determine if 25110 is divisible by 45​

Answer:

The requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.

Step-by-step explanation:

A normal-distribution is an accurate symmetric-distribution of experimental data-values.  

If we create a histogram on data-values that are normally distributed, the figure of columns form a symmetrical bell shape.  

If X [tex]\sim[/tex] N (µ, σ²), then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).

The distribution of these z-variates is known as the standard normal distribution.

Thus, the requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.

Step-by-step explanation:

It is not specified the compounding period, which in general is a month these days.  So we will assume money is compounded each month, otherwise there is no point depositing monthly.

1. Yolanda:

APR=5% is equivalent to

Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i

Monthly deposit = 100 = A

Future value after 14 years = 14*12 months = 168 months = n

FV1 =  A((1+i)^n-1)/i

=100*((1+1/240)^168-1)/(1/240)

= $24259.83

2. Zach

He deposits 1200 at the end of the year.  The last payment does not benefit from interest.

Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of

(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j

Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest

FV2 = A((1+j)^n-1)/j

= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200

= 22613.34

Summary

Total investments:

Yolanda = 12*100*14 = 16800

Zach = 1200 * 14 = 16800

So both investors have invested $16800 over the 14 year period.

Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.

Note:

If zach had invested annually at the beginning of the year, he would have obtained:

A((1+j)^n-1)/j

= 1200((1.051161897881733)^14-1)/(0.051161897881733)

= 24908.88

which is superior over Yolanda's return.

Answer:  C) -98, -686, -4,802, -33,614

Step-by-step explanation:

There are 5 steps from -14 to -235,298.

First, let's find the ratio (r):

[tex]-14r^5=-235,298\\\\r^5=\dfrac{-235,298}{-14}\\\\r^5=16,807\\\\r=\sqrt[5]{16,807} \\\\r=7[/tex]

Next, multiply each term by r = 7

-14 x 7 = -98

             -98 x 7 = -686

                            -686 x 7 = -4,802

                                             -4,802 x 7 = -33,614

                                                                  -33,614 x 7 = -235,298 [tex]\checkmark[/tex]

Answer:

x=25

Step-by-step explanation:

The actual question is shown in the image attached.

Solve for x.

sqrt(x)^(log_5(x) -1) = 5  ......................(1)

Solution:

from (1)

sqrt(x)^(log_5(x) -1) = 5  .......separate exponents, law of log a^(b-c)=a^b/a^c

sqrt(x)^log_5(x) / sqrt(x) = 5  .......... cross multiply

sqrt(x)^log_5(x) = 5sqrt(x)   .............. square both sides

(sqrt(x)^log_5(x))^2 = 25x     .............. modify base a^(2b) = (a^2)^b

(sqrt(x)^2)^log_5(x) = 25x

x^log_5(x) = 25x   .................... take log_5 on both sides

log_5(x) * log_5(x) = log_5(5^2*x)  ............... simplify RHS

log_5(x) * log_5(x) = log_5(25)+log_5(x)

log_5(x) * log_5(x) = 2+log_5(x) ........ simplify

log_5(x) ^2 -log_5(x) -2 = 0   ........... substitute y = log_5(x)

y^2 - y -2 = 0

(y-2)(y+1) = 0

y=2 or

y = -1   ................... y = log_5(x) >= 0 , y=-1 rejected

y = 2

log_5(x) = 2

raise to base of 5

5^log_5(x) = 5^2

x = 25

Check by substituting x = 25 in (1)

sqrt(x)^(log_5(x) -1)

= sqrt(25)^(log_5(25) -1)

= 5^(2-1)

= 5    equal RHS,  therefore solution is correct.

Answer:

35 degrees

Step-by-step explanation:

4x + 5 (the measure of the large angle) + x (the measure of the supplementary angle) = 180. Therefore x = 35

Answer:

35,145

Step-by-step explanation:

angle 1+angle 2=180 degrees

x=angle 1

x+4x+5=180

4x+5 is angle 2 (larger angle) bc it is 5 more than 4 time the measure of the smaller angle

now we solve

x+4x+5=180

5x+5=180

5x=175

x=35

the smaller angle is 35 degrees

4x+5=bigger angle

4(35)+5=

140+5=

145=bigger angle

Answer:

There is enough evidence to support the claim that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Step-by-step explanation:

The question is incomplete:

"A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 32 salespersons with a degree had an average weekly sale of $3599 last year, while 35 salespersons without a college degree averaged $3311 in weekly sales. The standard deviations were $468 and $642 respectively.

Required:

Is there evidence at the 5% level to support the retailer's belief?"

This is a hypothesis test for the difference between populations means.

The claim is that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

The significance level is 0.05.

