The exam results for the students in a class are shown in the frequency tree below

Answer:

Your answer should be: TRUE FALSE TRUE FALSE

I’m pretty sure it’s y = 0x+4

4500(1+0.055)^24

4500(1.055)^24

= 16,265.65456755

Answer: It should be 56

Step-by-step explanation:

first we know for 40 tank-tops with logos can be finished in 5 hours, but we need to know how many shirts can be printed in 7 hours.

First we have x as 40 and y as 5. How many times can 5 go into 40?.. 8 times. So now we have 8. 8 x 7=56

X=56

Y=8

I hope this helps! Just to make sure it may not be correct, very sorry if it didn't work! Have a nice day/night!

-GreenteaStudys

Let's call the time you drove "x" and the time your wife drove "y". We know that the sum of the two times is 20 hours:

x + y = 20

We also know the distance traveled during each part of the trip. The first part of the trip was 55x miles, and the second part of the trip was 65y miles. The total distance of the trip was 1170 miles:

55x + 65y = 1170

We can use the first equation to solve for x in terms of y:

x = 20 - y

We can then substitute this expression for x in the second equation:

55(20 - y) + 65y = 1170

Simplifying and solving for y:

1100 - 55y + 65y = 1170

10y = 70

y = 7

So your wife drove for 7 hours. We can use the first equation to find your driving time:

x + 7 = 20

x = 13

So you drove for 13 hours.

Answer:

13 hours

Step-by-step explanation:

The other side lengths of the triangle will be 24 and 26 units.

How to calculate the side?

The shortest side of a triangle similar to triangle XYZ is 20 units long and the shortest side on the other. triangle is 10. This means the proportion is [tex]\frac{20}{10}[/tex]=2

The other sides will be:

⇒12 × 2 = 24

⇒13 × 2 = 26

Therefore, the sides are 24 and 26 respectively.

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Answer: 5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

First do 18-2 which is 16
Then do 16 divided by 8 which is 2

Right now the equation is 8 - 1 - 2

Then we minus 8 by 1 which is 7
and then 7 - 2 which is 5
So then our final answer is 5

Answer:

a^2 -5a + 19

Step-by-step explanation:

(2a^2 - 5a + 10) - (a^2 - 9)

= (2a^2 - 5a + 10) - a^2 + 9 [Distribution]

= a^2 -5a + 19

The given trigonometric function Cosec 2A + cot 4A = cot A - cosec 4A​ can be proved using the properties of the trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given that,

Cosec 2A + cot 4A = cot A - cosec 4A​

Taking the LHS

= Cosec 2A + cot 4A

= 1 / sin 2A + cos 4A / sin 4A

To take the LCM we multiply and divide the first term by 2cos 2A:

= 2cos 2A / 2 sin 2A cos 2A + cos 4A/ sin4A

= 2cos 2A / sin 4A + cos 4A/ sin4A

= 2 cos 2A + 2 cos² A -1 / Sin 4A

= 2 cos 2A (1 + cos 2A) - 1 / sin 4A - 1/ sin 4A

=  2cos 2A 2cos² A / 2 sin 2A cos 2A - cosec 4A

= cos A / sin A - cosec 4A

= cot A - cosec 4A

Hence proved.

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The amount of money company B charges more for x miles than company A is 4¢

let

Number of miles= x

Company A:

35.50 + 9x

This means company A charges 9¢ per mile

Company B:

55.50 + 13x

This means company B charges 13¢ per mile

The amount of money company B charges more for x miles than Company A = 13¢ - 9¢

= 4¢

Therefore, company B charges 4¢ more than company A for x miles.

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Answer:

x = 56°

Step-by-step explanation:

x and 124° are a linear pair and sum to 180° , that is

x + 124° = 180° ( subtract 124° from both sides )

x = 56°

Answer:

56°

Step-by-step explanation:

angle on a straight line = 180°

124° + x =180°

x = 180° - 124

x = 56°

The average speed for the whole journey is 72.5 km/h. The result is obtained by using the formula for the average speed.

Average speed is the overall speed of a moving object during a given amount of time. It can be expressed as

Avg speed = Total distance covered / Total time taken

The speed itself is

v = s/t

Where

Orla drove 155 km in 2 hours. Then, she drove 48 km at a speed of 60 km/h. Find the average speed for the whole journey!

We have

The time taken in the second journey is

v₂ = s₂/t₂

60 = 48/t₂

t₂ = 48/60

t₂ = 0.8 h

The average speed will be

= total distance covered / total time taken

= (s₁ + s₂)/(t₁ + t₂)

= (155 + 48)/(2 + 0.8)

= (203)/(2.8)

= 72.5 km/h

Hence, the whole journey will have the average speed of 72.5 km/h.

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To find the missing coordinates of the points A and B [1], you can use the equation c -3/7x + 3 = y. Plugging in the given x-coordinates for A and B, you can solve for their y-coordinates.

A: x = -2, y = -3 B: x = 9, y = 6

To find the slope of the line, you can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates for A and B, you can calculate the slope as m = (6 - (-3))/(9 - (-2)) = 9/11.

