In the World of Numbers, there are many number-machines, which work in the following way: the machine adds the two beginning digits of the number and replaces them by their sum. For example, beginning with the number 87312 and using six machines we obtain:

87312-15312-6312-912-102-12-3

How many such machines should be used in order to get to the number 450 from the number 900?

To evaluate the expression x² + 3x for x = 4, we simply substitute 4 for x and simplify and we get 28.

What is expression ?

An expression is a combination of values, variables, and operators that represent a specific computation or operation. Expressions can be used to perform various operations such as arithmetic, logical, relational, and more. The value of an expression is determined by evaluating the expression, which involves simplifying and reducing it to a single value. In programming, expressions are a fundamental building block, and are used to write algorithms and control the flow of execution of a program.

To evaluate the expression x² + 3x for x = 4, we simply substitute 4 for x and simplify:

x² + 3x = 4² + 3 * 4 = 16 + 12 = 28

So, when x = 4, the expression x² + 3x = 28.

Hence, after evalution of the expression we get the result 28.

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The transformation that is used to transform the figure P to figure Q is described by (b) (x, y) → (x+5, y+3).

The Transformation of the "figure P" being translated 5 units to the right and 3 units up to create the "figure Q" is called as a type of "translation" in the coordinate plane.

When we shift a point (x, y) by "a" units to the right and "b" units up, the new coordinates become as ⇒  (x + a, y + b).

The coordinates of "figure P" is translated 5 units to the right and 3 units up, that means we will use the rule (x,y) → (x+5, y+3) to describe the transformation.

Therefore, the correct transformation used is  (b) (x, y) → (x+5, y+3).

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The given question is incomplete , the complete question is

A "figure P" was translated 5 units to the right and 3 units up to create "figure Q". Which rule describes this transformation ?

(a) (x, y) → (x-5, y-3)

(b) (x, y) → (x+5, y+3)

(c) (x, y) → (x-3, y-5)

(d) (x, y) → (x+3, y+5)

Answer:

5.1

Step-by-step explanation:

11.5 + 5.6 + 8.8 = 29.5

31 - 29.5 = 5.1

Answer:

4cm

Step-by-step explanation:

∵∆DEF ~ ∆ABC，AB/AC =2/3，

∴DE/DF=2/3.

∵DF=6cm，

∴DE=6*2/3=4cm.

The system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

Equation modelling is the process of writing a given mathematical statement (or word problem) in the form of a mathematical equation for the correct analysis of the given problem (or situation).

Given is that Jordan's t-shirt business sells long sleeve shirts for $18 and short sleeve shirts for $13. He needs to make at least $350 to buy a new heat press machine.

Let {S} represent the short sleeves and {L} represents the long sleeves. So, we can model the equations as -

S + L < 30

13S + 18L ≥ 350

Therefore, the system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

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Answer: 38 degrees

Step-by-step explanation:

HZJ and FZG are congruent angles so then that means that they are the same 38 degrees.

Answer: The distance between Star B and Star C can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side). In this case, the lengths of the two shorter sides are the distances from Star A to Star B (50 lightyears) and from Star A to Star C (120 lightyears).

So, we have:

(Star B to Star C)^2 = (Star A to Star B)^2 + (Star A to Star C)^2

(Star B to Star C)^2 = 50^2 + 120^2

(Star B to Star C)^2 = 2500 + 14400

(Star B to Star C)^2 = 16900

Taking the square root of both sides:

Star B to Star C = √16900

Star B to Star C = 129 lightyears

So, Star B and Star C are 129 lightyears apart.

Step-by-step explanation:

The length of PC and GC is 4.4 and 6.6 respectively.

What is centroid of a triangle?

A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1

Given ABC is the triangle.

In which G, H, J are the midpoints on AB, BC, AC sides respectively.

Then, AH, CG, BJ are the medians and they are intersect at the point P.

P is the centroid of the triangle.

Given, GP =2.2 we have  to find the PC and GC.

We know that the centroid divided the median in 2:1 ratios.

i.e., AP:PH = CP:PG = BP:PJ = 2:1

We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]

⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.

Hence, the length of PC and GC is 4.4 and 6.6 respectively.

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If we multiply the values by 3 and then add 4 the new mean are 79 and and variance are 144.

Mean = E(x) = 25 , and variance = var(x) = 16 multiply by the value by 3 and add 4

mean = 3 x 24 + 4 = 79

Variance = 3^2 x 16 = 9 x 16 = 144

=> mean = 79 , variance = 144

Variance is a statistical measure that represents the degree of dispersion or variation in a set of data. It is the average of the squared differences between each value and the mean of the data set. The variance shows how spread out the data is and how much each value deviates from the average.

A high variance indicates that the data points are spread out over a wide range, while a low variance indicates that the data points are clustered around the mean. Variance is useful in various fields, including finance, engineering, and social sciences, where it is used to analyze data, test hypotheses, and develop predictive models. Standard deviation is a more intuitive measure of variation as it is expressed in the same units as the data, while variance is expressed in squared units.

