There are 270 students in Year 7

Each student studies one of French or German or Spanish

Of these 270 students

study French

the number who study French : the number who study Spanish = 3:7

42 boys study German

Of the students who study German, what percentage are boys?

You must show your working.

The rate of change of each given function are:

To find the rate of change of given functions, we have to differentiate the given function w.r.t the variable provided. We will solve each part of the question and differentiate the functions step by step.

The function is, f(x) = 5x² + 3x - 7

Differentiating the above function, we get;

f'(x) = (5x² + 3x - 7)/dx

f'(x) = 10x + 3

Therefore, the rate of change of function f(x) = 5x² + 3x - 7 is 10x + 3.

Now, let us solve the second part of the question.

The function is,[tex]\( g(x)=\frac{-5 x+7}{2 x-3} \)[/tex]

Differentiating the above function using the quotient rule, we get;

[tex]\[\begin{aligned} g'(x)&=\frac{(2x-3)\cdot (-5)-(7)\cdot(2)}{(2x-3)^2}\\ &=\frac{-10x+11}{(2x-3)^2}\end{aligned}\][/tex]

Therefore, the rate of change of function [tex][tex]\( g(x)=\frac{-5 x+7}{2 x-3} \) is \( \frac{-10x+11}{(2x-3)^2} \).[/tex][/tex]

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The height of the cone is 11 mm and the slant height of the cone is 23 mm and the ant crawls 31 mm to get from the base of the cone to the top of the hill.

What is the volume of the right circular cone?

A right circular cone is a three-dimensional geometric shape that has a circular base and a vertex that is located directly above the center of the base. The axis of the cone is a line that passes through the vertex and the center of the base.

The volume of a right circular cone can be found using the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume of the cone, r is the radius of the circular base, and h is the height of the cone.

1) To find the height of the cone, we need to use the formula for the volume of a cone, which is [tex]V = (1/3)\pi r^2h[/tex]. Rearranging this formula, we get:

[tex]h = 3V / \pi r^2[/tex]

Substituting the given values, we get:

[tex]h = 3(8792) / (3.14)(20^2)[/tex]

h ≈ 11

Therefore, the height of the cone is approximately 11 mm.

2) To find the slant height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In the case of the cone, the slant height is the hypotenuse of a right triangle formed by the height and the radius of the base. Therefore, we have:

[tex]s^2 = r^2 + h^2[/tex]

Substituting the values we found in part 1, we get:

[tex]s^2 = 20^2 + 11^2[/tex]

s ≈ 23

Therefore, the slant height of the cone is approximately 23 mm.

3) To find the distance the ant crawls to get from the base of the cone to the top of the hill, we can use the Pythagorean theorem again. This time, we need to find the distance along the slant height from the base of the cone to the top of the hill. This distance is the hypotenuse of a right triangle formed by the distance from the base to the apex (which is the height of the cone) and the radius of the base. Therefore, we have:

[tex]d^2 = r^2 + s^2[/tex]

Substituting the values we found in parts 1 and 2, we get:

[tex]d^2 = 20^2 + 23^2[/tex]

d ≈ 31

Therefore, the ant crawls approximately 31 mm to get from the base of the cone to the top of the hill.

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Proved that if the function f(x,y)=e^(ax+by) with a^2+b^2=1, then f''(xx)+f''(yy)=1

To find the second partial derivatives of f(x, y), we differentiate f(x, y) twice with respect to x and y:

f'(x, y) = ae^(ax + by) and f''(xx) = a^2e^(ax + by)

f'(x, y) = be^(ax + by) and f''(yy) = b^2e^(ax + by)

Adding these second partial derivatives, we get:

f''(xx) + f''(yy) = a^2e^(ax + by) + b^2e^(ax + by)

Since a^2 + b^2 = 1, we have:

f''(xx) + f''(yy) = e^(ax+by)

But f(x, y) = e^(ax+by), so:

f''(xx) + f''(yy) = f(x, y)

Therefore, we have proved that f''(xx) + f''(yy) = 1.

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Infinite solution

The answer is 0. Therefore, there is Infinite solutions

Answer:

Using the quadratic formula, we find that:

x = 0.555 or x = 89.445

We can ignore the first solution since it doesn't make sense for the speed of a train. Therefore, the speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.

So, the answer is:

The speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.NOT SURE

Step-by-step explanation:

Answer: The equation of a line can be written in slope-intercept form as:

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the line has a slope of -3 and passes through the point (2, 2). We can use the point-slope form of the equation of a line to find the equation of this line:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Substituting the given values, we get:

y - 2 = -3(x - 2)

Expanding the right side:

y - 2 = -3x + 6

Adding 2 to both sides:

y = -3x + 8

Therefore, the equation of the line that has a slope of -3 and passes through the point (2, 2) is:

y = -3x + 8.

So the correct answer is:

y = -3x + 8

Step-by-step explanation:

Answer:

y=-3x+8

3x+y=8

y-2=-3(x-2)

u have a blessed day bru

Answer:

Step-by-step explanation:

Square (top right), rectangle (middle bottom), and trapezoid (bottom right)

if u do it right then u should get this answer.

Answer:

47 - 6√10

Step-by-step explanation:

Area of a square of side a = a²

Here a = √2 -3√5

Area A = a² = (√2 -3√5)²

We know that (a - b)² = a² -2ab +b²

So

A = (√2 -3√5)²

= (√2)² - 2(√2)(3√5) + (3√5)²

(√2)² = 2   because (√a)² = a

(3√5)² = 3² x (√5)² = 9 x 5 = 45

2(√2)(3√5) = 2 (√2 · 3 · √5)

= 2 x 3 √2 √5

√2√5 = √10

2 x 3 √2 √5 = 2 · 3 · √10 = 6√10

Therefore area = 2 - 6√10 + 45

= 47 - 6√10

Answer:

Step-by-step explanation:

To determine whether (3, 20) is a solution of y = 4x + 8, we need to substitute x = 3 and y = 20 into the equation and check whether the equation is true:

y = 4x + 8

20 = 4(3) + 8

20 = 12 + 8

20 = 20

Since the equation is true, we can say that (3, 20) is a solution of y = 4x + 8.

Answer:

Step-by-step explanation:

y= 4x+8

substituting x=3,

y= 4(3)+8

y= 12+8

y=20

∴ (3,20) is a solution of y= 4x+8

Answer:

64

Step-by-step explanation:

When you have 105+x=169

x=64

If you do 169-105 you get 64

64+105=169

The values in parts (a) and (b) are numerical summaries of the population.

Regarding the question on baseball players' salaries in 2015, the mean salary for all 868 professional baseball players is 3.856 million dollars and the standard deviation is 1.589 million dollars. The values in parts (a) and (b) are numerical summaries of the population.

The shape of the distribution of salaries for professional baseball players in 2015 is positively skewed, with the majority of the salaries clustering at the lower end of the salary range and a few salaries on the upper end. There is only one mode to the distribution.

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The Pacific Ocean is roughly 100 times bigger than the Gulf of Mexico.

Ocean is the largest and most prominent feature of the Earth's surface. It covers more than 70% of the planet and contains 97% of its water. Oceans are vital to life on Earth, providing food and resources, regulating the climate, and supporting a vast array of marine life. They are home to a variety of habitats including coral reefs, deep sea trenches, and shallow coastal estuaries.

The Pacific Ocean covers an area of roughly 63.8 million square miles (165.2 million square kilometers), while the Gulf of Mexico covers an area of only 615,000 square miles (1.6 million square kilometers). This means that the Pacific Ocean is roughly 6 x 105 (or 600,000) times bigger than the Gulf of Mexico.

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=3.6\\ h=4.2 \end{cases}\implies 3.6=\cfrac{\pi r^2(4.2)}{3}\implies 10.8=4.2\pi r^2 \\\\\\ \cfrac{10.8}{4.2\pi }=r^2\implies \sqrt{\cfrac{10.8}{4.2\pi }}=r\hspace{5em}\stackrel{\textit{diameter = 2r}}{2\sqrt{\cfrac{10.8}{4.2\pi }}} ~~ \approx ~~ \text{\LARGE 1.8}[/tex]

Answer:

Slope = (-3/2)

Step-by-step explanation:

Slope(m) = (Y2 - Y1) / (X2 - X1)

= (0-3) / (2-0)

= (-3/2) Is the ans....

