As storm clouds gathered, the temperature fell 4 degrees in 3/4 of an hour. At what rate was the temperature falling?

Answer:

this is a binomial, but its 2x^2-10x+8

Step-by-step explanation:

you use the distributive property

Step-by-step explanation:

y = 4x - 1

2x + 2y = 3

2x + 2(4x - 1) = 3

2x + 8x - 2 = 3

10x = 3 + 2

x = 5/10

x = 1/2

y = 4x - 1

y = 4(1/2) - 1

y = 2 - 1

y = 1

(x,y) = (1/2 , 1)

The interquartile range for the museum is 280

The interquartile range for the farm is 200

The interquartile range for the museum is greater than the interquartile range for the farm.

This suggests that the numbers of visitors to the museum are less consistent.

The interquartile range is solved using the formula

= top quartile - bottom quartile

Where

the bottom quartile is at the box's edge, the top side.

the top quartile is towards the box's edge the downside.

the museum

The interquartile range is

= top quartile - bottom quartile

= 500  -  220

= 280

the farm

The interquartile range is

= top quartile - bottom quartile

= 460  -  260

= 200

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Answer:

x=1

Step-by-step explanation:

simplify and create a chart of denominators until you find the common one.

Answer:

Step-by-step explanation:

1/2x - 3/4 = 3/8 - 5/8x

+ 5/8x                + 5/8x

9/8x - 3/4 = 3/8

         + 3/4   + 3/4

9/8x = 9/8

divide both sides by 9/8

x = 1

56 * (28/5) shows how the distributive property can be used to evaluate 7 times 8 and four-fifths.

7 times 8 = 56

4/5 = 28/5

Using the distributive property:

7 * 8 * (4/5) = (7 * 8) * (4/5) = 56 * (4/5) = 56 * (28/5) = 56 startfraction 28 over 5 endfraction

The distributive property states that for any numbers a, b, and c, a * (b + c) = a * b + a * c. To evaluate 7 times 8 and four-fifths, we can use the distributive property to separate the two factors. First, we calculate 7 times 8, which is equal to 56. Then, we calculate four-fifths, which is equal to 28/5. We then use the distributive property to multiply the two factors together, which is (7 * 8) * (4/5). This simplifies to 56 * (4/5) which is equal to 56 startfraction 28 over 5 endfraction.

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Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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Answer:

I need the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed

The total interest you will earn in 30 years is approximately $241.61.

To calculate the total interest earned in 30 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount is $200, the annual interest rate is 3% (or 0.03 as a decimal), the interest is compounded monthly (so n = 12), and the time period is 30 years (so t = 30).
Plugging in these values into the formula:
A = 200(1 + 0.03/12)^(12*30) - 200
Now we can simplify and calculate:
A = 200(1.0025)^(360) - 200
A = 200(2.208040033) - 200
A ≈ 441.6080066 - 200
A ≈ 241.6080066

