Use inequality notation to describe the domain and range.

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

To learn more about : depth

https://brainly.com/question/1441593

#SPJ8

Answer:

(A) The probability that a male spent less than $210 online before deciding to visit a store is 0.0668.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is 0.0655.

(C) Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

Step-by-step explanation:

We are given that the reports indicate that men spend an average of $240 online before they decide to visit a store. If the spending limit is normally distributed and the standard deviation is $20.

Let X = the spending limit

The z-score probability distribution for the normal distribution is given by;

                           Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = mean spending limit = $240

           \(\sigma\) = standard deviation = $20

So, X ~ Normal(\(\mu=\$240,\sigma^{2} =\$20^{2}\))

(A) The probability that a male spent less than $210 online before deciding to visit a store is given by = P(X < $210)

     P(X < $210) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{\$210-\$240}{\$20}\) ) = P(Z < -1.50) = 1 - P(Z \(\leq\) 1.50)

                                                            = 1 - 0.9332 = 0.0668

The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is given by = P($270 < X < $300)

     P($270 < X < $300) = P(X < $300) - P(X \(\leq\) $270)

     P(X < $300) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{\$300-\$240}{\$20}\) ) = P(Z < 3) = 0.9987

     P(X \(\leq\) $270) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{\$270-\$240}{\$20}\) ) = P(Z \(\leq\) 1.50) = 0.9332

The above probability is calculated by looking at the value of x = 3 and x = 1.50 in the z table which has an area of 0.9987 and 0.9332 respectively.

Therefore, P($270 < X < $300) = 0.9987 - 0.9332 = 0.0655.

(C) Now, we have to find ninety percent of the amounts spent online by a male before deciding to visit a store is less than what value, that is;

         P(X < x) = 0.90     {where x is the required value}

         P( \(\frac{X-\mu}{\sigma}\) < \(\frac{x-\$240}{\$20}\) ) = 0.90

         P(Z < \(\frac{x-\$240}{\$20}\) ) = 0.90

In the z table, the critical value of z that represents the bottom 90% of the area is given as 1.2816, i.e;

                     \(\frac{x-\$240}{\$20}=1.2816\)

                     \(x-240=1.2816\times 20\)

                     \(x=240 + 25.632\)

                     x = 265.632

Hence, Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

The absolute minima of the function is at 12.85 and the absolute  maxima  is at 15.42.

Let the function be ,

f(t) = 5t + 5 cot( t/2 ).

first derivative of the function,

f'(t)

=  d/dt ( 5t + 5 cot(t/2))

= d/dt(5t) + d/dt ( 5 cot (t/2))

= 5 - 5/2cos^2(t/2)

Taking the derivative equal to 0,

f'(t) = 0

t = pi/2 , 3pi/2 f

On evaluating the equation wrt to obtained critical value,

we will get ,

absolute minimum value 12.85

absolute maximum value 18.56.

The extrema of a function are the maxima and minima. The maximum and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, over its full range.

The terms "local maxima" and "local minima" refer to additional maxima and minima of a function that are not its absolute maxima and minima.

To learn more about maxima and minima

brainly.com/question/13766213

#SPJ4

Answer:

$1,125 in interest.

Step-by-step explanation:

We need the formula of I = P * i * t where P is the total principle, i is the rate of interest per year, and t is the total time in years.

So we have

P = $7,500

i = 5%

t = 3 years

I = 7500 * 0.05 * 3

I = 1,125 (Interest)

Now we need to find the amount using A = P + I

A = 7,500 + 1,125

A = 8,625

Therefore $8,625 is our total. While our interest is $1,125.

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

Learn more about function here:

https://brainly.com/question/11624077

#SPJ8

Answer:

Step-by-step explanation:

This is a composite function, in which we will first evaluate the s function at a value of 2, then we will use that value in the t function.

s(2) = 5(2)+ 5 so

s(2) = 15. Now we evaluate the t function at 15:

t(15) = 3(15) + 4 so

t(15) = 49

Answer:

como pongo en español

Answer: $94

If Mary spent 58 dollars on dinner, and had $36 remaining, we add both.

58 + 36 = 94

The answer is 94, Mary had $94 dollars before she spent it on dinner.

Hope this helps you!

Answer:

94

Step-by-step explanation:

Value of base and hypotenuse of triangle are 9√3 and 18 respectively.

A right triangle is a triangle with one interior angle measuring 90 degrees, known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are known as the legs of the right triangle. The length of the hypotenuse can be found using the Pythagorean theorem,  that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Height of triangle=9

Base of triangle=y

Hypotenuse of triangle=x

Using trigonometric ratio

Sin30°=Height/Hypotenuse

½=9/x

x=18

Cos30°=Base/hypotenuse

√3/2=y/18

y=9√3

Hence, value of base and hypotenuse of triangle are 9√3 and 18 respectively.

To know more about angles, visit:

https://brainly.com/question/28451077

#SPJ1

Answer: 340

Step-by-step explanation:

Because if you multiply 0.34x 10 to the 3rd power you get 340

Hope This helped :))

Answer:

340

Step-by-step explanation:

I think

i think this question answer is 734.76cm^3

120 many combinations are possible.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

Consider a collection of three integers P, Q, and R. The number of ways that we may choose two numbers from each group is thus determined by combination.

