They should produce 1091 units each day to yield a minimum cost.
What is the vertex formula?
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
We have,
C = 70,000 - 120x + 0.055x²
C = 0.055x² - 120x + 70,000
Hence, for this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, find and put the values of x.
minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )
= 120 ÷ 0.11
= 120 ÷ 0.11
= 1090.90 ≈ 1091 units
The minimum cost will be yield for 1091 units.
Therefore, They should produce 1091 units each day to yield a minimum cost.
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Eva says
3
4
is equivalent to
15
20
. Check her work by completing the table of equivalent ratios.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
What is a Ratio?A ratio indicates the number of times one number contains another.
To find the equivalent ratio of 3/4 write the table of 3 in one column of the table and write the table of 4 in another column of the table.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
The above table indicates that 3/4 = 6/8 = 9/12 = 12/16 = 15/20.
Therefore, from the table, 3/4 is equivalent to 15/20.
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Which criterion can be used to prove ABC and ADC are congruent? select the correct answer
ΔABC and ΔADC are congruent by angle-side-angle (ASA) postulate of triangle congruence.
In this question we have been given a quadrilateral ABCD and diagonal AC.
We need to prove triangle ABC and ADC are congruent.
In ΔABC and ΔADC,
∠BAC ≅ ∠ACD ...........(Given)
AC ≅ AC ...........(Common side)
∠ACB ≅ ∠DAC ..........(Given)
ΔABC ≅ ΔADC ..........(ASA postulate of triangle congruence)
Therefore, ΔABC and ΔADC are congruent by angle-side-angle (ASA) postulate of triangle congruence.
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Let a function of 2 variables be defined by f (a,b) =ab - (a-b) what is the value of f (8,9)
By using function, it can be calculated that
The value of f(8, 9) is 73
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the function is
f(a, b) = ab - (a - b)
f(8, 9) = 8 [tex]\times[/tex] 9 - (8 - 9)
f(8, 9) = 72 + 1
f(8, 9) = 73
So the value of f(8, 9) is 73
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Are the ratios 3:12 and 1:4 proportional? Show your work.
Explain:
Answer:
Yes
Step-by-step explanation:
3:12 both have a common factor of 3 you divide both sides by 3 to get 1:4
(6,10)
(a,8)
(4,b)
(2,2)
What are the values of a and b?
a=
b=
Answer:
Step-by-step explanation:
Put the value of a in equation 2. b² = 6² + a². b² = 36 + (81 / 4 ). b = √(225 / 4). b = 15 / 2. Therefore, the value of a and b will be 9.
Six trigonometric functions of the angle (20,21)
The exact values of the six trigonometric functions for the point (x, y) = (20, 21) are listed below:
sin θ = 21 / 29, cos θ = 20 / 29, tan θ = 21 / 20, cot θ = 20 / 21, sec θ = 29 / 20, csc θ = 29 / 21
How to determine the exact six trigonometric functions related to a point in rectangular format
Points in rectangular format are points of the form (x, y), where x and y represent the position of the point respect to the origin and along the respective orthogonal axis.
The line segment between the origin and that point represents the hypotenuse of a right triangle. Then, we can determine the six trigonometric functions by using the following formulae:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
cot θ = x / y
sec θ = √(x² + y²) / x
csc θ = √(x² + y²) / y
If we know that x = 20 and y = 21, then the exact values of the trigonometric functions are:
sin θ = 21 / √(20² + 21²)
sin θ = 21 / 29
cos θ = 20 / √(20² + 21²)
cos θ = 20 / 29
tan θ = 21 / 20
cot θ = 20 / 21
sec θ = √(20² + 21²) / 20
sec θ = 29 / 20
csc θ = √(20² + 21²) / 21
csc θ = 29 / 21
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Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two
different proportional relationships represented in different ways.
Will give points to first correct answer that follows all the steps right.
Answer:
I Need Help On That Too
Step-by-step explanation:
Tanisha and her children went into a restaurant that sells hamburgers for
$7.50 each and drinks for $1.75 each. Tanisha has $70 to spend and must buy
no less than 18 hamburgers and drinks altogether. If a represents the number
of hamburgers purchased and y represents the number of drinks purchased,
write and solve a system of inequalities graphically and determine one
possible solution.
"Solve the Equation."
if the equation only has one solution, enter "NS" (No Solution) .
if the equation has Infinite Many solutions, enter "IM"
1. 6(x+5)=6x+5
2. -4x=7x-33
The equation 6(x + 5) = 6x + 5 has NS (No Solution) and the equation -4x = 7x - 33 has IM (Infinite Many solutions).
Let us take the given equation
6(x + 5) = 6x + 5
⇒ 6x + 30 = 6x + 5
⇒ 6x - 6x = 5 - 30
⇒ 0 = -25
Hence, the given equation has No Solution (NS)
Let us take the given equation
-4x = 7x - 33
-4x - 7x = -33
-11x = -33
x = 3
Hence, the given equations has Infinite Many solutions (IM)
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Hi I don't understand this can you please help me. Maura multiply 1. 8 by 2. 4 and write the product as 0. 432. Tom says that her product is incorrect. How could Tom know this without multiplying a two numbers
The correct multiplication of 1.8 and 2.4 will be 4.32.The product 0.432 calculated by Maura was incorrect.
Define the term multiplication of number?One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. The symbols for multiplication are cross (×), asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks.For the given question-
Maura divide 1. 8 by 2. 4 and enter 0. 432 as the result.
Tom claims her product is unreliable.
Tom is able to make this deduction without the need for multiplication because the value 0.432 is less than even 1.8, which is not conceivable.
Thus,when multiplying by a number bigger than 1, the result will always be greater than the starting numbers.
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Which monomial function has a minimum value?
Oy = 5x¹0
Oy=-4x¹1
Oy=-x¹2
y=6x7
A monomial function that has a minimum value is y = 5x^10
In this question, we have been given four monomial functions.
y = 5x^10
y = -4x^11
y = -x^12
y = 6x
we need to find a monomial function that has a minimum value.
For function y = 5x^10, as x > 0 increases, f(x) increases. And as x < 0 decreases, f(x) increases.
We know that for even, positive monomial function if coefficient > 0 and exponent is even then a monomial has a minimum value.
Therefore, a monomial function that has a minimum value is y = 5x^10
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how many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6? repeated digits are allowed.
There will be 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 when repeated digits are allowed by fundamental counting principle.
What is fundamental counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting simplifies the approach to selection by taking into account all of the possible choices and their combinations in order to calculate the Probability.
Here,
Since there are 6 digit given,
In first place, there are 6 ways to arrange the digits. In second place, there are 6 ways to arrange the digits. In third place, there are 6 ways to arrange the digits.
This way,
6×6×6=216 ways
When repeated digits are allowed by the fundamental counting principle, 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6.
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Jade's Gem Shop is having its annual spring sale, when every item in the store gets marked down. During the sale, charm bracelets sell for $4 less than full price. Kristen purchases 5 identical charm bracelets: one for each of her friends. She pays a total of $45. Which equation can Kristen use to find how much money, c, each charm bracelet costs at full price?
Answer:
5(c−4)=45
5c - 20 = 45
5c = 45+20
5c = 65
c = 13
The full price of the bracelets was $13.
Step-by-step explanation:
Study the figure. What is the measure of the missing interior angle?
The value of the missing interior angle is 25°
What is a right-angled triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
given angles of the triangle, 90° and 65°
Let, the unknown angle be x
so that,
x + 90 + 65 = 180 ( sum of angles in a triangle)
x + 155 = 180
x = 180 - 155
x = 25°
In conclusion, the unknown angle is 25°
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Me ayudan porfavor 2 trinomios cuya diferencia sea 4x²-7x+5
Answer:
Δ = b² - 4ac
Step-by-step explanation:
do math
Marcus and jeremy both evaluated the expression −52 3. marcus said the answer was −22. jeremy said the answer was 28. who is correct? explain the error in the other student’s work.
Marcus is accurate. Jeremy is wrong because he overlooked the negative sign in the equation's initial addend. Since -25 has a greater absolute value than 3, it is obvious that the sum should be negative.
