Answer:
839.369863
(Might need to round it depending on what the question requests)
Step-by-step explanation:
Step 1: I divided $61,274 by 73.
Step 2: I multiplied 839.369863 by 73, and I got 61,274.
---------------------------------------------------------------
If it asks to explain say this:
"I divided the amount of money spent by the total amount of laptops bought, and i got 839.369863, To make sure it can be multiplied by 73 to get $61,274, I multiplied 839.369863 by 73 to get $61,274."
Hope this helps :)
Rhino poaching is a serious problem and has resulted in rhinos, particularly the black rhino, becoming an endangered species. Statistics suggest that there were 60 500 black rhinos at the beginning of 1970, but only 4 000 remained at the end of 2011. Determine the annual rate of depreciation that these statistics represent.
The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %
What is a rate of depreciation?The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.
The initial number of black rhinos in 1970 = 60,500
The number of black rhinos remaining in 2011 = 4,000
The annual rate of depreciation can be found using the formula;
[tex]FV = PV \cdot \left(1+\dfrac{r}{100} \right)^n[/tex]Where;
FV = The future value = 4,000
PV = The present value = 60,500
r = The annual depreciation rate
n = The number of years
[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]
[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]
[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]
The annual rate of depreciation is approximately 6.41%
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Find the slope of the line that passes through the pair of points.
(3, 1), (9, 1)
Answer:
gradient:
y2-y1/x2-x1
1-1/9-3
0/-6
= 0
someone please help!
in a hypothesis testing that you are conducting, you determine the confidence level needed is 99%. for you to reject the null hypothesis, the p-value needs to be:
The answer to the given question is <0.01.
What is confidence level?
The confidence level is the percentage of times we expect to get near to the same approximate if we run our experiment again or resample the population in the same way. The confidence level is the probability that the null hypothesis is true.
What is p-value?
P-value is the probability of getting the results you did, given that the null hypothesis is true.
When we are conducting a hypothesis testing and we determine the confidence level needed is 99%; then in order to reject the null hypothesis, the p-value needs to be below 0.01 (<0.01).
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What are the two square roots of 1/121
Answer:
-1/11, +1/11
Step-by-step explanation:
You want the two square roots of 1/121.
Square rootA square root can be either positive or negative.
[tex]\pm\sqrt{\dfrac{1}{121}}=\pm\dfrac{1}{\sqrt{121}}=\boxed{\pm\dfrac{1}{11}}[/tex]
__
Additional comment
The √ symbol generally means the principal square root, the positive root. To get the negative root, we precede the symbol with a minus sign. So, both square roots are identified as ±√( ).
A city planner wants to build a road perpendicular to d street. What should be the slope of the new road?.
If a line's angle with the x-axis is then, that line's slope will be tanα, and the new road's slope will be tan(0) = 0.
D Street is depicted as a vertical line with a 90° angle of inclination in the accompanying figure. In other words, D Street has an infinite slope.
The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.
A horizontal line now has zero slopes.
The new road has a zero slope as a result.
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a parking garage charges the rates in the table below. what is the rate of change? don’t forget your units.
n is an integer greater than 1
Prove algebraically that 10 + [tex]n^{2}[/tex] - (n-2)[tex]^{2}[/tex] is always an even number.
Your final line must have, "always even" as part of the line.
The algebraic proof that 10+n²-(n - 2)² is always an even number is 2(5+(2n-2))
How to prove algebraically that 10+ n² - (n - 2)² is always an even number?To show that this will always give an even number, we need to express in a form that it is 2 multiplied by some positive integer
Given: n is an integer greater than 1, prove 10+ n² - (n - 2)² algebraically
10+ n² - (n - 2)² = 10+ ( n² - (n - 2)² ) (factorize difference of two squares)
= 10+(n-(n-2))(n+(n-2))
= 10+(n-n+2)(n+n-2) (simplify)
= 10+(2)(2n-2) (factorize)
= 2(5+(2n-2))
Therefore, due to the factor of 2, the given expression is always even for integer n
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Write the linear equation in the slope intercept form.
(-6,0); slope= 2/3
Answer:
Step-by-step explanation:
y=2/3x+4
Epsilon3 is an exoplanet with a mass of 9.43x10^27g. It has a radius of 7.6x10^8cm. What is the density of the planet? What is it made of?
The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.
How to get the density of the planet?Density is defined as the quotient between mass and volume.
Here we know that the mass is:
9.43*10²⁷g
And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:
V = 3.14*(3/4)*R³
Then in this case the volume is:
V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³
Then the density is:
D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3
For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)
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The map above is being reduced by a scale factor of 1/9 and printed for the subway
station. How many square inches will the new map take up?
