Nathan receives a lump sum inheritance of $55 000 and invests the money into a savings account with an annual interest rate of 7.5%, compounded quarterly.(a) Calculate the value of Nathan's investment after 5 years, rounding your answer to thenearest dollar. After m months, the amount in the savings account has increased to more than $70000.(b) Find the minimum value of m, where me N.Nathan is saving to purchase a property. The price of the property is $150 000. Nathan puts down a 15% deposit and takes out a loan for the remaining amount.(c) Write down the loan amount.The loan duration is for eight years, compounded monthly, with equal monthly payments of$1500 made by Nathan at the end of each month.(d) For this lonn, find(i) the amount of interest paid by Nathan over the life of the loan.(i) the annual interest rate of the loan, correct to two decimal places After 5 years of paying this locu, Nathan decides to pay the outstanding loan amount in onefinal payment. (e) Find the amount of the final payment after 5 years, rounding your answer to the nearestdollarif Find the amount Nathan saved by making this final payment after 5 years, roundingyour answer to the nearst dollar.

The the height of the bottom of the hold after second day is 1517.45 feet.

What is height?

Height is a way to measure someone or something from base to top or head to toe

Day 1 height = -[tex]32^{2}/12[/tex] feet

Day 2 height = [tex]192^{2} /23[/tex] more than first day

=36864/23+(-1024/12)

=1602.78-85.33

=1517.45 feet

Therefore, the height of the bottom of the hole after the second day is 1517.45 feet.

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Answer:

-2 < 5 - 2x < 2

-7 < - 2x < -3

7/2 > x > 3/2

3.5 > x > 1.5

1.5 < x < 3.5

Formula for Profit Percentage = (Profit/C.P.) 100Where C.P. denotes the article's cost price, i.e. the price at which the article was originally purchased.

Jane bought a car for £24000

 she sold it for £26000

profit = 2000

profit percentage = 2000/26000 x100 = 7.7%

Here,

Jane bought a car for £24000

 she sold it for £26000

profit = 2000

profit percentage = 2000/26000 x100 = 7.69%

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Answer:

x = 8.9

Explanation:

The sine ratio for 43 degrees gives

Now, the side opposite to the 43 degree angle is x

Solution

Cos 12° expressed as an integer or as a decimal

Hence the value of cos 12° as a decimal to the nearest hundredth = 0.99

Previous concepts

We need to take in count that the intersection or the values of x that satisfy a system equations represent the solutions.

We have 3 possible cases when we have a system of equations:

1) One Solution

2) No solutions

3) Infinite solutions

Also we know that if we have one or more solutions then the system would be consistent otherwise would be inconsistent.

Solution

Let's analyze the situation with examples.

1) Case 1: One solution.

We have the following system of equations :

We can graph both equations and we can see this:

And as we can see we have an intersection point (-0.2, 1.4) with just one solution for this case.

2) Case 2: No solutions

We have the following system of equations : y  =  3x + 2, y  =  3x + 1

The value of p is 8 by the law of exponents.

What is exponents?

The base b and the exponent, or power, n, are used in the mathematical operation known as exponentiation. Its symbol is Bn, and its pronunciation is "b to the n."

An exponent is the number of times a number has been multiplied by itself. For instance, the phrase 2 to the third, which is represented as 23, means 2 to the power 3, 2 x 2 x 2 = 8, not 23, and 2 x 3 = 6, respectively.

Remember that every number multiplied by one is equal to itself. Exponents are a technique of expressing extremely large numbers in terms of powers.

The number of times a number has been multiplied by itself is the exponent, so to speak.

Given that,

9^p/9^5 = 9^3

By laws of exponents and power,

Here, p - 5 = 3

         p = 3 + 5

         p = 8

The value of p is 8 by the law of exponents.

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Notice that the empty circle means that the point circled doesn't belong to the range of the function. Otherwise, the fulfilled circle means the point belongs to that range.

The first horizontal line represents the values of the function for x in the interval 0 < x ≤ 15 (notice the empty circle in point (0, 35) ).

Since this line is horizontal, it means that the function has the same value for all those x's:

f(x) = 35, for 0 < x ≤ 15

Now, let's look at the other horizontal line. It represents the values of the function for all x's in the interval 15 < x ≤ 40 (again, notice the empty circle in point (15, 40) ).

Again, since it's a horizontal line, the function has the same value for all those x's:

f(x) = 40, for 15 < x ≤ 40

Finally, the third line has a slope that we have to consider in order to find the form of the function for the last values of x.