Answer:

See explanation below

Step-by-step explanation:

1/(sec - tan) - 1/cos = 1/cos - 1(sec + tan)

=> 1/(sec - tan) + 1(sec + tan) = 1/cos + 1/cos

Left side

(sec + tan)/[(sec - tan)(sec + tan)] + (sec - tan)/[(sec - tan)(sec + tan)]

= [sec + tan + sec - tan]/[(sec - tan)(sec + tan)]

= [2sec]/[(sec - tan)(sec + tan)]

since (a+b)(a-b) = a^2 - b^2

=> 2sec/(sec^2 - tan^2)

let's work on the denominator (sec^2 - tan^2)

we know sec = 1/cos and tan = sin/cos

=> (1/cos)^2 - (sin/cos)^2

=> 1/cos^2 - sin^2/cos^2

=> (1 - sin^2)/cos^2 = cos^2/cos^2 = 1

so 2sec/(sec^2 - tan^2) => 2sec/1

=> 2sec

since sec = 1/cos => 2sec = 2(1/cos) = 2/cos

Right side

1/cos + 1/cos = 2/cos

Answer:

a.4

Step-by-step explanation: You first work on the parentheses( 7+9)=16. Then you multiply m and 16. Which is 0.5(16) or 16/2=8 now it’s 8/2 which is 4 .

d is not a polynomial coz it has negative power

The probabilities of the events are:

a) P(A and B) = 0

b) P(A or B)  = 0.9

c) P(notA) = 0.55

d) P(notB) = 0.55

e) P(not(A or B)) = 0.1

f) P(A and (not B)) = 0.45

Probability is the measure of the likelihood or chance of an event occurring. It deals with the study of random events and the analysis of their outcomes.

Since A and B are mutually exclusive, they cannot happen at the same time. This means that P(A and B) = 0.

a) P(A and B) = 0

b) P(A or B) = P(A) + P(B)

P(A or B) = 0.45 + 0.45 = 0.9

c) P(notA) = 1 - P(A)

P(notA) = 1 - 0.45 = 0.55

d) P(notB) = 1 - P(B)

P(notB) = 1 - 0.45 = 0.55

e) P(not(A or B)) = 1 - P(A or B)

P(not(A or B)) = 1 - 0.9 = 0.1

f) P(A and (not B)) = P(A) - P(A and B)

P(A and (not B)) = 0.45 - 0 = 0.45

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In the year 2000, there were 44 hazardous waste sites in State Y.

Hazardous materials and activities are those that pose a risk to human health, safety and the environment. Examples of hazardous materials include chemicals, flammable and combustible substances, radioactive materials, explosives, biological agents and other substances that may cause harm. Examples of hazardous activities include working with hazardous materials, operating machinery, working with electricity, and performing construction activities. It is important to understand the potential risks associated with hazardous materials and activities in order to protect oneself and others from potential harm.

n + 8 = 2(34 - 8)
n + 8 = 2(26)
n + 8 = 52
n = 44
In the year 2000, there were 44 hazardous waste sites in State Y.

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The probability of either A or B occurring is 0.55625.

The probability of either A or B occurring when given that events A and B are independent, and P(A) = 0.25 and P(B) = 0.45, can be calculated as follows: 0.25 + 0.45 - 0.25*0.45= 0.55625.:

When the events A and B are independent, then the probability of the two events occurring together is given as:P(A ∩ B) = P(A) × P(B)This is a formula for independent events, and when events A and B are independent, it implies that P(A ∩ B) = 0.

Therefore:P(A ∪ B) = P(A) + P(B) - P(A ∩ B)When the probability of A and B is given as P(A) = 0.25 and P(B) = 0.45, we can substitute these values in the above equation as:P(A ∪ B) = P(A) + P(B) - P(A) × P(B)Thus:P(A ∪ B) = 0.25 + 0.45 - 0.25*0.45= 0.55625Therefore, the probability of either A or B occurring is 0.55625.

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If MNO is NMO, it means that the second and third vertices of the triangle have switched places, but the first vertex remains the same. Therefore, triangle MON is congruent to triangle NMO.

as they have the same side lengths and angles. Specifically, the sides MO, ON, and NM are congruent, and the angles at vertices M, O, and N are also congruent. We can represent this relationship between the two triangles using the symbol ≅, so we can say that triangle MON ≅ triangle NMO. The concept of congruent triangles is a fundamental principle in geometry. Two triangles are said to be congruent if their corresponding sides and angles are equal. When two triangles are congruent, we can say that they have the same size and shape, but they may be oriented differently in space. here are several ways to prove that two triangles are congruent, such as the side-angle-side (SAS), angle-side-angle (ASA), side-side-side (SSS), angle-angle-side (AAS), and hypotenuse-leg (HL) congruence criteria.

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The two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution are -1.46 and 1.46.

To find these z-scores, we need to first determine the area in the tails of the distribution. Since the middle 87.4% of the distribution is separated from the tails, the area in the tails is 100% - 87.4% = 12.6%. This means that there is 12.6% / 2 = 6.3% in each tail.

Next, we can use a standard normal table or a calculator to find the z-scores that correspond to the 6.3% in the tails. We want to find the z-scores that have an area of 0.063 to the left and to the right of them.

According to a standard normal table, the z-score that has an area of 0.063 to the left of it is -1.46, and the z-score that has an area of 0.063 to the right of it is 1.46.

Therefore, the two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution are -1.46 and 1.46.

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The measurements that does not express volume is (a) 4ft^2

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

The list of options

The measure of volume is represented by cubic unit

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

The measurement that does not express volume is 4ft^2.

4ft^2 is a measurement of area (square footage), whereas the other three options are measurements of volume.

This is so because:

So, the unit is (a) 4ft^2

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The dilation is an enlargement, and Tashi is correct.

To determine whether the dilation (scaling) is a reduction or an enlargement, we need to compare the distances between corresponding points on the original figure and the dilated figure.

Suppose a point P(x,y) is on the original figure. After the dilation with the rule (6/5x, 6/5y), the corresponding point P'(x', y') will be:

P' = (6/5x, 6/5y)

The distance between point P and the origin is given by:

d(P) = √(x² + y²)

The distance between point P' and the origin is:

d(P') = √((6/5x)² + (6/5y)²)

= 6/5 * √(x² + y²)

Since the dilation multiplies each coordinate by a factor of 6/5, the distance between any point and the origin is multiplied by a factor of 6/5.

Therefore, if 6/5 < 1, then the distances between corresponding points are reduced, and the dilation is a reduction. If 6/5 > 1, then the distances are increased, and the dilation is an enlargement.

In this case, we have:

6/5 > 1

Therefore, the dilation is an enlargement, and Tashi is correct.

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Answer:

B

Step-by-step explanation:

In answer choice B, there is the same number of medium bottles as the number of medium bottles that you are given in the question.

Because you know that there are 93 fluid ounces in six small bottles and four medium bottles, you know that any different amount of fluid ounces with the answer choice would be because of the increase in small bottles.

By having a consistent change with only one variable (which is the small bottle) you can find the rate of change. Once you figure out how many fluid ounces are in the small bottles, you can find the total amount of fluid ounces that are in the small bottles. The amount that remains is the total fluid ounces for medium bottles.

The nth term of an AP with the first term a_1 and the common difference d is given by a_n = a_1 + (n-1)d. The nth term of the given AP is a_n = -54 + (n-1)7.

Arithmetic Progression (AP) is a sequence of numbers in which the difference between the two consecutive numbers is always the same. Each number in the sequence is called a term of the progression. It is a type of sequence where the difference between consecutive terms is constant.

