tan 45- cos ~ 60° = x. Sin 45. ta​

Answer: 65-26=39

Step-by-step explanation: because when we have a portion of the apples that are green and the other is not the word problem indicates subraction and since we have both units of the expression already given we get a answer of 39 apples that were not green

Answer:

B = 3

Step-by-step explanation:

3x + 15 = 4x + 12

= 15-12=4x-3x

= 3 = x

X = 3

Answer:

The team needs to wash at least 30 cars to meet their goal.

Step-by-step explanation:

10n + 400 > 750

      - 400   - 400

10n > 350

n > 35

Answer: 35 Cars! :)

Step-by-step explanation:   They need 350$ to reach their goal. They are washing cars for 10$ each. So to find your answer you need to divide 350$ by 10$. You will end up with 35 cars!!  

Hope This helps!! :)

Answer:

A=-4

Step-by-step explanation:

Add 3 to both sides of the equation:

7a-3 = -31

7a -3 +3 = -31 +3

Simplify:

7a = -28

Divide both sides of the equation by the same term:

7a = -28

7a/7 = -28/7

Simplify again:

A= -4

Answer:

A = -4

Answer:

DB!

Step-by-step explanation:

Question 1: A rectangle's area is length x width. You add up all the portions for the full area.

Question 2: A rectangle's area is length x width. a is the width and the length is 2+3+4, so the area is a(2+3+4)

Hope I helped!

Answer:

29i

Step-by-step explanation:

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Answer:

A

Step-by-step explanation:

Root beer is the cheapest per ounce, i.e. root beer cost is 0.011 per ounce

When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.

Given finding the  cheapest per ounce,

A: a 2 L bottle (67.6 oz.) of root beer at $1.49

total weight of 2 liter bottle = 2 x 67.6 = 135.2 oz

135.2 oz = $1.49

1 oz = $1.49/135.2

1 oz = 0.011

root beer cost is 0.011 per ounce

B: a six-pack of 20-oz. bottles at $2.49,

total weight of 6 pack = 6 x 20 = 120 oz

120 oz = $2.49

1 oz = $2.49/120

1 oz = 0.21

bottles cost is 0.20 per ounce

C: a twelve-pack of 12-oz. cans at $2.99

total weight of 12 pack = 12 x 12  = 144 oz

144 oz = $2.99

1 oz = $2.99/144

1 oz = 0.021

can cost is 0.21 per ounce

Hence root beer is the cheapest per ounce.

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The amount of price will be $1672

Answer:

4030 or 3040 I think 4030 though

Step-by-step explanation:

I think this is it but 6*8 is 48....I used a little logic so hopefully this is right

Answer:

4030

Step-by-step explanation:

if 9× 7 = 3545 then it 7 × 5, 9× 5 which gives 3545

4x3 = 3× 5, 4×5 which gives 1520

so 6× 8 will give 8×5, 6×5 = 4030

Yes, the given data provide convincing evidence that the Nuthatches prefer particular types of trees while searching for seeds and insects.

A statistical hypothesis test used to examine if a variable is likely to come from a given distribution is the Chi-square goodness of fit test. It is frequently used to assess how well sampling data represents the entire population.

Given that the number of red-breasted nuthatches (n) is 156. By convention, the significance level is α=0.05.

First, let's state the null hypothesis and alternate hypothesis.

Null hypothesis H₀: Nuthatches don't prefer particular types of trees while searching for seeds and insects.

Alternate hypothesis H₁: Nuthatches prefer particular types of trees while searching for seeds and insects.

Given: p₁=54%=0.54, p₂=40%=0.40, p₃=6%=0.06

The expected frequency (E) for each probability is:

\(\begin{aligned}E_1&=np_{1}\\&=156\times0.54\\&=84.24\\E_2&=np_{2}\\&=156\times0.40\\&=62.4\\E_3&=np_{3}\\&=156\times0.06\\&=9.36\end{aligned}\)

The observed values (O) are given as 70, 79, and 7. Calculating chi-square, we get,

\(\begin{aligned}\chi^{2}&=\sum\frac{(O-E)^2}{E}\\&=\frac{(70-84.24)^2}{84.24}+\frac{(79-62.4)^2}{62.4}+\frac{(7-9.36)^2}{9.36}\\&=7.4182\end{aligned}\)

And the degree of freedom is given by df = n-1, where, n is the sample size. Here, the sample size is 3.

\(\begin{aligned}df&=n-1\\&=3-1\\&=2\end{aligned}\)

Then, the P-value from the table is given by, \(P(\chi^{2} > 7.4182) = 0.0245\).

This value is less than the significance level.  Therefore, the null hypothesis is rejected. So, an alternate hypothesis is accepted.

Therefore,  nuthatches prefer particular types of trees while searching for seeds and insects.

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An equation y = a(x - h)² + k is equivalent to the formula a = (y - k)/(x - h)², So Option D is correct

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

The equation,

y = a(x - h)² + k

Equivalent equation  = ?

by using rules of algebra, we can transform given equation,

the rules of algebra

1. If a number is in division operation then when it goes to another side of equal to, it will be in multiplication operation or vice-versa.

2. If a number is in addition  operation then when it goes to another side of equal to, it will be in subtraction operation or vice-versa.

So,

by transferring k to the left hand side,

y - k = a(x - h)²

Now, by transferring (x - h)² to the left hand side,

(y - k)/(x - h)² =  a

Hence, the equivalent equation is, a = (y - k)/(x - h)²

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The solution to this equation \(y" - 5y' + 4y = e^(3x)\) which is a non homogeneous differentia equation is  \(y(x) = c1 e^(4x) - (1/4) c1 e^(3x) + c2 e^(x) + (1/6) e^(4x)\), where c1, c2 are the arbitrary constants of  the integration.

The given equation is a non homogeneous second-order differential equation and to solve it using the method of variation of parameters, we must first find the the general solution of the corresponding homogeneous equation \(y" - 5y' + 4y = 0.\)

we have;

\(r^2 - 5r + 4 = 0\)

By factorization, it become;

(r - 4)(r - 1) = 0

With the roots as r = 4 and r = 1, The general solution of the homogeneous equation is given as;

\(y_h(x) = c1 e^(4x) + c2 e^(x)\)

Form of non homogenous equation is given as;

\(y_p(x) = u1(x) e^(4x) + u2(x) e^(x)\)

where u1(x) and u2(x) are functions to be determined.

First derivative of  y_p(x) '

\(y_p'(x) = u1'(x) e^(4x) + 4u1(x) e^(4x) + u2'(x) e^(x) + u2(x) e^(x)\)

Second derivative of  y_p(x) '

\(y_p''(x) = u1''(x) e^(4x) + 8u1'(x) e^(4x) + 16u1(x) e^(4x) + u2''(x) e^(x) + 2u2'(x) e^(x) + u2(x) e^(x)\)

When this y_p(x), y_p'(x), and y_p''(x) is inputed into the nonhomogeneous equation, we have

\(u1''(x) e^(4x) + 8u1'(x) e^(4x) + 16u1(x) e^(4x) + u2''(x) e^(x) + 2u2'(x) e^(x) + u2(x) e^(x) - 5[u1'(x) e^(4x) + 4u1(x) e^(4x) + u2'(x) e^(x) + u2(x) e^(x)] + 4[u1(x) e^(4x) + u2(x) e^(x)] \\= e^(3x)u1''(x) e^(4x) + 4u1'(x) e^(4x) + u2''(x) e^(x) + 2u2'(x) e^(x) = e^(3x)\)

\(u1''(x) + 4u1'(x) = 0\\u2''(x) + 2u2'(x) = e^(3x)\)

The solutions of the above equations are ;

\(u1'(x) = c1 e^(-4x)\\u2'(x) = (1/2) e^(3x)\)

Integrating u1'(x) with respect to x,

\(u1(x) = (-1/4) c1 e^(-4x) + c2\\u2(x) = (1/6) e^(3x) + c3\)

N.B: c1,c2,c3 are arbitrary constants of integration.

The solution of the nonhomogeneous equation is given as;

\(y_p(x) = (-1/4) c1 e^(-x) e^(4x) + (1/6) e^(3x) e^(x)\\y_p(x) = (-1/4) c1 e^(3x) + (1/6) e^(4x)\\y(x) = y_h(x) + y_p(x)\)

By substituting \(y_h(x)\)and \(y_p(x)\) into the above equation, we have

\(y(x) = c1 e^(4x) + c2 e^(x) - (1/4) c1 e^(3x) + (1/6) e^(4x)\\y(x) = c1 e^(4x) - (1/4) c1 e^(3x) + c2 e^(x) + (1/6) e^(4x)\)

Thus, the general solution of the non homogeneous equation \(y" - 5y' + 4y = e^(3x) is y(x) = c1 e^(4x) - (1/4) c1 e^(3x) + c2 e^(x) + (1/6) e^(4x)\), where c1, c2 are arbitrary constants of integration.

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Answer:

Step-by-step explanation:

x^2+64=(x+8i)(x-8i)

16x^2+49=(4x+7i)(4x-7i)

the firm has a total asset turnover of 0.6, which means that for every $1 of total assets, the firm generates $0.6 in sales. This ratio indicates the firm's efficiency in utilizing its assets to generate revenue

Total asset turnover is a financial ratio that measures a company's efficiency in generating sales from its total assets. It is calculated by dividing the total sales by the average total assets. In this case, the firm has $600,000 in sales and total assets of $1 million.

Total Asset Turnover = Total Sales / Average Total Assets

To calculate the average total assets, we sum the beginning and ending total assets and divide by 2:

Average Total Assets = (Beginning Total Assets + Ending Total Assets) / 2

Given that the firm's total assets are $1 million, the average total assets would also be $1 million.

Plugging in the values into the total asset turnover formula:

Total Asset Turnover = $600,000 / $1,000,000 = 0.6

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Answer:27.52 inches

Step-by-step explanation:

Given

Scale factor \(\frac{1}{64}\) i.e.

\(\dfrac{\text{Model}}{\text{Prototype}}\)

The diameter of the model tire is 0.43 inches

Scale factor = \(\dfrac{\text{dia. of model}}{\text{dia. of actual car}}\)

\(\frac{1}{64}=\frac{0.43}{D}\\D=64\times 0.43=27.52\ \text{inches}\)

Answer: c : 5

Step-by-step explanation:

5x4=20

20-7=9

9x6=54

The mean number who have immunity in samples of size 17  is 13.6

Sample Size =17

Immunity to a Particular disease=0.8

=17*0.8

=13.6

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The area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.

The three sides of the triangle are-

h = 24 ft, k = 21 ft, and p = 13 ft.

s = ( 24 + 21 + 13 ) / 2

s = 29

s - a = 29 - 24 = 5

s - b = 29 - 21 = 8

s - c = 29 - 13 = 16

Put in the formula,

Area = √s(s−a)(s−b)(s−c)

A = √ 29 x 5 x 8 x 16

A = 136.23

Thus, the area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.

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The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.

Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.

Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.

Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.

Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.

By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.

Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

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It will take 2 days for Anna and Wilson's accounts to contain the same amount of money. The two accounts will be the same when the amount of money Anna and Wilson have in their accounts is equal.

Let's represent the number of days it takes for this to happen as "d".

Anna's account is starting at $70 and adding $5 per day, so the amount of money she has after "d" days can be represented as:

70 + 5d

Wilson's account is starting at $60 and adding $10 per day, so the amount of money he has after "d" days can be represented as:

60 + 10d

To find when the two accounts will contain the same amount of money, we can set the two algebraic expressions equal to each other and solve for "d":

70 + 5d = 60 + 10d

Subtracting 60 from both sides, we get:

10 + 5d = 10d

Subtracting 5d from both sides, we get:

10 = 5d

Dividing both sides by 5, we get:

d = 2

Therefore, it will take 2 days for Anna and Wilson's accounts to contain the same amount of money. After 2 days, Anna will have $80 ($70 + 2*$5) and Wilson will have $80 ($60 + 2*$10).

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Answer:

2611.2

Step-by-step explanation:

I dont think its right though

Answer:

30 028.8 US$

Step-by-step explanation:

The median of the following set of numbers  (18, 26, 29, 18, 44) is 26. The correct option to this question is option A

To find median of the following sequence (18, 26, 29, 18, 44) we will arrange them in ascending order

                            18 , 18 , 26 , 29 , 44   . . . . . .  . . . .(1)

Since the number of terms is odd we will apply the formula

                     Median  = \(\frac{(n+1)}{2} th\) term . . . . . . .(2)

       Here n = number of terms

As per question the n = 5

Therefore putting in equation 2 we get

                      Median = \(\frac{(5+1)}{2} th\) term

                      Median = \(\frac{6}{2} th \\\)  term

                      Median = 3 term

Hence the third term from the sequence ( shown in 1 ) we get the median that is 26

Hence the median of the following set of numbers (18, 26, 29, 18, 44) is 26 .

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The median is:

26

Explanation:

First, we will arrange the numbers from least to greatest.

18, 26, 29, 18, 44

Rearrange

18, 18, 26, 29, 44.

Now, the median is the number in the middle, which is 26.

Answer:

Step-by-step explanation:

Equation

y = x^2 + 8x + 7                      Put brackets around the first two terms

y = (x^2 + 8x) + 7                    Take 1/2 the linear term's coefficient  (8)

8/2 = 4                                    Put this result inside the brackets and  square

y = (x^2 + 8x + 4^2) + 7          Take - 4^2 and add it to the seven.

y = (x^2 + 8x + 16) + 7 - 16       What you did, did not change the eqiuation

Y = (x^2 + 8x + 16) - 9              The first 3 terms make a perfect square

y = (x + 4)^2 - 9

The minimum should be at - 4,-9  Just to make sure it is, I'll graph the original equation. The y intercept should be at 7 and the two x roots should x = + 3 - 4 and x = -3 - 4. or x = -1 and x = - 7

Let's see if this all checks out.

Graph of original equation.

a.) To solve this problem, we can use a stars and bars approach. We need to distribute 8 books into 5 boxes, so we can imagine having 8 stars representing the books and 4 bars representing the boundaries between the boxes.

For example, one possible arrangement could be:

* | * * * | * | * *

This represents 1 book in the first box, 3 books in the second box, 1 book in the third box, and 3 books in the fourth box. Notice that we can have empty boxes as well.

The total number of ways to arrange the stars and bars is the same as the number of ways to choose 4 out of 12 positions (8 stars and 4 bars), which is:

Combination: C(12,4) = 495

Therefore, there are 495 ways to pack eight indistinguishable copies of the same book into five indistinguishable boxes.

b.) Using the same approach, we can distribute 7 books into 4 boxes using 6 stars and 3 bars.

For example:

* | * | * * | *

This represents 1 book in the first box, 1 book in the second box, 2 books in the third box, and 3 books in the fourth box.

The total number of ways to arrange the stars and bars is the same as the number of ways to choose 3 out of 9 positions, which is:

Combination: C(9,3) = 84

Therefore, there are 84 ways to pack seven indistinguishable copies of the same book into four indistinguishable boxes.

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Given the expression :

The expression will be equal:

so, the answer is option 4)

The total surface area of cylinder is 112π units².

The surface area of cylinder is -

A = 2πr(h + r)

Given is a cylinder as shown in the image attached.

We can write the total surface area of cylinder as -

A = 2πr(h + r)

A = 2π x 4 x (10 + 4)

A = 8π x 14

A = 112π

Therefore, the total surface area of cylinder is 112π units².

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An equilateral triangle is a type of triangles which can always be used as a counterexample to the statement ""all angles in a triangle are acute"".

An acute angle is one that is smaller than 90 degrees in length. If the arms of an angle open up less than a "L," an acute angle is created because a "L" shape forms at 90°.

Angle between 90 to 180 are known as obtuse angle.

Because an equilateral triangle is likewise equiangular, it can be used as a counterexample. So, each angle has a 360/3=60 measurement. Two angles are therefore acute, and the third's measure is also acute.

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the estimated answer is 6

The equation can be factorized as (x + 4/3) (x + 3/2).

The expression 2x² + bx - 9 will be prime for the the values of b = 18, 12, and -1.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

18. The zeroes of the expression ax² + b x + c can be found by,

x = [-b ± √(b² - 4ac)] / 2a

The given expression is 6x² + 17x + 12.

We have to factorize the expression.

x = [-17 ± √(17² - 4×6×12)] / [2 × 6]

  = [-17 ± √(289 - 288)] / 12

  = (-17 ± 1) / 12

x = -16/12 = -4/3 and x = -18/12 = -3/2

The expression can be factorized as (x + 4/3) (x + 3/2).

19. The expression is non factorable if the value of the discriminant is neither zero nor a positive perfect square.

For ax² + b x + c, Discriminant = b² - 4ac

The expression given is 2x² + bx - 9.

Discriminant = b² - (4 × 2 × -9) = b² + 72

When b = 18, b² + 72 = 396, not a perfect square root

When b = 3, b² + 72 = 81, a perfect square root

When b = 12, b² + 72 = 216, not a perfect square root

When b = -3, b² + 72 = 81, a perfect square root

When b = -7, b² + 72 = 121, a perfect square root

When b = -1, b² + 72 = 73, not a perfect square root

When b = 17, b² + 72 = 361, a perfect square root

So when b = 3, -3, -7 and 17, the expression is factorable.

When b = 18, 12, and -1, the expression is prime.

Hence the expression 2x² + bx - 9 is prime when the values of b are  18, 12, and -1.

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