ACTIVITY 2: Simplify the following.

In general, an antiderivative of a function f(x) is a function F(x) whose derivative is equal to f(x). The antiderivative of a polynomial function is obtained by adding one to the exponent of each term and dividing by the new exponent ⁵.

1. The linear regression equation is y = -1.17x+ 10.69

2. The correlation coefficient is -0.982.

3. This means there is a strong negative correlation between the gallons and hours.

4. The number of gallons is decreasing as the hours are increasing.

Step 1: find slope.

Formula for slope m = (n × Σ(xy) - Σx × Σy) / (n × Σ(x²) - (Σx)²)

Σx = 1 + 2 + 3 + 4 + 5 = 15

Σy = 9.2 + 8.4 + 7.7 + 6.1 + 4.5 = 35.9

Σ(xy) = (1 × 9.2) + (2 × 8.4) + (3 × 7.7) + (4 × 6.1) + (5 × 4.5) = 96

Σ(x²) = 1 + 4 + 9 + 16 + 25 = 55

n = 5

Therefore ∴

m = (5 × 96 - 15 × 35.9) / (5 × 55 - 15²) = -1.17

y-intercept b = (Σy - m × Σx) / n

b = (35.9 - (-1.17) × 15) / 5 = (53.15) / 5 = 10.63

Therefore the linear regression equation is y = -1.17x + 10.63

correlation coefficient (r): (n × Σ(xy) - Σx × Σy) / sqrt((n × Σ(x²) - (Σx)²) × (n × Σ(y²) - (Σy)²))

r = (5 × 96 - 15 × 35.9) / sqrt((5 × 55 - 15²) × (5 × 271.95 - 35.9²)) = -0.982

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Answer:

55

Step-by-step explanation:

0* .4

28*.5

410*.1

All four angles of the rhombus are 20, 160, 20, and 160 degrees.

Diagonals are the parts of a shape, in geometry, a diagonal is a line that join two vertices of a polygon or a solid shape , whose vertices are not on the same edge. In general, a diagonal is called  as a sloping line or the slant line, that connects to the vertices of a shape.

According to question a rhombus , all four sides are congruent and opposite angles are equal. Let's call the rhombus ABCD, where AB, BC, CD, and DA are the four sides, and AC and BD are the diagonals.

If one of the angles formed by diagonals and adjacent sides is 20 degrees, let's say that angle is ABD. We can draw a line from point A to point C, which will divide the rhombus into two congruent triangles, ABC and ACD.

Since triangle ABC is isosceles, with sides AB = BC, angles ABC and BCA are equal. Similarly, in triangle ACD, angles ACD and CDA are equal.

∴ angles ABD and CDA are adjacent angles formed by intersecting lines, they must add up to 180 degrees. Therefore, angle CDA is 160 degrees.

If triangles ABC and ACD are congruent, angle CAD is also 20 degrees.

Now we can use the fact that opposite angles in a rhombus are equal. Angles BCD and ABD are opposite angles, so angle BCD is also 20 degrees. Similarly, angles BAC and ADC are opposite angles, so angle BAC is also 160 degrees.

Therefore, all four angles of the rhombus are 20, 160, 20, and 160 degrees.

Complete question  If one of the angles formed by diagonals and adjacent sides. of Is 20, all four angles of the a rhombus are.

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Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses.

The parameter of interest is the difference in population proportions of females and males who took advanced math courses. We can denote this parameter by p₁ - p₂, where p₁ is the population proportion of females who took advanced math courses, and p₂ is the population proportion of males who took advanced math courses.

To construct a confidence interval for the difference in population proportions, we need to check the following conditions,

The sample of high school students should be a simple random sample.

The sample of high school students should be independent of each other.

Both groups of females and males who took advanced math courses should have at least 10 successes and 10 failures.

The sample proportions of females and males who took advanced math courses can be calculated as follows,

p₁ = 53/150 = 0.353

p₂ = 89/275 = 0.324

The sample size of females and males can also be calculated as follows,

n₁ = 150

n₂ = 275

The standard error of the difference in sample proportions can be calculated as follows,

SE = √[(p₁(1 - p₁))/n₁ + (p₂(1 - p₂))/n₂]

= √[(0.353(1 - 0.353))/150 + (0.324(1 - 0.324))/275] ≈ 0.048

Using a t-distribution with (n₁ + n₂ - 2) degrees of freedom and a 98% confidence level, we can construct a confidence interval for the difference in population proportions as follows:

(p₁ - p₂) ± t*SE

where t is the t-score corresponding to a 98% confidence level and (n₁ + n₂ - 2) degrees of freedom. Using a t-table, we can find that t ≈ 2.33.

Substituting the values into the formula, we get,

(0.353 - 0.324) ± 2.33*0.048

0.029 ± 0.112

True difference in population proportions of females and males who took advanced math courses lies between 0.029 and 0.147.

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain.

