A map of Québec has a scale of 1:1 500 000. On map, the distance between Trois-Rivières and Québec City is 2⅝ in. What is the distance between these cities to the nearest mile?​

the value inside the square root must be positive or zero, then:

x - 7 ≥ 0

x - 7 +7 ≥ 0 + 7 adding 7 at both sides

x ≥ 7

The only option greater than or equal to 7 is 8

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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The radius of convergence r is 1.

I assume that the function is f(x) = Σ(\(5^n * x^n\)) from n=0 to infinity, which can be written using sigma notation as f(x) = Σ(\(5^n * x^n\)) = \(1 + 5x + 25x^2 + 125x^3 + ...\)

The ratio test, which asserts that the series converges absolutely if the limit of the ratio of successive terms in the series is smaller than 1, can be used to determine the radius of convergence. The series diverges if the limit is bigger than 1 or does not exist. The test is not conclusive if the limit is exactly 1.

Using the ratio test, we have:

|5\(x^{(n+1)\)| / |5\(x^n\)| = |x|

Hence, the ratio of successive words cannot exceed:

lim |x| = |x|

n→∞

If |x| 1 and |x| > 1, the series absolutely converges and diverges. When |x| = 1, the series diverges because the terms do not approach zero.

Therefore, the radius of convergence r is 1.

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The answer is 3. Choosing from 3 red marbles, 4 yellow marbles, and 8 blue marbles. The model provides an accurate representation of the items in the bag as each item is equally likely to be chosen.

It is used in a variety of activities such as rolling dice games, probability experiments, and math activities.

The model of flipping a coin fifteen times is incorrect as it does not accurately represent the scenario. There is no representation of the different sports items in the bag.

The model of spinning a spinner with three equal sections is incorrect as the items in the bag are not equal and there are three sections in the spinner.

The model of rolling a number cube labeled one through six fifteen times is incorrect as the number cube does not accurately represent the sports items in the bag.

In conclusion, the best model to simulate the scenario with a sports bag containing 3 tennis balls, 4 baseballs, and 8 golf balls is 3. Choosing from 3 red marbles, 4 yellow marbles, and 8 blue marbles.

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(2 + 9m > - 25\)

Subtract sides 2

\( - 2 + 2 + 9m > - 2 - 25\)

\(9m > - 27\)

Divide sides by 9

\( \frac{9m}{9} > \frac{ - 27}{9} \\ \)

\(m > - 3\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\( - 9m + 10 > 28\)

\(28 < - 9m + 10\)

Add sides 9m

\(9m + 28 < 9m - 9m + 10\)

\(9m + 28 < 10\)

Subtract sides 28

\(9m + 28 - 28 < 10 - 28\)

\(9m < - 18\)

Divide sides by 9

\( \frac{9m}{9} < \frac{ - 18}{9} \\ \)

\(m < - 2\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The critical value in a chi-square test for independence depends on the number of categories and expected frequencies, and not on the normality or variance of the data.

The critical value in a chi-square test for independence is determined by the number of categories and expected frequencies in the data. This test is used to analyze the relationship between two categorical variables, and the expected frequencies are calculated based on the assumption of independence between these variables. The critical value is the minimum value of the test statistic that would result in rejecting the null hypothesis, which states that the two variables are independent.

The normality and variance of the data do not affect the critical value in a chi-square test for independence. This test does not assume a normal distribution of the data, and the variance is not used to calculate the expected frequencies. Instead, the expected frequencies are determined by the marginal frequencies of the two variables, assuming that they are independent.

It is important to use the correct critical value in a chi-square test for independence, as using the wrong value could result in incorrect conclusions about the relationship between the two variables. The critical value can be found using a chi-square distribution table or calculator, based on the number of categories and the level of significance chosen for the test.

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Answer:

y = -2x - 4

Step-by-step explanation:

y - 2 = -2 (x + 3)

y - 2 = -2x - 6

y = -2x - 4

The numerator for the given rational expression is 3 + 5k.

In the given rational expression, (3 + 5k) represents the numerator. The numerator is the part of the fraction that is located above the division line or the horizontal bar.

In this case, the expression 3 + 5k is the numerator because it is the sum of 3 and 5k. The term 3 is a constant, and 5k represents the product of 5 and k, which is a variable.

The numerator consists of the terms 3 and 5k, which are combined using addition (+). Therefore, the numerator can be written as 3 + 5k.

To clarify, the numerator is the value that contributes to the overall value of the fraction. In this case, it is the sum of 3 and 5k.

Hence, the correct answer for the numerator of the given rational expression (3 + 5k) / (74/k^2) is 3 + 5k.

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Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Answer:

∠ W = 30°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos W = \(\frac{adjacent}{hypotenuse}\) = \(\frac{WY}{WX}\) = \(\frac{2\sqrt{21} }{4\sqrt{7} }\) = \(\frac{1}{2}\) \(\sqrt{\frac{21}{7} }\) = \(\frac{\sqrt{3} }{2}\) , then

∠ W = \(cos^{-1}\) ( \(\frac{\sqrt{3} }{2}\) ) = 30°

Answer:

(i) 4000

(ii) $5.00

Step-by-step explanation:

Let no. of shares of Company A be X

Let share price of Company B on Day 7 be $y

Share price of Company B on Day 12 = $(y-0.50)

(i)

Consider Day 7:

4.60x - 2000y = 7400................ (1)

Consider Day 12:

4.80x - 5000(y-0.50) = -5800

4.80x - 5000y + 2500 = -5800

4.80x - 5000y = -8300............... (2)

(1)*2.5:

11.5x - 5000y = 18500................. (3)

(3)-(2):

11.5x - 4.80x - 5000y + 5000y = 18500 + 8300

6.70x = 26800

x = 4000

(ii)

Sub. x = 4000 into (1):

4.60(4000) - 2000y = 7400

-2000y = 7400 - 18400

-2000y = -11000

y = 5.5

Share price of Company B on Day 12

= 5.50 - 0.50

= $5.00

A: (0, 10)

B: (0, 75)

Domain = Highest and lowest x value

Range = Highest and lowest y value

Hope this helps

The given homogeneous system of equations can be represented as a matrix equation Ax = 0, where A is the coefficient matrix and x is the vector of variables.

To find the solution set in parametric vector form, we can perform row operations on the augmented matrix [A|0] and express the variables in terms of free parameters.

The augmented matrix for the given system is:

[3 3 6 | 0]

[-9 -9 -18 | 0]

[0 -7 -7 | 0]

Using row operations, we can transform this matrix to row-echelon form:

[3 3 6 | 0]

[0 -6 -12 | 0]

[0 0 -7 | 0]

Now, we can express the variables in terms of free parameters. Let x2 = t and x3 = s, where t and s are arbitrary parameters. Solving for x1 in the first row, we get x1 = -2t - 2s.

Therefore, the solution set in parametric vector form is:

x = [-2t - 2s, t, s], where t and s are arbitrary parameters.

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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In a case whereby the slide part of a water slide is 89 feet long and makes a 42 angle of depression with the ground, the lenght or how high up in the air  is 73.6 feet

We know that the length of the slide AB is 89 feet, and the angle of depression from A to B is 42 degrees. We want to find the height h of point A above the ground.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is h (the height we're looking for), and the adjacent side is AB (the length of the slide). So we can write base on trigonometery as ;

tan(42) = h / 89

h = 89 * tan(42)

h ≈ 73.6 feet

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To solve this problem, we need to find the antiderivative of f'(x) = 9x^1/2 + 10x^3/2. However, this function cannot be integrated directly using basic integration techniques. Instead, we need to rewrite f(x) as a sum of terms with fractional exponents, which can be integrated using the power rule. To do this, we can use the property that (a+b)^n = sum of (n choose k) * a^(n-k) * b^k, where (n choose k) represents the binomial coefficient. In this case, we have f(x) = V(9 + 10x) = (9(1 + 10x/9))^1/2 = 3(1 + 10x/9)^1/2. Using the binomial theorem, we can expand this expression as f(x) = 3(1 + 1/9(10x))^1/2 = 3(1/9(10x))^1/2 * sum of (1/2 choose k) * (1/9(10x))^k.

