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Answer:
y = 2
Step-by-step explanation:
Subtracting the second equation from the third gives ...
(2z +3x) -(2z -2x) = (-6) -(-6)
5x = 0
x = 0
Using this in the third equation, we have ...
2z +0 = -6
z = -3
And substituting these values into the first equation, we have ...
5y -3(0) -4(-3) = 22
5y = 10 . . . . . subtract 12
y = 2
__
The solution to the system is (x, y, z) = (0, 2, -3).
Statesville's population in 2010 was about 24,500, and was growing by about 1% each year. continues, what will Statesville's population be in 2019? [Round to the nearest person.]
Answer:
26,795 people
Step-by-step explanation:
P(x) = 24,500 × (1 + 0.01)^(2019-2010)
= 24,500 × (1.01)^9
= 24,500 × 1.0937
= 26,795 people
The required population of Statesville in the year 2019 will be 26,795.
Statesville's population in 2010 was about 24,500, growing by about 1% each year. Statesville's population be in 2019 to be determined.
The function which is in format f(x) = a^x where, a is constant and x is variable, the domain of this exponential function lies ( -∞, ∞ ).
Let Statesville's population in 2019 = x
Statesville's population in 2010 = 24500
Population growing by about 1% = 1/100
= 0.01
Difference in year n = 2019 - 2010
n = 9
Population in 2019,
x = 24500 * ( 1 + 0.01 )^9
x = 24500 * ( 1.01 )^9
x = 26, 795.295
To the nearest people x = 26,759
the population of Statesville in the year 2019 = 26,759
Thus, the required population of Statesville in the year 2019 will be 26,795.
Learn more about exponential function here:
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A computer disk that once sold for $2.25 now sells for 25% less. How much does the computer.
Answer:
$ 1.6875 or $1.69 or $1.70
Help me with moth of these questions please
Answer:
10. CD + DE = CE
11. BC + CE = BE
Step-by-step explanation:
10. CD and DE lie on a straight line, therefore, CD + DE = CE based on the segment addition postulate.
11. BC and CE lie on a straight line, therefore, BC + CE = BE based on the segment addition postulate.
In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC?
Answer:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
Step-by-step explanation:
Given
[tex]\triangle ABD \cong \triangle CBD[/tex]
Required
The congruent segments by CPCTC
From the question, we have:
[tex]\angle ADB \cong \angle CDB[/tex] --- given
[tex]\angle DBA \cong \angle DBC[/tex] --- given
Both triangles share a common side (length BD);
So, we have:
[tex]BD = BD[/tex]
Hence, the congruent segments are:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
Use the theoretical method to determine the probability of the outcome or event given below.
The next president of the United States was born on Monday
Answer:
[tex]\frac{1}{7}[/tex] probability that the next president of the United States was born on Monday
Step-by-step explanation:
A theoretical probability is given by the number of desired outcomes divided by the number of total outcomes.
The next president of the United States was born on Monday
Any person, including the next president of the United States, can be born on 7 possible days: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday or Saturday, one of which is Monday.
So
[tex]\frac{1}{7}[/tex] probability that the next president of the United States was born on Monday
Can you help please fellow people
Answer:
using 2 below points to draw:
(0, 7)
(3.5, 6)
Step-by-step explanation:
using
A factory produces 80 % round and 20 % square buttons. Suppose that 10 % of theround buttons and 50 % of the square buttons are red. What is the probability that arandomly selected red button is square?
Answer:
5/9
Step-by-step explanation:
Let the total number of buttons is x.
Round buttons = 80% of x = 0.8xSquare buttons = 0.2xNumber of red buttons:
0.1*0.8x + 0.5*0.2x = 0.08x + 0.1x = 0.18xNumber of red square buttons is 0.1x
Required probability:
P = 0.1x/0.18x = 10/18 = 5/9For the expression x-5, what would the value be if x=18?
Answer:
13
Step-by-step explanation:
Answer:
if x is 18 replace 18 where x is in the question so, it will be 18-5 = 13
If a line is equation 5 x + 6 Y is equal to 2 k together with the coronavirus access from a triangle of area 135 square unit.find the value of k.
Answer:
hdhdkdbddkdgsjshzcssjsn
verify that whether -2 and 3 are zeroes of the polynomial x^2-x=6
PLEASE HELP
Answer:
Both give remainder 0 for the polynomial
Step-by-step explanation:
p(-2) = (-2)² - (-2) - 6
= 6 - 6 = 0
p(3) = (3)² - 3 - 6
= 9 - 9 = 0
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
the sum of the square of the number and a second number is 42
Step-by-step explanation:
x+x squared =42. The square of the number is the number square. By my incredibly accurate guess and check strategy (works most of the time )6*6 = 36+6=42
determine the general solution of cos2X -7cosX -3=0
Answer:
x=2pi/3 +2pi n, 4pi/3 +2pi n for all integar of n.
Step-by-step explanation:
find the slope and y-intercept of line 3x +y -9=0
Answer:
x-intercept(s):(3,0)
y-intercept(s):(0,9)
Step-by-step explanation:
divide 64.050÷0.12. need whole process
Answer:
533.75
Step-by-step explanation:
Given the expression;
64.050÷0.12
Express first as a fraction
64.050 = 64050/1000
0.12 = 12/100
Divide both fractions
= 64050/1000÷12/100
= 64050/1000 *100/12
= 64050/10 * 1/12
= 64050/120
= 533.75
Hence the required answer is 533.75
An airplane can travel 350 mph in still air. If it travels 1995 miles with the wind
in the same length of time it travels 1505 miles against the wind, what is the speed of the wind?
Answer:
49 mph
Step-by-step explanation:
RT=D
T = D/R
[tex]\frac{1995}{(350 + x) } =\frac{1505}{350-x}[/tex]
1995(350-x) = 1505(350+x)
x=49
Determine if each proportion on the left is true or false
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Answer:
FalseTrueTrueTrueStep-by-step explanation:
An easy way to tell if the equation is true is to multiply it by the product of the denominators (cross multiply).
7×7 ≠ 12×4 . . . . proportion is False
9×8 = 36×2 . . . . proportion is True
8×9 = 24×3 . . . . proportion is True
5×104 = 8×65 . . . . proportion is True
She uses a scale of 1 centimeter to 6 inches
the scale drawing of the front face is
Answer:
change inches into centimeter and then divide it
hope this help
Select the correct answer. Simplify. (3x^2y^3/z^3)^3 A. B. C. D.
Answer:
options aren't given but the correct answer will be [tex]\frac{27x^6y^9}{z^9}[/tex]
Step-by-step explanation:
The simplified form of (3x²y³/z³)³ is 27x⁶y⁹/z⁹.
To simplify the expression (3x²y³/z³)³, we apply the rules of exponents. When we raise a power to another power, we multiply the exponents.
First, let's apply the exponent of 3 to each term inside the parentheses:
(3x²y³/z³)³ = 3³ × (x²)³ × (y³)³ / (z³)³
Simplifying further:
= 27 × x⁶ × y⁹ / z⁹
Therefore, the simplified form of (3x²y³/z³)³ is 27x⁶y⁹/z⁹.
This means that each term inside the parentheses is raised to the power of 3, resulting in the expression 27x⁶y⁹/z⁹.
The final expression represents the cube of the original expression, where each term is cubed individually. The exponents are multiplied by 3 to reflect this operation.
In summary, the simplified form is 27x⁶y⁹/z⁹.
To learn more about the exponents;
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Lorena and Julio purchased a home for $205,950. Their loan amount was $164,760, and the assessed value is now $200,500. Their tax rate is 1.5%. How much will their monthly taxes be?
Answer:
Monthly taxes = $250.63 (Approx.)
Step-by-step explanation:
Given:
Amount of purchase = $205,950
Loan amount = $164,760
Assessed value = $200,500
Tax rate is 1.5%
Find:
Monthly taxes
Computation:
Tax always calculated on Assessed value
Annual tax amount = 200,500 x 1.5%
Annual tax amount = 3,007.5
Monthly taxes = Annual tax amount / 12
Monthly taxes = 3,007.5 / 12
Monthly taxes = 250.625
Monthly taxes = $250.63 (Approx.)
i got some summer h.w it doesn't have a answer but like it asks for me to Create a table of x and y values that represents a proportional relationship. and i dont know how cause it wont let me draw a graph so i have to write something down apparently any help pls?
Answer:
So for example a graph in typed in word format could look like
Time Girls Boys
1 3 5
2 4 6
3 5 7
4 6 8
5 7 9
Not saying that this graph would be sufficient value wise for the answer, but this is how I would tackle it if I wasn't given the option to draw a graph.
Can someone please help?
Find the value of x for the right triangle.
Answer:
5
Step-by-step explanation:
cos60° = x / 10
10cos60° = x
10cos60° = 5
calculate the value of X in the diagram
Answer:
[tex]EA = \frac{21 \times 15}{7} = 45 \\ { \tt{ \frac{21}{7} = \frac{x}{45} }} \\ x = 135[/tex]
Which of the following best describes the data distribution of the histogram below?
