To calculate (g+j)(x) we need the function:
[tex]\begin{gathered} g(x)=-x^2+2x-5 \\ j(x)=6x^2-8x \end{gathered}[/tex]and we can made the addition so:
[tex]\begin{gathered} (g+j)(x)=g(x)+j(x) \\ (g+j)(x)=-x^2+2x-5+6x^2-8x \end{gathered}[/tex]and we can simplify
[tex](g+j)(x)=5x^2-6x-5[/tex]Daphne rolls two 6-sided number cubes. What is the probability that she rollsa sum equal to 3? Use the diagram of the sample space to help you. please help me
From the sample space, there are 2 results equal to 3, and there are 36 total results. Then the probability that she rolls a sum equal to 3 is: 2/36 or 1/18
After every score in a sample is multiplied by 5,the mean is found to be M = 40.What was the value for the original mean?
Since each of the data value is multiplied by 5, the new mean will be 5 times the original mean.
To get the original mean, we need to divide by 5.
Therefore the original mean is given by:
[tex]\frac{40}{5}=8[/tex]Answer: 8
Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume (000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
a.
What is the yield to maturity of the bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b. What is the current yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
a) The yield to maturity of the IOU Corporation's bond is -0.39%.
b) The current yield of the IOU Corporation's bond is 5.58%.
What is the yield to maturity?The bond's yield to maturity (YTM) is the total rate of return earned by a bondholder with all interest payments and the original principal repaid.
We can compute the yield to maturity using the following YTM formula:
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
Where:
FV = Face Value of the Bond
Price = Current Market Price
Maturity = Maturity Period.
Bond's face value = $2,000
Current date = April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume
(000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
Annual interest = $126 ($2,000 x 6.3%)
Maturity period = 16 (2037 - 2021)
Price = $2,259.4 ($2,000 x 112.97/100)
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
= [$126 + {($2,000 - $2,259.4)/16}] / [($2,000 + 2,259.4)/2]
= [$126 -$259.4)/16] / [($4,259.4)/2]
= -8.3375/2,129.7
= -0.39%
Current yield = Annual Coupon/Current Price
= 5.58% ($126/$2,259.4 x 100)
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In the following expression, place a decimal point in the divisor and the dividend that is 4368÷6208 to create a new problem with the same answer as in question 11 that is 7 meters / 7
---------------------------------
436.8m -------------------> 62.08s
xm -------------------------->1s
Using cross multiplication:
[tex]\begin{gathered} \frac{436.8}{x}=\frac{62.08}{1} \\ \text{solve for x:} \\ x=\frac{436.8}{62.08} \\ x=7.036082474m \\ \end{gathered}[/tex](1 point) For each trigonometric expression A,B,C,D, E, choose the expression from 1,2,3,4,5 that completes a fundamental identity. Enter the appropriate letter (A,B,C,D, or E) in each blank.
Answer:
Step-by-step explanation:
I would recommend looking up the magic trig hexagon, it has all of these identities and more within it.
1 - this corresponds with C as sin^2(x)+cos^2(x)=1
1-cos^2(x) - this corresponds with A, using the identity from number 1, we can rewrite it in the form sin^2(x)=1-cos^2(x)
cot(x) - for this it is important to know that cotangent is the inverse of tangent. Since tan(x)=sin(x)/cos(x), cot=cos(x)/sin(x) which is B.
sec^2(x) - much like the cos and sin pythagorean identity, sec and tan are related. sec^2(x)=tan^2(x)+1 which is answer choice E.
tan(x) - this is sin(x)/cos(x), choice D.
A middle school football game has four 12-minute quarters. Jason plays 8 minutes in each quarter.Which ratio represents Jason's playing time compared to the total number of minutes of playing time possible?1 to 3 2 to 33 to 24 to 1I’m
The total minutes in the game is 48. The total playing game for Jason is 32. The ratio is
[tex]\frac{32}{48}[/tex]Simplifying it, we have
[tex]\frac{32}{48}=\frac{16}{24}=\frac{8}{12}=\frac{4}{6}=\frac{2}{3}[/tex]So, the playing ratio is 2 to 3 for Jason.
The cost of a laptop computer decreased from $600 to $480. By what percentage did the cost of the computer decrease?
Initial value= $600
new value = $ 480
[tex]\begin{gathered} =\frac{600-480}{480}\times100 \\ =\text{ }\frac{120}{480}\times100 \\ =\text{ 25\%} \end{gathered}[/tex]25% decrease is the answer
Answer the questions about the figures below. 4 ft Figure A 6 ft 6 ft 4 ft (a) Which figures are parallelograms? Mark all that apply. Figure A O Figure B (b) Which figures are squares? Mark all that apply. Figure A Figure B (c) Which figures are rectangles? Mark all that apply. Figure A Figure B O Figure C Figure C Figure C 6 ft Figure B 4 ft 4 ft 6 ft None of the figures None of the figures None of the figures 6 ft X Figure C 6 ft 6 ft Ś 6 ft ?
A parallelogram is a 4 sided figures that has the opposite sides parallel.
Figure A has right angles so the opposite sides are parallel
Figure B has the opposite sides of equal length, so the opposite sides are parallel
Figure C has right angles so the opposite sides are parallel
For Question A, Figure A, B C are parallelograms
Squares have opposites sides parallel and all 4 sides of equal length and all angles right angles
The only figure with all 4 sides of equal length, all 4 angles right angles is Figure C ( opposites sides are parallel because 4 sides are equal length and all 4 angles are right angles)
The figure that is a square is Figure C
Rectangles are shapes that have opposite sides parallel and all 4 angles are right angles. Squares are special rectangles
Figure A has opposite sides parallel and all 4 angles equal length. Figure C is a square, which is a special rectangle
The rectangles are figures A and C
Production has indicated that they can produce widgets at a cost of $16.00 each if they lease new equipment at a cost of $40,000. Marketing has estimated the number of units they can sell at a number of prices (shown below). Which price/volume option will allow the firm to avoid losing money on this project?
The price/volume option that will allow the firm to avoid losing money on this project is C. 2,300 units at $34.00 each.
How is this option determined?To determine the correct option, we use the cost-volume-profit analysis tool.
The cost-volume-profit (CVP) analysis involves determining how the volume of sales drives profitability.
The CVP technique classifies costs into their variable and fixed cost elements for the purpose of this analysis.
Variable cost per unit = $16
Fixed cost = $40,000
Option A Option B Option C Option D Option E
Sales units 3,000 1,900 2,300 2,500 1,700
Unit selling price $29 $36.50 $34 $31.50 $39
Sales revenue $87,000 $69,350 $78,200 $78,750 $66,300
Variable costs 48,000 30,400 36,800 40,000 27,200
Fixed cost 40,000 40,000 40,000 40,000 40,000
Total costs 88,000 70,400 76,800 80,000 67,200
Thus, the price/volume option that meets the firm's goal is Option C because the sales revenue exceeds the total costs.
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Question Completion with Price/Volume Options:A. 3,000 units at $29.00 each.
B. 1,900 units at $36.50 each.
C. 2,300 units at $34.00 each.
D. 2,500 units at $31.50 each.
E. 1,700 units at $39.00 each.
What is 5 5/7 divided by 1 3/5 divided by 4 2/3 in simplest form?
The simplest form of the given division is,[tex][tex]\frac{550}{13}[/tex][/tex].
What is division?
The opposite of multiplication is division. Dividing a sum of numbers into equal pieces. A number is divided in division, which is a straightforward procedure.
Given that: (55/7)/(13/5)/(42/3)
First to simplify:
[tex](13/5)/(42/3)[tex]\frac{(\frac{13}{5}) }{(\frac{42}{3}) } = \frac{(\frac{13}{5}) }{14} \\[/tex] [tex]= \frac{13}{(5)(14)} \\= \frac{13}{70}[/tex][/tex]
So, expression becomes,
[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )}[/tex][/tex]
Now to simplify this expression.
Using:[tex][tex]\frac{(\frac{a}{b} )}{(\frac{c}{d} )} = \frac{ad}{bc}[/tex][/tex]
Then,[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )} = \frac{(55)(70)}{(7)(13)} = \frac{3850}{91} = \frac{550}{13}[/tex][/tex]
Therefore, [tex][tex]\frac{550}{13}[/tex][/tex] is the simplest form of the given division.
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What is the value of the expression below?2,816 x 714,57214,67219,61219,712
The given expression is
[tex]2,816\times7[/tex]We just have to multiply.