To further explore the topic, you can look into how to graph equations in slope-intercept form, as well as how to find equations of parallel and perpendicular lines. You can also learn how to use the equation of a line to calculate distances between points, and how to calculate the midpoint of a line segment.

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Answer:

w=6, L=24

Step-by-step explanation:

let the width be x,

then, L=4x

Perimeter=2(l+w)

                =2(4x+x)

the new dimensions,

perimeter=2(l+w)

           74 =2(4x+5+x+2)

               =2(5x+7)

               =10x+14

       10x=74-14

       10x=60

          x=60/10

           x=6

Therefore, The width is 6 cm

L=4x

 =4(6)

 =24

Therefore the length is 24 cm

Answer:80

Step-by-step explanation:

Twenty, four times is 80, turn the problem into different segments like 20+20+20+20=80

The greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

Let's call the total distance that Oleg jogged z. Then z = 2x.

The total distance that Oleg bicycled was 30 - z - 2. Let's call this distance w. Then w = 30 - 2x - 2.

Since Oleg bicycled for 2 hours, the speed that he bicycled was w / 2. So, w / 2 = y.

Substituting the expressions for z and w, we have:

y = (30 - 2x - 2) / 2.

Since y must be the greatest possible speed that Oleg could have bicycled that day, x must be the smallest possible value.

Since Oleg jogged for 2 hours, the minimum value of x is 2 / 2 = 1.

Substituting x = 1 into the expression for y, we have:

y = (30 - 2 * 1 - 2) / 2 = (26) / 2 = 13.

So, the greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

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The table is filled as follows

x    P(x)   x P(x)   (x - μ)²

3    3       9          961

4    7      28         900

5   22    110         841

6   60    360       784

7   85    595       729

8   32    256       676

9   8      72          625

mean, μ = 34.05

variance = 919.33

standard deviation = 30.32

The mean is calculated using the information provided as follows

= summation of (x P(x) ) / summation of x

= 1430 / 42

=34

The variance is solved by the formula

= summation of (x - μ)² / (n - 1), where n = 7

= 5516 / (7 - 1)

= 5516 / 6

= 919.33

the standard deviation is solved using the formula

= √variance

= √919.33

= 30.32

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The time it will take both of them to pick enough apples is 7.27 minutes.

The time it will take both of them to pick enough apples is calculated as follows;

Let the time = t ( minutes )

3t  + (5/2)t = 40

3t + ( 5t / 2 ) = 40

multiply through by 2

6t + 5t = 80

11t = 80

divide through by 11

t = 80 / 11

t = 7.27 minutes

Thus, the time to pick enough apples depends on the rate at which they are picking the apples.

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Let x be the amount of money invested in the 9% fund. Then the amount invested in the stock is $32,000 - x. The profit from the 9% investment is 0.09x and the loss from the stock investment is -0.03(32000 - x).

What exactly does compounding mean?

Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

The overall net profit was $2,040, so we can set up the following equation to solve for x:

0.09x - 0.03(32000 - x) = 2040

Expanding the second term,

0.09x - 9600 + 0.03x = 2040

Combining like terms,

0.12x - 9600 = 2040

Adding 9600 to both sides,

0.12x = 1640 + 9600

Simplifying,

0.12x = 11240

Dividing both sides by 0.12,

x = 93, 666.67

So, the amount invested in the 9% fund is $93,666.67 and the amount invested in the stock is $32,000 - $93,666.67 = $-61,666.67.

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The value of the other side is 9. 7 m

Using the Pythagorean theorem stating that the square of the hypotenuse side is equal or equivalent to the sum of the squares of the other two sides.

From the information given, we have that;

This is represented as;

12² = 7² + x²

Find the value of the squares, we get;

144 = 49 + x²

collect like terms. we get;

x² = 144 - 49

subtract the values, we have;

x² = 95

Find the square root of both sides

x = 9. 7 m

Hence, the value is 9. 7 m

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Clothilde thinks that going to the circus costs her less than Naomie and she is right

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let the cost of 1 child be "c"

Let the cost of 1 adult be "a"

Given a=1.5c

Clothilde buys a ticket for her, for her

husband and for her 2 children.

=> She buys for 2 adults and 2 children

price = 2a+2c

Substitute  a=1.5c

price = 2(1.5c )+2c

        = 3c+2c

        = 5c

Naomie

buys tickets for her 4 children and herself.

=> She buys for 1 adult and 4 children

price = a+4c

Substitute  a=1.5c

price = 1.5c +4c

         = 5.5c

5c  < 5.5c

So, Clothilde thinks that going to the circus costs her less than Naomie and she is right

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the difference of their volumes of the boxes is 2lh+2bh+2lb+4b+4l+4h+8.

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

Let the 1st box have length l, width b and height h.

So the 2nd box will have l+2, b+2 and h+2.

volume of 1st box is l*b*h.

volume of 2nd box is (l+2)*(b+2)*(h+2)= (lb+2l+2b+4)(h+2)

=lbh+2lh + 2bh+4h+2lb+4l+4b+8

The difference of their volumes = 2lh+2bh+2lb+4b+4l+4h+8

Hence the difference of their volumes of the boxes is 2lh+2bh+2lb+4b+4l+4h+8.

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Answer:

8 posters

Explanation:

first you need to find how many he posted the first week. You do this by multiplying 72 by 1/3, or 72/3. That is 24. Then, you need to subtract that amount, 72-24 is 48. Then, you need to figure out how many he posted the second week. To do that, you need to figure out what 1/6 of 48 is first. So you would need to divide 48 by 6, which equals 8. So if John posted 5/6 of 48, you then need to multiply 8 by 5, equaling 40. If john posted 40 of his 48, then 48-40 is 8, meaning he has 8 posters to post.

Answer:

306

Step-by-step explanation:

Let's call the number of fiction books "f" and the number of non-fiction books "n". From the given information, we know that the ratio of fiction books to non-fiction books is 5:2 and the total number of books is 1421, so we can write the following equation:

f + n = 1421

Since the ratio of fiction books to non-fiction books is 5:2, we can write:

f/n = 5/2

We can cross-multiply to solve for f:

f = (5/2) * n

Substituting this expression for f into the first equation:

(5/2) * n + n = 1421

Expanding the left side:

(5/2 + 2/2) * n = 1421

Simplifying the left side:

(5 + 2)/2 * n = 1421

(7/2) * n = 1421

Dividing both sides by (7/2):

n = 1421 * 2/7

n = 204

So there are 204 non-fiction books and 5/2 * 204 = 204 * 5/2 = 102 * 5 = 510 fiction books.

The difference between the number of fiction books and non-fiction books is 510 - 204 = 306. So there are 306 more fiction books than non-fiction books in the library.

Step-by-step explanation:

If the ratio of fiction and non-fiction books are 5:2. Therefore that means that the total books were divided into 7 parts and the fiction books took 5 parts while the non-fiction books took two parts.

To get the number of fiction and non-fiction books we first add the ratio

[tex]5 + 2 = 7[/tex]

So that means that 7 = 1421

After adding the ratio we now take

The total parts that the books took as the numerator and the total of the ratio as the denominator, and multiply the fraction by the total number of books which is 1421

[tex] \frac{5}{7} \times 1421 = number \: of \: fiction \: books[/tex]

[tex] \frac{2}{7} \times 1421 = number \: of \: non - fiction \: books[/tex]

let's work out each fraction separately

[tex] \frac{5}{7} \times 1421 = \frac{7105}{7} [/tex]

[tex] \frac{7105}{7} = 1015[/tex]

[tex] \frac{2}{7} \times 1421 = \frac{2842}{7} [/tex]

[tex] \frac{2842}{7} = 406[/tex]

To get the answer to the question we subtract the number of non-fiction books from the number of fiction books

[tex]1015 - 406 = 609[/tex]

Answer:

n = -3

Step-by-step explanation:

3n - 15 = 7n + n

3n - 15 = 8n

3n - 8n = 15

-5n = 15

n = -3

Y=2x+1 is an equation used in mathematics to calculate the relationship between two variables, X and Y.

An equation is a physical and mathematical statement that describing physical phenomena are describe the relationship between different physical quantities it typically consists of two or more variable which are simple representing physical quantity and then equal sign the variable may be quantity such as force velocity or energy.

This equation is a linear equation, meaning it is a straight line when graphed. It is a very basic equation and one of the most commonly used equations.

To use this equation, you will need to know the value of X. Once you have determined the value of X, you can plug it into the equation to calculate the value of Y. For example, if X=3, then the equation would look like this: Y=2(3)+1, which equals 7. Therefore, when X=3, Y=7.

The equation Y=2x+1 is often used in a variety of math problems, such as determining the slope of a line, calculating the area of a triangle, and finding the equation of a circle. It is also used in physics to calculate velocity or acceleration. As you can see, this equation is quite versatile and can be used in a variety of situations.

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Answer:

10.8s

Step-by-step explanation:

120÷11.1= 10.8s (to 3 s.f.)

Answer:

Step-by-step explanation:

(-1, 6/5) = logbase4(5x^2) etc

only 5 = ln(x+5) = ln (x-1) + ln(x+1)

only 3 = log(x-1) etc.

(-1, 5) = e^x^2 = e^4x+5

The equation involving an integral expression that can be used to find the value of k is π integration [(k - x²)² - (k - 4)²] dx.

We need to perform integration to find the value of k which will have same volume. Thus, tos over the question the clarity of concepts of volume of any area and integration is required.

The graph representing the mentioned situation is attached in the picture. So, now, writing the expression -

π integration [(k - x²)² - (k - 4)²] dx

Remember tha the integration limit in the mentioned equation will be -2 to 2.

On solving we will get the volume 256π/5.

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The comp question is -

The shaded region, R, is bounded by the graph of y = x² and the line y = 4, as

shown in the figure.

There exists a number k, k 4 , such that when R is revolved about the line y = k , the resulting solid has the same volume as the solid in part (b).

Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.