Last month, Claire's bank statement said that she overdrew her account. Her bank balance was -45. 32−45. 32minus, 45, point, 32 euros. This month, Claire's bank balance is 17. 9217. 9217, point, 92 euros. What does this mean?

Choose 1 answer:

Choose 1 answer:

Answer:

D. 81

Step-by-step explanation:

(81^¼)⁴ = 81^(¼×4) = 81¹ = 81

The mean amount of coffee to be dispensed from the vending machine should be set to 11.918 ounces to allow for a 2% overfill.

To determine the mean amount of coffee to be dispensed from the vending machine, we need to use the normal distribution and the given information that the standard deviation is 0.04 ounce and we can allow the cup to overfill 2% of the time.

First, we need to find the z-score associated with the 2% overfill. Using a standard normal distribution table or calculator, we can find that the z-score is approximately 2.05.

Next, we can use the formula z = (x - μ) / σ, where z is the z-score, x is the value of the random variable (the amount of coffee dispensed), μ is the mean, and σ is the standard deviation.

Substituting the values we have, we get:

2.05 = (12 - μ) / 0.04

Solving for μ, we get:

μ = 12 - 2.05 * 0.04

μ = 11.918

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a) We have shown that 4h - 64 = 2k is equivalent to 2h - 32 = k. b) Aaron is born on the 25th of the month and Belle is born on the 18th of the month.

In mathematics, two expressions or equations are said to be equivalent if they have the same value or solutions.

a) We are given that Aaron multiplies h by 4 and subtracts 64 to get the same result as Belle when she multiplies k by 2. Mathematically, we can write this as:

4h - 64 = 2k

We want to show that this is equivalent to 2h - 32 = k.

Starting with 4h - 64 = 2k, we can simplify it by adding 64 to both sides:

4h = 2k + 64

Dividing both sides by 2, we get:

2h = k + 32

Subtracting 32 from both sides, we get:

2h - 32 = k

Therefore, we have shown that 4h - 64 = 2k is equivalent to 2h - 32 = k.

b) We are given that Belle adds h to 5 times k and gets 115. Mathematically, we can write this as:

h + 5k = 115

We also know from part (a) that 2h - 32 = k. We can substitute this expression for k into the equation h + 5k = 115:

h + 5(2h - 32) = 115

Simplifying, we get:

h + 10h - 160 = 115

Combining like terms, we get:

11h = 275

Dividing both sides by 11, we get:

h = 25

Now we can use the expression 2h - 32 = k to solve for k:

2(25) - 32 = k

k = 18

Therefore, Aaron is born on the 25th of the month and Belle is born on the 18th of the month.

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When triangle ABC is dilated by a scale factor of 3/4 to create triangle MNO, we know that the corresponding sides of the two triangles will be proportional, and the corresponding angles will be congruent.

Triangle ABC and triangle MNO are similar triangles.

When a triangle is dilated, all corresponding sides of the two triangles are proportional, and all corresponding angles are congruent.

Since triangle ABC is dilated by a scale factor of 3/4 to create triangle MNO, we know that the lengths of corresponding sides in triangle MNO will be 3/4 times the lengths of the corresponding sides in triangle ABC. For example, if side AB in triangle ABC is 8 units long, then side MN in triangle MNO will be (3/4) * 8 = 6 units long.

Similarly, the measures of corresponding angles in triangle MNO will be equal to the measures of the corresponding angles in triangle ABC. For example, if angle A in triangle ABC is 45 degrees, then angle M in triangle MNO will also be 45 degrees.

In summary, when triangle ABC is dilated by a scale factor of 3/4 to create triangle MNO, we know that the corresponding sides of the two triangles will be proportional, and the corresponding angles will be congruent.

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Answer:

Complementary

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees, and since there is a 90 degree sign on the angles this is complementary.

Using the vertical line test, the graph that represents a function is: Graph C.

A simple test we can carry out quickly to determine if a graph represents a function is the vertical line test.

Using the vertical line test, a vertical line is drawn across the curve in the given plane. If the vertical line intersect the curve more than once, it is not a function, but if it intersects the curve at just exactly one point, then the graph represents a function.

If we draw a vertical line across each of the given graphs, only the graph in option C will be intersected at exactly only one point.

Therefore, graph C represents a function.

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The equation in spherical coordinates is a) 3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

b) 2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

a) The equation in Cartesian coordinates is 3x² - 2x + 3y² - 3z² = 0. To convert to spherical coordinates, we use the following substitutions:

x = ρsinϕcosθ

y = ρsinϕsinθ

z = ρcosϕ

Substituting these values into the Cartesian equation gives:

3(ρsinϕcosθ)² - 2(ρsinϕcosθ) + 3(ρsinϕsinθ)² - 3(ρcosϕ)² = 0

3ρ²sin²ϕcos²θ - 2ρsinϕcosθ + 3ρ²sin²ϕsin²θ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ(cos²θ + sin²θ) - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

Simplifying and dividing by ρ² gives:

3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

(b) The equation in rectangular coordinates is 2x + 4y + 5z = 1. To write it in spherical coordinates, we use the same conversion formulas as before:

2(ρsinφcosθ) + 4(ρsinφsinθ) + 5(ρcosφ) = 1

Simplifying and dividing by ρ, we get:

2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

This is the equation in spherical coordinates.

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Answer:

it took him 15 more minutes it would be 45 minutes in all

Step-by-step explanation:

I hope I helped!!

A researcher wished to estimate the difference between the proportion of users of two shampoos who are satisfied with the product at a 90% confidence level,

the true difference between the proportion of users satisfied with shampoo A and shampoo B is estimated to be between -0.0262 and 0.0482.

To construct a 90% confidence interval for the true difference between the two population proportions, we can use the formula for the confidence interval for the difference between two proportions.

Let's denote the proportion of users satisfied with shampoo A as p1 and the proportion of users satisfied with shampoo B as p2.

The sample proportion for shampoo A, denoted as 1, is calculated by dividing the number of users satisfied in the sample of 400 (78) by the sample size (400):

1 = 78/400 = 0.195

The sample proportion for shampoo B, denoted as 2, is calculated by dividing the number of users satisfied in the sample of 500 (92) by the sample size (500):

2 = 92/500 = 0.184

Next, we calculate the standard error, which measures the variability of the difference between the two proportions:

SE = sqrt[(1 * (1 - 1) / n1) + (2 * (1 - 2) / n2)]

where n1 is the sample size for shampoo A (400) and n2 is the sample size for shampoo B (500).

SE = sqrt[(0.195 * (1 - 0.195) / 400) + (0.184 * (1 - 0.184) / 500)]

SE = sqrt[(0.152025 / 400) + (0.151856 / 500)]

SE ≈ 0.0226

Now, we can calculate the margin of error by multiplying the standard error by the critical value corresponding to a 90% confidence level. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = 1.645 * 0.0226 ≈ 0.0372

Finally, we construct the confidence interval by subtracting and adding the margin of error from the difference in sample proportions:

Confidence Interval = (1 - 2) ± Margin of Error

Confidence Interval = (0.195 - 0.184) ± 0.0372

Confidence Interval = 0.011 ± 0.0372

Confidence Interval ≈ (-0.0262, 0.0482)

Therefore, at a 90% confidence level, the true difference between the proportion of users satisfied with shampoo A and shampoo B is estimated to be between -0.0262 and 0.0482.

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The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

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There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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Answer:

(n-7) ≤ 95

Step-by-step explanation:

We need to write the expression for the given statement.

Seven less than the product of a number n and  1 means (n-7).

It is no more than 95. No more than 95 means less than or equal to i.e.

(n-7) ≤ 95

Hence, the above inequality shows the given statement.

Answer:

he is right if u need further explonation it is b and c

Step-by-step explanation:

The inequality is given as –5h + 20 > –10. And the solution of the inequity will be h < 6.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The weather report says the temperature is 20 °C and will drop 5 °C per hour for the next 6 hours. Daryl plans to be gone for at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above –10 °C.

Let h be the number of hours.

The inequality is given as,

–5h + 20 > –10

And the solution of the inequity will be

–5h > –30

 5h < 30

   h < 6

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The correct option regarding the amount of coins is given as follows:

c 4 nickels, 10 dimes, 4 quarters

The amounts are obtained by a system of equations, for which the variables are given as follows:

Amy has 18 coins consisting of nickels, dimes, and quarters, hence:

x + y + z = 18.

She has the same amount of nickels as quarters, hence:

x = z.

Thus:

2x + y = 18

y = 18 - 2x.

She has a total of $2.20 worth of coins, hence:

0.05x + 0.1y + 0.25z = 2.2

0.3x + 0.1y = 2.2

Since y = 18 - 2x, the value of x is obtained as follows:

0.3x + 0.1(18 - 2x) = 2.2

0.1x = 0.4

x = 0.4/0.1

x = 4.

Hence the remaining values are given as follows:

Meaning that option c is correct.

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Answer:

Step-by-step explanation:

2x-3

x=2

The probability that exactly 5 out of 8 randomly selected people will not go to the restaurant is approximately 0.0238, or 2.38%.

To calculate the probability that 5 people out of 8 will not go to the restaurant, we need to consider the probability of each individual not going and then calculate the probability of this outcome occurring for exactly 5 out of the 8 people.

Let's break down the calculation step by step:

The probability that a single person does not go to the restaurant is 1 - 0.75 = 0.25. This is because if there is a 75% probability of going, then there is a 100% - 75% = 25% probability of not going.

