find the balance in the account: $3,000 principal, earning 3% compounding annually, after 4 years

The equations that can be used to solve for y, the length of the room are: y² - 5y - 750 = 0 , (y - 30)(y + 25) = 0 , y(y - 5) + 750 = 0

An equation is a mathematical statement that asserts the equality of two expressions, often with variables and constants.

To solve for y, we can use the same equation we used for x, since y represents the length of the room. Therefore, the equation we can use to solve for y is:

y² - 5y - 750 = 0

This equation can be factored as (y - 30)(y + 25) = 0, which gives us two solutions: y = 30 or y = -25. However, since the length of a room cannot be negative, the only valid solution is y = 30.

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Answer:

A positive line

Step-by-step explanation:

Answer:

Step-by-step explanation:

you get a straight line with a slope = 2

the line slants up and to the right

it passes through the y axis at the point (0, -3)

Answer: (2,-3) and (-2,5)

Step-by-step explanation:

Let us graph the two equations one by one.
If we compare this equation with the slope intercept form of a line which is given as we see that m = -1 and c =1

Hence the slope of the line is -2 and the y intercept is 1.

Hence one point through which it is passing is (0,1) . 
Let us find another point by putting x = 1 and solving it for y Let us find another point by putting x = 2 and solving it for y Hence the another point will be (2,-3)Let us find another point by putting x = -2 and solving it for y Hence the another point will be (-2,5)Now we have two points (0,1) ,(1,-1) ,  (2,-3) and (-2,5) we joint them on line to obtain our line  2.

 It represents the parabola opening upward with vertices (1,-4)Let us mark few coordinates so that we may graph the parabola.i) x=0 ; ; (0,-3)ii)x=-1 ;  ; (-1,0)iii) x=2 ;  ;(2,-3)iii) x=1 ;   ;(1,-4)iii) x=-2 ;  ;(-2,5)Now we plot them on coordinate axis and line them to form our parabolaWhen we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs. 

The true statement are:

A. 15m3-6m=3m(5m2-6m),

B. 40m6-4=4(10m6-1),

C. 6m2+18m=6m2(1+3m),

Therefore the correct option is A, B, C.

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The correct question is:

Which statements are true

15m3-6m=3m(5m2-6m),

40m6-4=4(10m6-1),

6m2+18m=6m2(1+3m),

32m4+12m3(8m+3)

Answer:

We can use the concept of proportions to solve this problem. We know that the ratio of the height of the tree to the length of its shadow is the same as the ratio of the height of the mailbox to the length of its shadow.

Let's call the height of the mailbox "x". Then, we can set up the proportion:

height of tree / length of tree's shadow = height of mailbox / length of mailbox's shadow

Plugging in the values we know, we get:

36 / 18 = x / 4

Simplifying the left side of the equation, we get:

2 = x / 4

To solve for x, we can multiply both sides of the equation by 4:

8 = x

Therefore, the mailbox is 8 feet tall.

Step-by-step explanation:

Answer:

Height of mail box = 8 ft

Step-by-step explanation:

Given information,

→ 18 ft shadow is formed by a 36 ft tree.

→ A mail box casts 4 foot shadow.

Now we have to,

→ Find the height of the mail box.

Let us assume that,

→ Height of mail box = h

Forming the equation,

→ 36/18 = h/4

Then the value of h will be,

→ 36/18 = h/4

→ h/4 = 36/18

→ h/4 = 2

→ h = 2 × 4

→ [ h = 8 ft ]

Hence, the value of h is 8.

The coordinates of the point that is halfway between G (2,4) and F (6,-6) is (4, -2).

Coordinate is a pair of numbers that represents a position on a two-dimensional plane. Coordinates are usually written in the form (x, y), with the x-coordinate representing a position along the horizontal axis, and the y-coordinate representing a position along the vertical axis. Coordinates can also be used to represent positions on a three-dimensional plane in the form (x, y, z). These coordinates can be used to pinpoint a specific location or to describe the shape of a figure on a graph.

This can be calculated by taking the average of the x coordinates (2 + 6 = 8/2 = 4) and the average of the y coordinates (4 - 6 = -2/2 = -2).
Therefore, the point is (4, -2).

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Answer: She

bought a total of 5 notebooks and 13 pencils.

Step-by-step explanation:

With 4.5% compounded semi-annually, Sarah will need to make installments for roughly 20.82 years in order to save $10,000. Hence, 20.82 is the answer.

Is every two years or semiannually?

Simply said, semiannual refers to events that occur twice a year. A couple might commemorate their nuptials each two years, a corporation might hold workplace celebrations each two years, as well as a family might go on vacation each two years. Every two years, something that happens twice a year does.

We can utilize the calculation again for future value of an annuity to resolve this issue:

FV = P × ((1 + r/n) - 1) / (r/n)

Where:

FV = Future value

P = Periodic payment

r = Annual interest rate

n = Compounding cycles per year, number

t = Number of years

In this instance, Sarah plans to deposit $300 each six months in order to save $10,000. She will so be required to make two payments each year. P thus equals $300, n equals 2, r equals 0.045 (decimalized 4.5%), and FV equals $10,000. The number of years, t, needs to be solved for.

$10,000 = $300 × ((1 + 0.045/2) - 1) / (0.045/2)

When we simplify this equation, we obtain:

20 = (1 + 0.0225) - 1

21 = (1 + 0.0225)

Using both sides' natural logarithms:

ln(21) = ln((1 + 0.0225))

ln(21) = 2×t × ln(1 + 0.0225)

t = ln(21) / (2 × ln(1 + 0.0225))

t = 20.82

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Answer:

The answer to your problem is, A. 900

Step-by-step explanation:

How we would need to find it:

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

27/150 = 0.18

Next, estimate the number of people who prefer mustard in the entire population of 5,000 attendees we can multiply/x this proportion by the total number of attendees:

0.18 x 5,000 = 900

Thus the answer to your problem is, A. 900

Answer:

B) CPCTC (stands for Corresponding Parts of Congruent Triangles are Congruent) should be included in the proof. This statement is necessary to show that ΔDBE ≅ ΔFCE, which then allows us to conclude that DB ≅ FC.

Step-by-step explanation:

The intervals during which the ball's height is increasing are: [0, 2.5] and

[5, 7.5]

In a graph, an interval represents a range of values along the x-axis or y-axis. It is a continuous segment of the axis between two points, often used to indicate a particular range of values or a specific time period.

Since the graph represents the height of the ball h in feet after t seconds, we can find the interval during which the ball's height is increasing by examining the slope of the graph.

If the slope of the graph is positive, the height of the ball is increasing. If the slope is negative, the height of the ball is decreasing.

Looking at the graph, we can see that the slope of the graph is positive between approximately 0 and 2.5 seconds, and between approximately 5 and 7.5 seconds.

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The triangle can be classified as follow:

15: obtuse

16: right

To classify the triangle as acute, obtuse, or right, follow the following steps:

1. Calculate the sum of squares of the two smaller sides.

2. Compare it to the square of the longest side.

3. If the sum is greater, your triangle is acute. If they are equal, your triangle is right. If the sum is less, your triangle is obtuse.

No. 15

10² + (2√39)² = 256

18² = 324

256 < 324 (obtuse)

No. 16

11² + (2√19)² = 197

(√197)² = 197

197 = 197 (right)

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Answer:

To make "x" the subject of the equation, we can isolate it on one side of the equation by multiplying both sides by 15:

x/15 = h

Multiplying both sides by 15 gives:

x = 15h

The equation in terms of "x" is x = 15h.

Step-by-step explanation:

Answer:

Step-by-step explanation:

m = 30

10√3 · √3 = 10·3 = 30

Answer: 11 and more

Step-by-step explanation:

For the first finding on job-search satisfaction scale, the estimated Cohen’s d is not provided in the question. However, assuming that it is provided in the actual data, the psychologist can use Cohen’s guidelines for interpreting the effect size based on the estimated Cohen’s d. According to Cohen’s guidelines, an effect size of 0.2 is considered small, 0.5 is considered medium, and 0.8 or higher is considered large. Therefore, the psychologist needs to compare the estimated Cohen’s d with these values to evaluate the effect size.

For the second finding on the number of months worked in the last year, the estimated Cohen’s d is also not provided in the question. The psychologist can use the same approach to evaluate the effect size using Cohen’s guidelines based on the estimated Cohen’s d.

Alternatively, the psychologist can also use r² as a measure of effect size. R² represents the proportion of variance in the outcome variable that is explained by the treatment or intervention. According to Cohen’s guidelines for r², an effect size of 0.01 is considered small, 0.09 is considered medium, and 0.25 or higher is considered large. Therefore, the psychologist can compare the estimated r² with these values to evaluate the effect size.

Based on the information provided, both findings show statistically significant results with treatment effects. However, the actual effect sizes cannot be evaluated without the estimated Cohen’s d or r² values.

Effect size for job-search satisfaction is Cohen's d = 0.7, t statistic = 4.12 and r² = 0.49.

According to Cohen's guidelines, a Cohen's d of 0.7 is considered a large effect size. This means that the workshop had a significant impact on the job-search satisfaction of the participants. The t statistic of 4.12 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.49 indicates that the workshop accounted for 49% of the variance in job-search satisfaction.

Effect size for months worked

Cohen's d = 0.36

t statistic = 2.38

r² = 0.13

According to Cohen's guidelines, a Cohen's d of 0.36 is considered a medium effect size. This means that the workshop had a significant impact on the number of months worked by the participants. The t statistic of 2.38 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.13 indicates that the workshop accounted for 13% of the variance in months worked.

Interpretation

Both of the effect sizes found by the psychologist are significant, indicating that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect size for job-search satisfaction is larger than the effect size for months worked, suggesting that the workshop had a greater impact on job-search satisfaction than on the number of months worked.

Conclusion

The psychologist's findings suggest that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect sizes for both outcomes are significant, and the effect size for job-search satisfaction is larger than the effect size for months worked. These findings suggest that the workshops may be an effective way to help unemployed people find jobs.

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The two cars will draw level at a distance of 12 kilometers from the starting point, taking their speed and into consideration, as further explained below.

Since both cars are traveling towards the same destination, the distance between them will decrease over time until they draw level. Let's call the distance between the starting point and the meeting point "d" kilometers. We can use the formula:

distance = rate × time

Since car A has a three-minute head start, car B will have to travel for three minutes less than car A. Let's call the time it takes for car B to catch up to car A "t" hours. Then:

time for car A = t + 3/60 hours

time for car B = t hours

We want to find the distance between the starting point and the meeting point, which is the same for both cars. So we can set up an equation based on their distances:

distance traveled by car A = distance traveled by car B

(rate for car A) × (time for car A) = (rate for car B) × (time for car B)

60 × (t + 3/60) = 70 × t

3 = 10t

t = 3/10 hours

Now that we know the time it takes for car B to catch up to car A, we can use either car's rate and time to find the distance between the starting point and the meeting point. Let's use car A's rate and time:

distance = rate × time

distance = 60 × (t + 3/60)

distance = 60 × (3/10 + 1/20)

distance = 60 × (4/20)

distance = 12 kilometers

Therefore, the two cars will meet 12 kilometers from the starting point.

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The expression that does not have the same value as -2 + 3×65 is 3×(65-2) which evaluates to 183, the correct option is D.

The expression -2 + 3×65 represents a mathematical calculation that involves the operations of addition and multiplication. The order of operations dictates that multiplication should be done before addition, so we start by multiplying 3 and 65 and then adding the result to -2.

The value of -2 + 3×65 is 193.

we need to evaluate each expression and compare it to 193.

Option A: 3×65 - 2 = 193

Option B: (3-2)×65 = 65

Option C: 65×3 - 2 = 193

Option D: 3×(65-2) = 183

expression that does not have the same value as -2 + 3×65 is option D: 3×(65-2) which evaluates to 183.

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The complete question is :

Which expression does not have the same value as −2+3×65?

Option A: 3×65 - 2 = 193

Option B: (3-2)×65 = 65

Option C: 65×3 - 2 = 193

Option D: 3×(65-2) = 183

If the 8th term of an A.P is twice the 4th term and the sum of the first terms is 47. the five common difference is 3.

Let the first term be "a" and the common difference be "d".

The 4th term of the AP is: a + 3d

The 8th term of the AP is: a + 7d

We know that the 8th term is twice the 4th term, so:

a + 7d = 2(a + 3d)

Simplifying and solving for "a", we get:

a = d

Substituting this value of "a" in the sum of the first terms, we get:

47 = (5/2)(2a + 4d)

47 = 5(a + 2d)

9.4 = a + 2d

Substituting the value of "a" from above, we get:

9.4 = 3d

d = 3.13333

d = 3 (approximately )

Therefore, the common difference (d) is approximately 3.

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Answer: 345.6149

Step-by-step explanation:

Answer:

345.6149

Step-by-step explanation:

let's keep in mind that in the IV Quadrant, the cosine is positive whilst the sine is negative, so hmm

[tex]\cos(\theta )=\cfrac{\stackrel{adjacent}{8}}{\underset{hypotenuse}{9}} \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{8}\\ o=opposite \end{cases}[/tex]

[tex]o=\pm\sqrt{ 9^2 - 8^2}\implies o=\pm\sqrt{ 81 - 64 } \implies o=\pm\sqrt{ 17 }\implies \stackrel{ IV~Quadrant }{o=-\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \tan(\theta )=\cfrac{\stackrel{opposite}{-\sqrt{17}}}{\underset{adjacent}{8}}~\hfill[/tex]

To find the value of tan(θ) when cos(θ) = 8/9 and θ is in the fourth quadrant, use the relation sin^2(θ) = 1 - cos^2(θ) to determine sin(θ). Then compute tan(θ) = sin(θ) / cos(θ). The result will be negative

Given the equation cos(θ) = 8/9 in the fourth quadrant of the Cartesian plane, you are required to determine the value of tan(θ). In the fourth quadrant, cosine values are positive, and sine values are negative. You can use the relation sin^2(θ) = 1 - cos^2(θ). So, sin(θ) would be -sqrt(1 - (8/9)^2). The tangent of an angle in any quadrant can be found by taking the ratio of the sine to the cosine, i.e., tan(θ) = sin(θ) / cos(θ). Substitute the values of sine and cosine to find the value of tan(θ). It turns out that tan(θ) will be negative in the fourth quadrant.

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Answer:

From the given figure, we can write the following equations:

n(A) = 2x + 4

n(B) = x + 5

n(A∪B) = n(A) + n(B) - n(A∩B)

Since we are given that n(A) = n(B), we can substitute the expressions for n(A) and n(B) to get:

2x + 4 = x + 5

x = 1

(a) x = 1

(b) n(A) = 2x + 4 = 2(1) + 4 = 6

(c) n(B) = x + 5 = 1 + 5 = 6

(d) n(A∪B) = n(A) + n(B) - n(A∩B)

We still need to find n(A∩B) to calculate n(A∪B). Looking at the figure, we can see that there are 2 elements that are common to both A and B. Therefore,

n(A∩B) = 2

Substituting this value, we get:

n(A∪B) = n(A) + n(B) - n(A∩B) = 6 + 6 - 2 = 10

Therefore, (d) n(A∪B) = 10.

Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be $240 which will cover the cost of the new motorbike.

The task can be completed by multiplying the data gathered using this type of nanosection along with two individuals variable  who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.

Here,

The quantity supplied and the quantity requested are equal when there is equilibrium. As a result, we can equalise the two formulae and find the equilibrium quantity:

=> -57P + 364 = 25P + 26

=> 82P = 338

=> P = 4.12

We can use either equation to determine the equilibrium amount now that we know the equilibrium price. Use the supply calculation as an example:

=> Q = 25P + 26

=> Q = 25(4.12) + 26

=> Q = 129.5

So, rounded to two decimal places, the equilibrium amount of beer is roughly 129.5.

=> $60 + $180 = $240

which will cover the cost of the new motorbike.

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Answer:

25% Profit = CP of 5 bats = 5x W

Step-by-step explanation:

Answer:

the formula for density is:

density = mass/volume

We know that the density of the object is 8 grams per liter, and its volume is 16 liters. We can use this information to solve for the mass:

density = mass/volume

8 g/L = mass/16 L

To solve for the mass, we can cross-multiply and simplify:

8 g/L * 16 L = mass

128 g = mass

Therefore, the mass of the object is 128 grams.

Therefore , Highest Common Factor (HCF) of two or more numbers by prime factorisation method can be done by following below given steps

This generally recognized ease, preexisting variables, and any necessary elements from the initial Diocesan customizable query may all be used to complete the job. Consequently, you might be given another chance to use the item. Otherwise, important impacts on algorithmic statistics will vanish.  

Here,

To find the Highest Common Factor (HCF) of two or more numbers by prime factorisation method, follow these steps:

Express each number as a product of prime factors.

Identify the common prime factors among the numbers.

Take the product of the common prime factors. This product will be the HCF of the given numbers.

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The way the principal can use a random - number table to pick 30 students from the school is explained below.

To use a random-number table to select 30 students at random from a school of 500 students, the principal should :

This method ensures that every student has an equal chance of being selected.

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Answer:

  C

Step-by-step explanation:

You want to identify the set of ordered pairs corresponding to the given pattern definitions.

The x-pattern starts at 2.

The y-pattern starts at 0.

The first (x, y) ordered pair is (2, 0). This matches answer choice C.

__

Additional comment

The x-rule tells you the sequence is ...

  2, 2+6 = 8, 8+6 = 14, 14+6 = 20 . . . . . {2, 8, 14, 20}

The y-rule tells you the sequence is ...

  0, 0+5 = 5, 5+5 = 10, 10+5 = 15 . . . . . {0, 5, 10, 15}

Then the (x, y) pairs are ...

  (2, 0), (8, 5), (14, 10), (20, 15)

Note that when X and Y are the variables involved, we conventionally use the ordered pair (x, y). When other variables are involved, the ordered pair may be different, not always alphabetic order.

Generally, the independent variable is listed first. Here, neither depends on the other, so that criterion does not apply. Listing X first here is also suggested by the fact that the X pattern rule is defined first.

Answer: According to the histogram, a sum of 28 is not unusually low. The bar representing a sum of 28 has a height of 9, which is relatively high compared to some of the other bars. Additionally, the histogram is roughly symmetric, so a sum of 28 is not far from the mean of the distribution.

To find the probability that a person would roll a sum less than 28, we can standardize the value using the formula z = (x - mu) / sigma, where x is the sum of 28, mu is the mean of 35, and sigma is the standard deviation of 5.72.

z = (28 - 35) / 5.72 = -1.22

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -1.22 is approximately 0.1112, or 11.12%. Therefore, there is about an 11.12% chance that a person would roll a sum less than 28.

Step-by-step explanation:

The ratio of 75:125 is 3:5.

The ratio 3 mm : 3000 mm is 1:1000.

The ratio of 7500g:2 Kg is 3.75:1.

The ratio of 250ml:2l is 1:8.

To simplify this ratio, we need to find the greatest common factor (GCF) of 75 and 125, and divide both terms by it.

The factors of 75 are: 1, 3, 5, 15, 25, 75.

The factors of 125 are: 1, 5, 25, 125.

The GCF is 25.

Dividing both terms by 25, we get:

75 ÷ 25 = 3

125 ÷ 25 = 5

Therefore, the simplified ratio is 3:5.

1.1.2. 3mm:3m

To simplify this ratio, we need to convert the units so that they are the same.

1 m = 1000 mm

So, 3 m = 3000 mm

Now, the ratio is 3 mm : 3000 mm.

We can simplify this ratio by dividing both terms by 3:

3 mm ÷ 3 = 1 mm

3000 mm ÷ 3 = 1000 mm

Therefore, the simplified ratio is 1:1000.

1.1.3. 7500g:2 Kg

To simplify this ratio, we need to convert either grams to kilograms or kilograms to grams so that both terms have the same unit.

7500 g = 7.5 kg (since 1 kg = 1000 g)

Now, the ratio is 7.5 kg : 2 kg.

We can simplify this ratio by dividing both terms by 2:

7.5 kg ÷ 2 = 3.75 kg

2 kg ÷ 2 = 1 kg

Therefore, the simplified ratio is 3.75:1.

1.1.4. 250ml:21

To simplify this ratio, we need to convert milliliters to a whole number.

We can convert 250 ml to 250/21 ml by dividing both terms by 21:

250 ml ÷ 21 = 11.9 ml (rounded to one decimal place)

Now, the ratio is 11.9 ml : 21.

We can simplify this ratio by dividing both terms by 0.1:

11.9 ml ÷ 0.1 = 119 ml

21 ÷ 0.1 = 210

Therefore, the simplified ratio is 119:210.

1.1.5. 250 kg:2 tonnes

To simplify this ratio, we need to convert either kilograms to tonnes or tonnes to kilograms so that both terms have the same unit.

1 tonne = 1000 kg

So, 2 tonnes = 2000 kg

Now, the ratio is 250 kg : 2000 kg.

We can simplify this ratio by dividing both terms by 250:

250 kg ÷ 250 = 1 kg

2000 kg ÷ 250 = 8 kg

Therefore, the simplified ratio is 1:8.

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