Amanda has been employed at a company for 37 years. The company is 24 years older than Amanda. The sum of Amanda age and the company’s age is 121 years. How old was Amanda when she started her job?

Answer:

work is shown and pictured

Answer:

Answer B. (6, 2)

Hope it works!

Step-by-step explanation:

Answer:

The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.

Step-by-step explanation:

First we need to find the z-value for a confidence of 99%

The value of alpha for a 99% confidence is:

[tex]1-\alpha/2 = 0.99[/tex]

[tex]\alpha/2 = 0.01[/tex]

[tex]\alpha = 0.005[/tex]

Looking in the z-table, we have z = 2.575.

Now we can find the standard error of the mean:

[tex]\sigma_{\bar{x} }= s_x/\sqrt{n}[/tex]

[tex]\sigma_{\bar{x} }= 14.4/\sqrt{100}[/tex]

[tex]\sigma_{\bar{x} }=1.44[/tex]

Finding the 99% confidence interval, we have:

[tex]99\%\ interval = (\bar{x} - z\sigma_{\bar{x}}, \bar{x} + z\sigma_{\bar{x}})[/tex]

[tex]99\%\ interval = (32.2 - 2.575*1.44, 32.2 + 2.575*1.44)[/tex]

[tex]99\%\ interval = (28.492, 35.908)[/tex]

The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.

Answer:

a) diagonal box = 12.9 in

b) diagonal base = 8.2 in

Step-by-step explanation:

w = 8 in

h = 10 in

L = 2 in

required:

a) diagonal of the box

b) diagonal of its base

referring into the attached image

a) the diagonal of the box = sqrt ( w² + h² + L²)

  diagonal box = sqrt (8² + 10² + 2²)

  diagonal box = 12.9 in

b) diagonal of its base = sqrt ( w² + L²)

   diagonal base = sqrt ( 8² + 2²)

   diagonal base = 8.2 in

Answer:

D

Step-by-step explanation:

We can plug in the numbers (15, 23, 25, 38, 53) into the equation for x, and see if we get the values given for the number of hits (4, 12, 14, 27, 47)

Answer:

The corresponding definite integral may be written as

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]

The answer of the above definite integral is

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]

Step-by-step explanation:

The given limit interval is

[tex]\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i[/tex]

[tex][a, b] = [-8, 6][/tex]

The corresponding definite integral may be written as

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]

[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]

Bonus:

The definite integral may be solved as

[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98[/tex]

Therefore, the answer to the integral is

[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]

Answer:

21.84 years

Step-by-step explanation:

From the compound interest formula;

F = P(1+r)^t .......1

ln(F/P) = tln(1+r)

t = ln(F/P)/ln(1+r) .......2

Where;

F = Final value = $45,117

P = Initial value = $15,540

r = rate = 5% = 0.05

t = time

Substituting the values into equation 2;

t = ln(45117/15540)/ln(1.05)

t = 21.84542292124 years

t = 21.84 years

It will take Bob 21.84 years

Answer:

sqrt(70)/7

Step-by-step explanation:

sqrt(10/7)

sqrt ( a/b) = sqrt(a)/ sqrt(b)

sqrt(10) / sqrt(7)

But we don't leave a sqrt in the denominator, so multiply by sqrt(7) /sqrt(7)

sqrt(10) /sqrt(7) * sqrt(7) / sqrt(7)

sqrt(70)/ sqrt(49)

sqrt(70)/7

Answer:

A.

Step-by-step explanation:

The angles are not always congruent as the only way for them to all be congruent is if it were to be a square, and not all parallelograms are squares.

Answer:

225

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

Answer:

  C(3) = R(3) = 840

Step-by-step explanation:

See the attached for a graph.

Answer:

z = -1.66

Step-by-step explanation:

Z-statistic:

[tex]z = \frac{X - p}{s}[/tex]

In which X is the found proportion.

p is the mean proportion.

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex] is the standard error for the data.

Out of 593 students who replied to her survey, 64 fit this criterion.

