Ella used 5 ⅔ cups of cereal and 4 ⅓ cups of marshmallows to make cereal bars. How many more cups of cereal than marshmallows did Ella use? ]

Answer:

2

Step-by-step explanation:

=-5+4=-1

=-1+3=2

=2

Hope this helps :)

Answer:

Here is your answer :

For option ( a )

We know that the longest side of any triangle is its hypotenuse.

So, hypotenuse = 15

Other sides = 9, 12

By Pythagoras Theroem ,

Hypotenuse^2 = Sum of Square of other sides

( 15 )^2 = ( 9 )^2 + ( 12 )^2

225 = 81 + 144

225 = 225

Hence,it can be sides of a right angled triangle.

For option ( b ),

We know that the hypotenuse of a right angled triangle is its longest side.

So, Hypotenuse = √38 = 6√2

Other sides = 2 , 6

By Pythagoras Theroem ,

Hypotenuse^2 = Sum of squares of other sides

( 6√2 )^2 = ( 6 )^2 + ( 2 )^2

72 = 36 + 4

72 ≠ 40

So, it can't be sides of a right angled triangle.

For option ( c )

We know the longest side of any right angled triangle is its hypotenuse.

So, Hypotenuse = √91

Other sides = 3 , 9

By Pythagoras Theroem ,

Hypotenuse^2 = Sum of squares of other sides

( √91 )^2 = ( 3 )^2 + ( 9 )^2

91 = 27 +81

91 ≠ 108

So, it can't be sides of a right angled triangle.

=================================

The final answer is option ( a ).

Step-by-step explanation:

Lisa's percentile rank is approximately 90.77

Lisa's percentile rank can be calculated as follows:

First, we need to find the number of scores below Lisa's score. Since Lisa's score was the 25th score from the top, there are 24 scores above her score. Therefore, the number of scores below her score is:

260 - 24 = 236

Next, we can calculate Lisa's percentile rank using the formula:

percentile rank = (number of scores below Lisa's score / total number of scores) x 100

Substituting the values, we get:

percentile rank = (236/260) x 100

percentile rank = 90.77 (rounded to two decimal places)

Therefore, Lisa's percentile rank is approximately 90.77, which means that she scored higher than approximately 90.77% of the students in the class.

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Answer:

Your answer

F(x1) = 350 -17.5x

F(x2) = 350 - 30x

F( x1-x2) = 12.5x

Mark it as Brainlist. Follow me for more answer.

Step-by-step explanation:

The angle between the two planes is approximately 64.63°.

The two planes x + 4 y − 3 z = 1 and − 3 x + 6 y + 7 z = 0 are neither parallel nor perpendicular. The angle between them can be determined by the following formula:

\(\theta = \cos^{-1}\left(\frac{A\cdot B}{\left\lvert A\right\rvert\left\lvert B\right\rvert}\right)\)
where A and B are the normal vectors of the two planes, and \theta is the angle between them.

A normal vector for the plane x + 4 y − 3 z = 1 can be calculated as:

A = \begin{bmatrix} 1 \\ 4 \\ -3 \end{bmatrix}

A normal vector for the plane − 3 x + 6 y + 7 z = 0 can be calculated as:

B = \begin{bmatrix} -3 \\ 6 \\ 7 \end{bmatrix}

The angle between the two planes can be found by plugging the vectors into the formula above:

\(\theta

= \cos^{-1}\left(\frac{A\cdot B}{\left\lvert A\right\rvert\left\lvert B\right\rvert}\right)

= \cos^{-1}\left(\frac{(-3)\cdot(-3) + 6 \cdot 4 + 7 \cdot (-3)}{\sqrt{1 + 16 + 9}\sqrt{9 + 36 + 49}}\right)

= \cos^{-1}\left(\frac{-37}{\sqrt{26}\sqrt{94}}\right)\approx 64.63^\circ\)

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The volume of the box is 72 cubic feet.

We have,

To find the volume of the box, we need to multiply its length, width, and height.

Given:

Length = 4 ft

Breadth = 6 ft

Height = 3 ft

The volume of the box is:

Volume = Length x Breadth x Height

Volume = 4 ft x 6 ft x 3 ft

Volume = 72 cubic feet

Therefore,

The volume of the box is 72 cubic feet.

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Answer:

9Pi  square units

Step-by-step explanation:

Area = Pi x Radius^2

Diameter = Circumference / Pi

                 = 6Pi / Pi

                 = 6

Radius = Diameter / 2

             = 6 / 2

             = 3

Area = Pi x 3^2

Hope this helps!!

\(x-8.2=-9.09\\\\\implies x = -9.09 +8.2 =-0.89\)

x = -0.89

Step-by-step explanation:

when subtracting a positive number to a negative it will always be negative or atleast 0. It is like a number line, when subtracting on a number line, you always go left, which is also why its negative.

How I solved it: (just another way to solve this)

9.10-8.20=0.89

since the 9.10 was actually a negative(-9.10), it would make 0.89 negative, making it -0.89.

The indefinite integral of e^x/(e^x + 1)^13 with respect to x is -1/12(e^-x/(e^x + 1)^12) + C.

To evaluate the indefinite integral, we can use the substitution u = e^x + 1. Then du/dx = e^x, and dx = du/e^x.

Substituting these into the integral, we have:

∫ e^x/(e^x + 1)^13 dx = ∫ 1/(u^13 - u^12) du/e^x

= ∫ 1/u^12(1 - 1/u) du/e^x

= ∫ (u^-12 - u^-13) du/e^x

Integrating each term separately, we get:

∫ u^-12/e^x du - ∫ u^-13/e^x du

= (-1/11)(e^-x/u^11) - (-1/12)(e^-x/u^12) + C

Substituting back for u, we get:

-1/12(e^-x/(e^x + 1)^12) + C, as the final answer.

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384,000 bacteria would be present at the end of 7 hours if it doubles itself every hour.

Initial number of bacteria=3000

Number of bacteria at the end = initial number of bacteria * (base)ⁿ

where, n= number of hours

Number of bacteria at the end=3000*2⁷

                                                    =3000*128

                                                     =384,000

Therefore, there will be 384000 bacteria at the end of seven hour if the bacteria doubles itself every hour.

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By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

a. To find the given series i.e.,  5∑n=0(9(2)n)−7(−3)nTo find 5∑n=0(9(2)n)−7(−3)n,

we need to find the first five terms of the series. The given series is,

5∑n=0(9(2)n)−7(−3)n5[(9(2)0)−7(−3)0] + [(9(2)1)−7(−3)1] + [(9(2)2)−7(−3)2] + [(9(2)3)−7(−3)3] + [(9(2)4)−7(−3)4]

After evaluating, we get:

5[(9*1) - 7*1] + [(9*2) - 7*(-3)] + [(9*4) - 7*9] + [(9*8) - 7*(-27)] + [(9*16) - 7*81]15 + 57 + 263 + 1089 + 4131= 5555b.

Given premises: p → q, ¬p → r, r → s.

We are to prove that ¬q → s. i.e.,

Premises: (p → q), (¬p → r), (r → s)

Conclusion: ¬q → s

To prove ¬q → s,

we need to assume ¬q and show that s follows.

Then we use the premises to derive s.

Proof:

1. ¬q        Assumption

2. ¬(¬q)    Double negation

3. p         Modus tollens 2,1 & p → q

4. ¬¬p      Double negation

5. ¬p        Modus ponens 4,3 (Conditional elimination)

6. r         Modus ponens 5,2 (Conditional elimination)

7. s         Modus ponens 6,3 (Conditional elimination)

8. ¬q → s     Conditional introduction (Implication)

Thus, ¬q → s is proven.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent, we need to show that their negation is equivalent. i.e.,

we show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p)Negation of (p ∨ ¬q) = ¬p ∧ q Negation of (q ∧ ¬p) = ¬q ∨ p

Thus, we are to show that (p ∨ ¬q) ↔ ¬(q ∧ ¬p) is equivalent to ¬p ∧ q ↔ ¬q ∨ p

Proof:

¬(q ∧ ¬p)  ≡  ¬q ∨ p       Negation of (q ∧ ¬p)(p ∨ ¬q)   ≡  ¬(q ∧ ¬p)  

De Morgan's laws ∴ (p ∨ ¬q) ≡ ¬q ∨ p

By using the same logic and identity, we can also say that ¬(p∨¬q) is equivalent to q∧¬p.

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a. The formula given is, ∑n=0(9(2)n)−7(−3)n. Let’s find out the first five terms of the given formula as follows:

First term at n = \(0:9(2)^0-7(-3)^0= 9 + 7= 16\)

Second term at n = \(1:9(2)^1-7(-3)^1= 18 + 21= 39\)

Third term at n = \(2:9(2)^2-7(-3)^2= 36 + 63= 99\)

Fourth term at n = \(3:9(2)^3-7(-3)^3= 72 + 189= 261\)

Fifth term at n = \(4:9(2)^4-7(-3)^4= 144 + 567= 711\)

Therefore, the first five terms of the given formula are: 16, 39, 99, 261, 711.

b. To prove that ¬q→s from p→q, ¬p→r, and r→s,

we need to use the law of contrapositive for p→q as follows:

¬q→¬p       (Contrapositive of p→q)¬p→r         (Given)

∴ ¬q→r        (Using transitivity of implication) r→s           (Given)

∴ ¬q→s        (Using transitivity of implication)

Therefore, ¬q→s is proved.

c. To show that ¬(p∨¬q) and q∧¬p are equivalent,

we need to use the De Morgan’s laws as follows:

¬(p∨¬q) ≡ ¬p∧q     (Using De Morgan’s law)      

≡ q∧¬p     (Commutative property of ∧)

Therefore, ¬(p∨¬q) and q∧¬p are equivalent.

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The mean, median, and mode are:

Mean = 10

Median = 8

Mode = 8

To find the mean, median, and mode of the given set of numbers: 5, 8, 18, 1, 14, 6, 8, 13, 8, 19, we can perform the following calculations:

Mean: The mean is calculated by summing up all the numbers and dividing by the total count of numbers.

Mean = (5 + 8 + 18 + 1 + 14 + 6 + 8 + 13 + 8 + 19) / 10

= 100 / 10

= 10

Therefore, the mean is 10.

Median: The median is the middle value when the numbers are arranged in ascending order. If there are an odd number of values, the median is the middle number. If there are an even number of values, the median is the average of the two middle numbers.

Arranging the numbers in ascending order: 1, 5, 6, 8, 8, 8, 13, 14, 18, 19

Since there are 10 numbers, the median is the average of the two middle numbers, which are the 5th and 6th numbers:

Median = (8 + 8) / 2

= 16 / 2

= 8

Therefore, the median is 8.

Mode: The mode is the number(s) that appear(s) most frequently in the set.

In this case, the number 8 appears three times, which is more than any other number.

Therefore, the mode is 8.

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i didn’t realize u were chill like that

Answer:

Explanation:

Let x represent the length of the third side of the given triangle.

We can go ahead and determine the value of x using the Pythagorean theorem as seen below;

So the length of the third side of the triangle is 9

We can now determine the value of sine theta as seen below;

We can see that sine theta is 40/41

Let's determine the value of cosine theta as seen below;

So cosine theta is 9/41

Let's determine the value of tangent theta as seen below;

So tangent theta is 40/9

Let's now determine the value of cosecant theta as seen below;

So the value of cosecant theta is 41/40

Let's determine the value of secant theta as seen below;

So the value of secant theta is 41/9

Let's determine the value of cotangent theta as seen below;

So the value of cotangent theta is 9/40

Answer:

you will have $133920 intrest monthly and $151920 in the bank

Step-by-step explanation:

Suppose you give $100 to a bank which pays you 5% simple interest at the end of every year. After one year you will have $105, and after two years you will have $110. This means that you will not earn an interest on your interest. Your interest payments will be $5 per year no matter how many years the initial sum of money stays in a bank account.

Factor the trinomial to find a possible combination of dimentions that the rectangle could have:

To factor the trinomial, remember that the following product of binomials is equal to:

Then, we need to find two numbers a and b such that their product is equal to the constant term -18 and their sum is equal to the linear coefficient -3.

Since the product is negative, one number is negative and the other is positive.

Since the sum is negative, the greatest number is negative.

Two numbers whose difference is 3 and whose product is 18 are 6 and 3.

Notice that:

Then:

Therefore, the dimensions of the rectangle, are:

Answer:

it is 7.5 rate

Step-by-step explanation:

I used a calculator to get the answer and it is correct.

Hey, not quite sure how to help you but I just wanted to say that you've got this! Whatever endeavors or problems you are facing right now I know that you are able to triumph over them. If it means anything at all you have someone rooting for you on my end. Have a great day!

Scenario 2 Magnifi Co. produces a high-end amplifier for musical aficionados. Historically, only 85% of the 200 amplifiers produced per month on average have met the company's demanding standards for quality control. Suppose a random sample of 50 amplifiers is taken from a month's production..

What is the probability that less than 40 of the amplifiers will meet the company's quality standards? b) What is the probability that between 40 and 45 inclusive of the amplifiers will meet the company's quality standards? c) What is the probability that more than 45 of the amplifiers will meet the company's quality standards? a) In order to solve for the probability that less than 40 amplifiers will meet the company's quality standards, we can use the binomial distribution formula: P(X < 40) = Σi=0^39 C(50, i) (0.85)i(1-0.85)50-i

This can be solved using a computer, calculator, or by using a binomial probability table. Using a binomial table, we can find that P(X < 40) = 0.024. Therefore, there is a 0.024 probability that less than 40 amplifiers will meet the company's quality standards. b) To solve for the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards, we can use the binomial distribution formula again. We need to solve for P(40 ≤ X ≤ 45): P(40 ≤ X ≤ 45) = Σi=40^45 C(50, i) (0.85)i(1-0.85)50-i This can also be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(40 ≤ X ≤ 45) = 0.435. Therefore, there is a 0.435 probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards. c) To solve for the probability that more than 45 amplifiers will meet the company's quality standards, we can use the binomial distribution formula one more time. We need to solve for P(X > 45): P(X > 45) = Σi=46^50 C(50, i) (0.85)i(1-0.85)50-i Once again, this can be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(X > 45) = 0.056. Therefore, there is a 0.056 probability that more than 45 amplifiers will meet the company's quality standards.Overall, it can be concluded that the probability that less than 40 amplifiers will meet the company's quality standards is low, the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards is relatively high, and the probability that more than 45 amplifiers will meet the company's quality standards is relatively low.

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The x-value of the endpoint refers to the specific value of x at the end of a given interval or range. It is important to distinguish between the x-value in the equation, which is a variable..

To find the x-value of the endpoint, you need to identify the context or problem that the equation is referring to. Once you have that information, you can determine the x-value by considering the given conditions or constraints. The x-value in the equation may or may not be the same as the x-value in the endpoint, depending on the specific situation.

In some cases, the x-value in the equation may correspond directly to the x-value of the endpoint. However, in other cases, the x-value in the equation may represent a different point within the interval. It is important to carefully analyze the given equation and consider the specific context to accurately determine the relationship between the x-value in the equation and the x-value of the endpoint.

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The values for R(detected), λ, and t into the equation, you can calculate the "true" count rate of your sample

To calculate the detected activity from the count rate due to background radiation and the sample of KCl, you can use the following equation:

R(detected) = R(total) - R(background)

In this equation, R(background) represents the count rate for background radiation, and R(total) represents the total count rate detected from your sample and background. By subtracting the count rate of background radiation from the total count rate, you can determine the detected count rate from your sample, R(detected).

To determine the "true" activity of your sample, you can use the following equation:

R(true) = R(detected) / (1 - exp(-λt))

In this equation, R(true) represents the "true" count rate of your sample, R(detected) represents the detected count rate from your sample, λ represents the decay constant of the radioactive isotope in your sample, and t represents the time during which the count rate is measured.

By plugging in the values for R(detected), λ, and t into the equation, you can calculate the "true" count rate of your sample, which represents the actual activity of the radioactive isotope in the sample.

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Complete question:

write a mathematical equations that show how you will calculate the detected activity from the count rate due to background radiation and the sample of KCl. also, write an equation that shows how you will determine the "true" activity of your sample. Use the following terms:

R(background) = count rate for background radiation

R(total) = total count rate detected from your sample and background

R(detected) = detected count rate from your sample less the background radiation

R(true) = the "true" count rate of your sample.

The length of side a in the triangle is 11.06 units.

We have,

To find the length of side a in the triangle, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant.

In this case,

Side opposite to angle 23 =  a

Side opposite to angle 42 = 22

Let's set up the equation using the Law of Sines:

sin(23°) / a = sin(42°) / 22

To find the value of a, we can rearrange the equation:

a = (sin(23°) x 22) / sin(42°)

Substituting the values using a calculator.

a = 11.06

Therefore,

The length of side a in the triangle is 11.06 units.

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The relation R is a partial order for the given set of data regarding over the set of people.  (Option 1)

A partial order is a binary relation that is reflexive, antisymmetric, and transitive. In this case, the relation R is reflexive since a person is always born before themselves. It is also transitive since if person A is born before person B, and person B is born before person C, then person A must be born before person C.

However, the relation R is not symmetric, since if person A is born before person B, then person B cannot be born before person A. Therefore, the relation R is not a total order.

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Complete Question:

in a relation r over a set of people, we have that a person x is related to person y if x's birth date is prior to y's birth date. no two people in the group have the same birth date. indicate the choice that correctly describes the relation r.

Answer:

Range is the extension of the values across the x-y plane. We can see the data extends as far as -13 and as far as 11 so (-13,11)

The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Richard earned a cumulative GPA of 2.5 in all four semesters.

Here, we know that the cumulative GPA for the first 3 semesters is 2.0

He had earned 42 credits in total in all three semesters.

Cumulative GPA = Total points earned/credits rewarded

Hence,

Total points earned in 3 semestes= 2 X 42

= 84 points

In the fourth semester,

he had earned 14 credits with a GPA of 4.0

Hence total points earned = 4 X 14

= 56 points

Therefore, total points earned in all four semesters = 84 + 56 points

140 points

Total credits = 14 + 42

= 56

Hence, the cumulative GPA of all 4 semesters

= 140/56

= 2.5 points.

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