An investor deposited some money at 1.7% annual interest, and two equal but larger amounts at 2.3% and 2.4%. The
total amount invested was $25,000, and the total annual interest earned was $568. How much was invested at each
rate?
At the rate 1.7%, $ was invested.

Answer:

\(X \sim N(99,4)\)  

Where \(\mu=99\) and \(\sigma=4\)

We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:

\( X = \mu -3\sigma\)

And replacing we got:

\( X = 99 -3*4 = 87\)

So then the Annie's score would be 87

Step-by-step explanation:

Let X the random variable that represent the test scores of a population, and for this case we know the distribution for X is given by:

\(X \sim N(99,4)\)  

Where \(\mu=99\) and \(\sigma=4\)

We want to find the Annie's score takign in count that the score is 3 deviations below the mean, so then we can find the value with this formula:

\( X = \mu -3\sigma\)

And replacing we got:

\( X = 99 -3*4 = 87\)

So then the Annie's score would be 87

Answer: 87

Step-by-step explanation:

We can work backwards using the z-score formula to find the x-value. The problem gives us the values for z, μ and σ. So, let's substitute these numbers back into the formula:

z−3−1287=x−μσ=x−994=x−99=x

We can think of this conceptually as well. We know that the z-score is −3, which tells us that x is three standard deviations to the left of the mean, 99. So we can think of the distance between 99 and the x-value as (3)(4)=12. So Annie's score is 99−12=87.

Answer:

True

Step-by-step explanation:

When you distribute the 3, you get x(2x3)-(12x3)

2x3=6

12x3=36

so 6x-36

and that is equivalent to the first expression.

Therefore, Mark had bought approximately 433 tokens.

A fraction is a numerical representation of a part of a whole, where the whole is divided into equal parts. It is expressed in the form of a ratio of two numbers, with the numerator representing the number of parts being considered and the denominator representing the total number of equal parts in the whole. For example, the fraction 2/5 represents two parts out of five equal parts of the whole. Fractions are commonly used in mathematics and everyday life, such as in cooking recipes, measurements, and financial calculations.

Here,

Let's say Mark bought "x" gift tokens.

According to the problem, Sally used 3/20 of the tokens on rides.

We can write this as:

3/20 * x = 65

To solve for x, we can first multiply both sides by 20/3:

20/3 * 3/20 * x = 20/3 * 65

x = 1300/3

x ≈ 433.33

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Answer:

x = 13°

Step-by-step explanation:

9x - 18 and 8x - 5 are congruent because they are vertical angles

Solve for x:

-Chetan K

Answer:

28 cups

Step-by-step explanation:

If 7 cups will only fill 1/4 of her pot, multiply 4 by 7 to get 28.

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Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

The value of the function (f-g)(x)=\(x-4x^{2} -x^{3} -3\).

What is a function?

A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.

f(x)= x¹ - x² +9

g(x) = x³ + 3x² + 12

To find (f-g)(x):

The operations on functions are as easy as the operations on numbers or polynomials.

We have to subtract the functions to find the above mentioned operation.

(f-g) (x)= f(x)-g(x)

          = (x¹ - x² +9)-(x³ + 3x² + 12)

The minus will change the signs of function g.

          = \(x-x^{2} +9-x^{3}-3x^{2} -12\)

          =\(x-4x^{2} -x^{3} -3\)

Hence, the value of the function (f-g)(x)=\(x-4x^{2} -x^{3} -3\)

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The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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For every 4 beef cattle there is 3 dairy cattle. For 24 dairy cattle there will be 32 beef cattle as per the given ratio of 3:4.

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.

Here,

a. No for every 4 beef cattle there is 3 dairy cattle.

b. 4/3=x/24

x=4*24/3

x=32 beef cattle

There are 3 dairy cattle for every 4 beef cattle. According to the stated ratio of 3:4, there will be 32 beef cattle for every 24 dairy cattle.

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Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

A) The Slope is: 2

B) The interpretation of the slope is that there are two races for each number of track meet.

C) The y-intercept from the graph is at: y = 4

D) Equation of the line is: y = 2x + 4

The general form of equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the given graph, we can see that the slope is gotten from the formula:

A) Slope = (y₂ - y₁)/(x₂ - x₁)

Thus:

Slope = (10 - 4)/(3 - 0)

Slope = 6/3

Slope = 2

B) The interpretation of the slope is that there are two races for each number of track meet.

C) The y-intercept from the graph is at: y = 4

D) Equation of the line is:

y = 2x + 4

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

\(\theta =\cfrac{20\pi }{3}\implies \theta =\cfrac{6\pi +6\pi +6\pi +2\pi }{3} \\\\\\ \theta =\cfrac{6\pi }{3}+\cfrac{6\pi }{3}+\cfrac{6\pi }{3}+\cfrac{2\pi }{3}\implies \theta =2\pi +2\pi +2\pi +\cfrac{2\pi }{3}\)

Check the picture below.

The first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would choose a salad was 0.64.

The idea of probability is used to calculate the possibility or probability of a specific occurrence.

It is a number between 0 and 1, where 0 indicates that the event is inconceivable and 1 indicates that it is guaranteed to happen.

Probabilities can be expressed using fractions, decimals, or percentages.

There is a 0.2 likelihood that any student will choose a salad if their lunch tastes are assumed to be independent of one another's.

If you ask the principal understudy, there is a 0.2 chance that they will answer they prefer a dish of mixed greens. You move on to the next youngster if they don't want a salad.

Because the first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would prefer a salad was (1-0.2) (1-0.2) = 0.64.

Since none of the n-1 understudies who came before them did, the likelihood that the nth understudy would like a platter of mixed greens is only 0.2. 1-0.2n-1 is the likelihood that none of the first n-1 students will choose a salad.

Therefore, in order to identify a student who prefers salad, you must ask an expected number of students the following questions:

E(x) = 1(0.2) + 2(1-0.2)(0.2) + 3(1-0.2)2(0.2) +...

Even though this is an infinite series, by truncating it after a predetermined amount of words, we can approximate it. Let's imagine we decide to quit after ten terms:

E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2) E(x) ≈ 2.48

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Answer and Step-by-step explanation:

\((2x^{2} )(3x)\)

I think this would be your answer, since it is a binomial and consists of 3, which is its greatest common factor.

I may be wrong though, so I'm sorry in advance if it is wrong.

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Given statement solution is :-12.9 liters are in milleters is  12,900 mL.

The metric system uses millilitres as the unit of volume, denoted by the letters ml or mL. One cubic centimetre, or one thousandth of a litre, is equivalent to one millilitre. That's a little sum in the imperial system.

A measure of volume in the metric system. One thousand milliliters equal one liter. Additionally known as cc, mL, and cubic centimetre.

To convert liters to milliliters, you need to multiply the number of liters by 1,000, since there are 1,000 milliliters in a liter.

So, multiplying 12.9 by 1,000 will give you the answer to how many millilitres are in 12.9 litres:

12.9 litres x litres per 1,000 = 12,900 mL

Therefore, option 3: 12,900 mL, is the milleters right response.

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The total volume of the composite figure is; 381 m³

The formula for volume of a prism is;

V = Bh

where;

B is area of triangular base

h is height of prism

Thus;

V = (¹/₂ * 3 * 5) * 6

V = 45 m³

Volume of bottom cuboid is given by the formula;

V = Length * width * height

Thus;

V = 16 * 7 * 3

V = 336 m³

Total volume of composite figure = 45 m³ + 336 m³

Total volume of composite figure = 381 m³

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Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

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The equation to represent this scenario is y = 43*(3)ˣ  , the correct option is (a) .

In the question ,

it is given that ,

Number of pennies that Kyle starts the fundraiser =  43 pennies

goal is to triple the number of pennies each day .

let  "x" to represent the number of days .

let the total number of pennies be "y" .

this situation is represented by an exponential increase ,

that can be represented as

y = 3ˣ * 43

y = 43*3ˣ

Therefore , The equation to represent this scenario is y = y = 43*3ˣ  .

The given question is incomplete , the complete question is

Kyle starts a fundraiser with 43 pennies. He recruits all of the players on his baseball team to participate. His goal is to triple the number of pennies each day. Assume Kyle meets his daily goal. Use x to represent the number of days and y to represent the total number of pennies .

Select the Equation that represents the this scenario ?

(a) y = 43(3)ˣ

(b) y = 3(43)ˣ

(c) y = [(43)(3)]ˣ

(d) y = 43(x)³

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Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

9514 1404 393

Answer:

  (i) ∠CDF = 86°

  (ii) ∠BAD = 141°

Step-by-step explanation:

(i) Angles CDF and GFD are "alternate interior" angles, so are congruent.

  ∠CDF = 86°

__

(ii) Angles BAD and CDA are "alternate interior angles, so are congruent. Angle CDA is the sum of angles CDH and HDA. Angle CDH is supplementary to angle CDF, so is ...

  ∠CDH = 180° -∠CDF = 180° -86° = 94°

Then ...

  ∠CDA = ∠CDH +∠HDA = 94° +47°

  ∠CDA = 141°

Answer:

-7b-8

Step-by-step explanation:

Hi there!

We are given the expression 2b-3-9b-5 and we want to simplify it by combining like terms

Like terms are terms that have the same variables (ex. 2x and x are like terms, -3 and 6 are like terms. However, x and x² are not like terms, neither are -3x and 8)

We can bold or underline the like terms to make it easier. Remember to include the sign, as those are important:

2b -3 -9b -5

Now add 2b and -9b together:

2b+ -9b= -7b

Now add -3 and -5 together

-3 + -5 = -8

Add -7b and -8 together

-7b + -8 = -7b-8

As -7b and -8 aren't like terms, we have to leave the expression as -7b-8.

Hope this helps!

The required solution for the profits in the year 2020 is $10452958.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

In 1990, the profit of the Gamma company was $11,218,614.

profits fell by $12,189 on average.

According to given question we have

Initial profit P(x)= $11900848

Fall rate= $48263 per year

The year in between  1990<x<2020

The Equation is

P(x)= 11900848 - (x-1990)*48263,

P(2020)= 11900848- 30*48263

= $10452958

Therefore, the required solution for the profits in the year 2020 is $10452958.

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The trigonometry expression (sin²x - cos²x)/(1 - sin²x) = tan²x – 1 has been proved below and the solution is tan x = 2 or tan x = -3

The equation is  given as

(sin^2x - cos^2x)/(1 - Sin^2x) = tan^2x – 1

Rewrite properly

So, we have

(sin²x - cos²x)/(1 - sin²x) = tan²x – 1

A trigonometry ratio states that:

1 - sin²x = cos²x

So, we have:

(sin²x - cos²x)/cos²x = tan²x – 1

Expand

sin²x/cos²x - cos²x/cos²x = tan²x – 1

Evaluate

tan²x – 1 = tan²x – 1

This means that the trigonometry expression has been proved

Solving further, we have

(sin²x - cos²x)/(1 - sin²x) = 5 - tan x

So, we have

tan²x – 1 = 5 - tan x

Evaluate the like terms

tan²x + tan x – 6 = 0

Expand

tan²x + 3 tan x – 2 tan x - 6 = 0

So, we have

tan x(tan x + 3) – 2 (tan x  + 3) = 0

This gives

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

So, we have

tan x = 2 or tan x = -3

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Answer:

It is expected that 26.25 inches of rain will fall over the next 7 days

Explanation:

Here, we want to get the total of inches of rain expected to fall

From the question, 3.75 inches of rain will fall daily

The amount of rain that will thus fall in 7 days will be the product of the amount per day and the number of days

Mathematically, we have this as:

Answer: 1.6

Step-by-step explanation:

each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces

Answer:

shown below

Step-by-step explanation:

golf balls per ounce = 5/8 or 0.625

ounces per gold ball = 8/5 or 1.6

Answer: The infinite geometric series converges to 38.4

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

Explanation:

Divide each term by its previous term

term2/term1 = 9.6/19.2 = 0.5

term3/term2 = 4.8/9.6 = 0.5

The common ratio is r = 0.5

Since -1 < r < 1 is true, this means the infinite geometric series converges.

It converges to...

S = a/(1-r)

S = 19.2/(1-0.5)

S = 38.4

Answer:

Top is right

Step-by-step explanation: