A classroom board is 36 inches wide and 24 inches tall. Cheryl
is putting ribbon along the outside edge of the board. How
many inches of ribbon will she need?
24 inches
36 inches
A 156 inches B 120 inches
C90 inches
D 60 inches

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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Answer:

0.2   [or 2/10    ;     or 1/5]

Step-by-step explanation:

100x = 1/10×200

100x = 20

÷100     ÷100

x = 0.2

check:

100 × 0.2 = 20

1/10 × 200 = 20

20 = 20

[true statement]

(Or, you know that 100 is half of 200, and to get from 100 to 200 we had to multiply by 2, and that 100 x 2/10 will be equal; this is harder to word though)

Answer:

D=140

E=140

F=80

G=140

H=140

I=80

L=100

M=110

N=80

P=70

Step-by-step explanation:

The sum of the interior angles of a hexagon is 720.

7x+7x+7x+7x+4x+4x=720

36x=720

x=20

D=140

E=140

F=80

G=140

H=140

I=80

The sum of the interior of a quadrilateral is 360.

2x+20+3x-10+2x+2x-10=360

9x=360

x=40

L=100

M=110

N=80

P=70

As the difference between consecutive terms is the same, the balances form an arithmetic sequence, and:

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

\(a_n = a_1 + (n - 1)d\)

In which \(a_1\) is the first term.

The sum of the first n terms is given by:

\(S_n = \frac{n(a_1 + a_n)}{2}\)

From the table, the first term and the common difference are given as follows:

\(a_1 = 12000, d = 2018\)

Hence the formula for the balance in the account n years after February 2015 is:

\(a_n = 12000 + 2018(n - 1)\)

2032 is 17 years after 2015, hence:

\(a_{17} = 12000 + 2018(17 - 1) = 44288\)

The sum is given by:

\(S_{17} = \frac{17(12000 + 44288)}{2} = 478,488\)

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Answer:

x = 2, x = 4

Step-by-step explanation:

The equation y = 10 - 9x is a linear equation and the value of either y or x can be found by substituting the given values of either y or x.

given that y = -8, and substituting this into equation y = 10 - 9x,

we have, -8 = 10 - 9x

10 + 8 = 9x

9x = 18; dividing both sides by 9

x = 2

given that y = -26, and substituting this into equation y = 10 - 9x,

we have, -26 = 10 - 9x

10 + 26 = 9x

9x = 36; dividing both sides by 9

x = 4

Answer: A

Step-by-step explanation: $88.74÷9=$9.86

$88.74 is the total amount

9 players, and each player has to pay the same amount

we have to divide it evenly in 9 pieces, so we divide $88.74 into 9 groups which then equals $9.86

Hope this helps!

9514 1404 393

Answer:

  2

Step-by-step explanation:

You need the smallest positive integer for which f(x) > 0.

  f(1) = 3 -4 -3 -1 = -5

  f(2) = ((3·2 -4)2 -3)2 -1 = (4 -3)2 -1 = 1

x = 2 is the smallest integer for which f(x) > 0.

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

Answer:

11.98

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

given functions:

\(\sf f(x)=x^2+3x-7\)

\(\sf g(x)=3x+5\)

\(\sf h(x)=2x^2-4\)

solving steps:

(a)

\(\sf f(g(x))\)

\(\sf \sf f(3x+5)\)

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

\(\sf 9x^2+30x+25+9x+15-7\)

\(\sf 9x^2+39x+33\)

(b)

\(\sf h(g(x))\)

\(\sf h(3x+5)\)

\(\sf 2(3x+5)^2-4\)

\(\sf 18x^2+60x+50-4\)

\(\sf 18x^2+60x+46\)

(c)

\(\sf (h-f)(x)\)

\(\sf 2x^2-4-(x^2+3x-7)\)

\(\sf 2x^2-4-x^2-3x+7\)

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

(d)

\(\sf (f+g)(x)\)

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

\(\sf x^2+6x-2\)

The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer:

1/6

Step-by-step explanation:

Answer:

3 1/5

Step-by-step explanation:

9514 1404 393

Answer:

  (b)  m∠1 = 67.4°, m∠2 = 104.5°

Step-by-step explanation:

It is easiest to find angle 2 first, then make your answer selection based on that.

The exterior angle 121.8° is the sum of the remote interior angles 17.3° and angle 2. Then ...

  angle 2 = 121.8° -17.3° = 104.5° . . . . . . . matches the second choice

__

Angle 2 is an exterior angle of the top triangle. It, too, is the sum of the remote interior angles:

  104.5° = angle 1 + 37.1°

  angle 1 = 104.5° -37.1° = 67.4°

Answer:

C!

Step-by-step explanation:

m∠1 = 75.5°, m∠2 = 67.4°

into1) To find those center measures, let's check if the data are organized

2) They are already. So let's proceed to calculate the Mean.

a) Mean

Note that the mean is found by the sum of the observations over the number of it.

b) The Median Since there are 6 observations then we can find the Median this way:

As it is an even number of observations, we pick the half (3rd and add to 4th observation)

c) The Mode. The Mode is the most common number, repetitive, in this case, the mode is 23.

2.) If a 90 yrs old person joins the class :

a) The Mean is going to be 32. 57

b) The median will remain the same because in an odd number of observations the median is going to be a number that divides the data in two halves, in this case, the number 23 is in the middle between the other ages.

c) The Mode will remain the same: 23

Answer:

0.42

Step-by-step explanation:

To solve the problem, we need to add the probability of picking a club to the probability of picking a face card, and then subtract the probability of picking a club that is also a face card (because we would have counted it twice).

There are 13 clubs in a standard deck, so the probability of picking a club is 13/52 or 0.25.

There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck, so the probability of picking a face card is 12/52 or 0.23.

However, there are 3 cards that are both clubs and face cards (the jack of clubs, queen of clubs, and king of clubs), so we need to subtract the probability of picking one of those cards. There are 3 of them out of 52 total cards, so the probability of picking a club that is also a face card is 3/52 or 0.06.

Therefore, the probability of picking a club OR a face card is:

0.25 + 0.23 - 0.06 = 0.42 (rounded to two decimal places).

So the answer is 0.42.

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

An equation is an expression that shows the relationship between two or more number and variables.

The possibility of selecting the password = 26 * 25 * 24 * 10 = 156000

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

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The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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Answer:

Step-by-step explanation:

[-5/13] 3/5 +12+13 [-4/5 = - 63/65

Answer:

4 rows of 28 kids

Step-by-step explanation:

Answer:

second option

Answer:

4,872 miles

Step-by-step explanation:

Step 1:

2,436 : 6

Step 2:

2,436 : 6 = x : 12

Step 3:

6x = 29,232

Answer:

x = 4,872

Hope This Helps :)

Step-by-step explanation:

they would get around 2.125 or 2 1/8 each. Hope thos helps!

Answer:there is no graphs

Step-by-step explanation:

poop

Answer:

see below

Step-by-step explanation:

50.4 -2.1 = 48.3

48.3/3 = 16.1 each

Answer: $16.10

Step-by-step explanation:

$50.40-$2.10=$48.3

$48.3/3=$16.1

Using the Green's Theorem, the one along which the work done by the force is 11π/16.

In the given question we have to find the one along which the work done by the force is the greatest.

The given closed curves in the plane is

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = \(\frac{x^{2}y}{4} + \frac{y^3}{3}\) and Q = x

So the partial differentiation is

\(\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2\) and  \(\frac{\partial Q}{\partial x}\) = 1

By the Green's Theorem, work done by F is given as

W= \(\oint \vec{F}d\vec{r}\)

W= \(\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy\)

W= \(\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy\)

Let C = x^2+y^2 = 1 and

x = rcosθ, y = rsinθ

0≤r≤1; 0≤θ≤2π

There;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr\)

and \(\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |\) = r

Thus;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr\)

After solving

W = 11π/16

Hence, the one along which the work done by the force is 11π/16.

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The right question is:

Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)