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Answer:

Pretty sure it's 3

Step-by-step explanation:

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

The customer will pay $6.30 for the 60 local calls that all lasted 3 minutes.

To find out how much the customer will pay, we need to calculate the total cost for all the local calls.
Step 1: Calculate the total number of minutes for all the calls
Since the customer made 60 local calls and each call lasted 3 minutes, we can multiply 60 by 3 to get the total number of minutes.
60 calls * 3 minutes/call = 180 minutes
Step 2: Calculate the total cost for all the minutes
The customer pays $0.035 per minute for local calls. To find the total cost, we can multiply the total number of minutes by the cost per minute.
180 minutes * $0.035/minute = $6.30

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The interest earned on the principal amount at the end of 10 years is 1662 (rounded to the nearest dollar).

Given that the principal amount invested is 2000 and the annual rate of interest is 6.5%, compounded quarterly.

We need to find the amount of interest earned on the principal amount at the end of 10 years.

Using the compound interest formula, the future value of the principal amount after 10 years is:

\(FV = P(1 + r/n)^(nt)\)

where

P = 2000,

r = 6.5% = 0.065,

n = 4 (quarterly compounding), and

t = 10 years

So, the future value of the principal amount after 10 years is:

\(FV = 2000(1 + 0.065/4)^(4×10)= 3662.14\)

The interest earned on the principal amount is the difference between the future value and the principal amount, which is:

3662.14 - 2000= 1662.14

Therefore, the interest earned on the principal amount at the end of 10 years is 1662.

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Answer:

33, 57

(not 100% sure this is correct)

Step-by-step explanation:

90= x +(24 +x)

(drag 90, plus the x's and drag the 24)

90 = 2x + 24

(Subtract 24 from 24 and 90 from 24)

66 = 2x

(Divide both by two)

33 = x

(now use x and plus it by 24)

24 + x = 57

The amount earned on the last day was $315.

What is interest?

Interest is the monetary charge for the privilege of borrowing money. Interest expense or revenue is often expressed as a dollar amount, while the interest rate used to calculate interest is typically expressed as an annual percentage rate(APR).

We can start by calculating the total amount earned over the first 6 days:

6 days x $160/day = $960

We can also calculate the total amount earned over the next 3 days:

3 days x $175/day = $525

So over the first 9 days, the total amount earned is:

$960 + $525 = $1485

To find out how much was earned on the last day, we can use the fact that the average wage over the entire 10 days was $180/day. We can set up the equation:

(10 days x $180/day) - $1485 = $1800 - $1485 = $315

Therefore, the amount earned on the last day was $315.

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Answer: Benchmark numbers can be used to state that the square root of 60 is between 6 and 7.

Answer: 50 and 100

Step-by-step explanation:

( sorry if this is not what you meant ;-; )

Answer:

Step-by-step explanation:

The nth term of an arithmetic sequence is expressed as:

Tn  = a + (n-1)d

a is the first term

n is the number of terms

d is the common difference

Let the sequence be 2, T1, T2, T3...Tn, 46

The common difference is expressed as d = b-a/n+1

T1 = 2 + d

Given b = 46 and a = 2

d = 46-2/n+1

d = 44/n+1

T1 = 2 + (44/n+1)

T1 = 2(n+1)+44/n+1

T1 = 2n+2+44/n+1

T1 = 2n+46/n+1

Similarly;

Tn =  2 + nd

Tn = 2 + n(44/n+1)

Tn = 2 + 44n/n+1

Tn = 2(n+1)+44n/n+1

Tn = (2n+2+44n)/n+1

Tn = 46n+2/n+1

If the ratio of the first mean to last mean is 1:7 then T1/Tn = 1/7

(2n+46/n+1)÷(46n+2/n+1) = 1/7

2n+46/n+1 * n+1/46n+2 = 1/7

2n+46/46n+2 = 1/7

Cross multiply and solve for n:

46n + 2 = 7(2n + 46)

46n + 2 = 14n + 322

46n - 14n = 322-2

32n = 320

n = 320/32

n = 10

Hence the value of n is 10

Answer:

it will take about 15 weeks

Step-by-step explanation:

15% of 674 is about 101.

so, 1500 divided by 101 is about 15

hope this helps :)

Answer:

49,800,000 is the answer

Answer:

50,000,000

Step-by-step explanation: What you would do is if you have to round up, remember this way to always get it right. 4 or below = stays the same 5 or above = rounds up. so 49,815,662. Well we would take the 8 and round it up to the 9 making it 10 so 49 turns into 50.

A trapezoid consists of two triangles.

A trapezoid does indeed contain two triangles within its structure. A trapezoid is a quadrilateral with one pair of parallel sides.

The other two sides, known as the legs, are not parallel and meet at a point. These legs, along with the two parallel sides, form two triangles within the trapezoid.

One triangle is formed by connecting the two legs and one of the parallel sides. The other triangle is formed by connecting the two legs and the other parallel side.

So, a trapezoid consists of two triangles.

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Answer:

11,703 feet

Step-by-step explanation:

Since absolute value is never negative, just add the distances to get the full span. Just think of above sea level as positive and below sea level as negative.

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.

The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

Given equation :

y=(x−2)2−8

y = 2x - 4 - 8

= 2x - 12

The final equation is y = 2x - 12.

Compare this equation with slope and y-intercept formula :

y = mx+c

So that c = -12

The value of y-intercept according to the solution is -12.

To find the vertex. Let's assume x=0; Substitute in the equation

y = 2(0) -12

y = -12

The first vertex will be (0, -12)

If x = 1; y = 2(1) -12

y = -10

Then the second vertex will be (1, -10).

Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

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Answer:

Step-by-step explanation:

ww 55+80 divided by 8 percent

The limit of the expression is determined as 0.

The limit of the expression is calculated as follows;

The given expression = lim (x ---> 9) [ ( x - 9 ) / √x - 3)

For the given limit in the expression, we have x maps to 9 or x tends to 9.

When x tends to 9, we will have;

x ---->9 = (9 - 9 ) / (√9 - 3)

= (0)/(-3 - 3)

note: since √x can be negative or positive, we will choose negative so that our solution will not be undefined.

= 0/-6

= 0

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\(\sf \longrightarrow \: \: \lim_{x\to \: 9} \: \: \: \frac{x \: - \: 9}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ({ \sqrt{x} \: )}^{2} \: - \: {(3)}^{2} }{ \sqrt{x} - 3 } \\ \)

Now , by using Identity:-

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)( \sqrt{x} - 3)}{ \sqrt{x} - 3 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3) \cancel{( \sqrt{x} - 3)}}{ \cancel{ \sqrt{x} - 3} } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)(1)}{1 } \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)(1) \\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{9} + 3)\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \sqrt{9} + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 3 + 3\\ \)

\(\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 6\\ \)

To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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Answer:

x=-7/2

Step-by-step explanation:

hope this helps

Answer:

191/20 or 9 11/20

Step-by-step explanation:

Answer:

13 8/25  is the answer

Step-by-step explanation;

    2. Add the numerator

    3. Add the denominator

      denominator is under.

You should get: 13 8/25

Decimal Form: 13.32

Hope this helps

Step-by-step explanation:

1/16 for Washington County.

5/76 for Webster County.

so, let's bring both to the same denominator (bottom part of the fractions).

this is usual the LCM of both denominators.

since 16 = 2×2×2×2

76 = 2×2×19

the least common multiple (LCM) is the combination of the longest sequence per prime factor involved :

2×2×2×2×19 = 16×19 = 304

1/16 = 19/304

5/76 = 5× 1/76 = 5× 4/304 = 20/304

so, now we know, 20/304 > 19/304, and therefore Webster County has the greater fraction of adults, who enjoy gardening.

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

The given information is:

- The function that represents the sales price at the superstore is:

- The function that represents the HST owed on a purchase with a selling price of x dollars is:

a. The function that represents the HST owed on an item with a price tag of x dollars after it has been beaten by 10% is given by the composite function:

So, we replace the x in the f(x) function with the g(x) value, as follows:

The equation is above.

b. How much HST would be charged on a $39.99 purchase if this price is also lowered by 10% first?

Then, by using the equation we found in part a, we replace x by 39.99 and solve:

$4.68 would be charged

Answer:

3 fours

Step-by-step explanation:

Answer:

d \(\frac{-4}{3}\)

Step-by-step explanation:

change in y over the change in x

\(\frac{-2-2}{1- -2}\) = \(\frac{-4}{3}\)

The solution to the equation -2(x + 3) = -6 is x = 0.

To simplify the expression 5t + 7 + 8b, we can combine like terms.

There are two like terms in the expression: 5t and 8b.

Combining the like terms gives us:

5t + 8b + 7

Therefore, the simplified form of the expression 5t + 7 + 8b is 5t + 8b + 7.

Regarding the equation -2(x + 3) = -6:

To solve this equation, we can follow these steps:

Distribute the -2 to the terms inside the parentheses:

-2 * x + (-2) * 3 = -6

This simplifies to:

-2x - 6 = -6

Move the constant term to the right side by adding 6 to both sides of the equation:

-2x = 0

Divide both sides of the equation by -2 to isolate the variable x:

x = 0 / -2

Simplifying the right side of the equation gives us:

x = 0

The solution to the equation -2(x + 3) = -6 is x = 0.

The simplified expression 5t + 7 + 8b remains as 5t + 8b + 7, and the solution to the equation -2(x + 3) = -6 is x = 0.

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