Determine values that would make f ( x ) = 3 − x x 2 − 4 equal 0.

Answer:c

Step-by-step explanation:

a) The group of student for whom all places are suitable is 15.

b) The presentation of the information in a Venn Diagram about the choices of locations for an educational trip by students of Class 10 studying at Shree Sharada Secondary School is attached.

c) The total number of students studying in Class 10 in Sharada Secondary School is 90.

d) The ratio of students who said that Pokhara was the only suitable place and Lumbini was the only suitable place is 4:5.

A Venn Diagram is a graphical representation of groups of data to show their contrasts or differences and their similarities.

Students of Class 10

Shree Sharada Secondary Schoo

Educational Trip Locations

Pokhara, P = 40

Lumbini, L = 30

Ilam, I = 45

All three places (P, L, and I) = 15

No Opinion = 5

The number of P only = 25 (40 - 15)

The number of L only = 15 (30 - 15)

The number of I only = 30 (45 - 15)

The number of P, L, and I = 15

The number expressing no opinion = 5

b) The Venn Diagram is attached.

c) The total number of students in Class 10 = 90 (25 + 15 + 30 + 15 + 5)

Ratios of Lumbibi as a suitable place to Pokhara only:

The number of P only = 25

The number of L only = 15

Initial ratio = 15:25 = 3:5

Addition of 5 to Lumbini:

The number of P only = 25

The number of L only = 15

d) Final ratio = 20:25 = 4:5

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Answer:

Step-by-step explanation:

Answer:

[tex]1.6*10^{-5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{0.02^2*0.01}{0.5^2}\\\\=\frac{0.0004*0.01}{0.25}\\\\=\frac{0.000004}{0.25}\\\\=\frac{4*10^{-6}}{2.5*10^{-1}}\\\\=\frac{4}{2.5}*10^{-6-(-1)}\\\\=1.6*10^{-5}[/tex]

Hope this helped!

Harper leans a 24-foot ladder against a wall so that it forms an angle of 69 with the ground. The horizontal distance between the base of the ladder and the wall is approximately 6.9 feet.

To find the horizontal distance between the base of the ladder and the wall, we can use trigonometric functions. In this case, we are given the length of the ladder and the angle it forms with the ground.

Let's denote the horizontal distance as x. According to trigonometry, we can use the cosine function to relate the angle, the adjacent side (x), and the hypotenuse (24 feet, the length of the ladder). The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.

cos(angle) = adjacent side / hypotenuse

In this case, we have:

cos(69°) = x / 24

To find x, we can rearrange the equation:

x = cos(69°) * 24

Using a calculator, we can evaluate the cosine of 69 degrees:

cos(69°) ≈ 0.3420

Now we can substitute this value into the equation:

x ≈ 0.3420 * 24

x ≈ 8.208

Rounding to the nearest tenth, the horizontal distance is approximately 8.2 feet.

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 6.9 feet.

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Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

Answer:

Step-by-step explanation:

We represent it as -5. Thus, the common difference/ratio of the given sequence in the simplest form is -5.

To determine if a sequence is arithmetic or geometric, we have to find the differences (common differences) between the terms in the sequence.

The differences between the terms are calculated to determine if they are consistent for the arithmetic sequence or if they have a common ratio for the geometric sequence.

Therefore, the sequence below is arithmetic:19, 14, 9, ...To determine the common difference, we subtract each term from the previous term.19 – 14 = 5; 14 – 9 = 5Therefore, the common difference is 5. Hence, this is an arithmetic sequence with a common difference of 5.

Also, we can say that 14 - 19 = -5, 9 - 14 = -5, and so on. This is a common difference of 5 in the opposite direction. We can say that the difference is -5.

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Answer:

45,54,63,72

Step-by-step explanation:

d=9

36+9

45+9

54+9

Answer: 45, 54, 63, 72

Step-by-step explanation

just look at each number and go up in the tens and down in the ones and once you get to 0 you start at 9 again

Answer:

y = 60

Step-by-step explanation:

given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

to find k use the condition when y = 30 , x = 6

30 = 6k ( divide both sides by 6 )

5 = k

y = 5x ← equation of proportion

when x = 12 , then

y = 5 × 12 = 60

112 hooded sweatshirts and 138 crewneck sweatshirts were sold during the first week of school.

