A meteorologist found that the rainfall in Newberg during the first half of the month was 1/5 of an inch. At the end of the month, she found that the total rainfall for the month was 1/2 of an inch. How much did it rain in the second half of the month?

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 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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The value of k depends on the specific functions f and g and their growth rates. The growth factor is a measure of how quickly a function grows relative to another function. To determine the value of k, you would need to compare the growth rates of f and g.

Here's how you can do to finding the value of k:

        n² = k * n

        n = k

This is just a simple example, and the specific value of k will depend on the growth rates of the specific functions you're comparing.

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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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Answer:

Step-by-step explanation:

a) The value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam, is 3/5. This is because out of the 5 students, 3 (Ashley, Brayden, and Carmen) got a 5 on the AP Statistics exam.

b) The 10 possible simple random samples of size n = 2 are:

Ashley, Brayden; P = 2/2 = 1

Ashley, Carmen; P = 2/2 = 1

Ashley, Dale; P = 1/2 = 0.5

Ashley, Eve; P = 1/2 = 0.5

Brayden, Carmen; P = 2/2 = 1

Brayden, Dale; P = 1/2 = 0.5

Brayden, Eve; P = 1/2 = 0.5

Carmen, Dale; P = 1/2 = 0.5

Carmen, Eve; P = 1/2 = 0.5

Dale, Eve; P = 0/2 = 0

c) To create the dotplot for the sampling distribution of p:

Label the number line with 0, 0.5, 1

For each sample proportion calculated, place a dot above the corresponding value on the number line

Repeat this process for all sample proportions

d) Yes, the sample proportion is an unbiased estimator of the population proportion. This means that on average, the sample proportion will equal the population proportion. In other words, the mean of the sampling distribution of the sample proportion will equal the population proportion.

The volume of each marble in a 26 liter glass tank is 12.

The tank's volume is listed as 26.

The tank requires 20.9 liters of water to fill when 85 marbles are placed inside.

So the volume of 85 marble

= 26-20.9 = 5.1

So, volume of each marble

= 5.1/85 = 0.06

Therefore, the volume that will be covered if William wishes to use 200 marbles is:

200*0.6 = 12

Therefore, the volume of marbles in a 26 litre tank is equal to 12

Water will therefore be needed to fill the tank.

=  26 - 12 = 14

Therefore, The volume of each marble in a 26 liter glass tank is 12.

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Complete question:

William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble? How much water is necessary if William uses 200 marbles?

Answer:

n = -3

Step-by-step explanation:

3n - 15 = 7n + n

3n - 15 = 8n

3n - 8n = 15

-5n = 15

n = -3

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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Based on the properties of a rhombus, the measure of each numbered angle is:

m<1 = 36°

m<2 = 72°

m<3 = 72°

m<4 = 72°

m<5 = 36°

Using the properties mentioned above, we can solve for the numbered angles as explained below:

ED and FG are parallel, therefore, m<3 = 72° (alternate interior angles)

m<4 = 72° [bisected angles of a rhombus by the diagonal]

m<2 = m<4 (alternate interior angles)

m<2 = 72°

m<1 = 180 - m<2 + 72 [sum of a triangle]

Substitute:

m<1 = 180 - 72 + 72

m<1 = 36°

m<5 = m<1 [opposite angles are equal in a rhombus]

m<5 = 36°

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Maria and Gabriella each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Maria spent $114 on 10 ft² of grass sod and 9 geraniums. Gabriella spent $90 on 5 ft² of grass sod and 10 geraniums. What is the cost of one ft² of grass sod and the cost of one geranium?

Answer:

$11/ft^2 of grass, $12/geranium

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

Slope = (y2 - y1) / (x2 - x1)

Plugging in the given points, we get:

Slope = (9 - (-7)) / (7 - (-3))

= 16 / 10

= 1.6

So the slope of the line passing through (-3, -7) and (7, 9) is 1.6.

Answer:

m = 8/5

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

(-3,-7) and (7,9)

We see the y increase by 16 and the x increase by 10, so the slope is

m = 16/10 = 8/5

So, the slope is 8/5

The equation that shows the height of the tree is 42.5 = 15x + 5

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let y represent the height of the small tree and x represent the average number of feet the tree grew each month. Hence:

A small tree was planted at a height of 5 feet. Hence, b = 5.

The tree has been planted for 15 months, and is now 42.5 feet tall. This makes:

42.5 = 15x + 5

The equation is 42.5 = 15x + 5

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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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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.

I’m pretty sure it’s y = 0x+4

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

If you draw five cards at random from a standard deck of 52 cards, the probability that there are at least 4 distinct characters (letters or numbers) is 0.8406.

This probability is calculated using the combination formula. The formula states that the number of possible outcomes when selecting r items from a set of n is equal to n!/(r! (n-r)!). consider a deck of 52 cards, each with a unique letter or number. When selecting 5 cards at random, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters.

This is because if there are 4 distinct characters, there must be a fifth card with a character that has already been drawn. Therefore, the probability of there being at least 4 distinct characters is the same as the probability of there being exactly 4 distinct characters. Since there are 52 possible characters and we are selecting 5 cards, the probability can be calculated using the combination formula and is equal to 0.8406.

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Answer:

  C. Exactly one solution

Step-by-step explanation:

You want to know the number of solutions of the system of equations shown in the graph.

A solution to a system of equations is the set of points on a graph where all of the equations are satisfied simultaneously. For a system of two linear equations, it will be the point(s) where the lines intersect.

Here, the lines intersect at one point, so there is exactly one solution.

Answer:

Δ = 20

Step-by-step explanation:

let triangle be Δ , then

32 - Δ = Δ - 8 ( subtract 32 from both sides )

- Δ = Δ - 40 ( subtract Δ from both sides )

- 2Δ = - 40 ( divide both sides by 2 )

Δ = 20

Answer: To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the original line and use the point-slope form of a line.

The equation of the original line is 5y = 2x - 4, which we can rearrange to get y = (2/5)x - 4/5. The slope of this line is 2/5. The negative reciprocal of the slope is -5/2.

Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the slope -5/2 and the point (0, 7), we get:

y - 7 = -5/2 (x - 0)

y - 7 = -5/2 x

y = -5/2 x + 7

So the equation of the line perpendicular to 5y = 2x - 4 and passing through (0, 7) is y = -5/2 x + 7.

Step-by-step explanation:

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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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: 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

Answer:80

Step-by-step explanation:

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

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 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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