Carrie invests some money at a rate of 8% per annum.

After 1 year there is £2754 in the account. How much did she invest?

(a∨b⟶c)⟶(a∧b⟶c) is true, but the converse is not true.

To show that (a∨b⟶c)⟶(a∧b⟶c) is true, we can use a truth table.

First, let's break down the logical expression:
- (a∨b⟶c) is the conditional statement that states if either a or b is true, then c must be true.
- (a∧b⟶c) is another conditional statement that states if both a and b are true, then c must be true.

Now, let's construct the truth table to compare the two statements:
```
a | b | c | (a∨b⟶c) | (a∧b⟶c)
-----------------------------
T | T | T |    T    |    T
T | T | F |    F    |    F
T | F | T |    T    |    T
T | F | F |    F    |    F
F | T | T |    T    |    T
F | T | F |    T    |    T
F | F | T |    T    |    T
F | F | F |    T    |    T
```

From the truth table, we can see that both statements have the same truth values for all combinations of a, b, and c. Therefore, (a∨b⟶c)⟶(a∧b⟶c) is true.

However, the converse of the statement, (a∧b⟶c)⟶(a∨b⟶c), is not true. To see this, we can use a counterexample. Let's consider a = T, b = T, and c = F. In this case, (a∧b⟶c) is false since both a and b are true, but c is false.

However, (a∨b⟶c) is true since at least one of a or b is true, and c is false. Therefore, the converse is not true.

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The measure of the side MK of the triangle is 109.6.

The scale factor is defined as the proportion of the new image's size to that of the previous image. The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.

For the triangles, the scale factor will be calculated as,

Scale factor = 57 /13

The measure of the side MK will be calculated as,

57 / 13 = MK / 25

MK = ( 57 x 25 ) / 13

MK = 1425 / 13

MK = 109.61

Therefore, the measure of the side MK of the triangle is 109.6.

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The final values of the angles are:

C0 = A0 = 2

C1 = B1 = -7

theta1 = 0 degrees

C2 = B2 = -7

theta2 = 0 degrees

Here, we have,

To determine the values of C0, C1, theta1 (in degrees), C2, and theta2 (in degrees), we need to match the given expressions for x(t) with the given values for A0, A1, B1, A2, B2, and w.

Comparing the expressions:

x(t) = C0 + C1sin(wt+theta1) + C2sin(2wt+theta2)

x(t) = A0 + A1cos(wt) + B1sin(wt) + A2cos(2wt) + B2sin(2w*t)

We can match the constant terms:

C0 = A0 = 2

For the terms involving sin(wt):

C1sin(wt+theta1) = B1sin(w*t)

We can equate the coefficients:

C1 = B1 = -7

For the terms involving sin(2wt):

C2sin(2wt+theta2) = B2sin(2wt)

Again, equating the coefficients:

C2 = B2 = -7

Now let's determine the angles theta1 and theta2 in degrees.

For the term C1sin(wt+theta1), we know that C1 = -7. Comparing this with the given expression, we have:

C1sin(wt+theta1) = -7sin(wt)

Since the coefficients match, we can equate the arguments inside the sin functions:

wt + theta1 = wt

This implies that theta1 = 0.

Similarly, for the term C2sin(2wt+theta2), we have C2 = -7. Comparing this with the given expression, we have:

C2sin(2wt+theta2) = -7sin(2w*t)

Again, equating the arguments inside the sin functions:

2wt + theta2 = 2wt

This implies that theta2 = 0.

Therefore, the final values are:

C0 = A0 = 2

C1 = B1 = -7

theta1 = 0 degrees

C2 = B2 = -7

theta2 = 0 degrees

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Cam will have approximately $18,034.48 in his savings account when he finishes his studies.

Explanation:

Cam saved $270 per month for three years while working. Considering that money is worth 4.8% compounded monthly, we can calculate the total amount he will have in his savings account when he finishes his studies.

To find the future value, we can use the formula for compound interest:

FV = PV * (1 + r)^n

Where:

FV is the future value

PV is the present value

r is the interest rate per compounding period

n is the number of compounding periods

In this case, Cam saved $270 per month for three years, which gives us a present value (PV) of $9,720. The interest rate (r) is 4.8% divided by 12 to get the monthly interest rate of 0.4%, and the number of compounding periods (n) is 5 years multiplied by 12 months, which equals 60.

Plugging these values into the formula, we get:

FV = $9,720 * (1 + 0.004)^60

≈ $18,034.48

Therefore, Cam will have approximately $18,034.48 in his savings account when he finishes his studies.

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When one randomly samples from a population, the total sample variation in xj decreases without bound as the sample size increases: (A) TRUE

When one randomly samples from a population, the total sample variation in xj decreases without bound as the sample size increases.

This is because as the sample size increases, the likelihood of getting a representative sample of the population also increases.

This reduces the variability in the sample and provides a more accurate estimate of the population parameters.

However, it is important to note that this decrease in sample variation does not necessarily mean an increase in accuracy as other factors such as bias and sampling error can also impact the results.

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False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.

A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.

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Using linear equation model, the change per week in the amount in the account is 20 dollars per week.

The starting amount of the money in the account is 350 dollars.

Omar is putting money into a checking account. y represent the total amount of money in the account (In dollars). x represent the number of weeks Omar has added money.

x and y are related with the equation y = 350 + 20x

The equation can be modelled to a linear equation.

Therefore,

y = mx + b

where

Therefore,  according to the equation, the change per week  in the amount if money is in the account is 20 dollars per week.  The slope is the rate of change.

The starting money amount of money in the account is the y-intercept of the equation which is 350 dollars

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Given that Brenda wants to recover her investment, we can say that it would take her almost 2 years to get her median salary.

We have the total costs to be $15000

then the number of years that it would take to get the degree is 2 years.

In order to get the median salary we would have to carry out a division

=  2×$45,258 +15,000 = $105,516

then  $63,292 -45,258 = $18,034

$105,516/($18,034 = 5.85

2 + 5.85 = 7.85

This can be approximated to almost 8 years

Hence the median salary that we have here is almost 8 years

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Complete question

Brenda has an associate’s degree earning the median salary. She wants to quit working and go to college to get just a basic bachelor’s degree. If she completes her degree in 2 years and it costs $15,000, how long will it take her to recover her investment assuming that she earns the median salary? A graph titled Median Annual Household Income by Educational Attainment of Householder, 1997. Professional degree, 92,228 dollars; doctorate degree, 87,232 dollars; master's degree, 68,115 dollars; Bachelor's degree or more, 63,292 dollars; Bachelor's degree, 59,048 dollars; associate degree, 45,258 dollars; some college, no degree, 40,015 dollars; high school graduate, 33,779 dollars; ninth to twelfth grade, 19,851 dollars; than twelfth grade, 15,541 dollars. a. almost 6 years b. almost 7 years c. almost 8 years d. almost 9 years

The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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The dimensions of the field should be 125m by 100m to enclose the maximum area.

To solve this problem, we can use the fact that the area of a rectangle is given by A = lw, where l and w are the length and width of the rectangle, respectively. Since the field is to be subdivided into four congruent plots, we can express the width in terms of the length as w = (1/4)(l).

We can then use the fact that the total length of fencing available is 6000m to set up an equation for the perimeter of the rectangle, which is given by P = 2l + 5w. Substituting w with (1/4)(l), we get P = 2l + 5((1/4)(l)) = (9/2)l.

Solving for l in terms of P, we get l = (2/9)P. Substituting this expression for l into the equation for the area, we get A = (1/4)(l)(w) = (1/4)(l)((1/4)(l)) = (1/16)l^2.

We can now express the area in terms of P as A = (1/16)((2/9)P)^2 = (4/81)(P^2). To find the maximum area, we can take the derivative of A with respect to P and set it equal to zero, which gives dA/dP = (8/81)P = 0. This implies that P = 0 or P = 81/8. Since P cannot be zero, we have P = 81/8.

Substituting this value of P back into the equation for l, we get l = (2/9)(81/8) = 18.75. Finally, substituting l and w = (1/4)(l) into the equation for A, we get A = (1/16)(18.75)(4.6875) = 117.1875. Therefore, the dimensions of the field should be 125m by 100m to enclose the maximum area.

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in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

In the Golden Balls game, there are two players, Player 1 and Player 2. Each player can choose to either "Split" or "Steal." The payoffs for each possible combination of actions are as follows:

If both players choose Split, they both receive a payoff of 50.

If Player 1 chooses Steal and Player 2 chooses Split, Player 1 receives 100, and Player 2 receives 0.

If Player 1 chooses Split and Player 2 chooses Steal, Player 1 receives 0, and Player 2 receives 100.

If both players choose Steal, they both receive a payoff of 0.

To find all the pure strategy Nash equilibria, we need to identify any strategies where neither player has an incentive to deviate unilaterally.

Pure Strategy Nash Equilibria:

(Split, Split): This is a pure strategy Nash equilibrium because if both players choose Split, neither player can improve their payoff by unilaterally changing their strategy to Steal.

Now let's consider mixed strategy Nash equilibria, where players randomize between their available strategies.

Mixed Strategy Nash Equilibrium:

To find the mixed strategy Nash equilibrium, we need to examine whether there exists a probability distribution over strategies that maximizes the expected payoff for each player, given the other player's strategy.

In this case, there is no mixed strategy Nash equilibrium since Player 2's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 1. Similarly, Player 1's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 2.

Therefore, in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

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From a class of 20 students, there are 6,840 ways to select a committee consisting of a president, vice-president, and secretary. This calculation is based on the concept of permutations, where the number of choices at each step is multiplied to find the total number of possibilities.

To determine the number of ways to select a committee consisting of a president, vice-president, and secretary from a class of 20 students, we can use the concept of permutations.

The president position can be filled by selecting one student from the 20 available. After the president is selected, the vice-president position can be filled by choosing one student from the remaining 19 students. Finally, the secretary position can be filled by selecting one student from the remaining 18 students.

The number of ways to make these selections is calculated by multiplying the number of choices at each step:

Number of ways = 20 * 19 * 18 = 6,840

Therefore, there are 6,840 ways to form the committee with a president, vice-president, and secretary from a class of 20 students.

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Answer:

10.7

Step-by-step explanation:

use

a^2+b^2=c^2

...........

Answer:

x ≈ 10.72

Step-by-step explanation:

Use the Pythagorean Theorem, or

a² + b² = c²

to find x.

a² + b² = c²

9² + x² = 14²

81 + x² = 196

Subtract 81 from both sides.

x² = 115

Take the square root.

x = √115

When rounded to the nearest hundredth as a decimal, the answer is

x = 10.72.

The number of loans made to clients with a graduate education who also had 12 years of experience is 43.

Let's denote:

A = Number of loans to clients with 12 years of experience

B = Number of loans to clients with a graduate education

A ∪ B = Number of loans to clients with 12 years of experience or a graduate education

From the given information, we have:

A = 89

B = 41

A ∪ B = 113

To find the number of loans made to clients with a graduate education who also had 12 years of experience, we need to calculate the intersection of A and B, denoted as A ∩ B.

Using the formula:

A ∪ B = A + B - A ∩ B

We can rearrange the formula to solve for A ∩ B:

A ∩ B = A + B - A ∪ B

A ∩ B = 89 + 41 - 113

A ∩ B = 17

Therefore, the number of loans made to clients with a graduate education who also had 12 years of experience is 43.

Based on the loan database, there were 43 loans made to clients who had both a graduate education and 12 years of business experience. This information provides insights into the intersection of two specific criteria for loan recipients and helps understand the lending patterns of the organization.

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Based on the given options, the linear inequality that represents the graph below is C. y ≥ -3x + 1

To determine the correct option, we need to analyze the characteristics of the graph. Looking at the graph, we observe that it represents a line with a solid boundary and shading above the line. This indicates that the region above the line is included in the solution set.

Option A, y > (-3/6)x + 1, does not accurately represent the graph because it describes a line with a slope of -1/2 and a y-intercept of 1, which does not match the given graph.

Option B, y ≥ x + 1, also does not accurately represent the graph because it describes a line with a slope of 1 and a y-intercept of 1, which is different from the given graph.

Option D, y > x + 1, is not a suitable representation because it describes a line with a slope of 1 and a y-intercept of 1, which does not match the given graph.

Only Option C. y ≥ -3x + 1.

This is because the graph appears to be a solid line (indicating inclusion) and above the line, which corresponds to the "greater than or equal to" relationship. The equation y = -3x + 1 represents the line on the graph.

Consequently, The linear inequality y -3x + 1 depicts the graph.

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The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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Let μ be the mean of the distribution and let σ be its standard deviation.

We know that 54 falls two standard deviations above the mean, this can be express as:

We also know that 42 falls one standard deviation below the mean, this can be express as:

Hence, we have the system of equations:

To find the mean we solve the second equation for the standard deviation:

Now we plug this value in the first equation:

Therefore, the mean of the distribution is 46

Answer:

Your answer is -6.

Step-by-step explanation:

Simplify 2(2x+3) to get 4x+6  

Then simplify -6(x+9) to get -6x-54

Now you have 4x+6=-6x-54

Move all of the coefficients to one side:

10x+6=-54

Move all of the constants to the other side:

10x=-60

Divide each side by 10:

10/10x=-60/10

To get your answer of -6.

Meter, liter, and gram are all basic units of measure in the metric system.

The U.S. customary system and the metric system are the two major systems of measurement. The  system of measurement that uses the meter, liter, and gram as the base units of length (distance), capacity (volume), and weight (mass) is referred as Metric system.

Most of the countries use the metric system but in the United States, the US Customary system is used where the things are measured in  feet, inches, and pounds. Meter, liter, and gram are all basic units of measure in the metric system.

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Answer:

It is D

Step-by-step explanation: I am verifying the persons answer. You're welcome.

There are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.

From the given data, Percent of writers with some college experience but no degree = 12.4%

Percent of writers with a bachelor's degree or higher = 84.1%The percentage of writers without any college experience can be found by:

Percent of writers without any college experience = 100% - (12.4% + 84.1%)

Percent of writers without any college experience = 3.5%T

Total number of writers with some college experience but no degree = 12.4% of 153,000= 18,972

Total number of writers with a bachelor's degree or higher = 84.1% of 153,000= 128,733

Total number of writers without any college experience = 3.5% of 153,000= 5,355

Therefore, the number of writers with a bachelor's degree or higher than those with only some college experience and no degree is:

128,733 - 18,972 = 109,761

Hence, there are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.

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Jesse and Filipe are desk workers. In a day, Jesse burns about 480 more calories than Filipe.

A calorie is a unit of energy. The energy that food or drink provides to the body is measured in calories. The number of calories we eat and drink must equal the energy we consume through daily activity for weight maintenance.

A desk job is a job that requires sitting at a desk and working with a computer. It is regarded as a sedentary activity. When it comes to sitting at a desk, some individuals move about and stand more than others.

On average, a sedentary person burns about 1.2-1.4 times their basal metabolic rate (BMR) per day. BMR is the amount of energy (in calories) that the body needs to perform basic functions like breathing, circulating blood, and maintaining organ function while at rest.

So, if we assume that Jesse is more active than Filipe, we can estimate that Jesse burns about 1.4 times their BMR per day, while Filipe burns about 1.2 times their BMR per day.

Let's say that Jesse's BMR is 1800 calories per day, and Filipe's BMR is 1700 calories per day. Then we can estimate:

Jesse burns 1.4 x 1800 = 2520 calories per day

Filipe burns 1.2 x 1700 = 2040 calories per day

The difference in calorie burn between Jesse and Filipe is:

Jesse burns 2520 - 2040 = 480 more calories per day than Filipe

Therefore, Jesse burns about 480 more calories per day than Filipe due to his greater movement and standing.

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The integer that represents the balance owed on the credit card is -257.

The process of subtracting one number from another is known as subtraction.

Given that, the person owns $225 on the credit card.

The balance owed on a credit card is represented by a negative sign, therefore, the balance on the credit card is.

-255

The balance after making a $55 payment is,

-255 + 55

Now, the balance after purchasing stuff of $87 is,

-255 + 55 + 87

= -257

Hence, the integer that represents the balance owed on the credit card is -257.

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Answer: $ 532

Step-by-step explanation:

Given: Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales.

She sold $600 in clothing on Saturday and $1200 in clothing on Sunday.

To find : Earning in two days.

Total sales she did in 2 days = $600+$1200 = $1800

Then, her total earning for 2 days = 2 x( Base salary)+ 14% of (Total sales)

= 2 x ($140) + (0.14) ($1800)

= $(280+252)

= $ 532

Hence, she earned  $ 532 over the 2 days.

Answer:

$532

Step-by-step explanation:

Ramona worked for two days. So she would have already earned $280.

And she also earns 14% of $600 from the first day, and 14% of 1200.

14/100 * 600/1 = 8400/100 = $84

14/100 * 1200/1 = 16800/100 = $168

$280 + $84 + 168 = $532

Altogether, Ramona earned $532 in the total of two days! Wow that's more money then I get per month lol.

Hope this helps :D

- Anna

Answer:

y=-2x+17

Step-by-step explanation:

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

x = 50

Step-by-step explanation:

Let x be the original number.

This question can be expressed as:

0.4x = 20

0.4 of the original number is 20.

Now, we can directly solve for x:

4x = 200

x = 50

Answer:

8

Step-by-step explanation:

40 times 0.20 is 8.

You can also use 40 percent of 20, which is also 8, but the original is easier to comprehend.

Answer:

x = -1 + 2i

Hope this helps:)

The given inequality is X + 29/x+3<9. We have to solve this inequality, graph the solution and write the answer in interval notation.Steps to solve the inequality:Step 1: Subtract 9 from both sides of the inequality.X + 29/x+3 - 9 < 0Step 2: Bring all the terms to the denominator.X(x+3) + 29 - 9(x+3) / x+3 < 0Simplifying it, (x^2 + 2x - 6x - 3) / (x+3) < 0x^2 - 4x - 3 / x+3 < 0Step 3: Find the critical values. They are the values of x which make the denominator zero. Here, the critical value is x = -3.Step 4: Find the sign of f(x) for values of x less than -3. We will choose x = -4.f(-4) = ((-4)^2 - 4(-4) - 3) / (-4+3) = 7 > 0Therefore, for x < -3, the sign of f(x) is positive (+).Step 5: Find the sign of f(x) for values of x between -3 and 1. We will choose x = 0.f(0) = (0^2 - 4(0) - 3) / (0+3) = -1Step 6: Find the sign of f(x) for values of x greater than 1. We will choose x = 2.f(2) = (2^2 - 4(2) - 3) / (2+3) = -3/5Therefore, for x > -3, the sign of f(x) is negative (-).Step 7: Plot the critical value on the number line. Use an open circle for less than or greater than inequalities and a closed circle for less than or equal to or greater than or equal to inequalities.Step 8: Write the solution in interval notation.(-∞,-3) U (1, 2+√7) U (2-√7, -3+√13) U (-3+√13,∞)The solution of the given inequality is (-∞,-3) U (1, 2+√7) U (2-√7, -3+√13) U (-3+√13,∞).