Yes, our interval from part A gives convincing evidence of a difference between the population proportions because it does not contain zero. The interval (0.029, 0.147) is entirely positive, which means that the proportion of females who took advanced math courses is higher than the proportion of males who took advanced math courses. Additionally, the interval does not contain the value of one, which means that the difference in population proportions is not due to chance. Therefore, we can conclude that there is a significant difference in the population proportions of females and males who took advanced math courses.

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Answer:

x = 5√2, x = 3√2

Step-by-step explanation:

Question 1:

Using the 30-60-90 triangle properties, YX = WX /√3.

YX = 5√3 /√3 = 5.

Using the 45-45-90 triangle properties, x = YX *√2.

x = 5 *√2 = 5√2.

Question 2:

Using the 45-45-90 triangle properties, BC = AB *√2.

BC = 6 *√2 = 6√2.

Using the 30-60-90 triangle properties, x = BC / 2.

x = 6√2 / 2 = 3√2.

If we substitute x = 21 into the equation Y = 25 - 2x, we get:

Y = 25 - 2(21)

Y = 25 - 42

Y = -17

Therefore, if x = 21, then Y = -17.

If we substitute x = 19 into the equation Y = 25 - 2x, we get:

Y = 25 - 2(19)

Y = 25 - 38

Y = -13

Therefore, if x = 19, then Y = -13.

Answer:

7

Step-by-step explanation:

We can use the fact that the corresponding sides of similar triangles are in proportion to each other.

Let's compare the corresponding sides of the two triangles:

Corresponding sides and ratio

Ratio

Since the triangles are similar, we know that these ratios are equal. That is,

6 / (x-3) = 12 / (x+1)

We can simplify this equation by cross-multiplying:

6(x+1) = 12(x-3)

Expanding and simplifying:

6x + 6 = 12x - 36

42 = 6x

x = 7

Therefore, x has a value of 7.

The result of the logarithm function is equal to 9. (Correct choice: D)

The statement shows an incomplete logarithm, whose result must be found by understing relationships between trascendent functions. Logarithm functions and exponential functions are related in the following way:

aᵇ = n ↔ ㏒ₐ n = b

Where:

If we know that (base) a = 3 and (exponent) b = 2, then the value of the result (n) is now defined:

n = 9

3² = 9

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The solution for the variable x is x = 8.4

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

The right triangle

Using the proportion of similar triagles, we have

x/7 = 10/x

This gives

x * x = 7 * 10

So, we have

x² = 70

Next, we have

x = √70

Evaluate

x = 8.4

Hence, the solution for the variable x is x = 8.4

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The area of the polygon is 33cm²

A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.

The area of a polygon is expressed as;

A = 1/2 × p × a

where p is the perimeter of the polygon and a is the apothem.A pentagon is a 5 sides polygon.

Therefore;

Perimeter = 5 × 4.4

= 22cm

apothem = 3cm

area = 1/2 × 22 × 3

= 11× 3

= 33 cm²

therefore the area of the Pentagon in is 33cm²

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The p-value from the hypothesis is 0.0583 which is not significant at p<0.05

To determine the p-value of the hypothesis, we need to use the formula;

z = (x - a) / √(a(1 - a)/n)

x = 93 / 900 = 31/300 = 0.103

a = 12% = 12/100 = 0.12

n = 900

Substituting the values into the formula;

z = (0.103 - 0.12)/√(0.12(1 - 0.12)/900)

z = -0.017 / √0.0001173

z = -1.569

Using a standard normal distribution table;

p-value = 0.058324

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Answer: 10w + 3 + 4.5w = 90

Step-by-step explanation:

a right angle is 90 degrees, so 10w + 3 and 4.5w have to add up to 90 degrees

Answer:

cot(65 deg)

Step-by-step explanation:

cot(x) is the complimentary func. of tan(x) with the relation:

tan x = cot (90 - x) and

cot x = tan (90 - x)

Answer:

1. f. System of Equations

2. e. No solutions

3. i. One solution

4. h. Like Terms

5. b. Substitution

6. c. Solution

7. a. Elimination

8. d. Infinitely Many Solutions

9. g. Variable

10. j. Coefficients

Step-by-step explanation:

Ur welcome :)

Answer:90% probability

Step-by-step explanation:

To calculate the experimental probability of the cup landing on its side, we can use the formula:

experimental probability = number of times the cup landed on its side / total number of trials

For the first set of trials, the experimental probability is:

experimental probability = 19/20 = 0.95

For the second set of trials, the experimental probability is:

experimental probability = 81/90 = 0.9

So the experimental probability of the cup landing on its side for the first set of trials is higher than for the second set of trials. However, since the number of trials is relatively small, it is possible that this difference is due to chance and does not reflect a real difference in the probability of the cup landing on its side. To determine this with more confidence, we would need to conduct more trials and perform statistical tests to determine whether the difference is statistically significant.

The distance between the points (6,−10) and (6,−7) is 3 units

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

Points (6,−10) and (6,−7)

Because the points have the same x coordinate, the distance between the points (6,−10) and (6,−7) is the difference between the y coordinates

Using the above as a guide, we have the following:

Distance = -7 - -10

Evaluate

Distance = 3

Hence, the distance between the points (6,−10) and (6,−7) is 3 units

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Answer:

37

Step-by-step explanation:

We are given the system of equations:

y = 4x^2 + 3x - 5

y = 2x^2 + x + 7

We can set the two equations equal to each other to get:

4x^2 + 3x - 5 = 2x^2 + x + 7

Simplifying, we get:

2x^2 + 2x - 12 = 0

Dividing both sides by 2, we get:

x^2 + x - 6 = 0

Factoring the left-hand side, we get:

(x + 3)(x - 2) = 0

Therefore, the solutions are x = -3 and x = 2.

To find the corresponding y-coordinates, we can plug these values of x into either of the original equations. Using the first equation, we get:

y = 4(-3)^2 + 3(-3) - 5 = 16

and

y = 4(2)^2 + 3(2) - 5 = 21

Therefore, the sum of the y-coordinates of the solutions is:

16 + 21 = 37

Answer: 37.

Answer:

a) 192Km

b) 50

Step-by-step explanation:

The probability of randomly selecting 42 cigarettes with a mean of 7.73 mg or less is:  0.0179

The formula to find the z-score of the given normal distribution is:

z = (x' - μ)/(σ/√n)

where:

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given:

x' = 7.73 mg

μ = 8.2 mg

σ = 1.45 mg

n = 42

Thus:

z = (7.73 - 8.2)/(1.45/√42))

z = -2.1

From online p-value from z-score calculator, we have:

p = 0.0179

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Answer:

C Exponential

Step-by-step explanation:

3x^2 -- its using an exponent

Answer:

A

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be there are roughly 7,000 grains of sand in 7 grammes of sand.

Instead of using random estimates, it is preferable to use shifting numbers that may also prove increasing, reducing, variable or blocking. They could only help one another by trading tools, information, or solutions to issues. The justifications, components, or quantitative comments for tactics like further disagreement, production, and blending may be included in the assertion of truth equation.

Here,

A kilogramme (1000 grammes) of sand is thought to contain around 1 million grains of sand. This indicates that 1 gramme of sand contains roughly 1000 grains of sand.

Using this calculation, we can determine how many sand grains there are in 7 grammes roughly as follows:

=> Number of sand grains in 7 grammes = (# of sand grains in 1 gramme) x (7 grams)

=> 1000 x 7 = the number of sand grains in 7 grammes.

=> 7,000 sand grains are included in 7 grammes.

In accordance with this calculation, there are roughly 7,000 grains of sand in 7 grammes of sand.

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I can't see the chart...

The factored form of 64d³ - 24d² is 8d²(8d³ - 3).

The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that divides evenly into two or more given numbers. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.

The greatest common factor (GCF) of the given terms is 8d². We can factor it out by dividing each term by 8d²:

64d³/8d² - 24d²/8d²

Simplifying the fractions:

8d³ - 3

Therefore, the factored form of 64d³ - 24d² is 8d²(8d³ - 3).

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The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.

To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:

B(1) = 325 - 0.005(325)

Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:

B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))

We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:

B(2) = 325(1 - 0.005)²

Generalizing this pattern, we can see that after t months, the balance will be:

B(t) = 325(1 - 0.005)ᵗ

Therefore, option A is the correct function that models the balance of Lily’s account.

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Answer:

Step-by-step explanation:

1) Find the upper bound of the confidence interval:

Upper bound = sample mean + margin of error

= 172.6 + 4.8

= 177.4

2) Find the lower bound of the confidence interval:

Lower bound = sample mean - margin of error

= 172.6 - 4.8

= 167.8

3) Estimate the total number of text messages sent in a month:

Total number of text messages sent = (number of students in the population / number of students in the sample) x sample mean

        = (3000 / 250) x 172.6

        = 2071.2

Therefore, the estimated number of text messages sent in a month is 2071.2, with a 95% confidence interval between 167.8 and 177.4 text messages.

Answer:

----------------------------

Find lower bound:

Find upper bound:

Lower bound:

Upper bound:

The estimated number of text messages sent in a month for all 3000 high-school students in the city is:

The exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].

The function B(t) can be represented by an exponential function of the form:

B(t) = a[tex]b^t[/tex]

where 'a' is the initial number of bacteria and 'b' is the growth factor or rate at which the number of bacteria quadruples.

Given that the initial number of bacteria is 15 and the number of bacteria quadruples every hour, we can express 'b' as:

b = 4¹ = 4

Substituting the values of 'a' and 'b' in the general form of exponential function, we get:

B(t) = 15 (4[tex])^t[/tex]

Therefore, the exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].

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