A car travels at 80km/h for 4 hours and then a speed of 100km/h for a further 2 hours .
1) Calculate the total distance travelled.
2) Calculate the average speed for the whole journey.

Answer: The 6th term would be 243.

Step-by-step explanation:

The pattern in this sequence is that it is multiplying by 3 each time.

1 x 3 = 3, 3 x 3 = 9, 9 x 3 = 27.

Now what you want to do is multiply 27 by 3 to get a product of 81, which would be the 5th term.

Lastly, you would multiply 81 by 3 to get an answer of 243.

Answer:

£250

Step-by-step explanation:

Divide $405 by $1.62 which is 250.

Multiply that by £1 which is £250.

Answer:

W=x/7+ 8z/7 + 4/7

Step-by-step explanation:

Triangle has a point at its orthocenter is C.

Orthocenter of a triangle is a point where the three altitudes of a triangle meet each other.

As, orthocenter is a point where three altitudes of a triangle meet each other.

Here, the figure C has a point at its orthocenter of the triangle.

As, each of the altitude arise from each vertex of a triangle.

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For the specified requirements, 97 sample size are required.

Given that,

Confidence Interval = 95

Margin of error (m) =0.099

We know , to find Sample size for  estimating a population proportion

n = (Z*/m)² P(1-P)

where , m is margin of error

             P is estimated proportional value.

If we have no preconceived of the value of the  population proportion

, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.

for a 95% confidence interval ,

Z* = 1.960 , m=0.099

Using equation we get

n = (1.96/0.099)²(0.5)( 1 - 0.5 )

By solving,

n = 97.02≅ 97

The necessary sample size is 97

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Answer:

The average monthly payment would be most affected by Mark's observation of one significantly lower payment. The reason is that the average is calculated by summing all the payments and dividing by the total number of payments, so any extreme values (such as the significantly lower payment) can have a substantial impact on the average value.

Step-by-step explanation:

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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Answer:

2, 800

Step-by-step explanation:

(3 x 1000) - (2 x 100)

3,000 - (2 x 100)

3,000 - 200

2, 800

Answer:

Step-by-step explanation:

2 because in a hour there is 60 minutes so you just divide 120 by 6 and you get 2 km per minute

The square root of negative 1, represented by the symbol "i", is an imaginary number.

Imaginary numbers are used to represent quantities that cannot be expressed as real numbers. For example, square roots of negative numbers are imaginary because square roots of positive numbers are always positive, but square roots of negative numbers are not real. The concept of imaginary numbers was introduced by mathematician Gerolamo Cardano in the 16th century.

In mathematics, imaginary numbers are often represented on the complex plane, where the x-axis represents the real part of a complex number and the y-axis represents the imaginary part. The number "i" is defined as the square root of negative 1, and all imaginary numbers can be represented as a multiple of "i".

In summary, the square root of negative 1 is an imaginary number represented by the symbol "i", and it is used to represent quantities that cannot be expressed as real numbers.

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The given function defines an inner product for polynomials p(x) and q(x) if it satisfies the following properties: (A) Linearity in the first argument, (B) Symmetry, (C) Linearity in the second argument, and (D) Positive definiteness.

:

A. Linearity in the first argument is satisfied as p, q = a0b0 + a1b1 + ... + anbn in Pn.
B. Symmetry is satisfied as p, q = q, p.
C. Linearity in the second argument is satisfied as p, q + w = p, q + p, w.
D. Positive definiteness is partially satisfied as p, p ≥ 0. However, p, p = 0 if and only if p = 0 is not explicitly stated in the given options.

Based on the provided information, the function satisfies properties A, B, and C, but it is unclear if it fully satisfies property D (positive definiteness). More information is needed to determine if the function defines an inner product for polynomials p(x) and q(x).

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Answer:

Following are the answer to this question:

In question, a) ordinal.

In question, b) ratio .

In question, c) true.

Step-by-step explanation:

For its "ordained" existence, regular data is used to conduct surveys and questionnaires. To identify respondents into different categories, a quantitative methodology is employed to sufficient excess.

