Given
gallons which have 20% antifreeze solution = 80
Final concentration = 50% antifreeze solution
Find
Number of galloons with 60% antifreeze solution
Explanation
Let the number of gallons with 60% antifreeze solution = x
According to question
0.6x+0.2(80) = 0.50(x+80)
0.6x+16=0.5x+40
0.1x=24
x=240
Final Answer
Hence 240 gallons of 60% antifreeze solution will be required
) POLYNOMIAL AND RATIONAL FUNCTIONSVord problem involving the maximum or minimum of a quadrati.
SOLUTION:
Case: Minimum and Maximum functions
Given:
[tex]\begin{gathered} C(x)=0.8x^2-352x+58,583 \\ \end{gathered}[/tex]Required: To find the minimum Unit cost
Method: we apply completing square on the function
Step 1: First we find the square of half the coefficient of x
[tex]\begin{gathered} C(x)=\text{ 0.8x}^2-352x+58583 \\ C(x)=\text{ 0.8\lparen x}^2-440x+73228.75) \\ \frac{1}{2}(440)=\text{ 220}^2\Rightarrow\text{ 48400} \end{gathered}[/tex]Step 2: Add and subtract the value to the Right Hand Side
[tex]\begin{gathered} C(x)=\text{ 0.8\lparen x}^2-440x+48400-48400+73228.75) \\ Completing\text{ squares in the bracket} \\ C(x)=\text{ 0.8\lbrack\lparen x-220\rparen}^2+24828.75] \\ C(x)=0.8(x-220)^2+\text{ 19863} \end{gathered}[/tex]Step 3: From the equation
The quantity need to be produced to get the minimum unit cost is 220.
The value of the minimum cost therefore is obtained at C(220).
This would give:
C(220)= $19863
Final answer:
The minimum unit cost is $19863. Ignore the dollar sign($) when entering your answer.
2. The graph below shows the relationship between the number of pages printed (x) at a print shop and the total price (y), in dollars. Print Shop Prices у 9 Total Price ($) Based on the graph, what is the unit price at the print shop?
Let:
[tex]\begin{gathered} (x1,y1)=(2,1) \\ (x2,y2)=(4,2) \\ so\colon \\ m=\frac{y2-y1}{x2-x1}=\frac{2-1}{4-2}=\frac{1}{2}=0.5 \end{gathered}[/tex]Determine whether the line that passes through points (-2, 1) and (6, 5) is parallel, perpendicular or neither to a line with a slope of -2.
We have a line with slope -2. A parallel line would have a slope of -2 too, and a line perpendicular to it will have a slope of 1/2.
If line A is perpendicular to B, the slope of B is the inverse multiplicative of the sloe of A. That is why a line perpendicular to the one with slope -2 is 1/2:
[tex]\text{Perpendicular Slope}=-\frac{1}{-2}=\frac{1}{2}[/tex]Now we know the slopes for both cases: parallel and perpendicular. If the slope is different to -2 or 1/2, we can say that is not parallel nor perpendicular to the line given.
Let's evaluate the slope of the line that passes through points (-2, 1) and (6,5).
The slope is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where x₁ and y₁ are the x and y-coordinates of the first point (-2 and 1), and x₂ and y₂ are the x and y coordinates of the second point (6 and 5, respectively).
Replacing values:
[tex]\begin{gathered} m=\frac{5-1}{6-(-2)}=\frac{4}{6+2}=\frac{4}{8} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]The slope of the line passing through the points given is 1/2, then, according to what was said above, that line is perpendicular to a line with slope -2.
write the equation Log 243 81= 4/5
Given
[tex]\log _{243}81=\frac{4}{5}[/tex]
Procedure
Exponential form
[tex]\begin{gathered} 243^{4/5}=81^{} \\ \end{gathered}[/tex]
Jack borrows $2,700 at a rate of 8.2% per year. How much total will he pay if it takes 3 months to repay the loan?