O 315 square inches
O 72 square inches
24 square inches
O 35 square inches
Answer:
35 square inches
Step-by-step explanation:
21x15=315
315/9=35
Therefore, the answer is 35 square inches
Factor and solve f(x) = x³ + 8x² - 23x - 30 given the fact that f(3) = 0
The factored form of f(x) = x³ + 8x² - 23x - 30 is (x - 3)(x + 10)(x + 1).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given a polynomial f(x) = x³ + 8x² - 23x - 30.
If f(3) = 0 then x - 3 is one of the factors of the polynomial f(x).
∴ f(x) = f₁(x)(x - 3), where f₁(x) is a quadratic equation we obtain it by long division or synthetic division.
f₁(x) = x² + 11x + 10.
Now, x² + 11x + 10 = 0.
x² + 10x + x + 10 = 0.
x(x +10) + 1(x + 10) = 0.
(x + 10)(x + 1) = 0.
x + 10 = 0 Or x = 1 = 0.
x = - 10 Or x = - 1.
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Use the given vertices to graph quadrilateral TUVW and its image after a dilation centered at the origin with scale factor
k=2/3
T(9,-3), U(6,0), V(3,9), w(0,0)
Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.
As here we have scale factor=3>1.
Hence, the dilation changes the original will expand the original figure.
Hence, each of the coordinate of a figure get multiplied by 3.
Hence, the co
ordinates of the image are given as:
i.e. A(0,0) → A'(0,0)
B(2,3) → B'(6,9)
C(1,-2) → C'(3,-6)
D(-3,-3) → D'(-9,-9)
Step-by-step explanation:
List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The simplified form of the given fraction is, 2/3.
What is greatest common factor?
The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.
Consider, the given fraction [tex]\frac{48}{72}[/tex]
The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
So, from above the greatest common factor of 48 and 72 is 24.
Therefore,
[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]
Therefore, the simplified form of the given fraction is, 2/3.
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K =
√2abc
1 + a²-b(squared)+c² - 5b
If a = 4, b = -2 and c = -1
evaluate K
K=
Find the perimeter of the triangle
HELPPPPPP
Answer: 4x + 29
Step-by-step explanation: add the like terms together.
Answer:
39 inches
Step-by-step explanation:
the triangle has all equal angles
this means it is equilateral and this also means all the sides are equal
so take 2 sides and set them equal to each other to find x
21 - x = x + 5
now solve
add x to both sides
21 = 2x + 5
subtract 5 to both sides
16 = 2x
divide everything by 2
8 = x
now flip it
x = 8
plug this is to one of the equations and multiply that by 3
8 + 5 = 13
13 * 3 = 39
that is the perimeter
Encuentre dos números positivos cuyo producto es 25 y cuya suma es un mínimo. (Especifica el valor minimo y maximo si los dos valores no son lo mismo.)
The two positive numbers are 5 , 5.
Given:
Product of two positive numbers = 25
sum of these number is minimum.
Let a and b be the two positive numbers.
a*b = 25
b = 25/a
sum s = a+b
= a + 25/a
apply derivation on both sides.
ds/da = 1 - 25/[tex]a^{2}[/tex]= 0.
1 = 25/[tex]a^{2}[/tex]
a = [tex]\sqrt{25}[/tex]
a = 5 , -5
since given are positive numbers so 5 is considered.
b = 25/5
b = 5
Therefore the two positive numbers are 5 , 5.
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5
link
!!!
MULTIPLE CHOICE QUESTION
Find the distance between (-3,-4) and (2,8).
Hint: plot the points on the coordinate plane and
then use the Pythagorean Theorem.
The distance between points (-3,-4) and (2,8) is 13.
What is a right angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, or it follows Pythagoreans theorem.
The horizontal distance = 5
And the vertical distance = 12
The vertical and horizontal lines make a right angle when they meet,
To find distance between points, use Pythagoreans theorem,
(D)² = (5)²+(12)²
(D)² = 25 + 144
(D)² = 169
D = 13
The distance between points (-3,-4) and (2,8) is 13.
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If was asked to think of a number and multiply it by 2, could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, multiply it by 5 and subtract 3 from the result."
The algebraic expression of the mentioned statement will be 5x-3.
According to the question,
An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.
Let the unknown number be taken as x.
If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,
x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).
For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).
Hence, algebraically the final statement will be 5x -3.
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What is 12 = -4(-6x - 3)
Answer:
no solution
Step-by-step explanation:
12=-4(-6x-3)
12=24x+12
0=24x
Find the length of a using
the Pythagorean Theorem.
8
a
6
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Answer:5.3
Step-by-step explanation:
using the Pythagorean theorem 8²-6²=28 √28=5.3
5
Step-by-step explanation:
Pythagoras theorem states that
a²+b²=c²
therefore a²=b²-c²
a²=8²-6²
a=√8²-6²
=√64-36
=√28
=5.3 or approximately 5
PLSSSS HELPPPPP MEEE !!!!!
All the angles in a triangle add up to 180 degrees.
40 + x + (5x + 14) = 180
54 + 6x = 180
6x = 126
x = 21 degrees
Answer:
x=21
Step-by-step explanation:
a triangle adds up to 180 degree so to find x we will use the formula
(5x+14)+x+40=180
subtract 40 from each side so we have
(5x+14)+x=140
we have 2 terms with the same factor (x) so combine like terms
6x+14=140
subtract 14 from both sides
6x=126
divide both sides by 6
x=21
check your answer
5(21)+14
105+14=119
119+ 21+40=180
so x is equal to 21
Which expression is equivalent to
94
94
310
95
94
310
(9².3³) ²₂
Answer:
Step-by-step explanation: The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
What is an integer exponent?
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
The question is incomplete.
The complete question is attached in the picture, please refer picture.
We have an expression:
Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.
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in a particular chi-square goodness-of-fit test, there are eight categories and 825 observations. use the 0.10 significance level. a. how many degrees of freedom are there?
By probability , 7 is degrees of freedom are there .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.It is predicated on the likelihood that something will occur. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of getting a head is 1 in 2.825 Observations and 8 categories .
Degree of freedom = k - 1
df = 8 - 1
df = 7
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can anyone help?????
Answer: 0
Step-by-step explanation:
Since y is 2, and it’s being multiplied by 4, you have 8 - 8 which =0
Y=2
4(2) - 8
8-8
0
Answer:
0
Step-by-step explanation:
4y - 8
Given that,
y = 2
To find the value of given expression, replace y with 2 and solve the expression.
Let us solve it now.
4y - 8
4 × 2 - 8
8 - 8
0
The attendance at an amusement park in a month of july was 178,383.What is the attendance rounded to the nearest thousand
Answer:
178 000
Step-by-step explanation:
178 383 8 is in the thousands place...if the number next to it (3) is ≥ 5 round it up by 1 o/w leave it alone
Answer:
178,000
Step-by-step explanation:
It's 178,000 because the number in front of the 8 in 178,383 was under five so the number dropped.
2(20x8) + 2(20x3)+2(8x3)
Answer:
488
Step-by-step explanation:
2(20x8) + 2(20x3)+2(8x3)
Assuming the "x" is not a variable.
The answer is 488
However, if "x" is a variable. The equation would be
40x^8 + 56x^3
Answer:
488
Step-by-step explanation:
using BODMAS
METHOD 1.
[tex]2(20 \times 8) + 2(20 \times 3 + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) = \\ = 320 + 120 + 48 \\ = 448[/tex]
METHOD 2.
[tex]2(20 \times 8) + 2(2 \times 3) + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) \\ = 2(160 + 60 + 24) \\ = 2 \times 244 \\ =488[/tex]
this is my last question please help asap!!
The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
The correct option is (A).
What is the average rate of change of a function?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
Using function notation, we can define the Average Rate of Change of a function f from a to b as:
[tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]
The given function is [tex]g(x) = 5(2)^{x}[/tex],
Now calculating the average rate of change of function from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]
Now, calculate the average rate of change of function from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]
The jump from m = 10 to m = 40 is "times 4".
So option (A) is correct.
Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
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Select all equations that are equivalent to
(6x + 2)
3
-=2(3x +14)
(Select all that apply.)
(6x + 2)
3
(6x + 2) = 2 (3x+14)
2x+3=2-(3x +14)
=-3x-12
6x + 2 = -9x-36
(6x + 2)
3
= -3x+16
Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 , the correct option is (a) and (d) .
In the question ,
it is given that
the equation is (6x+2)/3 = 2 - (3x+14)
solving the brackets on the right side of the equation ,
(6x+2)/3 = 2 - 3x - 14
(6x+2)/3 = -3x - 12 ....option(a)
On Cross Multiplying , we get
6x + 2 = 3(-3x - 12)
6x + 2 = -9x - 36 ....option(d)
Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 .
The given question is incomplete , the complete question is
Using Simplification , Select all equations that are equivalent to
(6x+2)/3 = 2 - (3x+14)
(a) (6x+2)/3 = -3x-12
(b) (6x+2) = 2 - (3x+14)
(c) 2x + 2/3 = 2 - (3x+14)
(d) 6x+2 = -9x-36
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HALF SOLVED PLEASE HELP