What is the slope of the line?

To describe the temperatures for the week, we can apply the following statistical tools:

a) Find the mean, median, mode, and range.

c) Construct a line graph.

d) Construct a stem and leaf plot.

We can describe temperatures using measures of central tendencies (especially the mean, median, and mode).

The mean temperature is the average, which shows the overall trend in temperature changes.  It is computed by adding up the temperatures for the period and diving by the number of data values.

In addition, the median gives the middle value when the data set is ordered in ascending or descending orders. Similarly, the mode gives the highest temperature occurrence within the period. It may not be useful here.

We can estimate the difference between the highest and lowest temperature for the week with the range.

A line graph (showing connecting lines) and a stem-and-leaf plot (like a bar graph) can graphically describe the temperatures for the week.

Thus, we can use Options A, C, and D to describe the temperature.

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What could you do to describe the following data, showing temperatures for the week? (Check all that apply.)

Mon - 65°

Tues - 67°

Wed - 66°

Thur - 70°

Fri - 72°

Sat - 68°

Sun - 69°

a) Find the mean, median, mode, and range.

b) Survey people about the weather.

c) Construct a line graph.

d) Construct a stem-and-leaf plot.

Answer:

4 pencils

Step-by-step explanation:

Interquartile Range (IQR) = the range of the rectangular box = Third quartile (Q3) - First Quartile (Q)

Third Quartile (Q3) = 6

First Quartile (Q1) = 2

Interquartile Range (IQR) = 6 - 2

Interquartile Range (IQR) = 4 pencils

Step-by-step explanation:

To simplify the expression x^-2y(x^3y^5)^3, we need to perform the operations inside the parentheses first, using the exponent rule that (a^m)^n = a^(mn):

x^-2y(x^3y^5)^3 = x^-2y(x^(33)y^(53)) = x^-2y(x^9y^15)

Next, we can simplify the expression by multiplying the coefficients (numbers) and adding the exponents of x and y, using the product rule that x^mx^n = x^(m+n) and (xy)^m = x^my^m:

x^-2y(x^9y^15) = (1y/x^2)(x^9*y^15) = y^(15+1)x^(9-2) = y^16x^7

Therefore, the simplified form of x^-2y(x^3y^5)^3 is y^16*x^7.

Note that this expression is defined for all values of x and y except for x=0.

A division is a process of splitting a specific amount into equal parts. The unit rate for $12.50 for 5 ounces is $2.5

A division is a process of splitting a specific amount into equal parts.

Given,

$12.50 for 5 ounces

We need to find for a unit rate.

For this we need to use division. We have to split $12.50 among 5 ounces.

12.50 as Divisor and 5 as dividend.

Twelve point five zero divided by five

$12.50/5

2.5

Hence the unit rate for $12.50 for 5 ounces is $2.5

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The value of side length x in diagram a) is 4.3mm and side length x in diagram b) is 309.7 m.

The figures in the image are right triangles.

A)

angle D = 17 degree

Adjacent to angle D = 14 mm

Opposite to angle D = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( 17 ) = x/14

x = tan( 17 ) × 14

x = 4.3mm

B)

angle Z = 82 degree

Adjacent to angle Z = 43.1 m

Hypotenuse = x

Using trigonometric ratio,

cosine = adjacent / hypotenuse

cos( 82 ) = 43.1 / x

x = 43.1 / cos( 82 )

x = 309.7 m

Therefore, the measure of x is 309.7 meters.

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Jeremy is incorrect because a negative plus a negative will always be a negative.

Answer:

9/4

Step-by-step explanation:

3/2 x 3/2= 9/4

Answer

5/136

Step-by-step explanation

Events

• A: a blue marble is drawn

• B: without replacing the first marble, a green marble is drawn

There are 17 (= 3 + 2 + 5 + 7) marbles in total in the bag. Two of them are blue, then the probability of drawing a blue marble is:

After a blue marble is drawn, 16 marbles are left in the bag. Five of them are green, then the probability of drawing a green marble is:

Finally, the probability of drawing a blue marble and then a green marble without replacement is:

The differentiable function f with the given properties is \(f(x)=4x^3-3x^2+10\).

What is a differentiable function:

A function with a differentiable value of one real variable is one whose domain contains a derivative. In other words, each interior point in the domain of a differentiable function's graph has a non-vertical tangent line.

The given properties for the differentiable function f are:

\((i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18\)

From (i) we can get \(f''(x)=2ax+b\)

By substituting (ii) in (i) we will get:

a+b=6 and 2a+b=18. By solving these two equations we will get the following:

a=12, b=-6.

We will integrate (i) on both sides, we will get:

\(f(x)=\frac{ax^3}{3} +\frac{bx^2}{2} +c\) where c is the integration constant.

In this equation, we will substitute a,b.

\(f(x)=\frac{12x^3}{3} +\frac{-6x^2}{2} +c\\ \\ f(x)= 4x^3-3x^2+c\)...................(iv)

Now we will substitute (iv) in (iii), and we will get:

\(\int\limits^2_1 {( 4x^3-3x^2+c)} \, dx =18\\ \\ (2^4-2^3+2c)-(1^4-1^3+c)=18\\ \\c=10\)

Therefore \(f(x)=4x^3-3x^2+10\).

Complete question:

Let f be a differentiable function, defined for all real numbers x, with the following properties. Find f(x). Show your work.

\((i) f'(x)=ax^2+bx\\ (ii) f'(1)=6, f''(1)=18\\ (iii) \int\limits^2_1 {f(x)} \, dx =18\)

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Answer:

Assuming you want to solve for x,

x = 2

Step-by-step explanation:

2x + y = 5

Solve for y

y = 5 - 2x

4x - 2y = 6

Solve for y

y = -3 + 2x

Since both these equations equal y, they must equal each other.

Make an equation for these to equal each other.

Then solve for x

5 - 2x = -3 + 2x

  + 2x        + 2x Add

5 = - 3 + 4x

+ 3  +3 Add

8 = 4x

/4  /4 Divide

2 = x

Using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem.

In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

A second-order equation of the form ax² + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.

So, we have the equation:

x²-3x+ 5 = 0

Now, solve it using the quadratic formula as follows:

x²-3x+ 5 = 0

a = 1

b = -3

c = 5

x = -(-3)±√(-3)² -4*1*5/2

Solve this further:

x = 3±√11/2

Therefore, using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.

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Correct question:

Solve x²-3x+ 5 = 0.

A.3+√-29 +VE/2 and 3- 2-29

B. 3+√29 and 3-√29

C. 3+√-11 and 3-√-11/2

D. 3+√11/2 and 3-√11/2

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

The perimeter of the square garden is 36 feet, which means that each side of the square is 36/4 = 9 feet long. Therefore, the total cost of the fences is $92.

The length of the outer fence, which is 2 feet away from the garden, is equal to the perimeter of a larger square with sides that are 2 feet longer than the sides of the original garden.

So, the length of the outer fence is 4(9+2) = 44 feet.

The length of the inner fence, which is around the perimeter of the garden, is equal to the perimeter of the original square garden, which is 4(9) = 36 feet.

The total length of both fences is the sum of the lengths of the inner and outer fences:

36 + 44 = 80 feet.

The cost of the fences is the total length of both fences multiplied by the cost per foot:

80 x $1.15 = $92.

Therefore, the total cost of the fences is $92.

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Answer:

The transformations used were rotations, reflections, and  R(–3, –3). After a dilation, the image of P is. P'(4, 12). What is the scale factor of the dilation? 5.The triangle formed by a 4-foot-tall mail box and its 6-foot shadow is similar to the triangle formed by a utility pole and its 15-foot shadow at the same time of day.

Step-by-step explanation:

Answer:

If the base and the negative exponent is in the denominator already

Step-by-step explanation:

Normally, a base with a negative exponent moves to the denominator.

Example: (2^-3 = 1 / (2)^3 = 1/8)

However, if the base and the negative exponent is already in the denominator, the base would move to the numerator and the exponent would become positive.

Example:  2 / (3)^-3 = 2 * 3^3 = 2 * 27 = 54

Given the graph

We want to find the polynomial of the graph f(x)

Solution

From the graph, one can tell that the its is a polynomial of power three

we first notice that the graph crosses the x-axis at x=-2 and x=3

so, x=-2 and x=3 are the roots of f(x)

Notice that at the root x=3, the graph change direction

That implies that x=3 (twice)

so we have

we are left with finding a

notice the coordinate on the y-axis is (0,9)

substituting,

Therefore,

The total surface area of the figure will be 1968.85 square meters.

To determine  the surface area of the figure, we need to find the area of each face and then add them together.