Its ratio data is defined as a statistical method with the same features as continuous variables, that recognize the proportion of each data to an absolute null as its source. In many other words, the meaning of the line graph may not be positive.

Its newest program gives the gap between exits data.

The joint density of the polar coordinates R and Θ is f(R,Θ) = 1/(πR), where 0 ≤ R ≤ 1 and 0 ≤ Θ ≤ 2π.

To find the joint density of the polar coordinates R and Θ, we need to use the transformation of variables formula for joint densities. Let us define the transformation from Cartesian coordinates (X, Y) to polar coordinates (R, Θ) as follows:

R = (X^2 + Y^2)^(1/2)

Θ = tan^-1(Y/X)

We can solve for X and Y in terms of R and Θ as follows:

X = R cos(Θ)

Y = R sin(Θ)

We can then compute the Jacobian of this transformation:

|dX/dR dX/dΘ| |cos(Θ) -R sin(Θ)|

| | = | |

|dY/dR dY/dΘ| |sin(Θ) R cos(Θ)|

The determinant of this matrix is R, so the joint density of R and Θ can be obtained as follows:

f(R,Θ) = f(X,Y) * |Jacobian|

= (1/π) * (1/(X^2 + Y^2)) * R

= (1/π) * (1/R^2) * R

= 1/(πR), 0 ≤ R ≤ 1, 0 ≤ Θ ≤ 2π

Therefore, the joint density of the polar coordinates R and Θ is f(R,Θ) = 1/(πR), where 0 ≤ R ≤ 1 and 0 ≤ Θ ≤ 2π.

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Step-by-step explanation:

Length = Area / Width = 104in² / 16in = 6.5in²

(who knows why the width is longer...)

Answer:

6.5in

Step-by-step explanation:

Area of rectangle = \(L\)×\(W\)

\(L\)×16 = 104

\(L\) = 104 ÷ 16

= 6.5

\(\therefore\) The length of the rectangle is 6.5in

Hope this helps :)

(a) The center of the sphere is in the first octant and is tangent to the xz-plane and to the yz-plane. This means that the center of the sphere is at a point of the form (a,b,5) where a,b≥0. The distance from the origin to the center of the sphere is  \(\sqrt{43}\), so we have \(x^{2} +x^{2} +(5-0)^{2} =43\) This gives us \(a^{2} +b^{2} =38\)

The radius of the sphere is the distance from the center of the sphere to the point where the sphere touches the xz-plane. This distance is equal to the length of the hypotenuse of a right triangle with legs of length a and b. Therefore, the radius of the sphere is \(\sqrt{a^{2}+ b^{2} } =\sqrt{38}\)

The equation of the sphere is \((x-a)^{2}+ (y-b)^{2}+ (z-5)^{2} =38\)

(b) The point where the sphere touches the xz-plane is (a,0,5). The distance between the origin and this point is \(\sqrt{a} ^{2}+\sqrt(5-0)^{2} =\sqrt{a^{2} +25}\)

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When three standard six-faced dice are rolled, the probability that the sum of the three numbers rolled is 9 is equal to 10/216 or 5/108.

Total number of ways three dice can be rolled = 6 × 6 × 6 = 216.

Each dice can have any number from 1 to 6. The probability of rolling a particular number on a dice = 1/6.

The probability of rolling a particular number on three dice = (1/6) × (1/6) × (1/6) = 1/216.

In order to get a sum of 9, there are four combinations that can be rolled:

3 + 3 + 3 = 9

3 + 4 + 2 = 9

3 + 5 + 1 = 9

4 + 3 + 2 = 9

The probability of rolling any of these combinations = probability of rolling 3-3-3 + probability of rolling 3-4-2 + probability of rolling 3-5-1 + probability of rolling 4-3-2

= (1/216) + (3/216) + (3/216) + (3/216)

= 10/216 or 5/108.

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Answer:

The answer is D: x + 2x = 108

Step-by-step explanation:

I finished the test and got them all right.

The required equation is x + 2x = 108 which represents the given problem. The correct answer would be an option (D).

Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols, known as variables in elementary algebra, indicate quantities with no set values. Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.