The given expression is an arithmetic progression (AP), in which the common difference between consecutive terms is 7. An AP is a sequence of numbers where each term after the first is formed by adding a fixed value to the preceding one.

The first term of the AP is given as a_1=-54 and the common difference (d) is 7. Thus, the nth term of the given AP can be found using the formula a_n = a_1 + (n-1)d. Substituting the values in this formula, we get a_n = -54 + (n-1)7.

Therefore, the nth term of the given AP is a_n = -54 + (n-1)7.

For example, if n = 10, then the 10th term of the given AP is a_10 = -54 + (10-1)7 = -54 + 63 = 9.

In general, the nth term of an AP with the first term a_1 and the common difference d is given by a_n = a_1 + (n-1)d.

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The nth term of the given AP is [tex]a_n[/tex] = -54 + (n-1)7. The nth term of an Arithmetic Progression with the first term [tex]a_1[/tex] and the common difference d is given by [tex]a_n[/tex] =    [tex]a_1[/tex]  + (n-1)d.

It is a sequence of numbers in which the difference between the two consecutive numbers is always the same. Each number in the sequence is called a term of the progression.

The given expression is an arithmetic progression (AP), in which the common difference between consecutive terms is 7.

The first term of the AP is given as [tex]a_1[/tex] =-54 and the common difference (d) is 7.

Thus, the nth term of the given AP can be found using the formula

[tex]a_n[/tex] =  [tex]a_1[/tex] + (n-1)d.

Substituting the values in this formula, we get

[tex]a_n[/tex] = -54 + (n-1)7.

Therefore, the nth term of the given AP is

[tex]a_n[/tex] = -54 + (n-1)7.

In general, the nth term of an AP with the first term [tex]a_1[/tex] and the common difference d is given by [tex]a_n[/tex] =  [tex]a_1[/tex]  + (n-1)d.

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Question:

Find the nth term by using the given data.

[tex]a_1[/tex] =-54 ; [tex]a_n[/tex] = [tex]a_(n-1)[/tex] +7

From the given data, the probability of Z less than 1.56, greater than 1.56, between 1.56 and 1.81 and less than 1.56 or greater than 1.81 is 0.9406, 0.0359, 0.0235 and 0.9765 respectively.

a. From the cumulative standardized normal distribution table, we can look up the value 1.56 in the left column and find the corresponding value of 0.9406 in the intersecting row. Therefore, the probability that Z is less than 1.56 is 0.9406.

b. From the cumulative standardized normal distribution table, we can look up the value 1.81 in the left column and find the corresponding value of 0.9641 in the intersecting row. Since we want the probability that Z is greater than 1.81, we subtract this value from 1 to get 1 - 0.9641 = 0.0359 (rounded to four decimal places as needed). Therefore, the probability that Z is greater than 1.81 is 0.0359.

c. To find the probability that Z is between 1.56 and 1.81, we need to subtract the probability that Z is less than 1.56 from the probability that Z is less than 1.81. From the table, we know that the probability that Z is less than 1.56 is 0.9406 and the probability that Z is less than 1.81 is 0.9641. Therefore, the probability that Z is between 1.56 and 1.81 is 0.9641 - 0.9406 = 0.0235 (rounded to four decimal places as needed).

d. The probability that Z is less than 1.56 or greater than 1.81 is the sum of the probabilities that Z is less than 1.56 and Z is greater than 1.81, since these events are mutually exclusive. From parts (a) and (b), we know that the probability that Z is less than 1.56 is 0.9406 and the probability that Z is greater than 1.81 is 0.0359. Therefore, the probability that Z is less than 1.56 or greater than 1.81 is 0.9406 + 0.0359 = 0.9765 (rounded to four decimal places as needed).

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Answer: One third

Step-by-step explanation: If you blow up a third of the balloons then you've blown 4 up because 12 divided by 3 is 4. Then you add the 5 balloons your friend blew up leaving you with 9 blown-up balloons in total. 9 blown-up balloons out of 12 is 2 thirds of the balloons leaving you with only one-third left to blow up.

Answer:

1/4

I hope this helps you <3