Surface Area of the rectangular prism = 2(lb + bh + hl)

= 2(16 × 9.5) + 2(9.5 × 14) + 2(16 × 14)

= 2(152 + 133 + 224) = 2(509)

= 1018 m²

Next, we need to find the area of the triangular prism on the front with dimensions 11 m, 12.7 m, and 14 m:

Surface Area of the triangular prism;

= (11 × 14) + 2(0.5 × 11 × 12.7) + 2(0.5 × 12.7 × 14)

= (154 + 350.35 + 445.5)

= 950.85 m²

Therefore, the total surface area of the figure will be;

Total Surface Area = Surface Area of rectangular prism + Surface Area of triangular prism

= 1018 m² + 950.85 m²

= 1968.85 m²

So, the surface area of the figure is 1968.85 square meters.

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Answer:

second one

Step-by-step explanation:

Answer:

It is the first one

Step-by-step explanation:

1+1=2  2+1=3 4+3=7  so it would be the top one 2 the number on the side is 3 and the bottom is 7

Answer:

5.96 with the repeating sign over the 6

Step-by-step explanation:

Answer:

6.

Step-by-step explanation:

Convert the decimal to a fraction:

2.33333....  = 2 1/3, so it is:

3 2/3 + 2 1/3

= 3 + 2 + 2/3 + 1/3

= 3 + 2 + 1

= 6.

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

The reciprocal of the divisor: Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged, then it is said to be its reciprocal. Suppose a fraction is a/b, then its reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number.

The reciprocal of the divisor 5 1/5 divided by 1/10

To the reciprocal of the divisor.

Equation: 5 1/5 divided by 1/10

1st: Flip the 1/10 to become 10/1

2nd: Change division to multiplication

New equation: 5.1/5.10/1

⇒ 50/5

       ⇒ 10.

The reciprocal of the divisor 5 1/5 divided by 1/10 is 10.

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Answer:

Step-by-step explanation:

Year 1: $850 * 0.91 = $773.50

Year 2: $773.50 * 0.91 = $704.69

Year 3: $704.69 * 0.91 = $641.95

...

Year 34: (continue the pattern)

We can continue this calculation for each year, but to save time, we can use an exponential decay formula:

Remaining Amount = Initial Amount * (1 - rate)^years

Substituting the values:

Remaining Amount = $850 * (1 - 0.09)^34

Calculating this expression:

Remaining Amount ≈ $850 * (0.91)^34 ≈ $255.88

After 34 years, approximately $255.88 will be left with Sally.

Answer:

3 30303/125000

Step-by-step explanation:

Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.

Given data ,

The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.

Number of students who walk to school = 5

Total number of students in the class = 32

Experimental probability = Number of students who walk to school / Total number of students

= 5 / 32

P = 0.15625

Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

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

    -y = -7x

+

    y = -4x + 3

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

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer: (5 , 1)

Step-by-Step explanation:

hihi your problem is a system of question y = x-4 and  y = -x+6 okay so  graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!

y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right

y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left

once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!

the solution is  x = 5 and y = 1 which is also (5 , 1)

hopefully this was helpful !

Answer:

x=9/2 Hope this helps!

Step-by-step explanation:

Let's solve your equation step-by-step.

x−6−(4.5−x)=−1.5

Step 1: Simplify both sides of the equation.

x−6−(4.5−x)=−1.5

x−6+−1(4.5−x)=−1.5(Distribute the Negative Sign)

x+−6+(−1)(4.5)+−1(−x)=−1.5

x+−6+−4.5+x=−1.5

(x+x)+(−6+−4.5)=−1.5(Combine Like Terms)

2x+−10.5=−1.5

2x−10.5=−1.5

Step 2: Add 10.5 to both sides.

2x−10.5+10.5=−1.5+10.5

2x=9

Step 3: Divide both sides by 2.

2x/2=9/2

x=9/2

Answer is 9/2.

It is true that the line segment AB equals 26

The given parameters are:

AB = x +16

BC = 4x + 11

AC = 77

The two-column proof is as follows:

AC = AB + BC                     Line segment formula

77 = x + 16 + 4x + 11            Substitution property of equation

77 = 5x + 27                        Addition property of equation

5x = 50                               Subtraction property of equation  

x = 10                                    Division property of equation

AB = 10 +16                          Substitution property of equation

AB = 26

Hence, the line segment AB has been proved to equal 26

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