well, a year has a total of 12 months, so 3 months is really 3/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2700\\ r=rate\to 8.2\%\to \frac{8.2}{100}\dotfill &0.082\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ A=2700[1+(0.082)(\frac{1}{4})] \implies A = 2700(1.0205)\implies A=2755.35[/tex]
Please help with #9 i’m on please help with angles
We know that two angles shown have to add to a right angle, which measures 90°, then we have the equation:
[tex]\begin{gathered} x+5x=90 \\ 6x=90 \\ x=\frac{90}{6} \\ x=15 \end{gathered}[/tex]Hence, the value of x is 15°; which means that:
[tex]\begin{gathered} x=15 \\ 5x=75 \end{gathered}[/tex]Therefore, the angles are 75° and 15°
What values of b satisfy 4(3b+2)^2=64
solve for b:
take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{4(3b+2)^2}=\sqrt[]{64} \\ \sqrt[]{4}\cdot\sqrt[]{(3b+2)^2}=\pm8 \\ 2(3b+2)=\pm8 \\ 6b+4=\pm8 \\ so\colon \\ b=\frac{\pm8-4}{6} \end{gathered}[/tex]therefore:
[tex]\begin{gathered} b=\frac{2}{3} \\ or \\ b=-2 \end{gathered}[/tex]Answer: b=2/3 and b=-2
Step-by-step explanation:
Use the distributive property to write an equivalent expression.
8(4n+ 3) =
12x-6=
5x+20=
3(x+6)=
7x-35=
20p + 16 =
The distributive property to write an equivalent expression.
8(4n+ 3) = 32n + 24
12x-6= 1/2
5x+20= 4
3(x+6)= 3x + 18
7x-35= 5
20p + 16 = 4/5
A distributive property in mathematics is defined:The distributive property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and combining the resulting products.
We use distributive property for what purposes?One of the most common properties in arithmetic is the distributive property. The multiplier is applied to each integer inside the parentheses, and the results are added to obtain the answer. This technique is used to simplify and solve multiplication problems.
According to the given data:the distributive property to write an equivalent .
8(4n+ 3)
= 8 * 4n + 3* 8
= 32n + 24
for 12x-6
12x-6 = 0
x = 6/12
x = 1/2
For 5x+20
5x+20 =
x = -4
For 3(x+6)
= 3 * x + 3 * 6
= 3x + 18
For 7x-35
= 35/7
= 5
For 20p + 16
= 20/16
= 5/4
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The lengths of the sides of a triangle are 5,6, and 7. If the perimeter of a similar triangle is 36, what is the length of the shortest side of the similar friangle? A) 5 B) 10 C) 4 D) 6
The length of the sides of a triangle are 5, 6 and 7.
If the perimeter of a similar triangle is 36
Perimeter of a triangle = a + b+ c
The perimeter of the first triangle is
P = 5 + 6 + 7
P = 11 + 7
P = 18
To find the smallest lengths
18 / 36 = 5 / x
Introduce cross multiplication
36 x 5 = 18 * x
180 = 18x
Divide both sides by 18
180/18 = 18x/18
x = 180/18
x = 10
The answer is 10
Write a biconditional for the following conditional. Then state the truth value of the statement
If two lines intersect at right angles, then they are perpendicular.
The biconditional for the conditional statement is : Two line intersect each other at right angles . The two lines are perpendicular.
A conditional statements are part of mathematical reasoning, a fundamental ability that enables students to evaluate a given hypothesis without reference to a particular context or meaning.
Simply put, when a scientific research or allegation is studied, the logic is not reliant on an individual's viewpoint. Deductions and evidence must have factual and scientific foundations.Conditionals are programming language instructions used to manage judgments in the field of computer science. They are also referred to as conditional statements, conditional expressions, and conditional constructions.One needs to be capable of logical reasoning and critical thinking in mathematics in order to respond to questions involving mathematical reasoning and conditionals.The truth value for the conditional statement is true as we know that when two lines intersect at 90° then they are said to be perpendicular.
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What’s the correct answer answer asap for brainlist
Answer:
I would say C but I'm really not sure hope this helps
Given the graph below write an equation of the form f(x) = Acos(w(x-c))+D
Amplitude = (Maximum + Minimum)/2 , = (1 + 1.8)/2= (2.8)/2= 1.4
Period = distance for the function to repeat. So, the distance is from -0.5 to 3.5, then it is 4, then it is smaller than 2 times pi number.
C is the distance from the Y axis to the function.
D is the horizontal line that passes through the middle of the distance between the maximum and minimum point, which is in that case the same one as the period has to use
Then, the formula is:
[tex]\begin{gathered} f(x)=Acos(w(x\text{ -c\rparen + D A is amplitude, C is horzontal distance and D}midpoint \\ \\ f(x)=1.4cos(4(x\text{ - 1.7\rparen+\lparen-0.4\rparen} \\ f(x)=1.4cos(4x\text{ - }6.8)\text{ - }0.4 \end{gathered}[/tex]how do you use Congruence and similarity criteria to prove relationships in geometric figures?
Congruence and similarity criteria are used to determine congruence and proportional relationships respectively. That is, congruence criteria is used to establish a relationship of equivalence, and similarity criteria is used to establish a relationship of proportion with a common ratio between the figures.
Week 1: saves $ 35 Week 2 : saves $ 10 Week 3: spends $ 20 Week 4: spends $ 5 Week 5 saves $15 Week 6: saves $10 Susan wants to go on a vacation to the beach with her friends . For six weeks she keeps track of how much money she spends and saves . For the next six weeks she plans on increasing the amount she saves by $10 and decreasing the amount she spends by $5. How will this affect the MEAN amount of money that Susan has ? A) The mean will not change . B) The mean will increase by approximately $5. ) The mean will increase by approximately $ 8. D) The mean will increase by approximately $15. E) The mean will increase by approximately $30.
B) The mean will increase by $5
1) The first scenario has the following mean, adding all the spendings and savings:
[tex]x=\frac{35+10+20+5+15+10}{6}=\frac{95}{6}=15.83[/tex]2) Since for the following week there's an increase of $10 for her savings and a decrease of $ 5 we can write:
[tex]\begin{gathered} x=\frac{(35+10)+(10+10)+(20-5)+(5-5)+(15+10)+(10+10)}{6}= \\ =\frac{45+20+15+0+25+20}{6}=\frac{125}{6}=20.83 \end{gathered}[/tex]3) We can see that the mean changes, and examining the options we can state that:
the answer is B, the mean will increase by $5
help me pls I don't understand what I'm supposed to put here
The feedback loops in each situation are classified as follows:
a) Positive.
b) Negative.
What are positive and negative feedback loops?A positive feedback loop is when there is an amplification or growth of the output signal.A negative feedback loop is when there is a damping of the output signal, which is equivalent to a reduction in it's effect.In the context of this problem, in item a, there is a continuous amplification of the output signal, which is the surface temperatures, as they keep increasing, the three effects listed contribute to the increase of temperature, then the system go back to the beginning still with increasing temperatures, hence it is a positive feedback loop.
In item b, we have a loop with changes in the temperature, it increases and then it decreases, and so on, hence it is a negative feedback loop.
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Which graph is the solution of the system
x+2y≤16
4x+y>6
1 2 3 4
Graph 1 shows the correct representation the solution of the system.
What is solution of system of linear equation?The point that satisfies all of the equations in a system of linear equations is called the solution. A system of linear equations could be solved through graphing as well as identifying the intersection point, or by solving the variables algebraically.For the given question;
The system of linear equation are given as;
x + 2y ≤ 16 .......eq 1
4x + y > 6 ......eq 2
Consider equation 1;
x + 2y = 16
For x = 0; y = 8 , Point = (0, 8)
For y = 0, x = 16, Point = (16, 0)
As the inequality of the eq 1 is less than equal to, the shaded region will lies below the line with solid lines.
Consider equation 2;
4x + y = 6
For x = 0; y = 6 , Point = (0, 6)
For y = 0, x = 1.5, Point = (1.5, 0)
As the inequality of the eq 2 is greater than, the shaded region will lies above the line with doted lines.
Thus, graph 1 shows the correct representation the solution of the system.
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If x = 9 and 4x + 7 = y
Then 4(9)+7 = y
This is an illustration of which property?
Answer: Substitution property
Step-by-step explanation:
It's substituting a variable into an equation.
You are the manager of a rental car company. A customer, Sandy Furrow, has asked you for an estimate of charges for a nine day rental of an SUV. She expects to drive 670 miles. If the company charges $55.50 per day plus 15 1/2 cents
per mile for this category of vehicle, what would be the total rental charge (in $) for Sandy's trip?
The total cost of her trip will be of $159.7.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation.
given:
Cost of 16 cents per mile= 16/100 = 0.16
Cost of $52.50 per day =52.50
linear function for the charge y in function of the number of miles x is:
y(x) = 0.16x + 52.50
The cost of driving 670 miles
So, y(670) = 0.16 x 670 + 52.50
y(670) = 107.2 + 52.50
y(670) = 159.7
Hence, The total cost of her trip will be of $159.7.
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The price of the TV, which cost € 1,260, was reduced by € 189. Calculate the percentage of this TV.
Initial TV price, $1,260
price reduction, $189
percentages:
reduction percentage or discount = 189/1260 = 0.15 = 15%
The above indicates the percentage by which the price was reduced or the discount obtained
percentage paid = (1260-189) / 1260 = 0.85 = 85%
This indicates that we paid 85% of the initial price.
Original price $27.00 Markdown 15%
The circumference of a circle is 16 M what is the diameter of the circle
Given
Circumference, C = 16m
Find
diameter
Explanation
We know Circumference of a circle
[tex]\begin{gathered} C=2\pi r \\ 16=2\times\frac{22}{7}\times r \\ \frac{16\times7}{2\times22}=r \\ \frac{4\times7}{11}=r \\ \frac{28}{11}=r \end{gathered}[/tex]diameter = 2r
[tex]undefined[/tex]
If a bug can flap its wings at a rate of 69 times in 4 seconds, how manytimes do they flap their wings in 1.476 minutes? Round to 1 decimal.w
First, we need to change 1.476 minute to seconds
1.476 minutes = 1.476 x 60= 88.56 seconds
Let the number of times they flap there wings in 1.476 minute be X
69 times = 4 seconds
X = 88.56 seconds
cross-multiply
4X = 69(88.56)
4X= 6110.64
Divide both-side of the equation by 4
X = 1 527.66 ≈ 1 528 times
Karma has 110 pounds of rice to sell. A vendor offers her $0.01 per 5 grams for her rice. How much money will karma make if she sells her rice to this vendor
Karma will make $99.78 if she sells 110 pounds of rice to the vendor
Quantity of rice available with Karma = 110 pounds
A pound is a unit of weight that is mostly used in the United States, Great Britain, and other English-speaking nations. A pound is approximately 0.454 kilos. A quantity of something is said to weigh one pound if it weighs that much.
The conversion rate of pounds to grams:
1 pound = 453.59 grams
So, 110 pounds will be equal to:
110*453.59
=49894.9 grams
Selling price for 5 grams = $0.01
Selling price for 1 gram:
The selling price of 5 grams/ Price for 5 grams
0.01/5
=$0.002
Selling price for 49894.9 grams = 49894.9*0.002
= $99.78
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Is 91.470 rational or irrational?
The number 91.470 is the rational number.
What is termed as the rational number?Rational numbers are written in the form p/q, in which p and q are any integer and q 0 respectively. The following are the various types of rational numbers.Integers such as -2, 0, 3, and so on are rational numbers.Rational numbers are fractions with integer numerators and denominators, such as 3/7, -6/5, and so on.Ending decimals such as 0.35, 0.7116, 0.9768, and so on are rational numbers.Rational numbers are non-terminating decimals with repeating patterns (just after decimal point), including such 0.333..., 0.141414..., and so on. These are commonly referred to as non-terminating recurring decimals.For the given number.
91.470 can be written in the fraction as;
91470/1000
Or 914/100
As, the form is p/q where q ≠ 0.
Thus, the number 91.470 is the rational number.
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The mean amount of gasoline charged by Key Refining Co.'s customers is $70 per month. The distribution of amount spent is approximately normal with a standard deviation of $10. Compute the probability (area under the curve) of selecting a customer who spent between $57 and $83 per month.
The probability (area under the curve) of picking a client who spends between $57 and $83 per month is 0.4032.
Given,
Mean, μ = $70
Standard Deviation, σ = $10
z = (x-μ) ÷ σ
P(The consumer was charged from around $70 and $83),
P(70 ≤ x ≤ 83) = P((70 - 70) ÷ 10)) ≤ z ≤ ((83-70) ÷ 10)) = P(0 ≤ z ≤ 1.3)
=P(z ≤ 1.3) - P(z ≤ 0)
=0.9032 - 0.500 = 0.4032 = 40.32%
P(70 ≤ x ≤ 83) = 40.32%
Customers with Key Refining Company loans typically spend an average of $70 monthly on gasoline and servicing. With either a standard deviation of $10, the expenditure distribution is about normal. For z = 1.3, the area under the curve is 0.4032.
