Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2
pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per
pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate
the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?

Answer:

8 hours

1 hour

8 hours

0.288675

Step-by-step explanation:

We complete the answer as follows;

mu = mean = 8 hours

sigma = standard deviation= 1 hour

Mu_x bar = mu = 8 hours

sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675

Answer:

a) $3700

b) $555

Step-by-step explanation:

The length of the loan is 3 years.

The interest after 3 years is $444.

The rate of the Simple Interest is 4%.

Simple Interest is given as:

I = (P * R * T) / 100

where P = principal (amount borrowed)

R = rate

T = length of years

Therefore:

[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]

P = $3700

She borrowed $3700

b) If the simple interest was 5%, then:

I = (3700 * 5 * 3) / 100 = $555

The interest would be $555.

Answer:

since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,

sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft

Answer:

Given:

AC = 14      and       BC = 9

AB = ?

Solution:

From the fig:

AC = AB + BC

Putting the values

14 = AB + 9

AB = 14 - 9

AB = 5

(you can also take AB = x or any other variable)

Step-by-step explanation:

Answer:

  73/55

Step-by-step explanation:

The cosecant (csc) is one of the reciprocal functions:

  csc(θ) = 1/sin(θ)

  sec(θ) = 1/cos(θ)

  cot(θ) = 1/tan(θ)

So, if we can find the sine, we can find the cosecant.

__

The mnemonic SOH CAH TOA reminds you that the sine is ...

  Sin = Opposite/Hypotenuse

The above tells you that ...

  Csc = 1/Sin = Hypotenuse/Opposite

The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...

  csc(θ) = 73/55

Answer:

[tex]csc (\theta)=\frac{33}{55}[/tex]

Step-by-step explanation:

Hello!

1) The cosecant function is the inverse the sine function. So we can write:

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

2) The sine function is the side opposite angle to [tex]\angle \theta[/tex] over the hypotenuse:

[tex]sin(\theta)=\frac{55}{33}[/tex]

3) So, remembering operations with fractions then the cosecant is:

[tex]csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}[/tex]

[tex]csc (\theta)=\frac{33}{55}[/tex]

Answer:

8a^5

Step-by-step explanation:

Well to start off 2*4=8

So the coefficent will be 8

and when multipling ezponents we add the exponents and 2+3=5 so the exponent will be 5.

So 8a^5 is the answer

Answer:

Ok, we have two words:

"Signature"

The letters are: "S I G N A T U R E"

9 different letters.

Now, we can make only words with 9 letters, so we can think on 9 slots, and in each of those slots, we can input a letter of those 9.

For the first slot, we have 9 options.

For the second slot, we have 8 options (because on is already taken)

For the second slot, we have 7 options and so on.

Now, the total number of combinations is equal to the product of the number of options in each selection:

C = 9*8*7*6*5*4*3*2*1 = 362,880.

Now, our second word is Restaurant.

The letters here are " R E S T A U N" such that R, T and A appear two times each, so we have a total of 10 letters and 7 unique letters.

So first we do the same as beffore, 10 slots and we start with 10 options.

The total number of combinations will be:

C = 10*9*8*7*6*5*4*3*2*1 = 3,628,800

A lot of combinations, but we are counting only unique words.

For example, as we have two R, we are counting two times the word:

Restaurant (because we could permutate only the two letters R and get the same word)

So we must divide by two for each letter repeated.

we have 3 letters repeated, we divide 3 times by 2.

C = ( 3,628,800)/(2*2*2) = 453,600

Answer:

30% constituents=20 mL

10% constituents=180 mL

Step-by-step explanation:

x= 30% volume

y=10% volume

For our first equation, we know the total volume is 200 mL and is the sum

x+y=200

y=200-x (1)

For our second equation, we do a mass balance for 200 mL of final solution.

12% w/v = 0.12 g/mL

This means that in 1 mL of solution, we have 0.12 g of NaCl.

For any solution, concentration multiplied by volume will give the mass of NaCl:

Mass in x mL= C*V (g/mL) (mL)

So in 200 mL, we have

0.12*200 (g/mL) (mL)

=24g of NaCl

Cx*Vx + Cy*Vy=24

0.3x+0.1y=24 (2)

Substitute y=200-x into (2)

0.3x+0.1(200-x)=24

0.3x+20-0.1x=24

0.2x=24-20

0.2x=4

Divide both sides by 0.2

0.2x/0.2=4/0.2

x=20

Substitute x=20 into (1)

y=200-x

y=200-20

y=180

30% constituents=20 mL

10% constituents=180 mL

4x+21+3x-5=121

7x+16=121

x=15

angle ABD =4(15)+21=81

Answer:

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Step-by-step explanation:

From the summary of the given statistical dataset

The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:

[tex]\mu_{\overline x} = \mu _x[/tex] = 64.5

[tex]\sigma_{\overline x }= \dfrac{\sigma}{\sqrt n}[/tex]

[tex]\sigma_{\overline x }= \dfrac{2.5}{\sqrt {25}}[/tex]

[tex]\sigma_{\overline x }= \dfrac{2.5}{5}[/tex]

[tex]\sigma_{\overline x }[/tex] = 0.5

Thus X [tex]\sim[/tex] N (64.5,0.5)

Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:

[tex]P(\overline X > 66) = P ( \dfrac{\overline X - \mu_\overline x}{\sigma \overline x }>\dfrac{66 - 64.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>\dfrac{66 - 64.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>\dfrac{1.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>3 })[/tex]

[tex]P(\overline X > 66) = 1- P ( Z<3 })[/tex]

[tex]P(\overline X > 66) = 1- 0.9987[/tex]

[tex]P(\overline X > 66) =0.0013[/tex]

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Answer:

Step-by-step explanation:

Hello!

Regarding the reasons that traffic accidents occur:

28% are caused by distracted drivers using cell phones or texting

11% of the drivers' user their phones at any time

The probability of a driver having an accident is 5.26%

a)

DC = event that a randomly selected driver is using a cell phone.

P(DC)= 0.11

b)

TA = event that a randomly selected driver has a traffic accident.

P(TA)= 0.0526

c) and f)

If both events are related, i.e. dependent, then you would expect that the occurrence of one of these events will affect the probability of the other one. If they are not related, i.e. independent events, then their probabilities will not be affected by the occurrence of one or another:

If both events are independent P(TA|DC)= P(TA)

If they are dependent, then:

P(TA|DC)≠ P(TA)

P(TA|DC)= 0.28

P(TA)= 0.0526

As you can see the probability of the driver having an accident given that he was using the cell phone is different from the probability of the driver having an accident. This means that both events are related.

d) and e)

You have to calculate the probability that "the driver was distracted with the phone given that he had an accident", symbolically P(DC|TA)

P(DC|TA) = [tex]\frac{P(DCnTA)}{P(TA)}[/tex]

[tex]P(TA|DC)= \frac{P(TAnDC}{P(DC)}[/tex] ⇒ P(DC∩TA)= P(TA|DC)*P(DC)= 0.28 *  0.11= 0.0308

P(DC|TA) = [tex]\frac{0.0308}{0.0526}= 0.585= 0.59[/tex]

I hope this helps!

Answer:

Hey there!

The cross section would be a rectangle. No matter where you cut the figure parallel to the base, the cross section would be a rectangle.

Let me know if this helps :)

Answer: Rectangle

Step-by-step explanation:

In a rectangular prism, every cross-section parallel to a side is a rectangle.

Hope it helps <3

Answer:

Range { 2,6,8}

Step-by-step explanation:

The domain is the input and the range is the output

Range { 2,6,8}

Answer:

2, 6, 8

Step-by-step explanation:

The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.

Answer:

Volume of water in the pool is 3,182 ft^3

Step-by-step explanation:

In this question, what we want to calculate is the volume of water in the pool.

We proceed as follows;

diameter of pool = 30ft

depth: 2 to 7ft linearly

average depth = (2 + 7)/2 = 9/2 = 4.5 ft

Volume = area * average depth

V = pi * radius^2 * 4.5

where radius = diameter/2 = 30/2 = 15 ft

V = pi * 15^2 * 4.5

V = 22/7 * 225 * 4.5

V = 3,182.14 ft^3

which is 3,182 ft^3 to nearest whole number

The volume of water in the pool is; Volume = 3181 ft³

We are given;

Diameter of swimming Pool; d = 30 ft

Thus; radius; r = d/2 = 30/2 = 15 ft

We are told that the depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end.

