF = 8 unit

ED = 10 unit

∠CEB = 53°

∠CEF = 90°

∠DEF = 37°

∠AED = 90°

∠AEF = 53°

tan53° = FA/FE

4/3 = FA/8

FA = 32/3

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The value of the given function f(x) and g(x) is [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere and are crucial for constructing physical relationships.

The given functions are:

[tex]f(x) = 5x^2 - 3 \\\\g(x) = x^2 -4x-8[/tex]

(f - g)(x) is equivalent to the following:

(f - g)(x) = f(x) - g(x)

[tex]f(x) - g(x) = 5x^2 - 3 - x^2 +4x+8\\\\f(x) - g(x) = 4x^2 +4x+5[/tex]

Hence, the value of [tex]f(x) - g(x) = 4x^2 +4x+5[/tex].

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Answer:

17/20

Step-by-step explanation:

The ratio 8.5 to 10 as a fraction in simplest form is 17/20. 8.5/10 = 85/100 = 17/20

(8.5:10 = 85:100 = 85/100 = 17/20)

Answer:

Step-by-step explanation:

a. Possible values for m and n to achieve a total number of 46 legs are: m = 23 and n = 11; m = 22 and n = 12; m = 21 and n = 13; m = 20 and n = 14; m = 19 and n = 15; m = 18 and n = 16.

b. If the number of 2 legged animals is 2 more than the number of 4 legged animals, there must be 24 2 legged animals and 22 4 legged animals in the exhibit (24 + 22 = 46).

c. The increase in the number of legs in the exhibit might be due to the addition of a new animal to the exhibit. If the new animal has 4 legs, the total number of legs in the exhibit will increase by 4.

Answer:

a)  Possible values of m and n:

b)  9 two-legged animals and 7 four-legged animals.

c)  Either 1 four-legged animal or 2 two-legged animals have been added to the exhibit.

Step-by-step explanation:

Given expression:

2m + 4n = 46

where:

Calculate the greatest number of four-legged animals by dividing the total number of animals by 4:

[tex]\implies 46 \div 4 = 11.5[/tex]

Therefore, the greatest number of four-legged animals is 11.

When there are no four-legged animals, n = 0.

Substitute n = 0 into the given equation:

[tex]\begin{aligned}\implies 2m+4(0)&=46\\2m&=46\\ m&=23\end{aligned}[/tex]

Therefore, there are 23 two-legged animals when there are no four-legged animals.

Each time the number of four-legged animals increases by 1, the number of two-legged animals decreases by 2.

Therefore, the possible values for m and n so that the total number of legs is 46 are:

If the number of two-legged animals is 2 more than the number of four-legged animals then:

Therefore, there are 9 two-legged animals and 7 four-legged animals.

If the number of legs in the exhibit increases by 4, then either:

The value that represents the smiley face is given as follows:

402.

The first three equations compose a system of equations, and then the three solutions to this system are used to obtain the value of the smiley face.

The variables and shapes are attributed as follows:

From the third equation, the square has the value obtained as follows:

8x - 6x + 3x = 60

5x = 60

x = 60/5

x = 12.

From the second equation, the value of the star is obtained as follows:

12(12) + 5y = 234

5y = 90

y = 90/5

y = 18.

From the first equation, the value of the triangle is given as follows:

12 + 3z + 18 = 57

3z = 27

z = 9.

Considering these values, the value of the smiley face is given as follows:

Smiley = 18(9 + 18 - 12) + 12(18/9 + 9)

Smiley = 18(15) + 12(2 + 9)

Smiley = 18 x 15 + 12 x 11

Smiley = 402.

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Hope it helps.

If you have any query, feel free to ask.

The domain and range of the rational function in this problem are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function.

The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the value outside the domain is:

x - 1 = 0 -> x = 1.

The range of a function is the set that contains all the output values that can be assumed by the function.

The function in this problem can be simplified by x - 1, hence at x = 1 it would assume a value of y = 7. However, for the range, we suppose that the function cannot be simplified, hence it is given by all real values except y = 7.

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Now your friend would also like to determine the most likely continent of origin for each coin. Logistic regression model best suited to predict the continent of origin. So the option b is correct.

A variable's value can be estimated using linear regression analysis depending on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Based on a given dataset of independent variables, logistic regression calculates the likelihood that an event will occur, such as voting or not voting. Given that the result is a probability, the dependent variable's range is 0 to 1.

The log chances of the outcomes are modelled as a linear combination of the predictor variables in multinomial logistic regression, which is used to model nominal outcome variables.

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The complete question is:

Now your friend would also like to determine the most likely continent of origin for each coin. Which model best suited to predict the continent of origin?

(1) Linear regression

(2) Logistic regression

(3) Multinomial logistic regression

Answer: 4xy²(5-y)

Step-by-step explanation:

To factorize, we must take out common multiples in both parts of the equation. Think of 20xy² and -4xy³ as two completely separate parts. Now, we need to see which parts of the equation are found in both. For instance, 4 can go into both, an x can go into both, and y² can go into both. Now, we simply factor.