Marcus is correct; the solution is -22.
The simplified expression is given as:
= -(5²)+ 3
= -(25) + 3
= - 22
The right response is this. Marcus saw the bracket or parentheses symbol when he condensed his sentence. This has major significance.
Jeremy scored 28. He squared -5 without noting that it was in a bracket or parenthesis, therefore his response is incorrect.
Consequently, Jeremy calculated this.
= -(5²) + 3
= 25 + 3
= 28
Jeremy gave a false response. He made a computation but failed to see the bracket.
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Complete Question
Marcus and Jeremy both evaluated the expression −(5²) + 3. Marcus said the answer was −22. Jeremy said the answer was 28. Who is correct? Explain the error in the other student’s work.
how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?how many 44-digit positive integers (that is, integers between 10001000 and 99999999, inclusive) having only even digits are divisible by 55?
There are 100 4-digit positive integers are possible between 1000 and 9999.
Our first step is to divide the four digit number into four places: tens, hundreds, and thousands.
To solve this problem, we must start from the right-hand side and find how many even numbers should be placed where the desired answer can be obtained.
There are a total of [0, 2, 4, 6, and 8] objects
There should only be one digit on one place, since it is the only digit that makes the number divisible by five
There are 1 ways to fill the one's place, so the total number is 1.
It is possible to take any number from the given sets of even numbers in the tens place,
There are five ways to fill one place, so there are five ways to fill it.
Taking a look at the hundreds place,
All numbers can be placed in the hundreds place from the given sets, so all numbers can be taken from the hundreds place.
Therefore, there are five ways to fill the hundreds place.
Taking a look at the thousands,
It is possible to fill thousands of places with 4 numbers from a given set of even numbers.
Therefore, there are four ways to fill the thousands place
The next step is to use the concept of factorial to find the number of ways to make a 4-digit number from even numbers that are divisible by 5.
To fill the respective places, we will multiply all the ways we calculated
= 4 × 5 × 5 × 1
= 100
Hence, there 100 4-digit positive integers possible.
Question
how many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?
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5 The table shows the weights of different packages.
What is the approximate total mass of packages A, B,
and D? (Hint: 1 lb ≈ 0.45 kg)
Package | Weight (lb)
A | 0.25
B | 0.8
C | 1
D | 1.75
answers:
F 1.26 g
G 2.8 g
H 280 g
J 1260 g
Answer:
1710 grams (not on the answer list)
Step-by-step explanation:
The total weight of the 4 packages is 3.8 pounds (lbs). The conversion factor is (0.45 kg/lb).
(3.8 lbs)*((0.45 kg/lb) = 1.71 kg or 1710 grams. Pease check the numbers provided.
I NEED HELP PLEASE DUE TODAY
Look at the picture for the problem
Please answer both parts
part a and b
a. The equation that represents the given data is y = 700x + 2,000.
b. The average daily attendance at Disneyland on its 80th anniversary is 58,000.
We are given the data about average daily attendance at Disneyland's anniversary celebrations. At Disneyland's 40th anniversary, the average daily attendance was 30,000 people. On the 60th anniversary, the average daily attendance was 44,000 people. We need to create an equation that would represent y, the average daily attendance, based on x, the number of years after Disneyland opened.
We can write the data in the form of points on the coordinate axes. The coordinates of the points are (40, 30,000) and (60, 44,000). We can use the two-point form to write an equation.
(y - y1) = [(y2 - y1)/(x2 - x1)]*(x - x1)
(y - 30,000) = [(44,000 - 30,000)/(60 - 40)]*(x - 40)
(y - 30,000) = [(14,000)/(20)]*(x - 40)
(y - 30,000) = (700)*(x - 40)
y = 700x - 28,000 + 30,000
y = 700x + 2,000
Now, we need to find out the average daily attendance at Disneyland on its 80th anniversary.
y = 700*80 + 2,000
y = 56,000 + 2,000
y = 58,000
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Indicate the distance of the segment using the given
information. Round to the nearest tenth.
5. Find AX. A(-4, 5), X (1, −2)
The distance of segment AX sis found to be 8.6 units using the distance formula.
What exactly is the distance formula?[tex]\sqrt{[x_{2}-x_{1}]^{2} + [y_{2}-y_{1}]^{2} }[/tex] is the distance formula. This works for any two points in two-dimensional space with coordinates (x₁, y₁) for the first and (x₂, y₂) for the second. You may easily remember it if you remember that it is Pythagoras' theorem, that the distance is the hypothenuse, and that the coordinate lengths are the difference between the x and y components of the points.Why do we employ the distance formula?In complex numbers, the distance formula is used to express the plane and its magnitude. Furthermore, distance formulae can be used to calculate the distance between two planes in three-dimensional or n-dimensional planes. It is also used to calculate the magnitude formula.Given: A(-4, 5), X (1, −2)
We need to find the distance of the segment AX.
Distance of AX is given as :
[tex]\sqrt{[1-(-4)]^{2} + [-2-5]^{2} } \\= \sqrt{25 + 49}\\ = \sqrt{74}\\ =8.6[/tex]
Therefore, the distance of segment AX sis found to be 8.6 units using the distance formula.
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Plssss helpppp
Graduation rate is one measure used to compare
colleges in national publications. One such publication
compared semester tuition against graduation rate,
defined as the percentage of students who graduate
within four years.
4-Year Graduation Rate (%)
100
80
60
40
College Comparisons
10 15 20 25 30 35
Semester Tuition (Thousands of Dollars)
Which statement best explains the relationship
between the variables?
O Higher tuition causes students to graduate at
higher rates.
O Tuition does not appear to have an association
with graduation rate.
O More selective colleges tend to have higher tuition
but lower graduation rates.
O More selective colleges tend to have higher tuition
and higher graduation rates,
The tuition does not appear to have an association with graduation rate.
A scatter plot is a particular kind of plot or mathematical diagram that displays values for generally two variables for a collection of data. It uses Cartesian coordinates. A dot is used to symbolize each point on the scatter plot. It is used to demonstrate the link between the dots by illustrating how many of them would fall within the path of a straight line.
It is clear that there is no relation between tuition and graduation rate. Some selective colleges may have higher tuition and higher graduation rates but there may be some selective colleges with higher tuition but lower graduation rates.
Hence, the tuition does not appear to have an association with graduation rate. Option 2 is correct.
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Answer:
I think it's A- Higher tuition causes students to graduate at higher rates.
Step-by-step explanation:
tell me if I'm wrong... forgive me if i am
PLEASE HELP ANSWER JUST ONE OF THEM AT LEAST!
Polly buys a drink at a convenience store for $1. 80. She also buys a bag of chips.
(a) The ratio of the cost of the chips to the cost of the water is 4:3. Find the cost of the chips.
$
(b) Polly has $6 to spend. Work out the total amount she spends on a drink and chips as a fraction of the $6. Give your answer in its lowest terms.
(c) The $6 is 37. 5% less than the amount Polly had to spend last week. Calculate the amount she had last week.
$
Answer:
(a) $2.40
(b) Chips: 4/7
Drink: 3/7
(c) $9.60
Step-by-step explanation:
Polly buys a drink at a convenience store for $1. 80. She also buys a bag of chips.
(a) The ratio of the cost of the chips to the cost of the water is 4:3. Find the cost of the chips.
chips : water = 4 : 3
chips/water = 4/3
c/1.8 = 4/3
3c = 1.8 × 4
c = 0.6 × 4
c = 2.4
$2.40
(b) Polly has $6 to spend. Work out the total amount she spends on a drink and chips as a fraction of the $6. Give your answer in its lowest terms.
4 + 3 = 7
Chips: 4/7
Drink: 3/7
(c) The $6 is 37. 5% less than the amount Polly had to spend last week. Calculate the amount she had last week.
Last week it was 100%.
This week it is 37.5% less.
100% - 37.5% = 62.5%
This week, it is 62.5% of last week.
Let x = last week's amount.
62.5% of (last week's amount) = $6
62.5% × x = 6
0.625x = 6
Divide both sides by 0.625
x = 6/0.625
x = 9.6
$9.60
Which expression is equal to 6(r2 – 3) + 2(r2 + 1)?
8r squared - 20
6r squared -2
8r squared -16
6r squared +2r-16
pls, help 20 points!
Answer:8r squared -16
Step-by-step explanation:
how many ways can a president, a vice-president and a secretary be chosen from 17 members of a club assuming that one person cannot hold more than one position?
The three posts can be given in 4080 ways among 17 students.
It is given that the number of people available to choose the posts from is 17.
There are three posts here- president, vice president, and secretary.
Now, if we choose a candidate for President first, there are 17 students available.
Next, if we select a Vice-President, there are 16 ways to select the vice-president, since one student already is the president.
At, last there are 15 students available to choose the secretary from as two students already hold a post.
Hence, the number of ways to select the President, Vice-President, and Secretary are-
17 X 16 X 15 ways
Therefore we get
4080 ways.
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Why is Mathematics called the queen of science (1 paragraph response please)
what two numbers add to "-5" and multiply to "-4"
The numbers that add to -5 and multiply to -4 are -5.7015 and 0.7015.
There are two numbers. The addition of the two numbers is -5. The multiplication of the two numbers is -4. We need to find the two numbers. Let the first number and the second number be represented by the variables x and y, respectively. Then, we can write the two following equations.
x + y = -5
x*y = -4
We will substitute the value of y from the first equation into the second equation.
x*(-5 - x) = -4
x*(x + 5) = 4
x² + 5x - 4 = 0
Now, we will use the quadratic formula.
x = [-5 ± √(5² - 4(1)(-4))]/2(1)
x = [-5 ± √(25 + 16)]/2
x = [-5 ± √41]/2
x = [-5 ± 6.403]/2
The values of x are -5.7015 and 0.7015. The corresponding values of y are 0.7015 and -5.705.
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The mean, median and mode of the numbers below are the same,
what is the value of a?
6, 2, a, 7, 4, 9,6
Answer:
8
Step-by-step explanation:
Put the numbers in order from lowest to highest. Add all the numbers together. We will ignore a for this step. You should get 34 when adding it all together. Then if you were to add 8 to that 34 you'd get 42. Divide 42 by the amount of numbers you have which is 7. Your answer is 6. Now to make sure 8 is our value. We want to make sure the median is also 6. to find the median you need to have the numbers in order for lowest to highest and find the number in the middle. Don't forget to add your new number 8 into that order. You should get 6 as the median. Therefore our answer is 8
6r+r-4 helpppppp like I need it
The value of the variable r in 6r+ r- 4 will be 4/7.
Given,
To solve the polynomial,
6r + r- 4,
and find the value of the variable r,
we have to convert the polynomial in to a quadratic equation by equating it with 0, or, in other words, making the polynomial equal to zero.
So, the quadratic equation will be,
6r + r- 4 = 0
=> (6r+ r) -4 =0
=> 7r -4 = 0
=> 7r = 4
=> r = 4/7.
Thus, the value of the variable r in the polynomial 6r + r -4 will be 4/7.
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Match each type of transformations with an example and a description of how it affects the graph of a function.
1. Translation; y= f(x) + 2
2. Reflection; y= -f(x)
3. Stretch; y= 2f(x)
4. Shrink; y= 1/2 f(x)
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
What is Reflection?A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
Given:
When f(x) shifts 2 units up, we have
y= f(x) + 2; Translation
When the graph of f(x) to a symmetric position on the opposite side of the x-axis
y= -f(x); Reflection
When it stretches f(x) by a factor of 2
y= 2f(x); Stretch
When it reduces f(x) by a factor of 1/2
y= 1/2f(x); Shrink
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3x + 4y = 7
2x - y = 12
please help?
Answer:
x=5
y=-2
Step-by-step explanation:
even though this looks like they want you to do it elimination ima do substation cause I like that better
2x-y=12
+y. +y
2x=12+y
-12 -12
2x-12=y
Now we can fill in y
3x+4(2x-12)=7
3x+8x-48=7
11x-48=7
+48. +48
11x=55
/11. /11
x=5
fill in X to find y
2(5)-y=12
10-y=12
-10. -10
-y=2
y=-2
hopes this helps please mark brainliest