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Complete Question: -

If we have a data set with a mean of 25 and a variance of 16, what are the new mean and variance if we multiply the values by 3 and then add 4?

A. Mean - 79, variance - 144

B. Mean - 79, variance - 48

C. Mean - 87, variance - 144

D. Mean - 87. variance - 48 ОООО

Answer:

433 1/8ft

Step-by-step explanation:

this is my answer

The fuel consumption per liter of Lilly's car is  12.5 kilometers per liter .

Average mileage The average mileage of a vehicle is the ratio of the distance traveled by the vehicle and the total amount of fuel used for that distance.

You can specify:

where (d) is the distance traveled and (n) is the fuel consumption.

Lily's car consumes 8 liters per 100km. This is your car's mileage or efficiency.

average mileage = 100/8 = 12.5 kilometers per liter

Therefore, the fuel efficiency in kilometers per liter of a Lily car with a fuel efficiency of 8 liters per 100 kilometers is 12.5 kilometers per liter.

Complete Question - Lily’s car has a fuel efficiency of 8 liters per 100 kilometers. What is the fuel efficiency of Lily’s car in kilometers per liter ?

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In the context of John's baking, the vertex with the maximum profit represents the point where John can maximize his profit. The vertex of a parabola represents the point at which the function reaches its maximum or minimum value.

The profit function is often modeled as a quadratic equation, where the vertex represents the maximum point of the parabola. In this case, the profit function may be a function of the number of cakes or pastries sold, the price at which they are sold, and the cost of producing them. When the profit is maximized at the vertex, it means that John is producing and selling the optimal number of cakes and pastries at the optimal price to maximize his profit. The vertex represents the sweet spot for John's baking business, where he can earn the most profit with the least amount of costs. Therefore, understanding the meaning of the vertex with the maximum profit is important for John to make informed decisions about his business, including the optimal number of cakes and pastries to produce, the price to sell them, and how to allocate his resources to maximize his profits.

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Answer:

Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]

Step-by-step explanation:

Let square side = [tex]a[/tex]

Area of square   [tex]A = a^2[/tex]

Given [tex]A = 81[/tex]  and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]

[tex]a = \sqrt{81} = 9\;in[/tex]

Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]

If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width

Perimeter P of rectangle = [tex]2(l + w)\\[/tex]

Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]

Given

[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]

[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]

Step-by-step explanation:

To find a percentage, it's the portion divided by the total. 100% represents the total between the children or adults respectively in the maintee and evening.

So, to answer, let's find the total of children and adults.

34+27 = 61 is the total for children.

38+46 = 84 is the total for adults.

Now, to find each percentage, take one of the numbers (Children-Maintee, Children-Evening) and divide it by the total we found.

34/61 = 0.557 or 55.7%

27/61 = 0.442 or 44.2%

I'm leaving it in fractional form in case you need a specific decimal answer.

As for adults, it's the same procedure.

38/84 = 0.452 or 45.2%

46/84 = 0.548 or 54.8%

Answer: B quadrant 2 or quadrant 3  

Step-by-step explanation:

The point (-1, 2) lies on the line 3x = 2x - 1.

The equation 3x = 2x - 1 can be simplified by subtracting 2x from both sides to get x = -1.

So the line passes through the point (-1, y) for any value of y.

To check which of the following points lie on the line, we can substitute the x and y coordinates of each point into the equation and see if it is true.

a) (0, -1)

3(0) = 2(0) - 1

0 = -1

This point does not lie on the line.

b) (-1, 2)

3(-1) = 2(-1) - 1

-3 = -3

This point does lie on the line.

c) (1, -4)

3(1) = 2(1) - 1

3 = 1

This point does not lie on the line.

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The population of the frogs will be double after 4 years when the current number of frogs were 100 and the annual rate of increment is 22%.

In the given question,

the current population of frogs are: 100

Annual rate of increase in population of frogs = 22%

Population required = double the current population = 2 x 100

                                                                                        = 200

Using the compound interest formula for amount, we can calculate the number of years in which the population of the frogs will be double:

Amount = principal ((1 + r%)^n) ,

here we will consider the amount to be population required, principal will be the current population, r is the annual rate of increment, and n is the time in years.

200 = 100 ((1 + 0.22) ^ n)

⇒ 200/100 = (1.22)^n

⇒ 2 = (1.22) ^ n

We plug digits in place of n and check for the closest result as 2.

We observe that (1.22)^4 = 2.2153 ≈ 2

Hence, we can say that the population of the frogs will be double after 4 years.

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Answer: x is anything from the set {2, 3, 5, 7, 11}

This is the list of primes between 1 and 11. The value 1 is not prime.

The systems of equations in slope intercept form is

y = -6x + 110

y = 9x + 54

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

As, We know Slope-intercept form is

y = mx + b

where b is the starting value and m is the change per day.

Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.

So, the Equation to show the Situation

y = -6x + 110

and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.

So, the Equation to show the Situation

y = 9x + 54

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Answer:

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Step-by-step explanation:

A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),

From the above data we can get,

k(x) = (x - 1)(x - 3)(x - 2i)

After expanding the equation ,

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Answer: 3/17 or 17.64%

Step-by-step explanation:

Just add everything (adds up to 17), then you put the color frequency number as the numerator of the fraction, then have the added up number as the denominator.

The required, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

Given: ABCD is a parallelogram. To prove: mZA + mZB + mZC + mZD = 360 degrees

A parallelogram is a quadrilateral consisting of pairs of parallel sides.

Here,
The proof you provided is correct! Here's a step-by-step explanation of the proof:

By the definition of a parallelogram, AD // BC and AB/DC.

Using AD as a transversal, ZA and ZD are same-side interior angles, so they are supplementary (meaning their measures add up to 180 degrees).

Using side AB as a transversal, ZB and ZC are same-side interior angles, so they are supplementary as well.

By the definition of supplementary angles, mZA + mZD = 180 degrees and mZB + mZC = 180 degrees.
Adding the two equations together, we get:

mZA + mZD + mZB + mZC = 180 degrees + 180 degrees

Simplifying the right side of the equation, we get:

mZA + mZB + mZC + mZD = 360 degrees

Therefore, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

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The system of linear equations represented in the graph have (b) ne solution at (2, −1)

From the question, we have the following parameters that can be used in our computation:

The graph

The graph represents two linear functions

The point of intersection of the linear functions represent the solution

In this case, the linear functions intersect at (2, −1)

Hence, it has one solution at (2, −1)

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Answer:

I picked "d. Infinitely many solutions" but it turned out to be wrong lol, so I'm guessing the person above is correct.

The most likely explanation for the inconsistency between the first and second studies is that the initial findings were a false positive, meaning that the effect observed was not actually present in the population being studied.

In the given scenario, the researcher tested a new laparoscopic treatment for chronic shoulder dislocation and found statistically significant results compared to an older treatment. This means that the difference between the two treatments was not due to chance and is likely to be a real effect.

However, a replication study failed to show statistical significance, which means that the difference between the two treatments could have been due to chance. This can happen even if the sample sizes were sufficient in all four studies. A lack of statistical significance in a replication study indicates that the effect observed in the first study may not be as strong or consistent as previously thought.

The fact that the third and fourth studies produced the same effects as the second could be attributed to random variation or other factors such as study design, sample selection, or measurement methods.

Statistical significance is a crucial concept in research as it helps to establish the credibility of a study's findings. However, it is important to understand that statistical significance alone does not necessarily mean that the effect observed is meaningful or important in practical terms.

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The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the sides of a right triangle.

The Pythagoras Theorem states that : in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of squares of lengths of other two sides.

Mathematically, the Pythagoras Theorem is written as:

⇒ c² = a² + b² ;

where c is = length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.

The Converse of Pythagoras Theorem states that : If in a triangle, the square of the length of the longest side is equal to the sum of squares of lengths of other two sides, then triangle is a right triangle.

Both the Pythagorean Theorem and its converse apply only to right triangles, which are triangles that have a right angle .

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The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality is -

10 - 1/2x < -18

Solve the inequality to get the value for x.

First collect all the like terms -

-1/2x < -18 + (-10)

Then use arithmetic operation of addition -

-1/2x < -28

Multiply (-1) to both the sides -

-1/2x × (-1) < -28 × (-1)

1/2x < 28

Then move the coefficient of variable to right hand side of the equation -

x < -1 / (2 × (-28))

Then use arithmetic operation of multiplication and division-

x < 1/56

Therefore, the inequality is 0 < x < 1/56.

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If one marble is drawn from a bag containing three red ones and one white one , then probability that it is a red one is 3/4 .

Total number of marbles in the jar is = 4 marbles ;

the number of red marbles in the jar is = 3 marbles ;

the number of white marbles in the jar is =  1 marble ;

The probability of drawing a red marble from the jar can be calculated as the number of red marbles divided by the total number of marbles in the jar:

⇒ P(red marble) = number of red marbles / total number of marbles

⇒ 3/4

⇒ 0.75

⇒ 75%

Therefore, the probability of drawing a red marble from the jar is 0.75 or 75%.

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The given question is incomplete , the complete question is

A jar contains four marbles: three red ones and one white ones , if one marble is drawn from the jar , find the probability that it is a red one ?

Answer:

14 bows

Step-by-step explanation:

.5 yards is need for one bow if you have 7 yards you have 14(.5) yards

easier way a half goes into 7, 14 times since 14 divide by two is 7

The profit of the company if the company has 1800 customers is 649124 dollars

What is profit ?

A monetary gain, specifically the sum remaining after expenses for purchasing, running, or producing an item have been deducted.

P = 8.5√c³  ------->(1)

c = 1800 customers = 18 hundreds

(1) => P = 8.5√(18)³

           = 8.5 √5832 ( cube of 18=5832

          = 8.5 * 76.3675

          = 649.124 thousands of dollars

( convert into dollars by multiplying by 1000)

          = 649124.025 dollars  

          ≈ 649124 dollars

The profit of the company if the company has 1800 customers is 649124 dollars

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Answer: 48148

Step-by-step explanation: