Find the value of x.

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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why is this in collage work this has to be 5th grade?

Answer:

hbhbhbb dsvjv wenvwe

Step-by-step explanation:

The   proceeds  is  $7,566.67 and  the effective rate charged by the bank to the nearest is 6.87%.

Given data:

Principal = $8,000

Rate =6 1/2% or 6.5%

Term= 300 Days

a. Proceeds

Interest  = Principal  x Rate  x Time

Interest  = $8,000 x 6.50% x 300/360

Interest = $8,000 x 0.065 x 0.8333

Interest  = $433.33

Now let find the Proceeds:

Proceeds = $8,000 - 433.33

Proceeds = $7,566.67

b. Effective Interest Rate:

Effective Interest Rate = 433.33 / 7566.67 x 300/360

Effective Interest Rate = 433.33 / 6305.56

Effective Interest Rate = 0.0687 × 100

Effective Interest Rate = 6.87%

Therefore  $7,566.67 is the proceeds and 6.87% is the interest rate.

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Answer:

4 L 600 mL

Step-by-step explanation:

1 L = 1000 mL

so 27 L 600 mL = 27000 + 600 = 27600 mL

27600/6 = 4600 mL

4 L 600 mL.

Answer:

5,00000000

Step-by-step explanation:

6000000000

Answer:

Step-by-step explanation:

To find the cost of each box divide the total cost by the number of boxes:

In store A:

→ A box of cotton candy cost = $ 1

→ 12 boxes cost = $ 12

In store B:

→ 12 boxes cost = $ 48

Now we have to,

find the cost of each box in the store B.

→ Total cost in B ÷ Total boxes in B

→ 48 ÷ 12 = 4

So, $ 4 is cost of each box in store B.

Answer: 47.6 is your answer hope this helped

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Step-by-step explanation:

Answer:

36 - 4

Step-by-step explanation:

(6x - 2)(6x + 2)

= (6x)(6x) + (6x)(-2) + (2)(6x) + (-2)(2)

= 36 - 12x + 12x - 4

= 36 - 4Step-by-step explanation:

Is true.

wksnsksndksndks

Answer:

Hola 15 es tu respuesta

Step-by-step explanation:

por 40% puedes convertirlo en 4, multiplicar por 15 y obtendrás 60

espero que esto ayude

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

Answer:

3.65

Step-by-step explanation:

The square root of 2 is 1.4 and the square root of 5 is 2.2 adding that together you get 3.6

If values prοvided then transfοrmatiοn οf vectοrs can be determined.

In mathematics, a vectοr is a mathematical οbject that represents a quantity with bοth a magnitude and a directiοn. Vectοrs can be used tο represent physical quantities such as velοcity, fοrce, and acceleratiοn, as well as mοre abstract cοncepts such as cοlοr, sοund, and temperature.

Withοut seeing the figure οr the values οf a1, a2, and a3, it is nοt pοssible tο determine whether the specified linear transfοrmatiοn T : R2 → R2 is οne-tο-οne and οntο.

Hοwever, in general:

A linear transfοrmatiοn T : Rn → Rm is οne-tο-οne if and οnly if its kernel (i.e., the set οf vectοrs that are mapped tο the zerο vectοr) is trivial, meaning that the οnly vectοr that maps tο the zerο vectοr is the zerο vectοr itself.

A linear transfοrmatiοn T : Rn → Rm is οntο if and οnly if its range (i.e., the set οf all vectοrs that can be οbtained by applying T tο sοme vectοr in Rn) is equal tο Rm.

Tο determine whether a linear transfοrmatiοn is οne-tο-οne οr οntο, we can examine its prοperties and characteristics, such as its kernel, range, rank, and determinant. We can alsο use geοmetric intuitiοn and visualizatiοn tο understand hοw the transfοrmatiοn maps pοints and vectοrs in Rn tο Rm.

If yοu prοvide mοre infοrmatiοn abοut the values οf a1, a2, and a3 and the figure that shοws the standard matrix A, it can help yοu determine whether the transfοrmatiοn is οne-tο-οne and οntο and draw the image οf the vectοr [-1, 1] under the transfοrmatiοn T.

Therefοre, if values prοvided then transfοrmatiοn οf vectοrs can be determined.

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Complete question -

In Exercises 33–36, determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. 14. Let T : R2 R2 be a linear transformation with standard matrix A = aaz], where a, and a, are shown in the figure. Using the figure, draw the image of under the transformation T. [-] 1

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

Answer:

2 students play both

Step-by-step explanation:n(u)=28

n(b)=7,n(b)=5,n(who play neither sport)=18

HERE,

n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)

28=7+5-n(BnB)+18

28=30-n(BnB)

n(BnB)=30-28

 =2 answer

9514 1404 393

Answer:

  -2 11/35

Step-by-step explanation:

Put the numbers where the variables are and do the arithmetic.

  \(\left(\dfrac{x^2}{x}-3\right)\div10\cdot z=\left(\dfrac{(-6)^2}{1.2}-3\right)\div10\cdot\left(-\dfrac{6}{7}\right)\\\\=\left(\dfrac{36}{1.2}-3\right)\div10\cdot\left(-\dfrac{6}{7}\right)=(30-3)\div10\cdot\left(-\dfrac{6}{7}\right)\\\\=\dfrac{27}{10}\cdot\left(-\dfrac{6}{7}\right)=-\dfrac{27\cdot6}{10\cdot7}=-\dfrac{27\cdot3}{5\cdot7}=\boxed{-\dfrac{81}{35}=-2\dfrac{11}{35}}\)

__

It is important to note here that the order of operations requires that the only value being divided by is 10, not 10z. The division by 10 occurs before the multiplication by z.

Answer:

0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

A telephone exchange operator assumes that 9% of the phone calls are wrong numbers.

This means that \(p = 0.09\)

Sample of 448

This means that \(n = 448\)

Mean and standard deviation:

\(\mu = p = 0.09\)

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{448}} = 0.0135\)

What is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%?

More than 9% + 3% = 12 or less than 9% - 3% = 6%. Since the normal distribution is symmetric, these probabilities are the same, so we find one of them and multiply by 2.

Probability it is less than 6%

P-value of Z when X = 0.06. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.06 - 0.09}{0.0135}\)

\(Z = -2.22\)

\(Z = -2.22\) has a p-value of 0.0132

2*0.0132 = 0.0264

0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%

Given:

A car can drive 119 miles on 5 gallons.

So, car drive 23.8 miles per gallon.

A) For 9 gallons the distance covered by car is,

The car can drive 214.2 miles on 9 gallons.

B) For 1190 miles,

The car will need 50 gallons to drive 1190 miles

Answer:

a command demonimater of 6 and 7 is 42

35/42 and 36/42

Hope This Helps!!!

Answer:

Nonequivalent fractions are not equal to each other. To determine if two fractions are nonequivalent, you must also cross multiply. For example, to determine if 1/3 and 2/5 are equivalent, you must multiply 1 times 5, which equals 5, and 3 times 2, which equals 6.

Step-by-step explanation:

Hope this helps u

Crown me as brainliest:)

The non examples equivalent ratios for 3/4 could be 3/4 ,7/9, 4/5 etc.

Equivalent ratios are the set of ratios which when reduced to simpler form are equal to each other.

Given is equivalent expression.

Assume that you have the following ratio -

3 : 4

Now, we can write its equivalent ratios expressed as fractions are -

6/8, 9/12, 12/16 etc

Now, the non - equivalent ratios are the set of ratios which when reduced to simpler form are not equal to each other. For example, we have -

3 : 4

As fraction -

3/4

There could be infinite number of possible equivalent and non - equivalent ratios. For 3/4, non equivalent ratios will be -

3/4 ,7/9, 4/5  etc.

Therefore, the non examples equivalent ratios for 3/4 could be 3/4 ,7/9, 4/5 etc.

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8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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The length of the loan in months is 151. 33 months

The formula for determining simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

Principal interest = $600

Simple interest = $681

Rate = 9%

Substitute the values into the formula

$681 = $600 × 9 × T/100

Multiply the numerators

$681 = 5400T/100

cross multiply

68100 = 5400T

Divide both sides by 5400

T = 68100/5400

T = 12. 61 years

Convert the years to months

T = 12.61(12)

T = 151. 33 months

Hence, the value is 151. 33 months

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Answer:

Expanding the expression 2(d+9) gives:

2(d+9) = 2*d + 2*9

Simplifying the expression gives:

2(d+9) =2d + 18

Therefore, 2(d+9) is equivalent to 2d +18.

The simplified expression is:

Work:

To simplify this expression, I distribute 2 through the parenthesis:

\(\sf{2(d+9)}\)

\(\sf{2\cdot d + 2 \cdot9}\)

\(\sf{2d+18}\)

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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The value of X is 3.25

Look at the attached picture

Hope it will help you

Good luck on your assignment

(a)Contrapositive: If an object does not have a border, then it is not red.

Converse: If an object has a border, then it is red.

Inverse: If an object is not red, then it does not have a border.

(b)Contrapositive: If an object is not red or does not have a border, then it is not a rectangle.

Converse: If an object is a rectangle, then it is red and has a border.

Inverse: If an object is not red or does not have a border, then it is not a rectangle.

(c)Contrapositive: If an object does not have a border, then it is not red or blue.

Converse: If an object is red or blue, then it has a border.

Inverse: If an object does not have a border, then it is not red or blue.

a) Original Conditional Statement (P - Q): If an object is red, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red.

Converse (Q - P) If an object has a border then it is red.

Inverse (not p → not q) If an object is not red then it does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may have a border but not be red.

b) Original Conditional Statement (P - Q): If an object is a rectangle, then it is red and has a border.

Contrapositive (not Q - not P): If an object is not red and does not have a border, then it is not a rectangle.

Converse (Q - P) If an object is red and has a border, then it is a rectangle.

Inverse (not p → not q) If an object is not a rectangle then it is not red or does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may be red and have a border but not be a rectangle.

c) Original Conditional Statement (P - Q): If an object is red or blue, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red or blue.

Converse (Q - P) If an object has a border then it is red or blue.

Inverse (not p → not q) If an object is not red or blue then it does not have a border.

The contrapositive and converse are true, while the inverse is false. For example, object H may have a border but not be red or blue.

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Answer:

y = 3x - 11

Step-by-step explanation:

(3, -2) and (5, 4)

m = 4+2/5-3

m = 6/2

m = 3

y = 3x + b

4 = 3(5) + b

4 = 15 + b

b = -11

y = 3x - 11