We can find the slope in the following way:

1. first, we choose two points in this line whose coordinates are easy for us to identify. Let's take the points (40, 40) and (45, 50).

2. then, we calculate the difference between the y values of these two points:

y2 - y1 = 50 - 40 = 10

3. then, we calculate the difference between the x values of these two points (remember to take the second one minus the first one):

x2 - x1 = 45 - 40 = 5

4. now, we divide the y's differences by the x's differences (this will be the slope m):

m = (y2 - y1)/(x2 - x1) = 10/5 = 2

Now we know the slope m, we write the function of this line in the form:

f(x) - f(x0) = m * (x - x0)

f(x) - f(x0) = 2 * (x - x0)

Finally, to find the final form of this function, we choose any point in the line and use its x value replacing x0, and its y value replacing f(x0). Let's use the point (40, 40):

f(x) - f(x0) = 2 * (x - x0)

f(x) - 40 = 2 * (x - 40)

f(x) - 40 = 2x - 80

f(x) = 2x - 80 + 40

f(x) = 2x -40

Notice that this function for x = 40 has to assume the same value as the one we find for x = 40 using the function for the second horizontal line (f(x) = 40 ), because they both are defined for the same point:

f(x) = 2x -40

f(40) = 2*40 - 40 = 80 - 40 = 40

For this reason, as the second line already defines the function for x = 40, we can write the third part of the function only for values above x > 40.

Therefore, the function that represents the whole graph is:

f(x) = 35, for 0 < x ≤ 15

f(x) = 40, for 15 < x ≤ 40

f(x) = 2x -40, for x > 40

We know that

• The ball is dropped from 1600 meters high.

• Each time it bounces 3/4 of its original height.

This situation creates a geometric sequence where the reason is 3/4. To find the first three terms of this sequence, we just have to multiply each term with 3/4. We know that the first term is 1600.

The second term is 1200 meters.

The third term is 900.

To find an equation, we have to use the geometric sequence formula-

Replacing the information we have the equation that represents the situation of this problem.

At last, the height after 4 bounces is

The height of the third bounce is 675 meters.

Therefore, the height of the ball after 4 bounces is 506.25 meters.

Answer:

D. (3, 7)

Explanation:

First, we need to draw the triangle to identify the hypotenuse, so using the points P(-2, 5), Q(5, 2), and R(8, 9), we get:

Therefore, the hypotenuse is side PR.

Then, the midpoint of a segment that goes from (x1, y1) to (x2, y2) is

So, replacing (x1, y1) = P(-2, 5) and (x2, y2) = R(8, 9), we get that the midpoint of the hypotenuse is

Therefore, the answer is D. (3, 7)

a.

The question can be answered using the permutations because the order of the flag strung on the mast determines the signal being sent.

Since there are 6 signal flags and the captain has to send a 3-signal flag. So, the number of signals that can be sent are:

Thus, the answer is 120.

b.

The question can be answered using the combination because the questions are randomly selected.

Since the total number of questions is 50 and the number of questions that have to be selected is 50.

So, the number of versions of the quiz that are possible are:

Thus, the answer is 15890700.

Answer:

Year     Jessica         Tom          Who earns more?
1              $400            $400        They earn the same amount

2             $408            $400         Jessica earns more

3             $416             $400         Jessica earns more

Step-by-step explanation:

At simple interest, the amount of interest is the same each year

First year: Since compounding takes place only at the end of the year, both of them earn the same amount of interest

Interest earned = 20,000 x 0.02 = $400

Same for both boxes for first year

Both of their deposits will increase by $400 to $20,400

For second year
Jessica's interest is calculated on 20,400 = 20,400 x 0.02 = $408
Her deposit value at the end of year 2 = 20, 400 + 408 = $20,808

Tom's interest is calculated on the original deposit since it is simple interest. So in year 2, Tom still makes $400.

In year 2 Jessica earns more interest than Tom
Jessica: $408
Tom : $400

For third year, Jessica's interest is calculated on her deposit value of 20,800 = 20,800 x 0.02 = $416

Tom's interest for 3rd year is the same as for the previous years = $400

So in third year, Jessica earns more

For a discontinuous function ,maximun value is found by replacing every region for the values x ,y

So then for x≤2. and y≤1 and f(x,y) = x +y

theres a maximum value but no minimum ( because is minus infinite). The maximum value for this area is

x+y = 2+1= 3

Now for area y ≥-2x -3

rearrange the equation as y+2x ≥ -3

is the equation of a plane , the plane or area that goes over the straight line y= -2x-3.

So now replace y = -2x-3 in the function f(x,y) = x+y

then f(x,y)= x -2x-3 = -x-3

Now the third region is y≥ 2x -3

this is the area over a line with slope positive equal to 2

now replacing again for this area we find

f(x,y) = x+y = 2x-3 +x = 3x -3

because x≤2. So then replace x by 2 in f(x,y) to find the maximum value

f(x,y) in 2nd region is f(x,y) = -x-3= -2-3= -5

f(x,y) in 3rd region is f(x,y) = 3x -3= 3•2 -3= 3

Finally in conclusion, the máximum value is 3 , the minimum value is -5

Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).

rate by an elevator ascends = 29.6 feet per second

height of the  building = 1,450 feet

Time to travel from the ground floor to the roof is calculated as :

we use rate formula.

i.e

rate = distance/ time

time = distance/rate

time = 1450/ (29.6 feet/sec )

time = 1450/29.6

       = 48.98sec

as we know

60 second = 1mint

1 second = 1/60 minutes

therefore,

 time = (48.98 / 60) minutes

time = 0.8163

time = 0.812 minutes

Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).

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Given data:

The given graph.

The domain is the value of x, for the given function domain is,

Thus, the domain is

The common ratio, r = (1/4)/(3/16)

= (1/4)(16/3)

= 4/3

OR

(1/3)/(1/4) = (1/3)(4/1)

= 4/3

The common ratio of a geometric sequence is the ratio of any two consecutive terms.

Suppose we are given a geometric sequence: a1, a2, a3, ...

The common ratio is given as:

a2/a1 = a3/a2 = ...

The inverse of the given equation is given by f⁻¹(x) = (x+8)²/49 - 8

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Equations are used to describe geometric shapes in Cartesian geometry. Since the investigated equations, such as implicit equations or parametric equations, have an unlimited number of solutions, the goal has changed. Now, one utilizes equations to analyze the attributes of figures rather than explicitly providing the solutions or counting them, which is impossible. The fundamental concept of algebraic geometry, a significant branch of mathematics, is presented here. Equations involving one or more functions and their derivatives are known as differential equations. By identifying a derivative-free formulation for the function, they may be resolved. Processes involving rates are modeled using differential equations.

given equation,

f(x) = 7√(x+8) - 8

y = 7√(x+8) - 8 (replace f(x) with y)

x = 7√(y+8) - 8 (interchange x and y)

y = (x+8)²/49 - 8 (solve for y)

f⁻¹(x) = (x+8)²/49 - 8 (replace y with f(x))

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Option (D) "Few trees, mostly grass, rich soil, cold winters, the average rainfall and good for agriculture" perfectly describes the climate and vegetation of Savana.

Therefore, option (D) "Few trees, mostly grass, rich soil, cold winters, the average rainfall and good for agriculture" perfectly describes the climate and vegetation of Savana.

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Answer:

C

Step-by-step explanation:

Its the Little Rain

First, we need to find the sample space for two dice. Since each dice has 6 faces, the sample space is

which consist in 36 elements.

Part A.

In this case, we need to find the combinations where the sum of the 2 dice is even. The combinations are:

for instance, in the upper left corner, the sum is 1+1=2, which is an even number and similarly for the other cases.

As we can note, there are 18 possible combinations. Then, the probability is

Part B.

In this case, we need to find the possible combinations where the sum of the 2 dices is greater than 7. The possible combinations are:

Since there are 15 possible combinations, the probability is given by

Part C.

This case is the intersection of the two cases from above. The possible combinations are:

Since there are 9 possible combinations, the probability is

Part D.

We need to find the possible combinations where the sum is even or the sum is greater than 7. Then, this case is the union of case A and B. Then the possible combinations are:

Since there are 18+6=24 combinations, the probability is

The graph on the right which is a graph of C is Option D. See the explanation below.

A graph is a graphic (such as a sequence of one or more points, lines, line segments, curves, or regions) that depicts the change of one variable in comparison to another.

What is the explanation for the above?

Note that the graph is calibrated at 25 per unit. Hence where x = 0, given the equation C(0) = 0.25x + 75

We have:

0.23 (0) + 75

Hence

C = 75

Tracing this back to the graph, by inference we see that the graph that depicts x as being on the x-axis with y on 75 is option D.

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The y-intercept of the total fee paid by Tyrell on his trip to Chicago when the cab travels 0 miles, the total fee will be $10.00.

The total fee paid by Tyrell is made up of a fixed cost and a variable cost. The fixed fee is the fee that is incurred regardless of the miles travelled. The variable fee is the fee that changes with the distance travelled.

The total fee paid can be modelled as a linear function. A linear function is a single variable that is raised to the power of one.

Total fee = fixed fee + variable fee

Variable fee = (change in total fee ) / (change in total miles)

(17.50 - 13) / (5 - 2)

4.50 / 3 = 1.50

Fixed fee = $13 - (1.50 x 2)

$13 - 3 = $10

The fixed fee, $10 is equivalent to the y-intercept.

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Answer:

its a- For every additional mile the cab travels, the total fee increases by $10.00.

Step-by-step explanation:

hope this helps

a. The linear equation that models the price-sales relationship is: y = -500x + 5000

b. daily sales: $1,250.

To write the linear equation for a relationship, find the unit rate/slope (m) and the starting value/y-intercept, then substitute the values into y = mx + b.

a. Using two points from the problem, (6, 2000) and (8, 1000), find the unit rate (m):

Unit rate (m) = change in y / change in x = (2000 - 1000)/(6 - 8)

Unit rate (m) = 1000/-2

Unit rate (m) = -500

Find the y-intercept (b) by substituting m = -500 and (x, y) = (6, 2000) into y = mx + b:

2000 = -500(6) + b

2000 = -3000 + b

2000 + 3000 = -3000 + b + 3000

5000 = b

b = 5000

To write the linear equation, substitute m = -500 and b = 5000 into y = mx + b:

y = -500x + 5000

b. Substitute x = 7.5 into y = -500x + 5000:

y = -500(7.5) + 5000

y = -3750 + 5000

y = 1,250

The daily sales would be $1,250.

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The equation for Tisha and her team is a equals T plus b plus c plus d all over 4 or , a = (T-b-c-d)/4

An equation is created by joining two expressions with the equals sign ("=").

The points that are earned from the three local matches are b , c, and d.

points earned from the district game = 4a

The total points earned is T

Therefore forming the equation:

T = (4a + b + c + d )

Now we make a the subject of formula:

or , a = ( T - b - c - d) / 4

Therefore the required equation is a equals T plus b plus c plus d all over 4 .

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Answer:

a = (T-b-c-d)/4

Step-by-step explanation:

took test

Write the mixed number -5 4/9 as a decimal

we have the number

5 4/9

step 1

convert to an improper fraction

5 4/9=5+4/9=49/9

and

49/9=5.444444...

Part 2

we have the number

7/-35-------> is the same that -7/35

simplify

Divide by 7 the numerator and denominator

-1/5

Find out an equivalent fraction

Multiply by (3/3)

-3/15

therefore

we have

7/-35

-7/35

-1/5

-3/15

decimal number

-1/5=-0.20

T(x) = 0.06x + 4.5

We are meant to find 'x' when T(x) = $ 11.70

Substitute for T(x) = $ 11.70 in the given function

Thus,

11.70 = 0.06x + 4.5

11.70 -4.5 = 0.06x

7.2=0.06x

Hence, the original price of the hotel room if the tax on the room was $1170 is $120

The percentage of the dealer markup from the original price will be; 1.24 %

Suppose the value of which a thing is expressed in percentage is "a Suppose the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part into 100 parts; then we multiply it by b so that we collect b items per 100 items(that is exactly what b percent means).

Given that the original price of a gold, watch was $500. And the dealer sells this item for $620.

Then the percentage of the dealer markup from the original price will be;

The change = amount/ original  x 100%

= 620/ 500  x 100%

= 1.24  x 100%

Therefore, The markup percentage was; 1.24 %.

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Given

-6 is less than x , 3 is greater than x

Find

Write the inequality

Explanation

-6 is less than x

this implies , -63 is greater than x

this implies , 3>x....................2

from 1 and 2 , we obtain

-6Final Answer

the inequality is - 6 < x < 3

You have the following inequality:

2(5t - 25) + 5t < -80

In order to solve the previous inequality, proceed as follow:

Expand the factor left side and simplify like term:

2(5t) - 2(25) + 5t < -80

10t - 50 + 5t < -80

15t < -80 + 50

15t < -30

Divide by 15 both sides and simplify:

t<-30/15

t<-2

Hence, the solution to the given inequality is t<-2