The triangular cross section of a prism is an isosceles right-angled triangle.


The volume of the prism is 203 cm


Use approximations to estimate the value of y.


You must show your working.


Your final line should say, Estimate for y is.


y cm


4. 13 cm


y cm

Answer:

Honestly, I feel you. I've been there. Being the new kid not also brings problems related to your character, but to your feelings. I totally think you're smarter than all your other classmates! :D. Keep being yourself and never let them bring you down. If you fall down and don't feel like getting back up, remember this message!

- Benji :)

Answer:

They may not know very much about you and assume things about you based on things they see and perceive that are separate from the grades that you get and/or they think you aren't intelligent on something to do with your emotions/behavior and/or someone or some amount of people have developed something against you, these are just potential situations.

Step-by-step explanation:

Regardless of what the reason is, move forward with what you do and meet people who enjoy your company. Those who treat you badly are not worth your time. Best of luck!

Answer:

13 ocicats

Step-by-step explanation:

Here, we are told that an Ocicat eats 3/5 pounds of food per day.

Now, we have a bag of 19 1/2 pound of food and we want to know the number of ocicats this will feed

What we just need to do is to divide the weight of the bag by the amount in pounds that can feed a single ocicat

Thus, we have;

19 1/2 divided by 3/5

= 39/5 divided by 3/5

= 39/5 * 5/3

= 13 Ocicats

Answer:

it will option A it is correct answer

Answer:

Step-by-step explanation:327.94x100/655.88=50%

Answer:

Step-by-step explanation:

The volume of the three tennis balls combined is approximately 4.88 cubic inches. The volume of the packaging cylinder is approximately 50.33 cubic inches. Thus, the volume of the three tennis balls is about 9.7% of the volume of their packaging cylinder.

To calculate this, we can use the formula for the volume of a sphere (V = 4/3 x π x r3) and the formula for the volume of a cylinder (V = π x r2 x h).

The radius of each tennis ball is half the diameter, or 1.35 inches. So, the volume of each tennis ball is 4/3 x π x (1.35)3 = 4.88 cubic inches.

The radius of the cylinder is the same as the diameter of each tennis ball, or 2.7 inches. The height of the cylinder is 8.1 inches. So, the volume of the cylinder is π x (2.7)2 x 8.1 = 50.33 cubic inches.

The volume of the three tennis balls is 4.88 x 3 = 14.64 cubic inches. The volume of the packaging cylinder is 50.33 cubic inches. Thus, the volume of the three tennis balls is 14.64 ÷ 50.33 = 0.097 = 9.7% of the volume of their packaging cylinder.

i. Vectors u and w are orthogonal.

ii. The two vectors orthogonal to v = √(2, -3) are u = (3, 2) and w = (-2, 3).

iii. The two unit vectors orthogonal to 7 are u = (1, -1) / √2 and w = (1, 1) / √2.

i. To show that vectors u = (a, b) and w = (-b, a) are orthogonal, we need to demonstrate that their dot product is zero.

The dot product of u and w is given by:

u · w = (a, b) · (-b, a) = a*(-b) + b*a = -ab + ab = 0

ii. To find two vectors orthogonal to vector v = √(2, -3), we can use the result from part i.

Let's denote the two orthogonal vectors as u and w.

We know that u = (a, b) is orthogonal to v, which means:

u · v = (a, b) · (2, -3) = 2a + (-3b) = 0

Simplifying the equation:

2a - 3b = 0

We can choose any values for a and solve for b. For example, let's set a = 3:

2(3) - 3b = 0

6 - 3b = 0

-3b = -6

b = 2

Therefore, one vector orthogonal to v is u = (3, 2).

To find the second orthogonal vector, we can use the result from part i:

w = (-b, a) = (-2, 3)

iii. To find two unit vectors orthogonal to 7, we need to consider the dot product between the vectors and 7, and set it equal to zero.

Let's denote the two orthogonal unit vectors as u and w.

We know that u · 7 = (a, b) · 7 = 7a + 7b = 0

Dividing by 7:

a + b = 0

We can choose any values for a and solve for b. Let's set a = 1:

1 + b = 0

b = -1

Therefore, one unit vector orthogonal to 7 is u = (1, -1) / √2.

To find the second unit vector, we can use the result from part i:

w = (-b, a) = (1, 1) / √2

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Answer:

time = 70 minutes

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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The diagrams are shown in the solution.

A rectangle is a quadrilateral with all four interior angles 90°.

(1) The rectangle diagram of 1/2 × 5/6 can be drawn by converting the fractions into integers.

The dimension can be written as:

1/2 : 5/6

Multiply the ratio by 6:

3 : 5

Hence, the rectangle of  1/2 × 5/6 is proportional to 3×5.

The diagram is shown.

Similarly, the diagrams of other rectangles are shown.

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Answer:

The first blank is $640.30

The second blank is 670

Step-by-step explanation:

The discrete probability distribution is discussed above.

Given is discrete probability distribution.

        \(${\displaystyle P(X\in E)=\sum _{\omega \in A}p(\omega )\delta _{\omega }(E)} =\)        

       \(${\displaystyle P(X\in E)=\int _{E}f(x)\,dx=\sum _{\omega \in A}p(\omega )\int _{E}\delta (x-\omega )=\sum _{\omega \in A\cap E}p(\omega )}\)

Therefore, the discrete probability distribution is discussed above.

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Answer:

Step-by-step explanation:

5= -1/3(6) + b

5= -2 +b

y= -1/3x+7

Answer: 95,400?

i think this is the closest answer

a) In an Excel Data Model, the foreign key column is typically chosen in the lookup table.

b) A PivotTable in Excel is called a "PivotTable" because it allows you to pivot or reorganize your data dynamically.

a) The lookup table is a table that contains the primary key values from the master table and the corresponding foreign key values that are used to establish relationships between the tables. This table is commonly used to create relationships between different tables in the data model.

b) A PivotTable is called a PivotTable because it allows you to pivot or rotate the data in order to view it from different perspectives. The term "pivot" refers to the action of changing the arrangement or structure of the data.

While a PivotTable offers filtering capabilities and can be connected to data in different sheets or sources, the fundamental aspect that distinguishes it is its ability to pivot or rotate the data to provide flexible analysis and visualization options.

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Answer: 45

Step-by-step explanation:

3(-2m + 5) -6(-4m - 2) =

-6m + 15 + 24m + 12=

18m + 27

18= a 27= b 27 + 18= 45

The value of the expression a + b is 45.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

First, we can simplify the expression using the distributive property:

3(-2m + 5) - 6(-4m - 2) = -6m + 15 + 24m + 12

Combining like terms, we get:

18m + 27

So, a = 18 and b = 27, which means:

a + b = 18 + 27 = 45

Therefore,

The value of a + b is 45.

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Answer:

B

Step-by-step explanation:

24 - 7 = 17.

If there are 365 days in a year, sometimes 366, you would multiply 17 by 365 or 366.

17 x 365 = 6205

17 x 366 = 6222.

if 3/4 years aren't leap year, then there answer would be B, 365.

Please mark brainliest! I had to make a new account. Hope this helps! <3

Answer:

there are 2 apples in the basket

there are 10 banana in the basket

Step-by-step explanation:

According to the Question,

let x for apple And y for banana So, x+y=12---Equation 1

Thus, 5x+7y=80 ----Equation 2

Now, (Equation 1) × 5 Subtract with (Equation 2) We get,

2y = 20 ⇒ y=10 (there are 10 banana in basket)

5x+70=80 ⇔ x=2(there are 2 apples in basket)

The price of the service before the tip will be equal to $35.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The total price of the service will be calculated as:-

20%   =   $7

10%   =    7/2

100%  =   10 x 7/2

100%    =   $35

Therefore the price of the service before the tip will be equal to $35.

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The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)

To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.

From the given information, we can observe that Lindsey's scores are increasing at the same rate.

This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.

Let's denote the first term as a₁ = 67 and the common ratio as r.

Recursive Formula:

In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:

aₙ = aₙ₋₁ \(\times\) r

For Lindsey's scores, the recursive formula would be:

aₙ = aₙ₋₁ \(\times\) r

Explicit Formula:

The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.

The explicit formula for a geometric sequence is:

aₙ = a₁ \(\times r^{(n-1)\)

For Lindsey's scores, the explicit formula would be:

aₙ \(= 67 \times r^{(n-1)\)

In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.

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Answer:

Step-by-step explanation:

\(f^-1\)\(\sqrt[3]{1/-1+x | + | 2x/-1+x}\)

Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: \(SA=2\pi rh+2\pi r^2\)

Volume: \(V=\pi r^2h\)

Therefore, the height of a cylinder given its volume would be \(h=\frac{V}{\pi r^2}\), thus:

\(SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2\)

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

\(\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r\)

\(0=-\frac{800}{r^2}+4\pi r\)

\(0=800\pi+4\pi r^3\)

\(-800\pi=4\pi r^3\)

\(-200=r^3\)

\(r\approx5.848\)

If \(0If \(r>5.848\), then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is \(r=5.848cm\), making the minimum height \(h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm\).

In conclusion, the 2nd option is correct.

Answer:

X = 35

Step-by-step explanation:

Since the line is crossing two parallel lines the measurements are equal then you solve for X.

2X + 20 = 3X - 15

-2X           -2X

20 = X - 15

+15      +15

35 = X

Answer:

x=35

Step-by-step explanation:

The expressions are corresponding angles which are congruent.

Set the two equations equal to each other.

2x+20=3x-15

Add and subtract like terms

35=1x

Divide:

35/1=35

X=35

Hope this helps! :)

Correct me if I'm wrong!

The average population between year 1 and year 10 is approximately 55,555 people.

To find the average population between year X and year Y, we need to first calculate the total population increase over that time period. We can do this by subtracting the population in year X from the population in year Y.

Population increase = Population in year Y - Population in year X

Once we have the population increase, we can divide it by the number of years between X and Y to get the average annual population increase.

Average annual population increase = Population increase / (Y - X)

Finally, to find the average population between year X and year Y, we need to add the average annual population increase to the population in year X.

Average population = Population in year X + Average annual population increase

For example, if the population of a city is expected to be 100,000 people after 10 years, and we want to find the average population between year 1 and year 10, we would do the following:

Population in year 1 = X = 50,000 (let's say)
Population in year 10 = Y = 100,000
Population increase = 100,000 - 50,000 = 50,000
Number of years between X and Y = 10 - 1 = 9
Average annual population increase = 50,000 / 9 = 5,555.56 (rounded)
Average population = 50,000 + 5,555.56 = 55,555.56 (rounded)

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The average population of the city between the starting year and 10 years later is estimated to be 625,000.

The average population of a city between two specific years, we will need to use the formula for calculating the arithmetic mean.

The sum of all the values divided by the number of values.

We will need to sum up the populations of the city for each year between the two given years and divide the result by the number of years included.
Let us assume that the population of the city in the year we are starting with is "P1" and the population after "n" years is "P2".

Therefore, the average population can be calculated as:
\(Average Population = (P1 + P2) / 2\)
The exact population figures for each year between the two given years, we will have to use an estimated population growth rate to make the calculation.

We can use the formula:
\(P2 = P1 \times (1 + r)^n\)
where "r" is the estimated annual growth rate and "n" is the number of years between the two given years.
Let's assume that the population of the city in the starting year is 500,000 and the estimated population after 10 years is 750,000. Using the formula, we can calculate the estimated annual growth rate as:
\(r = (P2 / P1)^{(1/n)} - 1   = (750,000 / 500,000)^{(1/10)} - 1   = 0.0473 or 4.73\%\)
The estimated annual growth rate, we can calculate the average population between the two given years using the formula:
\(Average Population = (P1 + P2) / 2 = (500,000 + 750,000) / 2 = 625,000\)

It is important to note that this is just an estimate based on the assumed growth rate, and the actual population may vary from this calculation.

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The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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Answer:

look at the photo

...................................

Answer:

hope it help u

Step-by-step explanation:

\(volume \: of \:triangular \: prism = \frac{1}{2} b \times h \times h \\ = \frac{1}{2} \times 9 \times 9 \times 12 \\ = 486ft {}^{3} \)

Answer:

positive

Step-by-step explanation:

x^59/2.3x × 4/5 = x^58 × 10/23 × 4/5 = x^58 × 8/23

x has even power so, it will have positive sign regardless of value of x

The nth term test is a mathematical method used to determine if a sequence converges or diverges. It helps to find the behavior of the sequence as n approaches infinity.

Here's how to do the nth term test:

Find the nth term formula for the given sequence.

Calculate the limit of the nth term as n approaches infinity.

Based on the value of the limit, determine if the sequence converges or diverges:

If the limit is finite and non-zero, the sequence diverges.

If the limit is finite and zero, the sequence converges to zero.

If the limit is infinite or does not exist, the sequence diverges.

The nth term test is important because it provides a quick and easy way to determine the behavior of a sequence, without having to calculate all the terms.

It's important to understand the nth term test and how to apply it, so that you can analyze the behavior of sequences in mathematics and other related fields.

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Answer:

x = 5

y = 37.5

We can graph the two equations to find our solution.

-> See attached

-> They intersect at point (5, 37.5) so this is our answer.

-> Coordinate points are in terms of (x, y)

Answer:

The answer is D

Step-by-step explanation:

Answer:

\((2a -b)^2\)

Step-by-step explanation: