Emily has 98 inches of ribbon to wrap some gifts. She uses 1/2 of the ribbon to wrap one gift and 3/8 of the remaining ribbon to make a bow. She also needs 35 inches of ribbon to tie around a second gift. Do you think Emily has enough ribbon to finish wrapping the second gift?

Clear y from both equations to find the slope y intercept form of the equations

Now, find the equation for the line that is perpendicular to Eq. 1 and has the same y intercept as Eq. 2

Eq. 3 is the equation for the line

The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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Based on mathematical operations, the number of people that 10 gallons of punch can serve is 192 persons.

The number of people can be determined using mathematical operations of multiplication based on converting the gallons to ounces and division.

The number of gallons of punch to serve at the first meeting = 10 gallons

The quantity of punch per serving = 8 ounces

1 gallon = 153.722 ounces

10 gallons = 1537.22 ounces

The persons that can be served 8 ounces from the 10 gallons = 192 (1,537.22/8).

Thus, mathematically, from the 10 gallons of punch, the PTA can serve 192 persons.

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Answer:

I think the answer might be -4 = 3x.

Step-by-step explanation:

-2 times x + 2 = -4 and 5 - 2x = 3x so i think the answer is -4 = 3x. Also, you're welcome if this helps.

Answer:

90

Step-by-step explanation:

Answer:

∠ EHK

Step-by-step explanation:

Adjacent angles are positioned next to each other on a straight line and are supplementary.

∠ IHK is next to ∠ EHK on the line DI and are adjacent

The probability of selecting two students has 10 ways

Total number of students = 5

Only two students can be selected for the conference who are equally qualified.

The probability that the first two students selected alphabetically is derived from the combinations.

Therefore, the final probability for selecting the students randomly is,

x = ⁵C₂

x = \(\frac{5!}{2!*(5 - 2)!}\)

x = 10

Hence, the probability of selecting two students has 10 ways.

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Answer:

OX = 5.4772 cm

Step-by-step explanation:

Please check image attached for the drawing of the circle with the chords and points.

From the theorem of intersecting chords, we have:

AE * EB = EF * EG

With AE = AX - EX, EB = BX + EX, EF = 6 - EO and EG = 6 + EO, we have:

(AX - EX) * (BX + EX) = (6 - EO) * (6 + EO)

(3 - EX) * (2 + EX) = 36 - EO^2

6 + EX - EX^2 = 36 - EO^2

EO^2 - EX^2 + EX = 30 (eq1)

From the triangle AEO, we have:

AE^2 + EO^2 = OA^2

(AX - EX)^2 + EO^2 = 6^2

(3 - EX)^2 + EO^2 = 36

9 - 6*EX + EX^2 + EO^2 = 36

EX^2 - 6*EX + EO^2 = 27 (eq2)

If we do (eq1) - (eq2), we have:

-2*EX^2 + 7*EX = 3

2*EX^2 - 7*EX + 3 = 0

Solving this quadratic equation, we have EX = 3 cm or EX = 0.5 cm

EX cannot be 3 cm, because AE would be 0 cm, so EX = 0.5 cm

Calculating EO, we have:

EO^2 - 0.5^2 + 0.5 = 30

EO^2 = 29.75

EO = 5.4544 cm

Now, using Pythagoras in the triangle EOX, we have:

EO^2 + EX^2 = OX^2

29.75 + 0.25 = OX^2

OX^2 = 30

OX = 5.4772 cm

The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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Answer:

It's B

please mark me as brainliest

Step-by-step explanation:

Using the remainder theorem, the value of P(3) for the polynomial P(x) = 2x^4 - 4x^3 - 4x^2 + 3 is 48. The quotient and remainder for the associated division are not required.

Explanation:

The remainder theorem states that if a polynomial P(x) is divided by x - a, then the remainder is equal to P(a).

In this case, we want to find P(3), which means we need to divide the polynomial P(x) by x - 3 and find the remainder.

