I don't know if I asked this already but: 3x+2y=11 2x-2y=14 Solve for the variables.

Answer:

Use a graphing calc or desmos

Step-by-step explanation:

Answer:

$15

Step-by-step explanation:

Each cup is 50 cents which is basically $0.50

Multiply $0.50 by 120= $60

Because you and your three friends equal 4 total people,

divide 60 by 4 to get your own profit:

60/4=15

Answer:

Step-by-step explanation:

First you need to find the slope of the line that contains those 2 points.

[tex]m=\frac{0-8}{0-(-4)}=\frac{-8}{4}=-2[/tex]

So the slope is -2. Now we can pick one of those points and sub it into the point-slope formula to find the equation:

y - 0 = -2(x - 0) gives us an equation of

y = -2x

Answer:

a = 5

b = 12

c = 13

Step-by-step explanation:

a^2+b^2=c^2

b-a=7(b=a+7)

c=a+8

Then, substitute

a^2+((a+7)*(a+7))=c^2

a^2+a^2+7a+7a+49=c^2

2a^2+14a+49=c^2

Because c = a+8

2a^2+14a+49=(a+8)(a+8)

2a^2+14a+49=a^2+16a+64

a^2-2a=15

a^2-2a-15=0

(a-5)(a+3)=0

a = 5,-3

a = 5(a side cannot be negative)

Plug in a=5 to the other equations to get

a = 5, b = 12, c = 13

Hope it helps <3

Answer:

The lengths of the sides are 5, 12, 13.

Step-by-step explanation:

In a right triangle, the two shorter sides are the legs. The longest side is the hypotenuse.

Let the shorter leg = x.

The longer leg is 7 cm longer, so its length is x + 7.

The length of the hypotenuse is 8 cm longer than the shorter leg, so its length is x + 8.

The lengths are:

x, x + 7, x + 8

Since the triangle is a right triangle, we can use the Pythagorean theorem.

a^2 + b^2 = c^2

x^2 + (x + 7)^2 = (x + 8)^2

Square the trinomials.

x^2 + x^2 + 14x + 49 = x^2 + 16x + 64

Combine like terms and place them all on the left side equaling zero.

x^2 - 2x - 15 = 0

Factor the left side.

(x - 5)(x + 3) = 0

x - 5 = 0   or   x + 3 = 0

x = 5 or x = -3

Since the length of a side of a triangle cannot be negative, we discard the solution x = -3.

x = 5

x + 7 = 5 + 7 = 12

x + 8 = 5 + 8 = 13

Answer: The lengths of the sides are 5, 12, 13.

Answer:

E. P(W | H)

Step-by-step explanation:

What each of these probabilities mean:

P(H): Probability of the game being at home

P(W): Probability of the game being a win.

P(H and W): Probability of the game being at home and being a win.

P(H|W): Probability of a win being at home.

P(W|H): Probability of winning a home game.

Which of the following probabilities do you need to find in order to determine the proportion of at-home games that were wins?

This is the probability of winning a home game. So the answer is:

E. P(W | H)

Answer:

7.5

Step-by-step explanation:

If we look at the 4 by 4 square around the triangle we can just do the area of the square minus the area of the 3 little triangles which is:

4 * 4 - 4 * 1 / 2 - 3 * 3 / 2 - 4 * 1 / 2

= 16 - 2 - 4.5 - 2

= 16 - 8.5

= 7.5

-2

0

2

Answered on edge

Answer:

-2, 0, 2

Step-by-step explanation:

edge 2020

Answer:

No solution

Step-by-step explanation:

Step 1: Write out equations

y = -1/4x + 2

3y = -3/4x - 6

Step 2: Substitution

3(-1/4x + 2) = -3/4x - 6

Step 3: Distribute

-3/4x + 6 = -3/4x - 6

From here, we can see that we have the same slope but different y-intercept. This means that the 2 lines are parallel and therefore never intersect.

Alternatively, you could graph the equations and see that the 2 lines are parallel and never intersect.

Answer:

No solution

Step-by-step explanation:

y = -1/4x + 2

3y = -3/4x - 6

Plug y as -1/4x + 2 in the second equation.

3(-1/4x + 2) = -3/4x - 6

-3/4x + 6 = -3/4x - 6

-3/4x + 3/4x = -6 -6

0 = -12

No solution.

Answer:

Option (1)

Step-by-step explanation:

Since the length of arc YZ = 12 units

m∠YXZ = one third of the full circle = [tex]\frac{360}{3}[/tex] = 120°

From the formula of arc length,

Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Where θ = Central angle subtended by the arc

r = radius of the circle

By substituting these values in the formula,

12 = [tex]\frac{120}{360}(2\pi r)[/tex]

12 = [tex]\frac{2}{3}\pi r[/tex]

[tex]18=\pi r[/tex]

r = [tex]\frac{18}{\pi }[/tex]

r = 5.73

r ≈ 6 units

Therefore, Option (1) will be the answer.

Answer:

solution,

Volume of cylinder=304 cm^3

height=10 cm

Radius=?

Now,

[tex]volume = \pi {r}^{2} h \\ or \: 304 = 3.14 \times {r}^{2} \times 10 \\ or \: 304 = 31.4 \times {r}^{2} \\ or \: {r}^{2} = \frac{304}{31.4} \\ or \: {r}^{2} = 9.68 \\ or \: r = \sqrt{9.68} \\ or \: r = \sqrt{ {(3.11)}^{2} } \\ r = 3.11 \: cm[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

The time spent studying is the response variable.

Step-by-step explanation:

The response variable, also known as the dependent variable is the main question which the experiment wants to provide an answer for. Usually, the predictors determine or affect the response variable.  In the study where Teresa investigates the effect of grade level on time spent studying, the response variable is the time spent studying, while the predictor which is the grade level provides an explanation as to the time spent studying.

The changes or variations on time spent studying depends on the grade level. This means that the grade level provides an explanation of the length of time dedicated to studying.

Answer:

x=½

y=5

Step-by-step explanation:

(8x+7y=39)2

16x+14y=78

4x-14y=-68 add the two equations

20x=10.

divide both sides by 20

x=½

8x+7y=39

4+7y=39

7y=39-4

7y=35

y=5

The value of x and y in the system of equation using elimination method is 1 / 2and 5 respectively.

8x + 7y = 39

4x – 14y = –68

Multiply by 2

16x + 14y = 78

-14y + 14y = 0

4x + 16x = 20x

-68 + 78 = 10

20x = 10

x = 1 / 2

8(1 / 2) + 7y = 39

4 + 7y = 39

7y  = 35

y = 35 / 7

y = 5

learn more on system of equation here: https://brainly.com/question/3861421?referrer=searchResults

Step-by-step explanation:

The given sequences are;

2,7,12,17......

difference =5

by using formula,

we get,

tn=a+(n-1)d

tn= 2+(n-1)5

Therefore, tn is 5n-3 is required formula for this arithmetic sequences.

Hope it helps....

Answer:

a) [tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]    

[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]    

b) For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong

Step-by-step explanation:

Information given

[tex]\bar X=28.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=23.1 represent the sample standard deviation

n=75 represent the sample size  

Part a

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=75-1=74[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] and the critical value would be [tex]t_{\alpha/2}=1.993[/tex]

Now we have everything in order to replace into formula (1):

[tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]    

[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]    

Part b

For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong

Answer:

The box weighs 220 grams.

Step-by-step explanation:

Since the box full of chocolates weighs 480 grams, and the same box full of mints weighs 350, the weight difference between them is 130 grams. According to the statement, the quantity of chocolate weighs twice that of mint, while the weight of the box does not vary.

Therefore, since chocolate weighs twice as much as mints, and the weight is reduced by 130 grams, that is the difference in weight between the two, with which chocolate weighs 260 grams and mints 130 grams.

Therefore, the box weighs 220 grams: 220 + 130 = 350, and 220 + 260 = 480.

Answer:

50 miles

Step-by-step explanation:

let he hiked a,b,c and d miles on each of the four days respectively.

then, according to the question.

a+b=26...i

b+c= 24...ii

c+d=28...iii

a+c=22...iv

now, adding i,ii,iii,iv we get

2(a+b+c+d) = 100

a+b+c+d= 50 miles.

Hence, he traveled in all 50 miles.

Answer:

show a picture

Step-by-step explanation:

Answer:

A)      [tex]y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ][/tex]

B)       [tex]\frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p[/tex]

Step-by-step explanation:

- The following initial value problem is given as follows:

                      [tex]my'' + cy' + ky = F(t) \\\\y(0) = 0\\y'(0) = 0[/tex]

- The above equation is the Newtonian mathematical model of a spring-mass-dashpot system. The displacement ( y ) and velocity ( y' ) are zeroed at the initial value t = 0.

- The equivalent mass ( m ) , damping constant ( c ) and the equivalent spring stiffness ( k ) are given as follows:

                      [tex]m = 2 kg\\\\c = 8 \frac{kg}{s} \\\\k = 80 \frac{N}{m} \\\\[/tex]

- The system is subjected to a sinusoidal force F ( t ) given. We will plug in the constants ( m , c, and k ) and applied force F ( t ) into the given second order ODE.

                      [tex]2y'' + 8y' + 80y = 20sin(6t)[/tex]

- The solution to a second order ODE is comprised of a complementary function ( yc ) and particular function ( yp ).

- To determine the complementary function ( yc ) we will solve the homogeneous part of the given second order ODE. We will assume the independent solution to the homogeneous ODE takes the form:

                           [tex]y = e^-^a^t[/tex]

Where,

                          a: The root of the following characteristic equation

- Substitute ( y ) into the given ODE as follows:

                          [tex]( 2a^2 + 8a + 80 )*e^-^a^t = 0\\\\2a^2 + 8a + 80 = 0[/tex]

- Solve the above characteristic quadratic equation:

                           [tex]a = 2 +/- 6i[/tex]

- The complementary solution for the complex solution to the characteristic equation is of the form:

                           [tex]y_c = e^-^\alpha^t * [ Acos (\beta*t) + Bcos (\beta*t) ][/tex]

Where,

                          a = α ± β

Therefore,

                           [tex]y_c = e^-^2^t * [ Acos (6t) + Bcos (6t) ][/tex]

- To determine the particular solution we will scrutinized on the non-homogeneous part of the given ODE. The forcing function F ( t ) the applied force governs the form of the particular solution. For sinusoidal wave-form the particular solution takes form as following:

                           [tex]y_p = Csin (6t ) + Dcos(6t )[/tex]

Where,

                           C & D are constants to be evaluated.

- Determine the first and second derivatives of the particular solution (yp) as follows:

                            [tex]y'_p = 6Ccos(6t) - 6Dsin(6t)\\\\y''_p = -36Ccos(6t) - 36Dcos(6t)\\[/tex]

- Plug in the particular solution ( yp ) and its derivatives ( first and second ) into the given ODE.

        [tex]-72Csin(6t) - 72Dcos(6t) + 48Ccos(6t) - 48Dsin(6t) + 80Csin(6t) + 80Dcos(6t) = 20sin(6t) \\\\sin(6t)* ( 8C -48D ) + cos(6t)*(8D + 48C ) = 20sin(6t)\\\\D + 6C = 0\\\\C - 6D = 2.5\\\\C = \frac{5}{74} , D = -\frac{15}{37}[/tex]

- The particular solution can be written as follows:

                        [tex]y_p = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)[/tex]

- Now we use the principle of super-position and combine the complementary and particular solution and form a function of general solution as follows:

                        [tex]y_g = y_c + y_p \\\\y_g = e^-^2^t* [ Acos(6t) + Bsin (6t) ] + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)[/tex]

- To determine the complete solution of the given ODE we have to calculate the constants ( A and B ) using the given initial conditions as follows:

                        [tex]y_g ( 0 ) = 1*[A(1) + 0 ] + 0 - \frac{15}{37}(1) = 0\\\\A = \frac{15}{37}\\\\y'_g = -2e^-^2^t*[Acos(6t) + Bsin(6t) ] +e^-^2^t*[-6Asin(6t) + 6Bcos(6t) ] + \\\\\frac{15}{37}cos(6t) +\frac{90}{37}sin(6t) \\\\y'_g(0) = -2*[A(1) + 0] + 1*[0 + 6B] + \frac{15}{37}(1) +0 = 0\\\\B = \frac{15}{6*37} = \frac{5}{74}[/tex]

- The complete solution to the initial value problem is:

           [tex]y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ][/tex]          

- To determine the long term behavior of the system we will apply the following limit on our complete solution derived above:

                 [tex]Lim (t->inf ) [ y_g ] = \frac{15}{37}cos(6t)* [ 0 - 1 ] + \frac{5}{74}sin(6t)* [ 0 + 1 ]\\\\Lim (t->inf ) [ y_g ] = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p[/tex]

- We see that the complementary part of the solution decays as t gets large and the particular solution that models the applied force F ( t ) is still present in the system response when t gets large.

Answer:

  305 calories, 120 from fat

Step-by-step explanation:

The ratio of the area of the larger pizza to that of the smaller pizza is the square of the ratio of the diameters. So, the larger pizza has an area that is ...

  (12/6)² = 4

times that of the smaller pizza. When that area is divided into 8 parts, each part has an area that is 4/8 = 1/2 the area of the smaller pizza.

We expect a slice of the larger pizza to have 1/2 the calories of a smaller pizza, so 305 calories, 120 from fat.

__

610/2 = 305; 240/2 = 120.

Answer:

  g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6

Step-by-step explanation:

We assume your function definition is ...

  [tex]g(x)=\left\{\begin{array}{ccc}-\dfrac{1}{2}x+5&\text{for}&x<6\\x-6&\text{for}&x\ge 6\end{array}\right.[/tex]

For each given value of x, determine which segment applies, then evaluate.

For x = -6 and for x = 0, the first segment applies:

  g(-6) = (-1/2)(-6) +5 = 3 +5 = 8

  g(0) = (-1/2)(0) +5 = 5

For x = 6 and x = 12, the second segment applies:

  g(6) = (6) -6 = 0

  g(12) = (12) -6 = 6

In summary, ...

  g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6

Answer:

d = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference , thus

a₇ = a₁ + 6d

a₄ = a₁ + 3d

Given a₇ - 2a₄ = 1 , then

a₁ + 6d - 2(a₁ + 3d) = 1, that is

a₁ + 6d - 2a₁ - 6d = 1

- a₁ = 1 ( multiply both sides by - 1 )

a₁ = - 1

Given a₃ = 0 , then

a₁ + 2d = 0 , thus

- 1 + 2d = 0 ( add 1 to both sides )

2d = 1 ( divide both sides by 2 )

d = [tex]\frac{1}{2}[/tex]

Answer:

(-1, 6)

(0, 7)

Step-by-step explanation:

Easiest and fastest way to do this is to graph both equations and analyze the graph for when they intersect each other.

Answer:

Hey there!

Elif can only arrange the chairs like: 4 by 7, and 7 by 4.

Hope this helps :)

Answer:

$1,600

Step-by-step explanation:

Inverse relation:

v = k/a

where v = value of car, and a = age in years.

