Erica brought $30.25 to the state fair. she bought a burger, a souvenir, and a pass. the burger was 1 6 as much as the souvenir, and the souvenir cost 3 4 the cost of the pass. erica had $4.00 left over after buying these items. what was the cost of each item?

The point (16, -99) is not a perfect fit in the linear model, and the slope-intercept equation for the remaining four data points (-8, 9), (-6, -9), (-2, -18), and (8, -63) is y = (-15/2)x + 3; the y-intercept (3) represents the net approval rating for the president when there is no change in the Dow Jones, and the slope (-15/2) indicates that for every 1-point increase in the Dow Jones, the net approval rating is expected to decrease by 7.5 percentage points.

To determine which point is not a perfect fit in the linear model, we need to compute the slopes for each pair of consecutive data points.

The slope of a linear model represents the rate of change between the two variables.

Using the given data points:

Points: -8, -6, -2, 8, 16

Percentage Points: 9, -9, -18, -63, -99

Let's compute the slopes:

Slope between (-8, 9) and (-6, -9):

slope = (change in percentage points) / (change in points)

slope = (-9 - 9) / (-6 - (-8))

slope = -18 / 2

slope = -9

Slope between (-6, -9) and (-2, -18):

slope = (-18 - (-9)) / (-2 - (-6))

slope = -9 / 4.0

slope = -2.25

Slope between (-2, -18) and (8, -63):

slope = (-63 - (-18)) / (8 - (-2))

slope = -45 / 10

slope = -4.5

Slope between (8, -63) and (16, -99):

slope = (-99 - (-63)) / (16 - 8)

slope = -36 / 8

slope = -4.5

The slopes for the first three pairs of points (-9, -2.25, -4.5) match, indicating a consistent linear relationship.

However, the slope between the last two points is -4.5, not -4.25 like the others.

Therefore, the point (16, -99) is not a perfect fit.

Removing the point (16, -99), we have four remaining data points:

(-8, 9), (-6, -9), (-2, -18), and (8, -63).

To find the slope-intercept equation for the linear model that passes through these four points, we can use the formula:

y = mx + b

Using the slope formula with two of the remaining points:

-9 = m(-6) + b

-18 = m(-2) + b

Solving these two equations simultaneously, we find:

m = -9/4

b = 9/2

So the slope-intercept equation for the linear model is:

y = (-9/4)x + 9/2

The practical meaning of the y-intercept (9/2) is that when the previous day's change in the Dow Jones is 0 points, the net approval rating for the president of the United States is expected to be 9/2 percentage points, or 4.5 percentage points.

The practical meaning of the slope (-9/4) is that for every 1-point increase in the previous day's change in the Dow Jones, the net approval rating for the president of the United States is expected to decrease by 9/4 percentage points, or 2.25 percentage points.

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Answer:

use distance formula

Step-by-step explanation:

enter each set of points into distance formula, find distance then sum all sides

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

Answer:

The function is f (x) = 100x + 34x^2 + C

Step-by-step explanation:

I wasn't sure if you were looking for the function or not, so...I just gave you the function.

Sorry if this isn't what you were looking for!

The probability that a bottle selected at random will contain at least one defect can be found using the complement probability of having no defect.

Let us denote the probability of having at least one defect in a bottle as P(A). P(A') is the probability of not having any defect in the bottle. Since the probability of an event occurring plus the probability of it not occurring is equal to 1, then \(P(A') = 1 - P(A).\)

Thus, the probability of having no defect in a bottle is

\(P(A') = (1 - 0.00001) = 0.99999\)

.Since a bottle has either no defect or at least one defect,

\(P(A) = 1 - P(A') = 1 - 0.99999 = 0.00001.\)

Therefore, the probability that a bottle selected at random will contain at least one such defect is \(0.00001 or 1/100,000.\)

This means that on average, only 1 bottle in 100,000 will contain such a defect.

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The problem statement is:You are shopping for baseballs and tennis balls at a sports store.

Each baseball costs $3 and each tennis ball costs $2. You want to buy not fewer than 45 baseballs and tennis balls altogether, and you have a $100 budget.a- Write a system of inequalities representing the number of balls you could buy.Solution: Let the number of baseballs be "b" and the number of tennis balls be "t".

Then the total number of balls can be represented as "b + t".Given that, you want to buy not fewer than 45 baseballs and tennis balls altogether. So,b + t ≥ 45Similarly, the total cost of baseballs and tennis balls is less than or equal to $100.

The cost of b baseballs is $3b and the cost of t tennis balls is \($2t. So,3b + 2t ≤ 100\)Thus, the system of inequalities representing the number of balls you could buy is:\(b + t ≥ 45 3b + 2t ≤ 100b ≥ 0, t ≥ 0b\)- Can you buy 20 baseballs and 30 tennis balls?

Justify your answer - show your work. Solution: Let's check if (b, t) = (20, 30) satisfies the system of inequalities. b + t ≥ \(45   ⇒   20 + 30 ≥ 45   ⇒   50 ≥ 45 (True) 3b + 2t ≤ 100  ⇒   3(20) + 2(30) ≤ 100  ⇒   60 + 60 ≤ 100\) (False)So, you cannot buy 20 baseballs and 30 tennis balls as it does not satisfy the system of inequalities.

Answer: Therefore, you can't buy 20 baseballs and 30 tennis balls.

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The probability of the product of the numbers present on the top faces of all the four six sided dice is equal to 1/108.

As given in the question,

Number of six sided dice to be rolled = 4

Number of outcomes on one dice = 6

Total number of outcomes of 4 dice = 6⁴

                                                            = 1296

Conditions for the product of the numbers of top faces all four dice is prime:

Favourable outcomes are : ( 1, 1, 1,2), (1,1,2,1), (1,2,1,1), (2,1,1,1),

( 1, 1, 1,3), (1,1,3,1), (1,3,1,1), (3,1,1,1),( 1, 1, 1,5), (1,1,5,1), (1,5,1,1), (5,1,1,1)

Total number of favourable outcomes = 12

Required Probability = 12 / 1296

                                  = 1 / 108

Therefore, the probability of the product of all the four numbers on the top faces of the dice is equal to 1/108.

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Answer:Older workers are staying in the workforce longer.

Step-by-step explanation: I had the same question as you it should be right.

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

Answer:

n = -7

Step-by-step explanation:

Add '-24' to each side of the equation.

24 + -24 + 6n = -18 + -24

Combine like terms: 24 + -24 = 0

0 + 6n = -18 + -24

6n = -18 + -24

Combine like terms: -18 + -24 = -42

6n = -42

Divide each side by '6'.

n = -7

Simplifying

n = -7

Answer:

Well, you would need to divide 44 by the numbers you have so 44/4=11

Answer:

-9

Step-by-step explanation:

        The additive inverse of 4 is -4. Why? 4 + -4 = 0

-4 - 5 = -9

Answer:

i think -9

Step-by-step explanation:

Answer:

The humpback whales are 37 times bigger than the krills they eat

Step-by-step explanation:

In this question, we are interested in knowing how much bigger are humpback whales compared to krill.

what is simply happening here is to divide the weight of the humpback whales by the weight of the krills.

From the question, weight of humpback whales = 8 * 10^4 while the weight of the krills are 2.1875 * 10^3

So the number of times the humpback whales are bigger is;

(8 * 10^4)/(2.1875 * 10^3) = 36.57 which are approximately 37 times bigger

Answer:

The answer to your problem is, 156

First lets find out how many feet or in one yard ?

Well 1 yard = 3 feet.

Now that we know that we can use our knowledge to answer the next question:

If Bill ran 52 yards, how many feet did he ran?

We can do math to solve our answer. :

1 x 52 = 52.

Now we need to multiply 52 x 3.

That is a little bit to much, so lets make the problem easier!

By breaking up the problem \/ to make it more easier.

50 x 3. ( 5 x 3 = 15, just add a zero! ) = 150

3 x 2 = 6.

Next add:

150 + 6 = 156.

Thus the answer to your problem is, 156

if 5 such rabbits breed initially and the warren has 30 rabbits.  the time it takes for the population to reach doomsday, which we can define as the point at which the population becomes unsustainable, is 3.03 months.

Assuming that the rabbit population grows exponentially, we can use the formula:

N(t) = N0 * e^(kt)

where N(t) is the population at time t, N0 is the initial population, k is the growth rate, and e is the mathematical constant approximately equal to 2.71828.

In this case, we know that the initial population N0 is 5, the population after three months N(3) is 30, and the growth rate k is 1.01.

Substituting these values into the formula, we get:

30 = 5 * e^(1.01 * 3)

Simplifying, we get:

6 = e^(3.03)

Taking the natural logarithm of both sides, we get:

ln(6) = 3.03

Therefore the number of months is 3.03 months.

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Answer:

There is no specific instruction in your question. I try to answer it based on what I understand from the equations. Hope this helps!

Step-by-step explanation:

Just rearrange the equation to solve the variable.

Answer:

C

Step-by-step explanation:

Got it right

Answer: 6.7

Step-by-step explanation:

We know that:

5.2*67 = 348.4

And we want to find the value of:

348.4/52 = x

So, let's return to the original equation.

5.2*67 = 348.4

Let's try to "construct" the quotient 348.4/52

The first step is to divide both sides by 5.2, then we get:

(5.2*67)/5.2  = 348.4/5.2

67 = 348.4/5.2

Now we have 5.2 in the denominator instead of 52, then we can divide both sides by 10 to get:

67/10 = ( 348.4/5.2)/10 = 348.4/(5.2*10) = 348.8/52

6.7 = 348.8/52

Then the solution to the quotient:

348.4/52 is 6.7​

a) Amount of sugar in the tank initially is 0.

b) The amount of sugar in the tank after t minutes is 13.6(1 - \(e^{\frac{4t}{1360} }\)).

c) The concentration of sugar in the solution in the tank after 60 minutes is 3.672.

a) Assign the sugar content of the tank for time t to the symbol A(t). Starting with only clean water, the tank

A(0) = 0

b) Sugar flows in at a rate of

(0.02 kg/L) × (2 L/min) = 0.04 kg/min

and flows out at a rate of

(A(t) ÷ 1360 kg/L) × (2 L/min) = (2A(t) ÷ 1360) kg/min

so that the net rate of change of A(t) is governed by the ODE,

dA(t) ÷ dt = (4 ÷ 100) - (2A(t) ÷ 1360)

A'(t) + (2A(t) ÷ 1360) = 2 ÷ 100

Multiply both sides by the integrating factor \(e^{\frac{4t}{1360} }\) to condense the left side into the derivative of a product:

\(e^{\frac{4t}{1360} }\) A'(t) + (2 \(e^{\frac{4t}{1360} }\) A(t) ÷ 1360) = 4 \(e^{\frac{4t}{1360} }\) ÷ 100

( \(e^{\frac{4t}{1360} }\) A(t))' = 4 \(e^{\frac{4t}{1360} }\) ÷ 100

Integrate both sides:

\(e^{\frac{4t}{1360} }\) A(t) = ∫ 4 \(e^{\frac{4t}{1360} }\) ÷ 100

\(e^{\frac{4t}{1360} }\) A(t) = 13.6 \(e^{\frac{4t}{1360} }\) + C

Solve A(t);

A(t) = 13.6 + C \(e^{\frac{4t}{1360} }\)

A(0) = 0, substitute the value

0 = 13.6 + C \(e^{\frac{4t}{1360} }\)

C = -13.6

so that the amount of sugar at any time t is,

A(t) =  13.6 - 13.6\(e^{\frac{4t}{1360} }\)

A(t) = 13.6(1 - \(e^{\frac{4t}{1360} }\))

c) As t → 60, the exponential term converges to 0 and is left with

\(\lim_{t \to \(60}\) A(t) = 13.6 × (1 - 0.73)

\(\lim_{t \to \(60}\) A(t) = 3.672 kgs of sugar.

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Answer:

x=23

Step-by-step explanation:

because its right

Answer:

x=23

Step-by-step explanation:

answer:

slope: -2/3

step-by-step explanation:

y=mx+b

m represents the slope, and b the y-intercept.

rearrange: 9x= -6y+18

---> -6y= -9x-18

divide all terms by -6.

-6y/-6= -9/-6x-18/-6

y= 3/2x+3 (slope/intercept form)

m= 3/2

---> 1/3/2= -2/3

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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(A) P(AB) = P(A B) = 0.5 denotes that there is a 0.5 chance that occurrences A and B will occur simultaneously. We cannot tell whether this relationship holds true for these specific events because the provided information does not specify whether A and B are independent or mutually exclusive.

(b) P(A'B) = P(A') + P(B') - P(A'B') = 0.6 denotes that there is a 0.6 chance that events A and B will occur together.

(c) The chance that either the complement of event A or the complement of event B will occur is 0.5. P(A'B') = 1 - P(AB) = 1 - 0.5 = 0.5.

(d) P(A|B) = P(AB) / P(B) = 0.5 / 0.2 = 2.5 denotes that there is a 2.5 percent chance that event A will occur provided that event B has already occurred.

If P(A) = 0.4 and P(B) = 0.2, respectively, then A and B are independent events.

(a) P(AB) is the probability that both occurrences A and B will occur at the same time. It is calculated as P(A) * P(B) = 0.4 * 0.2 = 0.08. The likelihood that A will occur is independent of the likelihood that B will occur since the two events are unrelated.

(b) P(A'B) = P(A') * P(B) = (1-0.4) * 0.2 = 0.12 is the likelihood that events A and B will occur in complement.

(c) The probability that either the complement of event A or the complement of event B will occur, or both, is given by P(A'B') = 1 - P(A'B) = 1 - 0.08 = 0.92.

(d) P(A|B) = P(AB) / P(B) = 0.08 / 0.2 = 0.4, which represents the likelihood that event A will occur in the absence of event B.

if P(A) = 0.4 and P(B) = 0.2, respectively, and A and B are events that cannot coexist.

(a) P(AB) = 0 (by definition of mutual exclusion), indicating that there is no chance that events A and B will occur simultaneously.

(b) The probability that event A's complement, event B, will occur is P(A'B) = P(B) = 0.2.

(c) The probability that either the complement of event A or the complement of event B will occur, or both, is P(A'B') = P(A') + P(B') = 0.6.

(d) Since P(AB) = 0, the probability of event A occurring provided that event B has already occurred is undefined. P(A|B) = P(AB) / P(B) = 0 / 0.2 = undefined.

 Roll a die once. The event of getting a "2" and the event of getting a "5" are mutually exclusive.

Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are independent events.

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Answer:

Step-by-step explanation:

Please refer to the attachement. I defined the height (H), width (W), and length (L) and set:

H = 4m and W = (1/3)L. The total cost of 640 Rs/m^2 is divided by the rate cost of Rs 5/m^2 to give 128 m^2 that was plastered. The total area of the walls must be 128 m^2, so then calculate the total wall area: The walls for the length are 2*LH and for the width are 2*WH. Substituting, we have a total of 8*L + (4/3)L = 128 m^2. Solve for L to obtain L = 12m. W is 1/3L, or 4m. The room is (W,L,H) 4, 12, and 4 meters. The floor is W*L, or 48m^2. At Rs 250/m^2, the rug will cost Rs 12000. Ouch.

Answer:

its P

Step-by-step explanation:

The correct response is C. If 56% of the houses take more than three months to sell, there is 1.4% chance that a random sample proportion would be as high as or higher than the one they obtained.

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Answer:

50.71

Step-by-step explanation:

Answer:

50.7142857 or 50 5/7

Step-by-step explanation:

71 x 5        355

---------  =   -------    = 50 5/7

1  x 7            7

Given that ACE is an isosceles triangle, the measure of ∠CDB is: 55°

The two base angles of any isosceles triangle are always congruent to each other.

Therefore:

m∠CBD = m∠CDB

m∠CBD = 180° - 125° (supplementary angles)

m∠CBD = 55°

Therefore:

m∠CBD = m∠CDB = 55°

In summary, given that ACE is an isosceles triangle, the measure of ∠CDB is: 55°

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The percent error for patricks estimate for the first day of school is 25%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Time patrick took= 45min

To find the percent error, we first need to find the difference between Patrick's estimate and the actual time it took him to get ready.

Actual time - Estimated time = Error

45 minutes - 45 minutes = 0 minutes

The error is 0 minutes, which means Patrick's estimate was exactly right and there was no error.

However, if we assume that Patrick made a mistake when he estimated and that his actual time is the correct value, then we can find the percent error as follows:

Error = | Actual time - Estimated time | = | 45 minutes - 60 minutes | = 15 minutes

Percent error = (Error / Estimated time) x 100% = (15 minutes / 60 minutes) x 100% = 25%

Therefore, the percentage error will be 25%.

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