Estimate the sum of the decimals below by rounding to the nearest whole
number. Enter your answer in the space provided.
3.145
1.824
+ 7.769

Answer:

Step-by-step explanation:

3.9

Answer:don’t know how to answer

Step-by-step explanation: by the looks of it ur just connecting dots there are three dots you have to connect

Answer:

Equation of straight line that passes through (-4, 2) and has slope 9/2 is

\(y-2=\frac{9}{2} (x+4)\)

Step-by-step explanation:

Equation of straight line in point slope form is given as

\(y-y_1=m(x-x_1)\) ---------(2)

Here

\(m = \frac {9}{2}\)   and  \((x_1, y_1) = (-4, 2)\)

Substituting values in equation (1)

\(y-2=\frac{9}{2} (x+4)\)

Answer:

4.29  (nearest hundredth)

Step-by-step explanation:

Given data set:

To find the mean absolute deviation:

Step 1

Calculate the mean:

\(\textsf{Mean}=\dfrac{15+5+12+14+18+16+4}{7}=12\)

Step 2

Calculate the absolute deviations - how far away each data point is from the mean using positive distances.

\(\begin{array}{c|c}\vphantom{\dfrac12} \sf Data \; point & \sf Distance \; from \; mean\\\cline{1-2} \vphantom{\dfrac12} 15 & |15-12|=3\\\vphantom{\dfrac12} 5 & |5-12|=7\\\vphantom{\dfrac12} 12 & |12-12|=0\\\vphantom{\dfrac12} 14 & |14-12|=2\\\vphantom{\dfrac12} 18 & |18-12|=6\\\vphantom{\dfrac12} 16 & |16-12|=4\\\vphantom{\dfrac12} 4 & |4-12|=8\end{array}\)

Step 3

Add the absolute deviations together:

\(\implies 3+7+0+2+6+4+8=30\)

Step 4

Divide the sum of the absolute deviations by the number of data points:

\(\implies \dfrac{30}{7}=4.29\)

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Step-by-step explanation:

;x = 0, 1, 2, ....n

Answer: 2 cm

Step-by-step explanation:

2 x 3 = 6

Answer:

bottom left, the one that looks like a v

Step-by-step explanation:

You can test if something is a function by looking to see if there is a place where an x has 2 ys. if there are 2 ys for an x it is not a function.

Answer:

bottom left

Step-by-step explanation:

Bottom right is not a function because you would get an infinite number of results. It does not exactly map one output of this function.

The top two graphs are incorrect because they have more than 1 output. You can do the Vertical Line test and see that the top two graphs do have more that one output.

In order for it to be a function it has to have one output.

Answer:

\( \frac{4}{5} \)

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Answer:

3000 feet or 1000 yards because there are 3 feet in a yard, and make sure there is a squared sign at the end of ft or yards( ft^2)    (yd^2)

Step-by-step explanation:

Answer: y=20x +0

Step-by-step explanation: y=mx (slope) + b (y-intercept). You can search more about how to find the slope of a equation and y-intercept

Answer:

Step-by-step explanation:

Number of weeks is x

Answer:

\(135+\frac{1}{2}x=143-\frac{1}{4}x\)

Step-by-step explanation:

Let E represent Erin’s weight, and let M reprevent Miranda’s weight.

And let x represent the amount of week that passes.

Eric is currently 135 pounds. However, she is gaining 1/2 pounds per week x.

Hence, we can write the following equation:

\(D=135+\frac{1}{2}x\)

Miranda currently weights 143 pounts. However, she is losing 1/4 pounds per week x.

Since she is losing weight, 1/4 is negative. Hence:

\(M=143-\frac{1}{4}x\)

When the two girls weigh the same, D=M. Thus:

\(D=M\)

Substitute them for their respective equations to acquire:

\(135+\frac{1}{2}x=143-\frac{1}{4}x\)

Notes:

To solve, first eliminate the fractions by multiplying everything by 4. This yields:

\(540+2x=572-x\)

Add x to both sides. Subtract 540 from both sides:

\(3x=32\)

Divide both sides by 3:

\(x=32/3\approx10.67\)

Hence, it will take about 11 weeks for the girls to weigh the same.

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

  y = 0

Step-by-step explanation:

You want the horizontal asymptote of y=2x^2/3x^3.

Degree of numerator: 2

Degree of denominator: 3

When the degree of the denominator (3) is greater than the degree of the numerator (2), the horizontal asymptote is ...

  y = 0

__

Additional comment

This reduces to (2/3)(1/x). The value of 1/x approaches zero when the magnitude of x gets large.

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Using proportions, the property tax on a house with an assessed value of $762,000 is of $8,890.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The tax rate, as a proportion, is:

7280/624000 = 0.011667.

Hence, the property tax on a house with an assessed value of $762,000 is of:

0.011667 x 762,000 = $8,890.

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Answer:

45

Step-by-step explanation

20x = 900

-----    -------

20       20

45

The equation for the line passing through the three points is y = (5/4)x.

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) between two expressions.

For example, the equation 2 + 3 = 5 shows that the expression 2 + 3 is equal to the expression 5. In this equation, the expressions on both sides of the equals sign have the same value.

To find the equation for the line passing through three points (0, 0), (4, 5), and (8, 10), we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

To find the slope of the line passing through the three points, we can use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the points (0, 0) and (4, 5) to calculate the slope, we get:

slope = (5 - 0) / (4 - 0) = 5/4

Using the points (4, 5) and (8, 10) to calculate the slope, we get:

slope = (10 - 5) / (8 - 4) = 5/4

Since we get the same slope using either pair of points, we can be confident that these three points are collinear, and lie on the same line.

Now, let's use the point-slope form to write the equation of the line using one of the points, say (0, 0). Substituting the slope and the point into the equation, we get:

y - 0 = (5/4)(x - 0)

Simplifying, we get:

y = (5/4)x

Therefore,  the equation for the line passing through the three points is y = (5/4)x.

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Given:

The expression is

Find-:

Combine line terms

Explanation-:

The simplification is:

The combined like term is 8x - 27

Answer:

2,3,5

Step-by-step explanation:

The equation that shows the relationship between r and w is r = w + 12 and 12 + w = r

An equation is an expression that shows the relationship between two or more numbers and variables.

Let r represent the number of minutes Diana runs and w represent the number of minutes she lifts weight.

Since Diana always spends more minutes running than lifting weights. Hence:

r = w + 12

The equation that shows the relationship between r and w is r = w + 12 and 12 + w = r

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Answer:

The point-slope form of the equation of the parallel line is y - 3 =  \(\frac{3}{4}\) (x - 4)

Step-by-step explanation:

Parallel lines have the same slopes and different y-intercepts

The slope-intercept form of the linear equation is y = m x + b, where

The point-slope form is of the linear equation is y - y1 = m(x - x1), where

∵ The equation of the given line is y = \(\frac{3}{4}\) x - 3

→ Compare it with the first form of the equation above

∴ m =  \(\frac{3}{4}\)

∴ The slope of it is  \(\frac{3}{4}\)

∵ Parallel lines have the same slopes

∴ The slope of the parallel line is  \(\frac{3}{4}\)

∵ The point-slope form is y - y1 = m(x - x1)

→ Substitute the value of the slope in the form of the equation above

∴ y - y1 =  \(\frac{3}{4}\) (x - x1)

∵ The line passes through the point (4, 3)

∴ x1 = 4 and y1 = 3

→ Substitute them in the equation above

∴ y - 3 =  \(\frac{3}{4}\) (x - 4)

∴ The point-slope form of the equation of the parallel line is

    y - 3 =  \(\frac{3}{4}\) (x - 4)

9514 1404 393

Answer:

  (3.5, 4.5)

Step-by-step explanation:

That point will be the midpoint of either diagonal.

  (A +C)/2 = ((-1, 3) +(8, 6))/2 = (-1+8, 3+6)/2 = (7, 9)/2 = (3.5, 4.5)

The center of the rhombus is (3.5, 4.5).

Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

--------------------------------------------------

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

----------------------------------------------------

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

-------------------------------------------------

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

--------------------------------------------------

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer:

(a) check the first one, and the second one

(b) check the last one

Step-by-step explanation:

This is quite easy actually.

3x+24 = 3 * x + 3 * 8

3(x+8) using distribute property.

3x + 24

You cannot simplify 3x+24 any further

And 3(8x+1) just doesn't work

since it's multiplying

The "*" is an X sign

The first, second, and third are not correct

But the last one is.

Answer:

\( \boxed{\sf x \degree = 62 \degree} \)

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

\( \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree\)

In the given figure, the value of x is 62°.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

The given angles are,

x°, 38° and 100°.

To find the value of angle x, use exterior angle property.

According to exterior angle property,

The  sum of two interior angles is equal to exterior angle.

Since, 100° is the exterior angle of x and 38.

x + 38 = 100

x = 100 - 38

x = 62.

The required value of angle x is 62°.

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Answer

Algebraic equation that shows the relationship is

P = 20S

Explanation

Number of college professors = P

Number of students = S

There are 20 times as many students as professors.

P = (S) (20)

P = 20S

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Answer:

$3.25

Step-by-step explanation:

This is division

29.25 divided by 9

9 goes into 29.25 3 times

29.25-27=2.25

2.25 is 1/4 of 9

2.25*4=9 because 2*4=8 and .25*4=1 so 8+1=9

So the answer is 3 1/4 or $3.25

In case whereby Jake rides his bicycle 6 miles in 3/5 of an hour. At this rate, the number of miles could he ride in 3 hours is 30 miles

The distance = bicycle 6 miles

number of hours =3/5 of an hour

then the rate = 6/ (3/5)

Then we can calculate the number of miles with the 6milesi n 3/5 hours  as;

= (6 * 5/3 )

=30/3

=10

Then the rate will be 10 miles in 1 hour , hence the number of miles he will ride in 3hrs

=10 * 3 hours

= 30 miles

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