The sample 1 (college degree), of size n1=32 has a mean of 3599 and a standard deviation of 468.

The sample 2 (non-college degree), of size n2=35 has a mean of 3311 and a standard deviation of 642.

The difference between sample means is Md=288.

[tex]M_d=M_1-M_2=3599-3311=288[/tex]

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

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{468^2}{32}+\dfrac{642^2}{35}}\\\\\\s_{M_d}=\sqrt{6844.5+11776.114}=\sqrt{18620.614}=136.4574[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{288-0}{136.4574}=\dfrac{288}{136.4574}=2.11[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=32+35-2=65[/tex]

This test is a right-tailed test, with 65 degrees of freedom and t=2.11, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>2.11)=0.019[/tex]

As the P-value (0.019) 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 the average sales are significantly greater for salespersons with a college degree than for salespersons without it.

Answer:

-7

Step-by-step explanation:

4 + (−3 − 8)

PEMDAS

Parentheses first

4 + (-11)

Add and subtract next

-7

Answer:

first I'm using BODMAS

4+(-11)

= -7

hope it helps

Answer:

[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]    

[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=32.9[/tex] represent the sample mean for the sample  

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

s=4.9 represent the sample standard deviation

n=8 represent the sample size  

Confidence interval

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=8-1=7[/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 for this cae would be [tex]t_{\alpha/2}=2.365[/tex]

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

[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]    

[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]    

Answer:

2x^3-26x^2+50x-650

Step-by-step explanation:

The standard form of polynomial is P(x) = [tex]2x^{3}-26x^{2} +50x-650.[/tex]

What is polynomial?

A polynomial is defined as an expression which consists of single or multiple terms. The term polynomial is originated from two different terms such as “poly” and “Nomial”. The term “poly” means many and “nomial” means terms. In short, a polynomial is an algebraic expression which has two or more algebraic terms. It has variables, constants, coefficients, exponents and operators.

Given, the roots of polynomial as 13, 5i, -5i.

and P(3) =-680 at x = 3

If roots are given, we find the polynomial with fomuala as,

P(x) = a(x-13)(x-5i)(x+5i)

using bodmas

[tex]P(x) = a(x-13)[x^{2} -5ix+5ix-25i^{2} ][/tex]

we know [tex]i^{2} = -1[/tex]

we get,

[tex]P(x) = a (x-13)(x^{2} +25)[/tex]

P(x) = [tex]a(x^{3} +25x-13x^{2} -325)[/tex]

at x = 3, P(3) = -680

[tex]-680 =a(3^{3}-13(3)^{2} +25(3)-325)[/tex]

a = 2

Hence, P(x) = [tex]2x^{3} -26x^{2} +50x-650[/tex]

To know more about polynomial, visit:

https://brainly.com/question/1496352

#SPJ2

Answer:

Number of ways = 40320 ways

Step-by-step explanation:

Total number of posters = 8

The points are to be arranged in the room without any definite pattern or configuration.

Since there is no definite pattern ir configuration to hang the posters, the number of ways f hanging the posters will be gotten by factorial method.

Number of ways = 8!

Number of ways= 8*7*6*5*4*3*2*1

Number of ways = 56*30*12*2

Number of ways = 1680 * 24

Number of ways = 40320

Answer:

Using the distributive property we get:

y(x) + y(4) - 3(x) - 3(4)

= xy + 4y - 3x - 12

Answer:

[tex]xy+4y-3x-12[/tex]

Step-by-step explanation:

=> (y-3)(x+4)

USING FOIL to solve brackets

=> [tex]xy+4y-3x-12[/tex]

Answer:

3x + 2y = 315 -----(1)

2x + 4y = 450 -----(2)

from (1) 3x + 2y = 315

2y = 315-3x

y = 157.5 - 3/2x ---- (3)

substitute (3) into (2)

2x + 4y = 450

2x + 4(157.5 - 3/2x ) = 450

2x + 630 - 6x = 450

-4x = -180

x = 45 ---- (4)

substitute (4) into (3)

y = 157.5 - 3/2x

y = 157.5 - 3/2(45)

y = 90

a haircut,x = 45 minutes

dye hair,y = 90 minutes

Answer:

Horizontal tangent

(x, y) = (1, 0)

Vertical tangent

(x, y) = DNE

Step-by-step explanation:

The equation for the slope (m) of the tangent line at any point of a parametric curve is:

[tex]m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]

Where [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex] are the first derivatives of the horizontal and vertical components of the parametric curves. Now, the first derivatives are now obtained:

[tex]\frac{dx}{dt} = -1[/tex] and [tex]\frac{dy}{dt} = 2\cdot t[/tex]

The equation of the slope is:

[tex]m = -2\cdot t[/tex]

