The ratio of the number of girls to the number of boys in choir is 6 to 8. There are 40 boys in the choir. How many girls are in the choir?

You should originally invest $148.

To solve this problem, we need to use the formula for present value of a bond:

\(PV = C/(1+r)^t\)

where PV is the present value, C is the annual coupon payment, r is the annual interest rate, and t is the time to maturity in years.

We know that the General Electric bonds had a time to maturity of 87 years and an annual rate of 5.25%. We also know that they paid a total of $6,630 at maturity. Let's call the original investment amount X.

Using the formula, we can set up the following equation:

\(6,630 = X/(1+0.0525)^{87\)

Simplifying this equation, we get:

\(X = 6,630 * (1+0.0525)^{-87\)

Using a calculator, we get:

X = $147.91

Rounding this to the nearest dollar, the answer is:

$148

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\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

As we observe the points, we can conclude that :

Translation along x axis is ~

\(\qquad \sf  \dashrightarrow \: 1 - ( - 3)\)

\(\qquad \sf  \dashrightarrow \:1 + 3\)

\(\qquad \sf  \dashrightarrow \:4 \: \: units \: \: towards \: \: left\)

Translation along y axis ~

\(\qquad \sf  \dashrightarrow \: - 8 - ( - 13)\)

\(\qquad \sf  \dashrightarrow \: - 8 + 13\)

\(\qquad \sf  \dashrightarrow \:5 \: \: units \: \: towards \: \: down\)

So, same goes with translation of (-5 , 9)

\(\qquad \sf  \dashrightarrow \: x \: \:coordinate = - 5 - 4 = - 9\)

\(\qquad \sf  \dashrightarrow \: y \: \:coordinate = 9 - 5 = 4\)

So, the required coordinates of the image under same translation is ~

\(\qquad \sf  \dashrightarrow \:(-9, 4)\)

Answer:

Please help look at the image I need help with number 4. I already did the line plot for number 3 and the data in on the chart. Thank you! :)

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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The measure of tangent angle QIA is 180 degrees.

m/QIA = 180 degrees.

If IA is the diameter of the circle, it means that angle QIA is a right angle (90 degrees). Since QN is tangent to the circle at point I, it is perpendicular to the radius IA at that point.

Therefore, in triangle QIA, we have a right angle at Q and a right angle at I. This implies that angle IQA is also 90 degrees.

In a right triangle, the sum of the angles is 180 degrees. Since angles QIA and IQA are both right angles, the remaining angle in the triangle, angle QAI, must be:

180 degrees - 90 degrees - 90 degrees = 0 degrees

Angle QAI is a degenerate angle, which means it has a measure of 0 degrees. Therefore, the measure of tangent angle QIA is 180 degrees.

To summarize, m/QIA = 180 degrees.

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Answer:

2800 is a good estimate

Step-by-step explanation:

Rounding to the nearest hundred

674 = 700

692 = 700

724 = 700

739 = 700

700+700+700+700 = 2800

Answer:

Circumference: 50.27 cm

Area: 201.06 cm²

Step-by-step explanation:

Hi there!

1) Determine the circumference

\(C=\pi d\) where d is the diameter of the circle

Plug in the diameter (16 cm)

\(C=16\pi\\C=50.27\)

Therefore, the circumference is 50.27 cm when rounded to the nearest hundredth.

2) Determine the area

\(A=\pi r^2\) where r is the radius

Plug in the radius (16/2=8)

\(A=\pi (8)^2\\A=64\pi\\A=201.06\)

Therefore, the area of the circle is 201.06 cm² when rounded to the nearest hundredth.

I hope this helps!

Answer:

1/3 means 1 out of 3 so that means that lets say hours they would do something 1 out of 3 hours so he would snore 1 hour

1 hour

Hope This Helps!!!

Answer:

x + y = 500

215x + 615y = 187,500

Step-by-step explanation:

The first equation can show the amount of land.  The farmer has 500 acres to plant corn, x, and cotton, y.

x + y = 500

The second equation can show the cost.  The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.

215x + 615y = 187,500

The system of equations is

x + y = 500

215x + 615y = 187,500

The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

And, Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season.

Now,

Let us take  'x' is plant acres of corn and 'y' is acres of cotton.

Since, A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

So, we can formulate;

⇒ x + y = 500

And, He has $187,500 to invest this season for corn costs $215 per acre to produce, and cotton costs $615 per acre to produce.

So, We can formulate;

⇒ 215x + 615y = 187,500

Thus, The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

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\(Q[x]/(x^2 - 4x + 3)\) is not a field since it is not an integral domain. An integral domain has no zero divisors. Let's observe that\((x-1)(x-3) = x^2 - 4x + 3\) This means that in \(Q[x]/(x^2 - 4x + 3), (x-1)(x-3) = 0.\)

This indicates that \(Q[x]/(x^2 - 4x + 3)\) has zero divisors. Since \(Q[x]/(x^2 - 4x + 3)\) has zero divisors, it cannot be a field. Therefore, \(Q[x]/(x^2 - 4x + 3)\) is not a field. It is crucial to comprehend that if the ideal generated by a polynomial is prime or maximal, the quotient ring is an integral domain or field.

