PLS ANSWER FAST!!! IM GONNA FAIL!!!

Mike and his friends bought cheese wafers for $2 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $25 to buy a total of 20 packets of wafers of the two varieties.

Part A: Write a system of equations that can be solved to find the number of packets of cheese wafers and the number of packets of chocolate wafers that Mike and his friends bought at the carnival. Define the variables used in the equations. (5 points)

Part B: How many packets of chocolate wafers and cheese wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)

Hi there!

To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).

First Question

What we have to do is to isolate cos first.

[tex] \displaystyle \large{ cos \theta = - \frac{1}{2} }[/tex]

Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.

Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.

Find Q2

[tex] \displaystyle \large{ \pi - \frac{ \pi}{3} = \frac{3 \pi}{3} - \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{2 \pi}{3} }[/tex]

Find Q3

[tex] \displaystyle \large{ \pi + \frac{ \pi}{3} = \frac{3 \pi}{3} + \frac{ \pi}{3} } \\ \displaystyle \large \boxed{ \frac{4 \pi}{3} }[/tex]

Both values are apart of the interval. Hence,

[tex] \displaystyle \large \boxed{ \theta = \frac{2 \pi}{3} , \frac{4 \pi}{3} }[/tex]

Second Question

Isolate sin(4 theta).

[tex] \displaystyle \large{sin 4 \theta = - \frac{1}{ \sqrt{2} } }[/tex]

Rationalize the denominator.

[tex] \displaystyle \large{sin4 \theta = - \frac{ \sqrt{2} }{2} }[/tex]

The problem here is 4 beside theta. What we are going to do is to expand the interval.

[tex] \displaystyle \large{0 \leqslant \theta < 2 \pi}[/tex]

Multiply whole by 4.

[tex] \displaystyle \large{0 \times 4 \leqslant \theta \times 4 < 2 \pi \times 4} \\ \displaystyle \large \boxed{0 \leqslant 4 \theta < 8 \pi}[/tex]

Then find the reference angle.

We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.

sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)

Find Q3

[tex] \displaystyle \large{ \pi + \frac{ \pi}{4} = \frac{ 4 \pi}{4} + \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{5 \pi}{4} }[/tex]

Find Q4

[tex] \displaystyle \large{2 \pi - \frac{ \pi}{4} = \frac{8 \pi}{4} - \frac{ \pi}{4} } \\ \displaystyle \large \boxed{ \frac{7 \pi}{4} }[/tex]

Both values are in [0,2π). However, we exceed our interval to < 8π.

We will be using these following:-

[tex] \displaystyle \large{ \theta + 2 \pi k = \theta \: \: \: \: \: \sf{(k \: \: is \: \: integer)}}[/tex]

Hence:-

For Q3

[tex] \displaystyle \large{ \frac{5 \pi}{4} + 2 \pi = \frac{13 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 4\pi = \frac{21 \pi}{4} } \\ \displaystyle \large{ \frac{5 \pi}{4} + 6\pi = \frac{29 \pi}{4} }[/tex]

We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.

For Q4

[tex] \displaystyle \large{ \frac{ 7 \pi}{4} + 2 \pi = \frac{15 \pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 4 \pi = \frac{23\pi}{4} } \\ \displaystyle \large{ \frac{ 7 \pi}{4} + 6 \pi = \frac{31 \pi}{4} }[/tex]

Therefore:-

[tex] \displaystyle \large{4 \theta = \frac{5 \pi}{4} , \frac{7 \pi}{4} , \frac{13\pi}{4} , \frac{21\pi}{4} , \frac{29\pi}{4}, \frac{15 \pi}{4} , \frac{23\pi}{4} , \frac{31\pi}{4} }[/tex]

Then we divide all these values by 4.

[tex] \displaystyle \large \boxed{\theta = \frac{5 \pi}{16} , \frac{7 \pi}{16} , \frac{13\pi}{16} , \frac{21\pi}{16} , \frac{29\pi}{16}, \frac{15 \pi}{16} , \frac{23\pi}{16} , \frac{31\pi}{16} }[/tex]

Let me know if you have any questions!

Elimination method

3x +4y ≥ 0

2x +3y ≥ 1

Multiply by 2, -3

6x +8y ≥ 0

-6x +-9y ≥ -3

Add

-1y ≥ -3

y = 3

3x + 12≥ 0

3x + ≥ -12

x = -4

answer: y = 3 x = -4

Answer:

supplement of 158 degree

x+158=180

x=180-158

x=22 degree.

