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1. What is the surface area of a rectangular prism with dimensions 15.5 inches by 6 inches by 4 inches?

2. The list represents the ages of students in a gymnastics class.

10, 10, 11, 12, 12, 13, 13, 14, 14, 15

If another student of age 15 joins the class, how is the mean affected?

3.What is the distance from (−5, −19) to (−5, 32)?

4.What is the perimeter, in centimeters, of a rectangle with vertices located at (−20, 14), (4, 14), (−20, −5), and (4, −5)?

5.What is the area of a right triangle with a base of 7 feet and a height of 16 feet?

6.A swimming pool in the shape of a rectangular prism has dimensions of 17.5 feet by 13 feet by 6 feet. What is the maximum amount of water that the pool can hold?

Answer:

2.48 x 10⁻² or 2.48 x 10^-2

Step-by-step explanation:

Alr, so 1.24 x 3.6/1.8 = 1.24 x 2 = 2.48

10² x 10⁻³ x 10⁻¹ = 10⁻²

Therefore, your answer is, 2.48 x 10⁻² or 2.48 x 10^-2.

Cheers!

Gradient-based optimization: This method is commonly used for more complex models, such as deep neural networks. The goal is to find the set of model parameters that minimizes a loss function.

Generally, There are a variety of ways to estimate mathematical models, depending on the type of model and the available data. Some common methods include:

Least squares: This method is commonly used for linear regression models, where the goal is to find the line of best fit through a set of data points. The least squares method finds the line that minimizes the sum of the squared differences between the predicted values and the actual values.

Maximum likelihood: This method is commonly used for probabilistic models, such as those used in statistics and machine learning. The goal is to find the set of model parameters that maximizes the likelihood of the observed data.

Bayesian inference: This method is similar to maximum likelihood, but it also incorporates prior knowledge or beliefs about the model parameters into the estimation process. This can be done by specifying a prior distribution over the parameters, which is then updated based on the observed data to give a posterior distribution.

These are just a few examples, and there are many other methods available depending on the type of model and the data available.

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Step-by-step explanation:

the conjugate is where we change the sign in the middle of the two terms

so we change the - to a +

x + 14 is our answer

Answer:

7

Step-by-step explanation:

77 divided by 11 is 7

Answer:

Step-by-step explanation:

B i guess

The function f( x ) = |cos( π x )| is differentiable everywhere on the interval ( 0 , 5 4 ) except at x= 1/2.

The correct option is (C).

In mathematics, a function is represented as a rule that produces a distinct result for each input x.

The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

Function, f( x ) = |cos( π x )|

Now, if we plot the graph for function f( x ) = |cos( π x )|.

The graph touches the x axis at two points, x= 0.5 and x= 1.25.

We know, the function touches at point on x- axis cannot be differentiable at that point.

Hence, except x= 0.5 the function is differentiable.

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As the trianlges are SAS congurant the side NK = 1.8.

What is congruent by ASA?

The Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

∠LJK=∠LMN

LM =4

MJ=2

LN=3.6

So, As the trianlges are SAS congurant the side NK = 1.8.

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The expression is 18/a

An algebraic expression can be described as mathematical expressions consisting of variables, coefficients, terms, factors and constants.

They are also made up of arithmetic operations, such as;

A quotient can be defined as a quantity determined  by the division of two numbers.

From the information given, we have that;

the quotient of 18 and a number a

This is represented as;

18/a

Hence, the representation is 18/a

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Using cosine law and sine law, the value of angle E and D are 14° and 35° and the length of side d is 19 units

The law of cosines is a mathematical formula used to calculate the measure of a third side of a triangle when two sides and the angle between them are known. It is also used to calculate the angles of a triangle when all three sides are known. The formula is: c² = a² + b² - 2ab cos(C).

In this given problem, triangle DEF can be;

f² = e² + d² - 2(e)(d) cos(F)

But we don't know the length of side d

Using sine law

f / sin F = e / sin E

25 / sin 131 = 8 / sin E

sin E = 8 * sin 131 / 25

E = 13.97°

E = 14°

Using sum of angles in a triangle

D + E + F = 180°

D = 180 - (14 + 131)

D = 180 - 145

D = 35°

Using cosine law;

d² = e² + f² - 2(e)(f)cos(D)

Substituting the values into the formula;

d² = 8² + 25² - 2(8)(25)cos(35)

d = 19

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Answer: 6

Step-by-step explanation:

Let's start by rewriting the expression. Essentially, this is asking us for 3 * (times) √4 (square root of four).

