What is the quotient 5^-6 over 5^3

Answer:

The total number of marbles in the bag is 50.

Step-by-step explanation:

Here, we have n trials, without replacement. So the hypergeometric distribution is used.

The mean of the hypergeometric distribution is:

[tex]E(X) = \frac{n*k}{N}[/tex]

In which n is the number of items in the sample, k is the number of items in the population that are classified a success and N is the size of the population.

15 marbles are drawn:

This means that [tex]n = 15[/tex]

A bag contains some number of marbles. It is known that 20 of them are red.

This means that [tex]k = 20[/tex], since a success is drawing a red marble.

Assuming E(X)=6 red, what is the total number of marbles in the bag?

We have to find N when [tex]E(X) = 6[/tex]

So

[tex]E(X) = \frac{n*k}{N}[/tex]

[tex]6 = \frac{15*20}{N}[/tex]

[tex]6N = 300[/tex]

[tex]N = \frac{300}{6}[/tex]

[tex]N = 50[/tex]

The total number of marbles in the bag is 50.

Answer:

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Step-by-step explanation:

From the given information;

the probability of getting returned p = 0.1

If eight rings are sold today, what is the probability that fewer than three will be returned;

According to binomial distribution

Binomial distribution is the probability of success or failure of an outcome of an experiment under observation which is usually repeated several trials. Binomial experiments are random experiment with fixed number of repeated experiment. If we cannot predict before head, the outcome of an experiment , the experiment is called a random experiment.

So , using binomial distribution to determine the probability that fewer than three will be returned;

i.e

[tex]P(X<3) =[/tex] [tex]\sum_{x=0}^{2}\binom{8}{x}(0.1)^{x}(1-0.1)^{8-x}[/tex]

[tex]P(X<3) =[/tex] [tex]0.9619[/tex]

Answer:

Half-life of the goo is 49.5 minutes

[tex]G(t)= 300e^{-0.014t}[/tex]

191.7 grams of goo will remain after 32 minutes

Step-by-step explanation:

Let [tex]M_0\,,\,M_f[/tex] denotes initial and final mass.

[tex]M_0=300\,\,grams\,,\,M_f=37.5\,\,grams[/tex]

According to exponential decay,

[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt[/tex]

Here, t denotes time and k denotes decay constant.

[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\\\ln \left ( \frac{37.5}{300} \right )=-k(150)\\-2.079=-k(150)\\k=\frac{2.079}{150}=0.014[/tex]

So, half-life of the goo in minutes is calculated as follows:

[tex]\ln \left ( \frac{50}{100} \right )=-kt\\\ln \left ( \frac{50}{100} \right )=-(0.014)t\\t=\frac{-0.693}{-0.014}=49.5\,\,minutes[/tex]

Half-life of the goo is 49.5 minutes

[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\Rightarrow M_f=M_0e^{-kt}[/tex]

So,

[tex]G(t)= M_f=M_0e^{-kt}[/tex]

Put [tex]M_0=300\,\,grams\,,\,k=0.014[/tex]

[tex]G(t)= 300e^{-0.014t}[/tex]

Put t = 32 minutes

[tex]G(32)= 300e^{-0.014(32)}=300e^{-0.448}=191.7\,\,grams[/tex]

Answer:

u=6

Step-by-step explanation:

One rule in algebra is what you do to one side, you do it to other side. So if you multiply a number in one side, multiply the same number in other side. Here in this question, you are trying to find the value of the variable u. Variable is called so because the value of it varies depending on different question. Here u is going to be a constant number which when multipled by 3 and then subtracted by 3 equals 15.

So first step is we try to get constants on one side. So we add 3 on both sides to get rid of 3 on left.

3u - 3 + 3= 15+3

3u= 18

Now we divide by 3 on both sides to get u by itself.

3u/3 = 18/3

u= 6

Answer:

The correct answer to the following question will be Option A (67.9%).

Step-by-step explanation:

As we know,

The number of total employees will be:

= 480

The number of employees having normal or low BP will be:

= 96 + 230

= 326

Hence, the percentage of low or normal BP workers will be:

= [tex](\frac{326}{480} )\times 100 \ percent[/tex]

= [tex]67.9 \ percent[/tex]

Note:- % (percent)

Answer:

7.He borrowed $1853.33

8.She received $28990.936

Step-by-step explanation:

7.Let x be the amount borrowed by Tyson

Rate of interest = 7.5%

Time = 2.5 years

Simple Interest = 347.50

Formula : [tex]Si = \frac{P \times T \times R}{100}[/tex]

Where SI = simple interest

P = Principal

T = Time

R = Rate of interest

Substitute the values in the formula :

[tex]347.50=\frac{x \times 2.5 \times 7.5}{100}\\\frac{347.50 \times 100}{2.5 \times 7.5}=x\\1853.33=x[/tex]

Hence he borrowed $1853.33

8) Principal = 20000

Rate of interest = 9.5%

No. of compounds per year = 2

Time = 4 years

Formula : [tex]A=P(1+\frac{r}{n})z^{nt}[/tex]

Where A= amount

r = Rate of interest

n = no. of compounds

t = time

Substitute the values in the formula :

So, [tex]A=20000(1+\frac{9.5}{200})^{2(4)}[/tex]

A=28990.936

Hence she received $28990.936

Answer:

a)3145 x 0.01 = 31.45  3145- 31.45 = 3113.55

Compute the sample correlation 3113.55 -? we find the least square pressing at least 15x on the calculator then minus this from 3113.55 to find a better fit and minimum regression.

We add the differences of units then divide by distribution as seen below.

b) unsure.

c) = (see below) just test each number shown unit sold per day / price then x can show the differences in each number from day 1 to day 2.

d) = 16 sold.

Step-by-step explanation:

a) We count the units up and deduct from it from the equation p is recognized as units sold. R1 is cost R2 is total days.

b) The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0).

c) r 2= decimal ; the regression equation has accounted for percentage of the total sum of squares. You cna do this one.

d) = 16 sold at $28 each. - Why ? We using 7 day data and prove a how many units can be sold p/d if the price of flash drive is set to $28 each per unit.

Day 1 = 34  /  28  =  1      =    1.21428571429 = 1 no difference day prior.

Day 2 = 336   / 28   = 12  = 12 = difference day prior is 11

Day 3 = 432  / 28  = 15    =  15.4285714286   = 15 difference day prior is 3

Day 4 = 635  / 28 =  23   =  22.6785714286  = 23 difference day prior is 8

Day 5  = 530  /  28 = 19    =  18.9285714286  = 19 difference day prior is minus - 4

Day 6 = 938  / 28  =  34   = 33.5 = 34 difference day prior is 15

Day 7 = 240  / 28  =   9    =   8.57142857143 = 9 difference day prior is minus -25

Total days 7 = Total revenue / price = average units sold

Average units sold total = 1+ 12+15 +23 +19+34+9 = 113 rounded.

Average units sold total = 1.21428571429 + 12 + 15.4285714286

+ 22.6785714286

+18.9285714286

+ 33.5

+ 8.57142857143 =  112.321428572 units sold weekly when priced at $28

To answer D we divide this by 7  to show;

112.321428572/ 7 = 16.0459183674

Daily units sold = 16

Answer:

  a.  235°

  b. 146.03 km

  c. 105 km

  d. 193 km

Step-by-step explanation:

a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:

  bearing of A from E = 55° +180° = 235°

__

b. The internal angle at E is the difference between the external angle at C and the internal angle at A:

  ∠E = 134° -55° = 79°

The law of sines tells you ...

  CE/sin(∠A) = CA/sin(∠E)

  CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km

  CE ≈ 146 km

__

c. The internal angle at C is the supplement of the external angle, so is ...

  ∠C = 180° -134° = 46°

The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:

  Sin = Opposite/Hypotenuse

  sin(46°) = PE/CE

  PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km

  PE ≈ 105 km

__

d. DE can be found from the law of cosines:

  DE² = DC² +CE² -2·DC·CE·cos(134°)

  DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43

  DE = √37099.43 ≈ 192.6 . . . km

  DE is about 193 km

Answer:

a = 29.3785

Step-by-step explanation:

Given ∠A = 46° and ∠B = 105°

we know that ∠A +∠B+∠C = 180°

                       46° + 105° +∠C = 180°

                      ∠C = 180 - 46 -105

                     ∠ C = 29°

By using sine rule

[tex]\frac{a}{sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]

[tex]\frac{a}{sin A} = \frac{c}{Sin C}[/tex]

Given ∠A = 46° and  ∠ C = 29° and c = 19.8

[tex]\frac{a}{sin 46} = \frac{19.8}{Sin 29}[/tex]

on cross multiplication , we get

[tex]a = \frac{19.8 X sin 46}{Sin 29}[/tex]

a = 29.3785

Answer:

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

Step-by-step explanation:

[tex]2\frac{1}{2}+1\frac{1}{3}\\\mathrm{Add\:whole\:numbers}\:2+1:\quad 3\\\mathrm{Combine\:fractions}\:\frac{1}{2}+\frac{1}{3}:\quad \frac{5}{6}\\=3\frac{5}{6}[/tex]

Answer:

Step-by-step explanation:

Generally's rational functions that have vertical asymptotes, even trig functions (which, like the tangent function, are often rational).

If the given function is the ratio of two functions, polynomial or otherwise, the graph of the given function has an asymptote at any x value for which the denominator is zero.  Example:  y = tan x = (sin x) / (cos x) has vertical asysmptotes at π/2, 3π/2, and so on, because the denominator cos x is zero for those angles.

Answer:

You would move 10 units to the right from zero on the x-axis.

The given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).

A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.

The given coordinate point (10, 8).

The distance of any point from the x-axis is called the x-coordinate.

In the point (10, 8), 10 units from the x-axis

Therefore, the given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).

Learn more about the coordinate plane here:

https://brainly.com/question/24134413.

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Answer:

The null hypothesis is rejected.

There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders (P-value = 0.004).

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that rates are higher for single male policyholders verses married male policyholders.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]

The significance level is 0.05.

The sample 1 (single group), of size n1=450 has a proportion of p1=0.1489.

[tex]p_1=X_1/n_1=67/450=0.1489[/tex]

The sample 2 (married group), of size n2=925 has a proportion of p2=0.1005.

[tex]p_2=X_2/n_2=93/925=0.1005[/tex]

The difference between proportions is (p1-p2)=0.0483.

[tex]p_d=p_1-p_2=0.1489-0.1005=0.0483[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{67.005+93}{450+925}=\dfrac{160}{1375}=0.1164[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.1164*0.8836}{450}+\dfrac{0.1164*0.8836}{925}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0001}=\sqrt{0.0003}=0.0184[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.0483-0}{0.0184}=\dfrac{0.0483}{0.0184}=2.62[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=P(z>2.62)=0.004[/tex]

As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that rates are higher for single male policyholders verses married male policyholders.

Answer:

Step-by-step explanation:

(x + k) is a factor of f(x)

x+k=0 => x= -k;    -k is a root of f(x)

=> f(-k)=0

[tex](x + k) is a factor of f(x)x+k=0 = > x= -k; -k is a root of f(x)= > f(-k)=0[/tex]

So the correct option is B.fl-k)=0.

The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression. The following are examples of rational functions: f(x)=√2x4−5 f ( x ) = 2 x 4 − 5 ; g(x)=3√4x−7 g ( x ) = 4 x − 7 3 ; h(x)=7√−8x2+4 h ( x ) = − 8 x 2 + 4 7 .

The root function is used to find a single solution to a single function with a single unknown. In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns. For now, we will focus on using the root function.

Learn more about root function here: https://brainly.com/question/13136492

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The image of P(-2,1) after it is rotated 90° is (-1,-2).

Answer:

  2082.12 was the total invested

Step-by-step explanation:

Let x represent the amount invested at 14%. Then the amount invested at 12% was (x-580). The total accumulated amount was ...

  112%(x -580) +114%(x) = 2358.60

  2.26x -649.60 = 2358.60

  2.26x = 3008.20 . . . add 649.60

  x = 1331.06 . . . . . . divide by 2.26

  x -580 = 751.06

The total invested was 1331.06 +751.06 = 2082.12 cedis.

__

Check

The investment at 12% was 751.06, so the accumulated amount of that investment was 751.06×1.12 = 841.19.

The investment at 14% was 1331.06, so the accumulated amount of that investment as 1331.06×1.14 = 1517.41.

The accumulated total amount was 841.19 +1517.41 = 2358.60.

Answer:

800 eggs

Step-by-step explanation:

You would first thing about the starting numbers, Then look at the number 100 and multiply by 8. This would give you 800. This means that you will need 800 eggs to serve 100 people.

Brainliest is greatly appreciated

Answered by: Skylar

6/8/2020

9:59 AM (Eastern Time)

Answer:

the answer is 12.5 i know because i divided 100 by 8 and got 12.5 then multiply then got 100

Step-by-step explanation:

got it right just did the test

Answer:

D. 5/13

Step-by-step explanation:

Cosin is adjacent/hypotenuse so, the adjacent would be 5 and the hypotenuse is 13 since it is the longest side. This is viewed from angle B.

Answer:

5/13 (answer D)

Step-by-step explanation:

cos beta = adjacent side / hypotenuse = 5 / 13 (answer D)

Answer:

(1) 4x + 28 (2) 18x- 27

Step-by-step explanation:

the first question 4(x + 7) can be simplified by multiplying the number outside the parenthesis (4) by both of the values inside:

4x + 28 or the last answer choice

in the second question you can use the same method:

9 (2x) = 18x

9 ( -3) = -27

therefore the correct answer choice is 18x - 27

hope this helps :)

Answer:

2

Step-by-step explanation:

Answer: y = 11 - x / -6

Step-by-step explanation:

X - 6y = 11

Since we are solving for y, we need to isolate the variable.

Move x to the other side of the equation.

- 6y = 11 - x

Now divide bith sides by -6 to cancel out -6y and get the variable y

-6y/ -6 = 11 - x/ -6

y = 11 - x / -6

Im not sure if it was solving for y, or if it was solve for x if y = 11

Answer:

c) Yes, because the p-value = 0.0172

Step-by-step explanation:

The following table is obtained:

Categories       Observed(fo)        Expected (fe)        (fo-fe)²/fe

NW Oregon        3109           4357*0.727=3167.539       1.082

SW Oregon        902             4357*0.207=901.899           0

Central Oregon    244          4357*0.048=209.136         5.812

Eastern Oregon    102           4357*0.028=121.996         3.277

Sum =                    4357        4357                                   10.171

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​:p1​=0.727,p2​=0.207,p3​=0.048,p4​=0.028

Ha​: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df=4−1=3, so then the rejection region for this test is R={χ2:χ2>7.815}.

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

[tex]X^2=\sum^n_{i=1}\frac{(O_i-E_i)^2}{y} \\\\= 1.082+0+5.812 +3.277 = 10.171[/tex]

(4) Decision about the null hypothesis

Since it is observed that

[tex]X^2 = 10.171 > X_c^2 = 7.815[/tex]

it is then concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis H_o is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.

Answer:

-5.7° C

Step-by-step explanation:

-2.7 °C (degrees Celsius) - 3 °C (degrees Celsius) = -5.7° C

Answer:

Step-by-step explanation:

Hello!

Given the data for the variables:

Y: Selling price of a house on the shore of Tawas Bay

X₁: Number of bathrooms of a house on the shore of Tawas Bay.

X₂: Square feet of a house on the shore of Tawas Bay.

X₃: Number of bedrooms of a house on the shore of Tawas Bay.

The multiple regression model is Y= α + β₁X₁ + β₂X₂ + β₃X₃ + εi

a. Using software I've entered the raw data and estimated the regression coefficients:

^α= a= -5531.01

Represents the mean selling price of the houses when 0 bathrooms, 0 square feet and 0 bedrooms.

^β₁= b₁= -1386.21

Represents the modification of the mean selling price of the houses when the number of bathrooms increases in one unit and the square feet and number of bedrooms remain unchanged.

^β₂= b₂= 60.28

Represents the modification of the mean selling price of the houses when the square feet increase in one unit and the number of bathrooms and bedrooms remain unchanged.

^ β₃= b₃= 54797.08

Represents the modification of the mean selling price of the houses when the number of bedrooms increase in one unit and the number of bathrooms and square feet of the houses remain unchanged.

^Y= -5531.01 -1386.21X₁ + 60.28X₂ + 54797.08X₃

b)

R²= 0.55

R²Aj= 0.49

The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables. Each time you add another explanatory variable to the regression the coefficient increases regarding of real contribution of the new variable. This could lead to thinking (wrongly) that the new variables are good to explain the dependent variable.  

The adjusted coefficient of determination is a correction made to the raw coefficient of determination to have a more unbiased estimation of the effect the independent variables have over the dependent variable.

⇒ As you can see both coefficient are around 50%, which means that these explanatory variables

c)

The standard error estimate, this is the estimate of the population variance of the errors. In the ANOVA is represented by the Mean Square of the errors (MME)

Se²= MME= 3837640577.01

Se= 61948.6931

d) and f)

For the hypotheses tests for each slope the t- and p-values are:

α: 0.05

β₁: [tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}[/tex] t= -0.06; p-value: 0.9528 ⇒ Do not reject H₀, the test is not significant.

β₂: [tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}[/tex] t= 2.56; p-value: 0.0180 ⇒ Reject H₀, the test is significant.

β₃: [tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}[/tex] t= 2.28; p-value: 0.0326 ⇒ Reject H₀, the test is significant.

e)

H₀: β₁= β₂= β₃

H₁: At least one βi is different from the others ∀ i=1, 2, 3

α: 0.05

F= 9.03

p-value: 0.0004

⇒ Reject H₀, the test is significant.

I hope it helps!

Answer:

(a)No. The probability of drawing a specific second card depends on the identity of the first card.

(b)4/663

(c) 4/663

(d) 8/663

Step-by-step explanation:

(a)The events are not independent because we are drawing cards without replacement and the probability of drawing a specific second card depends on the identity of the first card.

(b) P(ace on 1st card and jack on 2nd).

[tex]P$(Ace on 1st card) =\dfrac{4}{52}\\ P$(Jack on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(ace on 1st card and jack on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]

(c)P(jack on 1st card and ace on 2nd)

[tex]P$(Jack on 1st card) =\dfrac{4}{52}\\ P$(Ace on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(jack on 1st card and ace on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]

(d)Probability of drawing an ace and a jack in either order.

We can either draw an ace first, jack second or jack first, ace second.

Therefore:

P(drawing an ace and a jack in either order) =P(AJ)+(JA)

From parts (b) and (c) above:

[tex]P$(jack on 1st card and ace on 2nd) =\dfrac{4}{663}\\P$(ace on 1st card and jack on 2nd) =\dfrac{4}{663}\\$Therefore:\\P(drawing an ace and a jack in either order)=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}[/tex]

the answer is A: 146 ≤ 9c + 10

Answer:

sale prices = $252

Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252

Answer:

$189

Step-by-step explanation:

10% of 210 = 21

210 - 21  = 189

Answer:

$638641.33

Step-by-step explanation:

Adam earns $45,000 in his first year.

His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.

This is a geometric sequence where the:

(a)

Sum of  geometric series[tex]=\dfrac{a(r^n-1)}{r-1}[/tex]

Substituting the given values, Adam's total earnings over n years

[tex]=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}[/tex]

(b)When n=12 years

[tex]\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)[/tex]

Answer: 0.007

Step-by-step explanation:

Suppose that you have a ticket.

We have 3 prizes, and 300 tickets.

After the first tiket is drawn, someone win a prize, so now we have 299 tikets left and 2 prizes left.

Then, for the next draw, you have p = 1/299 of wining a prize.

If you did not win there, the probability for the third price is p = 1/298 (because there are 2 less tickets now)

Then the probability of winning at least one prize is:

P = 1/299 + 1/298 = 0.007