You bought a car that had factory installed tires marked as "P185 75/R14". You bought and installed tires on your car that are marked "P205 75/R14". What is the circumference of the P185 tire?
A) 24.93 inches
B) 27.93 inches
C) 78.31 inches
D) 81.99 inches

1a. The accumulated factor is 1.5986.

b. The accumulated value is K9591.60

c. The total compound interest earned is K3591.60.

2. Deal 1 is better since it gives a higher amount, K3591.60, of interest earned compared to Deal 2, of K2273.60.

3. The annual compound interest rate used is 5.42%.

4a. Under Plan A, it would take 5.38 years to reach his target of K8000.

b. It would take him 3.65 years to reach his target. under Plan B.

5a. Accumulation factor is 1.0816, accumulated value is K5408, and the total compound interest earned is K408.

b. Accumulation factor is 1.2167, the accumulated value is K6083.50, and the total compound interest earned is K1083.50

6. Total interest she will earn 5 years after the original investment is K4,595.69.

7. Sharon will reach her target in approximately June 2002 which is approx. 1.07 years.

8. The customer will have to pay back K6757.61 after 12 weeks.

1. (a) The accumulated factor is calculated as follows:

i = 4.0% per year, compounded quarterly

n = 8 years × 4 quarters per year = 32 quarters

Using the formula for the accumulated factor for quarterly compounding:

F = \((1 + i)^{n}\) = \((1 + 0.04/4)^{32}\) = 1.5986

Accumulated factor = 1.5986.

(b) Accumulated value: accumulated factor * principal amount:

A = F × P = 1.5986 × K6000 = K9591.60

Accumulated value = K9591.60.

(c) The total compound interest earned: principal -accumulated value:

I = A - P = K9591.60 - K6000 = K3591.60

Compound interest earned =K3591.60.

2. To compare the two deals, we will calculate the total amount of interest earned under each one.  

Under Deal 1, interest is compounded quarterly:

I = A - P = K9591.60 - K6000 = K3591.60

Under Deal 2: We shall use the formula: I = P × r × t

P = principal amount,

r = interest rate,

t = time in years.

I = K6200 × 0.046 × 8 = K2273.60

This means that the first deal is better since it gives a higher total amount of interest earned.

3. The annual interest rate:

Given::

P = K200

A = K310

n = 2 (compounded twice per year)

t = 10 years

A = \(P (1 + r/n)^{(nt)}\)

A = accumulated value,

P = principal amount,

r = interest rate,

n = number of times the interest is compounded per year,

t = time in years.

310 = \(200 (1 + r/2)^{(2 * 10)}\)

1.55 = \((1 + r/2)^{20}\)

Taking the 20th root of both sides, we get:

1 + r/2 = 1.0271

r/2 = 0.0271

r = 0.0542

Annual compound interest rate = 5.42%.

4. (a) Under Plan A,

Using I = P × r × t, we have:

I = K8000 - K6200 = K1800

r = 5.4%

t = I / (P × r) = K1800 / (K6200 × 0.054)  = K334.80

To reach K8000, the tutor will need to earn K1800 in interest, so he is to invest for:

K1800 / K334.80 = 5.38 years

(b) Under Plan B, interest is compounded monthly. using the formula A = \(P (1 + r/n)^{(nt)}\)

Monthly interest rate:

0.048 / 12 = 0.004

The amount of interest earned in one month is:

K6200 x 0.004 = K24.80

To reach K8000, the tutor will need to earn K1800 in interest, so he has to invest for:

log(K8000/K6200) / log(1+0.004) = 43.76 months

= 43.76/12

= 3.65 years.

5(a) After 2 years, the accumulation factor is:

\((1 + 0.04)^{2}\) = 1.0816

The accumulated value is:

K5000 x 1.0816 = K5408

Total compound interest earned is:

K5408 - K5000 = K408

(b) After 5 years, the accumulation factor is:

(1 + 0.04)⁵ = 1.2167

The accumulated value is:

K5000 x 1.2167 = K6083.50

The total amount of compound interest earned is:

K6083.50 - K5000 = K1083.50

6. Amount invested is K5000 + K6000 = K11,000.

Interest rate = 5% per annum compounded quarterly, so the quarterly interest rate is 1.25%.

The number of quarters in 5 years is 20.

Accumulated value after 5 years is:

\(K11,000 (1 + 0.0125)^{20}\) = K15,595.69

The total interest earned is:

K15,595.69 - K11,000 = K4,595.69

7. To calculate the time taken to reach K10,000, we use the compound interest  formula:

\(K8000 (1 + 0.04/4)^{4t}\)  = K10,000

where t =  time in years.

t = log(K10,000/K8000) / (4 log(1 + 0.04/4)) = 4.28 quarters

4 quarters in a year is ≈ 1.07 years, so Sharon will reach her target in approximately June 2002.

8. Weekly interest rate = 2%,

So daily interest rate ≈ 0.0286%.

The amount owed after 12 weeks:

\(K5000 (1 + 0.000286)^{84}\) = K6757.61

The customer will pay back K6757.61 after 12 weeks

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The measure of the angle that turns through 3/10 of the circle is 108 degrees.

An angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

Since a full circle has 360 degrees, 3/10 of the circle can be represented as:

(3/10) x 360 degrees = 108 degrees

Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.

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The complete question is :

The angle turns through 3/10 of the circle. What is the measure of the angle?

Answer:

m<2 = 100

Step-by-step explanation:

136 <abc Given

136-197= 39 = <1

so 136 - 39 = 197=<2

Here are the completed tables for each sequence:

Sequence 1 Sequence 2 Ordered Pair

5                    15                   (5, 15)

6                        14               (6, 14)

7                        13             (7, 13)

8                    12                 (8, 12)

9                   11                (9, 11)

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x.

The corresponding terms in the two sequences are related by a linear function. The slope of the line is 1, which means that for every 1 increase in y, there is a 1 increase in x. This means that the two sequences are increasing at the same rate.

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Answer:

-3

Step-by-step explanation:

Answer:

The answer will be 0

Step-by-step explanation:

Let me know Hope it helps

Answer:

261

Step-by-step explanation:

Before Andrei adds the marbles to the glass tank, the glass tank was empty. This means that the volume of the empty tank is when n = 0 and the volume is 32 liters.

Given that:

\(W = 32 - 0.05n\)

A linear function is represented as:

\(y = b + mx\)

Where

\(b \to\) y intercept

Literally, the y intercept is the initial value of the function.

In this function, the y intercept means the initial volume of the glass tank before filling it with marbles.

Compare \(y = b + mx\) and \(W = 32 - 0.05n\)

\(b = 32\)

This means that the volume of the glass tank is 32 liters.

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Answer:

0.05

Step-by-step explanation:

Answer:9

Step-by-step explanation: There are 6 while swuares and 6 traingles. 2 triangles is 1 square.6 plus 3 is 9.

The written description of x - 14 is given as the difference of variable x and integer 14 gives x -14.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Let x be a variable,

And 14 is an integer.

By using mathematical operations,

The difference of x and 14 can be given as,

x - 14.

The required expression x - 14 is the difference of variable x and 14.

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The inequality is used to find the domain of the given function is

5x-5 ≥ 0

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.

Since, the function is a square root function.

We know that,

The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.

The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :

5x-5 ≥ 0

Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0

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a) Null hypothesis: The mean number of pounds of fruit produced on the plot of land with the new fertilizer is equal to 400 lbs. (i.e., there is no increase in yield from the old fertilizer to the new fertilizer).

Alternative hypothesis: The mean number of pounds of fruit produced on the plot of land with the new fertilizer is greater than 400 lbs. (i.e., there is an increase in yield from the old fertilizer to the new fertilizer).

b) Null hypothesis: The mean caffeine content per cup of regular coffee served at the coffee shop is 100 mg.

Alternative hypothesis: The mean caffeine content per cup of regular coffee served at the coffee shop is different from 100 mg.

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Answer:

100 degrees

sorry if i wrong

Step-by-step explanation:

The length of the given line segment is calculated as; 13 units

The formula for the distance between two coordinate points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √[( y₂ - y₁)² + (x₂ - x₁)²]

From the attached graph, we see that the coordinates of the two endpoints of the line segment are (-5, -8) and (0, 4).

Now, the length of the line segment will be the distance between two endpoints (-5, -8) and (0, 4).

Thus, the distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √[(4 + 8)² + (0 - (-5))²]

D = √(144 + 25)

D = √169

D = 13 units

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Answer:

all real numbers

Step-by-step explanation:

when you multiply the bottom equation by 4, you can see the equations cancel out

The equation of the quartic function is \(y = -\frac{1}{2}\cdot x^{4}+x^{3} +\frac{3}{2}\cdot x^{2} -2\cdot x - 2\), whose factored form is \(y = (x-2)^{2}\cdot (x+1)^{2}\).

A quartic function is a fourth order polynomial, whose form is presented below:

\(y = a\cdot x^{4}+b\cdot x^{3} + c\cdot x^{2}+d\cdot x + e\), \(a, b, c, d, e\in \mathbb{R}\)  (1)

Where:

Given that such polynomial must be tangent to the x-axis in two place, slope must be zero and by differential calculus we have the following expression for the slope of the tangent line:

\(4\cdot a \cdot x^{3} + 3\cdot b\cdot x^{2} + 2\cdot c \cdot x + d = 0\) (2)

Then, we can construct the following system of linear equations:

\(e = -2\) (3)

\(a -b +c -d = -e\) (4)

\(-4\cdot a +3\cdot b -2\cdot c + d = 0\) (5)

\(16\cdot a + 8\cdot b + 4\cdot c + 2\cdot d = -e\) (6)

\(32\cdot a + 12\cdot b + 4\cdot c + d = 0\) (7)

The solution of the system is: \(a = -\frac{1}{2} , b = 1, c = \frac{3}{2}, d = -2\).

The equation of the quartic function is \(y = -\frac{1}{2}\cdot x^{4}+x^{3} +\frac{3}{2}\cdot x^{2} -2\cdot x - 2\), whose factored form is \(y = (x-2)^{2}\cdot (x+1)^{2}\).

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

-7 is the lowest number, since it is a negative. The absolute value of -2, or |-2|, is 2 making it the second lowest. 3 comes next. The absolute value of 4.5 is 4.5, being the greatest number.

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

First, let's find -2 and |4.5| .

Absolute value of a number is its distance from 0. Remember, absolute value is always zero or positive.

Now, let's use a number line to order the numbers. Numbers to the left are less than numbers to the right.

The values in order from least to greatest is as follows: -7, |-2|, 3, |4.5|.

Answer:

Hi! I'll do my best to explain for you.

-6(2x-3)+2x =0     First, set the equation equal to zero.

-12x+18+2x=0      Then, distribute the -6 by multiplying it with the -2 and -3.

-10x+18=0            Combine the like terms, which are -12x and 2x, to get -10x.

-10x=-18               You want to get the x on 1 side. Subtract 18 from both sides.

x=-18/-10              Divide by -10 on both sides.

x=1.8                    Simplify the fraction. The answer is x=1.8.

I hope this helped!

Answer:

61

Step-by-step explanation:

90-29=61

Answer:

98,000 bacteria.

Step-by-step explanation:

We are given the formula:

\(P=le^{kt}\)

Where l is the initial population, k is the rate of growth, and t is the time ( in hours).

We know that it has an initial population of 500. So, l is 500.

We also know that the population grows to 7000 after 2 hours.

And we want to find the population after 4 hours.

First, since we know that the population grows to 7000 after 2 hours, let's substitute 2 for t and 7000 for P. Let's also substitute 500 for l. This yields:

\(7000=500e^{2k}\)

Divide both sides by 500:

\(e^{2k}=14\)

We can solve for the rate k here, but this is not necessary. In fact, when can find our solution with just this.

Let's go back to our original equation. We want to find the population after 4 hours. So, substitute 4 for t:

\(P=500e^{4k}\)

We want to find the total population, P. Notice that we can rewrite our exponent as:

\(P=500(e^{2k})^2\)

This is the exact same thing we acquired earlier. So, we know that the expression within the parentheses is 14. Substitute:

\(P=500(14)^2\)

Square and multiply:

\(P=500(196)=98000\)

So, after 4 hours, there will be 98,000 bacteria.

And we're done!

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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Answer: C

Step-by-step explanation:

This is just a straight definition - for a normal distribution, the percent within 2 standard deviations of the mean is about 95.44%.

Answer:

Step-by-step explanation:

Use Pythagorean to verify:

As we see the equation is not true, so the answer is no

Let's use Pythagorean theorem to verify

\(\\ \sf\longmapsto H^2=P^2+B^2\)

\(\\ \sf\longmapsto 5^2=4^2+2^2\)

\(\\ \sf\longmapsto 25=16+4\)

\(\\ \sf\longmapsto 25\neq 20\)

Not a right triangle

Answer:

4:5 or 0.8

Step-by-step explanation:

if the correspond sides are 24 (smaller figure) and 30 (larger figure), then the requred scale factor is:

24:30=4:5 (or 0,8).

The period of the sound wave created by the tuba is approximately 0.0134 seconds.

The speed of sound in air is given as 343 meters per second. The formula relating the speed of sound, wavelength, and period of a wave is:

v = λ × f

Where:

v = speed of sound (343 m/s)

λ = wavelength (4.61 m)

f = frequency (unknown)

To find the period, we need to determine the frequency of the sound wave. The period (T) is the reciprocal of the frequency (f), so we can rewrite the formula as:

v = λ / T

Rearranging the equation to solve for the period (T), we get:

T = λ / v

Substituting the given values, we have:

T = 4.61 m / 343 m/s

Calculating the value, we find:

T ≈ 0.0134 seconds

Therefore, the period of the sound wave created by the tuba is approximately 0.0134 seconds.

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