Three sisters have were born in 3 consecutive years. The total of their ages is 30. What is the oldest sibling's age?

Answer:

15 is 50% of 30

and 75% of 20

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answers: 36

Step-by-step explanation:

Answer:

Step-by-step explanation:

(f.g)(x)=\(-3*(-3x)^{2}+3=-27x^{2}+3\)

The equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is; (x - 1)²/25 + (y + 3)²/49 = 1

The general format for equation of an ellipse with center (h, k) and vertical major axis is;

(x - h)²/b² + (y - k)²/a² = 1

We are given the following;

center at (1, -3)

a = 7

b = 5

Thus;

Equation of ellipse with given parameters is;

(x - 1)²/5² + (y + 3)²/7² = 1

This simplifies to;

(x - 1)²/25 + (y + 3)²/49 = 1

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Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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The length of BC is 5

The length of AC is 10

From the given information, we are to calculate the length of the given parts of line AC

From the given information,

B is the midpoint of AC

Thus,

We can write that

AB + BC = AC

and

AB = BC

Also, from the given information,

AB = 5

Therefore,

BC = 5

From the equation,

AB + BC = AC

Substitute the values of AB and BC

5 + 5 = AC

10 = AC

AC = 10

Hence, BC = 5 and AC = 10

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If the height is increased by 0.2 then the surface area will be increased by 1.14times the original.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height , p is the perimeter of the base and B is the base area

The scale factor in terms of height = 32/30

if x is the surface area of old prism and y for new

then area factor = (16/15)² = 256/225

256/225 = y/x

225y = 256x

y = 256/225 x

y = 1.14x

therefore the surface area will increase by 1.14times the original.

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\(\longrightarrow{\green{Option\:1.\:(14\:-\:7m)}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\(5 \: (4 - m) - 2 \: (m + 3) \\ \\ = 20 - 5m - 2m - 6\)

Combining like terms, we have

\( = 20 - 6 - 5m - 2m \\ \\ = 14 - 7m\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}\)

In conclusion  there are no points among the given options that are on the parabola.

why it is?

The vertex of the parabola is the midpoint between the point (6, 2) and the line y = 4, which is at (6, 3). Since the focus is below the vertex and the directrix is a horizontal line, the equation of the parabola is of the form:

(x - h)²2 = 4p(y - k)

where (h, k) is the vertex and p is the distance from the vertex to the focus (and from the vertex to the directrix).

Using the vertex and the given point (6, 2), we can find that p = 1. Therefore, the equation of the parabola is:

(x - 6)²2 = 4(y - 3)

Now we can check which of the given points satisfy this equation:

A. (4, 6)

(4 - 6)²2 = 4(6 - 3)

4 = 12 - 12

This point is not on the parabola.

B. (5, 7)

(5 - 6)²2 = 4(7 - 3)

1 = 16

This point is not on the parabola.

C. (6, 5)

(6 - 6)²2 = 4(5 - 3)

0 = 8

This point is not on the parabola.

D. (7, 6)

(7 - 6)²2 = 4(6 - 3)

1 = 12

This point is not on the parabola.

E. (8, 5)

(8 - 6)²2 = 4(5 - 3)

4 = 8

This point is not on the parabola.

Therefore, there are no points among the given options that are on the parabola.

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Complete question:

Which points are on the parabola defined as the set of points the same distance from (6,2) and the line y=4?

Answer:

Range & Isabella

Step-by-step explanation:

Part A:

Definitely not range mean or median, as that'll give you their average, not consistency.  None of their tables show any repeating values, so not mode either, and range would be the most hopeful for this.

Part B:

The results with the smallest range would be the most consistent:

Charles:
Lowest value = 39 and Highest Value = 57
Range = 57-39 = 18

Isabella:
Lowest value = 62 and Highest value = 71
Range = 71-62 = 9

Naomi:
Lowest value = 61 and Highest value = 94
Range = 94-61 = 33

Isabella achieved the most consistent results.  Hope this helps

Answer:

C.Tammy’s estimate is right, but the actual product should be 24.78.

Step-by-step explanation:

i took the assessment! thank you for your attention and i hope i helped!!

Answer:

the answer is C which is Tammy’s estimate is right, but the actual product should be 24.78.

Step-by-step explanation:

Answer:

The slope is the change in y over the change in x.

Look at the g(x) and the x.  \(\frac{2 - (-4) }{0 - (-12)}\) = \(\frac{6}{12}\) = \(\frac{1}{2}\).  The slope is 1/2

The y intercept is when x is zero.  So the point (0,2) is the intercept.  We say that the y intercept is 2.  That is where the line will cross the y axis.

Step-by-step explanation:

Answer: 7$

Step-by-step explanation: 40-4= 36 | 3x5=15 | 36-15=21 | 21/3=7

Answer:

To cover the remaining ten kilometres and average 40 km/hr, the autonomous car must drive at infinite speed (light speed)

Step-by-step explanation:

The average speed = (The total distance)/(The total time taken)

The given parameters are;

The required average speed of the autonomous car = 40 km/hr

The average speed of the car during the first 20 km = 40 km/hr

The  average speed of the car during the next 10 km = 20 km/hr

Therefore, we have;

The time taken = Distance/Speed

The time taken by the car during the first 20 km = 20 km/40 km/hr = 0.5 hour

The time taken by the car during the next 10 km = 10 km/20 km/hr = 0.5 hour

Therefore, the amount of time elapsed = 0.5 hour + 0.5 hour = 1 hour

The distance covered = 30 km

Which gives;

To drive the remaining distance of 10 km the car has 0 hour left,

The speed of the remaining 10 km must therefore be 10/0 =  Infinite (speed).

To cover the remaining ten kilometres and average 40 km/hr, the autonomous car must drive at infinite speed.

Answer:

Yes, it is a quadratic equation.

Step-by-step explanation:

Let's solve it to make it a quadratic equation:

=> \(\frac{x^2+1}{x^2} =5\)

=> x²+1 = 5x²

=> 5x²-x²-1 = 0

=> 4x²-1 = 0

Comparing it with the standard form of quadratic equation i.e.

\(ax^2+bx+c = 0\)

So, we get

a = 4 , b = 0 and c = -1

So, yes. It is a quadratic equation and it is a pure quadratic equation since b is equal to 0.

the total amount of oil that leaks out over the entire time interval [0, 120].

integral ∫₀¹₂₀ r(t) dt represents the total amount of oil that leaks from the tank in 120 minutes.

To see why, consider the definition of an integral. If we divide the interval [0, 120] into small subintervals of width Δt, then the amount of oil that leaks out during each subinterval is approximately r(t)Δt. Summing up all these small amounts over the entire interval gives:

Σᵢ r(tᵢ) Δt

where tᵢ is the midpoint of the i-th subinterval. As we take the limit as the subinterval width goes to zero, this sum becomes the integral:

∫₀¹₂₀ r(t) dt

which represents the total amount of oil that leaks out over the entire time interval [0, 120].

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Answer:

Let's denote the first term of the sequence as a, and the common difference between consecutive terms as d.

Then, we know that the fifth term is 5, so:

a + 4d = 5

Similarly, we know that the sixth term is 2.5, so:

a + 5d = 2.5

We can solve this system of equations by subtracting the first equation from the second:

(a + 5d) - (a + 4d) = 2.5 - 5

d = -2.5

Now, we can substitute this value of d into either equation to find the value of a:

a + 4d = 5

a + 4(-2.5) = 5

a - 10 = 5

a = 15

Therefore, the first term of the sequence is 15, and the common difference is -2.5. We can use this to find the value of the second term:

a + d = 15 + (-2.5) = 12.5

Therefore, the second term of the sequence is 12.5.

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Answer:

B

Step-by-step explanation:

Answer:

the answer B

Step-by-step explanation:

The dragster, starting from rest and accelerating at 32 m/s², reaches a speed of 128 m/s after 4.0 seconds.

A dragster starting from rest means that its initial velocity is zero. The dragster's acceleration is given as 32 m/s². To determine the speed of the dragster after 4.0 seconds, we can use the equation of motion:

where:

v = final velocity

u = initial velocity (which is 0 m/s since the dragster starts from rest)

a = acceleration (32 m/\(s^2\) in this case)

t = time (4.0 seconds in this case)

Substituting the given values into the formula:

v = 0 + (32 m/\(s^2\))(4.0 s)

v = 0 + 128 m/s

v = 128 m/s

Therefore, the dragster is traveling at a speed of 128 m/s after 4.0 seconds of acceleration.

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Answer:

3

Step-by-step explanation:

Answer:

360-540 calories

Answer:

y=12x+40

Step-by-step explanation:

The earnings are the initial payment per month plus the pay per hour times the number of hours.

Answer: Let the number = x

5x+10 = 120

Or, 5x = 120 - 10

Or, 5x = 110

Or, x = 110/5

Or, x = 2

Step-by-step explanation:

Answer:

x = - 14

Step-by-step explanation:

Step 1: Equation

x/2 - 7 = - 14

Step 2: Solve

x - 14 = - 28

Answer:

x = - 14

Hope This Helps :)

The directional derivative is (-3/2√10) + (2 ln(2)/√10).

To compute the directional derivative of f(x,y) = y² ln(x) at the point (2,1) in the direction of the vector v = -3i + j, first find the gradient of f and then take the dot product with the unit vector in the direction of v.

The gradient of f(x, y) is given by (∂f/∂x, ∂f/∂y) = (y²/x, 2y ln(x)). At the point (2,1), this becomes (1/2, 2 ln(2)).

Next, find the unit vector of v by dividing v by its magnitude: u = v/||v|| = (-3, 1)/√((-3)² + 1²) = (-3, 1)/√10.

Now, take the dot product of the gradient and the unit vector: ((1/2, 2 ln(2)) · (-3/√10, 1/√10)) = (-3/2√10) + (2 ln(2)/√10).

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To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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Answer:

A) A translation 8 units down

Step-by-step explanation:

It does not reflect over the x-axis because it would have flip.

Not 11 units down, only 8

it did not rotate 90 degrees, it went a little more past that