Thus, average depth is;

h_avg = (2 + 7)/2

h_avg = 4.5 ft

Formula for area is; A = πr²

Thus;

A = π × 15²

A = 225π

Formula for volume here is;

Volume = Area × depth

Volume = 225π × 4.5

Volume = 3180.86 ft³

Approximating to a whole number gives;

Volume = 3181 ft³

Read more at; https://brainly.com/question/15276135

Answer:

With calculator;√24.5 = 4.9497

With differentials;With calculator;√24.5 = 4.95

The value of the square root gotten using differentials is an approximate value of the one gotten with a calculator

Step-by-step explanation:

With calculator;√24.5 = 4.9497

Using differentials;

The nearest number to 24.5 whose square root can be taken is 25, so let us consider that x = 25 and δx = dx = - 0.5

Now, let's consider;

y = √x - - - (eq 1)

Differentiating with respect to x, we have;

dy/dx = 1/(2√x) - - - - (eq 2)

Taking the differential of eq 2,we have;

dy = (1/(2√x)) dx

Using the values of x = 25 and dx = 0.5,we have;

dy = (1/(2√25)) × 0.5

dy = 0.05

Now;

√24.5 = y - dy

√24.5 = √x - dy

√24.5 = √25 - 0.05

√24.5 = 5 - 0.05

√24.5 = 4.95

Answer:

option B

hope it was useful for you

stay at home stay safe

pls mark me as brain.....

Answer:

[tex]\boxed{Option \ B}[/tex]

Step-by-step explanation:

Area of a circle = [tex]\pi r^2[/tex]

Finding the area of the circle, we need to know what the radius of the circle is. So, We would get the area of the circle.

Answer:

  (–8, –6)

Step-by-step explanation:

The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...

  x/(x-intercept) +y/(y-intercept) = 1

  x/(-2) +y/2 = 1 . . . use the given intercepts

  x - y = -2 . . . . . multiply by -2

Then the system is ...

Using the first to substitute into the second, we get ...

  x - (2x +10) = -2

  -8 = x . . . . . . . . . . . add x+2, simplify

  y = 2(-8) +10 = -6

The solution is (x, y) = (-8, -6).

Answer:

(-8,-6)

Step-by-step explanation:

Got it right on edge soooo <3

Answer:

j < 2

Step-by-step explanation:

Simplify both sides of the inequality and isolating the variable would get you the answer

Answer:

D. is used to reveal an underlying pattern in the data.

Step-by-step explanation:

Smoothing a time series is achieved when a computer uses some pre-programmed calculation methods to remove noise from large volumes of data. Smoothing helps a user detect patterns in a set of data, thus making it possible to make future predictions. For example, smoothing can be used in the prediction of the rise and fall of stock prices. This helps the traders to have an idea of what to expect in the cost of trading.

Although smoothing reveals the patterns in a set of data, it provides no explanation as to why it is so. It is left to the researcher to draw conclusions as to the reasons for the patterns.

Answer:

X= 3

Y= 18

Each side of the triangle= 10 units

Step-by-step explanation:

LMN is equilateral so

LM = MN

3x+1= 4x-2

3x-4x = -2-1

-x = -3

X= 3

MP is the perpendicular bisector of line LN

so definitely angle lpm =90.

And lpm = 5y = 90

5y = 90

Y= 90/5

Y = 18°

For the side of the triangle

3x+1

But x= 3

3(3)+1

9+1

10

Each side of the triangle= 10 units

Answer:

18 is the first multiple of 3,6, and 9.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

We need to find the LCM (lowest common multiple) of 3, 6, and 9. Let's count by multiples of 3 to find it.

3 (not a multiple of 6 or 9), 6 (not a multiple of 9), 9 (not a multiple of 6), 12 (not a multiple of 9), 15 (not a multiple of 6 or 9), 18.

Since 18 is the first number that is a multiple of 3, 6, and 9, that is the answer.

Answer:

[tex]\approx[/tex] 17.5% per annum

Step-by-step explanation:

Given:

Money invested = $20,000 at the age of 20 years.

Money expected to be $500,000 at the age of 40.

Time = 40 - 20 = 20 years

Interest is compounded annually.

To find:

Rate of growth = ?

Solution:

First of all, let us have a look at the formula for compound interest.

[tex]A = P \times (1+\frac{R}{100})^T[/tex]

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.

Here, We are given:

P = $20,000

A = $500,000

T = 20 years

R = ?

Putting all the values in the formula:

[tex]500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%[/tex]

So, the correct answer is [tex]\approx[/tex] 17.5% per annum and compounding annually.

