Shelly and Jamie participate in a street relay race. Jamie must run from point B along AB⌢, which represents part of a roundabout, to pass off the baton to Shelly at point A.

If the central angle measures 123∘, and the radius of the roundabout is 50 meters, how many meters must Jamie sprint to reach Shelly?

Use π≈3.14 and round your answer to the nearest meter.

Enter your answer as a number, like this: 42

Answer:

Check Explanation

Step-by-step explanation:

The number line required to answer this question is missing.

But I'll explain how to get the total number of basketball cards Juan has, given the number that corresponds to 60% of the total number of cards.

Let the total number of basketball cards be x.

The first step is to check the number line presented. We furst require the number that corresponds to 60% of all of Juan's basketball cards..

Let us assume that the number of basketball cards according to the number line is 45.

This means that

60% of the total number of basketball cards = 45

60% × x = 45

0.6x = 45

x = (45/0.6) = 75 basketball cards.

So, the way to go is just to divide the number that the number line gives (which represents 60% of the total number of basketball cards) by 0.6 to obtain the total number of basketball cards.

Hope this Helps!!!

Answer:

48

Step-by-step explanation:

81 - 33 = 48

Answer:

48

Step-by-step explanation:

81 - 33 = 48

Do 81 - 30 first = 51

Then do 51 - 3 = 48

The first column is found by plugging in the x values to get corresponding y values. For instance, if x = -5, then y is...

y = x^2+3x-18

y = (-5)^2+3(-5)-18

y = 25-15-18

y = 10-18

y = -8

So that explains how they got -8 in the second column, next to x = -5.

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

The column of first differences is found by subtracting the adjacent terms in the y column. The distance from y = -8 to y = -14 is 6 units, so we'll write 6 in the first row of the "first differences" column. The rest of the values of this column are filled out in a similar fashion. This means that you'll need to completely fill out the y column before you can move onto the "first differences" column.

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

The second differences is found by subtracting the adjacent first differences. You should find the results of this column are all the same value. This is true of any quadratic function.

Answer:

The submarine is  307.8 yards below sea level.

Step-by-step explanation:

Since the 500 yards are the hypotenuse of the right angle triangle, the acute angle opposite the side of the triangle we need to find is known ([tex]38^o[/tex]), we can use the sine function to solve the problem:

[tex]sin(\theta)=\frac{opposite}{hypotenuse} \\sin(38^o)=\frac{x}{500} \\500\,*\,sin(38^o)=x\\x = 307.8307\,\,yards[/tex]

which rounded to the nearest tenth is : 307.8 yards

Answer: £6.80

Step-by-step explanation:

Kara bought 5 jumpers for the price of 4.  Thus, multiply 4.8*5 = 24.  Then divide 24/4 to get 6.

Hope it helps <3

Answer:

222222:#&&&#+17265262

Answer:

4a+5b

Step-by-step explanation:

Given:

Apple=£a

Banana=£b

Quantity of Apple=4

Quantity of banana=5

Find the cost of 4 apples and 5 bananas

Total cost=PaQa+PbQb

Where,

Pa=price of Apple

Qa=quantity of Apple

Pb=price of banana

Qb=quantity of banana

Total cost=PaQa+PbQb

=4*a+5*b

=4a+5b

Answer:

[tex]a_{10}=124[/tex]

Step-by-step explanation:

In an arithmetic sequence, we are given that:

[tex]a_{17}=82\\d=-6[/tex]

The nth term of an arithmetic sequence, [tex]a_n=a+(n-1)d[/tex]

When n=17, [tex]a_{17}=82,d=-6[/tex], we have:

[tex]a_{17}=a+(17-1)(-6)[/tex]

82=a+(16)(-6)

82=a-96

a=82+96

a=178

Therefore, the 10th term of the sequence

[tex]a_{10}=178+(10-1)(-6)\\=178+9(-6)\\=178-54\\a_{10}=124[/tex]

Answer:

36

Step-by-step explanation:

quick maths

Answer:

36 rectangles

Step-by-step explanation:

Assuming that all you are asking for is the individual number of squares (not the number of squares and rectangles that can be made when combining the individual ones), the answer is 36.

We get this by multiplying the six squares on one side by the six on the other side. This allows us to calculate the total number! You can do this on a calculator or by hand.

However, if you would like the TOTAL number of rectangles that includes combining the individual ones, this chessboard would have 91 squares and 441 rectangles.

Answer:

The gap in the histogram simply means that: out of all the automobiles sampled, there were none with number of miles driven between 17,500 miles and 32,500 miles.

Step-by-step explanation:

The histogram in question is missing from the question. It was obtained online and is attached to this solution.

A histogram is a chart that represents numerical data using bars. The dataset is split into intervals, each interval is represented by a bar, and the number of variables in each interval makes up the frequency for that interval.

If the bars are of equal width, the height of each bar corresponds to the frequency of the interval represented by that bar. If not, the frequency is given by the area of each bar (this is the major difference between a Bar chart and a histogram).

For this question, the histogram shows the number of miles driven by a sample of automobiles in New York City, the frequency of automobiles in each interval of miles driven is presented on the y or vertical axis and the miles driven is shown on the x-axis.

It is clear that 50 automobiles are in this sample and the class width of each interval of miles driven is 5000 miles.

So, the gap in between this histogram between the interval just after 17500 miles driven and just before 32500 miles driven simply means that none of the automobiles sampled had number of miles driven within this range.

Hope this Helps!!!

Answer: 56

Step-by-step explanation:

Let's organise our information :

The area of the cercle's quarter area is :

The area of the triangle is :

NOw the area of the shaded segment :

Answer:

Step-by-step explanation:

In a quadrilateral all the angles equal to 360 degrees

ADC= 136+90+62=288.

360-288=72

A straight line is equal to 180 degrees

CDE= 180-72=108

x=108

Answer:

the value of x is 62 degrees.

Step-by-step explanation:

we know that corresponding angles are equal, so the value of x is 62 degrees as x is an corresponding angle of 62°

Answer:

1/1001 < 4/10 < 49/100 < 357/10

Step-by-step explanation:

4/10 => 0.4

49/100 => 0.49

357/10 => 35.7

1/1001 => 0.0009

Ascending order is from smallest to the greatest.

Answer:

1/1001, 4/10, 49/100, 357/10

Step-by-step explanation:

Convert the fractions to decimals.

4/10 = 0.4

49/100 = 0.49

357/10 = 35.7

1/1001 = 0.0009

Arrange in ascending order.

0.0009, 0.4, 0.49, 35.7

Change back to fractions.

Answer:

  41%

Step-by-step explanation:

The table shows that 36 of the 88 students that like traveling out of state do not like camping. That percentage is ...

  36/88 × 100% ≈ 41%

Answer:

Variable

Step-by-step explanation:

A variable is a letter or symbol used as a placeholder for an unknown value in an expression or equation.

Hope this helps..

Good Luck!

Answer:

variable

Step-by-step explanation:

A symbol use to represent an unknown value in an expression or an equation is called a variable.

Answer:

587.18 square inches

Step-by-step explanation:

We would find the Total surface area of the cone

Diameter of the cone = 11 inches

Radius = Diameter ÷ 2 = 11 / 2 = 5.5 inches

Slant height ( l ) = 28.5 inches

Let's take π = 3.14

Total Surface Area of a cone = πrl + πr²

= πr(l + r)

= 3.14 × 5.5( 28.5 + 5.5)

= π × 5.5(34)

= 587.18 square inches

There the square inches of paper will she need to cover the entire cone is 587.18 square inches

Answer:

? = 44 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp side/ adjacent side

tan ? = 46/48

Take the inverse tan of each side

tan ^-1 ( tan ?) = tan ^ -1 ( 46/48)

   ? = 43.78112476

To the nearest degree

? = 44 degrees

Answer:

≈ 18.87 cm²

Step-by-step explanation:

The shaded area is the difference between the area of the trapezium and the semicircle.

The area (A) of the trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h( a + b)

where h is the height and a, b the parallel bases

Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus

A = [tex]\frac{1}{2}[/tex] × 4 × (14 + 8) = 2 × 22 = 44 cm²

area of semicircle = [tex]\frac{1}{2}[/tex]πr² = [tex]\frac{1}{2}[/tex]π × 4² = 8π cm²

Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places )

Answer:≈ 18.87 cm²

Step-by-step explanation:

Answer:

≈ 18.87 cm²

Step-by-step explanation:

The shaded area is the difference between the area of the trapezium and the semicircle.

The area (A) of the trapezium is calculated as

A = h( a + b)

where h is the height and a, b the parallel bases

Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus

A = × 4 × (14 + 8) = 2 × 22 = 44 cm²

area of semicircle = πr² = π × 4² = 8π cm²

Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places

Answer:

D

Step-by-step explanation:

Answer:

A (3, 1)

B (2, 2)

C (1, 2)

D (1, 1)

Step-by-step explanation:

When a point is rotated 90° (90 degrees) counterclockwise about its origin, the coordinate B (x, y) transforms into B' (-y, x).

A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)

Using the formula above B (x, y) ⇒ B' (-y, x), we have the coordinates for the polygon as:

A′ (-1, 3) ⇒ A (3, 1)

B′ (-2, 2) ⇒ B (2, 2)

C′ (-2, 1) ⇒ C (1, 2)

D′ (-1, 1) ⇒ D (1, 1)

∴  coordinates of the original polygon is given by the vertices:

A (3, 1), B (2, 2), C (1, 2), D (1, 1)

Answer:

18.0

Step-by-step explanation:

==>Given:

Triangle with sides, 16, 30, and x, and a measure of an angle corresponding to x = 30°

==>Required:

Value of x to the nearest tenth

==>Solution:

Using the Cosine rule: c² = a² + b² - 2abcos(C)

Let c = x,

a = 16

b = 30

C = 30°

Thus,

c² = 16² + 30² - 2*16*30*cos 30°

c² = 256 + 900 - 960 * 0.8660

c² = 1,156 - 831.36

c² = 324.64

c = √324.64

c = 18.017769

x ≈ 18.0 (rounded to nearest tenth)

Answer:

[(a + b), c]

Step-by-step explanation:

Midpoint of a segment with extreme ends represented by ordered pairs [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex],

Midpoint = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

It is given that extreme ends of the segment QS are Q(2b, 2c) and S(2a, 0)

Coordinates of the midpoint of QS will be,

= [tex](\frac{2a+2b}{2},\frac{2c+0}{2} )[/tex]

= [(a + b), c]

Therefore, ordered pair representing the midpoint of QS will be [(a + b), c].

Answer:

(a+b, c)

Step-by-step explanation:

CORRECT FOR ACELLUS

Answer:

Option (1)

Step-by-step explanation:

Let the number of adult tickets sold = x

And the number of child tickets sold = y

Cost of adult tickets sold = $8x

And the cost of child tickets sold = $4y

If the theater company needs to earn at least $1280,

8x + 4y ≥ 1280

2x + y ≥ 320 ---------(1)

Since community center has a capacity of 240 people,

x + y ≤ 240 ----------(2)

By graphing these inequalities with the help of a graphing tool,

Shaded area above the solid line will be represented by inequality (1) (red line)

And the shaded area below the line will be the represented by inequality (2) (blue line)

Common area of both the shaded regions will represent the solution area .

Option (1) will be the answer.

Answer:

x > 3

Step-by-step explanation:

Given 2 sides of a triangle then the third side x will be

difference of sides < x < sum of sides , that is

15 - 12 < x < 15 + 12, so

3 < x < 27

Thus x > 3

Answer:

C. 3

Step-by-step explanation:

x > 3

Ed 2020

Step-by-step explanation:

530pm = 17:50 in 24hr/military time

915pm = 21:15 in 24hr/military time

therefore..

24hr/military time. 21:15 - 17:50 = 3.65hr

our time. 3hr 45min

It took Sarah 3 hours and 45 minutes to finish her homework

The answer in 24 hour clock system is 3:45

The calculation can be done as follows

Sarah started her home work at 5:30 pm

She finished at 9:15pm

The time range here is 3 hours, 45 minutes

Please see the link below for more information

https://brainly.com/question/24991186?referrer=searchResults

Answer:

1+B,2+D,3+E,4+C and 5+A

Step-by-step explanation:

(A)161 (B)130 (C)168 (D)150 (E)132

1. 26 x 5=130

This is Option B, therefore we have the match:1+B

2. 25 x 6=150

This is Option D, therefore we have the match:2+D

3. 22 x 6=132

This is Option E, therefore we have the match: 3+E

4. 21 x 8=168

This is Option C, therefore we have the match: 4+C

5. 23 x 7=161

This is Option A, therefore we have the match:5+A

Answer:

40 students.

Step-by-step explanation:

There are 60 12th graders that voted for Nick and only 20 12th graders that voted for Garett. 60 - 20 = 40.

Hope this helps!

Answer:

To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;

3·4ⁿ is divisible by 3 and 51 is divisible by 3

Where we have;

[tex]S_{(n)}[/tex] =  3·4ⁿ + 51

[tex]S_{(n+1)}[/tex] = 3·4ⁿ⁺¹ + 51

[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ

[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ

∴ [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9

Given that we have for S₀ =  3×4⁰ + 51 = 63 = 9×7

∴ S₀ is divisible by 9

Since  [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9, we have;

[tex]S_{(0+1)}[/tex] - [tex]S_{(0)}[/tex] =  [tex]S_{(1)}[/tex] - [tex]S_{(0)}[/tex] is divisible by 9

Therefore [tex]S_{(1)}[/tex] is divisible by 9 and [tex]S_{(n)}[/tex]  is divisible by 9 for all positive integers n

Step-by-step explanation:

We have proven that ∠D ≅ ∠A as shown below

From the question, we are to complete the proof

Statements                                           Reasons

  AB ≅ DB                                             1. Given

1. EB ≅ CB

2. ∠ ABC ≅ ∠DBE                                2. Congruent postulate

3. ΔABC ~ ΔDBE                                3. Side-angle-side postulate

4. ∠D ≅ ∠A                                         4. CPCTC (Corresponding parts of

                                                               congruent triangles are congruent.)

Hence, we have proven that ∠D ≅ ∠A  

Learn more on Proof of angles here: https://brainly.com/question/11673033

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Answer:

[tex] \dfrac{1}{a^6} [/tex]

Step-by-step explanation:

[tex] a^{-6}x^0 = [/tex]

[tex] = \dfrac{1}{a^6} \times 1 [/tex]

[tex] = \dfrac{1}{a^6} [/tex]

Answer:

The ratio is 2:3

Step-by-step explanation:

The first thing we need to get here is how much was paid for the Van in total.

That would be;

23,500 + 20% of 23,500

= 23,500 + (20/100 * 23,500)

= 23,500 + (23500/5)

= 23,500 + 4,700 = £28,200

She pays a deposit, which of course wasn’t stated in the question.

But we know she pays the rest in 18 equal payments at £940 each.

The total amount she paid asides the deposit would be :

28,200 -(940 * 18) = 28,200 - 16,920 = £11,280

So what this means is that she paid a deposit of £11,280 and a cumulative installment payment of £16,920

So now, we want to find the ratio of the deposit to the 18 equal parts payment.

Mathematically, that would be;

11,280 : 16,920

= 1128 : 1692

Divide both by 1128

= 1: 1.5

= 1: 3/2

which is same as 2:3

The ratio of the deposit Emma pays to a total of the 18 equal payments is 2/3 and this can be determined by finding the deposit amount and total amount paid for the Van.

Given :

Emma buys a camping van for £23500 plus vat at 20% she pays the deposit then pays the rest of the cost in 18 equal payments of £940 each month.

The total amount paid for the Van is:

[tex]= 23500 + \dfrac{20}{100}\times 23500[/tex]

= 23500 + 4700

= £28200

The total deposit amount is given by:

[tex]= 28200-18(940)[/tex]

= 28200 - 16920

= £11280

So, the ratio of the Emma pays to a total of the 18 equal payments is:

[tex]\dfrac{11280}{16920}=\dfrac{1128}{1692}[/tex]

Further, simplify the above ratio.

[tex]=\dfrac{2}{3}[/tex]

Therefore, the ratio of the deposit Emma pays to a total of the 18 equal payments is 2/3.

For more information, refer to the link given below:

https://brainly.com/question/15385899