What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?

Answer:

Option (D)

Step-by-step explanation:

In the picture attached,

An obtuse angle triangle ABC has been given.

By applying Sine rule in the triangle,

[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]

Since, m∠A + m∠B + m∠C = 180°

45° + 110° + m∠C = 180°

m∠C = 180°- 155° = 25°

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]

[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]

b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]

b = 15.56

b ≈ 15.56

[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]

a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]

a = 11.712

a = 11.71

Therefore, Option (D) will be the answer.

This question is incomplete

Complete Question

A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)

(a) Greater than 64

(b) Less than 57

Answer:

(a) Greater than 64 = 0.1788

(b) Less than 57 = 0.1094

Step-by-step explanation:

To solve the above questions we would be using the z score formula

The formula for calculating a z-score :

z = (x - μ)/σ,

where x is the raw score

μ is the population mean = 61

σ is the population standard deviation = 13

(a) Greater than 64

z = (x - μ)/σ,

where x is 64

μ is the 61

σ is the 13

In the above question, we are given the number of samples = 16

Sample standard deviation = popular standard deviation/ √16

= 13/√16

z = 64 - 61 ÷ 13/√16

z = 3/3.25

z = 0.92308

Approximately, z values to 2 decimal places ≈ 0.92

Using the z score table of normal distribution to find the Probability (P) value of z score of 0.92

P(z = 0.92) = 0.82121

P(x>64) = 1 - P(z = 0.92)

= 1 - 0.82121

= 0.17879

Approximately , Probability value to 4 decimal places = 0.1788

(b) Less than 57

z = (x - μ)/σ,

where x is 57

μ is the 61

σ is the 13

In the above question, we are given the number of samples = 16

Sample standard deviation = popular standard deviation/ √16

= 13/√16

z = 57 - 61 ÷ 13/√16

z = -4/3.25

z = -1.23077

Approximately, z values to 2 decimal places ≈ -1.23

Using the z score table of normal distribution to find the Probability (P) value of z score of -1.23

P(z = -1.23) = P(x<Z) = 0.10935

Approximately , Probability value to 4 decimal places = 0.1094

Answer:

x= 37/36

Step-by-step explanation:

−12(3x−4)=11

Step 1: Simplify both sides of the equation.

−12(3x−4)=11

(−12)(3x)+(−12)(−4)=11(Distribute)

−36x+48=11

Step 2: Subtract 48 from both sides.

−36x+48−48=11−48

−36x=−37

Step 3: Divide both sides by -36.

−36x

−36

=

−37

−36

x=

37

36

Answer:

x=

37

36

-1/2(3x-4) = 11

Multiply both sides by -2:

3x-4 = -22

Add 4 to both sides:

3x = -18

Divide both sides by 3:

X = -6

Answer:

30.5

Step-by-step explanation:

This sequence is defined by f(n)=6.5 + 4.5

The term inside the parentheses (n) is the value you should input to get an output.

n varies from 0 to infinity

Now to find the fifth term put in mind that 0 is the first term.

This means that f(5) isn't the fifth term. In fact, it's the sixth term. So f(4) is the fifth term.

To find f(4) replace n by 4.

f(4) = 6.5 *4 +4.5 = 26+4.5=30.5

Answer:

[tex]\large \boxed{\sf \ \ \ (-8,0) \ \text{ and } \ (4,0) \ \ \ }[/tex]

Step-by-step explanation:

Hello,

from the expression of f(x) we can say that there are two zeroes, -8 with a multiplicity of 1 and 4 with a multiplicity of 1.

So the image of the parabolic lens crosses the x-axis at two points:

   (-8,0)

and

   (4,0)

For information, I attached the graph of the function.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

0, 3

Step-by-step explanation:

Hola,

[tex]x^2-3x=0\\\\x*x-3*x=0\\\\x(x-3)=0\\\\x= 0 \ or \ x=3\\[/tex]

Espero que esto ayudes

Answer:

x = 0      O       x = 3

Step-by-step explanation:

[tex]x^2-3x = 0[/tex]

tomando x común

x(x-3) = 0

Ya sea,

x = 0      O     x-3 = 0

x = 0      O       x = 3

Answer:

Hey there!

Jimmy has 15-7, or 8 apples left.

Hope this helps :)

Answer:

The sample size is  [tex]n = 87[/tex]

Step-by-step explanation:

From the question we are told that

      The standard deviation is  [tex]\sigma = 0.04 \ inches[/tex]

       The  precision is [tex]d = \pm 0.005 \ inches[/tex]

        The confidence level is [tex]C =[/tex]98%

Generally the sample size is mathematically represented as  

        [tex]n = \frac{ Z_{\frac{\alpha }{2} } ^2* \alpha^2 }{d^2}[/tex]

Where  [tex]\alpha[/tex]  is the level of significance which is mathematically evaluated as

        [tex]\alpha = 100 - 98[/tex]

        [tex]\alpha = 2[/tex]%

        [tex]\alpha = 0.02[/tex]

and  [tex]Z_{\frac{\alpha }{2} }[/tex] is the critical value of [tex]\alpha[/tex] which is obtained from the normal distribution table as  2.326

  substituting values

         [tex]n = \frac{2.326 ^2* 0.02^2 }{0.005^2}[/tex]

        [tex]n = 87[/tex]

Answer:

Perimeter: 33.7 mm

Area: 54 mm

Step-by-step explanation:

If you do 12 + 9.7 + 12 you will get the perimeter, and to get the area you would use the formula A = [tex]\frac{1}{2}[/tex] x base x height. Since the base is 12 and the height is 9, you would do 12 x 9 x 0.5 to get 54 mm for the area of the triangle.

Answer:

Step-by-step explanation:

When the input is 4, the output of f(x) = x + 21 is f(4).

Substitute x = 4 to f(x):

f(4) = 4 + 21 = 25

Answer:

25

Step-by-step explanation:

We can find the output by plugging in 4 as x into the function:

f(x) = x + 21

f(4) = 4 + 21

f(4) = 25

Answer:

you need to have values for w and v

but u basically have to do

MOVE V TO THE OTHER SIDE

SO

W/V=P

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

              ✌ -ZYLYNN JADE ARDENNE

Answer:

I think the correct answer is 45.

Step-by-step explanation:

Answer:

(x+2.3)^2 + (y) ^2 = (6/7)^2

Step-by-step explanation:

The equation of a circle can be written as

(x-h)^2 + (y-k) ^2 = r^2  where ( h,k) is the center and r is the radius

(x- -2.3)^2 + (y-0) ^2 = (6/7)^2

(x+2.3)^2 + (y) ^2 = (6/7)^2

Answer:

128

Step-by-step explanation:

You have two jars and seven marbles.

You do 2^{7}.

That is 128

Answer:

16384

Step-by-step explanation:

Its correct :)

Answer:

212

Step-by-step explanation:

Answer:

212

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ 10^2+11^2+12^2=13^2+14^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's note a a positive integer

5 consecutive integers are

a

a+1

a+2

a+3

a+4

so we need to find a so that

[tex]a^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2\\<=>\\a^2+a^2+2a+1+a^2+4a+4=a^2+6a+9+a^2+8a+16\\<=>\\3a^2+6a+5=2a^2+14a+25\\<=>\\a^2-8a-20=0\\<=>\\(a+2)(a-10)=0\\<=>\\a = -2 \ or \ a = 10\\[/tex]

as we are looking for positive integer the solution is a = 10

do not hesitate if you have any question

Answer:

[tex]5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{11}{2} [/tex]

So the answer is 11/2 .

Answer:

The answer is 11/2

Step-by-step explanation:

Simply multiply 2 and 5 to get 10 and then add 1 to get 11 so 11/2

Answer:

We conclude that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.

Step-by-step explanation:

We are given that based on information from a large insurance company, 67% of all damage liability claims are made by single people under the age of 25.

A random sample of 52 claims showed that 43 were made by single people under the age of 25.