Step-by-step explanation:

Answer:

the 4th option

Step-by-step explanation:

8 = 2³

so, when we convert

[tex] {8}^{x - 3} [/tex]

into a "2 to the power of" expression, we get therefore

[tex] ({2}^{3}) ^{x - 3} [/tex]

and when we have an exponent of an exponent, we can simplify by multiplying these two exponents.

3×(x-3) = 3x - 9

and therefore we get

[tex] {2}^{3x - 9} [/tex]

and by the way, we can now even easily solve this for x, as we know

[tex] {2}^{4x} = {2}^{3x + x} [/tex]

after all, because 4x = x + x + x + x = 3x + x = ...

and because we got also

[tex] {2}^{4x} = {2}^{3x - 9} [/tex]

we know that 3x + x = 3x - 9

and that gives us x = -9

Answer:

I believe the red one is the first image then the blue then the green because they show the prime sign

Step-by-step explanation:

Answer:

\I got not answer cause im da BUDDHA

But gimme brainliest squekky plssss

Answer:

Yes the sales manager claims can be refuted based on the calculated percentages

Step-by-step explanation:

From the table attached below

Total number of customers = 200

Calculated percentages

customers that prefer whole life insurance = 90 = 90/200 = 45%

customers that prefer universal life insurance = 15 = 15/200 = 7.5%

customers that prefer Annuities = 95 = 95/200 = 47.5

Expected percentages:

whole life = 20%

Universal life = 10%

Life Annuities = 70%

Answer:

i hope it will help you

Step-by-step explanation:

Working capital management is how companies are able to manage finances and continue operations.

Answer:

Yes one should consider to buy the policy as important to have insured plan that help at the time of need.

Step-by-step explanation:

Answer:

-8, 5 , 0 , -7 , 16

Step-by-step explanation:

Given

[tex]t_n = (-1)^{n+1}(n^2 - 9)[/tex]

Required

The first five terms

When [tex]n = 1[/tex]

[tex]t_1 = (-1)^{1+1}(1^2 - 9)[/tex]

[tex]t_1 = (-1)^{2}(1 - 9)[/tex]

[tex]t_1 = -8[/tex]

When [tex]n =2[/tex]

[tex]t_2 = (-1)^{2+1}(2^2 - 9)[/tex]

[tex]t_2 = (-1)^3 * (4 - 9)[/tex]

[tex]t_2 = 5[/tex]

[tex]t_3 = (-1)^{3+1}(3^2 - 9)[/tex]

[tex]t_3 = (-1)^{4}(9 - 9)[/tex]

[tex]t_3 = 0[/tex]

[tex]t_4 = (-1)^{4+1}(4^2 - 9)[/tex]

[tex]t_4 = (-1)^5(16 - 9)[/tex]

[tex]t_4 = -7[/tex]

[tex]t_5 = (-1)^{5+1}(5^2 - 9)[/tex]

[tex]t_5 = (-1)^{6}(25 - 9)[/tex]

[tex]t_5 = 16[/tex]

So, the first five terms are: -8, 5 , 0 , -7 , 16

Answer:

[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{c-2} - \sqrt c = 5[/tex]

Required

Isolate radical, then square both sides

We have:

[tex]\sqrt{c-2} - \sqrt c = 5[/tex]

Isolate radical

[tex]\sqrt{c - 2} = 5 + \sqrt c[/tex]

Square both sides

[tex](\sqrt{c - 2})^2 = (5 + \sqrt c)^2[/tex]

[tex]c - 2 = 25 + 2 * 5 * \sqrt c + c[/tex]

[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]

Answer:

12

Step-by-step explanation:

Range is the subtraction of the largest number and the smallest number.

The largest number is: 23

The smallest number is: 11

Now subtract:

23 - 11 = 12

Hope this helped.

Answer:

the lowest is 11 and the highest is 24 then subtract it you are going to have 13

Answer:

Step-by-step explanation:

This is the Law of Cosines. Use the following formula:

[tex]5.1^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x)[/tex] and simplify to

26.01 = 10.89 + 10.89 - 21.78cos(x) and a bit more to

4.23 = -21.78cos(x) and finally to

-.194214876 = cos(x) and use the 2nd button along with the cos button to find that the missing angle is 101.2 degrees

Answer:

B.

[tex]{ \tt{f(x) = \sqrt[3]{x + 11} }}[/tex]

let the inverse of f(x) be m:

[tex]{ \tt{m = \sqrt[3]{x + 11} }} \\ { \tt{ {m}^{3} = x + 11}} \\ { \tt{ {m}^{3} - 11 = x}} \\ { \tt{ {f}^{ - 1}(x) = {m}^{3} - 11 }}[/tex]

substitute for x in place of m:

[tex]{ \bf{f {}^{ - 1}(x) = {x}^{3} - 11 }}[/tex]

Answer:

x =5

Step-by-step explanation:

hope this helps you

please mark as brainliest

Answer:15

Step-by-step explanation:6x +2y=30

2(3x+y) =30

3x+y=30÷2

3x+y=15

Answer:

I believe it is (C).

This runner’s time was slower than the mean time by 0.75 standard deviations.

ED2021

Answer:

B) This runner’s time was faster than the mean time by 1.08 standard deviations.

Step-by-step explanation:

The runner is FASTER because of the negative z score

A well formatted table of the distribution is attached below :

Answer:

0.124

0.733

0.408

Step-by-step explanation:

Using the table Given :

1.) P(AP Statistics) = 90 / 725 = 0.124

2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733

3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408

Answer:

-1/3x+3 = x-1

Step-by-step explanation:

The solution is (3,-2)

Check and see if the point solves the equation

-1/3x+3 = x-1

-1/3(3) +3 = 3-1

-1+3 = 3-1

2=2 yes

Answer:

C

Step-by-step explanation:

Answer:

[tex](a+b)^{2} =a^{2}+2ab+b^{2}[/tex]

[tex](1)w^{2}+2(3)(1)w+3^{2}\\\\=(w+3)^{2}\\\\=(w+3)(w+3)[/tex]

Therefore, [tex]w^{2} +6w+9[/tex] makes a perfect squared.

This question is solved using relative frequency concepts, finding the following two way frequency table, with the - separating the values:

0.4290 - 0.0540 - 0.4839

0.0581 - 0.4581 - 0.5161

0.4871 - 0.5121 - 1

-------------------------------------------------------------------------------

Relative frequency:

The relative frequency of a to b is given by a divided by b.

-------------------------------------------------------------------------------

Democratic:

Total of 150 + 160 = 310 voters.

Of the 150 Democrats, 133 voted for the Democrat and 150 - 133 = 17 voted for the Republican.

The frequencies are:

[tex]\frac{133}{310} = 0.4290, \frac{17}{310} = 0.0548[/tex]

Proportion of democratic voters is:

[tex]\frac{150}{310} = 0.4839[/tex]

Thus, the first line is: 0.4290 - 0.0540 - 0.4839

-------------------------------------------------------------------------------

Republican:

Of the 160 Republicans, 142 voted for the Republican and 160 - 142 = 18 voted for the Democrat.

The frequencies are:

[tex]\frac{18}{310} = 0.0581, \frac{142}{310} = 0.4581[/tex]

The proportion of republican voters is:

[tex]\frac{160}{310} = 0.5161[/tex]

Thus, the second line is: 0.0581 - 0.4581 - 0.5161

-------------------------------------------------------------------------------

Third line:

0.4290 + 0.0581 = 0.4871

0.0540 + 0.4581 = 0.5121

0.4839 + 0.5161 = 1

Thus, the third line is: 0.4871 - 0.5121 - 1

-------------------------------------------------------------------------------

Two-way frequency table:

The two-way frequency table is:

0.4290 - 0.0540 - 0.4839

0.0581 - 0.4581 - 0.5161

0.4871 - 0.5121 - 1

A similar question is given at: https://brainly.com/question/24337228

Answer:

Democratic 133 18 151

Republican 17 142 159

Total        150 160 310

Step-by-step explanation:

Answer:

-1.87 (B)

865.93 - [968-3.34(30)] = -1.87

ED2021

Vertical asymptote:

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graphic, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0.

In this graphic:

Dashed vertical lines at: [tex]x = -3, x = 7[/tex], thus, for [tex]x - (-3) = x+3[/tex] and [tex]x - 7[/tex] the denominator is zero.

Thus, the function graphed is:

[tex]F(x) = \frac{1}{(x+3)(x-7)}[/tex]

And the correct answer is given by option C.