Now, we can solve √4. Since we know that 2*2 = 4. That means that 2² = 4, so essentially, if we take the square root of 4, we will get back to two.

Now, we can solve the rest: 3 * 2 = 6

In the end, 3√4 = 6. Hope this helps!

Hope it helps.

Please send your query through comment section.

The equation of a circle in general form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius.

To put the equation of circle in standard form x2+y2−4x+5y−3=0 you need to complete the square and

bring the equation to the form (x-a)^2 + (y-b)^2 = r^2

so the center of the circle is (-2,2) and the radius is 3

Answer:

according to BODMAS RULE

first step is to open the bracket , and solve

-82 - 6x - 12=  14x + 2 -6x -12

-82=14x + 2

-84 = 14x

x= -6

The standard deviation of the sampling distribution of sample means will be 0.6667.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Given information

μ= 38 and σ = 6; n = 81

The standard deviation of the sampling distribution is given as,

⇒ 6 / √81

⇒ 6 / 9

⇒ 0.6667

The standard deviation of the sampling distribution of sample means will be 0.6667.

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The speed of the boat in still water is 12mikes per hour and the speed of the current is 6milesper hour

Speed is defined as, the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

speed = distance /time

speed with downstream = 90/5 = 18miles per hour

speed against down stream = 90/15 = 6 miles per hour

represent the speed of the boat in still water by x and the speed of the downstream by y

therefore x+y = 18 equation 1

x-y = 6 equation 2

subtract equation 2 from 1

2y = 12

y = 12/2 = 6miles/hour

substitute 6 for x in equation 1

x + 6 = 18

x = 18-6 = 12 miles/hour

therefore the speed of the boat with in still water is 12miles per hour and the speed of the current is 6 miles per hour

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Answer:

-15,-14,-13

Step-by-step explanation:

Let x = the first integer

Let x + 1 = the second integer

Let x + 2 = the third integer

The addition of all three equal -42

x + x + 1 + x + 2 = -42  Combine like terms

3x + 3 = -42  subtract 3 from both sides

3x + 3 - 3 = -42 - 3

3x = -45  Divide both sides by 3

x  = -15

Check

-15 + -14 + -13 = -42

-42 = -42

Answer:

[tex] - 2 \sqrt{5} [/tex]

Step-by-step explanation:

[tex] \sqrt{20} - \sqrt{80} [/tex]

[tex]2 \sqrt{5} - 4 \sqrt{5} [/tex]

[tex](2 - 4) \sqrt{5} [/tex]

[tex] - 2 \sqrt{5} [/tex]

The function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given is a function under some transformations, 3 h(x) + 4 ;

If we consider h(x) as a parent function, then the result after the transformation is 3h(x)+4,

We see that, it is being multiplied by 3, we know that if a function is being multiplied by a number greater than 1 in transformation then it is dilated by a scale factor of the number, hence, the function is being dilated by a scale factor of 3.

Also, we see, here is an addition of 4, we know that, when function is added by a certain number then in the transformed function the function is shifted vertically and addition mean it shifted vertically upwards, sine, 4 is added to the function it means, the function is shifted 4 unit vertically upwards.

Hence, the function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

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Answer:

108

Step-by-step explanation:

average of first two multiples = 28

sum of first two multiples = 28 * 2 = 56

average of last two multiples = 44

sum of last two multiples = 44 * 2 = 88

average of all four multiples = ( 56 + 88 ) / 4 = 36

value of greater multiple = (88 + 56) - 36 = 108

Answer:

x<4

Step-by-step explanation:

_2*+13<_3 take-13 crossing the less sign acting same as equal then with number line, at point 13 go 3 steps to the left to get -16 then divide it by-2 to get x<4

The year-end balance interest rate for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00.

