show working these two questions​

The principal (p) is approximately $2200. To determine the missing value using the simple interest formula, we can rearrange the formula to solve for "p":

I = P * R * T

Where:

I is the interest,

P is the principal (initial amount),

R is the interest rate, and

T is the time in years.

In this case, we have:

I = $66 (interest)

R = 4% (interest rate)

T = 9 months (time)

To calculate the principal (P), we need to convert the time to years. Since the interest rate is given as an annual rate, we divide 9 months by 12 months to get the time in years:

T = 9 months ÷ 12 months = 0.75 years

Now we can substitute the known values into the formula:

$66 = P * 0.04 * 0.75

Simplifying further:

$66 = 0.03P

To solve for P, divide both sides of the equation by 0.03:

P = $66 ÷ 0.03 ≈ $2200

Therefore, the principal (p) is approximately $2200.

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The approximate volume of the larger candle is 244 cubic centimeters.

To find the volume of the larger candle, we need to compare the side lengths of the smaller and larger candles. Let's denote the side length of the smaller candle as "s."

According to the information given, the side length of the larger candle is five-fourths (5/4) as long as the side length of the smaller candle. Therefore, the side length of the larger candle can be calculated as (5/4) * s.

The volume of a square pyramid is given by the formula V = (1/3) * s^2 * h, where s is the side length of the base and h is the height.

Since both the smaller and larger candles have the same shape, their volume ratios will be equal to the ratios of their side lengths cubed.

Let's substitute the values into the volume ratio equation:

(125 / V_larger) = (s_larger / s_smaller)^3

Given that V_smaller = 125 cubic centimeters, we can rewrite the equation as:

(125 / V_larger) = ((5/4) * s_smaller / s_smaller)^3

Simplifying the equation:

(125 / V_larger) = (5/4)^3

Calculating (5/4)^3:

(125 / V_larger) = (125 / 64)

Cross-multiplying the equation:

125 * 64 = V_larger * 125

Solving for V_larger:

V_larger = (125 * 64) / 125

Approximating the value:

V_larger ≈ 64 cubic centimeters

The approximate volume of the larger candle is 244 cubic centimeters, rounded to the nearest cubic centimeter

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Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

Answer:

8 units²

Step-by-step explanation:

The area (A) of the shaded part (right triangle ) is calculated as

A = \(\frac{1}{2}\) × area of rectangle

   = 0,5 × 4 × 4 = 0.5 × 16 = 8 units²

Answer:

8 units ^2 are shaded

Step-by-step explanation:

The total area of the square is 4 * 4 = 16

1/2 of the square is shaded so

1/2 * 16 = 8

8 units ^2 are shaded

The main idea behind statistical inference is that through the use of sample data, we are able to draw conclusions about the population from which the data was drawn (option c).

Statistical inference allows us to make inferences and draw conclusions about a larger population based on the analysis of a smaller representative sample.

By collecting data from a sample, we can use statistical methods to analyze and summarize the information. These methods include estimating population parameters, testing hypotheses, and making predictions.

The key assumption underlying statistical inference is that the sample is representative of the larger population, allowing us to generalize the findings to the population as a whole.

Statistical inference provides a way to make reliable and informed decisions, identify patterns and relationships, and make predictions about future observations based on the available data. It allows researchers, scientists, and decision-makers to make evidence-based conclusions and draw meaningful insights from limited observations.

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The average memory access time (AMAT) for P1 is 6.31 ns and for P2 is 3.68 ns, and assuming a base CPI of 1.0 without any memory stalls, the total CPI for P1 is 1.3165 and for P2 is 1.074, indicating that P2 is faster.

To calculate the average memory access time (AMAT), we use the formula:

AMAT = L1 hit time + L1 miss rate x L2 hit time x L2 miss rate x main memory access time

For P1 with a 32 KiB L1 cache, 3 ns L1 hit time, 5% L1 miss rate, and 100 ns main memory access time, the AMAT is:

AMAT = 3 ns + 5% x 5.62 ns x 100% x 100 ns = 6.31 ns

For P2 with a 64 KiB L1 cache, 2.5 ns L1 hit time, 2% L1 miss rate, and 80 ns main memory access time, the AMAT is:

AMAT = 2.5 ns + 2% x 5.62 ns x 100% x 80 ns = 3.68 ns

Assuming a base CPI of 1.0 without any memory stalls, the total CPI for P1 and P2 can be calculated using the formula:

CPI = base CPI + memory stalls per instruction x average memory access time

For P1 with an L1 miss rate of 5%, the memory stalls per instruction is 0.05. Therefore, the total CPI for P1 is:

CPI_P1 = 1.0 + 0.05 x 6.31 = 1.3165

For P2 with an L1 miss rate of 2%, the memory stalls per instruction is 0.02. Therefore, the total CPI for P2 is:

CPI_P2 = 1.0 + 0.02 x 3.68 = 1.074

Based on the CPI calculations, P2 is faster than P1.

With the addition of an L2 cache to P1, we can recalculate the AMAT and CPI as follows:

AMAT_P1_new = 3 ns + 5% x 5.62 ns x 95% x (5.62 ns + 100 ns) = 9.96 ns

CPI_P1_new = 1.0 + 0.05 x 9.96 = 1.498

The AMAT has increased significantly due to the high L2 miss rate, and the CPI has also increased as a result. Therefore, it is unclear whether adding an L2 cache has improved the performance of P1 without additional information about the specific workload and performance metrics.

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Answer:

The answer is A actually. D is wrong

Step-by-step explanation:

Answer: its A got it right

Step-by-step explanation:

The amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.

What is average ?

The average is the ratio of the sum of the number of a given set of values to the total number of values present in the set.

It is given that restaurant earns $1073 on Friday and $1108 on Saturday.

The amount which restaurant needs to earn on Sunday to average $1000 per day over the three-day period can be calculated by finding the average.

The average is given by ratio of sum of amount on each day from Friday to Sunday and divide it by number of days.

Let's assume amount earn on Sunday is $x.

So ,

\(\frac{1073 + 1108 + x}{3}\) = 1000

1073 + 1108 + x = (1000 × 3)

2181 + x = 3000

Let's solve this equation to get the value of x.

x = 3000 - 2181

x = $819

So , amount earn by restaurant is $819.

Therefore , the amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.

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the rate is

wher d is distance and t, time

we replace our distance and our time

the answer is 10.03 meters per day

Answer:

1042-96i

Step-by-step explanation:

(3 + 16i)(6 - 64i)

6(3 + 16i)(3 - 32i)

(6) 9 - 96i + 48i +1024

Answer:

1.0954.

Step-by-step explanation:

Standard error  =  std dev / √n

=  6 / √30

= 1.0954.

Answer:

65%

Step-by-step explanation:

survey of 2,700 people who owned a certain type of​ car, 1,755 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Total car number of car owner= 2,700

Then the percentage that satisfied is

1,755

1755/2700*100= 65%

Answer:

1.5 Liters

Step-by-step explanation:

500ml=0.5L

(0.5L)x3= 1.5L

Answer:

Your answer: 24/96 = (24 ÷ 24)/(96 ÷ 24) = 1/4

Your answer is: 1:4

Step-by-step explanation:

Hope this helped : )

Answer:

1:4 is your ans

Step-by-step explanation:

please mark as brainliest

Answer:

5/3

Step-by-step explanation:

30/t = 18/r

Multiplying by r both sides,

30*r /t = 18

Dividing by 30 both sides,

r/t = 18/30 = 3/5

So, t/r = 5/3

9514 1404 393

Answer:

  t/r = 5/3

Step-by-step explanation:

Every proportion can be written 4 ways. I like to think of them as "upside down and sideways." They are ...

  \(\dfrac{30}{t}=\dfrac{18}{r}\qquad\dfrac{t}{30}=\dfrac{r}{18}\\\\\dfrac{30}{18}=\dfrac{t}{r}\qquad\dfrac{18}{30}=\dfrac{r}{t}\)

__

Knowing this, you can simply rewrite your proportion as ...

  t/r = 30/18

  t/r = 5/3

_____

More formally, you could multiply both sides by t/18:

  (30/t)(t/18) = (18/r)(t/18)

  30/18 = t/r . . . . as above

Reducing the fraction gives ...

  t/r = 5/3

__

Additional comments

The usually-recommended procedure for solving something like this is to "cross-multiply" as a first step. That will give ...

  30r = 18t

Of course, that is equivalent to multiplying both sides by rt, the product of the denominators.

From here, to get t/r, you need to divide both sides by 18r.

  (30r)/(18r) = (18t)/(18r)

  30/18 = t/r

The combination of the two steps, multiply by rt, divide by 18r, is equivalent to multiplying by (rt)/(18r) = t/18, as we did above. That is, you can save some work by doing both steps at once--or by simply rewriting the proportion.

Answer:

d is the right answer hope this helps

the vector function: \(r(t) = sin(2t)i + 3tj + 2sin²(t)k\)

The first step is to find the first derivative of the vector function as follows:

\(r'(t) = 2cos(2t)i + 3j + 4sin(t)cos(t)k\)

Then find the magnitude of the first derivative as follows:

\(|r'(t)| = \sqrt{ [(2cos(2t))^2} + 3^2 + (4sin(t)cos(t))^2= \sqrt{ [4cos^2(2t) + 9} + 16sin^2(t)cos^2(t)]= \sqrt{[4cos^2(2t)} + 9 + 8sin^2(t)(1 - sin^2(t))]\)Wnow that \(sin^2(t) + cos^2(t) = 1\).

Hence, \(cos^2(t) = 1 - sin^2(t)\).

Therefore: \(|r'(t)| = \sqrt{[4cos^2(2t) + 9 }+ 8sin^2(t)(cos^2(t))]= \sqrt{[4cos²(2t) }+ 9 + 8sin^2(t)(1 - sin^2(t))]= \sqrt{[4cos^2(2t) }+ 9 + 8sin^2(t) - 8sin^4(t)]\)So, the unit tangent vector T(t) is:r'(t) / |r'(t)| The unit tangent vector T(t) at any point on the curve is: \(r'(t) / |r'(t)|= [2cos(2t)i + 3j + 4sin(t)cos(t)k] / \sqrt{[4cos^2(2t) + 9 + 8sin^2(t) - 8sin^4(t)]\)

The unit normal vector N(t) is given by:N(t) = (T'(t) / |T'(t)|)where T'(t) is the second derivative of the vector function.

\(r''(t) = -4sin(2t)i + 4cos(2t)kT'(t) = r''(t) / |r''(t)|\)

The binormal vector B(t) can be obtained by using the formula: B(t) = T(t) × N(t)

Hence, Unit Tangent Vector \(T(t) = [2cos(2t)i + 3j + 4sin(t)cos(t)k] / \sqrt{[4cos²(2t) + 9 + 8sin^2(t) - 8sin^4(t)]\)\([2cos(2t)i + 3j + 4sin(t)cos(t)k] /\sqrt{[4cos^2(2t) + 9 + 8sin^2(t) - 8sin^4(t)]\)Unit Normal Vector \(N(t) = [-2sin(2t)i + 4cos^2(t)k] / \sqrt{[4cos^2(2t) + 9 + 8sin^2(t) - 8sin^4(t)]\)Binormal Vector \(B(t) = [8sin^2(t)i - 6sin(t)cos(t)j + 2cos(2t)k] / \sqrt{[4cos^2(2t) + 9 + 8sin^2(t) - 8sin^4(t)]\)The first step is to find the first derivative of the vector function and then the magnitude of the first derivative. By dividing the first derivative of the vector function by the magnitude, we can find the unit tangent vector T(t). To find the unit normal vector N(t), we need to find the second derivative of the vector function.

Then we can calculate the unit normal vector by dividing the second derivative of the vector function by its magnitude. Finally, we can obtain the binormal vector B(t) by using the formula B(t) = T(t) × N(t). The unit tangent vector, unit normal vector, and the binormal vector of \(r(t) = sin(2t)i + 3tj + 2sin^2(t)k\).

In this problem, we found the unit tangent vector, unit normal vector, and the binormal vector of the vector function at a given point using formulas and equations.

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Answer:

The answer is option:

C. 10% of her customers ordered an  appetizer and dessert.

Answer:

To put the expression in the standard form for a polynomial we need to multiply the two terms. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

Step-by-step explanation:

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Integral calculus is a branch of calculus that deals with the calculation of integrals. In calculus, integration is used to find the area under a curve, known as the definite integral. A definite integral can be used to calculate the area between a function and the x-axis in the range of integration.

When a function is integrated, it gives an anti-derivative of that function. The definite integral is the value of the integral when the range of integration is known. Let us evaluate the given integral step by step, and we use u-substitution to solve this problem.

∫(0 to 1) (x - x²)^(1/2) dxLet u = x - x² ; then du/dx = 1 - 2xdx = du / (1 - 2x) = du/u^(1/2)Substituting the values,∫(0 to 1) u^(1/2) du/u^(1/2) = ∫(0 to 1) du = u (1 to 0) = 1-0 = 1

In the given question, we have to evaluate the integral ∫₀¹√(x-x²)dx using the method of substitution.We know that∫f(x)dx=∫f(g(u))g’(u)duwhere x=g(u).In the given question,

x=x²-x=> x²-x-x=0=> x=0,x=1=> g(0)=0 and g(1)=1.We assume x-x²=u=> 1-2x=du/dx=> dx=du/(1-2x).

Now we substitute these values in the given integral.∫₀¹√(x-x²)dx=∫₀¹√u(1-2x)du/(1-2x)=∫₀¹√udu=√u(1 to 0)=1-0=1

Therefore, the value of the given integral is 1.

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Answer:

r = -19

Step-by-step explanation:

To find the value of r, we can use the slope formula and the two given points:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (3, r) and (x2, y2) = (1, -7).

Substituting these values, we get:

6 = (-7 - r) / (1 - 3)

Simplifying and solving for r, we get:

6 = (-7 - r) / (-2)

Multiplying both sides by -2, we get:

-12 = 7 + r

Subtracting 7 from both sides, we get:

r = -19

Therefore, the value of r is -19.

Answer:

\( \frac{3}{11} \)

Step-by-step explanation:

First add all the numbers, i.e. 8, 5, 6 and 3. You'll get 22. This will be your denominator. Now, as there are 6 green marbles, put 6 on the numerator. You get 6/22. As you can see, you can simplify this fraction by 2, hence you get 3/11.

Can you give me a brainliest? It's alright if you don't.

Using the speed - distance relationship, the time left before the appointed time is 27 minutes.

Recall :

At 10mph :

At 12 mph :

Equate (1) and (2) :

10t + 30 = 12t - 24

Collect like terms

10t - 12t = - 24 - 30

-2t = - 54

Divide both sides by - 2

t = 54 / 2

t = 27

Hence, the time left before the appointed time is 27 minutes.

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Answer:

7

Step-by-step explanation:

Answer:

Answer: 4. m³ + m²

Step-by-step explanation:

\({ \rm{ {2m}^{2} - {m}^{2} (7 - m) + {6m}^{2} }} \\ \\ { \rm{ = {2m}^{2} - {7m}^{2} + {m}^{3} + 6 {m}^{2} }} \\ \\ { \rm{ = (2 - 7 + 6) {m}^{2} + {m}^{3} }} \\ \\ = { \rm{ {m}^{3} + {m}^{2} }}\)

The most specific name for the figure is an isosceles trapezoid

From the question, we have the following parameters that can be used in our computation:

The figure

The properties of the given figure are

Using the above as a guide, we have the following:

The figure is a trapezoid

Because the nonparallel sides are congruent, then the most specific name for the figure is an isosceles trapezoid

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