⦁ Mr. Sanchez’s class sold fruit pies for $6 each and Mr. Kelly’s class sold bottles of fruit juice for $2 each. Together, the classes sold 22 items and earned $104.00 for their school.

Answer:

The six consecutive integers would be:

28, 29, 30, and 31, 32, 33, which, indeed total to 183, and the largest, obviously, is 33.

Step-by-step explanation:

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Answer: 28, 29, 30,31,32,33

Step-by-step explanation: To know the sum of integers, let the first integer is n.

Given, 6 consecutive integers. which means: n, n+1, n+2, n+3, n+4, n+5

Also given,

n + n+1+ n+2 + n+3 + n+4 + n+5 = 183

= n+ n+n+n+n+n+ 1+2+3+4+5= 183

= 6n+15 =183

= 6n = 183-15       (168)

= n = 168/6

= n = 28

So, as per the formula, n is 28 then 6 consecutive integers are 29, 30, 31, 32, 33.

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The answer is 4cd/3b

hope it's correct

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

Explanation:

Let x and y be the two integers such that |x| > |y|. This is another way of saying that x is further away from 0 compared to y.

Their quotient being 7 means x/y = 7 which rearranges to x = 7y

The sum of the integers is -32 which allows us to say....

x+y = -32

7y+y = -32

8y = -32

y = -32/8

y = -4

Use this y value to find x

x = 7y

x = 7*(-4)

x = -28

The two integers are -28 and -4.

Answer:

x=12

Step-by-step explanation:

12 =2 (x - 6)

Solve for x.

Divide each side by 2

12/2 =2/2 (x - 6)

6 = x-6

Add 6 to each side

6+6 = x-6+6

12 = x

Answer:

x = 12

Step-by-step explanation:

Simplify  both sides of the equation

Turn the equation around

Add 12 to both sides

Divide both the sides by 2

we can estimate that 46 out of 100 students who purchase fruit will most likely purchase bananas.

We can use proportional reasoning to estimate the number of students who will most likely purchase bananas if 100 students purchase fruit. Since we know that 23 out of 50 students purchased bananas, we can set up a proportion:

23/50 = x/100

where x is the number of students who will most likely purchase bananas if 100 students purchase fruit.

To solve for x, we can cross-multiply:

23 × 100 = 50 × x

2300 = 50x

x = 2300/50

x = 46

Therefore, we can estimate that 46 out of 100 students who purchase fruit will most likely purchase bananas. This is just an estimate, and the actual number may be slightly different due to factors such as individual preferences and availability of different types of fruit.

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The area of the rectangle is increasing at a rate of 122cm²/s if the length of the rectangle is 11 cm and the width is 9 cm.

The area of a rectangle can be described as the product of the length and width of that rectangle, therefore;

Area = L × W

Here L represents length and W represents the width

Now by differentiating using the product rule;

dA/dt = (dL/dt)(W) + (dW/dt)(L)

As the length is 11 cm and the width is 9 cm and the length is increasing at a rate of 5 cm/s and its width is increasing at a rate of 7 cm/s; substituting these values in the equation;

dA/dt = (5)(9) + (7)(11)

dA/dt = 45 + 77

dA/dt = 122

Hence,  the area of the rectangle is increasing at the rate of 122cm²/s.

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Answer:

Step-by-step explanation:

f(x)=-3x²+6x-7

=-3(x²-2x+1-1)-7

=-3(x²-2x+1)+3-7

=-3(x-1)²-4

Greatest value=-4 and is obtained at x=1

Answer: a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation: the y-intercept is where the line meets the y line which in this case is -3. I used slope formula to find the m of the equation ( slope ) take a look at the attached image to see how I solved it.

Answer:

a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation:

The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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Answer:

Modal average is the number that appears the most

Modal average: 3

1+2+3+4+5=15

15/3=    Mean: 3

Step-by-step explanation:

add all the bedrooms and divide that sum by the number of numbers added. That's the mean.

Hope this helps.

A) 4 is the mode of the table

B)

1+2+3+4+5=15

15/5=3

Answer:

She wrote a 4 instead of a 3.

There are only 3 numbers that are greater than 7. They are 8, 9, and 10. Mariah must have include 7 in her list. That is how she got 4 instead of 3.

Answer:

Mariah used 4 rather than 3.

Step-by-step explanation:

took a test with this question on it

The total price including tax will be = $34.32

What is Total Price?

The total price/cost (TC) is the lowest dollar cost of producing a certain quantity of output. This is the total economic cost of production, which consists of variable cost, which varies according to the quantity of a good produced and includes inputs such as labour and raw materials, and fixed cost, which is independent of the quantity of a good produced and includes inputs that cannot be changed in the short term, such as buildings and machinery, as well as possibly sunk costs.

Given,

sale tax where live = 4%

the price of pair of pants = $33

total price including tax

= Price of pair pant +sale tax

Total price = $33 + 33*4/100

= $33 + 1.32

= $34.32

Total price including tax = $ 34.32

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Some solutions for the given linear inequality:

y < 0.5x + 2

are:

{(0, 1), (1, 2), (2, 2)}

Here we have the linear inequality:

y < 0.5x + 2

To find the points we can evaluate the right side, and then find values of y such that the inequality is true.

For example, if we use x = 0, then we get:

y < 0.5*0 + 2

y < 2

A value of y such that this is true is y = 1

Then the point (0, 1) is a solution of the inequality.

Another example can be with x = 1:

y < 0.5*1 + 2

y < 2.5

This time we can select y = 2, then the solution is (1, 2).

To get a final solution we can evaluate in x = 2

y < 0.5*2 + 2

y < 3

Then a possible solution is y = 2 again, so the solution is (2, 2).

Notice that for each of these values of x, there are a lot of other points that are solutions.

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Answer:

8-y<25 hope this answers it

A.

The number of different ways the computers can be chosen is given by a combination of 10 choose 4.

A combination of n choose p is given by the formula below:

So we have:

B.

If the first computer chosen is the one defective, the probability of the first PC being defective is 4/10, the probability of the second one not being defective will be 6/9, for the third not being defective is 5/8 and for the fourth not being defective is 4/7.

Since the defective PC can be any of the 4 bought, we need to multiply the probability above by 4. So the final probability is:

Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

Answer:

In order of least to greatest- 99%, -9.9, sqaure root of 80, 1/9, sqaure root of 9, 19%

Step-by-step explanation:

Answer: a) Let Q be an orthogonal matrix and let λ be an eigenvalue of Q. Then there exists a non-zero vector v such that Qv = λv. Taking the conjugate transpose of both sides, we have:

(Qv)^T = (λv)^T

v^TQ^T = λv^T

Since Q is orthogonal, we have Q^TQ = I, so Q^T = Q^(-1). Substituting this into the above equation, we get:

v^TQ^(-1)Q = λv^T

v^T = λv^T

Taking the norm of both sides, we have:

|v|^2 = |λ|^2|v|^2

Since v is non-zero, we can cancel the |v|^2 term and we get:

|λ|^2 = 1

Taking the square root of both sides, we get |λ| = 1.

b) Let Q1 and Q2 be orthogonal matrices. Then we have:

(Q1Q2)^T(Q1Q2) = Q2^TQ1^TQ1Q2 = Q2^TQ2 = I

where we have used the fact that Q1^TQ1 = I and Q2^TQ2 = I since Q1 and Q2 are orthogonal matrices. Therefore, Q1Q2 is an orthogonal matrix.

The solution is Option C.

The L'Hopital's rule is applied to the equation lim x approaches 0 (1-cosx)/x

L'Hopital's rule then states that the slope of the curve when t = c is the limit of the slope of the tangent to the curve as the curve approaches the origin, provided that this is defined. The limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.The tangent to the curve at the point [g(t), f(t)] is given by [g′(t), f′(t)]

And , lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

The equation is A = lim x approaches 0 (1/x)

On simplifying the equation , we get

The limit diverges as the function diverges and limit does not exist

And ,  lim x approaches 0₊ (1/x) ≠ lim x approaches 0₋ (1/x) = ∞

b)

The equation is A = lim x approaches 0 ( 2x² - 1 ) / ( 3x - 1 )

On simplifying the equation , we get

when x = 0 ,

Substitute the value of x = 0 in the limit , we get

A = ( 2 ( 0 )² - 1 ) / ( 3 ( 0 ) - 1 )

A = ( 0 - 1 ) / ( 0 - 1 )

A = 1

c)

The equation is A = lim x approaches 0 ( 1 - cosx ) / x

On simplifying the equation , we get

Applying L'Hopital's rule , we get

lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

f ( x ) = ( 1 - cos x )

g ( x ) = x

f' ( x ) = sin x

g' ( x ) = 1

So ,

lim x approches 0 [ f' ( x ) / g' ( x ) ] = lim x approches 0 ( sin x / 1 )

when x = 0

sin ( 0 ) = 0

Therefore , the value of lim x approaches 0 (1-cosx)/x = 0

d)

The equation is A = lim x approaches 0 ( cos 2x ) / 2

On simplifying the equation , we get

when x = 0 ,

A = cos ( 2 ( 0 ) / 2

A = cos ( 0 ) / 2

A = 1/2

Hence , the L'Hopital's rule is applied to lim x approaches 0 ( 1 - cosx ) / x

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

The interquartile range of the data will be 13

When arranged from lowest to highest, the IQR reflects the median 50% of values. To calculate the interquartile range (IQR), firstly compute the median (middle value) of the data's lower and upper halves. All those are quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The interquartile range is the difference between quarters three and then one.

first, let us sort the data from lowest to highest

25,25,29,31,33,37,38,42,46

Q1- median of the lower half of the data=(29+25)/2=27

Q3-median of the upper half of the data=(38+42)/2=40

the interquartile range of the data will be Q3-Q1

40-27= 13

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Answer:

the amount that Fidel now have in his checking account is $140.24

Step-by-step explanation:

The computation of the amount that Fidel now have in his checking account is shown below:

= Ending balance  - Opening balance

= $357.42 - $217.18

= $140.24

Hence, the amount that Fidel now have in his checking account is $140.24

We simply applied the above formula so that the correct value could come

And, the same is to be considered

Answer:

dunno

Step-by-step explanation:

Answer:2.25

Step-by-step explanation:

3/4 is equal to 0.75 and 0.75*3=2.25

The answer of the given question based on the Characterizations of Continuity is, (a)  we have |(g ∘ f)(x) - (g ∘ f)(c)| = |g(f(x)) - g(f(c))| < ε, which completes the proof. , (b) it  holds for any sequence (xn) in A such that lim xn = c, we conclude that (g ∘ f) is continuous at c.

Characterizations of continuity are different ways of describing and defining the concept of continuity for a function. There are several equivalent characterizations of continuity. These characterizations provide different ways of understanding continuity and can be used interchangeably to prove continuity for a given function at a given point.

(a) Proof using the ε-δ characterization of continuity:

Let c be a point in A, and let ε > 0 be given. We want to show that there exists a δ > 0 such that for all x in A, if |x - c| < δ, then |(g ∘ f)(x) - (g ∘ f)(c)| < ε.

Since g is continuous at f(c), there exists a δ' > 0 such that for all y in B, if |y - f(c)| < δ', then |g(y) - g(f(c))| < ε.

Since f is continuous at c, there exists δ > 0 such that for all x in A, if |x - c| < δ, then |f(x) - f(c)| < δ'.

Now, consider any x in A such that |x - c| < δ. Then we have |f(x) - f(c)| < δ', which implies that |g(f(x)) - g(f(c))| < ε, by the continuity of g at f(c).

Finally, we have |(g ∘ f)(x) - (g ∘ f)(c)| = |g(f(x)) - g(f(c))| < ε, which completes the proof.

(b) Proof using the sequential characterization of continuity:

Let (xn) be any sequence in A such that lim xn = c. We want to show that lim (g ∘ f)(xn) = (g ∘ f)(c).

Since g is continuous at f(c), we know that for any sequence (yn) in B such that lim yn = f(c), we have lim g(yn) = g(f(c)).

Now, consider the sequence (f(xn)) in B. Since f is continuous at c, we have lim f(xn) = f(c). Thus, by the continuity of g at f(c), we have lim g(f(xn)) = g(f(c)).

But lim g(f(xn)) = lim (g ∘ f)(xn), so we have shown that lim (g ∘ f)(xn) = g(f(c)), as desired.

Since this holds for any sequence (xn) in A such that lim xn = c, we conclude that (g ∘ f) is continuous at c.

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The mean of the fitted exponential distribution is 66.67.

To find the mean of the fitted exponential distribution, we first need to estimate the parameter lambda using maximum likelihood estimation.

The probability density function of the exponential distribution is given by

f(x; lambda) = lambda * exp(-lambda * x)

where x is the claim size and lambda is the parameter to be estimated.

The likelihood function for the observed data is the product of the individual probabilities of each claim

L(lambda) = lambda^n * exp(-lambda * sum(x_i))

where n is the number of observed claims and x_i is the i-th claim size.

The log-likelihood function is given by:

ln L(lambda) = n * ln(lambda) - lambda * sum(x_i)

To estimate the parameter lambda, we need to maximize the log-likelihood function with respect to lambda:

d/d(lambda) ln L(lambda) = n/lambda - sum(x_i) = 0

Solving for lambda, we get

lambda = n / sum(x_i)

Substituting the observed values, we get

lambda = 6 / (20 + 45 + 50 + 80 + 100 + 2*100) = 0.015

Therefore, the estimated parameter of the fitted exponential distribution is lambda = 0.015.

The mean of the exponential distribution is given by

E(X) = 1/lambda

Substituting the estimated value of lambda, we get

E(X) = 1/0.015 = 66.67

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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Given: a=3, b=-4

Find:

Explanation:

Answer:

i believe the answer is A

Step-by-step explanation:

The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

When we have an inverse function, the domain and range are switched.

All x-coordinates become y-coordinates and vice-versa.

So, if the point (-7, -5) is a solution of h(x), the point (-5, -7) is a solution of h^-1(x)

If the point (-1, -2) is a solution of h(x), the point (-2, -1) is a solution of h^-1(x).

Therefore, the endpoints of the segment that represents the inverse function are the points (-5, -7) and (-2, -1).