Eight bowls cost $160, but Adrien wants only 5 of them so how much does he have to pay?

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's calculate the value of c using Pythagoras theorem ~

\(\qquad \sf  \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} \)

\(\qquad \sf  \dashrightarrow \: 40 {}^{2} = {24}^{2} + {b}^{2} \)

\(\qquad \sf  \dashrightarrow \: b² = \sqrt{40² - 24²} \)

\(\qquad \sf  \dashrightarrow \: b= \sqrt{1600-576} \)

\( {\qquad \sf  \dashrightarrow \: b= \sqrt{1024}} \)

\(\qquad \sf  \dashrightarrow \: b = 32 \: units\)

The length of "b"

\( {c}^{2} = {a}^{2} - {b}^{2} \)

\( {b}^{2} = {40}^{2} - {24}^{2} \)

\(b = 1024\)

\(b = \sqrt{1024} \)

\(b = 32\)

Hence, the length of "b" is 32.

According to the arithmetic progression, the value of a4 is 75

Arithmetic progression:

An arithmetic progression (A.P.) is the sequence of numbers that has a fixed common difference between any two consecutive numbers.

Given,

Here we have the value of a1 = 5 And the function for arithmetic progression which is an = 2(an-1) +5

Now we need to find the value of a4.

To find the value of a4, we have to find the value of a2 and a3.

For that, we have to apply the given value into the function,

So, the value of a2 is calculated as,

a2 = 2 (a2 - 1) + 5

WE know that the value of a1 = 5, then the value of a2 is

a2 = 2 (a1) + 5

a2 = 2(5) + 5

a2 = 15

So, the value of s3 is

a3 = 2 (a3 - 1) + 5

a3 = 2(a2) + 5

a3 = 2(15) + 5

a3 = 35

Finally, the value of a4 is calculated as,

a4 = 2 (a4 - 1) + 5

a4 = 2(a3) + 5

a4 = 2(35) + 5

a4 = 75.

Therefore, the value of a4 is 75.

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The probability of picking an odd number and then picking an even number 5/18

The probability of picking an odd number on the first card is 1/2 since there are 5 odd cards out of 10 total cards. After picking an odd card, there are now 4 odd cards and 5 even cards left out of a total of 9 cards. So the probability of picking an even card on the second draw is 5/9.

To find the probability of both events happening, we multiply the probabilities:

P(odd and even) = P(odd) * P(even | odd)

= (1/2) * (5/9)

= 5/18

Therefore, the probability of picking an odd number and then picking an even number is 5/18.

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Answer:

4.4 < x < 18.8

Step-by-step explanation:

11.6 - 7.2 = 4.4

11.6 + 7.2 =18.8

Answer:

60 and 100 degrees.

Step-by-step explanation:

Sum of the other 2 angles = 180-20 = 160 degrees.

3 + 5 = 8

160 / 8 = 20

- so the other 2 angles are:

3*20 = 60 and

5*20 = 100 degrees.

The equation of the trajectory which can be described using the equations for projectile motion is; y(t) = x·tan(θ) - g·x²/(2·v₀²·cos²(θ)), which is a quadratic equation with a path of a parabola

Projectile motion is the motion of an object that is projected in the air under the influence of gravitational attraction.

Let θ represent the angle at which the path of the object makes with the horizontal, and let v₀ represent the velocity of the object. The path of the object can be described using the equations of the motion of a projectile, as follows;

Horizontal component of the velocity, v₀ₓ = v₀ × cos(θ)

Vertical component of the velocity, \(v_{0y}\) = v₀ × sin(θ)

The horizontal motion of the object is therefore;

x(t) = v₀ₓ × t = v₀ × cos(θ) × t

The vertical motion which is under the influence of gravity is; y(t) = \(v_{0y}\)  × t - (1/2) × g × t²

v₀ × sin(θ) × t - (1/2) × g × t²

The horizontal component indicates that we get;

t = x/(v₀ × cos(θ))

Plugging in the above expression for t into the equation for y(t), we get;

y(t) = \(v_{0y}\)  × t - (1/2) × g × t² = \(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

\(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = (v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

(v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = x·tan(θ) - g·x²/(2·v₀×cos(θ))²

The equation, y = x·tan(θ) - g·x²/(2·v₀×cos(θ))², is a quadratic equation, which is an equation of a parabola, therefore, the trajectory of an object thrown at an angle to the horizontal is a parabola.

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The monthly rent during the 8th year of living in the apartment will be $2510

The cost of the apartment per month in the first year is $1600

The rent is set to go up by $130 per year

The monthly rent during the 8th year of living in the apartment

This can be calculated by using arthimetic progression

here a = 1600

d = 130

We need to caluclate a₈

a₈th = a + (8-1)d

= 1600 + 7 x 130

1600 + 910

= 2510.

Therefore, the monthly rent during the 8th year of living in the apartment will be $2510

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During the month of May, there were 130 births, of which the newborn death rate is 38.4615.

According to the question,

There were 130 births, of which 127 were full-term births and three were premature births. There were five newborn deaths.

In order to find the newborn death rate we have the formula:

=  \(\frac{number of death under 28 days of age }{Total live births in the same year}\)  × 1000

= \(\frac{5}{130}\) × 1000

=\(\frac{5000}{130}\)

=38.4615

Hence, the new born death rate is 38.4615.

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Answer:

Third Choice: a = 2, b = -3, c = -27

Step-by-step explanation:

The equation to be solved with the quadratic formula must be written in the form

ax^2 + bx + c = 0

2x^2 = 27 + 3x

Subtract 3x from both sides. Subtract 27 from both sides.

2x^2 - 3x - 27 = 0

Now we see we have

a = 2, b = -3, c = -27

Answer: Third Choice

Answer:

y= - 4/1x + 5

Step-by-step explanation:

Answer:

y=-4x+5

Step-by-step explanation:

4 equals the slope (rise over run) and 5 equals the y-intercept

The parameter c in the nonlinear function \(Y = aX^bZ^c\) measures the elasticity of Y concerning Z, indicating the percent change in Y for a 1 percent change in Z. Thus, the correct answer is option B: the percent change in Y for a 1 percent change in Z.

Elasticity is a measure of the responsiveness or sensitivity of one variable to changes in another variable. In this case, the elasticity of Y concerning Z indicates how much Y changes in percentage terms in response to a 1% change in Z.

When c is positive, it implies that an increase in Z leads to a proportionate increase in Y. In other words, a 1% increase in Z will result in a c% increase in Y. Conversely, when c is negative, it indicates an inverse relationship, where an increase in Z leads to a proportionate decrease in Y.

The parameter c plays a crucial role in understanding the impact of Z on Y and helps quantify the sensitivity of Y to changes in Z. By analyzing the value of c, we can determine the magnitude and direction of the relationship between Y and Z and evaluate the responsiveness of Y to changes in Z.

Thus, the correct answer is option C: the elasticity of Y concerning Z.

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The matrix A = [7 5; 0 k] is diagonalizable if and only if the eigenvalues of A are distinct. In this case, the eigenvalues of A are the solutions to the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix. The answer is k ≠ 7.

To determine the eigenvalues of A, we set up the characteristic equation:

det(A - λI) = 0,

where A is the given matrix and I is the identity matrix. Substituting the values from matrix A, we have:

|7-λ 5 |

| 0 k-λ |

Expanding the determinant, we get:

(7-λ)(k-λ) - (0)(5) = 0,

Simplifying further:

(7-λ)(k-λ) = 0.

To find the eigenvalues, we solve this equation:

(7-λ)(k-λ) = 0.

The eigenvalues are the values of λ that satisfy this equation. For A to be diagonalizable, the eigenvalues must be distinct. Therefore, we need to find the values of k for which the equation (7-λ)(k-λ) = 0 has distinct solutions.

If k = 7 or k = λ, then the eigenvalues are not distinct. However, if k ≠ 7, then the eigenvalues are distinct. Hence, the values of k for which A is diagonalizable are all real numbers except k = 7. Therefore, the answer is k ≠ 7.

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The probability that at most 52 out of 80 randomly selected college students say they drink more coffee during exam week is approximately 0.0579.

To solve this problem, we need to use the binomial distribution formula, which is used to calculate the probability of a specific number of successes in a fixed number of independent trials, given the probability of success in each trial.

The formula for the binomial distribution is:

\(P(X = k) = ^nC_k \times p^k \times (1-p)^{(n-k)}\)

Where:

P(X = k) is the probability of k successes in n trials

n is the number of trials

k is the number of successes

p is the probability of success in each trial

(1-p) is the probability of failure in each trial

nCk is the binomial coefficient, which is the number of ways to choose k items from a set of n items.

In this case, n = 80, p = 0.67 (since the survey reports that 67% of college students prefer to drink more coffee during exams week), and we want to find the probability that at most 52 students say they drink more coffee during exams week. To find this probability, we need to sum the probabilities of all possible values of k from 0 to 52:

P(X <= 52) = P(X = 0) + P(X = 1) + ... + P(X = 52)

Using the binomial distribution formula, we can calculate each of these probabilities and then add them together to get the final answer.

Using a calculator or software, we can find that:

P(X <= 52) ≈ 0.0579

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Ana, Betty and Carol in the ratio of 2:3:5 respectively

mom cut the $600 in (2+3+5) 10 parts

and gave 3 parts to betty

so B got 600 : 10 x 3 = $180

Answer: The meaning of the statement “ x vary inversely as y “ is “x is inversely proportional to y".

Final Answer // x=5yx is equal to 5 over y

Step-by-step explanation:

Answer:

$4026.52

Step-by-step explanation:

Given data

rate= 5%

time= 3years

A=$4630.50

P=?

we know that

A=P(1+rt)

$4630.50=P(1+0.05*3)

$4630.50=P(1+0.15)

$4630.50=P(1.15)

P=4630.50/1.15

P=$4026.52

The intitial amount is $4026.52

Answer:

4x^2

Step-by-step explanation:

Call the unknown side y

The area of the figure is

8x^3 *y = 32 x^5

Divide each side by 8 x^3

8x^3 *y / 8x^3 = 32 x^5 / 8x^3

y = 4 x^2

The unknown side is 4 x^2

Answer:

4x^2

Step-by-step explanation:

32x^5 / 8x^3 = 4x^2

or 4x^2 * 8x^3 = 32x^5

so 4x^2

192 inches square

Answer:

Solution Given:

Slant height (l)=8 inch

base (s)=8 inch

we have

Surface area of a regular square-based pyramid = \(s^{2} +2sl\)

=\(8^2+2*8*8\)

=192 inches square

Given the data from the question, the correct statement is: the ratio 1:5 is less than 3:10

To otain the comparison of both ratios, we shall determine the value of each ratio. This is illustrated below:

1 : 5 = 1 / 5

1 : 5 = 0.2

3 : 10 = 3 / 10

3 : 10 = 0.3

SUMMARY

Thus, we can conclude that 1:5 is less than 3:10

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Answer:

8!

Step-by-step explanation:

8!=8*7*6*5*4*3*2*1

What is Boussinesq equation used for?

In coastal engineering, Boussiness q-type equations are frequently used in computer models for the simulation of water waves in shallow seas and harbours.

What is the physical meaning of the Navier-Stokes equations?

What is the difference between NS equation and Euler's equation in terms of assumption?

The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow.

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Answer:

b = 10

-2d = -38

x = -1.2

Step-by-step explanation:

b = 10 and x = -1.2 only have one variable. You can divide -2 to both sides for -2d = -38 getting d = 19.

0.1 = 0.1 have no variable meaning that any number can be correct in the equation

1/3 ≠ 1/3 has a cross in the equal sign meaning that there is no correct answer for the equation.

Answer:

true

Step-by-step explanation:

because there's less humidity

The required polar integral is 0.14173.

To change the Cartesian integral into an equivalent polar integral, we can use the formula:

∫∫R f(x, y) dA = ∫θ₁ θ₂ ∫r₁ r₂ f(r, θ) r dr dθ

Given the Cartesian integral:

∫∫D f(x, y) dA = ∫₁ ₁ ∫₁ ₁ [n(x²y² + 1)] dx dy

We will convert this into a polar integral using the following transformations:

r = √(x² + y²)

θ = tan⁻¹(y/x)

Then, we replace x² + y² with r² and dx dy with r dr dθ.

Substituting r cos θ for x and r sin θ for y, we have:

r = √(x² + y²)

r = √(r² cos²θ + r² sin²θ)

r = √(r²(cos²θ + sin²θ))

r = √(r²) = r

Next, we need to change the limits of integration. The inequality x² + y² ≤ 1 represents a circle centered at the origin with a radius of 1. Thus, the region can be written as:

r cos θ² + r sin θ² ≤ 1

r² ≤ 1

Now we can evaluate the polar integral. Applying the transformation and integrating:

∫∫D f(x, y) dA = ∫₁ ₁ ∫₁ ₁ [n(x²y² + 1)] dx dy

∫∫D f(x, y) dA = ∫₀ ²π ∫₀ ¹ [n(r⁴ cos²θ sin²θ + 1)] r dr dθ

After obtaining the polar integral, we can evaluate it as follows:

Integrating with respect to r:

(r/5 + r³/3) ∣₀¹

Integrating with respect to θ:

(θ/10) ∣₀ π/10

Evaluating these expressions, we find:

0.14173

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We can do this by halving the coefficient of the x-term (-34/2 = -17) and squaring it to get the constant term (17^2 = 289). Thus, the constant term needed to complete the square is k = 289 - 10 = 279.

To complete the square of the quadratic equation x^2 - 34x + k = 10, we need to find the constant term that will make the quadratic a perfect square trinomial. Therefore, the answer is not listed in the given options. We can verify this by completing the square and writing the equation in vertex form: (x - 17)^2 = 289 - 10, which simplifies to (x - 17)^2 = 279. Thus, the constant term that should be used to complete the square is 279.

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Answer: $28.89

Step-by-step explanation: 2% of 1,444.50 is $28.89

The hypothesis is called the alternative hypothesis test.

According to the statement

We have to explain about the alternative hypothesis.

So, For this purpose, we know that the

The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.

From the given information:

she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.

Then

the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.

Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.

So, The hypothesis is called the alternative hypothesis test.

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Using a graphing calculator, the features of the function are given as follows:

In a graph, the domain and the range of the function are given as follows:

This function is defined for all real values and also assumes all real values, hence both the domain and the range are (-∞,∞).

From the graph, the function is classified as decreasing or increasing as follows:

Hence the intervals are given as follows:

The relative minimum is when the function changes from decreasing to increasing, hence it is at this following point:

(1.184, -1.089).

The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:

(2.816, 1.089).

The end behavior of the function is given by the limits of the function when x go to infinity, hence:

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