A researcher will use a regression equation to predict the relationship between the GPAS (y variable) and Hours of Studying per week (x-variable) for 100 students. The regression equation will try to predict the GPA for students who study 10 hours per week by estimating the relationship between the two variables. The regression equation is a mathematical model that is used to predict the value of one variable based on the value of another variable.
In this case, the regression equation will try to predict the GPA for students who study 10 hours per week based on the relationship between GPAS and Hours of Studying per week.
The goal of the regression equation is to provide an accurate prediction of the GPA for students who study 10 hours per week, based on the data collected by the researcher.
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Please help I’ll give brainliest
Answer:
[tex](5x-1)(x+4)[/tex]
Step-by-step explanation:
Given:
[tex]5x^2 +19x-4[/tex]
Factor the expression by grouping. First, the expression needs to be rewritten as [tex]5x^2 +ax+bx-4[/tex]. To find a and b, set up a system to be solved.
[tex]a+b=19[/tex]
[tex]ab=5(-4)=-20[/tex]
Since [tex]ab[/tex] is negative, a and b have the opposite signs. Since [tex]a+b[/tex] is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product [tex]-20[/tex].
[tex]-1,20[/tex]
[tex]-2,10[/tex]
[tex]-4,5[/tex]
Calculate the sum for each pair.
[tex]-1+20=19[/tex]
[tex]-2+10=8[/tex]
[tex]-4+5=1[/tex]
The solution is the pair that gives sum [tex]19[/tex].
[tex]a=-1[/tex]
[tex]b=20[/tex]
Rewrite [tex]5x^2+19x-4[/tex] as [tex](5x^2-x)+(20x-4)[/tex].
Factor out x in the first and 4 in the second group.
[tex]x(5x-1)+4(5x-1)[/tex]
Factor out common term [tex]5x-1[/tex] by using distributive property.
[tex](5x-1)(x+4)[/tex]
Therefore, [tex](5x-1)(x+4)[/tex].
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[SOLVED!]
-
-
-
[tex] \frac{ \sqrt{7} }{ \sqrt{3x} } [/tex]
help a girl out ??? :)
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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Chapter 10 Test
11. Nate uses a cube shaped bead with side lengths
measuring 6mm. Each bead has a circular hole in
the middle. The diameter of the circular hole is 3mm.
[not drawn to scale]
Answer:
Step-by-step explanation:
I'm guessing you need the volume of the bead with the hole.
We need to get the volume of two objects; a cube and a cylinder. We need the cylinder for the hole.
V(square) = 6^3
V(square) = 216 mm^3
V(cylinder) = pi(r^2)(h)
pi(1.5^2)(6)
Radius is half the diameter, and 6 represents the height, since it's as long as the cube.
V(cylinder) = 42.41 or 13.5pi
We need to do V(s) - V(c) to find the volume of the bead.
216 - 13.5pi = 173.588 or 173.59 or 173.6
I hope this helps!
7th grade math question pls answer a s a p will give brainlist thingy
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.
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
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.
1. In a dart tournament, the probabilities John,Sam and Grey will hit the target are 3/4, 1/2 and 4/5, respectively. Assuming the events each of them hits the target are independent, find the probability that
a) all three of them hit the target
b) none of them hit the target
c) only John hits the target
2. Plastic X has four red and two white marbles. Plastic Y has one green, two red and two white marbles. In a game, a die is thrown first and if the outcome is a number less than 3, a marble is chosen at random from plastic X. Otherwise, a marble is randomly chosen from plastic Y.
Draw a tree diagram to show all the possible outcomes of the game. Hence, find the probability that
a) a red marble is chosen from plastic X.
b) a white marble is chosen from plastic Y.
c) a red marble is chosen.
d) a marble is chosen from plastic Y if it is known that it is red.
1) the probability that all three of them hit the target is 3/10, none of them hit the target 1/40, only John hits the target 3/40, 2) a red marble is chosen from plastic X is 2/9, a white marble is chosen from plastic Y is 4/15, a red marble is chosen is 2/9, a marble is chosen from plastic Y if it is known that it is red is 2/5.
1. a) The probability that all three of them hit the target is the product of their individual probabilities:
P(all three hit the target) = P(John hits the target) × P(Sam hits the target) × P(Grey hits the target)
= (3/4) × (1/2) × (4/5)
= 12/40
= 3/10
b) The probability that none of them hit the target is the product of their individual probabilities of not hitting the target:
P(none hit the target) = P(John doesn't hit the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (1 - 3/4) × (1 - 1/2) × (1 - 4/5)
= (1/4) × (1/2) × (1/5)
= 1/40
c) The probability that only John hits the target is the product of his probability of hitting the target and the other two's probabilities of not hitting the target:
P(only John hits the target) = P(John hits the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (3/4) × (1 - 1/2) × (1 - 4/5)
= (3/4) × (1/2) × (1/5)
= 3/40
2. The tree diagram for this game is as follows:
Die
/ \
/ \
/ \
/ \
/ \
/ \
<3 >=3
/ \ / \
X Y X Y
/ \ / \ / \ / \
R W R W R W R W
a) The probability that a red marble is chosen from plastic X is the product of the probability of the die outcome being less than 3 and the probability of choosing a red marble from plastic X:
P(red from X) = P(die < 3) × P(red from X)
= (2/6) × (4/6)
= 8/36
= 2/9
b) The probability that a white marble is chosen from plastic Y is the product of the probability of the die outcome being greater than or equal to 3 and the probability of choosing a white marble from plastic Y:
P(white from Y) = P(die >= 3) × P(white from Y)
= (4/6) × (2/5)
= 8/30
= 4/15
c) The probability that a red marble is chosen is the sum of the probabilities of choosing a red marble from plastic X and from plastic Y:
P(red) = P(red from X) + P(red from Y)
= (2/9) + (4/15)
= 10/45
= 2/9
d) The probability that a marble is chosen from plastic Y if it is known that it is red is the probability of choosing a red marble from plastic Y divided by the probability of choosing a red marble:
P(Y | red) = P(red from Y) / P(red)
= (4/15) / (2/9)
= 12/30
= 2/5
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solve each system of equations by elimination. 3x-4y=-14 and 3x+2y=-2
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
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Express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form.
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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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.
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
100 POINTS IF YOU CAN HELP ME!!
Use the equation below to calculate the total cost of a payday loan for #6-8.
\Total Cost = Loan amount + finance charge ( 1 + Number of rollovers or renewals). Keep in mind, this does not include the initial loan cost, just the interest.
#6. Toby takes out a payday loan to pay for a medical bill that costs $450. The payday lender charges him $50 every two weeks. Toby has to roll over the loan 4 times before he can finally pay it off. What was the total cost of his loan?
7. Tabitha takes out a payday loan to pay for her son's emergency room bill that costs $300. The payday lender charges her $40 every two weeks. She has to roll over the loan 6 times before she can finally pay it off. What is the total cost of her loan?
8. Sariah takes out a payday loan to get a new set of tires in order to pass inspection. The bill is $500. She needs her car to get to and from work but does not have enough money in her savings to cover the bill so she takes out a payday loan. The payday loan will cost her $45 every two weeks. She has to roll over 7 times. What was the total cost of her loan?
Step-by-step explanation:
Toby's loan amount is $450 and the finance charge is $50 every two weeks. He rolls over the loan 4 times.
Total cost = $450 + ($50 x (1 + 4))
Total cost = $450 + ($50 x 5)
Total cost = $450 + $250
Total cost = $700
Therefore, the total cost of Toby's payday loan is $700.
Tabitha's loan amount is $300 and the finance charge is $40 every two weeks. She rolls over the loan 6 times.
Total cost = $300 + ($40 x (1 + 6))
Total cost = $300 + ($40 x 7)
Total cost = $300 + $280
Total cost = $580
Therefore, the total cost of Tabitha's payday loan is $580.
Sariah's loan amount is $500 and the finance charge is $45 every two weeks. She rolls over the loan 7 times.
Total cost = $500 + ($45 x (1 + 7))
Total cost = $500 + ($45 x 8)
Total cost = $500 + $360
Total cost = $860
Therefore, the total cost of Sariah's payday loan is $860
Answer:
#6.
Loan amount = $450
Finance charge = $50 every two weeks
Number of rollovers or renewals = 4
Total Cost = 450 + (50 x (1 + 4))
Total Cost = 450 + 250
Total Cost = $700
The total cost of Toby's loan is $700.
#7.
Loan amount = $300
Finance charge = $40 every two weeks
Number of rollovers or renewals = 6
Total Cost = 300 + (40 x (1 + 6))
Total Cost = 300 + 280
Total Cost = $580
The total cost of Tabitha's loan is $580.
#8.
Loan amount = $500
Finance charge = $45 every two weeks
Number of rollovers or renewals = 7
Total Cost = 500 + (45 x (1 + 7))
Total Cost = 500 + 360
Total Cost = $860
The total cost of Sariah's loan is $860.
Find the area of the circle which has a diameter 22 cm
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.
1. Classify each triangle by its side lengths and angle measurements. Circle the correct names.
Classify Using
Side Lengths
m
b.
Equilateral Isosceles
Math Day Or
Scalene
Classify Using
Angle Measurements
Acute Right Obtuse. Angel mea
There are three types of triangle according to sides and angles each.
What is a triangle?The triangle is a type of polygon having three sides, angles and vertices.
Classification of triangles :-
Based on sides :-
1) Scalene triangle :- A triangle with all different measurements of sides and angles are called a Scalene triangle.
2) Isosceles triangle :- A triangle with two of the sides and angles are congruent called an Isosceles triangle.
3) Equilateral triangles :- A triangle with all the same measurements of sides and angles is called an Equilateral triangle.
Based on angles :-
1) Acute angled triangle :- A triangle with all the angles less than 90°, are called acute angled triangle.
2) Obtuse angled triangle :- A triangle with all the angles greater than 90° and less than 180°, are called Obtuse angled triangle.
3) Right angled triangle :- A triangle with one angle equals 90° is called a Right angled triangle.
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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
an ellipse has an equation equal to 9x^2-144x+16y^2+96y+495=0. Compute the eccentricity of the curve
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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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
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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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)
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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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
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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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?
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
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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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
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:
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?
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]
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.
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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O RATIONAL EXPRESSIONS Adding rational expressions with common der Subtract. (z)/(z^(2)+4z-12)-(2)/(z^(2)+4z-12) Simplify your answer as much as possible.
The solution to the given rational expressions is (z - 2)/(z^(2)+4z-12).
To subtract rational expressions with common denominators, we simply subtract the numerators and keep the same denominator.
In this case, our common denominator is (z^(2)+4z-12), so we can subtract/add the numerators:
So, we will subtract the numerators, (z) - (2), and keep the same denominator:
(z)/(z^(2)+4z-12)-(2)/(z^(2)+4z-12) = (z - 2)/(z^(2)+4z-12)
Now, we can simplify the numerator by combining like terms:
(z - 2)/(z^(2)+4z-12) = (z - 2)/(z^(2)+4z-12)
Since the numerator and denominator cannot be simplified any further, this is our final answer:
(z - 2)/(z^(2)+4z-12)
Therefore, the solution to the subtraction of the given rational expressions is (z - 2)/(z^(2)+4z-12).
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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.
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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Bobby has 4 shoes and sells 5 shoes. How many shoes does Bobby have left?
Answer:
Step-by-step explanation:
4-5 would be less than 1 so it would be -1
Solve the system of equations by graphing. Graph both equations on the coordinate plane even if they represent the same line.
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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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
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
Is 5x^2+y=0 a direct variation
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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Find the greatest common factor
4q,6q
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.