Answers
2. The given quadratic equation is in the general form:
ax² + bx + c = 0
therefore:
a = 2
b = -4
c = -3
The quadratic formula is thus:
[tex]x=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex]
Substituting the values found for a, b, and c:
[tex]x=\frac{-(-4)+\sqrt{(-4)^2-4(2)(-3)} }{2(2)}[/tex] and [tex]x=\frac{-(-4)-\sqrt{(-4)^2-4(2)(-3)} }{2(2)}[/tex]
Therefore x = 2.58, x = -0.58
3. Using the same method as above, first, bring all values to one side, leaving the RHS = 0
a = 1
b = 2
c = -1
The quadratic formula is thus:
[tex]x=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex]
Substituting the values found for a, b, and c:
[tex]x=\frac{-(2)+\sqrt{(2)^2-4(1)(-1)} }{2(1)}[/tex] and [tex]x=\frac{-(2)-\sqrt{(2)^2-4(1)(-1)} }{2(1)}[/tex]
Therefore, x = 0.41, x = -2.41
[tex]2 {x}^{2} - 4x - 3 = 0[/tex]
A Here ,
[tex]\boxed{a = 2 }\\\boxed{b = - 4} \\ \boxed{c = - 3}[/tex]
B Filling in the values of a , b and c in the Quadratic formula below , we get
[tex]x = \frac{- (b)\pm \sqrt{( {b}^{2}) - 4(a)(c) } }{2(a)} \\ [/tex]
C Simplifying each section , we get
[tex]x = \frac{ - ( - 4) + \sqrt{( { - 4}^{2} ) - 4(2)( - 3)} }{2 \times 2} [/tex]
or
[tex]x = \frac{ - ( - 4) - \sqrt{ {( - 4})^{2} - 4(2)( - 3) } }{2 \times 2} [/tex]
D Simplifying answers from Part C , we get
[tex]\boxed{x = \frac{2 + \sqrt{10} }{2}} \: \: \: \: or \: \: \: \: \boxed{ x = \frac{2 - \sqrt{10} }{2} } \\ [/tex]
Therefore ,
[tex]\boxed{x = 2.58} \: \: \: \: and \: \: \: \: \boxed{x = - 0.58}[/tex]
Thus , option A. is correct!_____________________________________
[tex] {x}^{2} + 2x = 1 \\ \implies \: {x}^{2} + 2x - 1 = 0[/tex]
A Here ,
[tex]\boxed{a = 1} \\ \boxed{b = 2} \\ \boxed{c = - 1}[/tex]
B Filling in the values of a , b and c in the Quadratic formula below , we get
[tex]x = \frac{- (b)\pm \sqrt{( {b}^{2}) - 4(a)(c) } }{2(a)} \\ [/tex]
C Simplifying each section , we get
[tex]x = \frac{ - (2) + \sqrt{ ({2}^{2} ) - 4(1)( - 1)} }{2 \times 1} [/tex]
or
[tex]x = \frac{ - (2) - \sqrt{( {2}^{2}) - 4(1)( - 1) } }{2 \times 1} [/tex]
D Simplifying answers from Part C , we get
[tex]\boxed{x = - 1 + \sqrt{2} } \: \: \: \: or \: \: \: \: \boxed{x = - 1 - \sqrt{2} }[/tex]
Therefore
[tex]\boxed{x = 0.41} \: \: \: \: or \: \: \: \: \boxed{x = -2.41 }[/tex]
Thus , option D is correct.hope helpful! :)
Related Questions
According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide. What is the approximate area of the park? Show your work.
Answers
The approximate area of Central Park is about 450 square blocks.
What is the approximate area of the park?The given dimensions of the park stated in the question are
Length of Central Park = 50 blocks
Width of Central Park = 9 blocks
The approximate area of Central Park is the product of its length and width:
So, we have
Area of Central Park = Length x Width
When the given values are substituted into the the equation mentioned above, we obtain the subsequent expression
Area = 50 * 9
Evaluate
Area = 450
Hence, the approximate area is about 450 square blocks.
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an ellipse has an equation equal to 9x^2-144x+16y^2+96y+495=0. Compute the eccentricity of the curve
Answers
An ellipse has an equation equal to 9x^2-144x+16y^2+96y+495=0, the eccentricity of the curve is √7/4.
To compute the eccentricity of the curve of an ellipse, we must first complete the square for both x and y terms to put the equation in standard form.
Complete the square for x terms:
9x²- 144x + 495 = -16y² - 96y
9(x² - 16x) + 495 = -16(y² + 6y)
9(x²- 16x + 64) + 495 - 9(64) = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y)
Complete the square for y terms:
9(x - 8)² + 39 = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y + 9) + 16(9)
9(x - 8)² + 39 - 16(9) = -16(y + 3)²
9(x - 8)² - 105 = -16(y + 3)²
Move constant term to the right side of the equation and divide by -105:
9(x - 8)² - 16(y + 3)² = 105
-9(x - 8)²/105 + 16(y + 3)²/105 = 1
(x - 8)²/(105/9) + (y + 3)²/(105/16) = 1
Identify the values of a^2 and b^2:
a² = 105/9
b² = 105/16
Compute the eccentricity using the formula e = √(1 - (b²/a²)):
e = √(1 - ((105/16)/(105/9)))
e = √(1 - (9/16))
e = √(7/16)
e = √7/4
Therefore, the eccentricity of the curve is √7/4.
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help a girl out ??? :)
Answers
We can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.What is exponential function?The exponential function is of the form -
f(x) = eˣ
Given is to write the exponential growth and exponential decay equation.
{ 1 } -
The general exponential growth equation is -
[tex]$f(x)=a(1+r)^{x}[/tex]
{ 2 } -
The general exponential decay equation is -
[tex]$\frac {dN}{dt}= -\lambda N[/tex]
Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.
Therefore, we can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.To solve more questions on functions, visit the link-
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Find the area of the circle which has a diameter 22 cm
Answers
Answer:
Exact form: 121π
Decimal form: 380.1327111...
Step-by-step explanation:
The area of the circle is given by the formula A = πr², where A is the area of the circle and r is the radius.
Given the diameter of 22cm, we know that the radius is 11cm, as the radius is half the diameter.
We can then put this into the formula to find the area of the circle:
A = πr²
A = π * 11²
A = 121π
Note that the answer here is given in terms of π so it can be expressed in its exact form, as 121π is an irrational number roughly equivalent to 380.1327111... The answer you need to provide will depend on whether the question asks for the exact form, or to a certain number of decimal places / significant figures. If it the latter, you can round off the decimal answer as appropriate.
Is 5x^2+y=0 a direct variation
Answers
No, 5x^2+y=0 is not a direct variation.
What is a direct variation?Direct variation is a relationship between two variables, x and y, where y is directly proportional to x, meaning that as x increases, y increases in proportion to x, and as x decreases, y decreases in proportion to x.
The equation 5x^2+y=0 does not satisfy this relationship since y is not directly proportional to x. As x increases or decreases, y may change in a non-proportional manner due to the presence of the constant term.
An example of a direct variation equation is y = kx, where k is a constant. In this equation, y is directly proportional to x, with a constant of proportionality k.
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A person places $741 in an investment account earning an annual rate of 5.8%, compounded continuously. Using the formula =V=Pe^rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years.
again yea im putting my hw here
Answers
Step-by-step explanation:
Using the formula V = Pe^(rt), we have:
P = $741
r = 0.058 (since the interest rate is 5.8%)
t = 13
So, V = 741e^(0.05813) = $1613.87 (rounded to the nearest cent)
Therefore, the amount of money in the account after 13 years is $1613.87.
Answer:
Step-by-step explanation:
cylinder has a height of 16 centimeters and a radius of 4 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
By answering the above question, we may state that As a result, the cylinder cylinder's volume is around 804.23 cubic centimetres.
what is cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most fundamental curved geometric shapes. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinder" is also used to refer to an infinitely curved surface in a number of modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure with two bases that are both identical circles connected at its height, which is defined by the separation of the bases from the centre. Cans of iced drinks and the wicks from toilet paper are examples of cylinders.
The following is the formula for a cylinder's volume:
[tex]V = \pi r^2h[/tex]
where the volume is V, the radius is r, and the height is h.
Inputting the values provided yields:
[tex]V = \pi * 4^2 * 16 = 804.24[/tex]
To the closest hundredth, we round to:
V ≈ 804.24 ≈ 804.23 (rounded to two decimal places) (rounded to two decimal places)
As a result, the cylinder's volume is around 804.23 cubic centimetres.
