Ann's $6,900 savings is in two accounts. One account earns 3% annual interest and the other earns 8%. Her total interest for the year is $342. How much does she have in each account?

Answer:

The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.

Step-by-step explanation:

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].

In this question:

We apply the inverse Central Limit Theorem.

The mean monthy car payment for 123 residents of the local apartment complex is $624.

So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.

Answer:

x = 2, y = 5

Step-by-step explanation:

Hello,

   y=6x-7

   9x-2y=8

can be written as

   (1) 6x - y = 7

   (2) 9x -2y = 8

(2)-2*(1) gives

   9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6

   <=> -3x=-6

   <=> x = 6/3=2

and we replace it in (1)

  y = 6*2-7=12-7=5

hope this helps

Answer:

a) Fx=-5N  Fy=-5*sqrt(3) N   b) Fx= 5*sqrt(3) N    Fy=-5N

c) Fx=-5*sqrt(2) N    Fy=-5*sqrt(2)   N

Step-by-step explanation:

The arrow's F ( weight) component on axle x  is Fx= F*sinA  and on axle y is

Fy=F*cosA

a) The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(30)= -5 N      Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N

b) Now the x component  is co directed to axle x , and y component is opposite directed to axle y.

So x component is positive and y components is negative

So Fx = 10*sin(60)= 5*sqrt(3) N       Fy= -10*cos(60)= -10*1/2= -5 N

c)The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(45)= -5*sqrt(2)  N    

 Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N

Answer:

Step-by-step explanation:

greatest number=8643

smallest number=3468

difference=8643-3468=5175

6.1.  DCCLVI

CDXCIV

(II) 74,746

=============================================================

How I got that answer:

We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.

Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.

----------

You could use the slope formula to get the job done. This is because the slope represents the rise over run

slope = rise/run

The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...

In a more written out way, the steps would be

slope = rise/run

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

slope = (793 - 54)/(2004 - 1995)

slope = 739/9

slope = 82.111....

Answer:

The answer is below

Step-by-step explanation:

They would be written like this:

Arithmetic Progression:

Explicit formula

Tn = a + (n-1) * d

Recursive formula

Tn = Tn-1 + d

Where a is the first term, d is the common differance and n is the number of terms.

Geometric Progression:

Explicit formula

Tn = a * r ^ (n-1)

Recursive formula

Tn = Tn-1 * r

Where r is common ratio

Answer:

  2 1/4

Step-by-step explanation:

The volume of soil needed is ...

  (14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³

The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.

  You need to order 2 1/4 cubic yards.

___

There are 3 ft or 36 inches to a yard.

Answer:

A sample of 385 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample:

We need a sample of n.

n is found when M = 0.05.

We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample of 385 is needed.

Answer:

3/8

Step-by-step explanation:

Step 1: Find common denominators

1/2 = 4/8

2/4 = 4/8

Step 2: Evaluate

4/8 + 4/8 - 5/8

8/8 - 5/8

3/8

Alternatively, you can just plug this into a calc to evaluate and get your answer.

Answer:

3/8

Step-by-step explanation:

Look at the denominator:

2, 4, 8. The LCM (Lowest Common Multiple) is 8.

So this equation becomes

4/8+4/8-5/8=3/8

Answer:

  B)  112°

Step-by-step explanation:

After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:

  2·56° = 112°

_____

In the attached, lines l and m are separated by 56°, as required by the problem statement.

Answer:

B. Tanisha sold the CDs for $2 each.

Step-by-step explanation:

Answer:

  B

Step-by-step explanation:

You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).

The shading is below the line because y-values are less than (or equal to) values on the line.

Choice B matches the attached graph.

Answer:

it is graph b

Step-by-step explanation:

Answer:

Since both np > 5 and np(1-p)>5, it is  suitable to use the normal distribution as an approximation.

Step-by-step explanation:

When the normal approximation is suitable?

If np > 5 and np(1-p)>5

In this question:

[tex]n = 24, p = 0.6[/tex]

So

[tex]np = 24*0.6 = 14.4[/tex]

And

[tex]np(1-p) = 24*0.6*0.4 = 5.76[/tex]

Since both np > 5 and np(1-p)>5, it is  suitable to use the normal distribution as an approximation.

Answer:

Sum of 2 digit = 48

Sum of 3 digit = 317

Sum of 4 digit = 3009

Total = 3374

Step-by-step explanation:

Given:

9, 8 and 7

Required

Sum of Multiples

The first step is to list out the multiples of each number

9:- 9,18,....,99,108,117,................,999

,1008

,1017....

8:- 8,16........,96,104,...............,992,1000,1008....

7:- 7,14,........,98,105,.............,994,1001,1008.....

Calculating the sum of smallest 2 digit multiple of 9, 8 and 7

The smallest positive 2 digit multiple of:

- 9 is 18

- 8 is 16

- 7 is 14

Sum = 18 + 16 + 14

Sum = 48

Calculating the sum of smallest 3 digit multiple of 9, 8 and 7

The smallest positive 3 digit multiple of:

- 9 is 108

- 8 is 104

- 7 is 105

Sum = 108 + 104 + 105

Sum = 317

Calculating the sum of smallest 4 digit multiple of 9, 8 and 7

The smallest positive 4 digit multiple of:

- 9 is 1008

- 8 is 1000

- 7 is 1001

Sum = 1008 + 1000 + 1001

Sum = 3009

Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit

Sum of All = 48 + 317 + 3009

Sum of All = 3374

Answer:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

Step-by-step explanation:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.

Answer:

[tex]\boxed{11.78}[/tex]

Step-by-step explanation:

From observations, we can note that BC is the hypotenuse.

As the length of hypotenuse is not given, we can only use tangent as our trig function.

tan(θ) = opposite/adjacent

tan(67) = x/5

5 tan(67) = x

11.77926182 = x

x ≈ 11.78

Answer:

Step-by-step explanation:

c= 2(pi)r

Area = (pi)r^2

28.26 = (pi) r^2

r =[tex]\sqrt{9}[/tex] = 3

circumference = 2 (3.14) (3)

                        = 18.8 in

Answer:  approx 18.8 in

Step-by-step explanation:

The area of the circle is

S=π*R²   (1)   and the circumference of the circle is C= 2*π*R      (2)

So using (1)  R²=S/π=28.26/3.14=9

=> R= sqrt(9)

R=3 in

So using (2) calculate C=2*3.14*3=18.84 in or approx 18.8 in

Answer:

Step-by-step explanation:

Hello!

You have to determine the sample size to take to estimate the population proportion of Democrats among registered voters in Texas for a 96% interval with a margin of error of 0.01 and sample proportion p'= 0.28

The interval for the population proportion is

p' ± [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]

The margin of error of the interval is:

d= [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]

[tex]\frac{d}{Z_{1-\alpha /2}}= \sqrt{\frac{p'(1-p')}{n} }\\(\frac{d}{Z_{1-\alpha /2}} )^2= \frac{p'(1-p)}{n} \\n*(\frac{d}{Z_{1-\alpha /2}} )^2= p'(1-p)\\n= p'(1-p)*(\frac{Z_{1-\alpha /2}}{d} )^2\\[/tex]

[tex]Z_{1-\alpha /2}= Z_{0.98}= 2.054[/tex]

[tex]n= 0.28*(1-0.28)*(\frac{2.054}{0.01} )^2= 8505.33[/tex]

n= 8506 voters

I hope this helps!

Answer:

a) 4.8

b) 2.96

c) 4.4

d) 1.44

e) 3.76

Step-by-step explanation:

What we will do is solve point by point, knowing the following:

Fx (x) = P (X <= x) = (x - 1) / 4

a) P (X <-a) = 0.95

Fx (a) = 0.95

(a -1) / 4 = 0.95

a = 1 + 0.95 * 4

a = 4.8

b) P (X <a) = 0.49

Fx (a) = 0.49

(a -1) / 4 = 0.49

a = 1 + 0.49 * 4

a = 2.96

c) P (X <a) = 0.85

Fx (a) = 0.85

(a -1) / 4 = 0.55

a = 1 + 0.85 * 4

a = 4.4

d) P (X> a) = 0.89

P (X <a) = 1 - 0.89 = 0.11

Fx (a) = 0.11

(a -1) / 4 = 0.11

a = 1 + 0.11 * 4

a = 1.44

e) P (X> a) = 0.31

P (X <a) = 1 - 0.31 = 0.69

Fx (a) = 0.69

(a -1) / 4 = 0.69

a = 1 + 0.69 * 4

a = 3.76

Answer:

The 68% confidence interval is (6.3, 6.7).

The 95% confidence interval is (6.1, 6.9).

The 99.7% confidence interval is (5.9, 7.1).

Step-by-step explanation:

The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\bar x[/tex]

And the standard deviation of the sample means (also known as the standard error)is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]

As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.