Performing the division, we get:

        2x^3 - 10x^2 - 22x + 57

x - 3 ) 2x^4 - 4x^3 - 4x^2 + 3

        2x^4 - 6x^3

                    2x^3 - 22x^2

                    2x^3 - 6x^2

                              -16x^2 + 3

                              -16x^2 + 48x

                                        45x + 3

                                        45x - 135

                                                 138

Therefore, the remainder is 138, and P(3) = 138. The quotient is not necessary for finding P(3).

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Answer: (g^2 h^3) / 3

Step-by-step explanation:

Hope this helped!

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Answer:

g^2h^3 / 3.

Step-by-step explanation:

8g^3h^3/24g

= g^2h^3 / 3

Answer:

hope it helps plz mark me brainliest ;)

Step-by-step explanation:

A.P. -9,-14,-19,-24

first term (a) = -9

common difference of the A.P. (d) = -14 - (-9)

                                                        = -14 + 9

                                                        = -5

an = a + (n-1) d

here we find a30 and a20

so for 30th term

a30 = a+ (20-1) d

= -9 + (19) (-5)

= -9 -95

= -104

so

a30 - a20 = -154 - (-104)

= -154 + 104

= -50

therefore for the given A.P a30 - a20 = -50

Answer:

Different sequence but just in-case anyone needs it

d=-20

Explicit

Recursive

Step-by-step explanation:

Instructions: For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.

Sequence: 5,−15,−35,−55,…

Common Difference:

Answer -20

an=25−20n

Answer Explicit

an=an−1−20

a1=5

Answer Recursive

Answer:

Ghe661.25

Step-by-step explanation:

First to get the interest gotten for the first year, you'll multiply 15/100 by the principal amount which is 500. The value gotten will be 75. This means that the principal amount for the second year will be 500 + 75 which will amount to 575. Again, 15% of 575 will be added to 575 and this will give you the total amount at the end of the two years

Answer: 5^11

Step-by-step explanation:

If two exponents are being multiplied together, and they have the same base and different exponents then just add the exponents and let the base stay the same.

5^8 * 5^3 = 5^11

Answer:

If you are multiplying the two then your answer is 4.8828125  × \(10^{7}\) if you are combining them then your answer is \(5^{11}\)

The result is infinity (\(\infty\)), which implies that the volume of the solid is infinite when revolving the region bounded by the given curve and lines about the y-axis.

The region is bounded by the curve x = 6/y, the x-axis (x = 0), and the lines y = 0 and y = 1.

To find the volume using cylindrical shells, we integrate along the y-axis.

The radius of each cylindrical shell is given by the x-coordinate of the curve x = 6/y, which is x = 6/y. The height of each cylindrical shell is given by the difference between y = 1 and y = 0, which is 1 - 0 = 1.

The volume element of a cylindrical shell is given by the formula:

\(dV = 2\pi rh dy\)

where r is the radius and h is the height.

Substituting the values, we have:

\(dV = 2\pi (6/y)(1) dy\\= 12\pi /y dy\)

Now, we integrate the volume element over the interval [0, 1]:

\(V = \int [0,1] 12\pi /y dy\)

To evaluate the integral, we have:

\(V = 12\pi \int [0,1] (1/y) dy\\= 12\pi [ln|y|] [0,1]\\= 12\pi (ln|1| - ln|0|)\\= 12\pi (0 - (-\infty))\\= 12\pi (\infty)\)

Since the result is infinity (\(\infty\)), it implies that the volume of the solid is infinite when revolving the region bounded by the given curve and lines about the y-axis.

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Step-by-step explanation:

Assuming the order matters....i.e.  they stand up one at a time

  (question does not state how the 4 are chosen)

9 choices for first

8 choices for second

7 choices for third

6 choices for fourth

9 x 8 x 7 x 6 = 3024 ways

  this is   9 P 4  =  9!/5! = 3024

Answer:

c

Step-by-step explanation:

The number of total outcomes is 12.

Here is a tree diagram for the pizza options:

Copy code

     /  |  \

 Thick Thin

  /     |     \

Red White Red White

/  |  \   / |  \   / |  \

Pep Saus Veg Pep Saus Veg Pep Saus Veg

There are two (2) options for the crust, two (2) options for the sauce, and three (3) options for the topping. Therefore, the total number of outcomes is:

Total Outcomes = 2 (options for crust) x 2 (options for sauce) x 3 (options for topping)

Total Outcomes = 12

Therefore, there are 12 total outcomes.

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Answer: D

Step-by-step explanation:

The probability of certainty is 100%=1

If Probability(p)=0.34

then

Probability (p) +cProbability (!p) = 1 where !p is used to denote "not "p

0.34+Probability(!p)=1

Probability(!p)=1−0.34=0.66

The probability that the event will not happen is 0.66.

The probability of an event can be defined as the chance of happening that particular event.

The probability that the event will happen is P(E) = 0.34.

Therefore, the probability that the event will not happen is

= 1 - P(E)

= 1 - 0.34

= 0.66

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When you perform a 2D rotation of a point by swapping the x and y coordinates and negating the new y coordinate, the sign of the y-coordinate will change based on the quadrant in which the original point lies.

If the original point lies in the first or fourth quadrant, the new y-coordinate will be negative after rotation. In this case, if the new y-coordinate is already negative, then you do not need to negate it again.

On the other hand, if the original point lies in the second or third quadrant, the new y-coordinate will be positive after rotation. In this case, if the new y-coordinate is already negative, then you need to negate it to correctly represent the rotation.

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To prove the statement by contrapositive, we need to assume the negation of the conclusion and the negation of the hypothesis and then show that the contrapositive statement is true.

Negation of the conclusion: It is not the case that x>20 or y>20. In other words, x≤20 and y≤20. Negation of the hypothesis: xy≤400.

So, assuming x and y are positive real numbers, if x≤20 and y≤20, then xy≤400. Therefore, the negation of the hypothesis implies the negation of the conclusion. Thus, the contrapositive statement is: For any positive real numbers x and y, if x≤20 and y≤20, then xy≤400.

The assumed statement is: xy>400. Therefore, the contrapositive statement is false.

In conclusion, the assumed statement implies the original statement, but the contrapositive statement is untrue.

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Answer:

Y=0

Step-by-step explanation:

The x axis is the same making the line a horizontal line. A horizontal line has a slope of 0

Answer:

8

Step-by-step explanation:

d=√(−5−3)2+(−2−(−2))2

d=√(−8)2+(0)2

d=√64+0

d=√64

d=8

Answer:

W X = 83

W Y = 119

X Y = 36

Step-by-step explanation:

W X = 3y + 11

W Y = 6y - 25

X Y = y + 12

The density function of area is is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}}).

A random variable can be defined as a variable whose value is unknown or as a function that assigns numerical values to each of the outcomes of an experiment. It can also be defined as a rule that assigns a numerical value to each outcome in a sample space.

The density function (1.4-5)P(x) = an exp(-ax), if x0,0, if x>0, where an is any positive real number, defines the exponential random variable.

radius R has df f(r) ={\lambdae}^{-\lambdar}

area Y= *r2

r = \pm (Y/(\pi))1/2

hence P(Y<y) =F(Y) =P( *r2<y) =P(r<+/- (Y/( ))1/2 ) = \int_{{-y/\pi}^{1/2}}^{{(y/\pi)}^{1/2}}{\lambdae}^{-\lambdar} dr

= e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}}

Therefore P(df of y) = f(y) = d/dyf(y) =(d/dy) (e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}})

= ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})

Therefore the density function of area is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})

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when getting a bearing, we're referring to the angle from the North line moving clockwise, so of D from C?  well, the "from" point gets the North line and we check the angle from that North line clockwise to the other point, Check the picture below.

Answer:

Step-by-step explanation:

45342