Answer:
The percentage is
[tex]\frac{(98+100+100+Q4)}{400}=\frac{98}{100}[/tex]Solving for Q gives
[tex]Q=94[/tex]Is is possible to write a polynomial of degree 4 with zeros at 5, 3 and 8i? Explain your reasoning.
We know that if a polynomial has a complex root then the conjugate is also a root, in this case this means that if the polynomial has a root 8i then the number -8i is also a root. Taking this into account the polynomial that have the roots given would be:
[tex](x-5)(x-3)(x-8i)(x+8i)[/tex]this is a polynomial of degree 4.
A student leaving school walks 2.5 km north and then walks 1.0 km south. What is the student's displacement?A1.0 km southB.1.5 km northC. 2.5 km northD. 3.5 km south
Explanations:
Distance walked through North = 2.5 km
Distance walked through South = 1.0 km
Considering that the North and the South are in vertical directions to each other, it means the student first walked 2.5 km upwards (North), and then traced his way 1.0 km back downwards(South).
The Student's displacement = Distance across North - Distance across South
Student's displacement = 2.5 - 1.0
Student's displacement = 1.5 km North km upwards
Points A(-2, 4). B(1.3), C(4, -1) and D form a parallelogram. What are the coordinates of D?A. (5.5)B. (0,0)C. (1.-2)D. (1,0)E. (3,4)
Recall: The properties of the parallelogram: each two opposite sides are parallel.
The slopes of parallel lines are equal
slope to check AB
A(-2, 4). B(1.3)
[tex]Slope=\frac{3-4}{1--2}=-\frac{1}{3}[/tex]Slope CD
c(4,-1) D(1,0)
[tex]Slope\text{ =}\frac{0--1}{1-4}=-\frac{1}{3}[/tex]Slope BC
. B(1.3), C(4, -1)
[tex]Slope=\frac{-1-3}{4-1}=-\frac{4}{3}[/tex]Slope AD
A(-2,4) D(1,0)
[tex]Slope\text{ =}\frac{0-4}{1--2}=-\frac{4}{3}[/tex]Since AB is parralel to BC
and
BC is parrel to AD
Therefore, it is correct option D(1,0)
The final answer
Option D
At a certain high school, if a student is selected at random and asked what they plan to do after graduating, the probabilitydistribution for their response is given above, determine the following:
Solution:
a) 0.6
b) 0.1
c) 0.4
Analysis:
a) P(Do not attend any college): As we know the probabilities of attending a 4-year college or a junior college, we can subtract to find the complementary probability.
P(Do not attend any college)= 1-0.2-0.2
P(Do not attend any college) = 0.6
b)P(Attend a technical school): This probability is given in the chart. It's 0.1
c) P(Attend a college): We add probabilities of attending a 4-year college or a junior college.
P(Attend a college): 0.2+0.2 = 0.4
Hi im sorry to ask for help but im really stressed about this
Since, it is given that set of blueprint has an established scale that states
1 cm = 10ft.
Therefore 1.5 cm will be simply equal to
[tex]1.5\times10=15\text{ ft.}[/tex]Hence, the actual width of room on blueprint is 15ft.
Select all the expressions that correctly calculate the perimeter of the shape. 4020 80 + 20 0 120+200 300+ 1007 10 - 10 + 10 + 10 + 10 - 10
The perimeter of the shape is:
[tex]10+10+10+10+20\pi[/tex]This comes from the fact that we have four sides of lenght 10 and one full circle (remember that the perimeter of the circle is pi*D).
Therefore, the expression that correctly calculate the perimeter are:
[tex]40+20\pi[/tex]and
[tex]10+10+10\pi+10+10+10\pi[/tex]Mai and Jada are solving the equation 2.02 – 7,0 = 15 using the quadratic formula but found different solutions. Jada wrote: -(-7)+7-72 – 4(2)(-15) 2(2) 7+/-49- (-120) X = Mai wrote: -7 +72 - 4(2)(-15) 2(2) -7 +49-(-120) 4 -7 + 169 4 -7 + 13 4 3 = -5 2 * 7 + 71 x 4 х or X = If this equation is written in standard form, ax? - bx+c= 0, what is the value of c? Use + or - as needed when filling in your answers.
When using the quadratic formula, we always need to write the quadratic equation in standard form to see for the values of a, b and c. If we rewrite the quadratic equation in standard form, we have:
[tex]2x^2-7x=15\Rightarrow2x^2-7x-15=0[/tex]Having that the quadratic equation, in standard form, is:
[tex]ax^2+bx+c=0[/tex]Then, we have that, for this case, a = 2, b = -7, and c = -15. Thus, we need to use the quadratic formula using these values.
Therefore, the value for c is c = -15.
please thank you for your help
The initial expression is:
[tex]\frac{x-2}{3}+\frac{y+3}{4}=2[/tex]we can rewrite the function in the form:
[tex]y=mx+b[/tex]where m is the slope so:
[tex]\begin{gathered} \frac{y+3}{4}=-\frac{x-2}{3}+2 \\ \frac{y+3}{4}=-\frac{1}{3}x+\frac{2}{3}+2 \\ y+3=-\frac{4}{3}x+\frac{8\cdot4}{3} \\ y=-\frac{4}{3}x+10.6-3 \\ y=-\frac{4}{3}x+7.6 \end{gathered}[/tex]this means that the slope is -4/3 or -1.33
This is NoT from a test or graded assessment. This is an extra credit assignment.
We can use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]The principal value, P, is the initial amount of money: $4129.
The rate of interest, r, is 6.45%, or .0645.
The number of times compounded, n, per year is 1.
The number of years, t, is 7.
Plug all of these values into the equation and solve for A.
[tex]A=4129(1+\frac{.0645}{1})^{(1)(7)}[/tex]Evaluate the expression...
[tex]A=6395.3533[/tex]Rounded to the nearest dollar, this value becomes: $6395.
The investment will be worth $6395 after 7 years.
-4x-11 > 5 or 8x-7 > 9
Ok first we can solve x for each inequality
[tex]\begin{gathered} -4x-11>5 \\ -4x>5+11 \\ -4x>16 \\ x<\frac{16}{-4} \\ x<-4 \end{gathered}[/tex]when you remove a negative sign on inuquality you rotate the symbol
[tex]\begin{gathered} 8x-7>9 \\ 8x>9+7 \\ 8x>16 \\ x>\frac{16}{8} \\ x>2 \end{gathered}[/tex]so, we have
[tex]x<-4\text{ or x>2}[/tex]This is the graph, you dont take -4 and 2
The directions are with the pic below. It’s another pic coming. Couldn’t fit everything on the same page
Answer:
When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.
[tex]A(x,y)\Rightarrow A^{\prime}(-x,-y)[/tex]The coordinates are given below as
[tex]S(-1,3),T(-4,3),U(-3,1)[/tex]By applying the rule, we will have
[tex]\begin{gathered} S(-1,3)\Rightarrow S^{\prime}(-(-1),(-3)\Rightarrow S^{\prime}(1,-3) \\ T(-4,3)\Rightarrow T^{\prime}(-(-4),-3)\Rightarrow T^{\prime}(4,-3) \\ U(-3,1)\Rightarrow U^{\prime}(-(-3),-1)\Rightarrow U^{\prime}(3,-1) \end{gathered}[/tex]By graphing the triangle, we Will have
5 singles, 8 fives, 4 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game? State your answer in terms of dollars rounded to the nearest cent (hundredth).
The fair price to play the game is $23.61
Explanation:Number of singles = 5
number of fives = 8
Number of twenties = 4
number of $300 = 1
Total number = 5 + 8 + 4 + 1 = 18
fraction for each:
5/18 chance of getting singles
8/18 chance of getting fives
4/18 chance of getting twenties
1/18 chance of getting $300
We find the Expected values:
[tex]\begin{gathered} \text{singles = 1} \\ \text{Expected }value\text{ = (}\frac{5}{18}\text{ }\times1)\text{ +(}\frac{\text{ 8}}{18}\times\text{ 5)+ (}\frac{\text{4}}{18}\times20)\text{ + (}\frac{\text{1}}{18}\times300) \\ \text{Expected }value\text{ =}\frac{1}{18}\text{ \lbrack(}5\text{ }\times1)\text{ +(}8\times\text{ 5)+ (}4\times20)\text{ + (}1\times300)\rbrack \\ \text{Expected value =}\frac{1}{18}\text{(}5\text{ + 40 + 80 + 300)}_{} \\ \\ \text{fair price = }\frac{Total\text{ money in the hat}}{total\text{ number of bills}} \\ \text{fair price = }\frac{1}{18}\text{(}5\text{ + 40 + 80 + 300)}_{} \end{gathered}[/tex][tex]\begin{gathered} \text{fair price = }\frac{1}{18}\text{(}425\text{)}_{} \\ \text{fair price = \$23.61} \end{gathered}[/tex]In the absence of further information, fair price is $23.61
Which linear equation represents aline parallel to the graph of y=7x/4
Two lines are parallel if they have the same slope. The slope is the coefficient of the x variable when the equation is solved for y. In this case, the slope is
[tex]\frac{7}{4}[/tex]so, we need to ffind an equation with the same slope, that would be number 2
[tex]y=\frac{7}{4}x+5[/tex]8) -7x-2y=-13 x-2x= 11 1
having that x=3 we get
[tex]3-2y=11\rightarrow-2y=11-3=8\rightarrow y=-\frac{8}{2}=-4[/tex]so the answer is x=3 and y=-4
[tex]x-2y=11\rightarrow x=11+2y[/tex]having that we can replace in the first equation
[tex]\begin{gathered} -7\cdot(11+2y)-2y=-13\rightarrow-77-14y-2y=-13\rightarrow-16y=64 \\ y=-\frac{64}{16}=-4 \end{gathered}[/tex]having that y=-4 we get
[tex]x=11+2\cdot-4=11-8=3[/tex]What subtraction expression does the number line model show? HHHHHHHH - 10 -8 -6 -4 -2 0 2 4 0-0 O 3 + 6 O -3 - 6 -3 + (-6)
Each number on the number line is obtained by subtraction a number equivalent to the length of the given arrows.
In the red arrow points to -3, then you have from the starting point 0:
0 - 3 = -3
The blue arrow points to the position -9 from position -3, then the length of the arrow is 6. Subtract 6 to the previous number -3:
-3 - 6 = -9
Hence, the subtraction expression is - 3 - 6
The table below shows the elevation of four different landforms.Elevation of LandformsLandform Elevation (feet)Harper Hill 49Apple Valley -28.75Elburn Plain 371Lake Indigo-523If sea level is at 0 feet, which landform has an elevation that is farthest from sea level?Harper HillO Apple ValleyO Elburn PlainO Lake IndigoBack
To determine the landform that is farthest from sea level, consider only the positive numbers for the elevations, because the negative numbers mean under sea level.
The positive numbers are:
49
37 1/4 = 37.25
It is clear that 49 > 37.25.
Hence, the farthest landform is Harperhill
What is the probability of selecting a jack from a deck of cards?
Given,
The number of total cards in a standard deck is 52.
Required
The probability of getting jack.
The number of jack in the standard deck of cards is 4.
The probability of getting jack is,
[tex]\begin{gathered} P(jack)=\frac{number\text{ of jack}}{total\text{ cards}} \\ =\frac{4}{52} \\ =\frac{1}{13} \end{gathered}[/tex]Hence, the probability of getting jack is 1/13.
Rewrite y = a(0.5)^t/12 in the form y = a(1+r)^t or y = a(1-r)^t. Round each value to the nearest hundredth, if necessary. Then state the growth or decay rate.The rate is about %.It is a growth rate.
ANSWER :
[tex]y=a(1-0.5)^{\frac{t}{12}}[/tex]
The rate is about -50%
It is a decay rate
EXPLANATION :
From the problem, we have :
[tex]y=a(0.5)^{\frac{t}{12}}[/tex]Equate the term inside the parenthesis to (1 + r)
[tex]\begin{gathered} 1+r=0.5 \\ r=0.5-1 \\ r=-0.5 \end{gathered}[/tex]r is negative so the equation will be :
[tex]y=a(1-0.5)^{\frac{t}{12}}[/tex]The rate is the variable r x 100 which is -0.5 x 100 = -50%
Since the sign of r is negative, it is a decay rate.
The two figures are similar. Write the similarity statement. Justify your answer using factor and showing all work. Describe (in general since it isn't on a graph) the transformations from ABC to the new figure. First Triangle A to B: 40 B to C: 60 C to A: 50 Second TriangleX to Y: 31.25 Y to Z: 25 Z to X: 37.5
If two figures are similar, all of their pairs of corresponding sides have the same ratio:
To prove if the given figures are similar find the ratio between corresponding sides (to identify corresponding sides start with the smaller side in both figures and follow this logic):
[tex]\begin{gathered} \frac{AB}{YZ}=\frac{40}{25}=1.6 \\ \\ \frac{AC}{YX}=\frac{50}{31.25}=1.6 \\ \\ \frac{BC}{ZX}=\frac{60}{37.5}=1.6 \end{gathered}[/tex]As the ratio between corresponding sides is the same (1.6); triangle ABC is similar to traingle YZXTransformations from ABC to YZX: ABC (preimage) is dilated to get YZX (Image)
Find the factor of dilation:
[tex]\begin{gathered} Fd=\frac{Image}{Preimage} \\ \\ Fd=\frac{YZ}{AB}=\frac{25}{40}=\frac{5}{8} \end{gathered}[/tex]Then, the transformation from ABC to YZX is a dilation with a factor of 5/8Can you help me to do this please?Determine the inverse of the h(x)
Answer:
[tex]h^{-1}(x)=x^3+6x^2+12x+7[/tex]Explanation:
Given the below function;
[tex]h(x)=\sqrt[3]{x+1}-2[/tex]We'll follow the below steps to determine the inverse of the above function;
Step 1: Replace h(x) with y;
[tex]y=\sqrt[3]{x+1}-2[/tex]Step 2: Switch x and y;
[tex]x=\sqrt[3]{y+1}-2[/tex]Step 3: Solve for y by first adding 2 to both sides;
[tex]\begin{gathered} x+2=\sqrt[3]{y+1}-2+2 \\ x+2=\sqrt[3]{y+1} \end{gathered}[/tex]Step 4: Take the cube of both sides;
[tex]\begin{gathered} (x+2)^3=(\sqrt[3]{y+1})^3 \\ (x+2)^3=y+1 \end{gathered}[/tex]Step 5: Expand the cube power;
Recall;
[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]Applying the above, we'll have;
[tex]\begin{gathered} (x+2)^3=y+1 \\ x^3+3x^2\cdot2+3x\cdot2^2+2^3=y+1 \\ x^3+6x^2+12x+8=y+1 \end{gathered}[/tex]Step 6: Subtract 1 from both sides of the equation;
[tex]\begin{gathered} x^3+6x^2+12x+8-1=y+1-1 \\ x^3+6x^2+12x+7=y \\ \therefore y=x^3+6x^2+12x+7 \end{gathered}[/tex]Step 7: Replace y with h^-1(x);
[tex]h^{-1}(x)=x^3+6x^2+12x+7[/tex]Which of the following scenarios could be represented by the function f(x) = 500(1.04)^x? Select all that applyA. The total amount of money after x years in an account with an initial $500 investment and a 4% annual interest rateB. The number of rabbits bred each year at a growth rate of 104%, if you started with 500 rabbitC. The total population of a town growing at a rate of 4% each year if the town began with 500 inhabitantsD. The amount paid in sales tax on a $500 stereo in a state with 4% sales tax
A) The function applies to it because is composed interest.
B) The function also applies to this scenario because is analogous to the A question
C) The function is population growth and is analogous to the previous 2 questions
D) The function dosen't apply to this because is something static not depending on the time, then is not composed interest.
Using the the side lengths on the previous slide, use the Pythagorean Theorem to calculate the hypotenuse. Show your work
Okay, here we have this:
Considering the provided figure and side lenghts, we are going to calculate the requested hypotenuse, so we obtain the following:
[tex]\begin{gathered} h=\sqrt{(37.5in)^2+(21.1in)^2} \\ h=\sqrt{1406.25in^2+445.21in^2} \\ h=\sqrt{1851.46in^2} \\ h\approx43.03in \\ h\approx43in \end{gathered}[/tex]Finally we obtain that the hypotenuse is approximately 43 inches.
Write an equation in slope – intercept form for the line that passes through the given paint andis parallel to the given equation.1.(4, -3), y = 3x - 5
For parallel lines the slopes condition is as follows:
[tex]m1=m2[/tex][tex]m1=3[/tex]For the equation y = m1x + b
[tex]b=y-m1x[/tex][tex]b=-3-3\cdot4\rightarrow b=-15[/tex]The equation would be:
[tex]y=3x-15[/tex]factorize ax+ay+4x+4y
Identify the step where an error first occurred. Step 1(-2n+ n° - 7n") + (-n" +4% +12n) Step 2-2n+ n- 7n3 - n1 +4n3 + 12n2 Step 32n" - 3n3 + 14n2 Step 1 Step 2 Step 3 No error
EXPLANATION
Step 1 ---> Grouping in terms
Step 2 is well done ---> Removing the parentheses
Step 3 has an error ---> It's -3n^2
The rate of photosynthesis R for a certain plant depends on the intensity of light x, in lumens, according to R(x)=180x−90x2.a. Sketch the graph of this function on a meaningful window.b. Determine the intensity x that gives the maximum rate of photosynthesis
we have the function
[tex]R\mleft(x\mright)=180x-90x^2[/tex]this is the equation of a vertical parabola open downward
the vertex is a maximum
step 1
Find out the vertex
using a graphing tool
see the attached figure
the vertex is the point (1,90)
therefore
Part a ------> option C
Part b -----> the intensity x is 1 lumen that gives 90 (maximum rate of photosynthesis)
For the function f(x) = |x+5| -1, when is the function increasing?
This is the graph of the function
It increases from -5 to infinity
[tex]\lbrack-5,\text{ }\infty)[/tex]
Find the half-life of a radioactive element, which decays according to the function A(t) = Ao exp( -0.0294t), where t is the timein years.
Answer:
23.58 years.
Explanation:
The decay equation for the radioactive element is:
[tex]A(t)=A_oe^{-0.0294t}\text{ where }\begin{cases}A(t)=\text{Amount at time t} \\ A_o=\text{Initial Amount}\end{cases}[/tex]We want to find the half-life of the element.
The half-life of the radioactive substance is the time it will take for half of the initial amount of substance to decay. That is when:
[tex]\begin{gathered} \text{Present Amount=}\frac{1}{2}\text{ of Initial Amount} \\ \implies A(t)=\frac{1}{2}A_o \end{gathered}[/tex]Substitute A(t) into the formula.
[tex]0.5A_o=A_oe^{-0.0294t}[/tex]We then solve for t.
[tex]\begin{gathered} \text{Divide both sides by 0.5} \\ \frac{0.5A_o}{A_o}=\frac{A_oe^{-0.0294t}}{A_o} \\ e^{-0.0294t}=0.5 \\ \text{Take the natural logarithm of both sides} \\ \ln (e^{-0.0294t})=\ln (0.5) \\ -0.0294t=\ln (0.5) \\ \text{Divide both sides by }-0.0294 \\ \frac{-0.0294t}{-0.0294}=\frac{\ln(0.5)}{-0.0294} \\ t=23.58\text{ years} \end{gathered}[/tex]The half-life of the radioactive element is 23.58 years (correct to the nearest hundredth).
I think I have the right answer but I just want to check.
Expand the parenthesis using the distributive property twice:
[tex]\begin{gathered} (3+4i)(3-4i)=(3+4i)\cdot3+(3+4i)\cdot-4i \\ =3\cdot3+4i\cdot3+3\cdot-4i+4i\cdot-4i \\ =9+12i-12i-16i^2 \\ =9-16(-1) \\ =9+16 \\ =25 \end{gathered}[/tex]Therefore, the answer is:
[tex]25[/tex]i need help with rate of change on a linear graph please
Using the points (2014,22320) and (2020,0), we get the following slope:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{0-22320}{2020-2014}=\frac{-22320}{6}=-3720 \\ m=-3720 \end{gathered}[/tex]now we use the point (2020,0) to find the relation function:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \Rightarrow y-0=-3720(x-2020) \\ y=-3720(x-2020) \end{gathered}[/tex]to find the missing values, we substitute each one in x and see the result of y:
[tex]\begin{gathered} x=2015 \\ \Rightarrow y=-3720(2015-2020)=-3720(-5)=18600 \\ x=2017 \\ \Rightarrow y=-3720(2017-2020)=-3720(-3)=11160 \end{gathered}[/tex]therefore, in 2015 the debt was $18600 and in 2017 it was of $11160.
For year 2014 we have the total ($22320) and in 2020 we have that the debt is $0