(a)

Compute the 68% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]

The 68% confidence interval is (6.3, 6.7).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]

(b)

Compute the 95% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]

The 95% confidence interval is (6.1, 6.9).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]

(c)

Compute the 99.7% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]

The 99.7% confidence interval is (5.9, 7.1).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]

Answer:

B) [tex]x^2-3x+15[/tex]

Step-by-step explanation:

[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]

A) [tex]x^2+15x+15[/tex]

B) [tex]x^2-3x+15[/tex]

C) [tex]13x^2 + 3x + 15[/tex]

D) [tex]x^4-3x + 15[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

B. x² - 3x + 15

▹ Step-by-Step Explanation

7x² + 6x - 9x - 6x² + 15

Collect like terms

x² + 6x - 9x + 15

Subtract

x² - 3x + 15

Final Answer

x² - 3x + 15

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

2x-y=4

Step-by-step explanation:

Standard form of a line: Ax+by=c

Use slope intercept form: y=mx+b

slope= 2

y=2x-4

Add 4 to both sides.

y+4=2x

subtract y from both sides.

4=2x-y

Rotate the equation

2x-y=4

Answer:

2x-y=4

Step-by-step explanation:

y=2x-4 is the slope intercept.

y-2x=-4

-2x+y=-4

2x-y=4

Answer:

[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]

Now we can substitute in the equation

[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]

so the new equation is

[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]

the auxiliary equation is

[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]

so the solutions of the new equation are

[tex]y(t)=ae^{2t}+be^{-10t}[/tex]

with a and b real

as

[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]

[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]

hope this helps

do not hesitate if you have any questions

Answer:

The answer is 60cm^2.

hope it helps..

Answer:

D

Step-by-step explanation:

We calculate the z-score for each

Mathematically;

z-score = (x-mean)/SD

z1 = (1.9-2.1)/0.2 = -1

z2 = (2.3-2.1)/0.2 = 1

So the proportion we want to calculate is;

P(-1<x<1)

We use the standard score table for this ;

P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%

Answer:

68

Step-by-step explanation:

This is a great question!

When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -

[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]

____

Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,

[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]

Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,

( 1. The new store will have a profit of $3400 after its third month in business.  

( ​​2. The new store will have a profit of $2400 after its third month in business.

( 3. ​The new store will sell 2400 items in its third month in business.

( 4. The new store will sell 3400 items in its third month in business.

The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

The substitution method is the algebraic method to solve simultaneous linear equations.

Given function is,

[tex]r(x) = x^2+5x+14[/tex]...(1)

And [tex]c(x) = x^2-4x+5[/tex]...(2)

Now, substituting the value into the equation (1) and (2).

[tex]r(5) = (5)^2+5(5)+14=64[/tex]

[tex]c(5) = (5)^2-4(5)+5=10[/tex]

Therefore,

[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]

Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

Learn more about the topic Substitution:

https://brainly.com/question/3388130

Answer:

Step-by-step explanation:

3x2−5x−2=0

For this equation: a=3, b=-5, c=-2

3x2+−5x+−2=0

Step 1: Use quadratic formula with a=3, b=-5, c=-2.

x= (−b±√b2−4ac )2a

x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)

x= (5±√49 )/6

x=2 or x= −1 /3

Answer:

x=2 or x= −1/ 3

The solutions to the equation are x = -1/3 and x = 2.

Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:

First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Next, we set each factor equal to 0 and solve for x.

(3x + 1)(x - 2) = 0

3x + 1 = 0

3x = -1

x = -1/3

x - 2 = 0

x = 2

Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.

Here is the explanation for each of the steps:

Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.

Learn more about equation here: brainly.com/question/29657983

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Answer:

94 cm

Step-by-step explanation:

The formula for finding the circumference of a circle is;

Circumference = 2πr

where π = [tex]\frac{22}{7}[/tex] or 3.14 and

r = radius

Here radius is 15 cm so;

Circumference = [tex]2 * \frac{22}{7} * 15[/tex]

                         = [tex]\frac{660}{7}[/tex]cm

                         = 94.28cm

                         = 94 cm (  rounded to the nearest centimetre )

Answer: 4 pairs

Step-by-step explanation:

121-16=105.   However, 121 can be made by squaring -11 or 11.  16 can be made by squaring 4 or -4.  Thus, the choices are 11,4 11,-4 -11,4 -11,-4

Answer:

undefined

Step-by-step explanation:

Using the slope formula

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

and the given points

m = ( 8 - -1)/( 2-2)

    = (8+1) / 0

We cannot divide by 0 so the slope is undefined