A. Symmetric
B. Uniform
C. Bimodal
D. Unimodal
Answer:
D. Unimodal
Step-by-step explanation:
We can immediately tell the data is not symmetrical. That leaves B, C, D. The data of this histogram is also not uniform because the numbers vary- eliminating answer choice B. There are three modes of data distribution; unimodal, multimodal, and bimodal. The one demonstrated here is unimodal because there is one "hump" in the data distribution of the histogram and one mode.
The three modes of data distribution for visual context:
integrate G(x,y,z)=yz over the surface of x+y+z=1 in the first octant.
Parameterize the surface (I'll call it S) by
r(u, v) = (1 - u) (1 - v) i + u (1 - v) j + v k
with 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.
Take the normal vector to this surface to be
n = ∂r/∂u × ∂r/∂v = ((v - 1) i + (1 - v) j) × ((u - 1) i - u j + k) = (1 - v) (i + j + k)
with magnitude
||n|| = √3 (1 - v)
Then in the integral, we have
[tex]\displaystyle\iint_SG(x,y,z)\,\mathrm ds = \int_0^1\int_0^1 G((1-u)(1-v),u(1-v),v) \|\mathbf n\| \,\mathrm du\,\mathrm dv \\\\= \sqrt3 \int_0^1\int_0^1uv(1-v)^2\,\mathrm du\,\mathrm dv \\\\= \boxed{\frac1{8\sqrt3}}[/tex]
Alternatively, if you're not familiar with parameterizing surfaces, you can use the "projection" formula:
[tex]\displaystyle\iint_S G(x,y,z)\,\mathrm ds = \int_{S_{xy}}G(x,y,z)\sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}\,\mathrm dx\,\mathrm dy[/tex]
where I write [tex]S_{xy}[/tex] to mean the projection of the surface onto the (x, y)-plane, and z = f(x, y). We would then use
x + y + z = 1 ==> z = f(x, y) = 1 - x - y
and [tex]S_{xy}[/tex] is the triangle,
{(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}
Then the integral becomes
[tex]\displaystyle\int_0^1\int_0^{1-x}y(1-x-y)\sqrt{1+(-1)^2+(-1)^2}\,\mathrm dy\,\mathrm dx \\\\= \sqrt3\int_0^1\int_0^{1-x} y(1-x-y)\,\mathrm dy\,\mathrm dx \\\\= \frac{\sqrt3}{24} \\\\= \boxed{\frac1{8\sqrt3}}[/tex]
At a store sales tax is charged at a rate of 2% on the cost price of an item . the sales tax on a dress which cost $180 is
Answer:
$3.60
Step-by-step explanation:
100% = 180
1% = 180/100 = $1.80
2% = 1%×2 = 1.8×2 = $3.60
Suppose a life insurance company sells a $240,000 one-year term life insurance policy to a 19-year-old female for $240. The probability that the female survives the year is 0.999578. Compute and interpret the expected value of this policy to the insurance company. The expected value is $ (Round two decimal places as needed.)
Answer:
$138.72
Step-by-step explanation:
(1-0.999578)*$240,000 = $101.28
$240 - $101.28 = $138.72
solve the following by factolisation formula
1. x(2x+1)=0
2.4xsquere-11-3x=0
1.
X = 0
2x + 1 = 0
X = 0
X = - ½ (Because we brought the numbers from one side to the other)
2.
Not sure for number 2.
In how many ways can a sample of 6 keyboards be selected so that exactly two have an electrical defect
Answer:
15ways
Step-by-step explanation:
This is a combination question since combination has to do with selection. Hence the number of ways sample of 6 keyboards can be selected so that exactly two have an electrical defect is expressed as;
6C2 = 6!/(6-2)!2!
6C2 = 6!/4!2!
6C2 = 6×5×4!/4!×2
6C2 = 6×5/2
6C2 = 30/2
6C2 = 15
Hence this can be done in 15ways
In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.
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Answer:
x = 19
A = 30°
B = C = 75°
Step-by-step explanation:
In an isosceles triangle, the angles opposite the congruent sides have the same measures.
A = B
3x +18 = 7x -58
76 = 4x . . . . . . . . add 58-4x
19 = x . . . . . . . . . divide by 4
Then the equal angles measure ...
A = B = 3(19) +18 = 75
C = 2(19) -8 = 30
Angles A, B, C measure 75°, 75°, 30°, respectively.
_____
Alternate solution
The sum of angles in a triangle is 180°, so you could write ...
(3x +18) +(7x -58) +(2x -8) = 180
12x = 228 . . . . . add 48
x = 19 . . . . . divide by 12
