2x^2 + y^2 = 19
x + 3y = 0

Answer: 75 percent

Step-by-step explanation: I'm pretty sure

The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²

The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t

The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.

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Answer:

Yes

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

2/5 kilogram od soil = 1/3 of the container

So 2/5 + 2/5+ 1/5 = 1 kilo gram of soil

so 1 kilo will fit into the container

Given:

A box contains four tiles, numbered 1,4,5, and 8. Kelly randomly chooses one tile, places it back in the box, then chooses a second tile.

To find:

The probability that the sum of the two chosen tiles is greater than 7.

Solution:

A box contains four tiles, numbered 1,4,5, and 8. So, the total possible outcomes are:

S = {(1,1),(1,4),(1,5),(1,8),(4,1),(4,4),(4,5),(4,8),(5,1),(5,4),(5,5),(5,8),(8,1),(8,4),(8,5),(8,8)}

n(S) = 16

A : Sum of the two chosen tiles is greater than 7.

A = {(1,8),(4,4),(4,5),(4,8),(5,4),(5,5),(5,8),(8,1),(8,4),(8,5),(8,8)}

n(A) = 11

So, probability that the sum of the two chosen tiles is greater than 7 is

\(Probability=\dfrac{n(A)}{n(S)}\)

\(Probability=\dfrac{11}{16}\)

Therefore, the required probability is \(\dfrac{11}{16}\).

The probability that the sum of the two chosen tiles is greater than 7 is;

P(sum of the two chosen tiles is greater than 7) = 11/16

We are told that the four tiles are numbered as;

1, 4, 5 and 8.

Now, let us look at all the possible combinations that are greater than 7 and they are;

(1, 8), (8, 1), (4, 5), (4, 4), (5, 4), (5, 5), (4, 8), (8, 4), (5, 8), (8, 5), (8, 8)

Since there are 4 number, then the total number of possible two digit number that can be formed if the first tile is replaced after choosing before a second one is chosen is; 4 × 4 = 16 possible ways

There are 11 possible combinations that are greater than 7.

Thus;

P(sum of the two chosen tiles is greater than 7) = 11/16

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Answer:

I think it might be 1.25

Step-by-step explanation:

Answer:

LCM is 30.

Step-by-step explanation:

She forgot that they both can multiply into 30. She listed all their multiples and their LCM is 30. Not 60. That's her error.

Hope this helps and have a nice day!

The given statement 'By definition, a ratio initially takes on the form of a fraction' is true because a ratio is said to be a proportion of two values taken in the form of a fraction and then simplified.

The numerical equivalent of a percentage of a whole is a fraction. It consists of a denominator, which denotes the total number of parts in the whole, and a numerator, which denotes the number of parts being examined. A horizontal line denoting division separates the numerator and remainder.

Proper and improper fractions, mixed integers, and decimals can all be represented using fractions. They can be multiplied, split, added, and taken away. Ratios, proportions, and fractions of amounts are just a few examples of the many mathematical uses and ideas that use fractions.

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If both the upstairs and downstairs switches are in the up position, the light will be off

The given parameters are

Switches = 2 i.e. top and bottom

Also, we have:

When the upstairs switch is up and the downstairs switch is down, the light is turned on.

This means that the light is only on when the upstairs switch is up and the downstairs switch is down

Any other position of the switches, the light is off

From the question, we have

Both the upstairs and downstairs switches are in the up position

This is different from the required position to on the light

Hence, the light will be off

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ANSWER:

y=-4/5x+7

Subtract 8x from both sides of the equation.

10=70y −8x

Divide each term by 10 and simplify

cancel the comman factor to Cancel the common factor.

which is 10

Divide y by 1

Simplify  

    70     -8x

y= --- + --------

    10        10

write in y=mx+b form

so it y=-4/5x+7

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:

D

Step-by-step explanation:

Main value = .4142

A. sqrt(3)-sqrt(2) = .3178

B. sqrt(3)+sqrt(2) = pi

C. sqrt(2)+1 = 2.4142

D. sqrt(2)-1 = .4142 <-

Answer:

21

Step-by-step explanation:

his ratio of shots from the first game would be 14:40 or 7:20

so if he made the same ratio from 60 shots it would be

21:60

We are asked to prove that the equation 3x^50 + 1 = 0 has at least one real root.

To prove that the equation has at least one real root, we can make use of the Intermediate Value Theorem. According to the theorem, if a continuous function changes sign over an interval, it must have at least one root within that interval.

In this case, we can consider the function f(x) = 3x^50 + 1. We observe that f(x) is a continuous function since it is a polynomial.

Now, let's evaluate f(x) at two different points. For example, let's consider f(0) and f(1). We have f(0) = 1 and f(1) = 4. Since f(0) is positive and f(1) is positive, it implies that f(x) does not change sign over the interval [0, 1].

Similarly, if we consider f(-1) and f(0), we have f(-1) = 4 and f(0) = 1. Again, f(x) does not change sign over the interval [-1, 0].

Since f(x) does not change sign over both intervals [0, 1] and [-1, 0], we can conclude that there must be at least one real root within the interval [-1, 1] based on the Intermediate Value Theorem.

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The addition equation that can be used to represent how much coffee is remaining is 1+(-5/8)=3/8

Addition equation = 1+(-5/8)

= 1-5/8

= (8-5)/8

= 3/8

Total amount of sugar needed = Cookie recipe + Brownie recipe

= 1.5+1.25

= 2.75 cups of sugar

Therefore, the addition equation that can be used to represent the total amount of sugar Dante needs is 1.5+1.25=2.75

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So, the approximate probability of seeing more than 45 coin flips as heads out of 100 flips is approximately 0.1539, or 15.39%.

To approximate the probability of seeing more than 45 coin flips as heads out of 100 flips, we can use the central limit theorem. The central limit theorem states that for a large enough sample size, the distribution of the sum (or average) of independent and identically distributed random variables approaches a normal distribution.

In this case, each coin flip is a Bernoulli trial with a probability of success (getting heads) of 0.4. We can consider the number of heads obtained in 100 flips as a sum of 100 independent Bernoulli random variables.

The mean of a single coin flip is given by μ = np = 100 * 0.4 = 40, and the standard deviation is given by σ = sqrt(np(1-p)) = sqrt(100 * 0.4 * 0.6) ≈ 4.90.

Now, to approximate the probability of seeing more than 45 coin flips as heads, we can use the normal distribution with the mean and standard deviation calculated above.

Let X be the number of heads in 100 flips. We want to find P(X > 45).

Using the standard normal distribution, we can calculate the z-score for 45 flips: z = (45 - 40) / 4.90 ≈ 1.02

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score: P(Z > 1.02) ≈ 1 - P(Z < 1.02)

Looking up the value in the table, we find that P(Z < 1.02) ≈ 0.8461.

Therefore, P(Z > 1.02) ≈ 1 - 0.8461 ≈ 0.1539.

So, the approximate probability of seeing more than 45 coin flips as heads out of 100 flips is approximately 0.1539, or 15.39%.

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The least-squares line predicts the healthy weight of the 15-week-old calves.

The least-squares line is a linear regression model that determines the best-fit line through a set of data points.

In this case, it is used to predict the healthy weight of the 15-week-old calves.

The line is based on a statistical analysis of historical data and aims to minimize the sum of the squared differences between the predicted and actual weights.

To calculate the predicted weight, we would need additional information such as the specific equation of the least-squares line and any relevant coefficients or parameters.

Using this equation, we can input the age of 15 weeks to obtain the estimated healthy weight.

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The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .

In the question ,

we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,

we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .

the confidence interval are useful because ,

(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .

(ii) they make data analyses richer and help us to make more informed decisions about the research questions .

Therefore , the reason how confidence interval helps is mentioned above.

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Answer:

59.1 feet

Step-by-step explanation:

The formula for the circumference of a circle in C=2πr. Since the radius of the circle is given, all you have to do is plug it into the equation.

C=2πr

C=2π(9.4)

C=18.8π feet  <-- this is the exact answer

C=59.1 feet

The annual depreciation is approximately $117,333.33. The current book value is approximately $2,621,333.36. The after-tax salvage value is $1,350,000.

Part 1: Annual Depreciation

To calculate the annual depreciation, we need to determine the total depreciation over the useful life of the machine. In this case, the useful life is 15 years.

Total depreciation = Purchase cost + Installation cost - Salvage value

Total depreciation = $3,000,000 + $560,000 - $1,800,000

Total depreciation = $1,760,000

The annual depreciation can be calculated by dividing the total depreciation by the useful life of the machine.

Annual Depreciation = Total depreciation / Useful life

Annual Depreciation = $1,760,000 / 15

Annual Depreciation ≈ $117,333.33

Therefore, the annual depreciation is approximately $117,333.33.

Part 2: Current Book Value

To find the current book value, we need to subtract the accumulated depreciation from the initial cost of the machine. Since 8 years have passed, we need to calculate the accumulated depreciation for that period.

Accumulated Depreciation = Annual Depreciation × Number of years

Accumulated Depreciation = $117,333.33 × 8

Accumulated Depreciation ≈ $938,666.64

Current Book Value = Initial cost - Accumulated Depreciation

Current Book Value = ($3,000,000 + $560,000) - $938,666.64

Current Book Value ≈ $2,621,333.36

Therefore, the current book value is approximately $2,621,333.36.

Part 3: After-Tax Salvage Value

To calculate the after-tax salvage value, we need to apply the marginal tax rate to the salvage value. The salvage value is the amount the machine was sold for, which is $1,800,000.

Tax on Salvage Value = Salvage value × Marginal tax rate

Tax on Salvage Value = $1,800,000 × 0.25

Tax on Salvage Value = $450,000

After-Tax Salvage Value = Salvage value - Tax on Salvage Value

After-Tax Salvage Value = $1,800,000 - $450,000

After-Tax Salvage Value = $1,350,000

Therefore, the after-tax salvage value is $1,350,000.

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Answer:

∠ 7 = 45°

Step-by-step explanation:

∠ 5 and ∠ 7 are vertical angles and congruent, then

∠ 7 = ∠ 5 = 45°

Answer:

A): f(x) = (x – 1)² + 2

Step-by-step explanation:

The quadratic function, f(x) = (x – 1)² + 2 is in vertex form: y = a(x - h)² + k, where:

The function, f(x) = (x – 1)² + 2, provides the pertinent information that allows us to determine the parabola's minimum value, as the value of a is a positive, which implies that the parabola is upward facing, and the vertex, (1, 2) is the minimum point.

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Answer:kkkkkkk

Step-by-step explanation:

A)

I) 114.31

ii)114

iii) 114, 107

B)

x frequency

90-99: 1

100-109: 5

110-119: 2

120-129: 1

130-139: 2

Step-by-step explanation:

A x. f. fx

97. 1. 97

100. 1. 100

103. 1. 103

105. 1. 105

107. 2. 214

108. 1. 108

114. 2. 228

115. 1. 115

122. 1. 122

137. 1. 137

139. 1. 139.

13 1468

I) mean: £fx. =. 1468

£f. 13

= 114.3076

=114.31 to 2 decimal places

Ii) median: 97,100,103,105,107,107,108,114,114,115,122,137,139

:• median= 108

III) mode = 107,114

Answer:

The length of a leg is 12.5 and its base is 15

Step-by-step explanation:

Using Heron's formula, the area of the triangle A = √[s(s - a)(s - b)(s - c)] where s = (a + b + c)/2. Now, for an isosceles, a = b and c = its base.

So,  A = √[s(s - a)(s - a)(s - c)] = √[s(s - a)²(s - c)] = (s - a)√[s(s - c)] and s = (a + a + c)/2 = a + c/2 ⇒ s = a + c/2 (1)

Given that the perimeter a + b + c = 2a + c = 40 = 2s ⇒ s = 40/2 = 20 and A = hc/2 where h = length of altitude to base = 10.

So, A = 10c/2 = 5c

So, 5c = (s - a)√[s(s - c)]

From (1) s - a = c/2.

So, 5c = (s - a)√[s(s - c)]

5c = (c/2)√[s(s - c)]

10 = √[s(s - c)]

squaring by sides, we have

100 = s(s - c) since s = 20,

s(s - c) = 100

20(20 - c) = 100

20 - c = 100/20

20 - c = 5

c = 20 - 5

c = 15

From (1),

s = a + c/2

a = s - c/2

= 20 - 15/2

= 20 - 7.5

= 12.5

Since a = b = 12.5

So, the length of a leg is 12.5 and its base is 15

Answer:

True

Step-by-step explanation:

m+m+y+(5a+3m)=5a+5m+y (combine like terms, we do 3+1+1=5 for the coefficent of m

~cloud

Answer:

Area of the sector in red = 177.87 cm²

Area of the sector in blue = 437. cm²

Step-by-step explanation:

Area of the sector = \(\frac{\theta}{360}(\pi )(r)^2\)

Area of the sector shaded in blue = \(\frac{256}{360}(\pi )(14)^2\)

                                                        = 437.87 cm²

Central angle formed by sector shaded in red = 360 - 256 = 104°

Area of the sector shaded in red = \(\frac{104}{360}(\pi )(14)^2\)

                                                      = 177.884

                                                      ≈ 177.88 cm²

Therefore, area of the sector shaded in red = 177.87 cm² and area of the sector in blue = 437.88 cm²

Given:

Find-:

How many times greater the radius of Saturn is than the radius of Earth

Explanation:-

Let "x" times greater than the radius of Saturn is than the radius of Earth

So,

So Saturn's radius is 9.407 times greater than the radius of the earth.

The value of the arcsin of 3 is 90 - 100.998i

From the question, we are to determine the inverse sine or arcsine of the given number

The given number is 3

All the values for the sine of angles are less than or equal to 1

That is,

Given an angle θ,

sinθ ≤ 1

From this, we can infer that the arcsine of 3 will be an imaginary number.

The arcsine of 3 is

sin⁻¹(3) = 90 - 100.998i

Hence, the value of the arcsin of 3 is 90 - 100.998i

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Then , r ≈ 1.10 inches to the nearest hundredth. So, the radius of the cone is approximately 1.10 inches.

First, let's clarify the correct formula for the volume of a cone, which is V = 1/3 * pi * r^2 * h, where V is the volume, r is the radius, and h is the height.

Given the height (h) of 4 inches and the volume (V) of 13 cubic inches, we can use this formula to find the radius (r). Plugging in the given values, we get:

13 = 1/3 * pi * r^2 * 4

To find the radius, follow these steps:
1. Divide both sides by 4: 13/4 = (1/3 * pi * r^2)
2. Multiply both sides by 3: 39/4 = pi * r^2
3. Divide both sides by pi: (39/4)/pi = r^2
4. Take the square root of both sides: r = sqrt((39/4)/pi)
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The solution to the system of equations is x = 5 and y = -1.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation 2x - 6y = 16 and x + y = 4

Let's start with the second equation:

x + y = 4

We can solve for one of the variables, say y, by subtracting x from both sides:

y = 4 - x

Now we can substitute this expression for y into the first equation:

2x - 6y = 16

2x - 6(4 - x) = 16

Expanding and simplifying, we get:

2x - 24 + 6x = 16

Combining like terms, we get:

8x - 24 = 16

Adding 24 to both sides, we get:

8x = 40

Dividing both sides by 8, we get:

x = 5

Now we can substitute this value of x into either of the original equations to find y. Let's use the second equation:

x + y = 4

5 + y = 4

Subtracting 5 from both sides, we get:

y = -1

Therefore, The solution to the system of equations is x = 5 and y = -1.

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