To determine the probability of exactly 5 out of the 8 people not going, we use the binomial probability formula. The formula is as follows:

P(k successes) = C(n, k) × \(p^{k}\) × \((1-p)^{(n-k)}\)

Where:

P(k successes) is the probability of having k successes,

C(n, k) is the binomial coefficient, representing the number of ways to choose k items from a set of n items,

p is the probability of success (in this case, the probability of not going, which is 0.25), and

n is the total number of trials (in this case, the total number of people, which is 8).

Substituting the values into the formula:

P(5 people not going) = C(8, 5) × 0.25⁵ × (1-0.25)⁸⁻⁵

= 56  ×0.25⁵ ×0.75³

= 56  ×0.0009765625 ×0.421875

= 0.02381134

Therefore, the probability that exactly 5 out of 8 randomly selected people will not go to the restaurant is approximately 0.0238, or 2.38%.

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6. Writing each number in scientific notation based on the facts from Guinness World Records is as follows:

a) 162,760 = 1.6276 x 10⁵

b) 21,202,192 = 2.1202192 x 10⁷

c) 101,791 = 1.01791 x 10⁵.

Scientific notation refers to the shorthand manner of writing long or short numbers in their standard forms.

When a number is written in scientific notation, it is changed to the power of 10 and raised by the appropriate exponent marking the decimal place value.

a) 162,760 = 1.6276 x 10 raised to power 5 = 1.6276 x 10⁵

b) 21,202,192 = 2.1202192 x 10 raised to power 7 = 2.1202192 x 10⁷

c) 101,791 = 1.01791 x 10 raised to power 5 = 1.01791 x 10⁵

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One of the properties of a parabola is that it can act as a reflector. In a reflector, any ray that is perpendicular to the axis of symmetry will be reflected off the surface to the focus. So, correct option is C.

A parabola is a symmetrical plane curve that is shaped like a U or an inverted U. It is defined as the set of all points in a plane that are equidistant from a fixed point, called the focus, and a fixed line, called the directrix.

One of the properties of a parabola is that it can act as a reflector. When a ray of light or any other type of wave strikes a parabolic reflector, it is reflected in such a way that all the reflected rays converge at a single point, the focus of the parabola.

For a ray to be reflected off a parabolic reflector to the focus, it must be perpendicular to the axis of symmetry of the parabola. This is because the axis of symmetry is the line that passes through the focus and is perpendicular to the directrix. Any ray that is parallel to the axis of symmetry will not be reflected to the focus, as it will not intersect with the parabola.

Therefore, the answer to the given question is C. perpendicular. Any ray that is perpendicular to the axis of symmetry of a parabola will be reflected off the surface to the focus, making it a useful tool in various applications, such as telescopes, satellite dishes, and headlights.

So, correct option is C.

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Using the relation between velocity, distance and time, it is found that she traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.

Velocity is distance divided by time, that is:

v = d/t.

For the first part, we have that she cycled a distance of d m in t seconds, at a velocity of 10 m/s, hence:

10 = d/t

d = 10t.

For the second part, we have that she cycled a distance of 500 - d meters, in 22 - t seconds, at a velocity of 50 m/s, hence:

50 = (500 - d)/(22 - t).

Since d = 10t, and applying cross multiplication:

500 - 10t = 50(22 - t)

500 - 10t = 1100 - 50t

40t = 600

t = 600/40

t = 15.

22 - t = 22 - 15 = 7, hence:

She traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.

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The equation of the line tangent to the curve \(\(x^2y^2 = 10\)\) at the point (3, 1) is y = 1.

To find the equation of the line tangent to the curve \(x^2y^2 = 10\) at the point (3, 1), we can use implicit differentiation.

Let's start by differentiating both sides of the equation with respect to x:

\(\[\frac{d}{dx}(x^2y^2) = \frac{d}{dx}(10)\]\)

Using the chain rule, we can differentiate the left-hand side as follows:

\(\[\frac{d}{dx}(x^2y^2) = 2x \cdot y^2 \frac{dy}{dx} + x^2 \cdot 2y \frac{dy}{dx}\]\)

Simplifying the right-hand side, we get:

\(\[2xy^2 \frac{dy}{dx} + 2x^2y \frac{dy}{dx} = 0\]\)

Now let's substitute the given point (3, 1) into the equation. We have x = 3 and y = 1:

\(\[2(3)(1)^2 \frac{dy}{dx} + 2(3)^2(1) \frac{dy}{dx} = 0\]\)

\(\[6 \frac{dy}{dx} + 18 \frac{dy}{dx} = 0\]\)

Combining the terms, we get:

\(\[24 \frac{dy}{dx} = 0\]\)

Dividing both sides by 24, we obtain:

\(\[\frac{dy}{dx} = 0\]\)

This equation tells us that the slope of the tangent line at the point (3, 1) is zero, indicating a horizontal line.