Thus, one can check whether a ring is an integral domain or field by checking if the ideal generated by the polynomial is prime or maximal, respectively.

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Answer:

16,000 lbs. Theres 2,000 lbs to every ton.

If you're asking for 8 tons MINUS 8 pounds, it'd be 16,000 - 8 which equals 15,992 lbs.

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

From the question, we have the following parameters that can be used in our computation:

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer:

The answer is 351

Step-by-step explanation:

Hope this helps!

Answer:

0.13x+(70000-x)0.05=6000

We move all terms to the left:

0.13x+(70000-x)0.05-(6000)=0

We add all the numbers together, and all the variables

0.13x+(-1x+70000)0.05-6000=0

We multiply parentheses

0.13x-0.05x+3500-6000=0

We add all the numbers together, and all the variables

0.08x-2500=0

We move all terms containing x to the left, all other terms to the right

0.08x=2500

x=2500/0.08

x=31250

Step-by-step explanation:

Answer:

Ross = 15 hours

Russel = 40 hours

Step-by-step explanation:

Let Ross have used their sprinklers for x hours

Let Russell  have used their sprinklers for y hours

Together they used 55 hours

x+y = 55 hours

The output of Ross is 35 liters per hour and Russell is 30 liters per hour for a total of 1725

35x + 30y = 1725

Multiply the first equation by -30

-30(x+y=55)

-30x -30y = -1650

Add this to the second equation to eliminate y

-30x -30y = -1650

35x + 30y = 1725

-----------------------------

5x =75

Divide each side by 5

x = 15

Now find y

x+y = 55

y = 55-15

y = 40

The expected loss of a renter who has no insurance and no security system is $700. If the renter has a security system, the expected loss decreases to $200.

The loss from a theft is $10,000. The expected loss of a renter who has no insurance and no security system is given by 0.07 × $10,000 = $700.

If the renter has a security system, the probability of a theft decreases to 0.02, so the expected loss is 0.02 × $10,000 = $200.

Given that: Probability of theft if there is no security system = 0.07

Probability of theft if there is security system = 0.02

Additional cost of security system = $100Loss from theft = $10,000The renter's expected loss if she has no insurance and uses the security system is calculated below:

Probability of theft if there is a security system = 0.02Expected loss of a renter who has no insurance and no security system is 0.07 × $10,000 = $700

Summary: If the renter has no insurance, then their expected loss would be the probability of a theft occurring multiplied by the loss from a theft. If there is no security system, the probability of a theft is 0.07, while if there is a security system, the probability of a theft is 0.02. The loss from a theft is $10,000. The expected loss of a renter who has no insurance and no security system is $700. If the renter has a security system, the expected loss decreases to $200.

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Answer:

Step-by-step explanation:

Given system:

Graph each line and find the point of intersection of lines.

Graphical solution is attached.

The solution is (-2, -1)

(-2, -1)

y = x + 1 ... (1)

3x + y = -7 ... (2)

Graph in the picture.

Answer:  The answer is D. 16.57

Step-by-step explanation:

First, you do 2.86+1.57 = 4.43. Then you do 20-4.43. You then get the answer. P.S this is answered by a 7th grader so my step-by-step explanation is kinda bad.

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

6 to 4

Step-by-step explanation:

The amount of water is 6 and the amount of flour is 4 therefor there is 6 to 4 cups of water.

True.

\(10^{10}\) = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

      Its a factor which can be written in short and simplified form.

These functions have restricted domains: f(x) is defined only for x >= 3 and g(x) is defined only for x < 3.

A function is a mathematical concept that assigns exactly one output (or "output value") to each input (or "input value"). It provides a way to describe the relationship between inputs and outputs and can be thought of as a machine that takes inputs and produces outputs. Functions can be represented using equations or graphs.

In mathematical terms, a function can be formally defined as a set of ordered pairs (x,y), where x is the input (independent variable) and y is the output (dependent variable). The output value for a given input value is unique, and a single input value cannot correspond to multiple output values.

Functions are widely used in mathematics, science, and engineering to model real-world phenomena and to describe mathematical relationships. There are many types of functions, including linear functions, polynomial functions, exponential functions, logarithmic functions, and trigonometric functions, among others.

The equation y = 2|x - 3| + 5 can be rewritten as two separate linear functions, f(x) and g(x), as follows:

f(x) = 2(x - 3) + 5, for x >= 3

g(x) = -2(x - 3) + 5, for x < 3

So, for x >= 3, y is given by the linear function f(x) = 2(x - 3) + 5, and for x < 3, y is given by the linear function g(x) = -2(x - 3) + 5.