It is represented as: \(^nC_r\)

where, n = total number of objects in the set

r = number of choosing objects from the set

Given that,

Cell Phone Models A particular cell phone company offers:

4 models of phones

each in 6 different colors

each available with any one of 5 calling plans

Thus, possible combination numbers are:

= (No. of models) × (No. of colors) × (No. of calling plans)

= (4)× (6)× (5)

= 120 possibilities

To know more about combinations refer to:

https://brainly.com/question/28065038

#SPJ1

Answer:

your mom

Step-by-step explanation:

u gonna fail just give up on life

After 8 years, she will have accrued 21,318.33 in interest (Where P = Principal, R = Rate of Interest, and T = Time).

Therefore,

A = P(1+r)^t

= $2628 (1 + 1.4/100) 8

= $2628 (1.014)8

= $2628 (8.112)

= 21,318.33

Hence, After 8 years, she will have accrued 21,318.33 in interest (Where P = Principal, R = Rate of Interest, and T = Time).

To learn more about Compounded Interest refer to:

https://brainly.com/question/24274034

#SPJ1

Answer:

45°

Step-by-step explanation:

59 + x + 80 + 49 + x = 180  the sum of the interior angles of a triangle equal 180  Combine the like terms

2x + 188 = 180  Subtract 1588 from both sides

2x = -8  divide both sides by 2

x = -4  Now plug this in for A

49 + x

49 -4 = 45

Based on a system of equations, a pound of apples costs $0.89.

A system of equations is two or more equations solved at the same time or concurrently.

A system of equations is also referred to as simultaneous equations.

                    Apples     Pears     Total Cost

Janice              2              3             $3.85

Lisa                  4              2             $4.94

Let the cost of a pound of apples = x

Let the cost of a pound of pears = y

2x + 3y = 3.85 ... Equation 1

4x + 2y = 4.94 ... Equation 2

Multiply Equation 1 by 2:

4x + 6y = 7.7 ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 6y = 7.7

-

4x + 2y = 4.94

4y = 2.76

y = 0.69

Substitute y = 0.69 in Equation 1 or 2:

4x + 2y = 4.94

4x + 2(0.69) = 4.94

4x + 1.38 = 4.94

4x = 3.56

x = 0.89

Learn more about systems of equations at https://brainly.com/question/13729904.

#SPJ1

Answer:

A = Length × breath

A = 3 × 7

A = a × 4

A = m × m

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

For more questions on simplified form of the expression:

https://brainly.com/question/28323654

#SPJ8

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

<95141404393>

Answer:

g=93 h=87 k=122 m=58

Step-by-step explanation:

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

√10/10

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate.  

Hope this helps!! Please consider marking brainliest! Have a good one!!

Answer:

√10 / 10

Step-by-step explanation:

1/√10

To rationalize the denominator we need to get rid of any √ in the denominator. we do this by multiplying both sides by the square root:

1/√10 * √10/√10 = √10 / 10

Answer:

1 pie

Step-by-step explanation:

1/3 + 1/3 +1/3= 3/3

simplified = 1/1 or 1 whole

Answer:

1 pie

Step-by-step explanation:

1/3 +1/3 + 1/3 =3/3 = 1

If the denominator is the same you can keep it the same and just add the numerators.

Hope this helps:)

Answer:

4(5)+4 = 24

4+5+4 = 13

4+(5+4) = 13

5+(4+4) = 13

I was having trouble understanding your question; 20+16 = 36. None of the expressions are equivalent to the sum

Step-by-step explanation:

To calculate the correlation coefficient (r) given SSxx, SSxy, and other information, we need to use the following formula:

r = √(SSxy / SSxx)

Given SSxx = 950 and SSxy = 205.2, we can substitute these values into the formula:

r = √(205.2 / 950)

Calculating the value:

r = √(0.216)

r ≈ 0.465

The correlation coefficient (r) is approximately 0.465.

Interpretation: The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the value of r = 0.465 indicates a positive linear relationship between the variables, but it's not a strong relationship. The closer the value of r is to 1 or -1, the stronger the relationship. Since r = 0.465 is relatively close to zero, it suggests a weak positive linear association between the variables being an analyzed.

hope it help you

The Pearson's correlation coefficient (r) based on given data is approximately 0.44, implying a moderate positive correlation.

The formula for calculating Pearson's correlation coefficient (r) in this case is given as: r = SSxy / sqrt(SSxx * SSyy). However, we don't have the value for SSyy directly, but we can calculate it. We know that SSyy = Σy² -(Σy)² / n. Given that Σy² is 2028 and Σy is 120 and number of samples n is 12, we can calculate SSyy as: SSyy = 2028 - (120)² / 12 = 52. Now, substitute SSxx = 950, SSxy = 205.2 and SSyy = 52 in the formula to find r: r = 205.2 / sqrt(950 * 52), giving us an r-value of approximately 0.44. This value of r suggests a moderate positive correlation between the variables in the dataset.

https://brainly.com/question/34388750

#SPJ3

Answer:

I  would say too broad.

Step-by-step explanation:

Answer: Your not alone!

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time