Let p = population proportion of claims made by single people

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 67%     {means that the insurance claims of single people under the age of 25 is smaller than or equal to the national percent reported by the large insurance company}

Alternate Hypothesis, [tex]H_A[/tex] : p > 67%      {means that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company}

The test statistics that will be used here is One-sample z-test for proportions;

                          T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of claims made by single people under the age of 25 = [tex]\frac{43}{52}[/tex] = 0.83

           n = sample of claims = 52

So, the test statistics =  [tex]\frac{0.83-0.67}{\sqrt{\frac{0.67(1-0.67)}{52} } }[/tex]  

                                    =  2.454

The value of z-test statistics is 2.454.

Since in the question, we are not given the level of significance so we assume it to be 5%. Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 2.454 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.

Answer:

60

Step-by-step explanation:

x + 0.30x = 78

1.30x = 78

x = 60

Answer:

The answer is 60.

Step-by-step explanation:

here, let another number be x.

according to the question the number when increased by 30% will be 78. so,

x+ 30% of x =78

now, x+ 30/100×x =78

or, x+0.3x=78

or, 1.3x=78

Therefore the another number is 60.

Hope it helps...

Answer:

3:06

Step-by-step explanation:

primero debemos calcular a cuántos minutos equivale un ángulo de 54°. Para hacer esto utilizamos una regla de 3 simple donde 60 minutos equivale a 360° grados, entonces:

60 minutos ----- 360°

x minutos -------- 54°

Resolviendo para x, tenemos:

[tex]x=\frac{54*60}{360}=9[/tex]

Entonces si las manecillas están a 9 minutos de diferencia, el ángulo será 54°. Si la hora es después de las 3, significa que la manecilla de la hora estará en el minuto 15 y la otra debe estar 9 minutos antes, es decir en el minuto 6.

Por lo tanto, la hora después de las 3 en la cual se forma un ángulo de 54° por primera vez es a las 3:06

Answer:

Please refer to the graph in the attached area.

Step-by-step explanation:

Given:

Total money available with the customer is $10.

Cost of each hotdog is $2.

Cost of each drink is is $2.50.

To find:

The graph of inequality.

Solution:

Let number of hotdogs bought = [tex]x[/tex]

Total cost of hotdogs = [tex]2x[/tex]

Let number of drinks bought = [tex]y[/tex]

Total cost of drinks = [tex]2.5y[/tex]

Total cost = [tex]2x+2.5y[/tex]

And total money available is $10.

So, the total cost calculated above must be lesser than or equal to $10.

Hence, the inequality is:

[tex]2x+2.5y<10[/tex]

Also there will be two conditions on variables [tex]x[/tex] and [tex]y[/tex]:

[tex]x\ge0\\y\ge0[/tex]

To graph this, let us find the points on the equivalent equation:

[tex]2x+2.5y = 10[/tex]

Finding two points on the equation.

First put x = 0 [tex]\Rightarrow[/tex] y = 4    

Then put y = 0, [tex]\Rightarrow[/tex] x = 5

So, two points are (0, 4) and (5, 0).

Now, plotting the line.

Having point (1,2) in the inequality:

2 + 5 < 10 (True) hence, the graph of inequality will contain the point (1,2)

Please refer to the graph of inequality in the attached graph.

Answer:

A. 1.812

B. 1.753

C. 2.602

D. 3.747

E. 2.069

F. 2.453

Step-by-step explanation:

A. 95% confidence level, the level of significance = 5% or 0.05

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182

B. 95% confidence interval = 0.05 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753

C. 99% confidence interval = 0.01 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602

D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747

E. 98% confidence interval = 0.02 level of significance

Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069

F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31

Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453

Answer:

Step-by-step explanation:

you have to keep going cause if you count the fives there's a 25 but right next to the 25 there's 24 all you have to do is watch what your doing just watch your steps

Answer:

g(2) =10x+6

Step-by-step explanation:

g(x) =5x+3

g(2)=5x+3

g(2)=10x+6

have a great day

Answer: the numbers are 3 and -3

Step-by-step explanation:

let the unknown number be x

The first UNKNOWN NUMBER = X

The second unknown number is = 6 + x

Their product = -9

(X)(6 + X) = -9

6x +[tex]x^{2}[/tex]=-9

[tex]x^{2}[/tex] +6x +9=0

we multiply the coefficient of x which is 1 with 9

now, we look for two numbers that when multiplied will give us 9 and when added will give 6 and that is 3 and 3

[tex]x^{2}[/tex] +3x+3x +9 = 0

x(x+3) +3(x+3) = 0

(x +3 ) = 0

or (x +3)=0

x +3 =0

x=0 -3

x =-3

x +3=0

x =0-3

x =-3

since the numbers are the same ,we pick one

therefore,the first number =x =-3

the second number is 6 + x=6 + (-3)

6-3=3

Answer:

[tex]f(x)=(x-1)\,(x-3)\.(x+2)[/tex]

which agrees with the first answer shown in the list of possible options.

Step-by-step explanation:

Notice that there are three roots for this polynomial clearly shown on the graph's crossings of the x axis: x = 1, x = 3, and x = -2.

Therefore, based on such, we can write three binomial factors of the form [tex](x-root)[/tex]  for the polynomial:

[tex]f(x)=(x-1)\,(x-3)\.(x-(-2))=(x-1)\,(x-3)\.(x+2)[/tex]

Answer:

The cost of the paper book= $12

Step-by-step explanation:

Hardcover books costs $21

But paper book cost only a fraction of the hardcover book.

The paper book cost 4/7 of the hardcover book.

The cost of paper book= 4/7* paper book

The cost of paper book = 4/7*$21

The cost of the paper book= 4*3

The cost of the paper book= $12

Answer:

  152.53°

Step-by-step explanation:

The Law of Cosines is useful for finding an angle when sides are given.

  a^2 = b^2 +c^2 -2bc·cos(A)

  A = arccos((b^2 +c^2 -a^2)/(2bc))

  A = arccos((18^2 +17^2 -34^2)/(2(18)(17))) = arccos(-543/612)

  A ≈ 152.53°

Answer:

Step-by-step explanation:

Hello!

Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"

If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:

S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}

The sample space for the experiment has 7 possible combinations.

a)

Be X: the amount of money Miguel will receive or owe.

If two chips with the same number are chosen he will receive $2

If the chips have different number he will owe $1

Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)

So the probability of him receiving $2 will be 1/7

Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7

  xi  | $2 | -$1

P(xi) | 1/7 | 6/7

b)

To calculate the expected value or mean you have to use the following formula:

[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57

c)

The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.

d)

To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:

(2*4/7)+(-1*3/7)= $0.71

I hope this helps!

Answer:

Maddy's hourly pay is $8.50

Step-by-step explanation:

First, we need to use the information given to us to form a system of equations to determine either Maddy's pay, or her cousin's pay.  In this case, we are interested in Maddy's pay.

We know her cousin makes 30% more than Maddy, which means she makes 100% of what Maddy makes, and an additional 30%.  So we have our first equation:

C = M + .3M = 1.3M, where C is the amount the cousin makes and M is Maddy's pay.

The second piece of information is that in one week, Maddy worked 23 hours, and her cousin worked 27, and together they made $493.85.  So now we have our second equation:

27C + 23M = 493.85, where C is the amount the cousin makes and M is the amount Maddy makes.

Now we simply substitute are value of C from the first equation into the second equation like such:

27(1.3M) + 23M = 493.85

And now we solve for M to find Maddy's pay.

27(1.3M) + 23M = 493.85

35.1M + 23M = 493.85

58.1M = 493.85

M = 8.5

To verify our answer is correct, let's find the value of money earned per hour by the cousin using the first equation:

C = 1.3(8.5) = 11.05

Now let's see if the number of hours worked by each and their pay adds up to the 493.85 from the previous week:

27(11.05) + 23(8.5) =? 493.85

298.35 + 195.5 =? 493.85

493.85 == 493.85

So, now we have confirmed that Maddy makes $8.50 per hour, and her cousin makes $11.05 per hour.

Cheers.