Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 10 min. If the current in that part of the river is 2 km per hour, what was her boat speed in still water?

The measure of angle W in the kite WXYZ is 115°

A kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides.

Given that, In kite WXYZ, m ∠ x = 90° and m ∠ z =40°.

Please refer to figure attached,

We know that, in a kite, it has two opposite and equal angles.

According to figure, here,

m ∠ W = m ∠ Y

Let m ∠ W = m ∠ Y = x

Also, the sum of interior angles of quadrilateral = 360°

Therefore,

x + x + 90° + 40° = 360°

2x = 360° - 130°

2x = 230°

x = 115°

Thus, m ∠ W = m ∠ Y = 115°  

Hence, the measure of angle W in the kite WXYZ is 115°

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The correct measures of these two angles are, 30°  and 150°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

We know that, a ray is a line that continues on forever inn one direction with a point at it's start.

here, we have,

He also wants the measure of ∠A to be five times the measure of ∠D.

Let the smaller side is x then other side is 5x,

so, we get,

x+5x=180°[interior property]

on solving we get

6x=180°

x=30°

therefore, the other side is 5x

                                             =5*30°

                                             =150°

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The general term formula for the Fibonacci sequence would be   [tex]F_n=\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n - (\frac{1-\sqrt{5}}{2})^n)[/tex].

What is a Fibonacci Sequence?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, starting from 0 and 1. The sequence goes as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.

The Fibonacci sequence is given by

                              [tex]F_n-F_{n-1}-F_{n-2}=0[/tex]

So its characteristic polynomial is

                               [tex]x^2-x-1=0[/tex]

The roots of this are

                            [tex]\alpha=\frac{1+\sqrt{5}}{2}\\\\\beta=\frac{1-\sqrt{5}}{2}[/tex]
Each with multiplicity one. Hence,

                      [tex]F_n=A\alpha^n + B\beta^n\\\\\For $ F_1=1 $ $and $ $ F_2=1$\\\\A=1/\sqrt{5} \\\\B=-1/\sqrt{5}[/tex]

Thus,

                   [tex]F_n=\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n - (\frac{1-\sqrt{5}}{2})^n)[/tex]

Hence, the general term formula for the Fibonacci sequence would be   [tex]F_n=\frac{1}{\sqrt{5}}((\frac{1+\sqrt{5}}{2})^n - (\frac{1-\sqrt{5}}{2})^n)[/tex].

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The following statements about the data above which is true is that the estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A which is denoted as option B.

This is information that has been translated into a form that is efficient for movement or processing.

From the table we can deduce that the number of employees who vited for coffee is higher in Group B than A and is therefore the reason why it was chosen as the correct choice.

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Answer:

A. -7

That's it

Answer:

4/3

Step-by-step explanation:

sorry if I'm wrong

4/3

rise over run so up is rise side is run 4/3

The expression that can be used to find the area of the shaded portion will be C. 2/3 × 9² × π

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

In this situation, the circle has a radius of 9 inches and is divided into 6 equal parts. the area of a single section of the circle is equal to 13.5(pie) square inches.

The expression that can be used to find the area of the shaded portion will be:

= 4/6 × πr²

= 4/6 × 9² × π

= 2/3 × 9² × π

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Answer:

8.  TN = 22 units

9.  RT = √(165) units

Step-by-step explanation:

It appears that point T is the circumcenter of triangle MNP.

A circumcenter of a triangle is:

As a perpendicular bisector is a line that divides another line segment into two equal parts at a right angle, then:

As point T is the circumcenter, ΔMTN, ΔNTP and ΔMTP are isosceles triangles and MT, TP and TN are the radius of the circumcircle.

Therefore:

To find the length of TN, find the value of x by equating the given expressions for MP and TP:

[tex]\implies \sf MT = TP[/tex]

[tex]\implies 6x - 56 = 3x - 17[/tex]

[tex]\implies 3x = 39[/tex]

[tex]\implies x = 13[/tex]

Substitute the found value of x into the expression for TP:

[tex]\implies \textsf{TP} = 3(13) - 17[/tex]

[tex]\implies \textsf{TP} = 22[/tex]

Therefore, as TN = TP then TN = 22 units.

First find the value of x by equating the given expressions for TN and TP:

[tex]\implies \sf TN=TP[/tex]

[tex]\implies 4x-17=x+10[/tex]

[tex]\implies 3x=27[/tex]

[tex]\implies x=9[/tex]

Substitute the found value of x into the expression for TN:

[tex]\implies \textsf{TN} = 4(9) - 17[/tex]

[tex]\implies \textsf{TN} = 19[/tex]

As RT is the perpendicular bisector of MN, then ΔTRN is a right triangle where ∠TRN is 90°.

Given:

To calculate the length of RT, use Pythagoras Theorem:

[tex]\implies \sf RN^2+RT^2=TN^2[/tex]

[tex]\implies \sf RT=\sqrt{TN^2-RN^2}[/tex]

[tex]\implies \sf RT=\sqrt{19^2-14^2}[/tex]

[tex]\implies \sf RT=\sqrt{165}[/tex]

If there is an inflation rate of 2%, then the cost of  $60 pair of shoes in 5 years is,  $66.245

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

Rate of inflation = 2%

The cost of pair of shoes = $60

Cost after 5 years = ?

After 1 year cost will be,

⇒  $60 +  2% of original cost

2% of original cost =  (60 x 2)/100

                               =   0.02 x 60

⇒   $60 + $0.02 x 60

⇒   $60(1 + 0.02)

After 2 year cost will be,

⇒ $60(1 + 0.02) +  2% of cost after 1 year

2% of original cost =  ( 60(1 + 0.02) x 2)/100

                               =   0.02 x 60(1 + 0.02)

⇒   $60(1 + 0.02) + $0.02 x 60(1 + 0.02)

⇒   $60(1 + 0.02)(1 + 0.02)

Similarly, After 5 years,

⇒ $60(1 + 0.02)(1 + 0.02)(1 + 0.02)(1 + 0.02)(1 + 0.02)

⇒ $ 60 x 1.02⁵

⇒ $ 60 x 1.104

⇒ $ 66.245

Hence, the cost will be  $66.245

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Answer:

2/8 + 3/8 = 5/8

Step-by-step explanation:

Total: 8 marbles

Yellow: 3

Green: 2

8 - 3 - 2 = 3

Blue: 3

Fraction of yellow: 3/8

Fraction of green: 2/8

Fraction of yellow and green:

2/8 + 3/8 = 5/8

Answer:

3a + 3b

Step-by-step explanation:

The distributive property of multiplication over addition is

a(b + c) = ab + ac

Here we have

3(a + b)

We apply the distributive property and get

3 × a + 3 × b

which simplifies to

3a + 3b

Answer:

y=3x+5

Step-by-step explanation:

qqqqqqqqqqqqqqqqssssssssss

Probability that both donators are O blood type = 0.0203

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given,

A group of 46 people where 7 of them are O blood type

Probability of one donator to be O blood type

= No. of People with O blood type/total People in the group

= 7/46

No. of people left in the group left after choosing one donator = 46 - 1 = 45

No. of People left with O Blood type = 7 - 1 = 6

Probability of 2nd donator to be O blood type = 6/45

Probability that both are O blood type = 7/46 × 6/45

                                                                = 42/2070

                                                                = 0.0203

Hence, there is probability of 0.0203 that both donators are of O blood type.

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The amount invested at each rate of 2% and 7% respectively is $12000 and $2000

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent the amount invested at 2% by x and the amount invested at 7% by y

therefore x+y = 14000 equation 1

2x/100 + 7y/100 = 380

multiply through by 100

2x + 7y = 38000 equation 2

using elimination method

2x + 2y = 28000 equation 3

2x + 7y = 38000 equation 4

subtract equation 3 from 4

5y = 10000

divide both sides by 5

y = 10000/5

y = $2000

substitute 2000 for y in equation 1

x+2000 = 14000

x = 14000-2000

x = $12000

therefore the amount invested at 2% rate is $12000 and at 7% rate is $2000

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If you differentiate each piece with respect to x, you'd get

    [tex]\frac{d}{dx}(x)\cdot y + x \cdot \frac{d}{dx}(y) + \frac{d}{dx}(2x)+\frac{d}{dx}(3x^2)=\frac{d}{dx}(4)[/tex]

which becomes

    [tex]1\cdot y + x \cdot \frac{dy}{dx} + 2+6x^1=0[/tex]

which is equivalent to B.

The answer is B.

Answer: [tex]x=20, y=26[/tex]

Step-by-step explanation:

Opposite sides of a parallelogram are congruent.

The linear equation that models the population is:

p(t) = 2200*t - 4356000

And in 2010 the population was 66000.

We know that the population grows linearly.

Remember that the general linear equation can be written as:

y = a*t +b

Where a is the slope and b is the y-intercept.

And if the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the points (2005, 55000) and (2008, 61600)

Then the slope is:

a = (61600 - 55000)/(2008 - 2005)

a = 2200

Then the line is something like:

y = 2200*t + b

To find the value of b we can replace the values of the point (2005, 55000), then we will get:

55000 = 2200*2005 + b

55000 - 2200*2005 = b

-4356000 = b

The linear equation is

p(t) = 2200*t - 4356000

The population in 2010 is:

p(2010) = 2200*2010 - -4356000 = 66000

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If I paid $625 interest on $5000 that I borrowed at 5%, 2.5 years did I borrow it.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Here, we have,

formula: I = Prt.

given that,

I paid $625 interest on $5000 that I borrowed at 5%

let,  I borrow it for t yrs.

so, we get,

625= 5000*5%*t

solving we get,

t=2.5

Hence, If I paid $625 interest on $5000 that I borrowed at 5%, 2.5 years did I borrow it.