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13 If tan(x) = 13/8 (in Quadrant-1), find 8 cos(2x) = (Please enter answer accurate to 4 decimal places.)
Answers
The value of 8 cos(2x) accurate to 4 decimal places is -3.6009.
We can start by drawing a right triangle in Quadrant 1 with an angle x, where the opposite side is 13 and the adjacent side is 8.
Using the Pythagorean theorem, we can find the hypotenuse of the triangle:
[tex]c^2 = a^2 + b^2\\ c^2 = 13^2 + 8^2\\ c^2 = 169 + 64\\ c^2 = 233\\ c = \sqrt{(233)}[/tex]
Now we can use trigonometric identities to find cos(2x):
[tex]cos(2x) = cos^2(x) - sin^2(x)[/tex]
We can find sin(x) using the triangle we drew earlier:
sin(x) = opposite / hypotenuse
sin(x) = 13 / [tex]\sqrt{(233)}[/tex]
And we can find cos(x) using the triangle as well:
cos(x) = adjacent / hypotenuse
cos(x) = 8 / [tex]\sqrt{(233)}[/tex]
Plugging these values into the identity for cos(2x):
[tex]cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (8 / \sqrt{(233))^2} - (13 /\sqrt{(233))^2} \\cos(2x) = (64 / 233) - (169 / 233)\\cos(2x) = -105 / 233[/tex]
Finally, we can find 8 cos(2x):
8 cos(2x) = 8 * (-105 / 233)
8 cos(2x) = -3.6009 (rounded to 4 decimal places)
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At a fair last weekend, Zach sold homemade jewelry. If he sold the jewelry for R dollars and it cost him C dollars to make the jewelry, the formula P = R - C describes his profit P in dollars. If his profit was $49.32 and he sold the jewelry for $81.18, how much did it cost him to make the jewelry?
Answers
Answer:
We can use the given formula to solve for the cost C:
P = R - C
We know that P = $49.32 and R = $81.18, so we can substitute these values into the formula:
$49.32 = $81.18 - C
Next, we can solve for C by isolating it on one side of the equation:
C = $81.18 - $49.32
C = $31.86
Therefore, it cost Zach $31.86 to make the jewelry he sold at the fair.
show work and briefly explain
thank you for your help
Answers
The formula holds for k + 1.
What is mathematical induction?
Mathematical induction is a method of mathematical proof used to establish the truth of a statement for an infinite set of values.
To prove the formula for every positive integer n:
3 + 11 + 19 + 27 + ... + (8n - 5) = n(4n - 1)
using mathematical induction, we need to show two things:
The formula holds for n = 1, i.e., 3 = 1(4(1) - 1).If the formula holds for some positive integer k, then it also holds for k + 1.Step 1: Base Case
When n = 1, we have:
3 = 1(4(1) - 1)
Simplifying the right-hand side gives:
3 = 3
So the formula holds for n = 1.
Step 2: Inductive Step
Now assume that the formula holds for some positive integer k, which means:
3 + 11 + 19 + 27 + ... + (8k - 5) = k(4k - 1)
We need to show that the formula also holds for k + 1. That is, we need to show that:
3 + 11 + 19 + 27 + ... + (8(k+1) - 5) = (k+1)(4(k+1) - 1)
Starting with the left-hand side of this equation:
3 + 11 + 19 + 27 + ... + (8(k+1) - 5)
= (3 + 11 + 19 + 27 + ... + (8k - 5)) + (8(k+1) - 5) (by adding the next term)
= k(4k - 1) + (8k + 3) (by substituting the formula for k)
[tex]= 4k^2 - k + 8k + 3[/tex]
[tex]= 4k^2 + 7k + 3[/tex]
Now, we simplify the right-hand side of the equation:
(k+1)(4(k+1) - 1)
= (k+1)(4k + 3)
[tex]= 4k^2 + 7k + 3[/tex]
We can see that the left-hand side and the right-hand side are equal.
Hence, the formula holds for k + 1.
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Find the missing variable and indicated
angle measure.
X =
G
50°
K
H
28°
(15x-3)°
m2KHL =
J
O
Answers
The value of x is 7
What is angle on a straight line?The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°
Therefore ;
50+28+15x-3 = 180
78-3 +15x = 180
75 +15x = 180
collect like terms
15x = 180-75
15x = 105
divide both sides by 15
x = 105/15
x = 7
therefore the value of the missing variable (x) is 7
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Let f(x)=3x+5 and g(x)=1/(x−3). Find a.(f+g)(x) b.(f∙g)(x) c.(2f+3g)(x) d.(3g−4f)(x)
Answers
The requested functions are:
a. (f+g)(x) = (3x^2-4x-14)/(x−3)
b. (f∙g)(x) = (3x+5)/(x−3)
c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)
d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)
Given the functions f(x)=3x+5 and g(x)=1/(x−3), we can find the requested functions by applying the corresponding operations to the functions.
a. (f+g)(x) = f(x) + g(x) = (3x+5) + (1/(x−3)) = (3x(x−3)+5(x−3)+1)/(x−3) = (3x^2-4x-14)/(x−3)
b. (f∙g)(x) = f(x) ∙ g(x) = (3x+5) ∙ (1/(x−3)) = (3x+5)/(x−3)
c. (2f+3g)(x) = 2f(x) + 3g(x) = 2(3x+5) + 3(1/(x−3)) = (6x+10+3/(x−3)) = (6x(x−3)+10(x−3)+3)/(x−3) = (6x^2+7x-21)/(x−3)
d. (3g−4f)(x) = 3g(x) - 4f(x) = 3(1/(x−3)) - 4(3x+5) = (3-4(3x+5)(x−3))/(x−3) = (-12x^2+8x+57)/(x−3)
Therefore, the requested functions are:
a. (f+g)(x) = (3x^2-4x-14)/(x−3)
b. (f∙g)(x) = (3x+5)/(x−3)
c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)
d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)
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Find the greatest common factor
4q,6q
Answers
Answer:
12
Step-by-step explanation:
Its easy and right
Answer:
2
Step-by-step explanation:
For 4 and 6, the common factors are 1 and 2. Since 2 is the highest among the given factors, HCF will be 2 for 4 and 6.
i have 22 bucks and my mom took 2 for her weekly wine tasting, how many drank is my mom if i have 0 dollars left
Answers
Answer:
Step-by-step explanation:
you have 22 bucks and your mom took 2
22-2=20
My Answer:
22-2= 20, right? She can't drink anymore wine if you (shown as "i") used the remaining 20$. Tell me if this makes sense. No wine (none) is consumed if you have no money left.
Answer from Artificial Intellegence (to get another view on the question so you can figure out the best answer):
If you had 22 bucks and your mom took 2 dollars for her weekly wine tasting, you would have 20 dollars left. If you have 0 dollars left, this means your mom spent all of the remaining 20 dollars on wine. Assuming each wine bottle costs the same, we can divide the remaining 20 dollars by the cost of one wine bottle to find how many wine bottles your mom bought for her weekly wine tasting. Without knowing the exact cost of one wine bottle, we can't determine the exact number of wine bottles your mom drank.
Fran and Winston have a combined income
of $80 000. One quarter of Winston's income
is the same as one-sixth of Fran's income.
How much does each person earn?
Answers
F = Fran's income
W = Winston's income
[tex]F+W=80000\hspace{5em}\stackrel{ \textit{one quarter} }{\cfrac{W}{4}}=\stackrel{ \textit{one sixth} }{\cfrac{F}{6}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{F+W=80000}\implies F=80000-W \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{W}{4}=\cfrac{F}{6}}\implies \stackrel{\textit{substituting from above}}{\cfrac{W}{4}=\cfrac{80000-W}{6}}\implies 6W=320000-4W \\\\\\ 10W=320000\implies W=\cfrac{320000}{10}\implies \boxed{W=32000}~\hfill \stackrel{ 80000~~ - ~~32000 }{\boxed{F=48000}}[/tex]
solve each system of equations by elimination. 3x-4y=-14 and 3x+2y=-2
Answers
Answer: x=6, y=8
Using elimination means that we eliminate one of the variables in both equations which help find out the other variable, which we then substitute to find the whole equation.
3x-4y=-14
+ 3x+2y=-2
=>-4y=-14
+ 2y=-2
=>-2y=-16
=>y=8
So to find x,
3x-4(8)=-14
=3x=-14+32
=x=18/3 so x=6
PLEASE MARK BRAINLIEST IF THIS HELPED!
100 POINTS!! HELP!! MATH!!
Arrange in order from least to greatest (Radicals)
a. 4√3
b. 3√5
c. 5√2
d. 2√10
e. 2√13
f. 3√6
Answers
4/3=6.9
3/5=6.7
5/2=7
2/10=6.3
2/13=7.2
3/6=7.3
ANSWER
D,B,A,C,E,F
Bobby has 4 shoes and sells 5 shoes. How many shoes does Bobby have left?
Answers
Answer:
Step-by-step explanation:
4-5 would be less than 1 so it would be -1
Find the y-intercept of the line y=1/4x+6/5
1) Write your answer as an integer or as a simplified proper or improper fraction, not as an
ordered pair.
Answers
Answer: Y=6/5
Step-by-step explanation:
Y=1/4X+6/5
(set X to zero 1/4(0) = 0)
Y=0+6/5
Y=6/5
Express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form.
Answers
The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
To express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form, we need to multiply the two expressions together and then simplify. Here are the steps:
1. Distribute the first term of the first expression to the second expression: (4/3)x * (5/6)x + (4/3)x * (5/3) = (20/18)x^2 + (20/9)x
2. Distribute the second term of the first expression to the second expression: -6 * (5/6)x + -6 * (5/3) = (-30/6)x + (-30/3)
3. Combine the like terms: (20/18)x^2 + (20/9)x + (-30/6)x + (-30/3) = (20/18)x^2 + (-10/9)x + (-30/3)
4. Simplify the fractions: (10/9)x^2 + (-10/9)x + (-10)
So the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).
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A right circular cylinder has the dimensions shown below.
r = 5 cm
h = 9 cm
Find the exact surface area of the cylinder.
Include correct units.
Show all your work.
Answers
Answer:
The surface area of a right circular cylinder consists of three parts: the top and bottom circular faces, and the curved lateral surface.
The area of each circular face is given by the formula A = πr^2, where r is the radius. Therefore, the total area of the two circular faces is:
2A = 2πr^2
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Therefore, the lateral surface area of the cylinder is:
A = 2πrh
Substituting the given values, we get:
A = 2π(5 cm)(9 cm)
Simplifying, we get:
A = 90π cm^2
Adding the areas of the circular faces and the lateral surface, we get the total surface area:
Total surface area = 2A + A = 3A
Substituting the value of A, we get:
Total surface area = 3(90π cm^2) = 270π cm^2
Therefore, the exact surface area of the cylinder is 270π square centimeters.
Write an exponential function (y=ab^x) whose graph passes through the points (2,16) and (5,128)
Answers
Answer:
Well question is not clear rewrite
Using the point (2, 16), we get:
16 = ab^2
Using the point (5, 128), we get:
128 = ab^5
We can divide the second equation by the first equation to eliminate a:
(128/16) = (ab^5)/(ab^2)
8 = b^3
Taking the cube root of both sides gives:
b = 2
Now we can substitute this value of b into either equation to solve for a. Using the first equation:
16 = ab^2
16 = a(2^2)
16 = 4a
a = 4
Therefore, the exponential function that passes through the points (2, 16) and (5, 128) is:
y = 4(2^x)
Find the value of x and y
.Write your answer in
simplest form.
X
45°
X =
y =
6
y
Answers
Answer:
34
Step-by-step explanation:
3dds
7th grade math question pls answer a s a p will give brainlist thingy
Answers
10^2=100
100+64-5=159
Answer:
it’s 159 sorry
Step-by-step explanation:
10 to the second power is 10x10 which is 100 then 8 to the second power is 8x8 which is 64. 164-5 is 159, I apologize.
20. Find a \( 2 \times 2 \) matrix \( A \) for which \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \]
Answers
The matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]
To find a \( 2 \times 2 \) matrix \( A \) such that \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \], we can solve for A by multiplying both sides of the equation by the inverse of the left matrix. The inverse of \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] \] is \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right]. \] Multiplying both sides of the equation by this inverse gives \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right]A= \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right], \] which simplifies to \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \] Thus, the matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]
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The manager of a coffee shop record the number of costumers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age the results are shown in the table what percentage of these customers put chocolate creamer in their coffee during this hour
Answers
Throughout the hour, 70 percentage of customers add chocolate creamer to their coffee.
How do you find the percentage?Find the proportion of consumers who selected chocolate creamer and add up all of the customers who visited throughout the hour to determine the appropriate percentage.
The number of clients who selected chocolate creamer is calculated by dividing the total number of customers by 100.
Here it is,
For one hour, the manager of a coffee shop counted the number of patrons who added vanilla or chocolate creamer to their coffee.
The question given is:
Vanilla Chocolate
Age 18 - 30 2 6
Age 30 + 4 8
2 + 4 + 6 + 8 Equals 20 clients in this instance.
6 + 8 = 14 is the number of clients who select chocolate creamer.
Customers that used chocolate creamer made up: [14/20] / 100 = 70%
As a result, 70% of consumers at that time add chocolate creamer to their coffee.
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The complete question is:
The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?
Answer:
70%
Step-by-step explanation:
i did the quiz lol
Solve the system of equations by graphing. Graph both equations on the coordinate plane even if they represent the same line.
Answers
The point where the two lines come together (1,1). Hence, x = 1 and y = 1 are the answers to the system of equations.
What are the names of equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
How Do You Solve an Equation System?The technique of solving a system of equations involves calculating the unknown variables while maintaining the equations balanced on both sides. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true.
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Help Please!!
Let n = 773,186,2de be a base-ten numeral with d and e its last
two digits. Give all of the choices of the two-digit numbers de for
which n is divisible by 12.
The last "Expert" that ans
Answers
In order for a number to be divisible by 12, it must be divisible by both 3 and 4.
To be divisible by 3, the sum of the digits must be divisible by 3.
7 + 7 + 3 + 1 + 8 + 6 + 2 + d + e = 34 + d + e
Since 34 is not divisible by 3, we need d + e to be a multiple of 3 in order for the sum to be divisible by 3.
Possible values for d + e are 3, 6, and 9.
To be divisible by 4, the last two digits of the number must be divisible by 4.
Therefore, we need de to be a multiple of 4.
Possible values for de are 12, 16, 32, 36, 52, 56, 72, 76, and 92.
Out of these, only 12, 36, 52, and 76 have a sum of digits that is a multiple of 3.
So the possible values for de are 12, 36, 52, and 76.
Therefore, the choices of the two-digit numbers de for which n is divisible by 12 are 12, 36, 52, and 76.
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14 Data collected in mall recorded the shoe color worn by 30 customers. Based on this information, if
there are 360 customers in this mall, how many customers would you expect to have a black shoe?
Black
Brown
Number of
Customers
13
17
Answers
156 customers are expected to wear a black shoe.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
As per the given data:
Customers with black shoes = 13 out of 30
Customers with brown shoes = 17 out of 30
Total customers in the mall = 360
Probability that a customer wears black shoes:
P(B) = 13/30 = 0.433
Number of customers out of 360 expected to wear black shoes:
= P(B) × 360
= 0.433 × 360
= 156 customers.
Hence, 156 customers are expected to wear a black shoe.
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The Quick Meals Diner served 288 dinners. A child's plate cost $2.50 and an adult's plate cost $8.20. A total of $1,614.90 was collected. How many of each type of plate was served?
Round answers to the nearest whole person.
____ child plates were served.
___ adult plates were served.
Answers
The Quick Meals Diner served 131 child plates and 157 adult plates.
Let's use a system of two equations to represent the given information:
c + a = 288 (1) // The number of child and adult plates served add up to 288
2.5c + 8.2a = 1614.9 (2) // The total amount collected is the sum of the prices of all plates served
where c represents the number of child plates served and a represents the number of adult plates served.
We can use equation (1) to solve for c in terms of a:
c = 288 - a
Substituting this expression for c into equation (2), we get:
2.5(288 - a) + 8.2a = 1614.9
720 - 2.5a + 8.2a = 1614.9
5.7a = 894.9
a = 157
So, 157 adult plates were served. Substituting this value into equation (1), we get:
So, 157 adult plates were served. Substituting this value into equation (1), we get:
So, 131 child plates were served.
Therefore, The result is 131 child plates and 157 adult plates.
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