The equation that represents the problem is:

x + 2x = 108

This equation represents the total number of oranges Marta sold on Thursday (x) and Friday (2x) being equal to 108.

Hence, the correct answer would be an option (D).

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Answer:

\(2x + 2 = 5x - 4 \\ 2x - 5x = - 4 - 2 \\ - 3x = - 6 \\ x = \frac{ - 6}{ - 3} \\ x = 2\)

Answer:

x - (-3/4,0)

y - (0, 3/7)

Step-by-step explanation:

The root of this equation is determined to be approximately 0.567143.The root is found to be approximately -0.673253.

The Newton-Raphson method is an iterative numerical technique used to find the roots of equations. In the first equation, y = f(x) = e^x - x, the initial approximation x0 is set to 0. By applying the Newton-Raphson method, successive approximations of the root are calculated until convergence is achieved. The root of this equation is determined to be approximately 0.567143.

In the second equation, x^3 + 2x^2 + 6x + 3 = 0, the root is sought within the range (-1, 0). The Newton-Raphson method is employed again, starting with an initial approximation x0 of -1. Through iterative calculations, the root is found to be approximately -0.673253.

Both equations demonstrate the effectiveness of the Newton-Raphson method in finding roots within specific ranges by iteratively refining approximations until a satisfactory solution is obtained.

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1. Use the Pythagorean Theorem since this is a right triangle:

a^2 + b^2 = c^2

3^2 + b^2 = 4^2

b^2 = 4^2 - 3^2

b = √ 7

b = 3

answer : 3

Answer:

0 in both boxes

Step-by-step explanation:

The correct answer is D. The quadratic function has no real zeros if a > 0 and k>0 or a < 0 and k<0. This is because in the vertex form y=a(x- h2) + k, the value of k determines the vertical shift of the graph, and the value of a determines the direction of the graph. If a>0 and k>0, the graph will be shifted up and open upward, meaning it will not cross the x-axis and therefore have no real zeros.

Similarly, if a<0 and k<0, the graph will be shifted down and open downward, also not crossing the x-axis and having no real zeros.  The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. The value of a determines the shape of the parabola: if a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.

For a quadratic function to have no real zeros, it must not intersect the x-axis. This means that the vertex of the parabola must be above or below the x-axis, depending on the direction of the opening.

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Answer:

(0, 5)

Step-by-step explanation:

The quota sampling produces the same advantages for convenience sampling that stratified random sampling produces for probability sampling.

Sampling:

Sampling is defined as the process in statistical analysis where researchers take a predetermined number of observations from a larger population.

Given,

Here we need to find the type of sampling that produces the same advantages for convenience sampling quota sampling.

Before, move on to the result, first we have to know the details about quota sampling and the probability sampling.

Probability sampling defined as the selection of a sample from a determined number of population, when this selection is based on the principle of randomization, that is, random selection or chance.

In contrast to probability sampling, Quota sampling means a non-probability sampling method in which researchers create a sample involving individuals that represent a population.

Based on these definition we have identified that the method that is best suitable answer for this one is stratified random sampling.

Because the stratified random sampling means, is a probability sampling technique in which the total population is divided into homogenous groups to complete the sampling process.

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Answer

creon queens B. lo siento is me equivoco

The cash price of the article is 88 cedis.

In this question, the article has a price, but paid in cash, there are two discounts.

Thus, the cash price is:

\(P = 115\times0.85\times0.9 = 88\)

The cash price of the article is 88 cedis.

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Answer:

\(12x^4 + 9x^2 - 3\\\)

Step-by-step explanation:

Firstly, put the two equations side by side:

\((3x^2 + 3)(4x^2 - 1)\)

The FOIL method is very useful in this scenario, the formula is:

\((a + b)(c + d) = ac + ad + bc + bd\)

So plug in the known variables:

\(3x^2 * 4x^2 = 12x^4\\3x^2 * -1 = -3x^2\\3 * 4x^2 = 12x^2\\3 * -1 = -3\)

\(12x^4 - 3x^2 + 12x^2 - 3\\\)

This simplifies to:

\(12x^4 + 9x^2 - 3\\\)

Hope this helps!