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The conditional statement "T → (8<5)" is true because the antecedent "T" is false, and by the truth table of a conditional statement, a conditional with a false antecedent is always true, regardless of the truth value of the consequent.

what is antecedent?

In logic, an antecedent is the first part of a conditional statement (if-then statement) that precedes the word "if." It is the statement that implies or asserts the truth of the consequent. For example, in the conditional statement "If it is raining, then I will stay inside," the antecedent is "it is raining."

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The expression that most accurately describes the change in the patient's temperature is -2° (3).

Option 3 is the correct answer.

We have,

The expression that most accurately describes the change in the patient's temperature would be:

-2° + (-2°) + (-2°)

This expression represents the successive temperature drops of 2° each time.

By adding the negative values, we account for the decrease in temperature.

This can be written as,

= -2° x 3

= -2° (3)

Thus,

The expression that most accurately describes the change in the patient's temperature is -2° (3).

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Hey there! I'm happy to help!

Let's have the adult tickets be a and the children tickets be c.

a=2c (twice as many adult tickets as child tickets)

5a+2c=700 (dollar value of each ticket)

Have a wonderful day! I hope that the helps! :D

Step 1: The proposed probe for flaw detection in type 316L austenitic stainless steel plates is an eddy current probe with a suitable height, diameter, and frequency.

Step 2: Eddy current testing is an effective non-destructive testing method for detecting flaws in conductive materials. In this case, the eddy current probe should have a suitable height, diameter, and frequency to ensure accurate flaw detection.

The height of the probe should be adjusted to maintain a constant lift-off of 0.2 mm, which is the distance between the probe and the surface of the material being tested. This ensures consistent measurement conditions and reduces the influence of lift-off variations on the test results.

The diameter of the probe should be selected based on the size of the flaws and the desired spatial resolution. It should be small enough to accurately detect the flaws but large enough to cover the entire flaw area during scanning.

The frequency of the eddy current probe determines the depth of penetration into the material. Higher frequencies provide shallower penetration but higher resolution, while lower frequencies provide deeper penetration but lower resolution. The frequency should be chosen based on the expected depth of the flaws and the desired level of sensitivity.

Overall, the eddy current probe with suitable height, diameter, and frequency can effectively detect the artificial flaws in type 316L austenitic stainless steel plates fabricated using a powderbed-based laser metal additive manufacturing machine.

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From the two functions function 2 has the highest maximum value.

Given two functions,one is y=-\(x^{2} -2x-2\) and f(-2)=1,f(-1)=6,f(0)=9,f(1)=10,f(2)=9,f(3)=6.

We ae required to choose a function which is having highest maximum possible value.

Function is like a relationship between two or more variables expressed in equal to form. Each value of x of a function has some value of y.

The highest value in the second function is 10 which is at x=1. Put the value of x=1 in y=-\(x^{2} -2x-2\).

y=-1-2-2

y=-5

So it might not be highest value of this function.So the second function has highest maximum value of 10 at x=1.

Hence the second function has highest value.

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Inequality are expressions that are not separated by an equal sign. The solution to the given system of equation is x > 4

Inequality are expressions that are not separated by an equal sign.

Given the inequality

8x+2 > 34

Subtract 2 from both sides

8x + 2 - 2 > 34 - 2

8x > 32

Divide both sides by 8

8x/8 = 32/8
x > 4

Hence the solution to the given system of equation is x > 4

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Answer: 14/40 or 7/20

Step-by-step explanation: We need to set the fraction's denominators equal to each other and their LCM is 40 so Andrea ran 1/8 which =5/40. Billie ran 1/5 which =8/40. 5/40+8/40=13/40/ Carol ran both Andrea's and Billie's length combined so that's another 13/40 = 26/40. The whole length is 40/40 so 40/40-26/40=Dana's length which =14/40 or 7/20

Answer:

\((x + 4)( {x}^{2} - 5x + 6) \\ \\ = ( {x}^{3} - 5 {x}^{2} + 6x + 4 {x}^{2} - 20x + 24) \\ \\ = { \underline{ \underline{{x}^{3} - {x}^{2} - 14x + 24}}}\)

Hey there!

(x + 4) (x² - 5x + 6)

= x (x² - 5x + 6) + 4 (x² - 5x + 6)

= x³ - 5x² + 6x + 4x² - 20x + 24

= x³ - 5x² + 4x² + 6x - 20x + 24

= x³ - x² - 14x + 24 ⇨ Expanded form.

x³ - x² - 14x + 24

= (x + 4) (x² - 5x + 6) [Rational root theorem]

= (x + 4) (x² - 3x) + (-2x + 6)

= (x + 4) x (x - 3) - 2 (x - 3) [Take out the common factor]

= (x + 4) (x - 2) (x - 3) ⇨ Simplified form.

Hope it helps ya!

35300 x 10⁰

3530 x 10¹

353 x 10²

35,3 x 10³

3,53 x 10⁴

0,353 x 10⁵

Answer:

3.53x10^4

Step-by-step explanation:

your welcome

~Ren