As resulting expression is a linear function, there are no discontinuities and for that reason there are no vertical tangents. However, there is one horizontal tangent, which is:

[tex]-2\cdot t = 0[/tex]

[tex]t = 0[/tex]

The point associated with the horizontal tangent is:

[tex]x = 1 - 0[/tex]

[tex]x = 1[/tex]

[tex]y = 0^{2}[/tex]

[tex]y = 0[/tex]

The answer is:

Horizontal tangent

(x, y) = (1, 0)

Vertical tangent

(x, y) = DNE

Answer:

$420

Step-by-step explanation:

This the problem of compound interest

If any amount P is invested at rate of r% per year then its value after n years is given by

amount = [tex]p( 1+ r/100)^n[/tex]

______________________________

Given

p = $190

r =8%

n = 10 year then

[tex]amount = p( 1+ r/100)^n\\=> amount = 190( 1+ 8/100)^10\\=> amount = 190( 108/100)^10\\=> amount = 410.20[/tex]

Thus, value of the investment at the end of 10 years is $420.

Answer: 342

Step-by-step explanation:

This is a SIMPLE INTEREST question:

SI = prt

SI = 190 x 0.08 x 10

SI = 152

Amount = 190 + 152 = 342

Answer:

[tex]x^2-2x+1[/tex]

Step-by-step explanation:

=> (x-1)(x-1)

Using FOIL

=> [tex]x^2-x-x+1[/tex]

=> [tex]x^2-2x+1[/tex]

Answer:

[tex]\boxed{x^2-2x+1}[/tex]

Step-by-step explanation:

[tex](x-1)(x-1)[/tex]

Apply FOIL Method.

[tex]x(x-1)-1(x-1)[/tex]

[tex]x^2-x-x+1[/tex]

Combine like terms.

[tex]x^2-2x+1[/tex]

Answer:

CI: {0.4085; 0.6647}

Step-by-step explanation:

The confidence interval for a proportion (p) is given by:

[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]

Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:

[tex]p=\frac{22}{41}=0.536585[/tex]

Thus the confidence interval is:

[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]

The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}

Answer:

100,000 meters

Step-by-step explanation:

There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.

Answer:

it is 100000 kilometers

Step-by-step explanation:

use the metric system and you get 10000 kilometers.

Answer: (5, 42)

Step-by-step explanation:

22 + 4x= 42

if we test the options we will see this is the only one that works

42 - 22 = 20

4x = 20

x= 5

which is equal to X the number of weeks they have gotten the allowance.

Answer:

sorry i dont understand it

Step-by-step explanation:

Answer:

1 min 45 sec

Step-by-step explanation:

First convert 14 min to seconds.

14 x 60 = 840s

Now we can use ratios to find the answer

840s : 800m

Divide both sides by 8

105s : 100m

105s is 1 minute and 45 seconds

Answer:

Step by step explanation:

Time taken to swim 800 meter:

=14 minutes

Time taken to swim 1 meter:

[tex] = \frac{14}{800} minutes[/tex]

Time taken to swim 100 meter:

[tex] \frac{14}{100} \times 100[/tex]

[tex] = 1.75 \: minutes[/tex]

Here,

1 minute=60 Seconds

0.75 minute=0.75*60=45 seconds

So the answer is 1 minute and 45 seconds.

Hope this helps....

Good luck on your assignment....

Answer:

[tex]a + b \geq 30[/tex]

[tex]b - a \geq 10[/tex]

Step-by-step explanation:

Given

Two integers a and b

The first statement in the question says, their sum is at least 30

The keyword "at least" means their sum can not fall below 30 and this is represented mathematically as

[tex]a + b \geq 30[/tex]

The next statement says their difference is at least 10 and b is greater;

The keyword "at least" means the same as used above (i.e. can not exceed); The second statement is represented as:

[tex]b - a \geq 10[/tex]

Hence, the system of inequality that represents the statements are:

[tex]a + b \geq 30[/tex]

[tex]b - a \geq 10[/tex]

Answer:

70 weeks

Step-by-step explanation:

500g = .5kg

140 - .5w = 105

35 = .5w

70 = w

Answer:

1 - B

2 - A, C

3 - E

4 - D

5 - H

6 - D

7 - None

8 - F, G

Step-by-step explanation:

1. We know the equation that :

[tex]V = I \times R[/tex]

Where V is the voltage

I is the Electric Current and

R is the resistance

So,

[tex]I = \dfrac{V}{R}[/tex]

2. An equation of a linear curve is represented as:

y = mx+c or

Y = mX+C

So, the correct matches are:

A. Y = 8x + 6

and

C. y = 8x + 6

3. A constant:

The constant expression as in options is:

E. 12.23154687854

4. 1st order differential equation is the equation in which there is differentiation done once.