Bring the similarities out to the front: 4xy²()

Now, use division to find what would be inside the parenthesis: 5 - y

Now, combine these two parts: 4xy²(5-y)

To check your work, you can simply multiply the outside of the parenthesis by the inside, and you should get the same as what you started with. Hope this helps!

Answer: The slope is equal to "-3".

Explanation: You can obtain the slope of a linear graph if you know two points on it. In this case, these points are (-2,3) and (0, -3).

If you know these points, you can use the formula below:

Slope = (Difference between y values) / (Difference between x values)

Here => 3 - (-3) / (-2) - (0) = -3, this gives the slope.

In addition, we can conclude that the formula of the graph is (y = -3x - 3), by using a specific point with the known slope value on a linear equation (mx + n).

The expression that represents the magazine sale of  Graham's is 2a - 6.

Profit & Loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

The sentence "Graham sold 6 magazines less than double what Adrianne sold" can be represented by the expression 2a - 6, where a is the number of magazines Adrianne sold.

So, the expression that represents Graham's sales is 2a - 6.

Graham's magazine sales are represented by the expression 2a - 6.

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The solution of the trigonometric equation is θ = π/6 radian

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

2cosθ = √3

Divide both sides by 2:

cosθ = (√3)/2

θ = cos⁻¹[(√3)/2]

θ = 30°

Convert 30° to radian by multiplying it with π/180. That is:

θ = 30 × π/180

θ = π/6 radian

Thus, the solution is θ = π/6 radian

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The price of the carpet per square meter is $32.13. It will cost $1,556.86 to carpet an area of 1475 square feet.

1. To find the price of the carpet per square meter, first convert $28.99 per square yard to meters.

1 yard = 0.9144 meters

$28.99 per yard x (1 meter/ 0.9144 meters) = $32.13 per square meter

2. To find the cost of carpeting an area of 1475 square feet, first convert 1475 square feet to square yards.

1 square foot = 0.11111 square yards

1475 square feet x (1 square yard/ 0.11111 square yards) = 13,333.33 square yards

3. Multiply the cost per square yard by the number of square yards needed to carpet the area.

$28.99 per square yard x 13,333.33 square yards = $1,556.86

The complete question is:

a carpet sells for $28.99 a square yard. what is the price of the carpet per square meter? how much will it cost to carpet an area of 1475 square feet? 1 yard is equal to 0.9144 meters

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Answer:

Impossible: Pigs can fly. It will rain in the Sahara Desert for a week.

Probability is the likelihood that an event will happen.

Unlikely: It will snow today. Dying in a shark attack.

Likely: If you are underwater for more than 2 minutes, you drown. A cat chases a mouse.

Certain: The year is 2023.

The width of the rectangle is given as Area/length = 32xy³/l units.

A quadrilateral with four right angles is a rectangle. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

Rectangles have the following basic characteristics:

The area of the rectangle is 32xy³

The length of the rectangle is l units

So, the width of the rectangle is given as Area/length = 32xy³/l units.

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In the question, diagram is not given, so that a rough diagram is given for reference.

The correct answer is 5 white triangles coincide.

3 red, 5 blue, and 8 white triangles are present on each side. The 2 pairs of red triangles are also utilized, leaving 1 red triangle, 5 blue triangles, and 8 white triangles on each half.

Additionally, there are 3 pairs of blue triangles that are used up, leaving 1 red triangle, 2 blue triangles, and 8 white triangles on each half. Additionally, we offer 2 red-white pairs. Since there is only 1 on each side, it is evident that we cannot utilize 2 red triangles on one side.

As a result, we must use 1 red and 1 white triangle per side, leaving 2 blue and 7 white triangles on each. The remaining blue triangles must be coupled with white triangles in order to create 4 blue-white pairings, one for each of the remaining blue triangles.

Blue triangles cannot be matched with other blue triangles because it would result in more than 3 worth of blue pairs. This leaves 5 white triangles per side, which must be coupled with each other to create $5 white-white pairings.

Therefore, The correct answer is 5 white triangles coincide.

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The kind of triangle in the image above is a scalene triangle.

A scalene triangle is a type of triangle that has three sides with different lengths. It is one of the three main types of triangles, the other two being isosceles and equilateral triangles. They also have three different angles.

Scalene triangles do not have any congruent sides or angles, making them the most diverse and versatile type of triangle. They can be used to construct many different shapes and figures, and have many unique properties and characteristics that make them useful in a variety of fields, including mathematics, physics, and engineering.

In the image given, the three sides of the triangle appears to be of different sizes.

Therefore, we can conclude that the triangle is a scalene triangle.

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The data set would list each day in February with a temperature measurement, measured on an interval scale.

The data set in question would list the temperatures in Albany, NY each day in the month of February. This data set would be classified as interval data, as it would measure temperatures on a numerical scale. Interval data is composed of numerical values that are measured on an interval scale, meaning that the difference between any two values is the same, regardless of their position on the scale. Temperature is an example of an interval data type, as it is measured numerically and the difference between two temperatures is the same regardless of where they are on the scale (e.g. the difference between 50°F and 55°F is the same as the difference between 90°F and 95°F). This data set would be useful for tracking temperature trends over a period of time, and for making predictions about future temperatures in a certain area.

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