Here is the histogram of a data distribution. All class widths are 1

Which of the following numbers is closest to the mean of this distribution?

Answer:

none of them

Step-by-step explanation:

Answer:

c. 7/12

Step-by-step explanation:

There are 36 possible outcomes when you roll a die twice.

11, 12, 13, 14, 15, 16

21, 22, 23, 24, 25, 26

31, 32, 33, 34, 35, 36

41, 42, 43, 44, 45, 46

51, 52, 53, 54, 55, 56

61, 62, 63, 64, 65, 66

The desired outcomes are the ones whose first number is greater than or equal to the second number. They are shown in bold and underline above.

There are 21 desired outcomes.

p(first number ≥ second number) = 21/36 = 7/12

Answer: c. 7/12

The values of y and x are -7 and 2 respectively, completing the ordered pairs: (6,-7) and (2,1).

Given the equation in the question;

To find the y-value that completes the ordered pair ( 6,y ), replace all occurrence of x with 6 in the equation and solve for y.

y = −2x + 5

y = −2( 6 ) + 5

Multiply -2 and 6

y = -12 + 5

y = -7

Hence, the output value is -7, this forms an ordered pair of (6,-7).

To find the x-value that completes the ordered pair ( x,1 ), replace all occurrence of y with 1 in the equation and solve for x.

y = −2x + 5

1 = −2x + 5

Add 2x to both sides

1 + 2x = −2x + 2x + 5

1 + 2x = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, the input value is 2, this forms an ordered pair of (2,1).

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The perpendicular distance from R to PQ is ​346 feet.

What are the trigonometric functions?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

We have,

consider the sides of leaning tower are,

opposite side of the angle 56° (x) = 180.5 feet.

Adjacent side of the angle 56° (y) = 125 feet.

We know,

[tex]tan\theta =\frac{ opposite \ side}{ adjacent \ side} = \frac{x}{y}[/tex]

[tex]\theta = \ tan^{-1} \left(\frac{ opposite \ side}{ adjacent \ side} \right)[/tex]

The angle of elevation is  [tex]\theta = \ tan^{-1} \left(\frac{180.5 }{125} \right)[/tex]

θ = 56°

The perpendicular distance from R to PQ is RQ ​

[tex]sin\theta = \frac{opposite side}{hypotanous} = \frac{180.5}{y}[/tex]

sin(56) = 180.5/PQ

RQ = 180.5/sin(56)

RQ = - 346.08

RQ = 346 (distance never be negative),

Hence, the perpendicular distance from R to PQ is ​346 feet.

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Answer:

557.143

Step-by-step explanation:

195 / 35% = 557.14

Step-by-step explanation:

the angle TSW is the total angle and is 73°.

from that total angle, we have one part : angle 1 = 36°.

as angle TSW = angle 1 + angle 2

we have

73 = 36 + angle 2

angle 2 = 73 - 36 = 37°

The equation that represents the number of purses Paula must sell to pay for the new equipment is 5.00x = 5000.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Paula makes purses and the materials cost $2.25 per purse.

She sells them for $5.00 each now she wants to invest $5000 in some new equipment and we are assuming the no. of purses to be x.

Here the equation 5.00x - 2.25x = 5000 represents Paula's profit.

The equation that represents the no. of purses she must sell to pay for the new equipment is 5.00x = 5000.

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Answer: 5.00x - 2.25x = 5000

Step-by-step explanation:

The perimeter of the shape is 38 total unit.

The perimeter of a shape is a measure of the distance round the boundary or edge of the shape.

The given shape comprises of squares of 1 length each, hence to calculate for the perimeter of the shape, we add up each boundary of 1 unit length which will amount to 39 in total.

Therefore by careful observation, the perimeter of the plane shape is calculated to give us 39 total perimeter length.

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Answer: I believe both the x and y- intercepts are “(0,0)”

Step-by-step explanation: there is only one intercept and it is at the origin (0,0) making both the x and y - intercepts (0,0) :)

The largest multiple of 30 that is less than the number, 520, can be found to be 510.

To find the largest multiple that 30 has, which is also less than 520, first find the number of times that 30 can go into 520:

= 520 / 30

= 17.333

Then use this number to find the largest multiple below 520 by rounding 17.33 downwards to 17.

The multiple of 30 that is the largest and below 520 is then:

= 30 x Rounded down result of division of 520

= 30 x 17

= 510

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Answer:

B. After the booking fee the party will cost $20 per person

Answer:

the change is in %age of decrease of 10%

Step-by-step explanation:

original value = 20

new value = 18

decrease = 2

%age decrease = decrease/original value * 100

                         =  2/20 * 100

                         =  10%

The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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The system of equations has no solutions, meaning that the two lines never intersect, as shown by the image at the end of the answer.

A system of equations is a set of equations in the context of a problem, and these equations are solved to find the numeric value of each variable of the problem.

When the system involves linear equations, such as is the case in this problem, the solution is given by the intersection point between these two lines.

In this problem, the equations are given as follows:

From the second equation, it is found that:

x = 8 + 2y.

Replacing on the first equation, the solution for y can be obtained as follows:

2(8 + 2y) - 4y = 4

16 + 4y - 4y = 4

0y = -12

Which is a contradiction, hence the system has no solutions and the two lines do not intersect.

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The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The given triangle is a right-angled triangle

As Z² = X²+Y²

So sin (x) = 60/68=0.88

and sin(y) = 32/68=0.47

Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.

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The value after 11 years with annual compounding is $11,389.79

The value after 11 years with quarterly compounding is $11,552

The value after 11 years with monthly compounding is $11,589.68

The value after 11 years with continous compounding is $70,080.78.

When an amount is compounded annually, it increases in value once a year. When an amount is compounded quarterly, it increases in value four times a year. When an amount is compounded monthly, it increases in value twelve times a year. When an amount is compounded continuously, it increases continuously over the investment period.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Value after 11 years with annual compounding: $6,000 x (1.06)^11 = $11,389.79

Value after 11 years with quarterly compounding: $6,000 x (1 + 0.06 /4)^(11 x 4) = $11,552

Value after 11 years with monthly compounding: $6,000 x (1 + 0.06 /12)^(11 x 12) = $11,589.68

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

Value after 11 years: 6,000 x (2.718^0.06) x 11 = $70,080.78

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The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

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A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8

B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2

From the question, we are to solve the given equations

The given equation is log₄(x² - 12x + 48) = 2

From one of the laws of logarithm, we have that

logₐ x = n ⇒ x = aⁿ

Thus,

log₄(x² - 12x + 48) = 2 becomes

(x² - 12x + 48) = 4²

x² - 12x + 48 = 16

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

Solve the quadratic equation

x² - 12x + 32 = 0

x² - 8x - 4x + 32 = 0

x(x - 8) -4(x - 8) = 0

(x - 4)(x - 8) = 0

x - 4 = 0 OR x - 8 = 0

x = 4 OR x = 8

B) 27^(4x-6) =(1/9)^(2x-7)

Solve for x

27^(4x-6) =(1/9)^(2x-7)

Express the bases in index form

3^3(4x-6) =(3)^-2(2x-7)

Equate the powers

3(4x - 6) = -2(2x - 7)

12x - 18 = -4x + 14

12x + 4x = 14 + 18

16x = 32

Divide both sides by 16

16x/16 = 32/16

x = 2

Hence, the value of x is 2

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Answer:

x+5

Step-by-step explanation:

there are no like terms

The 160 feet range and 70 feet height of the path of Gunter Money which can be described with a quadratic equation, gives;

(a) The path is; y = -1.09375×10²·x² + 1.75·x

(b) The vertex form of the equation is; y = -1.09375·(x - 80)² + 70

(c) The angle at the start is approximately 60.3°

A quadratic equation is a single variable polynomial equation of the second degree.

The points in the path which is a path of a projectile and has a shape of a parabola are;

(0, 0), (80, 70), and (160, 0)

The equations are;

y₁ = a·x₁² + b·x₁ + c

y₂ = a·x₂² + b·x₂ + c

y₃ = a·x₃² + b·x₃ + c

Plugging in the coordinates of the three points in the path gives;

The matrix becomes;

[tex]A = \begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}[/tex]

[tex]X = \begin{bmatrix}a \\b \\c\end{bmatrix}[/tex]

[tex]Y = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

We have;

A·X = Y, which gives;

[tex]\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}\cdot \begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

[tex]X = \dfrac{Y}{A} = A^{-1}\cdot Y[/tex]

Where;

A⁻¹ = The inverse of the matrix A

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \frac{ \begin{bmatrix}0 \\70 \\0\end{bmatrix}}{\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}} = \begin{bmatrix}\dfrac{1}{12800} & -\dfrac{1}{6400} & \dfrac{1}{12800} \\\\-\dfrac{3}{160} &\dfrac{1}{40} & -\dfrac{1}{160} \\\\1 &0 &0 \\\end{bmatrix}\bullet \begin{bmatrix}0\\ \\70\\ \\0\end{bmatrix}=\begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]a = -\dfrac{7}{640}[/tex]

[tex]b = \dfrac{7}{4}[/tex]

c = 0

The equation for Gunter Money's path is therefore;

[tex]y = -\dfrac{7}{640} \cdot x^2 + 1\dfrac{3}{4} \cdot x + 0 = -1.09375\times 10^2 \cdot x^2 + 1.75\cdot x[/tex]

(b) The vertex of the path is (h, k) = (80, 70)

The vertex form of a quadratic equation is; y = a·(x - h)² + k

The equation of Gunter Money's path in vertex form is therefore;

[tex]y = -\dfrac{7}{640} \cdot \left(x - 80)^2 + 70 = -1.09375\times 10^2\cdot (x - 80)^2+70[/tex]

(c) The angle of the parabolic path of Gunter Money's motion at a point is given by the value of the arctangent of the differentiation of the function for the motion at the point as follows;

[tex]y' = -\dfrac{7\times 2}{640} \cdot x + 1\dfrac{3}{4}[/tex]

At the point Gunter Money takes off,  (0, 0), we have;

[tex]tan(\theta) = y' = -\dfrac{7\times 2}{640} \times 0 + 1\dfrac{3}{4} = 1\dfrac{3}{4} = 1.75[/tex]

[tex]\theta = arctan(1.75) \approx 60.3^{\circ}[/tex]

The angle is approximately 60.3°

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The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

The equation to find the roots, is a quadratic equation.

Hence,

2x² + 7x + 6

2x² + 3x + 4x + 6

x(2x + 3) + 2(2x + 3)

Hence,

(x + 2)(2x + 3) = 0

Therefore,

x + 2 = 0    or 2x + 3 = 0

x = -2 or x = -3 / 2

The roots of the equation is x = -2 and x = -3 / 2

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The diameter of a semicircle is 4 yards. The perimeter for a semicircle having a diameter of 4 yards is 10.28 yards.

The perimeter of a shape is the distance of the path or boundary that surrounds the shape.

The formula for the perimeter of a semicircle is πr + 2r

π(pie)=3.14

r(radius)=2 yards (∴ radius=1/2diameter)

∴ the perimeter of a semicircle = πr + 2r

                                                    = 3.14×2+2×2

                                                    =10.28 yards.

∴ The perimeter of a semicircle with a diameter of 4 yards is 10.28 yards.

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Answer:

y=3x+25

Step-by-step explanation:

we need start by making slope intercept form

lets move the 12x after moving it we get

-4y=-12x+4 we need to remove the - 4 from the y so we need to divide the whole equation by - 4

we get y=3x-1

now we can create an equation to get the parallel line

y+2=3(x+9) now distribute

y+2=3x+27 and subtract the two

y=3x+25

Answer:

C______________4_⁴________

The value of ∠FED is 120° and ∠CBD is complementary to ∠FDE

Complementary angles are two angles that sum up to 90°

For example 60° and 30° are complementary.

Either angle is called the complement of the other angle.

∠FED, ∠FDE and ∠DFE are in a triangle.

so,

∠FED + ∠FDE  +  ∠DFE = 180°

16x - 8 + 2x + 9 + 35 = 180 ( sum of angles in a triangle)

18x +36 = 180

18x = 180 - 36

18x = 144

x = 144/18

x = 8

so ∠FED = 16x - 8

Substitute x = 8 into the equation above we have

16(8) - 8 = 128 - 8 = 120°

∠FDE = 2x + 9

∠FDE = 2(8) + 9 = 25°

∠BED = 6x + 12

∠BED = 6(8) + 12

∠BED = 48 + 12

∠BED = 60°

∠CBD = -2x + 81

∠CBD = -2(8) + 81

∠CBD = 65°

so since ∠CBD = 65° and 90 - 65 = 25°

∠CBD is complementary to ∠FDE

In conclusion, ∠FED is 120° and ∠CBD is complementary to ∠FDE

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Answer:

The height of the flagpole is about 25.6 feet.

Step-by-step explanation:

The figure is omitted--please sketch it.

Put your calculator in degree mode.

Let h be the height of the flagpole.

[tex] \tan(52) = \frac{h}{20} [/tex]

[tex]h = 20 \tan(52) = 25.6[/tex]

The observation of the graphing speed versus time is given below.

The rate at which the speed is changing is known as acceleration.

From the graph, the line segment OA and DE have linear acceleration which increases the velocity.

Similarly, from the graph, the line segment BC and EF have linear deacceleration which decreases the velocity.

From the graph, line segment AB has constant acceleration which increases the velocity.

And from the graph, the line segment CD has zero acceleration which makes the velocity to be constant.

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Order of operation to simplify this expression as follows:

   [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+7\div 8)\times 1)\div 2[/tex]

⇒ [tex]((0.25+0.875)\times 1)\div2[/tex]

⇒ [tex](1.125\times 1)\div2[/tex]

⇒ [tex]1.125\div 2[/tex]

⇒ [tex]0.5625[/tex]

What is order of operation?

The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.

The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.

PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.

Given Expression is ; [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]

Firstly we calculate the highest priority between(+,-, x, and [tex]\div[/tex])

Here, division is the highest priority ,

[tex]((0.25+7\div 8)\times 1)\div 2[/tex]

[tex]((0.25+0.875)\times 1)\div2[/tex]

and then we solve parathesis,

[tex](1.125\times 1)\div2[/tex]

now we do multiply,

[tex]1.125\div 2[/tex]

and the final answer will be [tex]0.5625[/tex]

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