You are told that one of the internal angles of a parallelogram is 54 degrees. This means at least one other angle must be equal to

Answer:

x = 1

y = 4

Step-by-step explanation:

5x + 2y = 13

x + 2y = 9

Add both equations.

6x + 4y = 22

Solve for x.

6x = 22 - 4y

x = 22/6 - 4/6y

Put x as 22/6 - 4/6y in the second equation and solve for y.

22/6 - 4/6y + 2y = 9

-4/6y + 2y = 9 - 22/6

4/3y = 16/3

y = 16/3 × 3/4

y = 48/12

y = 4

Put y as 4 in the first equation and solve for x.

5x + 2(4) = 13

5x + 8 = 13

5x = 13 - 8

5x = 5

x = 5/5

x = 1

Answer:

x = 1, y = 4

Step-by-step explanation:

5x+2y = 13

x+2y = 9

Subtracting both equations

=> 5x+2y-x-2y = 13-9

=> 4x = 4

=> x = 1

Now, Putting x = 1 in the first equation

=> 5(1)+2y = 13

=> 2y = 13-5

=> 2y = 8

=> y = 4

Answer:

hyg

Step-by-step explanation:

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:

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:

2400

Step-by-step explanation:

using simple ratio

we have Account A : account B as

8:12

2:3 .....the 8% account gets

2/5 × 6000

= 2× 1200 = 2400

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

#SPJ2

Answer:

85%

Step-by-step explanation:

Given data

Exam score earned by student = 87

class average = 78

s = 8.69

Calculate the percentage of people that earned a score below your score

P ( z < 1.04 ) = 0.8508 = 85%

Note : Z ( z score ) = (exam score - class average) / s

                   = (87 - 78) / 8.69 = 1.04

Answer: 73 degrees and 107 degrees.

Step-by-step explanation:

The total of supplementary angles are 180 degrees. So you add 2x+3 and 3x+2. Then you get 5x+5=180.

Subtract 5 from both sides. Now the equation is 5x=175.

Divide 5 on each side. x=35

Replace x with 35 in the equations. The angles are 73 and 107.

They both add up to 180 degrees so it is correct.

Answer:

10 and 5.

Step-by-step explanation:

Let the integers be x and y.

xy = 50

x = 2y

Put x as 2y in the first equation.

(2y)y = 50

2y² = 50

y² = 50/2

y² = 25

y = √25

y = 5

Put y as 5 in the second equation.

x = 2(5)

x = 10

Answer:

900°

Step-by-step explanation:

interior angles of a polygon = (n−2)×180°, where n is number of sides

for heptagon it is: (7-2)×180°= 900°

Answer:

a. $240.03

b. $43,205.04

c. Principal = 46.29%

   Interest = 53.71%

Step-by-step explanation:

The computation is shown below:

a. For computing the monthly payment we need to apply the PMT formula i.e to be shown in the attachment below

Given that,  

Present value = $25,000

Future value or Face value = 0

RATE = 12% ÷ 12 months = 1%

NPER = 15 years × 12 months = 180 months

The formula is shown below:  

= PMT(RATE;NPER;-PV;FV;type)  

The present value come in negative  

So, after applying the above formula the monthly payment is $240.03

b. Now the total amount paid is

= Monthly payment × time period

= $240.03 × 180 months

= $43,205.04

c. Now the percentage is

For principal

= $25,000 ÷ $43,205.04 × 100

= 46.29%

And, for the interest, it is

= 100% - 46.29%

= 53.71%

Answer:

3/4

Step-by-step explanation:

Rise over run.

Go up 3 units and 4 units to the right to find the next point

Answer:

Using points ( 8 , 9 ) and ( 4 , 6)

Slope = 6-9/4-8

= -3/-4

= 3/4

Hope this helps

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: 69, 70, 71

x + x + 1 + x + 2 = 210

3x + 3 = 210

3x = 210 - 3

x = 207 / 3

x = 69

x + 1 = 70

x + 2 = 71

Answer:

Step-by-step explanation:

There are two ways to find the value of X

[tex]x + 35 = 180[/tex] ( sum of co-interior angles)

Move constant to R.H.S and change its sign

[tex]x = 180 - 35[/tex]

Calculate the difference

[tex]x = 145[/tex]°

You can use another way too.

[tex]x = 145[/tex]° ( being vertically opposite angles)

Vertically opposite angles are always equal.

Hope this helps...

Best regards!!

Answer:

x = 145°

Step-by-step explanation:

Vertically opposite, also interior angles always add up to 180° so if you want to double check this, do 145° + 35° you should get 180°

I hope this helped you :)

━━━━━━━☆☆━━━━━━━

▹ Answer

[tex]3\frac{5}{6}[/tex]

▹ Step-by-Step Explanation

6 drinks = 6 Pack (one pack)

23 ÷ 6 = [tex]\frac{23}{6} = 3\frac{5}{6}[/tex]

Mixed number - [tex]3\frac{5}{6}[/tex]

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer: It's 3 5/6

but isn't this 4th-grade work?

Step-by-step explanation:

Answer: The second image, the second image where b' is right above b is the correct answer for this, hope this helped!

<!> Brainliest is appreciated! <!>

Step-by-step explanation:

Answer

i woukldnt know

Step-by-step explanation:

ahahahahahahahahahahahahhahahahahaha

Answer:

There is no mode

Step-by-step explanation:

Mode is the most occurring no. and there's no number which is the most occurring.

Answer:

No mode

Step-by-step explanation:

In a set of numbers, mode is the most repeated number.

1, 4, 24, 14, 98, 37

There are no repeated numbers in this set.

Answer:

a. 0.0385

b. 3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.43, n = 165[/tex]

a. Calculate the appropriate standard error calculation for the data.

[tex]s = \sqrt{\frac{0.43*0.57}{165}} = 0.0385[/tex]

b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?

This is 1 subtracted by the pvalue of Z when X = 0.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.5 - 0.43}{0.0385}[/tex]

[tex]Z = 1.82[/tex]

[tex]Z = 1.82[/tex] has a pvalue of 0.9656

1 - 0.9656 = 0.0344

3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home

Answer: 0.003757(approx).

Step-by-step explanation:

Total number of combinations of selecting r things out of n things is given by:-

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Total cards in a deck = 52

Total number of ways of choosing 8 cards out of 52 = [tex]^{52}C_8[/tex]

Total number of ways to choose 5 clubs and 3 cards with one of each remaining suit = [tex]^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]  [since 1 suit has 13 cards]

The required probability = [tex]=\dfrac{^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1}{^{52}C_8}[/tex]

[tex]=\dfrac{\dfrac{13!}{5!8!}\times13\times13\times13}{\dfrac{52!}{8!44!}}\\\\=\dfrac{24167}{6431950}\\\\\approx0.003757[/tex]

Hence, the required probability is 0.003757 (approx).

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:

C Nasir was more successful because he had the greater measure of center

Step-by-step explanation:

Answer: C

Step-by-step explanation:

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:

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:

C. 9π

Step-by-step explanation:

r=x-1

A=πr^2

--------

--------

A= πr^2= π*(4-1)^2= 9π, option C.

Answer:

1. [tex]V(t) = -32500t + 245000[/tex]

a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.

b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).

c. The formula is: [tex]V(t) = -32500t + 245000[/tex]

2. t-intercept: [tex]t = 7.5385[/tex]

The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.

3. Graph in the image attached.

4. The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].

5. [tex]V(8) = -15000[/tex]

It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.

6. After 3.6 years.

7. Between 3.23 years and 5.63 years.

Step-by-step explanation:

1.

The inicial value is 245,000, and each year the value decreases 32,500, so we can write the equation:

[tex]V(t) = -32500t + 245000[/tex]

a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.

b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).

c. The formula is: [tex]V(t) = -32500t + 245000[/tex]

2.

To find the t-intercept we just need to use V(t) = 0 and then find the value of t:

[tex]0 = -32500t + 245000[/tex]

[tex]32500t = 245000[/tex]

[tex]t = 7.5385[/tex]

The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.

3.

The graph of the function is in the image attached.

4.

The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].

5.

[tex]V(8) = -32500*8 + 245000 = -15000[/tex]

It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.

6.

[tex]128000 = -32500t + 245000[/tex]

[tex]32500t = 117000[/tex]

[tex]t = 3.6[/tex]

After 3.6 years.

7.

[tex]62000 = -32500t + 245000[/tex]

[tex]32500t = 183000[/tex]

[tex]t = 5.6308[/tex]

[tex]140000 = -32500t + 245000[/tex]

[tex]32500t = 105000[/tex]

[tex]t = 3.2308[/tex]

Between 3.23 years and 5.63 years.

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

Answer:

1. Is (A) Subtract 2 to both sides

2. Is (C)

Step-by-step explanation:

Answer:

Independent measures, or repeated measures,

Step-by-step explanation:

I would use those experimental designs because it is used to compare different participants over a length of time.