This means that [tex]X = \frac{64}{593} = 0.108[/tex]

She finds that the proportion of binge drinkers nationally is 13.1%.

This means that [tex]p = 0.131[/tex]

Also

[tex]s = \sqrt{\frac{0.131*0.869}{593}} = 0.014[/tex]

The z statistic for this data is

[tex]z = \frac{X - p}{s}[/tex]

[tex]z = \frac{0.108 - 0.131}{0.014}[/tex]

[tex]z = -1.66[/tex]

Answer:

9/24 or 37.5%

hope this helps :)

Hi,  

first thing you must do with a  probability problem is to count how many thing you have in your universe.

Here we are dealing with sweets. So let's count  :  5 +4+8+4+3 = 24  

and there is  5 yellow  so probability to pick up a yellow is  5/24

and there is 4 orange  so probabilitu to pick up a orange is  4/24

To say  :   Ola will pick orange or  yellow  mean  if she pick either one of the two sort is good.  So you add the proba of each :   5/24 +4/24 = 9/24

and then you must reduce if you can :   9/24 = 3*3 /8*3 =  3/8

So the probability that Ola pick a  yellow or orange sweet is  3/8 = 0.375

Answer:

c = 20.5x + 5.59

Step-by-step explanation:

c = mx + b

c = mx + 5.59

108.09 = m(5) + 5.59

5m = 102.5

m = 20.5

c = 20.5x + 5.59

Answer:

[tex]D_{\vec{v}}V(6,6,5)=48[/tex]

Step-by-step explanation:

You have the following potential function:

[tex]V(x,y,z)=5x^2-3xy+xyz[/tex]           (1)

To find the rate of change of the potential at the point P(6,6,5) in the direction of v = i + j - k, you use the following formula:

[tex]D_{\vec{v}}V(x,y,z)=\bigtriangledown V(x,y,z)\cdot \vec{v}[/tex]           (2)

First, you calculate the gradient of V:

[tex]\bigtriangledown V(x,y,z)=\frac{\partial}{\partial x}V(x,y,z)\hat{i}+\frac{\partial}{\partial y}V(x,y,z)\hat{i}+\frac{\partial}{\partial z}V(x,y,z)\hat{i}\\\\\bigtriangledown V(x,y,z)=(10x-3y+yz)\hat{i}+(-3x+xz)\hat{j}+(xy)\hat{k}\\\\\bigtriangledown V(6,6,5)=(10(6)-3(6)+(6)(5))\hat{i}+(-3(6)+(6)(5))\hat{j}+((6)(6))\hat{k}\\\\\bigtriangledown V(6,6,5)=72\hat{i}+12\hat{j}+36\hat{k}[/tex]

Next, you replace in the equation (2):

[tex]D_{\vec{v}}V(6,6,5)=(72\hat{i}+12\hat{j}+36\hat{k})\cdot(\hat{i}+\hat{j}-\hat{k})\\\\D_{\vec{v}}V(6,6,5)=48[/tex]

Then, the rate of change of the potential at the point P(6,6,5) in the direction of v, is 48.

Answer:

a) 0.1178

Step-by-step explanation:

The calculation is shown below:-

Mean = np

= 50 × 0.35

= 17.5

Standard deviation is

= [tex]\sqrt{n\times p\times q}[/tex]

= [tex]\sqrt{50\times 0.35 \times 0.65}[/tex]

= 3.373

Therefore, as we know that

P which is Less than 14

So,

= P(X < 13.5)

= P(z < (13.5 - 17.5) ÷ 3.373

= P(z < -1.186)

= 0.1178

Hence, the correct option is a. 0.1178

basically we used the above formulas i.e mean and standard deviation

Answer:  186

Step-by-step explanation:

                     Jazz                      Rock or Pop  

7-12:          200 - 142 = 58                  142

13-18:        72 - 58 = 14                200 - 14 = 186

It is given that 142 out of 200 students in age group 7-12 like Rock or Pop.

Therefore, 200-142 = 58 in that age group like Jazz.

Total Jazz in both age groups is 72, so 72 - 58 (7-12: Jazz) = 14 students in age group 13-18 like Jazz.

There are 400 students total and 200 are in age group 7-12, which leaves 400-200 students in age group 13-18.  200 - 14 (13-18: Jazz) = 186 students in age group 13-18 like Rock or Pop.

Answer: 186

Step-by-step explanation:

The answer is 186 or D :)

Answer:

Step-by-step explanation:

Just definitions :)

Hope it helps <3

Step-by-step explanation:

just just solve the equation and then substitute the value of the first equation in the second one.

Answer:

D.

Step-by-step explanation:

y - int is value of y when x = 0,

We have y int = 1,

D. x = 0, y = (0 - 1)(0 - 1) = 1

x-int = 1,

D. y = 0, So, answer is D.

Answer:

D

Step-by-step explanation:

First, note that the graph "bounces" off the x-axis at x=1. This is telling us two things: (1) the graph has a zero at x=1 and (2), since the graph bounces, it has a factor with a multiplicity of 2. Since it is a quadratic, the only way that it can have a multiplicity of two is if the function is a perfect square trinomial. In other words, it can be factored into (x-a)^2.

A, B, and C are not perfect square trinomials. They cannot be factored into the form (x-a)^2.

D is (x-1)(x-1) which equals (x-1)^2, a perfect square trinomial. Its zero is also at x=1. D is correct.

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

The order to us solve is:

Let's go:

[tex]25(1.2\times 3 - 1.25) + 3.45\\25(3.6-1.25)+3.45\\25\times 2.35 + 3.45\\58.75+3.45\\62.2[/tex]

Therefore, the result is 62.2.

Answer:

4.0375

Step-by-step explanation:

.25(3.6-1.25)+3.45

.25(2.35)+3.45

.5875+3.45

4.0375

HOPE  THIS HELPS:)

Answer:

19/9 because it equals to 2.111..  Which is greater than 1

Step-by-step explanation:

By the way if it's right can i get brainliest.

Answer:

1 < 19/9

Step-by-step explanation:

1  vs 19/9

Rewriting 19/9 as 9/9 + 9/9+ 1/9

1 vs 1+1 +1/9

1 vs 2 1/9

1 < 19/9

Answer:

13 is D. 32

14 is x=41

15 is 72

Answer:

It would take 1 more mile if he took route Street A and then Street B rather than just Street C.

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

We use the Pythagorean Theorem to find the length of Street C:

2² + 1.5² = c²

c = √6.25

c = 2.5

Now we find how much longer route A and B is compared to C:

3.5 - (2 + 1.5) = 3.5 - 2.5 = 1

Answer:

Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.

The domain is all of the x values. Therefore the domain is {-1, 2}.

The range is all of the y values. Therefore the range is {-4, -3, 2}.

We don't use ( ) or [ ] because T is a discrete relation.

Answer:

5(3x + 2)

Step-by-step explanation:

15x + 10

1. 5(3x + 2)

Answer:

The only way of getting to 10 using 2x it should mean that x = 5

2 * 5 = 10

Answer:

Y=1/4x-4

Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25

Answer:

24*26= 624 students

hope this helps!

Answer:

624 seats

Step-by-step explanation:

Total classrooms = 24

Each classroom has seats = 26

Total Number of seats = 24*26

=> 624 seats

Answer:

no solution

Step-by-step explanation:

hello

[tex]6(x+5)=6x+11\\<=> 6x+30=6x+11\\<=> 30=11[/tex]

this is always false so there is no solution

Let's to expand this equation:

[tex]6(x+5) = 6x+11\\6x + 6\times 5 = 6x + 11\\6x + 30 = 6x + 11[/tex]

Perceive that in two members of equations, we have "6x", so we can to eliminate it. But, when we make it, we have this situation:

[tex]6x + 30 = 6x + 11\\30 = 11[/tex]

How [tex]30 \neq 11[/tex] this is a absurd. Therefore, this equation don't have solutions.