Of the 200 graduate students who were interviewed for a par time position at a call center, 110 had a bicycle, 25 had a master card and 130 had a mobile phone. 50 of them had both, a bicycle and a master card, 30 had both, a master card and a mobile phone and 60 had both, a bicycle and mobile phone and 10 had all three. How many candidates had none of the three?

Answer:

-4^0, 2^-3, (-3)^0, 5^1

Step-by-step explanation:

2^-3= 1/8 (the same as 0.125)

(-3)^0= 1

-4^0= -1

5^1 = 5

these numbers from lowest to largest would be -1, 0.125 (1/8), 1 and finally 5

making the answer -4^0, 2^-3, (-3)^0, 5^1

Answer:

This inequality is impossible. Assuming this is realistic, Linda cannot sell part of a box of cookies and therefore cannot make less than $220.

Step-by-step explanation:

Given

To find

We know that,

Let the third angle be ,'x'

then,

Hence,the third angle would measure 30°

The length of side KL is approximately 4.8 cm.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides of the triangle. In other words:

a/sin(A) = b/sin(B) = c/sin(C)

Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

Using the Law of Sines, we can set up the following proportion:

l/sin(L) = m/sin(M)

Where l is the length of side KL, L is the measure of angle KLM (which is 72 degrees), m is the length of side LM, and M is the measure of angle KML (which we can find by subtracting L from 180 degrees).

M = 180 - L

= 180 - 72

= 108 degrees

Now we can substitute the given values into the proportion and solve for l:

l/sin(72) = 5.9/sin(108)

l = sin(72) * (5.9/sin(108))

≈ 4.8 cm (rounded to the nearest 10th of a centimeter)

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Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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a. It represents the spread of the middle 50% of the data.

b. At least 50% of the students scored between 80 and 86.

c. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

How evenly distributed the middle 50% of the data is is determined by the interquartile range. In order to calculate it, the first quartile is subtracted from the third quartile.

A. The interquartile range (IQR) in a box-and-whisker plot is the distance between the first quartile (Q1) and the third quartile (Q3) of the data. It represents the spread of the middle 50% of the data.

B. To determine what percent of the students got 80% or higher, we need to find the upper fence, which is defined as 1.5 times the IQR above Q3. From the box-and-whisker plot, we can see that Q3 is approximately 86 and Q1 is approximately 71. Therefore, the IQR is 86 - 71 = 15. The upper fence is 1.5 * 15 + 86 = 108.5.

Looking at the plot, we can see that there are no data points above 100, so we can safely assume that no students scored above 100%. The highest score is 94, which is within the whiskers of the box-and-whisker plot. Therefore, we know that the percent of students who scored 80% or higher is between the percent of students who scored 80% or higher and the percent of students who scored 94% or higher.

From the plot, we can see that the median is approximately 80 and the third quartile (Q3) is approximately 86. This means that at least 50% of the students scored between 80 and 86. Additionally, we know that the maximum score is 94, so we can say that at least some students scored higher than 86. However, we don't know how many students scored between 86 and 94.

C. Based on the interquartile range, we can say that the middle 50% of the students scored between approximately 71 and 86. This suggests that there is a significant amount of variability in the test scores, as the range is quite wide. Additionally, we know that at least some students scored above 86, but we don't have enough information to determine how many or how high their scores were. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

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Answer:

-2/7x+3

Step-by-step explanation:

1/7x+6-4/7x-3

-3/7x+3

Answer:

Step-by-step explanation:

Answer:

The first discount of 50% means Jason paid 50/100 x £88 = £44 for the jacket.

Then, the second discount of 25% means he paid 75/100 x £44 = £33 for the jacket.

Therefore, the final sale price that Jason paid for the jacket was £33.

Answer:

396/538

Step-by-step explanation:

By graphing the polynomial, we conclude that there is only one real root, so the correct option is A.

We have the polynomial:

\(y = -3x^2 + 12x - 12\)

To see how many real roots this polynomial has, we can graph it and see how many times the graph intercepts the x-axis.

The graph can be seen below:

There we can see that there is only one intercept, so there is only one real root.

So the correct option is A.

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Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) +             2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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Answer:

5

Step-by-step explanation:

Answer:

we need to factorise if imaginary number is in the denominator. no action is required if its in the numerator.

you can factorise an imaginary number by multiplying both the numerator and denominator by the conjuncate of the complex number

for instance,

we've given a complex number as follows

\( \frac{x}{3x + 4i} \)

factorising

\( \frac{x}{3x + 4i} \times \frac{3x - 4i}{3x - 4i} \)

as 3x -4i is the conjugate of 3x + 4i

and 4i is the imaginary number

\( \frac{ x(3x - 4i)}{9x {}^{2} - 4 {i}^{2} }\)

and since i² = -1

\(\frac{ x(3x - 4i)}{9x {}^{2} + 4}\)

hence factorised

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The solution of the function 3f(1) - 4g(-2)  is -19.

The functions can be solved as follows;

f(x) = 7x - 4

g(x) = 11 - x²

Therefore, let's solve the composite function as follows:

A composite function is generally a function that is written inside another function.

Hence,

3f(1) - 4g(-2) = ?

f(1) = 7(1) - 4 = 7 - 4 = 3

g(-2) = 11 - (-2)² = 11 - 4 = 7

Therefore,

3f(1) - 4g(-2) = 3(3) - 4(7) = 9 - 28 = -19

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Answer:

The quadrilateral'area is 96cm².

Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

Measure of angle 2 = 82°

Step-by-step explanation:

m∠1 = (10 x + 8)°

m∠3 = (12 x - 10)°

2 lines are said to intersect to form 4 angles. And the labelling of the angles was done starting from top left, clockwise: the angles are 1, 2, 3, 4.

Find attached the diagram obtained from the given information.

Vertical angles are angles opposite each other when two lines intersect. As such, they are equal to each other.

Considering our diagram

m∠1 = m∠3

m∠2 = m∠4

Sum of all four angles firmed = 360° (sum of angles at a point)

m∠1 +m∠2 + m∠3 + m∠4 = 360°

m∠1 = m∠3

(10 x + 8)°= (12 x - 10)°

10x-12x = -10-8

-2x = -18

x= 9°

Also m∠2 = m∠4, let each equal to y

(10 x + 8)°+ y + (12 x - 10)° + y = 360

10x + 12x - 10 +8 +2y = 360

Insert value of x

22(9) -2 + 2y = 360

2y = 360-196

2y = 164

y = 82°

m∠2 = m∠4 = y = 82°

Measure of angle 2 = 82°

Answer:

2 = 82°

Step-by-step explanation:

Answer:

f{3x}=6x-5

Step-by-step explanation:

There isn't really much to do: if you perform the division between function you get a new function:

\(h(x)=\dfrac{g(x)}{f(x)}=\dfrac{3x}{2x-5}\)

Answer:

1. d)

4.a)

2.a)

5.d)

Step-by-step explanation:

The probability that in a given week in September, it will rain on at most two days is 0.12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The probability that it rains on any given day in September = 0.3.

P ( rains ) = 0.3

And,

The probability that it will not rain on any given day in September.

P (no rain) = 1 - 0.3

P(no rain) = 0.7

Now,

The probability is that in a given week in September, it will rain on at most two days.

= P (x ≤ 2)

= P(no rain) + P(rain) + P(rain)

= 0.7 + 0.3 + 0.3

= 0.12

Thus,

The probability that in a given week in September, it will rain on at most two days is 0.12.

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First, you need to find the median, which is the medium value of the ordered data set, and if it is an even number, you take the one from the left. The median is 6 in this case. The maximum value is 11. The minimum is 4. Then you need calculate the first and third quartil, which are calculated in the following way:

For the given  system t is not application. There is no solution for the system.

In mathematics, the phrase "solution" refers to a particular value or set of values that satisfies a given equation or set of equations. Finding a solution to the problem is a necessary step in solving a system of equations.

A value for the unsolved variable that makes the equation true is referred to as the solution.

The solutions are all the values of x in the domain such that f(x) = g if we have two functions f and g that both map to the same co-domain (x).

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

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On solving the provided question, we cans ay that lateral surface area of cuboid = 2h(l+b) = 2*2(5+4) = 36 cm sq.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

lateral surface area of cuboid = 2h(l+b)

h = 2cm

l = 5cm

b = 4cm

lateral surface area of cuboid = 2h(l+b) = 2*2(5+4) = 36 cm sq.

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Answer:

The answer is that the runner can run 10 miles in 70 minutes.

Step-by-step explanation:

To solve for the number of miles that the runner can run in 70 minutes, start by setting up the information given from the problem in the form of a proportion.

A proportion is an equation which defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In a proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The proportion for this problem will look like \(\frac{2 miles}{14 minutes}=\frac{x}{70 minutes}\). (x) will be used as the variable for the number of miles that the runner can run in 70 minutes.  

To solve the proportion, start by cross multiplying to form an equation, and the equation will look like \((14)(x)=(2)(70)\). Next, simplify the equation, which will look like \((14)(x)=140\). Then, solve the equation by dividing both sides of the equation by 14, and it will look like \(x=10\). The final answer is that the runner can run 10 miles in 70 minutes.

The line slants downward from left to right, indicating that as x increases, y decreases.

The given linear equation is -x = 2y + 1. To represent this equation graphically, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.Rearranging the given equation, we get:2y = -x - 1

Dividing both sides by 2:y = (-1/2)x - 1/2

The slope of the line is -1/2, which means that for every unit increase in x, y decreases by 1/2 unit. The y-intercept is -1/2, indicating that the line intersects the y-axis at (0, -1/2).

Based on this information, the best graph that represents the linear equation y = (-1/2)x - 1/2 is a straight line with a negative slope of -1/2, starting at the point (0, -1/2) and extending infinitely in both directions.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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