To take a look at a problem with asymptote, you can check this item https://brainly.com/question/4084552.

The graph is for the rational function f(x) = 1/(x + 3)(x - 7).

Option C is the correct answer.

We have,

To understand the graph of the function f(x) = 1/((x + 3)(x - 7)).

Vertical Asymptotes:

The function has vertical asymptotes at the values of x for which the denominator becomes zero.

The denominator is (x + 3)(x - 7), so the vertical asymptotes occur at

x = -3 and x = 7.

Horizontal Asymptote:

The highest power of x in the denominator is x², and there is no x² term in the numerator, the function approaches 0 as x goes to positive or negative infinity.

The horizontal asymptote is y = 0.

x-Intercept:

To find the x-intercept, we set y = 0 and solve for x:

0 = 1/((x + 3)(x - 7))

Since the numerator can never be zero, the only way the fraction can be zero is if the denominator is zero:

(x + 3)(x - 7) = 0

Solving for x:

x + 3 = 0

x = -3

x - 7 = 0

x = 7

So, the x-intercepts are (-3, 0) and (7, 0).

y-Intercept:

To find the y-intercept, we set x = 0:

f(0) = 1/((0 + 3)(0 - 7)) = 1/(-3 * -7) = 1/21

The y-intercept is (0, 1/21).

Thus,

The graph is for the rational function f(x) = 1/(x + 3)(x - 7).

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ6

Answer:

6000 hope this helps

if the question is 5,422 then the round figure is 5000

but the question is 5,821 its above 5500 will be 6000

the answer is

10² ( ten square )

step by step :

10² = 10 × 10

= 100

Answer: 100

Step-by-step explanation: 10*10=100

The differential equation

[tex]y^{(4)}-n^2y'' = g(x)[/tex]

has characteristic equation

r ⁴ - n ² r ² = r ² (r ² - n ²) = r ² (r - n) (r + n) = 0

with roots r = 0 (multiplicity 2), r = -1, and r = 1, so the characteristic solution is

[tex]y_c=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}[/tex]

For the non-homogeneous equation, reduce the order by substituting u(x) = y''(x), so that u''(x) is the 4th derivative of y, and

[tex]u''-n^2u = g(x)[/tex]

Solve for u by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by u₁ and u₂. Now we look for a particular solution of the form

[tex]u_p = u_1z_1 + u_2z_2[/tex]

where

[tex]\displaystyle z_1(x) = -\int\frac{u_2(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx[/tex]

[tex]\displaystyle z_2(x) = \int\frac{u_1(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx[/tex]

where W (u₁, u₂) is the Wronskian of u₁ and u₂. We have

[tex]W(u_1(x),u_2(x)) = \begin{vmatrix}e^{-nx}&e^{nx}\\-ne^{-nx}&ne^{nx}\end{vmatrix} = 2n[/tex]

and so

[tex]\displaystyle z_1(x) = -\frac1{2n}\int e^{nx}g(x)\,\mathrm dx[/tex]

[tex]\displaystyle z_2(x) = \frac1{2n}\int e^{-nx}g(x)\,\mathrm dx[/tex]

So we have

[tex]\displaystyle u_p = -\frac1{2n}e^{-nx}\int_0^x e^{n\xi}g(\xi)\,\mathrm d\xi + \frac1{2n}e^{nx}\int_0^xe^{-n\xi}g(\xi)\,\mathrm d\xi[/tex]

and hence

[tex]u(x)=C_1e^{-nx}+C_2e^{nx}+u_p(x)[/tex]

Finally, integrate both sides twice to solve for y :

[tex]\displaystyle y(x)=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}+\int_0^x\int_0^\omega u_p(\xi)\,\mathrm d\xi\,\mathrm d\omega[/tex]

Answer:

x = -4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The x-coordinate of this point would be 6.

Step-by-step explanation:

Answer:

w

Step-by-step explanation:

w

Answer:

x= -2

y= -1

z= -3

Step-by-step explanation:

x-y= -1 (1)

x+z= -5 (2)

y-z= 2 (3)

(1)+(3)==> x-z= 1 (4)

(4)+(2)==> 2x= -4 ==> x= -2

we replace x by its value in equation (2):

-2+z= -5 ==> z= -3

we replace z by its value in equation (3):

y-(-3)= 2 ==> y+3=2 ==> y= -1