Next, we can integrate each term using the power rule, which states that the antiderivative of x^n is (1/(n+1))x^(n+1) + C, where C is the equation of integration. Applying the power rule, we get f(x) = 3(1/9(10x))^1/2 * sum of (1/2 choose k) * (1/(k+1))(1/9(10x))^(k+1) + C.To find the constant of integration C, we use the fact that f(1) = 14. Substituting x = 1 into the expression for f(x), we get f(1) = 3(1/9(10))^1/2 * sum of (1/2 choose k) * (1/(k+1))(1/9(10))^(k+1) + C = 3/3 + C = 1 + C. Therefore, C = 14 - 1 = 13.In summary, the antiderivative of f'(x) = 9x^1/2 + 10x^3/2 is f(x) = 3(1/9(10x))^1/2 * sum of (1/2 choose k) * (1/(k+1))(1/9(10x))^(k+1) + 13. The constant of integration C is found by using the condition that f(1) = 14, which gives C = 13.

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Using the normal distribution, it is found that:

a) Her waist is at the 2.74th percentile.

b) 99.86% of female soldiers requires custom uniform pants.

what is Normal Probability Distribution ?

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

.

Item a:

The percentile is the p-value of Z when X = 26.1, hence:

Z = (X- μ)/σ

Z = 26.1 - 28.4/1.2

Z = -1.92

Z = -1.92 has a p-value 0.0274 = 2.74th percentile.

Item b:

The proportion is the p-value of Z when X = 32 subtracted by the p-value of Z when X = 24, hence:

X = 32:

Z = (X- μ)/σ

Z = 32 - 28.4/1.2

Z = 3.

Z = 3 has a p-value 0.9987.

X = 24:

Z = (X- μ)/σ

Z = 24 - 28.4/1.2

Z = -3.67.

Z = -3.67 has a p-value 0.0001.

0.9987 - 0.0001 = 0.9986 = 99.86% of female soldiers requires custom uniform pants.

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The correct option is B. The equation B. 0.1x = 2.30 can be used to determine the number of laps Ronkeata swam, and the solution is x = 23.

The equation that can be used to determine the number of laps Ronkeata swam is B. 0.1x = 2.30.
This is because her uncle pledges to give $0.10 for every lap Ronkeata swims. So, the amount of money her uncle gives can be represented as 0.1 times the number of laps she swims.
We know that her uncle gave the team $2.30 based on the number of laps Ronkeata swam. Therefore, we can set up the equation 0.1x = 2.30, where x represents the number of laps Ronkeata swam.
To solve for x, we can divide both sides by 0.1:
0.1x/0.1 = 2.30/0.1
x = 23
Therefore, Ronkeata swam 23 laps during the fundraiser.
In conclusion, the equation B. 0.1x = 2.30 can be used to determine the number of laps Ronkeata swam, and the solution is x = 23.

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Hello,

\(34 = p + 19\)

\(34 - 19 = p + 19 - 19\)

\(15 = p\)

\(p = 15\)

For all values of x greater than or equal to -2, the function f(x) = √(x + 2) + 2 will yield real outputs. So, x = -2.

To determine the input value at which the function f(x) = √(x + 2) + 2 begins to have real outputs, we need to find the values of x for which the expression inside the square root is non-negative. In other words, we need to solve the inequality x + 2 ≥ 0.

Subtracting 2 from both sides of the inequality, we get:

x ≥ -2

Therefore, the function f(x) = √(x + 2) + 2 will have real outputs for all values of x greater than or equal to -2.

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The vectors v = 6i - 3j and w = i + 2j are orthogonal.

To determine if the vectors v and w are orthogonal, we need to find their dot product. If the dot product is 0, the vectors are orthogonal.