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solve for x: 3/2+1/2x=2x
Here we will try to solve an equation involving a variable ( x ) given as follows:
[tex]\frac{3}{2}\text{ + }\frac{1}{2}\cdot x\text{ = 2x}[/tex]We use the following basic mathematical operations when solving any equation:
[tex]\text{Multiplication, Division, Addition, Subtraction}[/tex]We will first try to isolate our vairable ( x ) on either side of the " = " sign. We will try to isolate ( x ) on the right hand side of " = " sign. To do this we will employ the mathematical operation of " Subtraction ".
We will subtract ( 1 / 2 x ) from both sides of " = " sign:
[tex]\begin{gathered} \frac{3}{2}\text{ + }\frac{1}{2}\cdot x\text{ - }\frac{1}{2}\cdot x\text{ = 2x - }\frac{1}{2}\cdot x \\ \\ \frac{3}{2}\text{ = x}\cdot\text{ (}\frac{4\text{ - 1}}{2}) \\ \\ \frac{3}{2}\text{ = }\frac{3}{2}\cdot x \end{gathered}[/tex]The next mathematical operation we will apply is " Division ". We will divide the left hand side of the equation with right hand side constant as follows:
[tex]\begin{gathered} x\text{ = }\frac{\frac{3}{2}}{\frac{3}{2}} \\ \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1}} \end{gathered}[/tex]The solution to the given equation is as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1 }}[/tex]HELP ME WITH THESE THREE QUESTIONS PLEASE (GIVING BRAINLIEST TO THE BEST ANSWER.) 50 points
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answer:
6 units13 units5 unitsStep-by-step explanation:
You want the lengths of the unknown sides in the given trapezoid figure, knowing that the perimeter is 18 units.
1.The side AB is a vertical line segment, so its length can be found by finding the difference of y-coordinates of its end points.
AB = (2) -(-4) = 2+4 = 6
The length of AB is 6 units.
2.The sum of the lengths of vertical and horizontal segments is ...
AB +BC +CD = 6 +4 +3 = 13
The total distance from A to D along vertical and horizontal segments is 13 units.
3.The perimeter is the sum of the lengths of all sides.
perimeter = AB +BC +CD +AD
18 = 13 + AD . . . . . . substitute known values
5 = AD . . . . . . . . . subtract 13
The length of segment AD is 5 units.
__
Additional comment
Finding the length of a vertical or horizontal line is no different than finding the distance between two points on a number line.
Instructions: Find the measure of the indicated angle to thenearest degree.
Given:
• Length of side adjacent the indicated angle = 48
,• Length of hypotenuse = 56
Let's find the measure of the indicated angle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for cosine:
[tex]cos\theta=\frac{adjacent}{\text{ hypotenuse}}[/tex]Thus, we have:
[tex]\begin{gathered} cos\theta=\frac{48}{56} \\ \\ cos\theta=\frac{6}{7} \\ \\ \text{ Take the inverse cosine of both sides:} \\ \theta=cos^{-1}(\frac{6}{7}) \\ \\ \theta=31^o \end{gathered}[/tex]Therefore, the measure of the indicated angle is 31 degrees.
ANSWER
Please help me solve question 6 on this algebra 1 worksheet
We have that one simply way to write that equation is
[tex]\frac{2}{3}(21q^2-3q+7)[/tex]Because we have that
[tex]undefined[/tex]1. Angle AOC has what measurement according to the protractor?
In order to find the measure of angle AOC, let's start looking at point A.
Point A is in position 180, if we look in the upper numbers, and in position 0, if we look in the lower numbers.
Since it's easier to find the angle if one vertex is at position 0, let's consider position 0° for A.
Then, looking at point C, it is in position 130° in the upper numbers and 50° in the lower numbers.
Since we choose the lower numbers for A, we need to do the same for C.
Therefore A is in position 0° and C is in position 50°.
To find angle AOC, let's subtract both measurements/positions:
[tex]\text{AOC}=50\degree-0\degree=50\degree[/tex]Therefore angle AOC measures 50°, and the correct option is C.