The nth term of a geometric sequence is given by an = 27(0.1)n - 1. Write the first five terms of this sequence.

Answer:

xy + 8x - y - 8

Step-by-step explanation:

We can use the FOIL method to expand these two binomials. FOIL stands for First, Outer, Inner, Last.

F: The First means that we multiply the first terms of each binomial together. In this case, that would be x · y = xy.

O: The Outer means that we multiply the outer terms, or the first term of the first binomial and the second term of the last binomial, together. In this case, that would be x · 8 = 8x.

I: The Inner means that we multiply the inner terms, or the second term of the first binomial and the first term of the second binomial, together. In this case, that would be (-1) · y = -y.

L: The Last means that we multiply the last terms of each binomial together. In this case, that would be (-1) · 8 = -8.

Adding all of these together, we get xy + 8x - y - 8 as our final answer.

Hope this helps!

Answer:

[tex]xy+8x-y-8[/tex]

Step-by-step explanation:

=> (x-1)(y+8)

Using FOIL

=> [tex]xy+8x-y-8[/tex]

Answer:

Laura tiene 15 años mientras que su madre tiene 35 años.

Step-by-step explanation:

Deje que la edad de Laura sea L.

Deje que la edad de su madre sea m.

Tiene 3/7 de la edad de su madre:

L = 3 m / 7

En 5 años, la edad de su madre será el doble de su edad:

(m + 5) = 2 (L + 5)

m + 5 = 2L + 10

m - 2L = 5

Pon el valor de L:

m - 2 (3 m / 7) = 5

m - 6 m / 7 = 5

Multiplica por 7:

7m - 6m = 35

m = 35 años

=> L = 3 * 35/7 = 15 años

Laura tiene 15 años mientras que su madre tiene 35 años.

Answer:

4x-3y

Step-by-step explanation:

Answer:

Yes, it contradict this prior belief as there is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes.

Test statistic t=2.238>tc=1.708.

The null hypothesis is rejected.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the true average escape time is significantly higher than 6 minutes (360 seconds).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=360\\\\H_a:\mu> 360[/tex]

The significance level is 0.05.

The sample has a size n=26.

The sample mean is M=370.69.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=24.36.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{24.36}{\sqrt{26}}=4.777[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{370.69-360}{4.777}=\dfrac{10.69}{4.777}=2.238[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=26-1=25[/tex]

The critical value for a  right-tailed test with a significance level of 0.05 and 25 degrees of freedom is tc=1.708. If the test statistic is bigger than 1.708, it falls in the rejection region and the null hypothesis is rejected.

As the test statistic t=2.238 is bigger than the critical value t=1.708, the effect is significant.  The null hypothesis is rejected.

There is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes (360 seconds).

Answer:

9/14

Step-by-step explanation:

3/7 + 50%×3/7 =

= 3/7 + 1/2×3/7

= 3/7 + 3/14

= 6/14 + 3/14

= 9/14

The required fraction which 50% grater than 3/7 is 9/14.

Fraction to determine that 50% grater than 3/7.

Fraction of the values is number represent in form of Numerator and denominator.

Here, fraction = 50% grater than 3/7
                     = 1.5 x 3/7
                    = 4.5/7
                     =  45/70
                     = 9/14

Thus, The required fraction which 50% grater than 3/7 is 9/14.

Learn more about fraction here:
https://brainly.com/question/10354322

#SPJ5

An event that is impossible has a probability of 0

An event that is certain to happen has a probability of 1

The probability scales from 0 to 1, referring from no chance to will happen.

Answer:

E. The parameter is μmale - μfemale and the statistic is xmale - xfemale.

Step-by-step explanation:

The sample statistic is a piece of information about the individuals or objects that were selected from a given population. The sample is just a fraction of the total population. Since it is a herculean task studying an entire population, the sample forms a manageable size that allows us to have an insight into the entire population. The sample statistics are now the piece of information about the sample being studied such as the average, mean, median, or mode.  The sample statistics have to be as specific as possible of the factors being measured. In the question, we would have to obtain the mean of both the male and female genders. This gives us an insight into the population under study.

The parameter, on the other hand, is a description of the entire population being studied. For example, we might want to determine the population mean. That is the factor we seek to measure. It is represented by the sign mu (μ).  

Answer:

-18 < -x-4 < -8

Step-by-step explanation:

We start with the initial range as:

4 < x < 14

we multiplicate the inequation by -1, as:

-4 > -x > -14

if we multiply by a negative number, we need to change the symbols < to >.

Then, we sum the number -4, as:

-4-4> -x-4 > -14-4

-8 > -x-4 > -18

Finally, the range for -x-4 is:

-18 < -x-4 < -8

Answer:

n^2+3

Step-by-step explanation:

As we can see in the diagram

1st pattern consists from 1 square 1x1 +3 squares 1x1 each

2nd pattern consists from 1 square 2x2 +3 squares 1x1 each

3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each

4-th pattern consists from 1 square 4x4 + 3 squares 1x1  each

We can to continue :

5-th pattern consists from 1 square 5x5+3 squares 1x1 each

So the nth    pattern consists from 1 square nxn+3 squares 1x1 each

Or total amount of 1x1 squares in nth pattern N= n^2+3

The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."

From the given diagram

We can see that every term is made up with a square which side is n and three small square side is 1.

So,

1st term is 1 × 1 + 3 = 4

2nd term is 2 × 2 + 3 = 4

3rd term is  3 × 3 + 3 = 12

4th term is 4 × 4 + 3 = 19

So, nth term is [tex]n^{2} +3[/tex]

Hence, The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

Learn more about nth term of a sequence here

https://brainly.com/question/24306119

#SPJ2

Answer:

If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution

Step-by-step explanation:

For this problem we are assumeing that the random variable X is :

[tex] X \sim Bin(n,p)[/tex]

If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution and if we don't satisfy this two conditions:

[tex] n p>10[/tex]

[tex]n(1-p) >10[/tex]

Then we can't use the normal approximation

Answer:

Step-by-step explanation:

Hello friend

The answer is 5:15 in 12 hour clock

Answer:

5:15 PM

Step-by-step explanation:

12:00 + 5:00

17:00 in 12 hour clock is 5:00 PM.

15 minutes + 5:00 PM

⇒ 5:15 PM

Answer:

The z–score corresponding to 45 is z=2.

Step-by-step explanation:

We have a random variable X represented by a normal distribution, with mean 35 and standard deviation 5.

The z-score represents the value X relative to the standard normal distribution. This allows us to calculate probabilities for any given normal distribution with the same table.

The z-score for X=45 can be calculated as:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{45-35}{5}=\dfrac{10}{5}=2[/tex]

The z–score corresponding to 45 is z=2.

Answer:

AB=4

Step-by-step explanation:

The transitive property states if A=B and B+C than A+C  Next substitute

AB=x and x=4 so AB=4

Hope this helps, if it did, please give me brainliest, it helps me a lot. :)

Have a good day!

Answer:

The period is of [tex]\frac{\pi}{3}[/tex] units.

The horizontal shift is of 30 units to the left.

Step-by-step explanation:

The secant function has the following general format:

[tex]y = A\sec{(Bx + C)}[/tex]

A represents the vertical shift.

C represents the horizontal shift. If C is positive, the shift is to the right. If it is negative, it is to the left.

The period is [tex]P = \frac{2\pi}{B}[/tex]

In this question:

[tex]y = 7\sec{6x - 30}[/tex]

So [tex]B = 6, C = -30[/tex]

Then [tex]P = \frac{2\pi}{6} = \frac{\pi}{3}[/tex]

The period is of [tex]\frac{\pi}{3}[/tex] units.

The horizontal shift is of 30 units to the left.

Answer:

y - 3 = (1/2)(x - 1)

Step-by-step explanation:

As we go from (1, 3) to (5, 1), we see that x (the run) increases by 4 and y (the rise) decreases by 2.  Hence, the slope is m = rise / run = 2/4, or m = 1/2.

Then the desired point slope equation is  y - 3 = (1/2)(x - 1).

Answer:

never intersect

Step-by-step explanation

parallel lines do not intersect and neither do parallel planes

Answer:

6

Step-by-step explanation:

nerd physics

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be [tex]h(t) = -16\cdot t^{2} + 128\cdot t + 320[/tex], the first and second derivatives are, respectively:

First Derivative

[tex]h'(t) = -32\cdot t +128[/tex]

Second Derivative

[tex]h''(t) = -32[/tex]

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

[tex]-32\cdot t +128 = 0[/tex]

[tex]t = \frac{128}{32}\,s[/tex]

[tex]t = 4\,s[/tex] (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

[tex]h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320[/tex]

[tex]h(4\,s) = 576\,ft[/tex]

The highest altitude that the object reaches is 576 feet.

Answer:

when a number is divisible by 9, then the number is divisible by 3.

Step-by-step explanation:

They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:

when a number is divisible by 9, then the number is divisible by 3.

Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .

Answer:

a

Step-by-step explanation:

Answer:

1. Test statistic t=1.581.

2. The null hypothesis H0 failed to be rejected.

There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.

NOTE: if the null hypothesis is µ = 40, there is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40 (test statistic t=3.161).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean number of calls per salesperson per week is significantly more than 41.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=41\\\\H_a:\mu> 41[/tex]

The significance level is 0.025.

The sample has a size n=38.

The sample mean is M=42.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-41}{0.633}=\dfrac{1}{0.633}=1.581[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=38-1=37[/tex]

This test is a right-tailed test, with 37 degrees of freedom and t=1.581, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>1.581)=0.061[/tex]

As the P-value (0.061) is bigger than the significance level (0.025), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.

For µ = 40:

This is a hypothesis test for the population mean.

The claim is that the mean number of calls per salesperson per week is significantly more than 40.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=40\\\\H_a:\mu> 40[/tex]

The significance level is 0.025.

The sample has a size n=38.

The sample mean is M=42.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-40}{0.633}=\dfrac{2}{0.633}=3.161[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=38-1=37[/tex]

This test is a right-tailed test, with 37 degrees of freedom and t=3.161, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>3.161)=0.002[/tex]

As the P-value (0.002) is smaller than the significance level (0.025), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40.  

Answer:

Step-by-step explanation:

a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.

The principal P that must be invested at rate r for n annual withdrawals of amount A is ...

  P = A(1+r)(1 -(1 +r)^-n)/r

  P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95

__

b) 20 withdrawals of $60,000 each total ...

  20×$60,000 = $1,200,000

__

c) The excess over the amount deposited is interest:

  $1,200,000 -636,215.95 = $563,784.05

Answer: a) 503.2m

b) 621.6m

Step-by-step explanation:

The diagram representing the scenario is shown in the attached photo.

A represents her starting point.

CD = x = how far east she is from her starting point

BC = y = how far south she is from her starting point

Angle BAC = 180 - 129 = 51°

Angle ACD = angle BAC = 51° because they are alternate angles

To determine x, we would apply the cosine trigonometric ratio

Cos 51 = x /800

x = 800Cos51 = 800 × 0.629 = 503.2m

To determine y, we would apply the sine trigonometric ratio

Sin 51 = y /800

y = 800Sin51 = 800 × 0.777 = 621.6m

Answer: (d) 88/ 2π

Step-by-step explanation:

Perimeter = 88m

Perimeter of a circle = 2πr

88 = 2π x r

r = 88 / 2π

Answer:

88/2π​ = r

Step-by-step explanation:

The circumference is 88 m

The circumference is given by

C = 2*pi*r

88 = 2 * pi *r

Divide each side by 2 pi

88 / 2pi = 2 * pi *r / 2 * pi

88 / 2 pi = r

Answer:

x = 25; both labeled angles are 65º

Step-by-step explanation:

To find the value of x, recall that the angles formed by two parallel lines on the same line are equal if they correspond to each other.

In the figure given above, we have two parallel line given. The angle formed by each parallel line is corresponding to the other. Therefore, both angles formed are equal.

Thus,

(3x - 10)° = (x + 40)°

Solve for x

3x - 10 = x + 40

Subtract x from both sides

3x - 10 - x = x + 40 - x

3x - x - 10 = x - x + 40

2x - 10 = 40

Add 10 to both sides

2x - 10 + 10 = 40 + 10

2x = 50

Divide both sides by 2

2x/2 = 50/2

x = 25

*Plug in the value of x to find the measure of each labelled angles:

(3x - 10)° = 3(25) - 10 = 75 - 10 = 65°

(x + 40)° = 25 + 40 = 65°

Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

The probability P(A) that an event A will occur is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question,

=>The event A is selecting a king the second time from a 52-card deck.

=> In the card deck, there are 4 king cards. After the first selection which was a king, the king was returned. This makes the number of king cards return back to 4. Therefore,

number-of-possible-outcomes-of-event-A = 4

=> Since there are 52 cards in total,

total-number-of-sample-space = 52

Substitute these values into equation above;

P(Selecting a king the second time) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

Answer:

$11,450

Step-by-step explanation:

thats the median price according to Google

Answer:

A.

Step-by-step explanation:

It's the first one. The angles are supplementary not complementary.

Answer:

I would have to say A

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

We can find the slope of this line by using two points

(1,-3) and (3,0)

m = (y2-y1)/(x2-x1)

    = (0- -3)/(3 -1)

    = (0+3)/(3-1)

    = 3/2

Answer:

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]

And the best option would be:

d. 1.19.

Step-by-step explanation:

Data given and notation  

[tex]n_1 = 24 [/tex] represent the sampe size 1

[tex]n_2 =16[/tex] represent the sample size 2

[tex]s^2_1 = 32[/tex] represent the sample variance for 1

[tex]s^2_2 = 38[/tex] represent the sample variance for 2

The statistic for this case is given by:

[tex]F=\frac{s^2_1}{s^2_2}[/tex]

Hypothesis to verify

We want to test if the true deviations are equal, so the system of hypothesis are:

H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]

Always the numerator for the statistic needs to be higher than the denominator. And replacing we got:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{38}{32}=1.19[/tex]

And the best option would be:

d. 1.19.