To find k, we use a known value

2400 = k/10

k = 24000

The inverse relation is

v = 24,000/a

At 15 years, a = 15.

v = 24,000/15 = 1,600

The value of Jackie’s car when it is 15 years old will be $1,600.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given data;

Let y be the car’s value and x is the age then, if there is an inverse relation between them;

y = k/x

Substitute the given values;

k=xy

k=2400 × 10

k = 24000

Substitute the value of k;

y = 24000/x

Condition 2;

at x = 15 and y = ?

y = 24,000/15

y= 1,600

Hence, the value of Jackie’s car when it is 15 years old will be 1600.

To learn more, about equations, refer;

https://brainly.com/question/10413253

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Answer:

C.) 60°

Step-by-step explanation:

The triangle is an equilateral triangle. So that means that all the angles measure the same. And we have to remember that a triangle always equals 180°

So, to find out the measure of an angle. We must divide 180 by 3. Which is 60

=60°

Hope this helps you out! : )

Answer:

12

Step-by-step explanation:

( J , Q, K 4 each)

so prob that for 2 cards, both cards are face

= C(12,2)/C(52,2) = 66/1326 = 11/221

Answer:

The solution to this expression is 61,224.74

Step-by-step explanation:

To solve we initially have to convert the percentage to a decimal:

[tex]1.8\% = \frac{1.8}{100} = 0.018[/tex]

So

56000*(1+1.8%)^5 = 56000(1+0.018)^5 = 56000(1.018)^5 = 61,224.74

The solution to this expression is 61,224.74

Answer:

[tex]\boxed{Option \ D}[/tex]

Step-by-step explanation:

The combination of a rational number (3) and an irrational no. ([tex]4i[/tex]) is called a complex number.

So,

[tex]3+4i[/tex] is a complex no.

Answer:

D. Complex number.

Step-by-step explanation:

This number is not irrational, since 3 is rational.

The number is not entirely rational, since 4i is irrational.

The number is not real because i is not real.

So, the number is a Complex number, since it includes both real and nonreal numbers.

Hope this helps!

Answer:

a) 2.3

b) 1.4

c) 1.2

d) On average, 2.3 out of 6 women would consider themselves baseball fans.  The standard deviation is 1.2 women, so in most samples of 6 women, the number of women who consider themselves baseball fans would differ from the mean by no more than 1.2.

Step-by-step explanation:

For each woman, there are only two possible outcoes. Either they are a fan of professional baseball, or they are not. The prbability of a woman being a fan of professional baseball is independent of other woman. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The variance of the binomial distribution is:

[tex]V(X) = np(1-p)[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

38% of women consider themselves fans of professional baseball.

This means that [tex]p = 0.38[/tex]

Six women are sampled:

This means that [tex]n = 6[/tex]

(a) Find the mean of the binomial distribution.

[tex]E(X) = np = 6*0.38 = 2.3[/tex]

(b) Find the variance of the binomial distribution

[tex]V(X) = np(1-p) = 6*0.38*0.62 = 1.4[/tex]

(c) Find the standard deviation of the binomial distribution.

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6*0.38*0.62} = 1.2[/tex]

(d) Interpret the results in the context of theâ real-life situation.

On average, 2.3 out of 6 women would consider themselves baseball fans.  The standard deviation is 1.2 women, so in most samples of 6 women, the number of women who consider themselves baseball fans would differ from the mean by no more than 1.2.

Answer:

1.79% probability that the number of times that the coin lands tails will be less than 40

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

100 times

[tex]n = 100[/tex]

Then

[tex]\mu = E(X) = np = 100*0.5 = 50[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5[/tex]

What is the probability that the number of times that the coin lands tails will be less than 40

Using continuity correction, this is [tex]P(X < 40 - 0.5) = P(X < 39.5)[/tex], which is the pvalue of Z when X = 39.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{39.5 - 50}{5}[/tex]

[tex]Z = -2.1[/tex]

[tex]Z = -2.1[/tex] has a pvalue of 0.0179

1.79% probability that the number of times that the coin lands tails will be less than 40