Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as
y
=
−
10.51
x
+
15.05

and the
r
=
−
0.45
.

The slopes of the two diagonals of the rhombus are: A. b - f/a - e and -a + e/b - f.

To find the slope, the formula used is: change in y/change in x.

If two lines are perpendicular to each other, their slope values will be negative reciprocals.

In a rhombus, the two diagonals in the rhombus bisects each other at angle 90 degrees. This means that the two diagonals of a rhombus are perpendicular to each other. Therefore, the slope of the diagonals of any rhombus would be negative reciprocals.

The slope of the diagonals of the rhombus given would therefore be negative reciprocals to each other.

Given two endpoints of one of the diagonals as:

(a, b) = (x1, y1)

(e, f) = (x2, y2)

Slope (m) = change in y / change in x = b - f/a - e

The negative reciprocal of b - f/a - e is -a + e/b - f.

Therefore, the slopes of the two diagonals are: A. b - f/a - e and -a + e/b - f.

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Answer: [tex]\pm1,\pm3,\pm5, \pm15[/tex]

Step-by-step explanation:

We can list the possible rational roots of this polynomial using the Rational Root Theorem. This theorem states that all the possible rational roots of an equation follow the structure [tex]\frac{p}{q}[/tex], where p is any of the factors of the constant term and q is any of the factors of the leading coefficient.

In this example, -15 is the constant term and 1 is the leading coefficient ([tex]x^4[/tex] has a coefficient of 1).

The factors of -15 are [tex]\pm1,\pm3,\pm5, \pm15[/tex], while the factors of 1 are [tex]\pm1[/tex]. p is can be any one of the factors of -15, while q can be any of the factors of 1.

[tex]\frac{\pm1,\pm3,\pm5, \pm15}{\pm1}[/tex]

The possible roots can be any of the numbers on the top divided by any of the numbers on the bottom. Since dividing by 1 or -1 won't change any of the numbers on the top, the rational roots of this function are [tex]\pm1,\pm3,\pm5, \pm15[/tex].

The required two-digit number is 75.

In mathematics, it deals with numbers of operations according to the statements.

let the number in tenth place be x.
And has two fewer units than tens.
= x - 2

The two-digit number can be given as
= 10x + (x - 2)

= (11x - 2)

Reversing the digits
= (x - 2)10 + x
= 11x -20

The difference between twice the number and the number reversed is 93.

[tex]2(11x - 2) - (11x - 20) = 93\\22x-4-11x+20 = 93\\11x+16 = 93\\11x = 93-16\\11x = 77\\x = 7[/tex]

Now the required two-digit number is,
=  11x -2
=  11*7 - 2
=  77 -2
= 75

Thus the required two-digit number is 75.

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The radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit

The circle equation of the graph is given as:

(x + 3/8)^2 + y^2 = 1

The general equation of a circle is represented using the following formula

(x - a)^2 + (y - b)^2 = r^2

Where the center of the circle is represented by the vertex (a, b) and the radius of the circle is represented by r

By comparing the equations (x - a)^2 + (y - b)^2 = r^2 and (x + 3/8)^2 + y^2 = 1, we have the following comparison

(x - a)^2 = (x + 3/8)^2

(y - b)^2 = y^2

1 = r^2

Rewrite the last equation as follows:

r^2= 1

Take the square root of both sides of the equation

√r^2 = √1

Evaluate the square root of 1

√r^2 = 1

Evaluate the square root of r^2

r = 1

Hence, the radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit

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By solving a linear equation, we conclude that you bought 4 buns and 5 cakes.

We will define the two variables:

We know that you spent exactly £4.35, then we only need to solve the linear equation:

x*0.40 + y*0.55 = 4.35

We need to solve that equation for x and y, such that the values of x and y can only be positive whole numbers.

We can rewrite the equation as:

y*0.55 = 4.35 - x*0.40

y = (4.35 - x*0.40)/0.55

Now we only need to evaluate it in different values of x, and see for which value of x, the outcome y is also a whole number.

We will see that for x = 4, we have:

y = (4.35 - 4*0.40)/0.55 = 5

So you bought 4 buns and 5 cakes.

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40p + 55p = 95p

435p ÷ 95p = 4.57...

So, the sum of the two pairs can go into £4.35 four times.

That meant if I increase the buns & cakes four times, it will help me get closer to the sum of £4.35 & work out which was extra

(40 x 4 = 160) & (55 x 4 = 220)

160 + 220= 380p or £3.80

Adding them up I get 380 pence & that's 55p short to getting to the sum of 435p or £4.35

(435-380=55p)

Thus, the extra is the cake, meaning you bought 4 buns and 5 cakes.

Hope this helps!

Answer: Look in step-by-step explanation

Step-by-step explanation:

Area has a unit of cm^2 or m^2, whilst Volume has a unit of cm^3 or m^3

Using this information, we can see that we have to square both sides of the similarity ratio for the area ratio and cube both sides of the similarity ratio for the volume ratio
For example, question 2 states that the similarity ratio is 3:6, so the area ratio is 3^2:6^2 or 9:36 and the volume ratio is 3^3:6^3 = 27:216

You can do the rest from here

Answer:

= 5.375

Step-by-step explanation:

Use the algorithm method.

7  9 9 10

8 . 0 0 0

- 2 . 6 2 5

5 . 3 7 5

= 5.375

Answer:

5 3/8

Step-by-step explanation:

change it so that every number is a improper fraction and same denominator

64/8 - 21/8 = 43/8 = 5 3/8

The decimal notation for the given value in scientific notation is 215400.

Very large or very small numbers are denoted in scientific notation to simplify complex calculations.

The scientific notation is represented by: a × 10ⁿ

Wher a - any number or decimal number

n - the power of 10; it is an integer number

To convert this into decimal notation,

The given number is in the scientific notation,

2.154 × 10⁵

Since the power of 10 is positive, the decimal point in the number 2.154 moves towards the right. I.e,

2.154 × 10⁵ = 215400

Here power is 5. So, the decimal point moved five places to the right.

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The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.

8x² + 16x + 3 = 0

8x² + 16x = -3

8(x² + 2x) = -3

8(x² + 2x + 1) = -3 + 8

8(x² + 1) = 5

(x² + 1) = 5/8

(x + 1) = ± √5/8

x = -1 ± √5/8

Therefore,

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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Answer: B

Step-by-step explanation:

The horizontal change is 6.

The vertical change is 5.

So, the distance is [tex]\sqrt{6^2 + 5^2}=\sqrt{61}[/tex]

Answer: 40

Step-by-step explanation:

Sub x=4 into 3x²-2x+1

∴ 3(4)²-2(4)+1

=3(16)-8+1

=48-8+1

=40

Answer:

41

Step-by-step explanation:

substitute the x to 4

so 3(4)² - 2(4) + 1 = 41

The denominator cannot be zero, so

[tex]e^x - 9 = 0 \implies e^x = 9 \implies x = \ln(9)[/tex]

is not in the domain of [tex]f(x)[/tex].

[tex]\ln(x)[/tex] is defined only for [tex]x>0[/tex], and we have

[tex]\ln(x+1) > 0 \implies e^{\ln(x+1)} > e^0 \implies x+1 > 1 \implies x>0[/tex]

so there is no issue here.

By the same token, we need to have

[tex]x+1 > 0 \implies x > -1[/tex]

Taking all the exclusions together, we find the domain of [tex]f(x)[/tex] is the set

[tex]\left\{ x \in \Bbb R \mid x > 0 \text{ and } x \neq \ln(9)\right\}[/tex]

or equivalently, the interval [tex](0,\ln(9))\cup(\ln(9),\infty)[/tex].

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex]\large\bm{ -4}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Before performing any calculation it's good to recall a few properties of integrals:

[tex]\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}[/tex]

[tex]\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }[/tex]

So we apply the first property in the first expression given by the question:

[tex]\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}[/tex]

And we solve the second integral:

[tex]\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }[/tex]

[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }[/tex]

Then we take the last equation and we subtract 10 from both sides:

[tex]\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}[/tex]

[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}[/tex]

And we divide both sides by 2:

[tex]\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }[/tex]

[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}[/tex]

Then we apply the second property to this integral:

[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}[/tex]

Then we use the other equality in the question and we get:

[tex]\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}[/tex]

[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}[/tex]

We substract 8 from both sides:

[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}[/tex]

• [tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}[/tex]

Option A. The total share expense that the company would share would be given as 512,000

These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.

