A-18. Evaluate the expressions below for the given values.
a. 4d +3 if d=-1
b. x² + y2 if x = 7 and y = 5

Answer:

6 trips

Step-by-step explanation:

12 divided by 4 equals 3

18 divided by 3 equal 6

she will have to take six trips to drive 18 kilometers.

Answer: 12=2

x y =3 so 2x3+2x3=12 (2x3 = 6) so 6+6=2 6+6=12 so therefore 12=2

Answer:

4x^5 (7x^3+4)

Step-by-step explanation:

factor 4x^5 out of the equation

The width and height of the model are;

Width of model = 13.5 inches

Height of model = 2.25 inches

A scale model is defined as a physical model that is geometrically similar to an object. Scale models are usually smaller than large prototypes such as vehicles, buildings, or people. However, these scale models may be larger than small prototypes such as anatomical structures or subatomic particles.

Now, we are given that the dimensions of the new medical complex are;

Length = 400 ft

Width = 180 ft

Height = 40 ft

Thus, for a scale model with length of 30 in(2.5 ft) long, the scale factor is; Scale factor = 2.5/400

Thus;

Width of model = 180 * (2.5/400)

= 1.125 ft = 13.5 inches

Height = 30 * (2.5/400)

= 0.1875 ft = 2.25 inches

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Answer:

140°

Step-by-step explanation:

The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)

20 + 120 = 140

Answer:

y= 140

Step-by-step explanation:

first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.

Two triangles if the side between any two corners of one triangle cornor corresponds to the side between the corresponding two angles of the second triangle corner are said to be congruent by the ASA rule.

Create a point F' on ray AC such that BF' is equal to DE.

Angle BAF' = angle BAC, which equal to

angle EDF, AB = DE (given), so ∆ DEF

= ∆ ABP

Point F' has two possibilities: F' is equal to point C please.

If F' is not on C, line AC and ray BC intersect only at C, so F' is not on ray BC. Therefore the angle ABF' is not = the angle ABC. But this is a contradiction. Because angle ABF' = angle DEF (because ∆ DEF = ∆ ABF') and angle DEF = angle ABC (given). So, this case does not occur.

Therefore, F' = C must be true.

∆ABC = ∆ABF' = ∆DEF.

The reasonwe only need some parts to

prove congruence of triangles is that from these parts we can (in Euclidean geometry) derive other parts. This is because the basic axioms and definitions allow us to make "guesses" that turn out to be true every time.

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Answer:

a) 614.8km

b) $185.25

Step-by-step explanation:

25L = 265km

58L = \(\frac{58}{25}\) × 265km

       = 614.8km

To find the cost of the petrol used, we need to find the amount of petrol used for 1007km first. You already know 265km requires 25L of petrol based on the question.

265km = 25L

1007km = \(\frac{1007}{265}\) × 25L

             = 95L

You also know for 1L, the cost is $1.95. Thus, you can find the cost for 95L.

1L = $1.95

95L = 95 × $1.95

      = $185.25

The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188​), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).

To compute the probabilities:

P(X = 2): nb(2;6, 8/18)

P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)

P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)

To calculate the mean value and standard deviation of X:

Mean (μ) = r * (1 - p) / p

Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))

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Answer:

because he left you and your mom and now you are sad because you have no dad also yer dads j e r k

Step-by-step explanation:

Answer:

he is walking 5000000000000000000000000000% slower than a sloth

Step-by-step explanation:

sloths are slow

The given statements are True , False, False, True and True.

They are elaborated in points below:

(a) True:

Let x and y be even integers.

Then, by definition, x = 2a and y = 2b for some integers a and b.

Adding these equations, we get x + y = 2a + 2b = 2(a + b), which is an even integer. Therefore, the statement is true.

(b) False:

A counterexample is x = 1 and y = 3. Then x + y = 4, which is even, but neither x nor y is even.

Therefore, the statement is false.

(c) False:

A counterexample is x = -2 and y = 4. Then x² = (-2)²= 4 and y = 4² = 16, but x ≠ y. Therefore, the statement is false.

(d) True:

Since x < y, we have y - x > 0. Multiplying both sides by y + x, we get y² - x² > 0.

Rearranging the terms, we have x² < y².

Since x and y are both non-negative, we can take the square root of both sides to get x < y.

Therefore, the statement is true.

(e) True:

Since x and y are positive, we can take the square root of both sides of the inequality x < y to get √x < √y.

Then, multiplying both sides by √x + √y, we get x + 2√xy + y > x + y.

Since x + y is positive, we can divide both sides by x + y to get 1 + 2√(xy)/(x+y) > 1.

Rearranging the terms, we get √(xy) < (x + y)/2. Squaring both sides, we get xy < (x + y)²/4.

Simplifying, we get x²/4 - xy + y²/4 > 0. Rearranging the terms, we get (x - y/2)² > 0, which is always true since the square of any non-zero number is positive. Therefore, the statement is true.

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Answer:

a

Step-by-step explanation: bc i just did it

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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Answer:

It is not linear because it is not a consistant amount being removed from the y side

Step-by-step explanation:

Answer:

it is not linear.

Step-by-step explanation:

There is no sequential consistency (when graphed, the points do not form a line.

The product of the two given binomials can be expressed as the trinomial 2561104x³ + 684636x² + 87719x + 736, which is in its simplest form.

In this case, we will multiply the first two binomials (12x+1)(21x+1) and then multiply the second two binomials (65x+32)(56x+23). We will then multiply the two resulting expressions to get the final trinomial.

To multiply (12x+1)(21x+1), we can use the distributive property of multiplication, which states that a(b+c) = ab + ac. Therefore, we have:

(12x+1)(21x+1) = 12x(21x) + 12x(1) + 1(21x) + 1(1) = 252x² + 12x + 21x + 1 = 252x² + 33x + 1

Similarly, to multiply (65x+32)(56x+23), we have:

(65x+32)(56x+23) = 65x(56x) + 65x(23) + 32(56x) + 32(23) = 3640x² + 1495x + 1792x + 736 = 3640x² + 3287x + 736

Now, to find the product of the two expressions, we can multiply them using the distributive property again:

(252x² + 33x + 1)(3640x² + 3287x + 736) = 252x²(3640x²) + 252x²(3287x) + 252x²(736)

   • 33x(3640x²) + 33x(3287x) + 33x(736)

   • 1(3640x²) + 1(3287x) + 1(736)

Simplifying this expression by combining like terms, we get:

= 917280x⁴ + 1573824x³ + 684636x² + 87719x + 736

This final expression has four terms, but it can be simplified further to a trinomial by combining the first two terms using the associative property of addition. We have:

917280x⁴ + 1573824x³ + 684636x² + 87719x + 736 = (917280x⁴ + 1573824x³) + (684636x² + 87719x + 736) = 2561104x³ + 684636x² + 87719x + 736

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Complete Question:

Express the product of(12x+1)(21​x+1) and(65x+32)(56​x+23​) as a trinomial in simplest form

Another name for the regression line is the least squares line because it was chosen to make the sum of the squares of the differences between the observed y values ​​and the values ​​predicted by the line as small as possible.

A regression line (LSRL - Least Squares Regression Line) is a straight line that describes how the response variable y changes when the explanatory variable x changes. The line is the mathematical model used to predict the value of y for a given x.

Least squares is a form of mathematical regression analysis used to determine the line of best fit for a data set, providing a visual demonstration of the relationship between data points. Each data point represents the relationship between a known independent variable and an unknown dependent variable.

If the data shows a weak relationship between two variables, the line that best fits this linear relationship is called a least-squares regression line, and it minimizes the vertical distance of the data points from the regression line. The term "least squares" is used because it is the minimum of the sum of squared errors, also known as "variance". In regression analysis, the dependent variable is shown on the vertical y-axis and the independent variable is shown on the horizontal x-axis. These specifications form the equation for the line of best fit, which is determined by the method of least squares.

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Answer:

c

Step-by-step explanation:

c

Answer:

it is commutative property

Step-by-step explanation:

I read the rules for the commutative property

The multiple regression linear regression equation is:

i = -20000 + -60000*x1i + 40000*x2i

The multiple regression equation here will be of the form

i = a*x1i + b*x2i + c

Where i is the annual revenue

a is the coefficient of x1i which is distance from CBD

where b is the coefficient of x2i average price of a dish

C is the constant term.

Given that moving one mile away from the CBD x1i , the annual revenues will i will decrease by $60000. So, the coefficient of x1i, a is -60000

Given that increasing the average price of dish x2i by $1 , the annula revenue will i will increase by $40000. So the coefficient of x2i, b is 40000

The data shows  that the restaurant at the center of the CBD which means, x1i = 0 and giving away its food for free which means x2i = 0 is resulting in a loss of $20000. so the value of the constant term is c=20000.

so the multiple regression linear regression equation is:

i = -20000 + -60000*x1i + 40000*x2i

hence option A is correct

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analyzing problem

4 to the power of -5 is

1/4^5

which is

1/1024

Answer:

1/1024

Step-by-step explanation:

1) Since you are putting 4/1 to the power of a negative number, you'd have to flip the fraction first to get 1/4.

2) Now you need to put 1/4 to the 5th power, ignore the 1 on top, only put 4 to the 5th power.

3) The answer is now 1/1024.

Answer:

  see attached

Step-by-step explanation:

The attachment is my effort to complete the proof. It appears to me the idea is to show that B=3+1 and that 1=3+C. Then you substitute (3+C) for 1 and you've got the proof you want.

_____

The given statements and reasons are intended to give you enough clues that you can figure out the logic that is being used. Once you have done that, you fill in the missing details.

One of the mnemonic phrases that can help to remember the trig ratios of sine, cosine, and tangent is SOHCAHTOA. This phrase stands for Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent.

To create a story that explains this phrase, we can imagine ourselves at a beach party where we meet three new friends: Sally, Carl, and Tim.Sally loves to surf, so we can remember that the Sine ratio is Opposite over Hypotenuse. Carl loves to sit on the beach and tan, so we can remember that the Cosine ratio is Adjacent over Hypotenuse. Tim loves to play beach volleyball, so we can remember that the Tangent ratio is Opposite over Adjacent. We can imagine that these three friends are holding a sign that reads "SOHCAHTOA" to help us remember the ratios. Thanks to our new friends, we'll never forget how to find the trig ratios again!This story has a beginning, middle, and end.

The beginning introduces the mnemonic phrase, the middle explains how the story can help to remember the ratios, and the end provides a conclusion by stating that the storyteller will never forget the ratios thanks to the new friends they met. This is a creative and original way to remember the trig ratios and provides an entertaining way to learn a mathematical concept.

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The slope of a logarithmic graph depends on the type of logarithm used.

For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.

For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.

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Answer:

0.2

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

The correct solution for the equation \(x^5+10x^3+20x-4 = 0\) is \(x \approx 0.8432\).

Given expression:

\(x^5+10x^3+20x-4 = 0\)

To solve the equation \(x^5+10x^3+20x-4 = 0\) use the Newton-Raphson method, which is a form of linear approximation.

The Newton-Raphson method is an iterative numerical technique for finding approximations to the roots of a real-valued function.

The formula for the Newton-Raphson method is as follows:

\(x_{n+1} = x_n - \dfrac{f(x_n)}{f'(x_n)}\)

Where:

\(x_{n+1}\)   next approximation of the root.

\(x_n\) be the current approximation of the root.

\(f(x_n)\)  value of the function at \(x_n\).

\(f'(x_n)\)  be the derivative of the function at  \(x_n\).

For equation \(f(x) = x^5+10x^3+20x-4\) .

find the derivative of the function, \(f'(x)\):

\(f'(x) = 5x^4 + 30x^2 + 20.\)

Now, choose an initial guess for the root, \(x_0\) = 1.

Iteration 1:

\(x_1 = x_0 - \dfrac{f(x_0)}{f'(x_0)}\)

\(x_1 = 1 - \dfrac{(1^5 + 10(1^3) + 20(1) - 4)} { 5(1)^4 + 30(1)^2 + 20}\)

\(x_1 \approx 1 - \dfrac{7} {55}\)

\(x_1 \approx 0.8727\)

Iteration 2:

\(x_2 = x_1 - \dfrac{f(x_1)} {f'(x_1)}\)

\(x_2 \approx 0.8432\)

Iteration 3:

\(x_3 \approx 0.8432\)

The  value of x  is approximately \(0.8432\).

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James has 60 cars

john has 20 cars

this statement implies that James has 3 times has the number of cars jokhn hax

= 60/ 20

= 3

Step-by-step explanation:

Given equation

1. Rearrange it to make a the subject

2. Rearrange it to make b the subject

Answer:

see explanation

Step-by-step explanation:

(1)

P = 2a + 4b ( subtract 4b from both sides )

P - 4b = 2a ( isolate a by dividing both sides by 2 )

\(\frac{P-4b}{2}\) = a

and

(2)

P = 2a + 4b ( subtract 2a from both sides )

P - 2a = 4b ( isolate b by dividing both sides by 4 )

\(\frac{P-2a}{4}\) = b

Answer:

0.9999

Step-by-step explanation:

One way to calculate the probability that at least one of them need repairs is that we can calculate the opposite (none need repairs) and subtract that from 1 (100%).

The probability that a car does not need repairs is 0.2. To find the probability that six cars all fulfill this 0.2 probability, we can get \(0.2^{6} =0.000064\) . This is the probability that none require repairs. The opposite of this is that at least one needs repairs, so 1-0.000064 - 0.999936. Rounded to 4 decimal places, the probability is 0.9999

Answer: 3\(\sqrt{2}\)

Answer:

Step-by-step explanation:

area of card board=(6+4+6+4)×10+2×6×4

=200+48

=248 in²

Based on simulation, the estimated probability that the profit per unit will be less than $4 is 31.6%.

To estimate the probability, we can simulate the profit per unit using a random number generator with a normal distribution based on the given mean and standard deviation. We can then count the number of times the simulated profit per unit is less than $4 and divide by the total number of simulations to get the estimated probability. By repeating the simulation multiple times and taking the average, we can increase the accuracy of the estimate. In this case, the simulation result suggests that there is a significant chance that the project may not be sustainable if the profit per unit is less than $4.

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Integers are a type of number used in mathematics that represent whole numbers. They are typically denoted by the symbol Z, and can be positive, negative, or zero.

Integers do not include fractions or decimal points, so they are distinct from real numbers.

In Mathematics, integers are the collection of whole numbers and negative numbers.

18 matches 9

-14 matches 7

11 matches - 65

13 matches 65

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