[tex]y'[/tex] or [tex]\dfrac{dy}{dx}[/tex] are used to represent it.

So, correct option is D. y' - 8x - 6 = 0

5. A 2nd order differential equation is the equation in which there is differentiation done once.

[tex]y''[/tex] or [tex]\dfrac{d^2y}{dx^2}[/tex] are used to represent it.

So, correct option is H. y" = 8

6. An ordinary differential equation (1st order)

Same as answer to part 4.

[tex]y'[/tex] or [tex]\dfrac{dy}{dx}[/tex] are used to represent it.

So, correct option is D. y' - 8x - 6 = 0

7. A partial differential equation is an equation that contains a term represented as:

[tex]\dfrac{\partial y}{\partial x}[/tex]

but there is no such term given here, so no option matches.

8. An integration equation:

The correct options are F and G.

F. [tex]100 y = \int(8x + 6)dx[/tex]

G. [tex]\int dz = \int 8xdx + \int 8dy[/tex]

Answer:

Choice C.

Step-by-step explanation:

Your choice is correct

2 stands for a starting point which is 2 feet from the home

As the ant moves, over time, the distance increases according to the function

Answer:

Option (C)

Step-by-step explanation:

Given expression is,

[tex]4+4\times \text{log}_2(x)=14[/tex]

By subtracting 4 from both the sides of the equation.

[tex]4\times \text{log}_2(x)=14-4[/tex]

Now divide the equation by 4

[tex]\text{log}_2(x)=\frac{10}{4}[/tex]

[tex]\text{log}_2(x)=2.5[/tex]

[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]

[tex]x=(2)^{2.5}[/tex]

[tex]x = 5.657[/tex]

x ≈ 5.66

Therefore, Option C will be the correct option.

4+4•log2 x=14

x= 5.66

Answer:

The probability that there are 2 or more fraudulent online retail orders in the sample is 0.483.

Step-by-step explanation:

We can model this with a binomial random variable, with sample size n=20 and probability of success p=0.08.

The probability of k online retail orders that turn out to be fraudulent in the sample is:

[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{20}{k}\cdot0.08^k\cdot0.92^{20-k}[/tex]

We have to calculate the probability that 2 or more online retail orders that turn out to be fraudulent. This can be calculated as:

[tex]P(x\geq2)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0)=\dbinom{20}{0}\cdot0.08^{0}\cdot0.92^{20}=1\cdot1\cdot0.189=0.189\\\\\\P(x=1)=\dbinom{20}{1}\cdot0.08^{1}\cdot0.92^{19}=20\cdot0.08\cdot0.205=0.328\\\\\\\\P(x\geq2)=1-[0.189+0.328]\\\\P(x\geq2)=1-0.517=0.483[/tex]

The probability that there are 2 or more fraudulent online retail orders in the sample is 0.483.

Answer:

7/2x

Step-by-step explanation:

Well first we need to put,

2x + 7y = 5,

into slope intercept

-2x

7y = -2x + 5

Divide y to all numbers

y = -2/7x + 5/7

So the slope for the given line is -2/7,

the slope of the line that is perpendicular to it is its reciprocal.

Meaning the slope of the perpendicular line is 7/2.

Thus,

the slope of the perpendicular line is 7/2x.

Hope this helps :)

Answer:

The slope of the perpendicular line is 7/2

Step-by-step explanation:

2x+7y=5

Solve for y to find the slope

2x-2x+7y=5-2x

7y = -2x+5

Divide by 7

7y/7 = -2/7 x +5/7

y = -2/7x + 5/7

The slope is -2/7

The slope of perpendicular lines multiply to -1

m * -2/7 = -1

Multiply each side by -7/2

m * -2/7 *-7/2 = -1 * -7/2

m = 7/2

The slope of the perpendicular line is 7/2

Answer: 25%

Step-by-step explanation:

[tex]\frac{(75*.5)+(125+.1)}{75+125}[/tex]

Get ".5" and ".1" from converting 50% and 10% to decimals versions.

Answer:

SOLUTION SET={x<-3/2   or   x≥48/5} option A

Step-by-step explanation:

12x+7<-11                           and            5x-8≥40

solving the both inequalities

12x+7-7<-11-7                     and             5x-8+8≥40+8

12x<-18                              and              5x≥48

12x/12<-18/12                     and               5x/5≥48/5

x<-3/2                                and               x≥48/5

SOLUTION SET={x<-3/2   or   x≥48/5}

i hope this will help you :)

Answer:

C. HL

Step-by-step explanation:

The Hypotenuse-Leg Theorem is the only viable way to determine congruency between 2 right triangles.