Let's assume that the number of hooded sweatshirts sold is represented by the variable "h," and the number of crewneck sweatshirts sold is represented by the variable "c."

According to the given information, the price of a hooded sweatshirt is $39.50, and the price of a crewneck sweatshirt is $34.50. In the first week, a total of 250 sweatshirts were sold, so we can write the following equation based on the number of sweatshirts sold:

h + c = 250 ---(1)

Additionally, the total value of the sweatshirts sold in the first week was $9185. We can express this information in terms of the prices and quantities of each type of sweatshirt:

39.50h + 34.50c = 9185 ---(2)

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply equation (1) by 34.50 to match the coefficients of "c" in both equations:

34.50h + 34.50c = 8625 ---(3)

Now, subtract equation (3) from equation (2) to eliminate "c":

(39.50h + 34.50c) - (34.50h + 34.50c) = 9185 - 8625

5h = 560

h = 560 / 5

h = 112

Substitute the value of h back into equation (1) to find the value of c:

112 + c = 250

c = 250 - 112

c = 138

Therefore, 112 hooded sweatshirts and 138 crewneck sweatshirts were sold during the first week of school.

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Answer:  

Step-by-step explanation:

The degree is 4 the leading coefficient is even/positive.  There are 3 distinct real 0's and 3 relative extreme values

Explanation:

4th degree.   Degree is the highest exponent.  The number of 0's (times it hits the curve)tells you the degree.  The curve goes through the x 2 times, which means 2 x's. Then it bounces off x 1 time which means there are 2 x's there too but because this one bounces off it means it's not a distint solution it's a multiplicity ex (x-3)².  So that accounts for 4 solutions

Even/positive coefficient.  That's the first number in the equation.  Because it's facing up it's a positive but all the ends are both facing up so that tells you it's even.  Think of a parabola that is an even function, this follows those rules too.

3 distinct zeroes.    This is explained in 4th degree.   Zeroes are solutions, when it hits x axis.  Goes through x 2 times and bounces once.  So there are 3 distinct zeroes

3 relative extreme values. This is how many "mini" max and mins you have.  

The graph of the inequality -2y + 3 < 5 is a shaded region below the line y = -1.

1. Start by rewriting the inequality with y on the left side: -2y + 3 < 5.

2. Subtract 3 from both sides of the inequality: -2y < 2.

3. Divide both sides of the inequality by -2. Since we are dividing by a negative number, the inequality sign flips: y > -1.

4. This means that y must be greater than -1 to satisfy the inequality.

5. To graph this inequality, draw a number line and mark -1 with an open circle (since y is not equal to -1).

6. Shade the region to the right of -1, since y must be greater than -1.

7. Since there are no other variables or coefficients in the inequality, the line y = -1 is a horizontal line passing through -1 on the y-axis.

8. Indicate on the graph that the line itself is not part of the solution by making it a dashed line instead of a solid line.

9. Therefore, the graph of the inequality -2y + 3 < 5 is a shaded region below the line y = -1.

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The line passing through p₁ and q₁ is parallel to the line passing through p₂ and q₂.

(a) To find the center and radius of a circle with the equation x² + y² + 2x + 8y = 8, we need to rewrite the equation in the standard form of a circle, which is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.

We start by completing the square for both x and y terms:

x² + 2x + y² + 8y = 8

(x² + 2x) + (y² + 8y) = 8

To complete the square for x terms, we add (2/2)² = 1 to both sides inside the parentheses:

(x² + 2x + 1) + (y² + 8y) = 8 + 1

(x + 1)² + (y² + 8y) = 9

To complete the square for y terms, we add (8/2)² = 16 to both sides inside the parentheses:

(x + 1)² + (y² + 8y + 16) = 9 + 16

(x + 1)² + (y + 4)² = 25

Now the equation is in the standard form. We can see that the center of the circle is (-1, -4) and the radius is the square root of 25, which is 5. Therefore, the center of the circle is (-1, -4) and the radius is 5.

(b) To show that the line through p₁(3, -4) and q₁(-2, 6) is parallel to the line through p₂(-3, 6) and q₂(9, -18), we need to demonstrate that the slopes of the two lines are equal.

The slope of the line passing through p₁ and q₁ is given by:

m₁ = (y₂ - y₁) / (x₂ - x₁)

  = (6 - (-4)) / (-2 - 3)

  = 10 / -5

  = -2

The slope of the line passing through p₂ and q₂ is given by:

m₂ = (y₂ - y₁) / (x₂ - x₁)

  = (-18 - 6) / (9 - (-3))

  = -24 / 12

  = -2

We can see that both slopes are equal to -2. Therefore, the line passing through p₁ and q₁ is parallel to the line passing through p₂ and q₂.

By demonstrating that the slopes of the two lines are equal, we have shown that the line through p₁(3, -4) and q₁(-2, 6) is parallel to the line through p₂(-3, 6) and q₂(9, -18).

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The number of possible license plates that can be issued using this system is 17,576,000.

To find the number of possible license plates that can be issued using this system, we need to determine the number of options for each character in the license plate.

For the first character, there are 26 letters in the English alphabet, so we have 26 options.

Similarly, for the second and third characters, we also have 26 options each.

For the fourth character, there are 10 possible numbers (0-9).

And for the fifth character, there are again 10 possible numbers.

To find the total number of possible license plates, we need to multiply the number of options for each character together.

Number of possible license plates = Number of options for the first character * Number of options for the second character * Number of options for the third character * Number of options for the fourth character * Number of options for the fifth character

Number of possible license plates = 26 * 26 * 26 * 10 * 10

Calculating this expression gives us:

Number of possible license plates = 17,576,000

Therefore, the number of possible license plates that can be issued using this system is 17,576,000.

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Given sec 0= radical 10/2, cos(0) is equal to √10/5.

To find the value of cosine (cos) given the value of secant (sec), we can use the reciprocal identity between these two trigonometric functions.

The reciprocal identity states that:

sec(x) = 1/cos(x)

In this case, we are given sec(0) = √10/2.

We can rewrite this as:

1/cos(0) = √10/2

Multiplying both sides by cos(0), we get:

cos(0) * (1/cos(0)) = cos(0) * (√10/2)

The cos(0) terms cancel out on the left side, giving us:

1 = (√10/2) * cos(0)

Now, to isolate cos(0), we divide both sides by (√10/2):

1 / (√10/2) = cos(0)

To simplify the expression on the left side, we rationalize the denominator:

(1 * 2) / √10 = cos(0)

2/√10 = cos(0)

To express cos(0) in simplified radical form, we multiply the numerator and denominator by √10:

(2 * √10) / (√10 * √10) = cos(0)

(2√10) / 10 = cos(0)

Simplifying further, we get:

√10 / 5 = cos(0)

Therefore, cos(0) is equal to √10/5.

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Answer:

Yes

Step-by-step explanation:

0.3983 is a number between 0 and 1, it can represent a probability.

This statement follows from the fact that m∠4 + m∠6 = 180°. The statement that completes the proof is C. ∠4 and ∠7 are supplementary.

To complete the proof, let's analyze the given statements and reasons:

m ∥ n (Given) - This statement establishes that lines m and n are parallel.

m∠6 = m∠7 (Vertical angles theorem) - When two lines intersect, the vertical angles formed are congruent.

? (Same-side interior angles theorem) - This step is missing in the given proof. To prove that ∠4 and ∠6 are supplementary, we need to use the same-side interior angles theorem.

The same-side interior angles theorem states that when two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal are supplementary. In this case, lines m and n are parallel, and the transversal is the line that intersects them.

To complete the proof, we can include the missing statement:

∠4 and ∠6 are interior angles on the same side of the transversal (Same-side interior angles theorem).

Now, we can continue with the remaining steps of the proof:

m∠4 + m∠7 = 180° (Definition of supplementary angles) - Supplementary angles add up to 180 degrees.

m∠4 + m∠6 = 180° (Substitution property of equality) - We substitute ∠7 with ∠6 since they are congruent.

∠4 and ∠6 are supplementary (Definition of supplementary angles) - This statement follows from the fact that m∠4 + m∠6 = 180°.

Therefore, the statement that completes the proof is:

C. ∠4 and ∠7 are supplementary.

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[tex]P=100\left( \frac{1}{2} \right)^{\frac{t}{30000}} \\\\[-0.35em] ~\dotfill\\\\ \boxed{A}\\\\ t=20000\hspace{5em}P=100\left( \frac{1}{2} \right)^{\frac{20000}{30000}}\implies P=100\left( \frac{1}{2} \right)^{\frac{2}{3}}\implies P\approx 63.0 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ P=40\hspace{5em}40=100\left( \frac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{40}{100}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}\implies \cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{t}{30000}}[/tex]

[tex]\cfrac{2}{5}=\left( \cfrac{1}{2} \right)^{\frac{1}{30000}t}\implies \log\left( \cfrac{2}{5} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}t} \right] \\\\\\ \log\left( \cfrac{2}{5} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{30000}} \right]\implies \cfrac{\log\left( \frac{2}{5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{30000}} \right]}=t\implies 40000\approx t[/tex]

The relation of a line graph is visualized by drawing lines between all of the points on a grid is false.

A line graph is a type of graph that uses lines to connect data points. The points are typically plotted on a grid, but the lines do not need to connect all of the points. In fact, it is often more helpful to only connect the points that are relevant to the data that you are trying to visualize.

For example, when graphing temperature over time, there is only need to connect the points that represent the temperature at each hour. There is no need to connect the points that represent the temperature at midnight, 2am, 4am, etc.

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Complete question:

The relation of a line graph is visualized by drawing lines between all of the points on a grid. Is this true or false? Explain your answer.

The trust fund will earn approximately $9,540.25 in interest per year. This amount is available for scholarships each year.

To determine the amount available from the trust fund for scholarships each year, we need to calculate the interest earned on the initial investment. The interest is compounded semi-annually at a rate of 3.8%.

The formula to calculate compound interest is:

A = P(1 + r/n)^(nt)

Where:

A = the final amount (including principal and interest)

P = the principal amount (initial investment)

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = number of years

In this case, the principal amount (P) is $250,000, the annual interest rate (r) is 3.8% or 0.038 (in decimal form), the interest is compounded semi-annually (n = 2), and we want to find the interest earned per year (t = 1).

Plugging in these values into the formula, we have:

A = 250,000(1 + 0.038/2)^(2*1)

Simplifying further:

A = 250,000(1 + 0.019)^2

A = 250,000(1.019)^2A ≈ 250,000(1.038161)

A ≈ $259,540.25

Therefore, the trust fund will earn approximately $9,540.25 in interest per year. This amount is available for scholarships each year.

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Answer:

[tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]

Step-by-step explanation:

Let [tex]\sin(2\arccos(-\frac{3}{5}))=\sin(2\theta)=2\sin\theta\cos\theta[/tex] and [tex]\theta=\arccos(-\frac{3}{5})[/tex] so that [tex]\cos\theta=-\frac{3}{5}[/tex]. Now we'll need to find [tex]\sin\theta[/tex] having known [tex]\cos\theta[/tex]:

[tex]\displaystyle \cos\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{-3}{5}\\\\\sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{\sqrt{5^2-(-3)^2}}{5}=\frac{\sqrt{25-9}}{5}=\frac{\sqrt{16}}{5}=\frac{4}{5}[/tex]

Therefore, [tex]2\sin\theta\cos\theta=2(\frac{4}{5})(-\frac{3}{5})=2(\frac{-12}{25})=-\frac{24}{25}[/tex], which makes [tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-1}{0 +4} \implies \cfrac{ -1 }{ 4 } \implies - \cfrac{1}{4}[/tex]

The composite function for this problem is given as follows:

16.

The composite function of g(x) and f(x) is defined by the function presented as follows:

(g ∘ f)(x) = g(f(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is given as follows:

(g ∘ f)(x) = g(f(x)) = g(4) = 5(4) - 4 = 20 - 4 = 16.

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Step-by-step explanation:

Weighted Average = (A * 1 + B * 1 + C * 2) / (1 + 1 + 2)

Since the weights are 1, 1, and 2 respectively, we can simplify the equation further:

Weighted Average = (A + B + 2C) / 4

Therefore, the average of the points A, B, and C with weights 1, 1, and 2 respectively is (A + B + 2C) / 4.

The average of the points A, B, and C with respective weights of 1, 1, and 2 can be calculated using the weighted average formula: (1*a + 1*b + 2*c) / (1+1+2). The values of points A, B, and C are represented as a, b, and c.

The question asks for the average of points A, B, and C, which are weighted 1, 1, and 2 respectively. To calculate a weighted average, we multiply each value by its respective weight and then sum these products. We then divide this sum by the sum of the weights. So, let's assume the values of points A, B, and C be a, b, and c respectively. Using the formula for weighted average we get Average = (1*a + 1*b + 2*c) / (1+1+2)This formula will give us the average of the points A, B, and C with the specified weights.

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The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

[tex]D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}[/tex]

D = 5 units.

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The expected number of investigators who will report that 3, 4, or 5 people are consumers of rice is 57 investigators.

The binomial distribution B(n, p) describes the behavior of a count X of successes in n independent trials, each with its own boolean-valued outcome: success (with probability p) or failure (with probability q = 1-p).

We want to find the probability that an investigator reports 3, 4, or 5 people are consumers of rice. The probability P(X=k) for a binomial distribution is given by the formula:

P(X=k) = C(n, k) * p^k * q^(n-k)

So we want to find P(X=3) + P(X=4) + P(X=5) :

P(X=3) = C(10, 3) * (0.5)^3 * (0.5)^(10-3)

= 0.117

P(X=4) = C(10, 4) * (0.5)^4 * (0.5)^(10-4)

= 0.205

P(X=5) = C(10, 5) * (0.5)^5 * (0.5)^(10-5)

= 0.246

The expected number of investigators who will report three or less of the people interviewed consumed is :

= P(X=3) + P(X=4) + P(X=5)

= 0.117 + 0.205 + 0.246

= 0.568

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Full question is:

Suppose that half the population of a town are consumers of rice. Each of 100 investigators interviews 10 individualas to see wheather they are consumers of rice. How many investigators do you expert to report that three or more but less than six people are consumers of rice?

The solution for the system of equations is (x, y) = B. (3, -5).

The correct option is B. (3, -5).

To find the solution for the system of equations:

{4x + y = 7

{2y + 3 = 3x - 16

We can solve it using the method of substitution or elimination. Let's use the method of elimination:

First, let's multiply the second equation by 2 to eliminate the variable y:

2(2y + 3) = 2(3x - 16)

4y + 6 = 6x - 32

Rearranging this equation, we get:

6x - 4y = 38 ----(1)

Now we have the system of equations:

4x + y = 7 ----(2)

6x - 4y = 38 ----(1)

Next, let's multiply equation (2) by 4 to eliminate the variable y:

4(4x + y) = 4(7)

16x + 4y = 28

Now we have the system of equations:

16x + 4y = 28 ----(3)

6x - 4y = 38 ----(1)

Adding equations (3) and (1) eliminates the variable y:

(16x + 4y) + (6x - 4y) = 28 + 38

22x = 66

x = 66/22

x = 3

Substituting the value of x into equation (2), we can solve for y:

4(3) + y = 7

12 + y = 7

y = 7 - 12

y = -5

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The man would receive a commission of R3,600 on sales totaling R70,000, with a 6% commission rate excluding the first R10,000.

To calculate the commission, we first need to determine the sales amount on which the commission applies.

In this case, the first R10,000 is excluded from the commission calculation.

Therefore, the commission would be calculated on the remaining amount of R70,000 - R10,000 = R60,000.

To find the commission, we multiply the sales amount by the commission rate of 6%:

Commission = R60,000 * 6% = R3,600.

Therefore, the man would receive R3,600 in commission.

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Answer:

All Real Number

Step-by-step explanation:

5x + 3(x - 5) = 6x + 2x - 15

5x + 3x - 15 = 8x - 15

8x - 15 = 8x - 15

-15 = -15

Since the -15 = -15, the equation will always be true for any value of x.

So, the answer is All Real Number.