The Problem
The school band is making a large banner for its annual fall concert. After the
band members worked for one hour, the band director entered the room and
asked how many feet long the completed banner would be. The trombone
section leader replied, "We're not sure. The trombone section and the
clarinet section work at different rates, but we are sure that the length of the
banner will be 40 feet and 1/2 the total banner's length."
How long will the banner be?

The quadratic equation with a vertex at (-1, -5) that passes through (2, 13) is:

y = 2*(x + 1)^2 - 5

A quadratic equation with a leading coefficient a and a vertex (h, k) is written as:

y = a*(x - h)^2 + k

Here we know that the vertex is (-1, -5), then our parabola is something like:

y = a*(x + 1)^2 - 5

Now we also know that the quadratic equation contains the point (2, 13), then we can replace the values to get:

13 = a*(2 + 1)^2 - 5

13 = a*3^2 - 5

13 = a*9 - 5

13 + 5 = a*9

18/9 = a

2 = a

Then the quadratic equation is:

y = 2*(x + 1)^2 - 5

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Using the properties of half-life we calculate that approximately 22.33 grams of radium will be present after 720 years.

The half-life of radioactive element radium = 1690 years.

Time = 720 years

the formula for calculating half life is given by:

[tex]N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}[/tex]

Now we substitute the values to find the N(t) which is the amount of radium left after 720 years.

t = 720

half life = 1690

N₀ (initial mass) = 30gm

[tex]N(t)&=30\left({\frac {1}{2}}\right)^{\frac {720}{1690}[/tex]

N(t) = 22.329 gm

N(t) ≈ 22.33 gm

The half-life of a substance is the amount of time required for it to reach that point. The phrase is widely used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.

Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay). For instance, a term used in the medical sciences is the biological half-life of drugs and other compounds in the human body.

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Answer:

-5

Step-by-step explanation:

Answer:

The right whale is 100 times more massive that the polar bear

Step-by-step explanation:

7 x 10^2 = 700 kg

7 x 10^4 = 70,000kg.

Check: 700 x 100 = 70,000

(the equivalent mass of 10 polar bears equals that of one whale)

:)

Answer:

28

Step-by-step explanation:

64 - 9(4)

64 - 36

28

They could have biked on first day at the speed of x/4 miles per hour and on the second day at the speed of (88-x)/6 miles per hour where x is the distance covered on first day.

According to the question,

We have the following information:

Jaden and Emilia biked 88 miles from Daytona Beach to Jacksonville in 2 days. They spent 4 hours biking the first day and 6 hours biking the second day. They biked at one speed the first day and a different speed the next day.

Now, let's take the distance covered on first day to be x miles.

Distance covered on second day = 88-x miles

Following formula is used to find the speed of an object:

Speed = distance/time

Speed of first day = x/4 miles per hour

Speed of the second day = (88-x)/6 miles per hour

Hence, they could have biked on first day at the speed of x/4 miles per hour and on the second day at the speed of (88-x)/6 miles per hour where x is the distance covered on first day.

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$943,000 Beep Blair receive in royalties last year.

Given,

In the question:

Rock singer and writer Beep Blair is paid 11.5% on her CD sales and music downloads.

and, She sold 1.22 million CDs and 2.1 million music downloads. The CDs were sold to music stores for $5 each, and the music downloads were $1 each.

To find the how much did Beep Blair receive in royalties last year?

Now, According to the question:

The total amount involved in the sells and downloads are:

1.22 x 5 + 2.1 x 1 = 8.2 million.

She was paid 11.5% of that, hence:

0.115 x 8.2 = 0.943 million = $943,000.

She earned $943,000 from CD sales.

Hence, $943,000 Beep Blair receive in royalties last year.

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Answer: 2,666 children

Step-by-step explanation:

This player makes $3.2 M per year.  10% of his salary is $320,000

($320,000) / ($120/child) = 2,666 children

The cost per ounce when a 3.5 ounce bag of crackers for $1.61 is $0.46.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations.

From the information, the 3.5 ounce bag of crackers is $ 1.61, the cost per ounce will be:

= Total amount / Number of ounce

= $1.61 / 3.5

= $0.46

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Complete question

A 3.5 - ounce bag of crackers cost $ 1.61. Fund the cost per ounce.

Hey there! I would be glad to help you out.

For the first two miles, the price would be six dollars total.

For every mile after that, you would be charged two dollars.

Assuming that you travel 8 miles, you would have to pay six dollars for the first two miles (3*2), and twelve dollars for the last six miles, totaling eighteen dollars.

So the price of an eight mile ride would be eighteen dollars.

You can use this logic for the 50 miles trip too. After traveling 2 miles ($6), there will be 48 more miles.

For these 48 miles, it'll only charge you two dollars each, which would total 96 dollars.

So the price of a fifty mile ride would total $102.

I wish you luck on your homework!

Since the triangles are congruent, their angles are the same

2x = x + 10

x = 10

Angle A = x + 10 = 10 + 10 = 20

If two cubes have sides of length 5 cm and 6cm. The ratio of their respective surface​ areas is 36 : 25.

Using this formula to find the ratio

Ratio of their surface area  = a /a'

Where:

a = 6

a' =5

Let plug in the formula

Ratio of their surface area  = 6a² /6a'²

Ratio of their surface area  = 6(6)² / 6(5)²

Ratio of their surface area  = 36 / 25

Ratio of their surface area  = 36 : 25

Therefore the ratio is 36 : 25.

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The distance from the house to the school is 0.09km

It should be noted that from the information, Just measures 50 cm from his house to school and arrives at 180 steps.

Therefore, the total distance will be:

= 50 × 180

= 9000 cm

1 kilometer = 100000 cm

Therefore, 9000 cm will be:

= 9000 / 100000

= 0.09km

The distance is 0.09km.

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The image after the first reflection is (-x, y)

The image after the second reflection is (-x, -y)

This is equivalent to a rotation of 180°.

First, we start with a reflection across the y-axis. This type of reflection only changes the sign of the x-value of our point.

So, if we start with the point (x, y), the image after the reflection is:

(-x, y)

Now we apply a reflection across the x-axis, this one changes the sign of the y-value, then the image after the reflection is:

(-x, -y)

Notice that a change in both signs is equivalent to a 2 quadrant motion, which is equivalent to a rotation of 180°.

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The slope of the line in the image is a zero slope.

The slope of a line can be defined as the ratio of a line's vertical change to the line's horizontal change, which is rise/run or change in y / change in x.

An horizontal line has horizontal change but no vertical change. Therefore, no matter the horizontal change of the line, the slope of a horizontal line would always be zero. Therefore, horizontal lines have zero slope.

The line in the image is a horizontal line, therefore, the slope is neither positive nor negative, but a zero slope.

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Claire is 18 years old and her mother is 40 years old.

Answer with explanation:

Let Claire's age = x years

Age of Claire's mother =(2 x +4 ) years

Sum of the ages of Claire and her mother =58 years

If we write the above statement in terms of equation , it will be

⇒ x + 2 x +4=58

⇒3 x +4=58

⇒3 x =58 -4

⇒3 x =54

Dividing both side by , 3 , we get

→x=18

Claire's age = 18 years

Age of Claire's mother =(2 x +4 )=2×18+4=36+4= 40 years

The sum of their ages is 58. The "sum of their ages" includes:

Claire's age + 2(Claire's Gage) + 4 = 58

3(Claire's age) + 4 = 58

3 x Claire's age = 58 -4 = 54

Claire's age= 54/3 = 18

Claire is 18 years old.

Since Claire's mom is 4 years older than twice clears age, her age is (18 x 2) + 4 = 40

So Claire is 18 and her mother is 40

I hope this helps!

The two way table to display the relative frequency by row is:

            Lasagna orders

                           veggie        meat         total      

Tomato sauce     44.871%     55.128%   100%

cream sauce        76.67%       23.33%    100%

Given:

Tomato sauce = 35 veggie + 43 meat

= 78

cream sauce = 46 veggie + 14 meat

= 60

veggie % in tomato sauce = 35 * 100/78 = 3500/75 = 44.871%

meat % in tomato sauce = 43 * 100 / 78 = 4300/78 = 55.128%

veggie % in cream sauce = 46 * 100 / 60 = 4600/60 = 76.67%

meat % in cream sauce = 14 * 100 / 60 = 1400/60 = 23.33%

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Answer:

(-12, 10)

Step-by-step explanation:

2x + 4y = 16

-2x - 3y = -6

Add the equations to eliminate x.

y = 10

2x + 4y = 16

2x + 4(10) = 16

2x = -24

x = -12

Solution:

x = -12; y = 10

(-12, 10)

Answer:

3/5= 60%

60% of 2,750= 1650 tickets sold

40% of 2,750 = 1100 tickets left

32 is the next term in the arithmetic sequence of 24,16,8,0,...

To find out what is the next term of the arithmetic sequence

24, 16, 8, 0, ...

To show the explicit equation:

We have an arithmetic sequence because the difference between the terms is constant:

0 → 8: Δ → 8

8 → 16: Δ → 8

16 → 24: Δ → 8

From this the next term is simply:

24 + 8 = 32

And this sequence can be explicitly written as:

[tex]a_{n} = a_{1}(n-1)d[/tex]

Where:

[tex]a_{n}[/tex] = nth term

[tex]a_{1}[/tex] = first term

d = distance between the terms

n = any index number

Therefore we have:

[tex]a_{n} = 1.(n-1)8 = 8.(n-1)\\\\a_{n} = 8. (n-1)[/tex]

Hence the answer is 32 is the next term in the arithmetic sequence of 24,16,8,0,...

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Answer:

The correct Answer is 4:2:3

Step-by-step explanation:

ABC in the ratio 1 by 3 1/2 1/4 money is distributed ABC is equal to 2 by 3 egg be caused by a and c equal to 1 by 4 BC value a + b + c will be 7200

36 X + 1 by 4 X equal to 7203 B12 for dual is right down here now divide 12343 12 and 4 x is 144 Avenger 4 Hindi 2020 worldwide 6 then it will be 2 and 2 X 1 will be 2 + 12 and 72 value will be 9 x 12 equal to make a call to 7212 989 and

n7200 will be divided by 3 and answer will be 2424 4 will be 9696 amount of a 1 by X equal to 1 by 3 X 9600 equal to 3200 amount of the one my c equal to 1 by 6 multiply 9600 be 1602 14 x 9600 will be 2400

solution of this question

Answer:

8x+7+11x+2=180

11x_8x +7+11=180

3x+18=180

3x=180_18

3x=168

x=168÷3

x=56

From the given data of traffic circle, the center of the circular monument is covering approximately 148,000 square feet then the radius of the monument is equal to 217.10 feet.

As given in the question,

Given that traffic circle is a round intersection.

It has circular monument in the center.

Area covered by circular monument is equal to 148,000 square feet.

Let us consider radius of the circular monument be 'r'

Area of circular monument  = 148,000

⇒ πr² = 148,000

⇒r² = 148,000 / π

⇒ r² = 148,000/ 3.14

⇒ r = √148,000/ 3.14

⇒ r = 217. 103... feet

⇒ r = 217.10 feet ( nearest hundredth)

Therefore, from the given data of traffic circle, the center of the circular monument is covering approximately 148,000 square feet then the radius of the monument is equal to 217.10 feet.

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Answer:

30

Step-by-step explanation:

A number that is a multiple of 2 and 5 is a multiple of 10.

A multiple of 10 between 10 and 50 can only be 20, 30, 40.

3 is not a factor of 20 or 40, but it is a factor of 30.

Answer: 30

The equation of a line is y  = -6x + 8 if the line is perpendicular to the line t and passes through (2, -4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The slope of the line t:

M = 1/6

The slope of the line which is perpendicular to the line t

m = -6

The equation of the line:

y + 4 = -6(x - 2)

y = -6x + 12 - 4

y  = -6x + 8

Thus, the equation of a line is y  = -6x + 8 if the line is perpendicular to the line t and passes through (2, -4).

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Answer: 2656 bacteria after 996 minutes

Step-by-step explanation:

This has to do with exponential growth-

996/332=3, which means we must think about it in terms of doubling the bacteria numbers three times over the course of 996 minutes.

1st: 332*2=664

2nd: 664*2=1328

3rd: 1328*2=2656 bacteria after 996 minutes

Answer:3016

Step-by-step explanation:

By using slope intercept form of equation of line, it can be inferred that Point C is on the line y = x - 5

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here, the given slope intercept form is y = x - 5

For Point A

Putting x = -3

y = -3 -5 = -8 which is not equal to 2

Point A is not on the line y = x - 5

For Point B

Putting x = 1

y = 1 -5 = -4 which is not equal to 6

Point B is not on the line y = x - 5

For Point C

Putting x = 3

y = 3 -5 = -2

Point C is on the line y = x - 5

For Point D

Putting x = -2

y = -2 -5 = -7 which is not equal to -3

Point D is not on the line y = x - 5

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The value of x in the polygon is 9

A heptagon is a polygon that has seven sides. It is a closed figure having 7 vertices. A heptagon is also sometimes called Septagon.

In Geometry, the shape that is bounded by at least three straight lines or at least three interior angles is called polygon. The most common examples of polygons are

Triangle ( 3 sided polygon)

Quadrilateral ( 4 sided polygon)

Pentagon ( 5 sided polygon)

The polygon is a heptagon with number of sides n = 7

sum of interior angles of a polygon = (n - 2) x 180

if n = 7,

Sum of the interior angles = (7 -2) x 180

                                            = 5 x 180

                                            = 900

summing all the angles in the given polygon, we have

135 + 3x + 31 + 4x + 15 + 6x - 8 = 120 + 7x - 64 + 5x - 4 = 25x + 675

25x + 675 = 900

25x = 900 - 675

25x = 225

x = 225/25

x = 9

In conclusion, the value of x for the given polygon is 9

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The decision rule for rejecting the null hypothesis, considering the t-distribution, is of:

At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means is of zero, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means different of zero, hence:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value.

Considering the significance level of 0.05, with 75 + 46 - 2 = 119 df, the critical value for the test is given as follows:

|t| = 1.9801.

Hence the decision rule is:

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