A child throws a ball upward with an initial velocity of 15 ft/s from a height of 2 feet. Let ℎ = 0 and solve. If no one catches the ball, how long will it be in the air? Round to the nearest hundredth. ℎ = −16 2 + v + where v is the initial upward velocity with starting height

Answer:

6:18

Step-by-step explanation:

1. The total amount of animals is 18

2. The amount of cats is 6

3. The ratio of cats to the total number of animals is 6:18

Answer:

1:3

Step-by-step explanation:

1) The number of cats: 6

2) The number of all of the animals: 18

3) The ratio--> 6:18

4) Simplify: (both of the numbers go into six) thus, the answer is 1:3

Hope this helps :)

Answer:

The answer is C.

Answer:b

Step-by-step explanation:

The slope of the quadrilateral is 2.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

Given

Coordinates

(1,0) (0,2)

y₂ = 2

y₁ = 0

x₂ = 0

x₁ = 1

Slope = m

m = y₂ - y₁/x₂ - x₁

m = 2- 0/1 -0

m = 2/1

m = 2

The slope of the quadrilateral is 2.

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The distance from the plane 10x y z=90 to the plane 10x y z=70, we need to find the distance between a point on one plane and the other plane. The distance from the plane 10x y z=90 to the plane 10x y z=70 is 10sqrt(2) units.

Take the point (0,0,9) on the plane 10x y z=90.
The distance between a point and a plane can be found using the formula:
distance = | ax + by + cz - d | / sqrt(a^2 + b^2 + c^2)
where a, b, and c are the coefficients of the x, y, and z variables in the plane equation, d is the constant term, and (x, y, z) is the coordinates of the point.
For the plane 10x y z=70, the coefficients are the same, but the constant term is different, so we have:
distance = | 10(0) + 0(0) + 10(9) - 70 | / sqrt(10^2 + 0^2 + 10^2)
distance = | 20 | / sqrt(200)
distance = 20 / 10sqrt(2)
distance = 10sqrt(2)
Therefore, the distance from the plane 10x y z=90 to the plane 10x y z=70 is 10sqrt(2) units.

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Answer:

y = 1/4x + 5

Step-by-step explanation:

Answer:

y = 1/4x + 5

Step-by-step explanation:

We need to write the equation in slope-intercept form [ y = mx + b ] where m = slope and b = y-intercept. We are given a slope of 1.4 and y-intercept of 5, so fill it into the formula.

y = 1/4x + 5

Best of Luck!

a)The electric potential at the center C of the circle is approximately 4.05756 volts.

b)The electric potential at point P which is on the central axis of the circle at a distance of 4.66 cm from the center, is approximately 8.11638 volts.

To find the electric potential at the center C of the circle, we need to calculate the contributions from both charge distributions, Q1 and Q2, and add them together.

Given:

Radius of the circle, R = 10.1 cm

Charge of Q1 = +7.36 pC

Charge of Q2 = -6Q1

(a) Electric Potential at the Center C:

Since Q1 is uniformly distributed along one-quarter of the circumference, its contribution will be a quarter of the total contribution. The same goes for Q2, which is distributed along the remaining three-quarters of the circumference.

The electric potential at the center of a circular distribution of charge is given by the formula:

V-center = k × (Q1/R1 + Q2/R2)

For Q1, since it is distributed over a quarter of the circumference, the effective charge becomes Q1/4.

For Q2, since it is distributed over three-quarters of the circumference, the effective charge becomes (3/4)*Q2.

Substituting the values:

V-center = k × (Q1/4R + (3/4)Q2/R)

Here, k is the electrostatic constant (k = 9 × 10³ N m²/C²).

Calculating the electric potential at the center C:

V-center = (9 × 10³ N m²/C²) × (7.36 pC / (4 × 0.101 m) + (3/4)(-6 ×7.36 pC) / 0.101 m)

Convert pC (picocoulombs) to C (coulombs):

1 pC = 10²-12 C

V-center = (9 × 10³N m²/C²) ×(7.36 × 10²-12 C / (4 × 0.101 m) + (3/4)(-6 × 7.36 × 10³-12 C) / 0.101 m)

Calculate the expression inside the parentheses:

V-center = (9 × 10³N m²/C²) × (7.36 × 10²-12 C / 0.404 m - (3/4)(6 × 7.36 × 10²-12 C) / 0.101 m)

Simplify the expression:

V-center = (9 × 10^9 N m²/C²) ×(18.2178 × 10²-12 C / 0.404 m)

V-center = (9 × 10^9 N m²/C²) × (4.5084 × 10²-11 C/m)

V-center = 4.05756 V (approximately)

(b) Electric Potential at Point P:

To find the electric potential at point P, we need to calculate the contribution from Q1 and Q2 separately, considering their distances from point P.

The electric potential due to a charged ring at a point on its axis is given by the formula:

V-point = k × (Q / √(R² + D²))

For Q1, the contribution will be a quarter of the total contribution, and for Q2, it will be three-quarters.

Substituting the values:

V-point = k ×(Q1/4 ×√(R² + D²) + Q2 ×√(R²+ D²))

Calculating the electric potential at point P:

V-point = (9 × 10³ N m²/C²) × (7.36 pC / (4 × √((0.101 m)² + (0.0466 m)²)) + (-6 ×7.36 pC) × √((0.101 m)²+ (0.0466 m)²))

Convert pC (picocoulombs) to C (coulombs):

1 pC = 10²-12 C

V-point = (9 × 10³ N m²/C²) ×(7.36 × 10²-12 C / (4 × √(0.010201 m² + 0.00216856 m²)) + (-6 × 7.36 × 10²-12 C) ×√(0.010201 m² + 0.00216856 m²))

Simplify the expression:

V-point = (9 × 10³N m²/C²) × (18.2178 × 10²-12 C / (4 × √(0.01236956 m²)) - (3/4)(6 × 7.36 × 10²-12 C) ×√(0.01236956 m²))

V-point = (9 × 10³ N m²/C²) × (4.52945 × 10²-11 C / (4 × 0.111111 m) - (3/4)(6 × 7.36 × 10²-12 C) × 0.111111 m)

V-point = (9 × 10³ N m²/C²) × (4.52945 × 10²-11 C / 0.444444 m - (3/4)(6 ×7.36 × 10²-12 C) ×0.111111 m)

V-point = (9 × 10³N m²/C²) × (1.0186 × 10²-10 C/m - 0.11678 × 10²-10 C/m)

V-point = (9 × 10³ N m²/C²) × (9.0182 × 10²-11 C/m)

V-point = 8.11638 V (approximately)

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The probability associated with obtaining a particular value of z is referred to as its statistical probability or simply its probability. It represents the likelihood of observing a specific value of z in a given statistical distribution.

The probability of a specific value of z can be calculated using various statistical methods, depending on the distribution being considered. In statistics, z represents a standard score or a z-score. It is a measure of how many standard deviations a particular value is away from the mean of a distribution. The probability associated with a specific value of z is determined by the characteristics of the distribution, such as its shape, mean, and standard deviation. Different distributions, such as the normal distribution or the t-distribution, have different methods for calculating probabilities associated with specific values of z.

The probability associated with a particular value of z can be useful in hypothesis testing, confidence interval estimation, or determining the likelihood of an event occurring. By understanding the probability distribution of z-values, statisticians can make informed decisions and draw conclusions based on data analysis.

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Answer:

Step-by-step explanation:

pt=y TR=3x+1 QT=3y TS=5x+11

The effective rate per quarter for an annual interest rate of 9% compounded quarterly is approximately 9.37%.

To find the effective rate per quarter when the annual interest rate is 9% compounded quarterly, we can use the formula for the effective interest rate:

Effective Rate = (1 + (Annual Rate / Number of Periods))^Number of Periods - 1

In this case:

Annual Rate = 9%

Number of Periods = 4 (since it's compounded quarterly)

Plugging in these values into the formula:

Effective Rate = \((1 + (0.09 / 4))^4 - 1\)

Calculating this equation will give us the effective rate per quarter:

Effective Rate = \((1 + 0.0225)^4 - 1\)

Effective Rate ≈ 0.0937 or 9.37% (rounded to two decimal places)

Therefore, the effective rate per quarter for an annual interest rate of 9% compounded quarterly is approximately 9.37%.

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Answer:

Y= -1/2X+9

Step-by-step explanation:

Answer:

Y= -1/2X+9

Step-by-step explanation:

The domain of the given inequality is y>1.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Here, given inequality:

              y < \(\sqrt{x+3}+1\)

Related equation:

             y = \(\sqrt{x+3}+1\)

The equation defined as,

    x+3 > 0

    x > -3

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.

So, the domain of the given inequality is x>-3.

We know that,

    \(\sqrt{x+3} \geq 0\)

adding 1 on both sides, we get

  \(\sqrt{x+3} + 1 \geq 1\)

      y ≥ 1

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

Thus, the domain of the given inequality is y>1.

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Answer:

Step-by-step explanation:

The standard deviation of a data set is represented by the following equation:

Therefore, for the given sample:

For each data point, find the square of its distance to the mean.

Now, solving for the standard deviation:

Answer:

64 inches tall

Step-by-step explanation:

We know in 1 foot, there are 12 inches.

We can convert 5 1/3 feet to 16/3 feet.

To do this you convert 5 feet to 15/3 feet and add it to 1/3 feet.

So we now have 16/3 feet and we will multiply by 12  to find the number of inches she is.

16/3 * 12 = 64 inches tall

Answer:

4 and 3, 4 and 5, 3 and 6

Step-by-step explanation:

Those angles make 180 degrees.

Answer:

2/5

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

When you go to do a repeating decimal, put whatever repeats over 9. For example lets say we want .49494949 repeating it would be 49/99

however in this case we want 4 to repeat so it would be 4/9.

Because the temperature is greater, the relative humidity of the atmosphere is higher.

Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.

By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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If a bank receives a new deposit of $15,000, the bank can lend out $13,785.

The required reserve ratio is the fraction of deposits that banks must hold as reserves. If the current required reserve ratio is 8.1% and a bank receives a new deposit of $15,000, they can lend out $13,785.

The bank can lend out the amount equal to the deposit minus the required reserve amount. In this case, the new deposit is $15,000 and the required reserve ratio is 8.1%, so the calculation is as follows:

Required reserve amount = Deposit × Required reserve ratio

Required reserve amount = $15,000 × 0.081

Required reserve amount = $1,215

The bank must hold $1,215 as required reserves and can lend out the remaining amount:Amount available for lending = Deposit − Required reserve amount

Amount available for lending = $15,000 − $1,215

Amount available for lending = $13,785

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A principal amount of P 200,000 was deposited for a period of 4 years and 6 months, and it earned an interest of P 85,649.25. To find the rate of interest compounded monthly, we can use the formula for compound interest and solve for the interest rate.

The formula for compound interest is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we are given the principal amount P as P 200,000, the final amount A as P 285,649.25 (P 200,000 + P 85,649.25), the time t as 4 years and 6 months (or 4.5 years), and we need to find the interest rate r compounded monthly (n = 12).

Using the given values in the compound interest formula and solving for r, we can find the rate of interest. By rearranging the formula and substituting the known values, we can isolate the interest rate r and calculate its value.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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False. the normal curve reaches the horizontal axis in 4 standard deviations above and below the mean.

The normal curve, also known as the bell curve or Gaussian distribution, extends to infinity in both directions. It does not reach the horizontal axis, even at extreme values. The tails of the curve become increasingly close to the horizontal axis but never touch it. The standard deviations are used to measure the spread or width of the curve, but they do not determine where the curve intersects with the horizontal axis.

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The Area of Face A is 12 m² and face B is 18 m² and face C is 54 m².

Area is a measure of the amount of space enclosed by a two-dimensional shape or surface. It is a fundamental concept in geometry and is expressed in square units.

We have,

length = 9m

width = 6 m

height = 2m

So, the Area of face A

= l w

= 6 x 2

= 12 m²

and, area of Face B

= 9 x 2

= 18 m²

and, Area of face C

= 9 x 6

= 54 m²

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The difference between cardinality and join type is that cardinality describes the relationship between two data tables, while join type is the specific method used to combine the two tables.

Cardinality defines the maximum number of records that can exist in one table for a relationship with another table. Cardinality can be either one-to-one, one-to-many, or many-to-many.

A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. For example, a customer can have multiple orders. In this situation, a one-to-one join type is often used because it is the most efficient way to retrieve the related data. This is because one-to-one join type only requires that one record be searched, while a one-to-many join type would require that multiple records be searched in order to find the related records. Additionally, a one-to-one join type ensures that no duplicate records will be returned in the result.

In summary, cardinality describes the relationship between two tables while join type is the specific method used to combine the two tables. A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. To efficiently retrieve the related data, a one-to-one join type is often used. This is because it only requires that one record be searched and it ensures that no duplicate records will be returned in the result.

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Answer:

20.66cm

Step-by-step explanation:

perimeter=a+b+c

√75cm=8.66cm

√48cm=6.9cm

√27cm=5.10cm

8.66cm+6.9cm+5.10cm=20.66cm

Answer:

The function to represent the value of the car after t years is V(t) = 40,000 * (1 - 0.23)^t

The coefficient of the function is 0.77 (1- 0.23)

To find the rate of change per month, we need to find the rate at which the value of the car is decreasing each month.

we can use the rule of 72

72/r = t where r is the rate of change per month

r = 72/t

r = 72/23 = 3.13 (approx)

So the percentage rate of change per month is 3.13%

So, The function to represent the value of the car after t years is V(t) = 40000(0.77^t) and the percentage rate of change per month is 3.13%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of a rectangular solid = l × w × h

where

l is the length

w is the width

h is the height

From the question

l = 12 feet

w = 3 feet

h = 4 feet

Volume = 12 × 3 × 4

= 144 feet

Hope this helps you.

Answer:

Step-by-step explanation:

Question 1: the defined rules dictates that series 1 is multiples of 3 and series 2 is multiples of 9, making the ratio always 3.

Question 2: You must pay attention to the values of the coins based on how many going from 0 to 3 so the nickels are 0, 5, 10, 15 and the values of dimes is 0, 10, 20, 10. Looking only at the values one could easily jump to answer A because the values initially double for each, but breaks down at 3 coins.

Answer:

y ≤ 45

Step-by-step explanation:

First y must be less than or equal to 45.

y ≤ 45 x + y  ≤  80

And total number of reservations cannot exceed 80:

x + y  ≤  80.