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Answer: The real part of the complex number is 0.

Step-by-step explanation:

Complex numbers are always in the format: a + bi

On the given complex number, -i√5 , it is representing the "bi" part of the standard complex number expression.

We are looking for the real part. The real part is the real number. Since -i√5 doesn't show a real part, we can infer that its real part is 0.

If you rewrite the expression with 0 as the real number, it is equivalent to the principle of the original:

0 + -i√5

This concept is similar to the idea:

y = mx + b

if the equation said:

y = 3x

we know that b is 0, although its not stated. This principle is used in complex numbers.

Thank you.

Answer:

B

Step-by-step explanation:

orignal height：length＝1：3

for B＝3：9 same as 1：3

Answer:

1.) 55.3896

2.) 30.1754

Step-by-step explanation:

Follow steps in the image. (didn't know if you had to round, so i just left the numbers as they are.)

-Hope this helped

1 ]

Given:-

[tex] \: [/tex]

To Find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \rm{Area \: of \: circle = πr²} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{= 3.14×(4.2)²} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{=3.14× 17.64} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{\rm{ \red{= 55.3896}}}}[/tex]

———————————————————————

2]

Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \rm{Area \: of \: circle = \rm{\frac{(π×d²)}{4} } }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: = \rm{\frac{3.14×38.44}{4} }\\ \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ = \cancel\frac{120.7016}{4} }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{\rm{ \green{=30.1754}}}}[/tex]

[tex] \: [/tex]

hope it helps!:)

The standard form for this number is 7.1509 x [tex]10^4[/tex].

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(9 × 1) + (5 × 1100) + (6 × 11,000)

The standard form for this number is written with a decimal number greater than 1 but less than 2 with an exponent of 10.

Now,

= 9 + 5500 + 66,000

= 71509

= 7.1509 x [tex]10^4[/tex]

Thus,

The standard form is 7.1509 x [tex]10^4[/tex].

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Answer:

71509

Step-by-step explanation:

Answer:

adult tickets purchased = 9

student tickets purchased = 3

Step-by-step explanation:

a = # of adult tickets purchased

s = # of student tickets purchased

(1)   a + s = 12

(2)  $5a + $3s = $54

solve equation (1) for s:

s = 12 - a    now substitute this into equation (2) so you have an expression all in terms of a

$5a + $3(12 - a) = $54    solve for a

5a + 36 - 3a = 54

2a = 54 - 36 = 18

a = 18/2 = 9     substitute this into equation (1) and solve for s

9 + s = 12

s = 12 - 9 = 3  

The requried area of 3 of the pieces is 231 square feet. Option B is correct.

The area of a circle is the amount of space enclosed by the circle in a two-dimensional plane. It is given by the formula:

A = πr²

where "A" is the area of the circle, "r" is the radius of the circle, and "π" (pi) is a mathematical constant with an approximate value of 3.14159.

Here,
The area of a full circle with a radius of 14 feet is given by:

A = πr²

A = (22/7) × (14)²

A = (22/7) × 196

A = 616 square feet (rounded to the nearest whole number)

If the circle is cut into 8 equal pieces, each piece will have an area of:

616 ÷ 8 = 77 square feet

Therefore, 3 pieces will have an area of 3 × 77 = 231 square feet.

Thus, the requried area of 3 of the pieces is 231 square feet. Option B is correct.

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The equation of line passes through the point (-8, 7) will be;

⇒ y = - 9x - 65

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (-8, 7).

And, The parallel line is,

⇒ y = - 9x + 8

Now,

Since, The equation of line passes through the point (- 8, 7).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = -9x + 8

m = dy/dx = - 9

m = - 9

Thus, The equation of line with slope - 9 is,

⇒ y - 7 = - 9 (x - (-8))

⇒ y - 7 = - 9 (x + 8)

⇒ y - 7 = - 9x - 72

⇒ y = - 9x - 72 + 7

⇒ y = - 9x - 65

Therefore, The equation of line passes through the point (-8, 7) will be;

⇒ y = - 9x - 65

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The value of a is 6 and b is 12.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

given:

a + b= 18.......(1)

a/b= 1/2

or, a= b/2......(2)

Put the value of a from equation (2) in (1) we get

b/2 + b= 18

3b/2 = 18

3b= 36

b= 36/3

b= 12

and, a= b/2 = 12/2 = 6

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When x is 4, the output of the equation is greater.

The value for x that produces the same output in both the graph and the equation is equal to 6.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios, a straight line, and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.

By critically observing the graphs, we can reasonably infer and logically deduce that they would produce the same output (range) at the ordered pair (4, 6).

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The length of the side D'E' is 9 units for the given translated triangle D'E'F'.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

As we know that the translation does change the change location but it can't change the shape of the figure.

According to the given question, triangle DEF is translated as 6 units right and 6 units up.

This means there are no changes in the dimensions.

So D'E' =  DE

Thus, D'E' = 9 units

The length of the side D'E' is 9 units

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