decimal numbers are written by putting digits into place-value columns that are separated by a decimal point. express the place value of each of the columns shown using a power of 10.
Hundreds:
Tens:
Ones:
Tenths:
Hundreths:
Thousandts:
Ten-thousandts:

Answer: $1,200 + 5.5% + $45,000= 46200.055 or 46200

Step-by-step explanation: All you have to do is just add because if you read the text it has a key word total.

Caleb has a guaranteed minimum salary of $1,200 per month, or 5.5% of his total monthly sales (as commission), whichever is higher. Last month, his total sales were $45,000. What was his gross pay?​

2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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Answer: 2.5 lbs

Step-by-step explanation: Divide 40 by 16 to get the weight she needs.

The greatest possible value of x is approximately 4.24. To find the greatest value of x, we need to use the fact that angle AC is not an obtuse angle. This means that angle ABC must be acute.

Looking at the diagram, we can see that x is the length of side AB, and we know that the length of side BC is 3. To find the greatest value of x, we need to maximize the length of side AC.

We can do this by drawing a perpendicular line from point B to side AC, creating a right triangle with sides of x and y (where y is the length of the perpendicular line). Using the Pythagorean theorem, we can find the length of side AC:

AC = √(x^2 + y^2)

To maximize AC, we need to maximize y. We know that angle ABC is acute, so the perpendicular line must be inside the triangle. This means that y is less than 3.

To find the greatest possible value of x, we can use the fact that AC is not an obtuse angle. This means that angle BAC must be acute. We know that angle ABC is acute, so angle BCA must be obtuse.

Using the law of cosines, we can find the cosine of angle BAC:

cos(BAC) = (3^2 + AC^2 - x^2) / (2 * 3 * AC)

Since angle BCA is obtuse, cosine is negative. We want to maximize AC, so we want to minimize the absolute value of cosine.

The smallest absolute value of cosine occurs when cos(BAC) = -1, which means:

3^2 + AC^2 - x^2 = -2 * 3 * AC

Simplifying, we get:

AC^2 + 6AC + x^2 - 9 = 0

This is a quadratic equation in AC. Solving for AC using the quadratic formula, we get:

AC = (-6 ± √(36 - 4(x^2 - 9))) / 2

Simplifying further:

AC = -3 ± √(x^2 - 15)

Since we want to maximize AC, we take the positive square root:

AC = -3 + √(x^2 - 15)

We know that y is less than 3, so:

√(x^2 - 9) < 3

x^2 - 9 < 9

x^2 < 18

x < √18

Therefore, the greatest possible value of x is approximately 4.24.

Since the diagram of triangle ABC is not provided, I will provide a general explanation using the terms you mentioned.

In triangle ABC, angle AC is not an obtuse angle. This means that angle AC is either an acute angle (less than 90 degrees) or a right angle (90 degrees). To find the greatest value of x, we will assume that angle AC is a right angle.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's label the sides of triangle ABC as follows: side a (opposite angle A), side b (opposite angle B), and side c (opposite angle C). Since angle AC is a right angle, side c (AC) is the hypotenuse.

The greatest value of x is achieved when side a and side b are as close in length as possible without violating the Triangle Inequality Theorem. Therefore, the greatest value of x is when a + b > c and a - b < c, which maximizes the difference between the two shorter sides of the triangle.

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It can be expected that the spinner will land on a multiple of 3 approximately 12.6 times when spun 42 times. Since we cannot have a fraction of a spin, we can expect it to land on a multiple of 3 about 12 times.

To determine how many times the spinner can be expected to land on a multiple of 3 when spun 42 times, we need to consider the probability of landing on a multiple of 3 on each spin.

Out of the 20 equal sections on the spinner, the numbers that are multiples of 3 are 3, 6, 9, 12, 15, and 18. There are six multiples of 3 in total.

The probability of landing on a multiple of 3 in one spin is given by the ratio of the favorable outcomes (multiples of 3) to the total outcomes (20 sections).

Probability of landing on a multiple of 3 = (Number of favorable outcomes) / (Total number of outcomes)

= 6 / 20

= 0.3

Therefore, the probability of landing on a multiple of 3 in one spin is 0.3 or 30%.