Answer:

16.1%

Step-by-step explanation:

(the other person is wrong, trust me)

Answer:

It should be 10 for the first box, 1000 for the second box and 100 for the third box.

Step-by-step explanation:

Each extra decimal place value added, u have to multiply it by the next value place such as tenths/hundreths/thousandths

Answer:

AB = 2 sqrt(35)   (or 11.83 to two decimal places)

Step-by-step explanation:

Refer to diagram.

ABO'P is a rectangle (all angles 90)

=>

PO'  =  AB

AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)

using Pythagoras theorem.

Answer:

a= -243

r=81/-243, r= -0.33(common ratio)

to find the 5th term; T5= -243×(0.33)^(5-1)

T5= -243 × (0.33)^4

T5= -3

to find the 6th term; T6= -243 ×(0.33)^(6-1)

T6= -243 ×(-0.33)^5

T6= 1

Answer:

Answer above is correct

Step-by-step explanation:

–243, 81, –27, 9 …

What is the common ratio?

–1/3

What is the fifth term in the sequence?

–3

What is the sixth term in the sequence?

1

Answer:

D.$80

Step-by-step explanation:

$5.26 x 15.5= $81.53

The closest amount to $81.53 is D.$80

Answer:

Option A is the correct option

Step-by-step explanation:

Since, we know that angle at center is double that of the circumference.

JL = 2 × 84°

calculate the product

= 168°

Hope this helps..

Best regards!!

Answer:

Option A is the correct answer.

Step-by-step explanation:

By the incribed angle theorem, we have

1/2of angle JKL.

so, JL = 84°×2

Therefore, the answer is 168°.

Hope it helps..

Answer:

D

Step-by-step explanation:

Any number multiplied by an even number will always be even. 10 is an even number.

Answer:

d. 10 times a number is always even

Step-by-step explanation:

multiples of 9 contain 81 and 36 which one is even and the other is odd

multiples of 10 ONLY contain even numbers because   the unit digit for a multiple of 10 is 0.

So whenever you multiply a number by 10 it will be even

Answer:

Nicholas

Step-by-step explanation:

If you want an explanation I can add one

Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:

f(x) = λ.[tex]e^{-\lambda.x}[/tex]

and the cumulative distribution function, which describes the probability distribution of a random variable X, is:

F(x) = 1 - [tex]e^{-\lambda.x}[/tex]

(a) Probability of distance at most 100m, with λ = 0.0143:

F(100) = 1 - [tex]e^{-0.0143.100}[/tex]

F(100) = 0.76

Probability of distance at most 200:

F(200) = 1 - [tex]e^{-0.0143.200}[/tex]

F(200) = 0.94

Probability of distance between 100 and 200:

F(100≤X≤200) = F(200) - F(100)

F(100≤X≤200) = 0.94 - 0.76

F(100≤X≤200) = 0.18

(b) The mean, E(X), of a probability distribution is calculated by:

E(X) = [tex]\frac{1}{\lambda}[/tex]

E(X) = [tex]\frac{1}{0.0143}[/tex]

E(X) = 69.93

The standard deviation is the square root of variance,V(X), which is calculated by:

σ = [tex]\sqrt{\frac{1}{\lambda^{2}} }[/tex]

σ = [tex]\sqrt{\frac{1}{0.0143^{2}} }[/tex]

σ = 69.93

Distance exceeds the mean distance by more than 2σ:

P(X > 69.93+2.69.93) = P(X > 209.79)

P(X > 209.79) = 1 - P(X≤209.79)

P(X > 209.79) = 1 - F(209.79)

P(X > 209.79) = 1 - (1 - [tex]e^{-0.0143*209.79}[/tex])

P(X > 209.79) = 0.0503

(c) Median is a point that divides the value in half. For a probability distribution:

P(X≤m) = 0.5

[tex]\int\limits^m_0 f({x}) \, dx[/tex] = 0.5

[tex]\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx[/tex] = 0.5

[tex]\lambda.\frac{e^{-\lambda.x}}{-\lambda}[/tex] = [tex]-e^{-\lambda.x} + e^{0}[/tex]

[tex]1 - e^{-\lambda.m}[/tex] = 0.5

[tex]-e^{-\lambda.m}[/tex] = - 0.5

ln([tex]e^{-0.0143.m}[/tex]) = ln(0.5)

-0.0143.m = - 0.0693

m = 48.46