a skater skates all the way around the two circles shown below. each circle has a diameter or 20 meters. what is the approximate total distance skated?

Answer:

the image is sideways

Step-by-step explanation:

Answer:

well buddy see you thinking to hard its right there just relax and look closely

Step-by-step explanation:

Answer:

\(2x^3-5x^2-7x-2\)

Step-by-step explanation:

1)  Expand by distributing sum groups.

\(2x(x^2-3x-2)+x^2-3x-2\)

2) Expand by distributing terms.

\(2x^3-6x^2-4x+x^2-3x-2\)

3) Collect like terms.

\(2x^3+(-6x^2+x^2)+(-4x-3x)-2\)

4) Simplify.

\(2x^3-5x^2-7x-2\)

Thanks!

- Eddie

Step-by-step explanation:

Sorry for writing BTS Army but I do lov* them all...

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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Answer:

32768x¹⁰

Step-by-step explanation:

by applying the law of indices

multiply the powers inside the parentheses with the power outside of the parentheses

then evaluating 2¹⁵ equals 32768

multiply by x¹⁰

the answer is 32768x¹⁰

Answer:

quotient is the answer to division. So if 7/2=3 with a remainder of 1, then the quotient is 3

The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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Answer:

0.6341 = 63.41% probability that his commute today took more than 35 minutes

Step-by-step explanation:

Randomly distributed = Uniform distribution.

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

\(P(X > x) = \frac{b - x}{b - a}\)

Randomly distributed with a minimum of 20 minutes, a maximum of 61 minutes.

This means that \(a = 20, b = 61\).

What is the probability that his commute today took more than 35 minutes?

\(P(X > 35) = \frac{61 - 35}{61 - 20} = 0.6341\)

0.6341 = 63.41% probability that his commute today took more than 35 minutes

Answer:

The sequence is increasing by 5 at each step. So, we can write:

a1 = 30

a2 = 30 + 5 = 35

a3 = 30 + 25 = 40

a4 = 30 + 35 = 45

a5 = 30 + 4*5 = 50

We notice that the nth term is given by:

an = 30 + (n-1)5

So, the explicit formula for the nth term is:

an = 25n + 5

Step-by-step explanation:

to find the sum of nth term

equation is

n/2 ( 2a + (n-1)d) where a is the 1st term and d is the common difference

5/2 ( 120 +( 4 × 31))

5/2 ( 120 + 124)

5/2 × 244

5 × 122 dividing 244 by 2

610

Answer: 610

Step-by-step explanation:

This sequence starts at 60 and increases by increments of 31.  Thus, to get the last two numbers, do 122+31=153, and 153+31=184.  Then add 60+91+122+153+184 to get 610.

Hope it helps <3

9514 1404 393

Answer:

  multiply the radius by √1.2 ≈ 1.0954

Step-by-step explanation:

Let the original depth and radius be represented by 30 and r. Let the modified depth and radius be represented by 25 and r'. Assuming the pond is uniform depth, the formula for the volume of a cylinder applies. The volume of a cylinder is given by ...

  V = πr²h

In this application, we want the original and modified volumes to be the same.

  πr²(30) = π(r')²(25)

  (r')² = r²(30/25) = r²(6/5)

  r' = r√(6/5)

The radius can be multiplied by √1.2 to maintain the original volume of the pond.

Answer:

∠ ABC = 49°

Step-by-step explanation:

the chord- tangent angle ABC is half the measure of the intercepted arc AB

∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°

We may conclude after answering the provided question that As an example, a rectangle with a length of 4 cm and a width of 4 cm has a perimeter of 16 cm.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

2 x (Length + Width) = Perimeter

If we choose L as the length and W as the breadth, we can write the equation:

16 = 2 x (L + W)

When we simplify this equation, we get:

8 = L + W

2 x (4 + 4) = 16 Perimeter

As an example, a rectangle with a length of 4 cm and a width of 4 cm has a perimeter of 16 cm.

1 cm in length, 7 cm in width

2 cm in length, 6 cm in width

3 cm in length, 5 cm in width

4 cm in length, 4 cm in width

5 cm in length, 3 cm in width

6 cm in length, 2 cm in width

7 cm in length, 1 cm in width

And so forth.

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Answer:

p = 8

Step-by-step explanation:

Divide -5 to both sides

-5p = -40

5p = 40

p = 8

So p = 8

Answer:

the fourth one

Step-by-step explanation:

hope it helped!!!

Answer:

geometric sequence.

Step-by-step explanation:

Given the sequence an = 4 * 3(n-1)

The type of sequence written in this form is a geometric sequence. It is expressed Mathematically as;

an = ar^n-1

On comparison, we can see  that;

a = 4

r = 3

a is the first term]

r is the common ratio

Answer: x= -11

Step-by-step explanation: Substitute y for -9, and move 2 to the other side, which would be -9-2=-11. So x=-11

Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining  $2,000 in her savings account.

Future value = $20,000

Simple interests rate = 1.5%

The return rate on bonds= 4.5%

The return rate on stocks = 6.2%

Total amount made on invests =  $942

Time period = 1 year

Let us assume that the amount of money Emily invested = x

Amount invested in stock = y

If the amount is twice = 2y

The interest earned = x * 0.015

Interest on bond = 2y * 0.045

Interest on stocks = y * 0.062

The equation will be:

(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942

0.015x + 0.152y = 942  ------ Equation 1

Total future value is given as $20,000

x + 2y + y = 20000

x + 3y = 20000

x = 20000 - 3y

Substituting the x value in the first equation:

0.015(20000 - 3y) + 0.152y = 942

300 - 0.045y + 0.152y = 942

0.107y = 642

y = 6000

Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.

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Answer:

im not super sure but i think its 70

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

(4*8) (5 -3)

= (32)(2)

= 64

Answer: The number is 14

Step-by-step explanation:

A number is increased by 20:  (X + 20)

Then doubled: 2(X + 20)

5 times the number: 5X

2 less than 5 times the number: 5X - 2

Setting the bold statements equal: 2(X+20) = 5X - 2

Distribute left side: 2X + 40 = 5X - 2

Move X's: 40 = 3X - 2

Move numbers: 42 = 3X

Divide both sides by 3: X = 14

The required slope of WZ is 3/2 for the given situation.

Since WXYZ is a rectangle, WZ is perpendicular to XY, and the slope of WZ is the negative reciprocal of the slope of XY.

The slope of the line is defined as the angle of the line. It is denoted by m

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The slope of XY is:

m = (y₂ - y₁)/(x₂ -x₁ ) = (-7 - (-5))/(-1 - (-4)) = -2/3

The negative reciprocal of -2/3 is:

-1/(-2/3) = 3/2

Therefore, the slope of WZ is 3/2.

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Given:

Total number of bills of one, five and ten = 165

Total amount = $893

There are twice as many five dollar bills as there are ones and tens combined.

To find:

Number of bills of each type.

Solution:

Let number of bills of one, five and ten are x, y and z respective.

Total number of bills of is 165.

\(x+y+z=165\)         ...(i)

Total amount is $893.

\(1x+5y+10z=893\)         ...(ii)

There are twice as many five dollar bills as there are ones and tens combined.

\(y=2(x+z)\)     ...(iii)

From equation (iii), we get

\(\dfrac{y}{2}=x+z\)       ...(iv)

Putting \(x+z=\dfrac{y}{2}\) in (i), we get

\(\dfrac{y}{2}+y=165\)

\(\dfrac{3y}{2}=165\)

\(3y=330\)

\(y=110\)

Putting y=110 in (iv), we get

\(x+z=\dfrac{165}{2}\)

\(x+z=55\)

\(x=55-z\)       ...(v)

Putting y=110 and x=55-z in (ii), we get

\((55-z)+5(110)+10z=893\)

\(55-z+550+10z=893\)

\(9z+605=893\)

\(9z=893-605\)

\(9z=288\)

Divide both sides by 9.

\(z=32\)

Putting z=32 in (v), we get

\(x=55-32\)

\(x=23\)

Therefore, the number of one, five and ten bills are 23, 110 and 32 respectively.

There are 23 bills of $1 type.

There are 110 bills of $5 type.

There are 32 bills of $10 type.

According to the given situation

You are given $893 in one, five, and ten dollar bills.

Let the number of $1 bills be "x"

Let the number of $5 bills be "y"

Let the number of $10 bills be "z"

Total number of bills = x + y + z  

Also it is given that there are twice as many five dollar bills as there are ones and tens combined

hence we can write the equations in the form of 3 variables

\(\rm x + y + z = 165........(1) \\x +5y + 10z = 893.........(2) \\y = 2\times (x+z) ..........(3) \\\)

These are three linear equations  with 3 variables that can be solved for x, y and z .

On solving equations (1) , (2),  and (3) we get

\(x = 23 \\y = 110 \\z = 32 \\\)

So we can conclude that there are 23 bills of $1 type.

There are 110 bills of $5 type.

There are 32 bills of $10 type.

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Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

790

Step-by-step explanation:

7098uuilu4645

Answer:

37y +3?

Step-by-step explanation:

L×B=Area

(7y+1)(2y+3)

According to the given figure ,

Formula to find the area of a rectangle is given by -

\( \:\:\:\:\:\:\star\small \underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} = Length \times Breadth }}}}\\\)

On substituting the values-

\( \:\:\:\:\:\:\longrightarrow \sf { Area_{(rectangle)}= \bigg(7y+1\bigg)\times \bigg(2y+3\bigg)}\\\)

\( \:\:\:\:\:\:\longrightarrow \sf { Area_{(rectangle)} = \bigg ( 14y^2+21y+2y+3\bigg)}\\\)

\( \:\:\:\:\:\:\longrightarrow \sf { Area_{(rectangle)} = 14y^2+23y +3}\\\)

\( \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{Area_{(rectangle)}=\underline{14y^2+23y +3}}}}}\\\)

\( \\ \therefore \underline{ \cal{ \pmb{Correct \:option \: is \: \frak{\purple{ C)\:\underline{14y^2+23y +3 }}. }}}}\\\)

Answer: 10g +12

Step-by-step explanation:

Combine like terms!

Answer:

tan

Step-by-step explanation:

take 19 degree as reference angle

using tan rule

tan 19=opposite/adjacent

0.34=14/x

x=14/0.34

x=41.17

x=41.2

The guests in the birthday party ate 33 cookies.

We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.

Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.

6 1/4 dozen = 25/4 dozen

3 1/2 dozen = 14/4 dozen

Now we can subtract the number of cookies that were left from the number of cookies that were made:

25/4 - 14/4 = 11/4 dozen

To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.

There are 12 cookies in one dozen, so:

11/4 x 12 = 33

Therefore, the guests ate 33 cookies.

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Answer:

70/100=x/20 cross multiply you get 1400/100=14

If Ashley sold 70% of her candy bars it means she has 30% left to sell

of means times

30%=.30

20 x .30= 6 candy bars to sell

Step-by-step explanation:

give brainliest please :)

Answer:

6

Step-by-step explanation:

70% of 20 is 14

20-14=6

let me  know if im wrong