Here are the steps to find the dot product of v = 6i - 3j and w = i + 2j,

1. Identify the components of the vectors: v = (6, -3) and w = (1, 2)

2. Multiply the corresponding components of the vectors:

\((6 \times 1) + (-3 \times 2) = 6 - 6 \)

3. Add the products: 6 - 6 = 0 Since the dot product is 0, the vectors v = 6i - 3j and w = i + 2j are orthogonal.

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Correct question is " Are these vectors orthogonal? v = 6i - 3j and w = i+2j"

The number

To determine where a number is in relation to another number on a number line, we need to compare their positions.

If is seven units to the left of , we can represent this as: = - 7. Therefore, is to the right of on the number line.

Similarly, if a number is to the left of another number, it means that it has a smaller value and its representation would have a negative sign. For example, if the number is three units to the left of , we can represent it as: = - 3.

Conversely, if a number is to the right of another number, it means that it has a greater value and its representation would have a positive sign. For example, if the number is five units to the right of , we can represent it as: = + 5.

Thus, we can determine the positions of numbers in relation to each other on a number line by using their distance and direction.

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Answer:

y>-4

Step-by-step explanation:

Divide both sides by 2 and you get y>-4, which is B.

Answer:

y>−4 is the answer for y (djidjdejksekekek) [only for 20 characters sorry]

Answer:

see attached pdf

Step-by-step explanation:

see attached pdf

Answer:

B

Step-by-step explanation:

B Rounded to nearest ten thousand

The attendance that aligns with rounding to 120,000 is B) 116,390.

To determine the possible attendance at the amusement park if it was rounded to the nearest ten thousand, we need to consider the rounding process.

When rounding to the nearest ten thousand, we look at the digit in the ten thousand place. If this digit is 5 or greater, we round up to the next ten thousand. If it is less than 5, we round down to the previous ten thousand.

In this case, the attendance was rounded to 120,000. To round to the nearest ten thousand, we look at the digit in the ten thousand place, which is 2. Since 2 is less than 5, we round down.

Therefore, the attendance at the amusement park could have been rounded to 120,000 people if it was rounded to the nearest ten thousand.

Among the given options, the attendance that aligns with rounding to 120,000 is B) 116,390.

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Answer:

10.54263764

Step-by-step explanation:

\(3300=2000e^{.0475t}\\\\1.65=e^{.0475t}\\\ln(1.65)=.0475t\\.500775288=.0475t\\t=10.54263764\)

Answer:

It will take about 10.5 years for the investment to reach $3,300.

Step-by-step explanation:

Continuous compound is given by:

\(\displaystyle A=Pe^{rt}\)

Where P is the principal, e is Euler's number, r is the rate, and t is the time (in this case in years).

Since our principal is $2,000 at a rate of 4.75% or 0.0475, our equation is:

\(\displaystyle A=2000e^{0.0475t}\)

We want to find the number of years it will take for our investment to reach $3,300. So, substitute 3300 for A and solve for t:

\(3300=2000e^{0.0475t}\)

Divide both sides by 2000:

\(\displaystyle e^{0.0475t}=\frac{33}{20}\)

We can take the natural log of both sides:

\(\displaystyle 0.0475t=\ln\left(\frac{33}{20}\right)\)

Therefore:

\(\displaystyle t=\frac{1}{0.0475}\ln\left(\frac{33}{20}\right)\approx 10.54\text{ years}\)

It will take about 10.5 years for the investment to reach $3,300.

x > -4

Step-by-step explanation:

2x - 7 > -15

2x > -15 + 7

2x > -8

2x/2 > -8/2

x > -4

Answer:

huh I'm confused. lollolol

Answer:

umm whats the question

Step-by-step explanation:

and the statement is true

Answer:

3/5

can also be written as 3:5

Step-by-step explanation:

Use:

squares/circles

Fill in the given info.

6/10

simplify (reduce the fraction)

6/10 = 3/5

3/5 is the ratio in simplest form.