Interest is the cost of borrowing money or the amount of money that is earned on an investment. It is the amount of money paid by a borrower to a lender or earned by an investment, in exchange for the use of the lender's or investor's money.

Here,

To calculate the year-end balance for each principal using the given annual interest rates, we can use the formula:

End of year balance = Principal + (Principal x Interest rate x Number of years)

For a principal of $100.00, the annual interest rate is 5%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $100.00 + ($100.00 x 0.05 x 1) = $100.00 + $5.00 = $105.00

For a principal of $550.00, the annual interest rate is 2%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $550.00 + ($550.00 x 0.02 x 1) = $550.00 + $11.00 = $561.00

For a principal of $1,200.00, the annual interest rate is 7%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $1,200.00 + ($1,200.00 x 0.07 x 1) = $1,200.00 + $84.00 = $1,284.00

For a principal of $5,000.00, the annual interest rate is 11%, and the number of years is 1. So, the end-of-year balance is:

End of year balance = $5,000.00 + ($5,000.00 x 0.11 x 1) = $5,000.00 + $550.00 = $5,550.00

Hence, the year-end balance for a principal of $100.00 is $105.00, for a principal of $550.00 is $561.00, for a principal of $1,200.00 is $1,284.00, and for a principal of $5,000.00 is $5,550.00

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The missing vertices of the square are B(x, y) = (- 2, 1) and D(x, y) = (6, - 7), respectively.

Squares are quadrilaterals with four sides of equal length and four internal right angles. This kind of quadrilaterals have two diagonals perpendicular to each other. In this case, we know the coordinates of the endpoints of diagonal AC and we need to determine the location of points B and D.

This can be done by means of the following definition: A(x, y) = (a, b), C(x, y) = (c, d), B(x, y) = (a, d), D(x, y) = (c, b). If we know that a = - 2, b = - 7, c = 6 and d = 1, then the location of points B and D are, respectively:

B(x, y) = (- 2, 1), D(x, y) = (6, - 7)

Lastly, we graph the resulting figure.

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Answer:

1.6 g/cm³

Step-by-step explanation:

230g = 0.23 kg

0.23 kg x 8 = 1.84 kg

So, the weight of chutney in the 8 jars is 5.68kg - 1.84kg = 3.84kg or 3840g.

So, 1 jar weight is 3840g/8 or 480g of chutney.

Density = 480/300 or 1.6 g/cm³

Answer:

2.36

Step-by-step explanation:

5.68 kg into grams = 5680 and 300*8 is 2400

5680/2400 is 2.36

The graph that represents a geometric sequence is Graph A.

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the preceding one by a fixed, non-zero number called the common ratio.

Examples of geometric sequences include:

2, 4, 8, 16, 32, ... (common ratio of 2)

1/3, 2/3, 4/3, 8/3, ... (common ratio of 2/3)

5, -25, 125, -625, ... (common ratio of -5)

Geometric sequences have the property that the ratio of any two consecutive terms is always the same, and the quotient of any two consecutive terms is the common ratio.

This is shown only in the first graph so Graph A shows the geometric sequence.

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Answer:

Step-by-step explanation:

1. Important information: The original balance of the savings account is 400 dollars, x is the number of dollars added, and y is the total balance of the savings account.

2. I need to find: The total balance of the savings account (y).

3. What is the equation: y = 400 + x

4. Is the equation additive or multiplicative: Additive

5. I know my answer is correct because: I can use the equation y = 400 + x to calculate the total balance and then double-check my answer using mental math or by subtracting 400 from the total balance to find the amount added (x).

The change between outputs found by dividing one output by its previous output is called output elasticity.

What is output elasticity?

Output elasticity is defined as the division of change in output by change in input which is the previous output.

General, elasticity is a concept that is used to measure the change in the aggregate quantity demanded of a good or service in relation to price movements of that good or service.

A product is considered to be elastic if the quantity demand of the product changes more than proportionally when its price increases or decreases.

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Answer:

Step-by-step explanation:

a PERSON SHOULD SPEND AT LEAST 35 DOLLARS A WEEK ON COFFEE

Answer:

d=9

Step-by-step explanation:

d-1(-3)=12

d+3=12

subsctract 3 both sides

12-3=9

d = 9