[tex]2,816\times7=19,712[/tex]Hence, the right answer is D.if the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
since n, mand r are the constants for a, b,c n=6
Chris took four math quizzes and achieved a 68, 90, 95, and 75. What is his mean quiz average?
The average of a set is computed as follows:
[tex]\text{Average = }\frac{Tota\text{l sum of all numbers}}{\text{ number of items in the set}}[/tex]In this case,
[tex]\text{Average =}\frac{68+90+95+75}{4}=\frac{328}{4}=82[/tex]The value of an IBM share one day was $ 74.50 more than the value of an AT&T share.
An algebraic expression we can use to compare the price of IBM shares as being $74.50 more than AT&T shares is x + 74.50, where x is the value of AT&T shares.
What is an algebraic expression?An algebraic expression consists of variables, terms, constants, and mathematical operations, including addition, subtraction, multiplication, division, and others.
The five algebraic expressions include monomial, polynomial, binomial, trinomial, multinomial.
We can also describe algebraic expressions as falling under the following categories:
Elementary algebraAdvanced algebraAbstract algebraLinear algebraCommutative algebra.An example of an algebraic expression is 2x + 3y.
Let the value of AT&T share = x
Let the value of IBM share = x + 74.50
Thus, we can, algebraically, conclude that AT&T's share price is x while the price of IBM's share is x + 74.50 on that particular day.
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solve the inequality for 5x + 9 ≤ 24
From the problem, we have an inequality of :
[tex]5x+9\le24[/tex]Subtract 9 to both sides of the inequality :
[tex]\begin{gathered} 5x+9-9\le24-9 \\ 5x\le15 \end{gathered}[/tex]Divide both sides by 5 :
[tex]\begin{gathered} \frac{5x}{5}\le\frac{15}{5} \\ x\le3 \end{gathered}[/tex]The answer is x ≤ 3
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chefwants to make 370 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
Assuming these are volume percentages and the volumes don't change when you mix them, we can calculate this using a system of equations.
But first we need to identify each equation and variable.
let x be the volume of 7% vinegar used and y be the volume of 12% vinegar used.
The total volume is the sum of those and it must be equal to 370 mL, so:
[tex]x+y=370[/tex]The amount of vinegar in the x volume of 7% vinegar can be calculated by multiplying x by the 7%, that is, by 0.07:
[tex]0.07x[/tex]Similarly, the amount of vinegar in y is:
[tex]0.12y[/tex]So, the total amount of vinegar after the mixture is:
[tex]0.07x+0.12y[/tex]Since the percentage of the final mixture is 8%, the amount after the mixture can also be calculated by taking 8% of the final volume of 370mL, that is:
[tex]0.08\cdot370=29.6[/tex]The two ways of calculating the amount of vinegar in the mixture must be the same, so we have got our second equation:
[tex]0.07x+0.12y=29.6[/tex]So, the system of equations is:
[tex]\begin{gathered} x+y=370 \\ 0.07x+0.12=29.6 \end{gathered}[/tex]We can solve this by substitution:
[tex]\begin{gathered} x+y=370 \\ x=370-y \end{gathered}[/tex]Thus:
[tex]\begin{gathered} 0.07x+0.12y=29.6 \\ 0.07(370-y)+0.12y=29.6 \\ 0.07\cdot370-0.07y+0.12y=29.6 \\ 25.9+0.05y=29.6 \\ 0.05y=29.6-25.9 \\ 0.05y=3.7 \\ y=\frac{3.7}{0.05} \\ y=74 \end{gathered}[/tex]And, going back to the first equation:
[tex]\begin{gathered} x=370-y \\ x=370-74 \\ x=296 \end{gathered}[/tex]what is its base of the parallelogram is72 meters²
The area of a parallelogram is computed using the formula base x height.
Here we have a parallelogram with an area of 72 square meters and a height of 9 meters. Using the formula, we can solve for the base.
[tex]\begin{gathered} A=bh \\ 72=b(9) \\ \\ \frac{72}{9}=\frac{b(9)}{9} \\ \\ 8=b \end{gathered}[/tex]The base is 8 meters long.
Compute the area of each triangle. Round to the nearest tenth.
The triangle ΔDEF has the following coordinates
[tex]\lbrace D(-1,6),E(-4,-6),F(3,-5)\rbrace[/tex]To find the area of a triangle in coordinate geometry, we have a formula. Given 3 vertices A(x1, y1), B(x2,y2) and C(x3,y3), the area of this triangle is given by
[tex]Area(\Delta ABC)=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]Using this formula for our problem, we have
[tex]Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))|[/tex]Solving this equation, we have
[tex]\begin{gathered} Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))| \\ =\frac{1}{2}|(-1)((-6+5)+(-4)(-5-6)+3(6_{}+6)| \\ =\frac{1}{2}|(-1)(-1)+(-4)(-11)+3(12)| \\ =\frac{1}{2}|1+44+36| \\ =\frac{1}{2}|81| \\ =\frac{81}{2} \\ =40.5 \end{gathered}[/tex]And this is our answer Area(ΔDEF) = 40.5
About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
The total points that the four students score in round 1 is 75 points.
How to calculate the value?Based on the information given, it's important to convert the numbers to while numbers and then add.
John has 19.5. This will be 20.
Adam had 21.2. This will be 21.
Peter has 23.8. This will be 24.
Grace has 10.2. This will be 10.
The total points will be:
= 20 + 21 + 24 + 10
= 75
The complete question is given below.
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The points of four students are:
John 19.5
Adam 21.2
Peter 23.8
Grace 10.2
About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
use the number line to find the distance between -3 and -9
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
Please help me no other tutor could or understand it
We must find the equation that models the amount of medication in the bloodstream as a function of the days passed from the initial dose. The initial dose is a and we are going to use x for the number of days and M for the amount of mediaction in the bloodstream. We are going to model this using an exponential function which means that the variable x must be in the exponent of a power:
[tex]M(x)=a\cdot b^x[/tex]We are told that the half-life of the medication is 6 hours. This means that after 6 hours the amount of medication in the bloodstream is reduced to a half. If the initial dose was a then the amount after 6 hours has to be a/2. We are going to use this to find the parameter b but first we must convert 6 hours into days since our equation works with days.
Remember that a day is composed of 24 hours so 6 hours is equivalent to 6/24=1/4 day. This means that the amount of medication after 1/4 days is the half of the initial dose. In mathematical terms this means M(1/4)=M(0)/2:
[tex]\begin{gathered} \frac{M(0)}{2}=M(\frac{1}{4}) \\ \frac{a\cdot b^0}{2}=a\cdot b^{\frac{1}{4}} \\ \frac{a}{2}=a\cdot b^{\frac{1}{4}} \end{gathered}[/tex]We can divide both sides of this equation by a:
[tex]\begin{gathered} \frac{\frac{a}{2}}{a}=\frac{a\cdot b^{\frac{1}{4}}}{a} \\ \frac{1}{2}=b^{\frac{1}{4}} \end{gathered}[/tex]Now let's raised both sides of this equation to 4:
[tex]\begin{gathered} (\frac{1}{2})^4=(b^{\frac{1}{4}})^4 \\ \frac{1}{2^4}=b^{\frac{1}{4}\cdot4} \\ b=\frac{1}{16} \end{gathered}[/tex]Which can also be written as:
[tex]b=16^{-1}[/tex]Then the equation that models how much medication will be in the bloodstream after x days is:
[tex]M(x)=a\cdot16^{-x}[/tex]Using this we must find how much medication will be in the bloodstream after 4 days for an initial dose of 500mg. This basically means that a=500mg, x=4 and we have to find M(4):
[tex]M(4)=500mg\cdot16^{-4}=0.00763mg[/tex]So after 4 days there are 0.00763 mg of medication in the bloodstream.
Now we have to indicate how much more medication will be if the initial dose is 750mg instead of 500mg. So we take a=750mg and x=4:
[tex]M(4)=750mg\cdot16^{-4}=0.01144mg[/tex]If we substract the first value we found from this one we obtained the required difference:
[tex]0.01144mg-0.00763mg=0.00381mg[/tex]So the answer to the third question is 0.00381mg.
I inserted a picture of the question can you please hurry
Given:
[tex](-2,-5)\text{ and (}1,4)\text{ are given points.}[/tex][tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{4+5}{1+2} \\ \text{Slope}=\frac{9}{3} \\ \text{Slope}=3 \end{gathered}[/tex]For the diagram below, if < 4 = 4x - 2, and < 6 = 2x + 14, what is the value of x?Select one:a.8b.16c.4d.5
x = 8
ExplanationsFrom the line geometry shown, the line a and b are parallel lines while line "t" is the transversal.