To find the expected number of times the spinner will land on a multiple of 3 in 42 spins, we multiply the probability of each spin by the total number of spins:

Expected number of times = (Probability of landing on a multiple of 3) * (Number of spins)

= 0.3 * 42

= 12.6

Therefore, it can be expected that the spinner will land on a multiple of 3 approximately 12.6 times when spun 42 times. Since we cannot have a fraction of a spin, we can expect it to land on a multiple of 3 about 12 times.

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Proving the statements by mathematical induction: (a) $\forall\text{ }n\in\text{ N},\sum_{i=1}^{n}(2i-1)^{2}=\frac{3n(2n+1)(2n-1)}{3}$. (b) For all integers $n\geqslant 3,$ $n^{2}\geqslant 2n+1$.Part a Consider $\sum_{i=1}^{1}(2(1)-1)^{2}=\frac{3\cdot 1(2\cdot 1+1)(2\cdot 1-1)}{3}$$\implies 1=1$ (true).

Suppose that

$\sum_{i=1}^{k}(2k-1)^{2}=\frac{3k(2k+1)(2k-1)}{3}$.

Consider the case where $n=k+1$, then

:$$\sum_{i=1}^{k+1}(2i-1)^{2}=\sum_{i=1}^{k}(2i-1)^{2}+(2(k+1)-1)^{2}$$$$=\frac{3k(2k+1)(2k-1)}{3}+(2k+1)^{2}$$$$=3k(2k+1)(2k-1)+(2k+1)^{2}$$$$=3(2k+1)(k+1)(2k+1-1)$$$$=\frac{3(k+1)(2(k+1)+1)(2(k+1)-1)}{3}$$T

herefore, by mathematical induction, it holds that

$\forall\text{ }n\in\text{ N},\sum_{i=1}^{n}(2i-1)^{2}=\frac{3n(2n+1)(2n-1)}{3}$.

Part b Consider the case where $n=3$, we get $3^{2}\geqslant 2(3)+1$. Thus, for $n=3$, the inequality holds. Suppose the inequality holds for some integer $k\geqslant 3$, so $k^{2}\geqslant 2k+1$. Then for the case where $n=k+1$, we have

$(k+1)^{2}=k^{2}+2k+1\geqslant 2k+1+2k+1=4k+2\geqslant 2(k+1)+1$.$$\implies (k+1)^{2}\geqslant 2(k+1)+1$$Therefore, by mathematical induction, it holds that for all integers $n\geqslant 3,$ $n^{2}\geqslant 2n+1$ .

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The property of the triangle congruence state that a ≅ B then B ≅ A are:

The triangle is a polygon that has 3 edge and vertices. Triangle is one of the basic shape in the geometric. The area of the triangle is formulated as base of the triangle * height of triangle x 0,5. The value of three triangle edge degree is 180°.

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The probability P(z>0.46) for a standard normal random variable z is 0.8228 or 82.28%.

The probability P(z>0.46) for a standard normal random variable z can be found using the standard normal distribution table or a calculator with a normal distribution function.

Using the table, we can locate the value 0.46 in the first column and the tenths place of the second column. This gives us a corresponding area of 0.1772. However, we need the probability of the right tail, which is 1-0.1772 = 0.8228.

Alternatively, we can use a calculator with a normal distribution function. The function requires the mean (which is 0 for a standard normal distribution) and the standard deviation (which is 1 for a standard normal distribution) and the upper bound of the integral (which is 0.46 in this case). Using this information, we can calculate the probability P(z>0.46) as follows:

P(z>0.46) = 1 - P(z<0.46)

= 1 - 0.6772

= 0.8228

Therefore, the probability P(z>0.46) is 0.8228 or approximately 82.28%.

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Answer:

-2 and -3

Step-by-step explanation:

a negative multiplied by a negative is a positive so -2 multiplied by -3 equals 6. And, -2 + -3 = -5

Answer:

c

Step-by-step explanation:

Answer:

C is corect answer to this exercice

Population in 2011 is 361.606 million, Population in 2025 is 438.094 million, Year when population will be 2 billion is 2136

What is Function?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given the function of the population = P(t) = 3111(1+0.0138)^t

1. Population of Indonesia in 2011

= P(11) = 311 (1.0138)^11

= P(11) = 361.606 million

2. Population of Indonesia in 2025

= P(25) = 311 (1.0138)^25

= P(25) = 438.094 million

3. Year when population is 2 billiion

2000 million= 311(1.0138)^x

x = 136 years approx. i.e. 2136

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Answer:

The horizontal cross-sections of the prisms at the same height must have the same area.

Step-by-step explanation:

A pyramid and a cone are both 12 centimeters tall and have the same volume.... What is the volume?

Volume is the quantification of the three-dimensional space a substance occupies.

We have to determine the true statement, and it is

The horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.

The horizontal cross-sections of the prisms at the same height must have the same area thus the correct option is A.

A pyramid and a cone are both 12 centimeters tall and have the same volume, we know that Volume is the quantification of the three-dimensional space a substance occupies.

We have to determine the true statement, and it is the horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.

If we cross-section the figures at the same height, it won't get the same shape but we should get the same area, as the area of the cross-section will be proportional to the base area, and the base area of both figures are the same.

Thus, the correct option is A.

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In linear equation, 17 seconds it will take to do a complete gaussian elimination of this size.

What are a definition and an example of a linear equation?

Given that your computer completes a 5000 equation back substitution in 0.005 seconds.

then here Work is: n = 5000 and its rate is = (n2) / 0.005 = 5000000000

and Given formula : The approximate operation counts = ((2n^3)/3) = (2.0 * (n3)) / 3.0 = 83333333333.33

then we can found time = operations / rate = 83333333333.33/5000000000 = 16.67 = 17 seconds

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Answer:

S = 3770.25 in^2

Step-by-step explanation:

20/15 = 4/3

5027/ 4/3 = 3770.25

Answer: 693 students are female

Step-by-step explanation: Calculating fourty-nine point five of one thousand, four hundred. How to calculate 49.5% of 1400? Simply divide the percent by 100 and multiply by the number. For example, 49.5 /100 x 1400 = 693 or 0.495 x 1400 = 693.

Answer:

707 females

Step-by-step explanation:

1400 x 0.495 = 693

Then,

1400 - 693 = 707

707 are girls.

Answer:

An equilateral triangle with a perimeter = 30 has each side = 10.

The height of an equilateral triangle = side * sqr root (3) / 2 =

10 * 1.7320508076 / 2 = 17.320508076 / 2 = .866025...

http://www.1728.org/triang.htm

Step-by-step explanation:

Answer:

this makes no sense

Step-by-step explanation:

thnx for the points

Answer:

The dollar bills d are the independent variable while the number of quarters q are the dependent variable

Step-by-step explanation:

Here, we want to state the variable that is dependent and the one that is independent

from the question, she has to put in dollars to get the quarters

so the number of quarters she gets is dependent on the number of dollars put into the machine

Thus, we can conclude that;

The dollar bills are the independent variable while the number of quarters q are the dependent variable

Independent variables are those who are not dependent on other variables. In contrast, their exists dependent variables whose value depends on some other variable(s)' value(s).

For given case, the number of dollar bills 'd' is independent variable with respect to variable 'q'.

The number of quarters 'q' is dependent variable.

Independent variables are those who are not dependent on other variables for their evaluation.

Those variables whose value is decided by the values of other variables. This shows that the variable in consideration is dependent on other variables for its values, thus called dependent variable.

If you see it carefully, you'll see that the quarters received from the change machine is depending on how much dollar bills you're feeding to the machine.

Thus, the value of 'q' is dependent on the value of d.

But since d takes its value independent of q (it exists before q exists and doesn't need q to get its values), thus, d is not dependent on q or is independent variable with respect to q(i said "with respect to q" since d might be dependent on some other variable which we do not know right know)

Thus:

The variable 'q' is dependent variable (depends on d)

The variable 'd' is independent variable with respect to 'q.

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The mean in minutes of the length of time given= 9.1

The formula used for the determination of mean when a frequency table is given is

= total/n

Where total = frequency×midpoint

n = 42

To calculate the total, the mid point of each length of time is determined as follows;

1+4/2 = 2.5 × 4 = 10

4+7/2= 5.5 × 8 = 44

7+10/2 = 8.5 × 14= 119

10+13/2 = 11.5× 9 = 103.5

13+16/2= 14.5×5 = 72.5

16+19/2= 17.5× 2= 35

Total= 10+44+119+103.5+72.5+35 = 384

Therefore mean = 384/42= 9.1

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Answer:

13.8 minutes

Step-by-step explanation:

If 3 liters came out it would take 2 minutes

if 4.5 liters came out it would take 3 minutes

Therefor the time is the volume divided by the rate

20.7 / 1.5 = 13.8

13.8 minutes

Answer:

15.5884572681

Step-by-step explanation:

The coefficients of the identical terms in both polynomials are added or subtracted to determine the sum or difference of two polynomials. For instance, when the coefficients of x and y are added together, the sum of (2x + 3y) + (4x + 9y) + (4x + 12y) is equal to 6x + 12y.

1. (2x + 3y) + (4x + 9y)

2x + 3y + 4x + 9y = 6x + 12y

2. (6s + 5t) + (4t + 8s)

6s + 5t + 4t + 8s = 10s + 9t = 14s + 9t

3. (5a + 9b) - (2a + 4b)

5a + 9b - 2a - 4b = 3a + 5b

4. (11m - 7n) - (2m + 6n)

11m - 7n - 2m - 6n = 9m - 13n

5. (m2 - m) + (2m + m2 )

m2 - m + 2m + m2 = 3m2 + m = 2m2 + m

Find each product.

1. (3x + 4y)(2x - 9y) 6x2 - 33xy + 8y2

2. (2a + 5b)(a - 7b) 2a2 - 19ab + 35b2

3. (7s - 4t)(s + 2t) 7s2 + 10st - 8t2

4. (4m + 6n)(m - n) 4m2 - 2mn + 6n2

5. (3x2 + 2x)(5x + 7) 15x3 + 31x2 + 14x

By adding or removing the coefficients of the identical terms in both polynomials, one can determine the sum or difference of two polynomials. Finding the similar terms in both polynomials is the first step in accomplishing this. The corresponding words, for instance, are x and y in the case of (2x + 3y) + (4x + 9y). The sum of the x coefficients is 2 + 4 which equals 6, and the y coefficients is 3 + 9 which equals 12. Because of this, the expression (2x + 3y) + (4x + 9y) = 6x + 12y. Two polynomials can be subtracted using the same procedure

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Fernando Designs is considering a project that has the following cash flow and WACC data.

The project's discounted payback can be calculated using the following formula:

PV of Cash Flows = CF / (1 + r)n

Where: CF = Cash Flow, r = Discount Rate n = Time Period

PV of Cash Flows = -$200,000 + $60,000 / (1 + 0.12) + $60,000 / (1 + 0.12)2 + $60,000 / (1 + 0.12)3 + $60,000 / (1 + 0.12)4 + $60,000 / (1 + 0.12)5= -$200,000 + $53,572.65 + $45,107.12 + $38,069.49 + $32,169.11 + $27,168.54= -$4,413.09

Discounted Payback Period (DPP) = Number of Years Before Investment is Recovered + Unrecovered Cost at the End of the DPP / Cash Inflow during the DPP= 4 + $4,413.09 / $60,000= 4.0736 ≈ 4.07 years.

Hence, the project's discounted payback is approximately 4.07 years (option E).

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Answer: You need more information to solve this.

Step-by-step explanation:

a= how many cards you have overall

B= how many blue cards there are

C= how many blue cards you have after you took one out

D= how many cards you have overall after you took one out

B/a*C/D= your answer

Answer:

A = 4π units²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius ) , then

A = π × 2² = 4π units²

a) To find the left-hand limit of (x) as x approaches 1, we consider the values of (x) for x approaching 1 from the left side. In this case, for x < 1, (x) = x. Therefore, the left-hand limit is:

lim x→1− (x) = lim x→1− x = 1.

b) To find the limit of (x) as x approaches 1, we consider the values of (x) at x = 1. Here, (x) = 3 when x = 1. Therefore, the limit is:

lim x→1 (x) = (x) = 3.

The left-hand limit of (x) as x approaches 1 is 1, and the limit of (x) as x approaches 1 is 3.

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The mean number of billionaires per state in these five Midwest states is approximately 10.2 (to the nearest tenth).

To find the mean number of billionaires per state in the given five states, we need to calculate the average by summing up the number of billionaires in each state and dividing it by the total number of states.

Given:

Illinois: 20 billionaires

Wisconsin: 10 billionaires

Michigan: 10 billionaires

Minnesota: 6 billionaires

Ohio: 5 billionaires

To find the mean number of billionaires, we sum up the number of billionaires in each state:

20 + 10 + 10 + 6 + 5 = 51

Next, we divide the total number of billionaires by the total number of states (which is 5):

51 / 5 = 10.2

Therefore, the mean number of billionaires per state in these five Midwest states is approximately 10.2 (to the nearest tenth).

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