8 ABC please trig assignment

Using linear functions, we have that:

A linear function is modeled by:

y = mx + b

In which:

We consider the initial values as the y-intercepts. Randall's house decayed 58 thousand dollars in 3 years, hence the slope is:

m = -58/3 = -19.

Hence the function for the value, in thousands of dollars, is:

f(t) = -19t + 234.

Damien's initial value was of 110, and it increased 44 thousand in 3 years, hence the slope is:

m = 44/3 = 14.67

Hence the function for the value of Damien's house, in thousands of dollars, in t years after 2003, is:

g(t) = 14.67t + 110

They will have the same value when:

f(t) = g(t)

-19t + 234 = 14.67t + 110

33.67t = 124

t = 124/33.67

t = 3.68

They will have the same value in 3.68 years since the start of 2000.

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In the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0

Radical equations are expression that are under the square root. For instance √x is a radical expression.

Given the equation expressed as:

x − 5 = √3x −11

Square both sides to have;

(x-5)² = (√3x −11 )²

This can be further expressed as:

(x-5)² =3x −11

Expand

x² -10x + 25 = 3x - 11

Equate to zero

x² -10x + 25 - 3x +11 = 0
x² -10x - 3x +36 = 0
x² - 13x + 36 =0

Hence in the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0

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The solutions for the Questions are

a) Given that, the minimum requirement is 58 out of 75.

a=0.7733

b) For  16 out of a total of 75

b=0.2133

c)  For 11 out of a total of 75

c =0.1466

Generally, we need to determine the total number of students who exhibit each behavior by seeing the habits and assets contained inside a Venn diagram.

Therefore, let's assume that:

- In Set A, I watched one of the Naruto episodes.

Set B: Observed a new segment of the anime series Death Note.

Hence, 23 of them have seen an episode of Death as well as an episode of Naruto, which means that

(A intercept B) equals 23.

In addition to this, it is a given that 42 has seen one episode of Death Note.

This indicates that B is equal to 42.

This pertains to us:

[tex]B = (B-A)+(A \cap B)[/tex]

In this case, members of B through A are individuals who have only viewed Death Note. So

42=(B−A)+23

(B-A) = 11

Finally, It is a known fact that 39 of the members have seen at least one episode of Naruto.

Therefore, the value of A is 39.

A=(A−B)+(A intercept B)

39=(A−B)+23

(A−B)= 16

(A union B)= 42+ 39- 23

(A union B)=58

In conclusion, the total number of pupils is:

58 with at least one and 17 with none, for a total of 75

a) Given that, the minimum requirement is 58 out of 75.

a=58*100/75

a=0.7733

b) For  16 out of a total of 75

b= 16/75*100

b=0.2133

c)  For 11 out of a total of 75

c= 11/75*100

c =0.1466

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Step-by-step explanation:

4W-8=3W+6

4W-3W=6+8

W=14°

lets find the value of W in this straight line

4W-8°=180°(angle on a straight line)

collect like terms

4W=180°+8°

4W=188°

divide both sides by the coefficient of W which is 4

W=47°

if i am correct pls rate it

The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

The given parameters are:

Rate, r = doubles every two days

Initial number of strain, a = 1

This means that the function is an exponential function.

An exponential function is represented as:

A(d) = a * r^d

Since the strain doubles every two days, we have:

A(d) = a * r^(d/2)

Substitute the known values in the above equation

A(d) = 1 * 2^(d/2)

Evaluate the product

A(d) = 2^(d/2)

When there are 256 bacterial cells, the equation becomes

2^(d/2) = 256

Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

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By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

Herein we have a trigonometric equation which has to be simplified. Simplification procedure consists in applying trigonometric expressions and algebra properties to transform the function from the form f(cos 12x) to the form f(cos 6x). Now we present the solution in detail:

By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

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The value of the evaluation of logarithm e^in4 is 4

Given the expression as;

e^in4

To put in logarithmic form, equate to the power of the "Lin,ln value"

Now, let's equate it to the value of the exponential

e^in4 = 4

We have that'

[tex]loge x = loge 4[/tex]; this is the logarithmic form of the expression but we need to find the value of 'x'

To find the value, let's cancel out the like variables, we have

[tex]x = 4[/tex]

Then we have the value to be

x = 4

Thus, the value of the evaluation of logarithm e^in4 is 4

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The percentage when Potiphar woke up late is 14.4%.

From the information, it was stated that Potiphar takes a horse and buggy to work everyday. In order to come on time, he must wake up promptly at 6.30am and then hop on the buggy and that anytime he wakes up late or the horse was in traffic, he will be late.

It was further illustrated based on the information given in the question that he was late 24.4% of the time and the horse was in traffic for 10% of the time.

Therefore, the percentage when he woke up late will be gotten by simply subtracting the percentages that we have above. This will be illustrated below:

= 24.4% - 10%

= 14.4%

Therefore, the percentage when Potiphar woke up late is 14.4%.