Now, we need to find the equation of this horizontal line. Since the slope is zero, the line is of the form y = c, where c is a constant. Since the line passes through the point (3, 1), we know that y = 1.

Therefore, the equation of the line tangent to the curve \(x^2y^2 = 10\) at the point (3, 1) is y = 1.

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Answer:

see the picture

Step-by-step explanation:

attached

Answer:

The previous number keeps getting multiplied by - 5

Step-by-step explanation:

5 × -5 = -25

-25 × -5 = 125

125× -5 = -625

-625 × -5 = 3,125

3125 × -5 = -15,625

-15,625 × -5 = 78,125

78,125 × -5 = -390, 625

-390,625 × -5 = 1,953,125

1,953,125 × -5 = 9,765,625

:)

The 9th term of the geometric sequence is 5⁹.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The formula to find nth term of the geometric sequence is \(a_n=ar^{r-1}\). Where, a = first term of the sequence, r= common ratio and n = number of terms.

The given geometric sequence is 5, 25, 125,..

To find the common ratio, divide the second term by the first term:

r = 25/5

r = 5

The formula for the nth term of a geometric sequence is:

aₙ = a₁ rⁿ⁻¹

Substitute n = 9, r = 5, and a₁ = 5:

a₉ = 5 (5)⁹⁻¹

a₉ = 5 (5)⁸

a₉ = 5⁹

Hence, the 9th term of the geometric sequence is 5⁹.

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From distance formula, the distance covered by a particle with position (x, y) as time, t is equals to the \( 18\sqrt{2}\).

The distance d, traveled by the particle with position vector, r(t) = <x(t), y(t) > over the interval [a,b] is calculated by following

\(d = \int_{a}^{b} ( (\frac{dx}{dt})² +(\frac{dy}{dt})² )dt\). We have a particle with position value (x, y) as t varies in the time interval. The parametric equations are, x = 3 sin² (t), y = 3 cos²(t), on the

time interval [0,3π]. Now the derivative of above parametric equations with respect to time t are \(\frac{dx}{dt} = 6 sin(t)cos(t) \) = 3 sin(2t)

\(\frac{dy}{dt} = -6 sin(t)cos(t) \)

= - 3 sin(2t)

Therefore, the required distance travelled by particle in the interval [0,3π] is written as \(d = \int_{0}^{3π} \sqrt{( (3 sin(2t))² + (-3 sin(2t))²) dt} \\ \)

\(= \int_{0}^{3π} \sqrt{ ( 9 sin²(2t) + 9sin²(2t))}dt \\ \)

\(= \int_{0}^{3π} \sqrt{18sin²(2t)dt}\)

\(= 3\sqrt{2}\int_{0}^{3π} |sin(2t)|dt\)

\(= 3\sqrt{2}[ \int_{0}^{\frac{π}{2}} sin(2t)dt - \int_{\frac{π}{2}}^{π} sin(2t)dt + \int_{π}^{\frac{3π}{2}} sin(2t)dt - \int_{\frac{π}{2}}^{2π}sin(2t)dt + \int_{2π}^{\frac{5π}{2}}sin(2t)dt - \int_{\frac{5π}{2}}^{3π}sin(2t)dt \\ \)

\(= 3\sqrt{2}([ \frac{cos(2t)}{2}]_{0}^{\frac{π}{2}} - [\frac{cos(2t)}{2}]_{\frac{π}{2}}^{π} + [\frac{cos(2t)}{2}]_{π}^{\frac{3π}{2}} - [\frac{cos(2t)}{2}]_{\frac{3π}{2}}^{2π} + [\frac{cos(2t)}{2}]_{2π}^{\frac{5π}{2} }- [ \frac{cos(2t)}{2}]_{\frac{5π}{2}}^{3π})\\ \)

\(= 3\sqrt{2}([ \frac{1}{2} +{\frac{1}{2}] - [\frac{-1}{2}- \frac{1}{2}}] + [\frac{1}{2}+ \frac{1}{2}] - [\frac{-1}{2} - \frac{1}{2}] + [\frac{1}{2} + \frac{1}{2}]- [ \frac{-1}{2} - \frac{1}{2}])\\ \)

\(= 3\sqrt{2}(6)\) =\(= 18\sqrt{2}\)

Hence, the required distance is \( 18\sqrt{2}\).

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Answer:

12

Step-by-step explanation:

Answer:

desculpe pela resposta, estou tendo que fazer isso pois quero acumular pontos para poder ajudar meu irmão autista, pode comentar coisas aleatórias nas minhas perguntas se quiser tbm:( me desculpe mesmo eu até pesquisei no g0gl3 mais não achei nada sorry sorry