Since the horizontal lines are parallel, hence;
[tex]\angle4=\angle6(alternate\text{ exterior angle})[/tex]Given the following parameters
[tex]\begin{gathered} \angle4=4x-2 \\ \angle6=2x+14 \end{gathered}[/tex]Equate both expressions to have:
[tex]\begin{gathered} 4x-2=2x+14 \\ 4x-2x=14+2 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Hence the value of x is 8
(8-4) mulitiply (3-2)=
Ramon has assets that sum up to $253,000. He has liabilities that sum up to $216,345. what is his net worth?
Net worth is equal to total assets minus total liabilities (debt).
So,
Total Assets = 253000
Total Liabilities = 216345
Hence,
Net Worth = 253000 - 216345 = $36,655
Help!!!! (Show ur work)
There are two questions
Answer:
Question 1: 3
Question 2: $120
Step-by-step explanation:
Set up a proportion
[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex] fill in the numbers that you know and solve for the unknow.
[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex] Cross multiply
5x =7.5(2)
5x = 15 Divide both sides by 5
x = 3
If we take 40% off that means that we leave 60% on
Percent means per hundred
[tex]\frac{60}{100}[/tex] When you divide by hundred, you move the decimal two places to the left.
200(.6)
$120.00
A number between 280 and 380 when rounded to the nearest hundred is 45 less than the original number what number is the original number
If the unknown number is an integer between 280 and 349;
When rounded to the nearest hundred, the unknown number is 300.
If the unknown number is an integer from 350-380;
When rounded to the nearest hundred, the unknown number is 400.
If the approximation is 45 less than the original number, thus it cant be in the range of 350-380.
But;
[tex]300+45=345[/tex]When 345 is rounded to the nearest hundred, it is 300.
And the difference between the approximated value and the original value is 45.
Hence, 345 is the original number.
CORRECT ANSWER: 345
My name is Nika and I need help in math I’m 73 and done with school but still don’t under algebra
The given equation is
[tex]2x-3=9[/tex]To solve this equation we have to isolate x on one side and put the numbers on the other side
To do that we will add 3 to each side to move 3 from the left side to the right side
[tex]2x-3+3=9+3[/tex]Simplify it
[tex]\begin{gathered} 2x+0=12 \\ 2x=12 \end{gathered}[/tex]Now we need to move 2 from the left side to the right side, then
Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Then the solution of the equation is
x = 6
In which graph does the height difference between Winter Hill and Frozen Field equal the height of BlizzardRun?Choose 1 answer:605040Height (in meters)30.©20100Blizzard RunSnow SlopeWinter HillFrozen FieldSledding hill
In graph A, you can see that:
• The height of Frozen Field is 50 meters
,• The height of Winter Hill is 15 meters
,• The height of Blizzard Run is 35 meters
Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.
[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=50m-15m=35m_{}=\text{ Height of Blizzard Run }[/tex]In graph B, you can see that:
• The height of Frozen Field is 45 meters
• The height of Winter Hill is 10 meters
• The height of Blizzard Run is 55 meters
Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.
[tex]\text{ Height of Frozen Field }-\text{ Height of Winter Hill }=45m-10m=35m\ne55m_{}=\text{ Height of Blizzard Run }[/tex]Therefore, the graph where the height difference between Winter Hill and Frozen Field is equal to the height of Blizzard Run is graph A.
Recall that two angles are complementary if the sum of their measures is 90°.
Find the measures of two complementary angles if one angle is 18° more than two times
the other angle.
The smaller angle measures
...
Complementary angles - The smaller angle is 24 degrees in size.
what are complementary angles?
Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.
Let x equal the first angle's measurement for the sake of explanation.
Let y be the size of the first angle's complement.
One angle, which we'll refer to as y, is 18 more than twice as large as another, x.
y = 18 + 2x
Complementary angles add up to 90 degrees.
x + 18 + 2x = 90
By substituting for y,
we get x + 18 + 2 x = 90.
Putting like phrases together and taking 18 off on both sides...
3x + 18 = 90
- 18 -18
3x = 72
By dividing both sides by 3, you get
3x/3 = 72/3
24 degrees is the angle between the two that is smaller. and the other angle would be,
y= 18+2x
=18+2(24)= 66 degrees.
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