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Answer:

Step-by-step explanation:

        a² + b² = c²

  a² + (21.5)² = (31.9)²

a² + 462.25 = 1017.61    

               a²  = 555.36

                  a = 23.6

Answer:

4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

Step-by-step explanation:

28[tex]v^{7}[/tex]x³[tex]y^{6}[/tex] - 12[tex]v^{9}[/tex][tex]x^{9}[/tex] ← factor out 4[tex]v^{7}[/tex]x³ from each term

= 4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

Answer:

A cone has one -third times the volume of a cylinder with the same base and altitude. True

The answer is A. True.

Assuming the cylinder and cone have same base and altitude, the formulas are :

Based on this, we can understand that :

A cone has one-third times the volume of a cylinder with the same base and altitude.

Answer:

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a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

We have,

(a) To write the number 0.00000896 moles per liter in scientific notation, we move the decimal point to the right until there is one

non-zero digit to the left of the decimal point.

The number of decimal places we moved to the decimal point will be the exponent of 10 in the scientific notation.

So,

= 0.00000896

= 896/100000000

= 896 x 100/100 x [tex]10^{-8}[/tex]

= 896/100 x [tex]10^{-8 + 2}[/tex]

= 8.96 × [tex]10^{-6}[/tex]

(b)

To write the number 1.1105 pounds in standard notation, we simply write the number as it is, without any scientific notation or exponent.

1.1105 pounds is written in standard notation as 1.1105 pounds.

Thus,

a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

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The option B is correct, The second expression gives the correct value -24.

According to the statement

we have given that the some expression and a = -2 and b = 3 and we have to which expression gives a output of answer -24 after put the values in the expressions.

So, For this purpose

First expression:

[tex]a\sqrt{16} + b - 10[/tex]

Put a = -2 and b = 3

then

[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]

Second expression:

[tex]a(\sqrt{16} + b) -10[/tex]

Put a = -2 and b = 3

then

[tex]a(\sqrt{16} + b) -10\\-2(4 +3) -10\\-14-10\\-24[/tex]

Now,

Third expression:

[tex]a\sqrt{16} + (b - 10)[/tex]

Put a = -2 and b = 3

then

[tex]a\sqrt{16} + (b - 10)-2*4 + (-7)\\-8-7\\-15[/tex]

Now,

Fourth expression and first expression are same,

So,

Fourth expression:

[tex]a\sqrt{16} + b - 10[/tex]

Put a = -2 and b = 3

then

[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]

The second expression gives the correct value -24.

So, The option B is correct, The second expression gives the correct value -24.

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Answer: 0

Step-by-step explanation: I am going by the words , there WERE 3 ponies. So Sarah couldn’t take any rides.

Answer:

85 C

Step-by-step explanation:

Temperature range means the difference between the maximum and minimum in temperature for an area. 40C-(-45C)=85 C

The length of the vine wounded to the tree is 21 feet.

Circumference is the perimeter of a circular object. Therefore,

circumference = 2πr

where

The circumference of the tree is 3 feet. A vine was wound around 7 times .

The length of the vine can be calculated as follows:

Therefore,

circumference = 3 ft

length of the vine = 7 × 3

length of the vine = 21 feet

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For the given set A, A is a set of x, where x depends on n. x= 11, where the values of n in ascending order are 1,2,3,4.

Simply put, a set in mathematics is a grouping of different items.

An element of the set is any component of the set. When writing a set, curly brackets are utilized.

The components of a set can be represented using a variety of notations. Typically, sets are represented using a set builder form or a roster form.

According to the question,

A = {11,22,33,44}

The elements of set A are all multiples of 11. These can be expressed as 11*n, here, n has the values of 1,2,3 and 4.

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Answer: (x-2)

Step-by-step explanation:

This problem is a middle-term factorization, or factoring by splitting the middle term.

We have the equation

x^2 - 18x + 32

This equation represents the area, and area = length x width for all rectangles. We also know the width, x-16, which makes it easier for us. The length must also be in the same format.

x^2 - 18x + 32

= x^2 - 16x - 2x + 32

= x(x-16) - 2(x - 16)

= (x-16) (x-2) -------> we get this through taking (x-16) common

We could also pretend that the length is x - y, where y is the number we need to finish the equation.

x^2 - 18x + 32

= (x-16) (x-y)

= x^2 -16x - xy + 16y

-16 minus 2 is -18, which is our middle term.

Therefore, y = 2. This is also verified because is 16y = 32, the constant term, then through transposing we get y = 2.

Our answer is that the length is (x-2).

Answer:

Step-by-step explanation:

Begin by filling in x as -2 and y as √12 in the given expression:

[tex]2(3(-2)^3+2(\sqrt{12})^2)[/tex].  Work inside the parenthesis first and deal with those exponents:

(-2)³ is the same as (-2)(-2)(-2) which is -8;

(√12)² is the same as (√12)(√12) which is √144 which is 12.

Filling those simplifications in:

[tex]2(3(-8)+2(12))=2(-24+24)=2(0)=0[/tex]

Answer:

y = 1/2 x  + 3

Step-by-step explanation:

Find slope, m = (y1-y2)/(x1-x2) =  (7-0) / (8- - 6)  = 7/14 = 1/2

   ( does not matter which one you assign as point 1 or point 2)

Point (-6,0)  slope form ( you can use either point)

(y-0) = 1/2 (x- -6)

y = 1/2 x +3

By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.

According to the image, we have a composite figure formed by two right prisms. The surface area of this figure is the sum of the areas of its faces, represented by squares and rectangles:

A = 2 · (4 cm) · (5 cm) + 2 · (2 cm) · (4 cm) + (2 cm) · (5 cm) + (3 cm) · (5 cm) + (5 cm)² + 4 · (3 cm) · (5 cm)

A = 166 cm²

By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.

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The most convenient way to capture [tex]D[/tex] is with the parameterization

[tex]D = \left\{(x,y) \mid -1 \le y \le 3 \text{ and } -\dfrac{y+1}2 \le x \le y+1\right\}[/tex]

so we only need one iterated integral.

[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-1}^3 \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx \, dy[/tex]

Compute the integral with respect to [tex]x[/tex].

[tex]\displaystyle \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx = e^{x-y} \bigg|_{x=-(y+1)/2}^{x=y+1} = e^{(y+1)-y} - e^{-(y+1)/2-y} = e - e^{-(3y+1)/2}[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_{-1}^3 \left(e - e^{-(3y+1)/2}\right) \, dy = \left(ey + \frac23 e^{-(3y+1)/2}\right)\bigg|_{y=-1}^{y=3} \\\\ ~~~~~~~~ = \left(3e + \frac23 e^{-(9+1)/2}\right) - \left(-e + \frac23 e^{-(-3+1)/2}\right) \\\\ ~~~~~~~~ = \boxed{\frac{10e}3 + \frac2{3e^5}}[/tex]

If we had chosen the opposite order of variables, we would have used

[tex]D = \left\{(x,y) \mid -2 \le x \le 4 \text{ and } \max\left(-2x-1,x-1\right)\le y\le3\right\}[/tex]

where

[tex]\max(-2x-1, x-1) = \begin{cases} -2x-1 & \text{when } x<0 \\ x-1 & \text{when } x\ge0\end{cases}[/tex]

so we would have needed two iterated integrals,

[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-2}^0 \int_{-2x-1}^3 e^{x-y} \, dy \, dx + \int_0^4 \int_{x-1}^3 e^{x-y} \, dy \, dx[/tex]

Step-by-step explanation:

since the sumation of f(x) of a probability is 1

thw probability to win is o.5 and to lose is o.5 so expected value is xf(x

your expected value will b 0.5 multiply by 5 thats is 2.5 thats your expected gain

Step-by-step explanation:

(7m - 3)² = 49m² - 42m + 9

play it through and do the actual multiplication behind the square :

(7m - 3)² = (7m - 3)(7m - 3) =

= 7m×7m + 7m×(-3) + (-3)×7m + (-3)(-3) =

= 49m² - 2×21m + 9 = 49m² - 42m + 9

When the acceleration is 7 m/s², it means that the force will be 70 N.

From newton's first law of motion, we know that;

F = ma

where;

m is mass

a is acceleration

We are given;

F = 60 N

a = 6 m/s²

Thus;

m = F/a = 60/6

m = 10 kg

When acceleration is 7 m/s², we have;

F = 10 * 7

m = 70 N

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The amount she should invest today in the annuity is $455,450.40.

The first step is to determine the future value of the monthly annuity.

Future value = monthly payment x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Future value : 3250 x [(1.003^180) - 1] / 0.003 = 774,171.92

The second step is to determine the present value of this future annuity:

774, 171.92 / (1.036^15) = $455,450.40

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The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

Given that the function is f(x)=IxI+5.

We are required to find the range of the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.

Function is f(x)= IxI+5

We know that IxI=x for x>=0 and -x<0.

We have to just put the value of IxI in f(x) to get the range of function.

f(x)=x+5 for x>=0 and -x+5 for x<0.

Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

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The value of the probability P(A) is 0.40

The given parameters about the probability are

P(A or B) = 0.6

P(B) = 0.3

P(A and B) = 0.1

To calculate the probability P(A), we use the following formula

P(A and B) = P(A) + P(B) - P(A or B)

Substitute the known values in the above equation

0.1 = 0.3 + P(A) - 0.6

Collect the like terms

P(A)= 0.1 - 0.3 + 0.6

Evaluate the expression

P(A)= 0.4

Hence, the value of the probability P(A) is 0.40

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The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

Given the function;

f(x) = −4| x-3 | + 12

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

f(x) = −4| x-3 | + 12

y = −4| x-3 | + 12

0 = −4| x-3 | + 12

−4| x-3 | + 12 = 0

−4| x-3 | = -12

Divide both sides by -4

| x-3 | = 3

We remove the absolute value sign

x - 3 = ±3

x = 3±3

x = 3-3, 3+3

x = 0, 3

Hence, x-intercepts are: ( 0, 0 ), ( 6, 0 )

Next, we find the y-intercept by substituting 0 for x and solve for y.

f(x) = −4| x-3 | + 12

y = −4| 0-3 | + 12

y = −4| -3 | + 12

We remove the absolute value sign

y = −4(3) + 12

y = −12 + 12

y = 0

Hence, y-intercept is: ( 0, 0 ).

The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

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