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The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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To express 88% as a fraction, we can write it as 88/100. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4. So, 88/100 simplifies to 22/25. Therefore, 88% can be expressed as the fraction 22/25.

~~~Harsha~~~

Answer:

part b

Step-by-step explanation:

denominater remains same,numerater will add up

1+1+1+1+1+1+1=7

hence

it will become 7/8

Answer:

1.75 as a decimal or 1 3/4 as a mixed number

The total weight of the two animals is 1.3 x 10^4 lbs.

The given parameters are

Animal 1 = 4.23 x 103 lbs.

Animal 2 = 8.7 x 103 lbs.

Rewrite the parameters properly

Animal 1 = 4.23 x 10^3 lbs.

Animal 2 = 8.7 x 10^3 lbs.

The total weight of the two animals is calculated as

Total weight = Animal 1 + Animal 2

This gives

Total weight = 4.23 x 10^3 lbs + 8.7 x 10^3 lbs.

Factor out 10^3 lbs

Total weight = (4.23 + 8.7) x 10^3 lbs.

Evaluate the sum

Total weight = 12.93 x 10^3 lbs.

Rewrite as

Total weight = 1.293 x 10^4 lbs.

Approximate

Total weight = 1.3 x 10^4 lbs.

Hence, the total weight of the two animals is 1.3 x 10^4 lbs.

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Answer:

The slope is ZERO. It has no slope

Step-by-step explanation:

The probability of randomly picking a nickel twice in a row from four nickels and eight dimes is 1/9.

Given that there are four nickels and eight dimes in your pocket, the total number of coins is twelve. If you randomly pick a coin and then return it to your pocket, there are still twelve coins in your pocket, and the probability of picking a nickel remains the same. Therefore, the probability of picking a nickel on the first draw is 4/12, which simplifies to 1/3.

Now, you pick another coin from the pocket, and again there are twelve coins. Since the first coin was returned to the pocket, the probability of picking a nickel on the second draw is also 4/12 or 1/3.

To calculate the probability of both events occurring together, we multiply the probability of the first event by the probability of the second event.

Thus, the probability of picking a nickel on the first draw AND picking a nickel on the second draw is (1/3) x (1/3) = 1/9.

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There are 362,880 ways to select 9 players for the starting lineup and a batting order for the 9 starters based on the concept of combinations.

To calculate the number of ways to select 9 players for the starting lineup, we need to consider the combination formula. We have to choose 9 players from a pool of players, and order does not matter. The combination formula is given by:

\(C(n, r) =\frac{n!}{(r!(n - r)!}\)

Where n is the total number of players and r is the number of players we need to select. In this case, n = total number of players available and r = 9.

Assuming there are 15 players available, we can calculate the number of ways to select 9 players:

\(C(15, 9) = \frac{15!}{9!(15 - 9)!} = \frac{15!}{9!6!}\)

To determine the batting order, we need to consider the permutations of the 9 selected players. The permutation formula is given by:

P(n) = n!

Where n is the number of players in the batting order. In this case, n = 9.

P(9) = 9!

Now, to calculate the total number of ways to select 9 players for the starting lineup and a batting order, we multiply the combinations and permutations:

Total ways = C(15, 9) * P(9)

          = (15! / (9!6!)) * 9!

After simplification, we get:

Total ways = 362,880

There are 362,880 ways to select 9 players for the starting lineup and a batting order for the 9 starters. This calculation takes into account the combination of selecting 9 players from a pool of 15 and the permutation of arranging the 9 selected players in the batting order.

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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Answer:

1/6

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

Answer:

its 85

Step-by-step explanation:

Answer:

Step-by-step explanation:

it has 2 solutions, 0 and 11

The function \($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)  is continuous on (-∞, ∞).

As per the given data the function f(x) is given by:

\($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)

Here we have to determine that the function f(x) is continuous on (-∞, ∞)

If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)

What are continuous function?

A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.

To show f(x) is continuous at x = 1

\(\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}\) f(x)

\(\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\\)

= 1 - 1

= 0

\(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\\)

= ln 1

= 0

Therefore  \(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0\).

Hence f(x) is continuous on (-∞, ∞)

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Answer:

29.12%

Step-by-step explanation:

Given that :

A = 49

B = 50

C = 38

D = 60

E = 75

Total = (49 + 50 + 38 + 60 + 75) = 272

Pie chart % for each :

A = (49 / 272) * 360 = 64.85

B = (50 / 272) * 360 = 66.18

C = (38 / 272) * 360 = 50.29

D = (60 / 272) * 360 = 79.41

E = (75 / 272) * 360 = 99.26

Difference between C and D

(79.41 - 50.29) = 29.12%

The correct answer is A.To determine which line is orthogonal to the plane, we need to find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The normal vector of the plane 2x + 4y - 2z = 10 is [2, 4, -2].

Calculating the dot product of this normal vector with the direction vectors of the given lines, we find:

A. [2, 4, -2] ⋅ [-1, 0, 1] = 0 (orthogonal)
B. [2, 4, -2] ⋅ [1, 1, 1] = 4 (not orthogonal)
C. [2, 4, -2] ⋅ [2, 1, 0] = 4 (not orthogonal)
D. [2, 4, -2] ⋅ [-1, 1, 1] = 0 (orthogonal)

Based on the dot products, options A and D have direction vectors that are orthogonal to the plane. Therefore, the lines described by options A and D are orto to the plane. The correct answer is A.

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Answer:

Hello,

Answer A

Step-by-step explanation:

Not C since for x=-1,y=(-1-5)²+78= 36+78 ≠ 0

Not D since for x=-1, y= (-1)²+2=1+2=3 ≠ 0
remains A and B
Not B since for x=0, y=0²-1=-1 ≠ -2

Verifying A:
F(-1)=3*(-1)²+(-1)-2=3-3=0 ok
F(0)=3*0²+0-2=-2 ok

F(5)=3*5²+5-2=75+3=78 ok

F(10)=3*10²+10-2=300+8=308 ok

Answer A

We can be 93% confident that the true proportion of adult residents who are parents in this county lies between 0.74 and 0.86.

To find the z-score corresponding to a 93% confidence level, we need to determine the critical value. We can use a standard normal distribution table or a calculator to find this value. For a two-tailed test, the critical value corresponds to (1 - (1 - confidence level) / 2).

Using the formula:

Critical value = (1 - (1 - 0.93) / 2) = (1 - 0.07 / 2) = 0.965

Now we have the critical value, z = 0.965. Substituting the values into the formula, we can calculate the margin of error:

Margin of error = z * sqrt((p * (1 - p)) / n)

= 0.965 * √((0.8 * (1 - 0.8)) / 200)

≈ 0.060

Finally, we can construct the confidence interval using the sample proportion and the margin of error:

Confidence interval = p ± margin of error

= 0.8 ± 0.060

Expressing this in the tri-inequality form, we have:

0.8 - 0.060 < p < 0.8 + 0.060

Simplifying the inequality, we get:

0.74 < p < 0.86

This means that if we were to take many samples and construct confidence intervals for each sample, approximately 93% of those intervals would contain the true population proportion.

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Answer:

the car would use 49 gallons because you get a decimal of 49.49 so you would put got decimal to the nearest 1's place and that would be 49

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Answer:

42

Step-by-step explanation:

Answer: D. 42°

Step-by-step explanation: RIGHT ON EDGE 2023