The sea turtle habitat at the zoo is made by connecting two large aquariums. The first aquarium is 6 m long, 4 m wide, and 2 m high The second aquarium is 8 m long 9 m wide and 3 m high how many cubic meters of space do the sea turtles have in their habitat

Answer: \(12m^2+19m-18\)

Step-by-step explanation:

Given

Speed of boat \(v=3m-2\ \text{knots per hour}\)

\(\text{time t= }4m+9\ \text{hours}\)

\(\Rightarrow \text{Distance =speed}\times \text{time}\)

\(\Rightarrow \text{Distance d=}(3m-2)\cdot (4m+9)\\\Rightarrow d=12m^2+19m-18\)

Answer:

(7,4)

Step-by-step explanation:

Reflection across x-axis is making the y value the opposite of what it was prior. (x, y)→(x,-y)

That is the formula.

(Pls mark me brainiest if it's correct :)

Yes, whole numbers are closed while adding. As a result, the assertion that is made is true.

In addition, the idea of a set, is being explored. Adding any two members of the set will result in a value that is also a member of the set if the set is closed.

In other words, addition is closed for the set of all numbers.

The addition of the set of positive integers is closed because the sum of any two integers is also an integer.

example,

let W be the set of whole numbers

let ,

a = 7 and b =78

=a+ b

= 7 + 78

=85  which is a whole number

Therefore a , b are closed under addition.

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Answer:

Step-by-step explanation:

B

B. 9

Step-by-step explanation:

35-25=10

65+10=75 (8x+3=75)

8x+3=75

8x=72

x=72/8

x=9

Step-by-step explanation:

(x - h)² + (y - k)² = r²

with (h, k) being the center and r the radius.

in our case the center is (1, 3), the radius is 3.

so, the right answer is the third answer option

(x - 1)² + (y - 3)² = 9

The contrapositive of the conditional statement is D. If the graph of two variables is not a linear function, then the two variables are not directly proportional.

"In the event that the graph of two variables fails to exhibit linearity, it can be inferred that the two variables are not directly proportional.

This contrapositive statement provides an alternative perspective on the relationship between variables and the nature of their corresponding graphs.

By examining the contrapositive, we employ an analytical approach that explores the logical implications arising from the negation of the original conditional statement. Consequently, if the graph of two variables deviates from the linear pattern, it leads us to the logical conclusion that the variables themselves are not directly proportional.

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The percentage of ball that hit into the outfield would be represented by the equation = 15/8 = X/100. That is A.

The total number of balls that that where present at the battling practice by Alexis = 15.

The number of balls that hit into the outfield = 8

The number of balls that hit outside the outfield = 15-8= 7

The percentage (x) of the balls that are outside the outfield;

X = 8/15 × 100/1

x ×15 = 8 × 100

15/8 = X/100.

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100 is the answerrrrrrrrrrrrrrrrrrr

60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

\(^{5} P_{3}\)

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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The work done by the gas during the isothermal expansion is 331.32 J.

Isothermal Expansion refers to a process in which the temperature of a system stays constant while the volume increases. In this process, an ideal gas expands from 1.1 m³ to 1.8 m³, and the gas constant is R = 8.314 J/(mol K).

The work done by the gas during the isothermal expansion can be calculated as follows:Answer:During an isothermal process, the change in internal energy of the system is zero since the temperature remains constant.

Therefore,ΔU = 0The first law of thermodynamics is given by:ΔU = q + w

where q is the heat absorbed by the system, and w is the work done on the system.Since ΔU = 0 for an isothermal process, the above equation reduces to:w = -q

During an isothermal process, the heat absorbed by the system is given by the equation:q = nRTln(V₂/V₁)Where, n is the number of moles, R is the gas constant, T is the temperature, V₁ is the initial volume, and V₂ is the final volume.

Substituting the given values, we have:q = (1 mol) × (8.314 J/(mol K)) × (293 K) × ln(1.8 m³ / 1.1 m³)q = 331.32 J

Therefore, the work done by the gas during the isothermal expansion is given by:w = -qw = -(-331.32 J)w = 331.32 J

Thus, the work done by the gas during the isothermal expansion is 331.32 J.

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If a tumor is injected with 0.2 grams of iodine-125, which has a decay rate of 1.15% per day. The  exponential model representing the number of grams f of iodine-125 remaining in the tumor after t days is: m = m0e^kt.

First is to use this formula to find the t day

t = - ln (2) / k

Where,

k = decay rate = 1.15% or 0.0115

Let plug in the formula

t = - In (2) / - 0.0115

t = 60.27

t = 60 (Approximately)

Now let make use of the exponential model to find the gram

m = m0e^kt

​where,

m0 =0.2 initial mass

t = 60 time in days

k = -1.15 / 100 = -0.0115 (continuous growth rate)

m0e^kt = 0.2×e^[-0.0115×60]

= 0.2×e^(-0.69)

= 0.100g

Therefore the exponential model is m = m0e^kt.

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

Explanation:

and so on.

We have the arithmetic sequence 50, 60, 70, ...

We'll use the formula below to also plug in n = 20 to determine how many seats there are in the 20th row.

\(a_n = a_1 + d(n-1)\\\\a_n = 50 + 10(n-1)\\\\a_{20} = 50 + 10(20-1)\\\\a_{20} = \boldsymbol{240}\\\\\)

There are 240 seats in the 20th row of the center section.

Answer:

Yes

Explanation:

To find our whether Marrissa's budget will be enough for the party, we need to find the linear equation relating the cost and the number of guests. The linear equation is the form

where y is the cost in dollars. m is the cost per guest, and b can be interpreted as additional charges for the party facility.

The cost per guest is given by the slope of cost vs. guest graph.

Let us pick two values (100, 1325) and (50, 725) and compute the slope:

With the value of slope m in hand, we now find b by using the values x = 100, y = 1325 (the choice of these values is arbitrary)

Hence, the equation relating the cost and the number of guests is

Now, for 75 guests the cost will be

Therefore, Marrissa's budget, which is $1200, is greater than the cost of the party, meaning it will be enough.

Answer:

Step-by-step explanation:

Good Question but i don't know

Answer:

4

Step-by-step explanation:

Answer:

carman and Zackery live the same distance away.

The different arithmetic progression is \(11, 18, 25\) and the rule is to add \(7\).

What is an arithmetic progression?

A series of numbers known as an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

We have,

                      \(8, 11, 13, 18, 25, 37\)

Given arithmetic progression is  \(8, 13, 18\)  and the constant difference is \(5\).

By using this phenomenon we can create new arithmetic progression like,

                                             \(11, 18, 25\)

Here the constant difference or rule is \(7\).

Hence the new and different arithmetic progression is \(11, 18, 25\).

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Answer:

3f + d or d +3f

The smallest number that is possible for Toby to make is 8.

Significant figures are used to establish the number which is presented in the form of digits.

Also significant digits in arithmetic convey the value of a number with accuracy.

Significant digits are the number of digits used to express a calculated or measured.

If Toby arranges the number cards shown to make a number that gives 8.3, the smallest number that is possible for Toby to make is determined as follows;

number arranged = 8.3

smallest number possible without affecting the original value = 8.0 (rounded to the nearest whole number).

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The defining characteristic of a representative sample is that it is selected in such a way as to assure that it accurately represents the larger population from which it is drawn.

In other words, a representative sample should possess similar characteristics, proportions, and attributes as the population it is intended to represent.

To achieve representativeness, the sample selection process should be carefully designed to minimize biases and ensure that every member of the population has an equal chance of being included in the sample. This typically involves using random sampling techniques, such as simple random sampling or stratified sampling, to eliminate any systematic patterns or favoritism in the selection process.

By obtaining a representative sample, researchers can make valid inferences and generalizations about the population based on the characteristics and findings observed in the sample. It allows them to draw conclusions that can be applied to the larger population with a certain degree of confidence.

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Answer:

c. 2(x-1)(x-4)

Step-by-step explanation:

c. 2(x-1)(x-4)

a = 3, b = 4, and c = 2

a + b = c

3 + 4 = 2

3a + 4b = 2c
       -4     -4
     3a = -6c
      3       3
       a = -2

3a + 4b = 2c
-3             -3
      4b = -1c
        4     4

The value of P in the expression \(x^2-10x+P=(x-A)(x-B)\) is 25

Given the expression \(x^2-10x+P=(x-A)(x-B)\)

To get the value of P, we will use the completing the square method;

Add the square of the half of the coefficient of x

Hence the complete quadratic expression will be \(x^2-10x + 25\)

Hence the value of P in the expression \(x^2-10x+P=(x-A)(x-B)\) is 25

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Answer:

Bacteria doubles every hour

Step-by-step explanation:

1 to 2

2 to 4

4 to 8

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The solution to the given differential equation, subject to the initial conditions, is y(x) = (x^2/10 + 1)ex/5.

To solve the differential equation by variation of parameters, we follow these steps:

1. Find the complementary solution (y_c) by solving the homogeneous equation (25y'' - y = 0). The characteristic equation is r^2 - (1/25) = 0, which gives us the solutions r = ±1/5. Therefore, the complementary solution is y_c = c1e^x/5 + c2e^(-x/5).

2. Next, we need to find the particular solution (y_p) by assuming a solution of the form y_p = u1(x)e^x/5. We substitute this into the original equation and solve for u1(x). Differentiating y_p twice, we find y_p'' = (2/25)u1 + (2/25)xu1' + xu1''.

Substituting these expressions into the original equation and simplifying, we get (2/25)u1(x) = xex/5. Solving for u1(x), we find u1(x) = (x^2/10) + 1.

3. The general solution is given by y(x) = y_c + y_p. Substituting the values of y_c and y_p, we have y(x) = c1e^x/5 + c2e^(-x/5) + [(x^2/10) + 1]ex/5.

4. Finally, we use the initial conditions y(0) = 1 and y'(0) = 0 to determine the values of c1 and c2. Plugging in these initial conditions and solving the resulting equations, we find c1 = 1 and c2 = -1.

Thus, the solution to the given differential equation, subject to the initial conditions, is y(x) = (x^2/10 + 1)ex/5.

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The given expression (3x²+x-1)/√x simplifies to √x(3x+1-1/x).

The given expression is given as follows:

(3x²+x-1)/√x

To simplify the expression (3x²+x-1)/√x, we can start by multiplying the numerator and denominator by √x.

This will allow us to eliminate the square root in the denominator and simplify the expression:

(3x²+x-1)/√x × √x/√x

= √x(3x²+x-1)/x

= √x(3x+1-1/x)

Therefore, (3x²+x-1)/√x simplifies to √x(3x+1-1/x).

We multiplied the numerator and denominator by √x to eliminate the square root in the denominator and then simplified the resulting expression by dividing the numerator by x.

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The complete question is as follows:

Solve this expression:

(3x²+x-1)/√x

The total sum of squares is 1870. (option c)

The slope of the regression equation is -0.667. (option a)

The Y-intercept is 100. (option c)

The sum of squares due to error is 1870. (option c).

The mean square error (MSE) is 935 (option d)

The coefficient of correlation is -0.2295 (option a).

In this case, we are given ΣY, which is the sum of all Y values, and n, which is the sample size. We can use these values to calculate Y₁:

Y₁ = ΣY / n

Plugging in the given values, we get:

Y₁ = 340 / 4 = 85

Next, we can use the formula for SST to calculate the total sum of squares:

SST = Σ(Y - Y₁)² = ΣY² - (ΣY)² / n

= 1974 - (340)² / 4

= 1870

Hence the correct option is (c).

The slope of the regression equation measures the change in Y for a one-unit increase in X. It is given by the formula:

b = Σ[(Y - Y₁)(X - x₁)] / Σ(X - x₁)²

where x₁ is the mean of X. In this case, we are given ΣX and n, which we can use to calculate x₁:

x₁ = ΣX / n = 90 / 4 = 22.5

We are also given Σ(Y - )(X - ), which is a term that appears in the numerator of the formula for b. To calculate b, we can plug in the given values:

b = Σ[(Y - Y₁)(X - x₁)] / Σ(X - x₁)²

= -156 / 234

= -0.667

Hence the correct option is (a).

The Y-intercept of the regression equation is the value of Y when X is 0. It is given by the formula:

a = Y₁ - bx₁

Using the values we have already calculated, we can find the Y-intercept:

a = Y₁ - bx₁ = 85 - (-0.667)(22.5) = 100

Hence the correct option is (c).

We can use this formula to calculate the predicted value of Y for each observation in the dataset. Then we can use the formula for SSE to calculate the sum of squares due to error:

SSE = Σ(Y - Ŷ)²

Using the given values, we can calculate SSE:

SSE = Σ(Y - Ŷ)²

= (98 - 93.5)² + (102 - 90.5)² + (94 - 88.5)² + (46 - 83.5)²

= 1870

Using the given values, we can calculate MSE:

MSE = SSE / (n - 2)

= 1870 / (4 - 2)

= 935

Hence the correct option is (d)

The coefficient of correlation measures the strength and direction of the linear relationship between X and Y. It is given by the formula:

r = Σ(X - x₁)(Y - Y₁) / √[Σ(X - x₁)²Σ(Y - Y₁)²]

Using the values we have already calculated, we can find r:

r = Σ(X - x₁)(Y - Y₁) / √[Σ(X - x₁)²Σ(Y - Y₁)²]

= -156 / √[234 * 1974]

= -0.2295

Hence the correct option is (a).

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