Last year, there were 113 pies baked for the bake sale. This year, there were k pies baked. Using k, write an expression for the total number of pies baked in the two years.

Answer:

the answer is c hope this helps have a nice day:)

Step-by-step explanation:

The exit temperature of the river water is 18°C.

The heat balance equation for a heat exchanger can be expressed as follows:

Q = m * Cp * ΔT

Where:

Q is the heat transferred

m is the mass flow rate of the fluid

Cp is the specific heat capacity of the fluid

ΔT is the temperature difference across the heat exchanger

In this case,  given the flow rate of the river water, which is 1.2 × 10^8 L/h. To use this value in the equation,  need to convert it to the mass flow rate. Since the specific gravity of water is 1 g/mL, we can assume that 1 L of water is equivalent to 1 kg. Therefore, the mass flow rate (m) is 1.2 × 10^8 kg/h.

The specific heat capacity of water (Cp) is approximately 4.18 kJ/kg°C.

There are also given the initial temperature of the river water, which is 18°C. And need to find the exit temperature.

Now, let's calculate the heat transferred (Q) using the heat balance equation:

Q = m * Cp * ΔT

Since the condenser is a low-temperature heat exchanger,  can assume that the temperature difference across the condenser is relatively small. Therefore, approximate ΔT as the difference between the initial temperature and the exit temperature.

Q = m * Cp * (T_exit - T_initial)

Substituting the given values into the equation:

Q = (1.2 × 10^8 kg/h) * (4.18 kJ/kg°C) * (T_exit - 18°C)

Simplifying the equation, we can cancel out the units:

Q = 5.016 × 10^8 (T_exit - 18)

Since the heat transfer (Q) is zero in a heat exchanger, set the equation equal to zero:

0 = 5.016 × 10^8 (T_exit - 18)

Solving for T_exit:

T_exit - 18 = 0

T_exit = 18°C

Therefore, the exit temperature of the river water flowing through the condenser is 18°C.

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Answer:

ok all I know is that #1 is 9+12 in simplified form and the value is 21 if x=1

Step-by-step explanation:

I'm sorry i don't know the other two:(

The remaining eigenvalue is λ = -0.007. Thus, the eigenvalues of A are:
X1 = 0
X2 = 0
X3 = -0.007
Arranging them in ascending order, we get:
X1 = -0.007
X2 = 0
X3 = 0

To find the characteristic polynomial of A, we first need to compute the determinant of (A - λI), where I is the identity matrix and λ is a scalar variable:

|0-λ  0.00 0.007|
|0.00 0-λ  0.00 |
|0.00 0.00 0-λ  |

Expanding along the first row, we get:

(0-λ) |0-λ  0.00| - 0.00 |0.00 0-λ | + 0.007 |0.0 0.00|
       |0.00 0-λ |            |0.0 0.00|                 |0.00 0-λ |

Simplifying, we obtain:

-λ³ + (-0.007)λ² = 0

Factoring out λ², we get:

λ²(-λ - 0.007) = 0

Therefore, the characteristic polynomial of A is:

p(A) = λ³ + 0.007λ²

To find the eigenvalues of A, we need to solve the equation p(A) = 0. We can see that one of the roots is λ = 0, which has multiplicity 2 (since it appears as a factor of λ² in the characteristic polynomial). To find the third eigenvalue, we need to solve:

λ³ + 0.007λ² = 0

Factoring out λ² again, we obtain:

λ²(λ + 0.007) = 0

Therefore, the remaining eigenvalue is λ = -0.007. Thus, the eigenvalues of A are:

X1 = 0
X2 = 0
X3 = -0.007

Arranging them in ascending order, we get:

X1 = -0.007
X2 = 0
X3 = 0

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Answer: The two numbers are 10 and 12.

Step-by-step explanation:

Let the two consecutive numbers are x and x +2.

As per given, we have

\((x+2)+3x=42\\\\\Rightarrow\ 4x+2=42\\\\\Rightarrow\ 4x=40\\\\\Rightarrow\ x=10\)

Smaller number = 10

Larger number = 10+2=12

Therefore, The two numbers are 10 and 12.

Answer:

whats this

Step-by-step explanation:

Based on the monthly data on the price of bitcoin, the average monthly growth rate can be calculated by taking the difference in price from the previous month and dividing it by the previous month's price. Using the average monthly growth rate, you can estimate the future value of your $1,000 Bitcoin investment.

Once this is done for each month, the resulting growth rates can be averaged to find the average monthly growth rate. As for the standard deviation of the monthly growth observations, this can be calculated using a statistical software or a calculator that has the capability to perform statistical calculations. Without the actual data, it is not possible to provide an exact answer to the question. However, it is important to note that investing in bitcoin can be volatile and unpredictable, so it is important to do thorough research and understand the potential risks before making any investment decisions. To estimate the average monthly growth rate and standard deviation of your Bitcoin investment, follow these steps:
1. Compile the monthly price data for Bitcoin.
2. Calculate the monthly growth rate for each month by using the formula: (Current Month Price - Previous Month Price) / Previous Month Price.
3. Add up all the monthly growth rates and divide the sum by the number of months in your data sample. This will give you the average monthly growth rate for Bitcoin.
4. To calculate the standard deviation, first find the variance. Subtract the average monthly growth rate from each individual growth rate, square the result, and find the average of these squared differences.
5. Finally, take the square root of the variance to get the standard deviation.

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The value of Erica's investment after 6 years is approximately $4,939.05.

To find the value of Erica's investment after 6 years, we can use the compound interest formula. The formula for compound interest is given as:

A = P\((1 + r/n)^(nt)\)

Where:

A is the final amount or value of the investment.

P is the initial principal or investment amount.

r is the annual interest rate (as a decimal).

n is the number of times the interest is compounded per year.

t is the number of years.

In this case, Erica's initial investment is $4000, the annual interest rate is 4% (or 0.04 as a decimal), and the investment is growing annually. Therefore, we have:

P = $4000

r = 0.04

n = 1 (since the interest is compounded annually)

t = 6 years

Plugging these values into the compound interest formula, we can calculate the final value of the investment:

A = $4000(1 + \(0.04/1)^(1*6)\)

A = $4000(1 + 0.04)^6

A = $4000(1.04)^6

Evaluating this expression, we find:

A ≈ $4,939.05

Therefore, the value of Erica's investment after 6 years is approximately $4,939.05.

This calculation assumes that no additional investments or withdrawals were made during the 6-year period and that the interest rate remains constant at 4% per year.

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For given linear equation x will be 5.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given linear equation is

15-x=10

x=15-10

x=5

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If 1 > 0, then the linear function of time e(yt) = 0 + 1t displays an upward trend.

In the given linear function of time e(yt) = 0 + 1t, the coefficient of the time variable (t) is positive (1), and it is stated that 1 > 0. This indicates that as time increases, the value of yt also increases. This pattern signifies an upward trend.

An exponential trend would require an exponential function with a positive exponent, which is not the case here. Similarly, a downward trend would require a negative coefficient for time, which is also not the case. A quadratic trend would involve a time variable raised to the power of 2, but the given function is a simple linear function with only a first-degree time variable.

Hence, based on the condition that 1 > 0, the linear function of time e(yt) = 0 + 1t displays an upward trend.

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Given:

Answer:

|x| = 25

Step-by-step explanation:

Original Equation:

|x - 4| = 21

Just add 4 to both sides

|x| = 25

Hope this helped :)

Answer:

the answer is 25 or -17

Answer:

Angle 1 and angle 2

x=9

Step-by-step explanation:

The angle pair is complementary since it makes a right angle, so you could technically name it anything like angle 1 and angle 2. You make the equation 4x+8+5x+1=90. Then, you combine like terms and get 9x+9=90. Then, subtract the 9 from 90, 81. 9x=81. Then, divide the 9 from 81. X=9.

Answer:

\(1 \frac{5}{8} > 1.6\)

Step-by-step explanation:

\(1 \frac{5}{8} \: ... \: 1.6\)

\( \frac{1 \times 8 + 5}{8} \: ... \: 1.6\)

\( \frac{8 + 5}{8} \: ... \: 1.6\)

\( \frac{13}{8} \: ... \: 1.6\)

\( \frac{13}{8} \: ... \: \frac{16}{10} \)

\( \frac{13 \times 5}{8 \times 5} \: ... \: \frac{16 \times 4}{10 \times 4} \)

\( \frac{65}{40} \: ... \: \frac{64}{40} \)

\( \frac{65}{40} > \frac{64}{40} \)

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We can conclude that  1.625 is greater than 1.6 (1.625 > 1.6).

So, to know that if 1⅝ > 1.6, calculate as follows:

Then: 1.625 > 1.6

Therefore, we can conclude that  1.625 is greater than 1.6 (1.625 > 1.6).

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Answer:

the answer and explanation is in the picture

please like and Mark as brainliest

hope this helps

75% of the beads are green in color.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Chase ordered a set of beads

He received 4,000 beads in all.

3,000 of the beads were green.

We need to find the  percentage of the beads were green of 4000.

x/100×4000=3000

40x=3000

Divide both sides by 40

x=75%

Hence, 75% of the beads are green in color.

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Answer:

25% is called a quarter of 900

Step-by-step explanation:

\({ \tt{25\% = \frac{25}{100} = \frac{1}{4} }} \\ \)

i think its

225 is percentage

25% is rate

and 900 is base

In linear equation, 4 cups of pasta are used per cup of sauce.

What are instances of linear equations?

We have,

3 cups of pasta = 3/4 cup of sauce

We need to make 3/4 cup of sauce as 1 cup of sauce.

Multiply 4/3 on both sides.

4/3 x 3 cups of pasta = 4/3 x 3/4 cup of sauce

4 cups of pasta = 1 cup of sauce

Thus 4 cups of pasta are used per cup of sauce.

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Answer:

x = 15

Step-by-step explanation:

Opposite angles are equal. Therefore, x = 60 - 45. Which is 15.

The Opposite angles are equal :—

So,

\(x = 60° - 45°\)

\(x = 15°\)

Answer:

18/25

Step-by-step explanation:

Total number of students = 23+14+10+3 = 50.

14 out of 50 are playing sport and taking a foreign language.

So the answer is (50 - 14) / 50

= 36/50

= 18/25.

=========================================================

Explanation:

The wording your teacher provided is a bit strange in my opinion. Though I think they are referring to the people who aren't taking both classes at the same time, but they could be taking exactly one class.

We have 23+14+10+3 = 50 students total and 14 of them are taking both classes. So 50-14 = 36 students are taking exactly one class, or they are taking neither of the classes.

This leads to a probability of 36/50 = (2*18)/(2*25) = 18/25 which points to choice B as the answer.

------------------

Side note:

If it asked "what is the probability that a student is not taking a sport AND not taking a foreign language?", then the probability would be 3/50 because there are 3 people not taking either class out of the 50 total. So the keyword "and" is the change made here, instead of the "or".

The probability of including k specified members in a random sample of size n without replacement from a population of size N can be calculated using the hypergeometric distribution.

The hypergeometric probability mass function is given by:

\(\[P(X = k) = \frac{{\binom{K}{k} \cdot \binom{N-K}{n-k}}}{{\binom{N}{n}}}\]\)

where:

- K is the number of specified members in the population.

- n is the size of the sample.

- k is the number of specified members in the sample.

- N is the total population size.

In this case, we want to find the probability that k specified members are included in the sample, so the probability can be calculated using the hypergeometric distribution formula.

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Answer:

Centre: \((\frac{1}{2} ,2)\)

Radius = \(2\)

Step-by-step explanation:

General formula for a circle: \((x-a)^2+(y-b)^2=r^2\), where \(r=\) the radius of the circle and \((a,b)\) is the centre of the circle.

To find the centre and radius of the circle we should re-write the given equation in the form of the general formula.

So, put the terms with the same variables together:

\(4x^2-4x+4y^2+16y+1=0\)

We can see that there is a common factor of \(4\), so let's simplify by dividing by \(4\):

\(x^2-x+y^2+4y+\frac{1}{4} =0\)

Here we can get it into the general formula by completing the square.

We do this by turning a quadratic with form \(ax^2+bx+c=0\) into the form \((x-d)^2-e+c=0\), where d is half of the coefficient of \(x\), e is \(d^2\) and c is the constant of the quadratic.

So let's re-write the equation of the circle:

\((x-\frac{1}{2} )^2-\frac{1}{4} +(y-2)^2-4+\frac{1}{4} =0\)

Simplify: \((x-\frac{1}{2} )^2 +(y-2)^2-4} =0\)

Now we can see that it's very similar to the general equation and all we have to do is bring the \(4\) over to the right side.

\((x-\frac{1}{2} )^2 +(y-2)^2} =4\)

So, now we can find the radius and centre.

\((a,b) = (\frac{1}{2} ,2)\)

\(r^2=4, r=2\)

Answer:

E and F

Step-by-step explanation:

(16/20 = 0.80)

14/8 = 1.75

9/10 = 0.90

8/5 =1.60

13/10 = 1.30

4/5 = 0.80

8/10 = 0.80

You have to to put the reduce the fractions and then put them in to decimal form then see if they are the same as the one you want it to be.

To calculate the annual deposit Randy Hill needs to make, we can use the formula for the future value of an ordinary annuity:

\[ FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \]

Where:

FV = Future value (desired retirement amount)

P = Annual deposit

r = Interest rate per period

n = Number of periods (years in this case)

Plugging in the given values:

FV = $1,500,000

r = 0.10 (10% per year)

n = 20

\[ $1,500,000 = P \times \left(\frac{(1 + 0.10)^{20} - 1}{0.10}\right) \]

Simplifying the equation:

\[ P = \frac{$1,500,000}{\left(\frac{(1 + 0.10)^{20} - 1}{0.10}\right)} \]

Evaluating the expression:

\[ P \approx $26,189 \]

Therefore, Randy Hill needs to deposit approximately $26,189 each year to reach his goal of $1,500,000 in 20 years. Therefore, the correct answer is c) $26,189.

Answer:

D. X=6.08, x=-0.58

Step-by-step explanation:

Given the rational expression

\(\frac{2x}{x-4}-\frac{2x-5}{x^2-10x+24} = \frac{-3}{x-6}\\\frac{2x}{x-4}-\frac{2x-5}{x^2-4x-6x+24} = \frac{-3}{x-6}\\\frac{2x}{x-4}-\frac{2x-5}{x(x-4)-6(x-4)} = \frac{-3}{x-6}\\ \\\frac{2x}{x-4}-\frac{2x-5}{(x-4)(x-6)} = \frac{-3}{x-6}\\Rerrange;\\\frac{2x-5}{(x-4)(x-6)} = \frac{2x}{x-4}+ \frac{3}{x-6}\\\frac{2x-5}{(x-4)(x-6)} = \frac{2x(x-6)+3(x-4))}{(x-4)(x-6)}\\\)

Cancel out the denominator on both sides

\(2x-5 = 2x(x-6)+3(x-4)\\Expand\\2x-5 =2x^2-12x+3x-12\\2x-5 = 2x^2-9x-12\\Equate \ to \ zero\\2x^2-9x-12-2x+5 = 0\\2x^2-11x - 7 = 0\\\)

Factorize

\(x = -(-11)\pm\frac{\sqrt{(-11)^2-4(2)(-7)} }{2(2)}\\x = 11\pm\frac{\sqrt{121+56} }{4}\\x = 11\pm\frac{\sqrt{177} }{4}\\x = 11\pm\frac{13.3 }{4}\\x = \frac{11+13.3}{4} \ and \ x = \frac{11-13.3}{4} \\x = 6.08 \ and \ - 0.58\)

Hence the required solution is X=6.08 and -0.58