The total number of the employees that are knwon to satistfy condition are given as

800 * 0.8

= 640

The options that are estmated that would be exercised

This is given as the employees * share option

= 640×50

=32000.

The total shae for the company would be gotten as

= 32000× $16

This gives us $512,000.

Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.

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The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

Given that; 1 - cos(6x) = ?

First, we rewrite using trig identity

1 - cos(2 × 3x)

Using the double angle identity, { cos2(x) = 1 - 2sin²(x) }

1 - ( 1 - 2sin²(x) )

Eliminate the parentheses

1 - 1 + 2sin²(x)

2sin²(x)

The solution to 1 - cos(6x) is 2sin²(x).

Hence, option B) 2sin²(x) is the correct answer.

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Answer:

Step-by-step explanation:

x² + 2x = x(x + 2)

[tex]\sf \dfrac{x +5}{x + 2}-\dfrac{x+1}{x^2+2x}=\dfrac{x + 5}{x +2}-\dfrac{x+1}{x(x+2)}[/tex]

LCM = x(x+2)

                        [tex]\sf =\dfrac{(x+5)*x}{(x+2)*x}-\dfrac{x+1}{x(x+2)}\\\\=\dfrac{x*x + 5*x}{x^2+2x}-\dfrac{x+1}{x^2+2x}\\\\=\dfrac{x^2+5x - (x+1)}{x^2+2}\\\\=\dfrac{x^2+5x -x - 1}{x^2+2x)}\\\\=\dfrac{x^2+4x-1}{x^2+2x}[/tex]

The equations of the three altitudes of triangle ABC include the following:

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Also, the point-slope form of a straight line is given by this equation:

y - y₁ = m(x - x₁)

Assuming the following parameters for triangle ABC:

For the equation of altitude AM, we have:

Slope of BC = (2 - 8)/(4 - 0)

Slope of BC = -6/4

Slope of BC = -3/2

Slope of AM = -1/slope of BC

Slope of AM = -1/(-3/2)

Slope of AM = 2/3.

The equation of altitude AM is given by:

y - y₁ = m(x - x₁)

y - 0 = 2/3(x - (-2))

3y = 2(x + 2)

3y = 2x + 4

3y - 2y - 4 = 0.

For the equation of altitude BN, we have:

Slope of CA = (2 - 0)/(4 - (-2))

Slope of CA = 2/6

Slope of CA = 1/3

Slope of BN = -1/slope of CA

Slope of BN = -1/(1/3)

Slope of BN = -3.

The equation of altitude BN is given by:

y - y₁ = m(x - x₁)

y - 8 = -3(x - 0)

y - 8 = -3x

y + 3x - 8 = 0.

For the equation of altitude CL, we have:

Slope of AB = (8 - 0)/(0 - (-2))

Slope of AB = 8/2

Slope of AB = 4

Slope of CL = -1/slope of AB

Slope of CL = -1/4

The equation of altitude CL is given by:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 4)

4y - 2= -(x - 4)

4y - 2= -x + 4

4y + x - 2 - 4 = 0.

4y + x - 6 = 0.

In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:

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Answer:

equation 1 has no solution

Step-by-step explanation:

when you compare each of the equations, all the equations gives a correct answer with the exception of equation 1

The total number of common tangents that can be drawn to the circles is 1

The tangent lines of a circle are the lines drawn, that touch the circle at only one point

The complete question is added as an attachment

From the attached figure, we have the following highlights:

The one point of intersection is the only point where both circles can have common tangents

Since there is only one point of intersection, then the number of common tangents on the circles is 1

Hence, the total number of common tangents that can be drawn to the circles is 1

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Answer:

3

Step-by-step explanation:

2+ (-2/3)^2 ÷ 1/3

make -2/3 postive because its being raised by an even exponent

you never divide by fractors so make 1/3 into 3 and make it multiplication

2+ (2/3)^2 × 3

raise the fraction to the power of 2

2+ (4/9)× 3

cancel out the GCF

2+ 4/3

add

10/3

simplify

3.3 ≅ 3

Answer:

12. standard deviation =6.22972...

. variance = 38.80952...

Using the law of sines, it is found that the distance between the kite and the dog is of 284.77 meters.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

For the situation described, we have that:

Hence:

[tex]\frac{\sin{42^\circ}}{h} = \frac{\sin{87^\circ}}{425}[/tex]

Applying cross multiplication:

[tex]h = 425\frac{\sin{42^\circ}}{\sin{87^\circ}}[/tex]

h = 284.77 meters.

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Answer:

10, -7, -35, 5

Step-by-step explanation:

f(9) = -5(-9 + 7) = 10

0 = -5(x + 7)

0 = x + 7

x = -7

f(0) = -5(0 + 7) = -35

-60 = -5(x + 7)

12 = x + 7

x = 5

Answer:

Step-by-step explanation:

A new baby grew:

Total inches during two months:

Based on the calculations, the area of a rectangle to the nearest hundredth is equal to 1143.92 ft².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

By drawing a line between the points representing wicket 3 and wicket 9, we can logically deduce that wicket 2 forms a perpendicular bisector. Thus, the distance between the points representing wicket 3 and wicket 9 is given by:

Distance = 1/2 × 36.77

Distance = 36.77/2

Distance = 18.39 ft.

For the height of this triangle, we would apply Pythagorean's theorem:

h² = 25.02² - 18.39²

h² = 626.0004 - 338.1921

h² = 287.8083

h = √287.8083

h = 16.97 ft.

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 36.77 × 16.97

Area of triangle = 311.99 ft².

For area of the rectangle, we have:

Mathematically, the area of a rectangle can be calculated by using this formula;

Area = LW

Area = 36.77 × 31.11

Area = 1143.92 ft².

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Answer:

See below

Step-by-step explanation:

Distance = rate * time

              = 65 m/hr * 2 1/4 hr = 146.25 miles

rate = distance / time

for Declan :   rate =  146.25 miles / (2 hrs + 35/60 min) = 56.61 mph

Explanation:

There are 25 choices for president. Then we have 25-1 = 24 choices for the secretary, and 24-1 = 23 choices for treasurer. This countdown (25,24,23) is because any given person cannot serve in more than one position.

Multiply out those values: 25*24*23 = 13800

Side note: you could use the nPr permutation formula as an alternative path. Plug in n = 25 and r = 3.

From the constraint, we have

[tex]x+y+z=9 \implies z = 9-x-y[/tex]

so that [tex]s[/tex] depends only on [tex]x,y[/tex].

[tex]s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy[/tex]

Find the critical points of [tex]g[/tex].

[tex]\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9[/tex]

[tex]\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0[/tex]

Using the given constraint again, we have the condition

[tex]x+y+z = 2x+y \implies x=z[/tex]

so that

[tex]x = 9 - x - y \implies y = 9 - 2x[/tex]

and [tex]s[/tex] depends only on [tex]x[/tex].

[tex]s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2[/tex]

Find the critical points of [tex]h[/tex].

[tex]\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3[/tex]

It follows that [tex]y = 9-2\cdot3 = 3[/tex] and [tex]z=3[/tex], so the only critical point of [tex]s[/tex] is at (3, 3, 3).

Differentiate [tex]h[/tex] again and check the sign of the second derivative at the critical point.

[tex]\dfrac{d^2h}{dx^2} = -6 < 0[/tex]

for all [tex]x[/tex], which indicates a maximum.

We find that

[tex]\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)[/tex]

The second derivative at the critical point exists

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex] for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

[tex]$&\frac{\partial g}{\partial x}[/tex] = 9 - 2x - y = 0

[tex]$&\frac{\partial g}{\partial y}[/tex] = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

[tex]$\frac{d h}{d x}=18-6 x=0[/tex]

⇒ x = 3

It pursues that y = 9 - 2 [tex]*[/tex] 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex]

for all x, which suggests a maximum.

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The number paths between c and d of length 2.

Find the number of paths between c and d in the graph of length:

The number of paths between c and d is 0.

There is the number of paths between c and d of length 2.

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Answer:

675

Step-by-step explanation:

100%-32%=68%

459/0.68= 675

Hope this helps! :)