If the measure of angle ø is 3pie/4, which statements are true?
The measure of the reference angle is 45°.
cos (0) = √2
sin (0) = √2
The measure of the reference angle is 60°.
The measure of the reference angle is 30°.
tan (0) = 1

Answer:

30.7

Step-by-step explanation:

sin 71° = 29/ ladder length

so length = 29/ sin 71° = 30.7

Given,

The diagram of the circle is,

Required

The radius of the circle O.

The radius of the circle is the line segment that join the center of the circle to any point on the circle.

In the circle, AO, FO, EO, CO and DO joins the center of the circle to the point on the circle. Hence AO, FO, EO, CO and DO are radius.

So, option D( All of the listed choice ) is correct.

Answer:

x > 1

Step-by-step explanation:

Subtract 3 from both sides

8x + 3 - 3 > x + 10 - 3

Simplify

8x > x + 7

Subtract x from both sides

8x - x > x + 7 - x

Simplify

7x - 7

Divide both sides by 7

7x/7 > 7/7

Simplify

x > 1

Answer:

Ratio of sandwiches with white bread and brown bread is 10:3. Of the white sandwiches 2/3 are vegetarian, of the sandwiches that are brown half are vegetarian. What fraction of the sandwiches are vegetarian?

Step-by-step explanation:

Givens

The ratio between white bread and brown bread is 10:3, that is, for every 10 white bread, there are 3 brown bread.

2/3 of white sandwiches are vegetarian.

1/2 of brown sandwiches are vegetarian.

We know that white bread is represented by 10, and brown bread is represents by 3. So, 2/3 of 10 are vegetarians, and 1/2 of 3 are vegetarians. The sum of them is

2/3 of 10 are vegetarians = \(\frac{2}{3} \times 10 = \frac{20}{3}\)

1/2 of 3 are vegetarians = \(\frac{1}{2} \times 3 = \frac{3}{2}\)

\(=\frac{20}{3}+\frac{3}{2}\\\\=\frac{40+9}{6}\\\\=\frac{49}{6}\)

Therefore, 49/6 represents all the sandwiches which are vegetarian.

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

1. (2x + 1) (x - 4)

2. (3y +2 ) (y + 1)

3. (w - 3) (3w + 5)

4. (4s - 1) (s + 7)

5. (x + 5) (2x - 3)

Step-by-step explanation:

Lots of good articles on factoring quadratics - that is what this is called.

Answer:

1. (2x + 1) (x - 4) 

2. (3y +2 ) (y + 1)

3. (w - 3) (3w + 5)

4. (4s - 1) (s + 7)

5. (x + 5) (2x - 3)

Step-by-step explanation:

The data represented in the line plot is symmetric, with a range of 10. This means that the highest number of bouquets sold is 10, while the lowest number of bouquets sold is 1.

This indicates that the market offers a steady rate of sales, with a few special offers that increase the rate of sales.The range can be calculated using the formula Range = Maximum Value - Minimum Value. In this case, the range is 10 = 10 - 1.The symmetry can be seen by looking at the number of dots above each number. For the numbers 1, 6, 7, 9, and 10, there is one dot above each. For the number 8, there are three dots above it. This indicates that the number of bouquets sold over each number is almost the same, creating a balanced and symmetric distribution of the data. This suggests that the market offers steady sales, with a few promotional offers that increase the rate of sales.The data represented in the line plot is symmetric, with a range of 10. This means that the highest number of bouquets sold is 10, while the lowest number of bouquets sold is 1.

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Answer:

y = 34

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

you would add 4 to both sides and get

102=3y

then you would divide by three and get

34=y

Answer:

A. y = 3x + 3

Step-by-step explanation:

y=mx+b

b is the y-intercept (0,y) so lets start with that

We can see that the line touches 3 on the y intercept to get (0,3) meaning b=3

For the slope (m) I like to count rise over run so if we start from (0,3) and go up 3 over 1 we get 3/1 or 3 for m

The whole equation is y=3x+3

Answer:

1 acre is equal to 43,560 square feet.

Step-by-step explanation:

Hope it helped!

The answer for question 4 is C and the answer for question 5 is D.

The solution to the equation 30 = w/2 + 10 for w is w = 40

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

30=w/2 (fraction) +10

Express properly

So, we have the following representation

30 = w/2 + 10

Subtract 10 from both sides

This gives

w/2 = 20

Multiply through by 2

w = 40

Hence, the solution to the equation is w = 40

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Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

According to the question we have been given that,

Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours

First we will convert it into simple fraction which is

         \(16\frac{3}{4} = \frac{67}{4} \\\) hours

Number of consulting projects = 3

And Matilda spends same amount of time to each of the project.

To find the time she spend on each project is by using unitary method

that is,            3 projects = \(\frac{67}{4}\) hours

                      1 project = \(\frac{67}{4} / 3\)

                                     = 67/12

                                     = \(5\frac{7}{12}\) hours

Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

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The binomial expansions for the given expressions \((a-b)^{2} = 1a^{2} + 2ab + 1b^{2} and (a-b)^{3} = 1a^{3} + 3a^{2}b+ 3ab^{2} + 1b^{3}\) are related to the pascal's triangles 3rd and 4th rows.

An expression that has been raised to any finite power can be expanded using the binomial theorem known as binomial expansion. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem.

The triangle is named after the French mathematician and philosopher Blaise Pascal (1623–1662) who, in his dissertation Traité du triangle arithmétique (Treatise on Arithmetical Triangle), published the first structured study on the characteristics and uses of the triangle in 1653.

Pascal's triangle is a triangular array of numbers that can be used to help expand binomials. Each number in the triangle is the sum of the two numbers directly above it. The first row of the triangle consists of a single 1, and each subsequent row begins and ends with a 1, with the other numbers being the sum of the two numbers directly above it.

For example, the first few rows of Pascal's triangle look like this:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

To use Pascal's triangle to expand a binomial, you can start by writing out the terms of the binomial, with a blank space for each coefficient. Then, you can fill in the blanks using the numbers from Pascal's triangle. For example, to expand (a + b)^3, you can write out the terms like this:

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Then, you can fill in the blanks using the numbers from Pascal's triangle:

(a + b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3

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Answer:

The coefficients of the terms come from rows of the triangle.If the exponent is n, look at the entries in rown.

Step-by-step explanation:

Yes, there exists a function f that satisfies the given conditions: f(0) = 21, f(2) = 4, and f(9(x)) < 2 for all x.

f(x) = { 21, if x = 0
        4, if x = 2
        (2/9)x, otherwise

To construct this function, we can use piecewise linear functions. Let's define the function f as follows:
f(x) = { 21, if x = 0
        4, if x = 2
        g(x), otherwise
where g(x) is a function that satisfies the inequality f(9(x)) < 2 for all x.
Step 1: Define a function g(x) for the inequality f(9(x)) < 2 for all x:
Since we need f(9(x)) < 2 for all x, we can define g(x) as a linear function with a slope less than 2/9.
g(x) = (2/9)x
Step 2: Combine f(x) and g(x) to create the desired function:
Now, we can redefine our function f(x) by combining the conditions for f(0), f(2), and g(x):
f(x) = { 21, if x = 0
        4, if x = 2
        (2/9)x, otherwise
This function satisfies all the given conditions. It has f(0) = 21, f(2) = 4, and f(9(x)) = (2/9)(9x) = 2x < 2 for all x (since x can be any real number).

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Answer:

Sarim can iron 30shirts in 15 min

, therefore, for 1 shirt it will take

= 15/30 minutes = 1/2 minutes

therefore for 35 shirt it will take

= 35 * 1/2

Step-by-step explanation:

Hop it's helpful,

if it is helpful, the please follow me,,, (◠‿◕)

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Answer:

the line crosses the parabola at (-2,4) and (3,9)

Step-by-step explanation:

y=x^2

y=x+6

set them equal to each other

x^2=x+6, now set it equal to zero

x^2-x-6=0, now find the root

(x+2)(x-3)=0, the x=-2, and x=3; now substitute into any of the equation to find the points where graphs intercept

at x= -2, y=(-2)^2=4, so one point is (-2,4)

at x=3, y=(3)^2=9, so other point is (3,9)

the line crosses the parabola at (-2,4) and (3,9)

Answer: \(167.5\ in.^3\)

Step-by-step explanation:

Given

Height of paper cone \(h=10\ in.\)

Radius of cone \(r=4\ in.\)

The volume of the cone is given by

\(\Rightarrow V=\dfrac{1}{3}\pi r^2h\)

Insert the values

\(\Rightarrow V=\dfrac{1}{3}\times 3.14\times 4^2\times 10\\\\\Rightarrow V=167.5\ in.^3\)

Thus, the volume of the cone is \(167.5\ in.^3\)

Answer:

10.4

Step-by-step explanation:

m² =10²+3² = 109

so m =√109 = 10.4

Answer:

V = 960 cm^3

Step-by-step explanation:

Volume of a rectangular prism = L * W * H

V = 12 * 8 * 10

V = 960 cm^3

Answer:

d. 960 cm^3

Step-by-step explanation:

The formula for volume is length x width x height. To solve you have to multiply 12 by 8 by 10 to get 960

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Given :

Subtract 5 from each side :

Take the root on each side :

Hence, the values of x are :

\(x^2+5=6\\x^2=1\\x=1 \vee x=-1\)

Therefore, the probability that a randomly selected value is between 215.2 and 241 is approximately 0.1366.

To solve this problem, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

For the value of 215.2:

z1 = (215.2 - 193.6) / 43.1 = 0.4995 (rounded to 4 decimal places)

For the value of 241:

z2 = (241 - 193.6) / 43.1 = 1.0912 (rounded to 4 decimal places)

Now we can use a standard normal table or calculator to find the area under the standard normal curve between these two z-scores:

P(0.4995 < Z < 1.0912) = 0.1366

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Answer:

See below.

Step-by-step explanation:

top left

9 × 9 = 81

9/81 = 1/9

top right

9 × 9 = 81

36/81 = 4/9

bottom left

6/72 = 1/12

bottom right

12/72 = 1/6

Answer:

look at picture :) !

Step-by-step explanation:

There are approximately 0.976 grams of carbon (C) in the given sample of the carbohydrate (C9H11O6).

To find the number of grams of carbon (C) in the sample, we need to first determine the molar mass of the carbohydrate.

The molar mass of C is approximately 12.01 g/mol. The molar mass of H is approximately 1.01 g/mol, and the molar mass of O is approximately 16.00 g/mol.

The molar mass of the carbohydrate (C9H11O6) can be calculated as follows:

(9 * 12.01 g/mol) + (11 * 1.01 g/mol) + (6 * 16.00 g/mol) = 162.18 g/mol

Next, we can use the Avogadro's number (6.022 x 10^23) to determine the number of moles in the sample:

4.9 x 10^22 molecules / 6.022 x 10^23 molecules/mol = 0.0813 mol

Finally, we can calculate the mass of carbon in the sample by multiplying the number of moles by the molar mass of carbon:

0.0813 mol * 12.01 g/mol ≈ 0.976 g

So, there are approximately 0.976 grams of carbon in this sample.
There are approximately 0.976 grams of carbon (C) in the given sample of the carbohydrate (C9H11O6).

To find the mass of carbon in the sample, we first need to determine the molar mass of the carbohydrate. The molar mass of an element or compound is the mass of one mole of that substance. In this case, we have the formula C9H11O6, which indicates that the carbohydrate consists of 9 carbon atoms (C), 11 hydrogen atoms (H), and 6 oxygen atoms (O).

The molar mass of carbon is approximately 12.01 g/mol, hydrogen is approximately 1.01 g/mol, and oxygen is approximately 16.00 g/mol. To calculate the molar mass of the carbohydrate, we multiply the number of atoms of each element by their respective molar masses and sum them up.

Therefore, the molar mass of C9H11O6 is

(9 * 12.01 g/mol) + (11 * 1.01 g/mol) + (6 * 16.00 g/mol) = 162.18 g/mol.

Next, we can use the Avogadro's number (6.022 x 10²³) to determine the number of moles in the given sample. The given sample contains 4.9 x 10²²molecules of the carbohydrate. Dividing this by Avogadro's number gives us the number of moles:

4.9 x 10 molecules / 6.022 x 10^23 molecules/mol = 0.0813 mol.

Finally, we can calculate the mass of carbon in the sample by multiplying the number of moles by the molar mass of carbon: 0.0813 mol * 12.01 g/mol ≈ 0.976 g. Therefore, there are approximately 0.976 grams of carbon in the given sample.

In conclusion, the sample of the carbohydrate (C9H11O6) contains approximately 0.976 grams of carbon (C).

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Answer:

46.7

Step-by-step explanation:

Sp-Cp

$44-$30=$14

14/Cp x 100

= 14/30 x 100=46.66%

Ans= 46.7%

Proof

% x CP

46.66/100 x $30= $13.998

$13.998= SP-CP

Hope it helps

Jim's got profit percentage is 46.67%

Profit percentage is refer to "the amount of profit that has been incurred in terms of  percentage".

According to the question,

Jim buys a wardrobe for £30 which is cost price of wardrobe and he sells £44.

In order to find profit percentage we have to use formula.

Profit percentage = \(\frac{selling price - cost price }{cost price}\) × 100

= \(\frac{(44-30)}{30}\) × 100

= \(\frac{14}{30}\) × 100  

= 46.6667%  ≈ 47%

Hence, Jim's got profit percentage is 46.67%.

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Answer: Yes, it is

-When you're simplify 18/21 , You will devided both denominator and numerator by 3 . Which means : \(\frac{18/3}{21/3}\) = \(\frac{6}{7}\)

-For example, when you got the answer, you should make the fraction to the SIMPLIEST FORM .

HOPE IT HELPS ^^

The solution to the given system of differential equations and with the given initial condition, is (a) x(t) = [[-2\(e^{t}\)], [2\(e^{2t}\)], [-\(e^{t}\)]], and (b) x(t) = [[0], [\(e^{2}\)], [\(e^{t}\)]].

To find the solution to the given system of differential equations, we can use the matrix exponential method.

For (a) x(0) = [[-2], [2], [-1]]:

First, we need to find the eigenvalues and eigenvectors of the coefficient matrix [[1 0 -1], [0 2 0], [1 0 1]]. The eigenvalues are λ = 1 and λ = 2, with corresponding eigenvectors v1 = [[-1], [0], [1]] and v2 = [[0], [1], [0]], respectively.

Using the eigenvalues and eigenvectors, we can write the solution as:

x(t) = c1e^(λ1t)v1 + c2e^(λ2t)v2,

Substituting the given initial condition x(0) = [[-2], [2], [-1]], we can solve for c1 and c2:

[[-2], [2], [-1]] = c1v1 + c2v2,

Solving this system of equations, we find c1 = -2 and c2 = 0.

Therefore, the solution for (a) is x(t) = [[-2\(e^{t}\)], [2\(e^{2t}\)], [-\(e^{t}\)]].

For (b) x(-π) = [[0], [1], [1]]:

Using the same procedure as above, we find c1 = 0 and c2 = 1.

Hence, the solution for (b) is x(t) = [[0], [\(e^{2}\)], [\(e^{t}\)]].

Thus, the solutions to the given system with the respective initial conditions are x(t) = [[-2\(e^{t}\)], [2\(e^{2t}\)], [-\(e^{t}\)]], and (b) x(t) = [[0], [\(e^{2}\)], [\(e^{t}\)]].

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The correct question is:

Find the solution to the given system that satisfies the given initial condition.

\(x'(t)=\left[\begin{array}{ccc}1&0&-1\\0&2&0\\1&0&1\end{array}\right]\\\\x(0)=\left[\begin{array}{ccc}-2\\2\\-1\end{array}\right] x(-\pi )=\left[\begin{array}{ccc}0\\1\\1\end{array}\right]\)  

Answer:

i do not know

Step-by-step explanation: