7. A man wishes to invest $3500. He can buy savings bonds which pay simple
interest at the rate of 12% per annum or he can start a savings account which
pays compound interest at the same rate. Calculate the difference in the
amounts of the two investments at the end of the 3 years.
a)
1200 x 9 x2
=​

The length of the side a , to the nearest 10th of a centimeter is 75cm

It is important to note that the sum triangle theorem states that the sum of the interior angles of a triangle is equal to 180 degrees.

Then, we have;

m< A + m< B+ m < C = 180

substitute the values, we have;

m < A = 180 - 154 - 13

subtract the values

m < A = 13 degrees

Using the sine rule, we have that;

sin A/a = sin B/b = sin C/c

Where; the capital letters are the angles and the small letters are the sides.

We have;

sin A/a = sin C/c

substitute the values

sin 13/a = sin 13/75

cross multiply

a = sin 13 × 75/sin 13

a = 75cm

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The value οf f(-2) fοr this functiοn is 12.

A functiοn is a mathematical rule οr prοcess that assigns a unique οutput value tο each input value. In οrder tο evaluate a functiοn at a specific input value, we need tο knοw the functiοn itself. The functiοn can be given in different fοrms, such as an equatiοn οr a graph, and we use these fοrms tο determine the οutput value fοr a given input value.

Fοr example, if we are given the equatiοn οf a functiοn[tex]f(x) = x^2 - 3x + 2,[/tex] we can evaluate f(-2) by substituting -2 for x in the equation:

[tex]f(-2) = (-2)^2 - 3(-2) + 2 = 12[/tex]

Therefοre, the value οf f(-2) fοr this functiοn is 12. Hοwever, if we are nοt given the equatiοn οr any οther infοrmatiοn abοut the functiοn, we cannοt determine its οutput at a specific input value.

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Complete Qustion:

How to find f (- 2 for a function?

If the student correctly answers a question, the probability that the student really knew the correct answer is  0.941.

The probability that the student knows the answer to the question and correctly answers it is 0.8 x 1 = 0.8. The probability that the student guesses and correctly answers the question is 0.2 x 0.25 = 0.05. The probability that the student correctly answers the question is 0.8 + 0.05 = 0.85.

The probability that the student really knew the correct answer given that they correctly answered the question is 0.8 / 0.85 = 0.941. Therefore, the probability that the student really knew the correct answer is approximately 94.1%.

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The polynomial 0 can be written in the form at^2 + bt + c as 0t^2 + 0t + 0. In this case, a, b, and c are all equal to 0.

It will take 10.4 years for the value of the car to depreciate to 5500 dollars.

The equation for calculating the number of years until the value of the car is 5500 dollars is:

y = (19700 - 5500) / 0.0925

y = 10.4 years

In order to calculate the number of years until the value of the car is 5500 dollars, we can use the equation y = (19700 - 5500) / 0.0925. This equation uses the initial value of the car (19700) and the desired value (5500), as well as the depreciation rate of 9.25% per year. By solving this equation, we can determine that it will take 10.4 years for the value of the car to depreciate to 5500 dollars.

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The z-score is a measure of how many standard deviations a data point is from the mean. It can be calculated using the formula
z = (x - μ) / σ,
where x is the data point, μ is the mean, and σ is the standard deviation.

a. The z-score for a backyard structure costing $2300 can be calculated as follows:

z = (2300 - 3100) / 1200 = -800 / 1200 = -0.67

b. The z-score for a backyard structure costing $4900 can be calculated as follows:

z = (4900 - 3100) / 1200 = 1800 / 1200 = 1.

c. The z-score in part (a) is -0.67, which means that the backyard structure costing $2300 is 0.67 standard deviations below the mean. The z-score in part (b) is 1.5, which means that the backyard structure costing $4900 is 1.5 standard deviations above the mean. Neither of these z-scores are extreme enough to be considered outliers, as they are both within 2 standard deviations of the mean.

d. The z-score for the backyard shed-office combination costing $13,000 can be calculated as follows:

z = (13000 - 3100) / 1200 = 9900 / 1200 = 8.25

This z-score is much larger than 2, which means that the structure costing $13,000 is more than 8 standard deviations above the mean. This is an extreme value and should be considered an outlier.

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Answer:

14.2665 feet above the ground

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the height of the ladder on the wall "h". Then we have:

sin(72°) = h/15

Multiplying both sides by 15, we get:

h = 15 sin(72°)

Using a calculator, we find that sin(72°) is approximately 0.9511. So:

h ≈ 15 × 0.9511

h ≈ 14.2665

Therefore, the top of the ladder is approximately 14.2665 feet above the ground.

Answer:

Option B

Step-by-step explanation:

Vertical angles are a pair of angles which have the following characteristics:

(i) Equal in measurement

(ii) Located on opposite sides of two intersecting straight lines

AND

(iii) Have the same vertex

Vertical angles in this figure:
∠ERT and ∠MRC

∠KRC and ∠ERH

∠KRE and ∠CRH

In this case, it means that the company fails to identify components that absorb too much humidity, leading to a potential safety hazard for customers.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The consequence of a Type II error in this context is that the company believes the humidity absorbed is not more than 3%, when in fact it is more than 3%.

This means that the company will fail to detect components that absorb a dangerous level of humidity, and these components will be sold to customers, potentially causing a safety hazard. This is because the null hypothesis in this case is that the humidity level absorbed is 3%, and the alternative hypothesis is that it is more than 3%. A Type II error occurs when the null hypothesis is not rejected, even though it is false, and the alternative hypothesis is true.

Therefore,  In this case, it means that the company fails to identify components that absorb too much humidity, leading to a potential safety hazard for customers.

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Expression B has the least value if  g and h are whole numbers, and

g < h.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given that,

g < h

To determine which expression has the least value, we need to simplify each expression as much as possible and compare the results.

First, let's simplify expression A:

A = (h + g) * (h - g)

 = h*h - g*g

Next, let's simplify expression B:

B = h*h- 2hg + g*g

Finally, let's simplify expression C:

C = h*h + 2hg + g*g

Now we can compare the expressions. We know that g < h, so g*g < h*h. Therefore, the smallest value will be produced by the expression with the smallest coefficient for the h*h term.

A has a coefficient of 1 for the h*h term, while B and C have coefficients of -2h and 2h, respectively. Since h is positive, -2h is the smallest coefficient, so expression B has the smallest value.

Therefore, expression B has the least value.

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Answer:

adult ticket £17

child ticket £9

Step-by-step explanation:

Let the cost of an adult ticket be X and child ticket be Y

make two simultaneous equations

2X+3Y=61

3X+5Y=96

solve for each variable by either substitution or elimination method

2X+3Y=61

X=(61-3Y)/2

3[(61-3Y)/2]+5Y=96

(183-9Y)/2 + 5Y=96

183-9Y+10Y=192

Y=9

X=(61-3(9))/2

X=17

The measure of angle NSR.

The situation in the picture is when two chords intersect in a circle in this case the angle NSR is calculated using the formula

angle NSR = 1/2 (arc NR + arc QP)

Plugging in the values

angle NSR = 1/2 (176 + 50)

angle NSR = 1/2 (226)

angle NSR = 113 degrees

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Triangle JKL has a greater area than triangle XYZ, as it has an area of 98 square inches

To determine which triangle has the greater area, we need to use the formula for the area of a triangle, which is half the product of the base and height.

For triangle JKL, with a base of 14 inches and a height of 14 inches, we have:

Area = (14 x 14) / 2 = 98 square inches

For triangle XYZ, with a base of 20 inches and a height of 8 inches, we have:

Area = (20 x 8) / 2 = 80 square inches

Therefore, triangle JKL has a greater area than triangle XYZ, as it has an area of 98 square inches compared to 80 square inches for triangle XYZ. This is because the base and height of triangle JKL are both larger than those of triangle XYZ.

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Draw triangle​ JKL, with a height of 14 inches and a base of 14​inches, and triangle​ XYZ, with a height of 8 inches and a base of 20 inches. Which triangle has the greater​ area? in 100 words

If Sam purchases a new car for $29,500 and the car depreciates at a rate of 13. 25% per year, then the value of the car after 7 years is $11652.50

We can use the formula for exponential decay to find the value of the car after 7 years:

V = P × e^(-rt)

where:

V = value of the car after 7 years

P = initial price of the car

r = annual depreciation rate (as a decimal)

t = time in years

Plugging in the values we get:

V = 29500 × e^(-0.1325 × 7)

V = 29500 × e^(-0.9275)

V = 29500 × 0.395

V = $11652.50

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Jermaine bought 9 large shirts for $12, and 12 small shirts for $8 for his 21 employees.

Let's represent the number of large shirts Jermaine bought as "L" and the number of small shirts as "S". We can set up a system of equations based on the information given:

L + S = 21 (equation 1, the total number of shirts is 21)

12L + 8S = 204 (equation 2, the total cost of the shirts is $204)

To solve for L, we need to eliminate S. We can do this by multiplying equation 1 by 8 and subtracting it from equation 2:

12L + 8S = 204

8L + 8S = 168 (multiply equation 1 by 8)

4L = 36

Dividing both sides by 4, we get:

L = 9

Therefore, Jermaine bought 9 large shirts for his 21 employees. We can find the number of small shirts by substituting L = 9 into equation 1:

L + S = 21

9 + S = 21

S = 12

So, by using linear equation system we find that Jermaine bought 9 large shirts and 12 small shirts for his 21 employees.

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Answer:

look at image

Step-by-step explanation:

The cοrrect statement is "The greater the value οf the base, the greater the functiοn's rate οf grοwth"

An expοnential functiοn is a mathematical functiοn οf fοrm f(x) = abˣ,

where a and b are cοnstants, and x is the variable.

The base b is a pοsitive cοnstant and is typically greater than 1. The expοnent x represents the degree οf grοwth οr decay οf the functiοn.

Expοnential functiοns are cοmmοnly used tο mοdel grοwth οr decay in variοus real-wοrld phenοmena, such as pοpulatiοn grοwth, cοmpοund interest, radiοactive decay, and the spread οf disease.

When b is greater than 1, the functiοn represents expοnential grοwth. As x increases, the functiοn grοws at an increasing rate.

When b is between 0 and 1, the functiοn represents expοnential decay. As x increases, the functiοn decays at a decreasing rate.

Therefοre,

The cοrrect statement is "The greater the value οf the base, the greater the functiοn's rate οf grοwth".

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The expression "5 less than the conscious number and 2" can be written mathematically as: n - 5 = 2

A math expression is a combination of mathematical symbols, numbers, and variables that represents a mathematical statement or calculation. It can be as simple as a single number, such as 5, or as complex as a multi-term equation, such as 3x + 4y = 12.

Expressions can include arithmetic operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions such as exponents, logarithms, and trigonometric functions.

Where "n" represents the number in question. To find the value of "n", you can add 5 to both sides of the equation:

n - 5 + 5 = 2 + 5

This is the result:

n = 7

Therefore, the number in question is 7.

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The question in English is:

(What is) 5 less than the conscious of a number and 2

The mοde value fοr the table οf data given is οptiοn D. 10.

A mοde is described as the value in a grοup οf values that οccurs mοre frequently. The value that appears the mοst frequently is this οne.

The mοde is nοt necessarily unique tο a given discrete distributiοn, since the prοbability mass functiοn may take the same maximum value at several pοints x1, x2, etc. The mοst extreme case οccurs in unifοrm distributiοns, where all values οccur equally frequently.

The data is given fοr the average number οf days οf rain in each mοnth οf the year.

The mοde will the number οf days repeating itself mοre number οf times.

It can be seen that 10 is repeated 4 times amοng the data given.

Therefοre, the mοde value is 10.

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Answer:

From the problem, we know that:

s + h = 137 (the total number of sodas and hot dogs sold is 137)

s = h + 49 (the number of sodas sold is 49 more than the number of hot dogs sold)

Now we can substitute the second equation into the first equation:

(h + 49) + h = 137

Simplifying this equation:

2h + 49 = 137

Subtracting 49 from both sides:

2h = 88

Dividing both sides by 2:

h = 44

Now we know that 44 hot dogs were sold. We can use the second equation to find the number of sodas sold:

s = h + 49

s = 44 + 49

s = 93

Therefore, 93 sodas were sold.

Number of sodas sold: 93

Number of hot dogs sold: 44

Step-by-step explanation:

Answer: Let's use variables to represent the number of sodas and hot dogs sold.

Let x be the number of hot dogs sold.

According to the problem, the number of sodas sold was 49 more than the number of hot dogs sold, so the number of sodas sold is x + 49.

The problem also tells us that the combined total of sodas and hot dogs sold was 137. So we can set up an equation:

x + (x + 49) = 137

Simplifying the left side:

2x + 49 = 137

Subtracting 49 from both sides:

2x = 88

Dividing both sides by 2:

x = 44

So the number of hot dogs sold was 44.

To find the number of sodas sold, we can use the expression we set up earlier:

x + 49

Substituting in our value for x:

44 + 49 = 93

So the number of sodas sold was 93.

Answer: Number of sodas sold: 93, Number of hot dogs sold: 44.

Brainliest Appreciated  

The initial fee per meter is $110.

Although the fundamentals of speed, time, and distance stay the same, the kind of problems posed in exams may vary.

Most of the time, applicants will be given 1-2 word problems based on Speed, Time, and Distance, but they should also be prepared for questions on data sufficiency and data interpretation based on the TDS (Time, Distance, and Speed) theme.

At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.

F(d) models the fee (in dollars) for climbing d meters.

F(d)=110+0.12d

To find the initial amount, substitute d=0 int the above function, and we get

F(0)=110+0.12(0)=110

Hence, the initial fee is $110.

The complete question is-

At Simba Travel Agency, the price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per meter.F(d)models the fee (in dollars) for climbing d meters. F(d)=110+0.12d. What is the initial fee?

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Answer:    y=1x+6

Step-by-step explanation:

The equation of a line is y=mx+c

m is the gradient and c is the y intercept.

on the graph the line intercepts the y axis at 6- the y intercept!

The gradient is the difference in y divide by the difference in x.

(0,6) and (4,10)

10-6=4

4-0=

4

4/4 is 1! so the equation is

y=1x+6

Answer:

y = x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (4, 10) ← 2 points on the line

m = [tex]\frac{10-6}{4-0}[/tex] = [tex]\frac{4}{4}[/tex] = 1

the line crosses the y- axis at (0, 6 ) ⇒ c = 6

y = x + 6 ← equation of line

The probability of X not occurring is 0.34.

What is Probability?

Probability is a branch of mathematics concerned with measuring the likelihood of events. It involves studying random phenomena, such as coin tosses, rolling dice, or weather patterns, and assigning numerical values to the likelihood of different outcomes .The formal definition of probability is based on the concept of equally likely outcomes, where the probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes

If P(X) = 0.66, then the probability of not X occurring (i.e., X complement or X bar) is:

P(X bar) = 1 - P(X)

P(X bar) = 1 - 0.66

P(X bar) = 0.34

Therefore, the probability of X not occurring is 0.34.

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The probability that 11 or more of these consumers have called an 800 or 900 telephone number for information about some product is approximately 0.326.

The number of successes in a certain number of independent trials that all have the same probability of success are described by the discrete probability distribution known as the binomial probability distribution. The probability of success is constant during all trials, and it is used in statistics to describe situations where there are two alternative outcomes (success or failure).

The binomial probability distribution is given as:

P(X ≥ k) = 1 - P(X < k)

Here, p = 0.60, and the sample size is n = 20.

Thus,

P(X ≥ 11) = 1 - P(X < 11)

= 1 - ∑(20 choose x) (0.6)ˣ (0.4)⁽²⁰⁻ˣ⁾ for x from 0 to 10

P(X ≥ 11) = 0.326

Hence, the probability that 11 or more of these consumers have called an 800 or 900 telephone number for information about some product is approximately 0.326.

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The complete question is:

Answer:

[tex]\frac{8}{3}[/tex]

Step-by-step explanation:

We know that

Line q's slope = [tex]-\frac{3}{8}[/tex]

AND we know that line q is perpendicular to line p.

When a line is perpendicular to another line, this means that the slope is the opposite reciprocal of the other slope.

This means that we simply have to flip our fraction and change the sign.

Thus, the slope is [tex]\frac{8}{3}[/tex]

From the given information provided, the given sentences in the form of algebraic expressions are as follows:

1. 4 + x

2. 2D

3. 6n + 41

4. x + 17

5. Mary's height - Frank's height

6. Iquan's age / 4

7. 50Arielle's age

8. 75 + x

9. 400 - 2x

10. 11 + x

11. 2d

12. 2x + 10

13. 3v - 40

14. 2t - 60

15. x/15 - 3

16. 5 + x

17. x - 33

18. 2S - 15

19. 60 - 2x

20. 4D

Question - 1. Four plus a number 2. Twice Dharia's age 3. Six times a number plus forty-one 4. The sum of a number and 17 5. The difference between Mary's height and Frank's height 6. The quotient of Aquaman's age and 4 7. The product of Arielle's age and 50 8. Seventy-five increased by a number 9. Four hundred decreased by twice a number Eleven ples more than a number 10. 11. Twice as many dogs 41X 12. A number doubled plus ten 13. A variable tripled less 40. 14. Twice the temperature minus 60 degrees 15. A number divided by fifteen less than 3 16. Five more than a number 17. Thirty-three less than a number 18. Twice Solomon's weight less fifteen pounds 19. The difference between sixty and twice a number 20. The factor of a variable and the coefficient four. Translate the following into algebraic expression.

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As given the conversion unit: 1 cup = 0.237 liters. Sameer drinks 0.71 liters of coffee.

Any physical quantity can be measured by comparing it to a recognised standard, and the magnitude is almost always expressed in terms of the reference standard known as a unit.

The FPS system, which measures length, mass, plus time in feet, pounds, and seconds, is one of the three systems that also was utilised for the measurement. The MKS system, which stands for metre, kilogramme, and seconds, has replaced the CGS system in centimetre, gramme, and seconds as the one that is widely used.

Units of Capacity are given as:

System Units      Metric System Units

1 gallon       -       3.79 liters

1 quart        -       0.95 liters

1 cup           -       0.237 liters

Coffee Intake of Sameer:  3 cups

1 cup           -       0.237 liters

Multiply both sides by 3.

1*3 cup           -       0.237*3 liters

3 cup           -        0.711  liters

Thus, Sameer drinks 0.71 liters of coffee (rounded off nearest tenth).

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Complete question:

Units of Capacity are given as:

System Units      Metric System Units

1 gallon       -       3.79 liters

1 quart        -       0.95 liters

1 cup           -       0.237 liters

Sameer usually drinks 3 cups of coffee in the morning. How many liters of coffee does he drink? Round your answer to the nearest tenth.

Answer:

Step-by-step explanation: