According to the description we will have undercoverage bias. Since we are only surveying juniors.
Factor completely over the set of complex numbers using the factoring pattern Show all work
Given:
[tex]81m^2+25[/tex]To factorize it completely over the set of complex numbers using the factoring pattern:
[tex]\begin{gathered} 81m^2+25=(9m)^2+(5)^2 \\ =(9m)^2-(i5)^2 \end{gathered}[/tex]Using the formula,
[tex]a^2-b^2=(a+b)(a-b)_{}[/tex]Hence, the factorized form is,
[tex](9m+5i)(9m-5i)[/tex]Find the equation of the line which passes through the points(-5,8) And is perpendicular to the given line express your answer in slope intercept form simplify your answer
Given: The equation below
[tex]4x+7y=4y-7[/tex]To Determine: The equation of the line that passes through the point (- 5, 8) and is perpendicular to the given equation
Solution
Let us determine the slope of the given equation
[tex]\begin{gathered} 4x+7y=4y-7 \\ 7y-4y=-4x-7 \\ 3y=-4x-7 \\ \frac{3y}{3}=\frac{-4x}{3}-\frac{7}{3} \\ y=-\frac{4}{3}x-\frac{7}{3} \end{gathered}[/tex]The slope-intercept form of a linear equation is given as
[tex]\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex]Comparing the slope-intercept form to the given equation
[tex]\begin{gathered} y=-\frac{4}{3}x-\frac{7}{3} \\ y=mx+c \\ slope=m=-\frac{4}{3} \\ c=-\frac{7}{3} \end{gathered}[/tex]Note: If two lines are perpendicular to each other, the slope of one of the line is equal to the negative inverse of the other
Therefore, the slope of the perpendicular line is as shown below
[tex]\begin{gathered} slope(given-equation)=m \\ slope(perpendicular-line)m_2=-(m)^{-1} \\ So \\ m=-\frac{4}{3} \\ m_2=-(-\frac{4}{3})^{-1} \\ m_2=-(-\frac{3}{4}) \\ m_2=\frac{3}{4} \end{gathered}[/tex]If the perpendicular line passes through (-5,8), the equation of the line can be derived using the formula below
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=slope \\ (x_1,y_1)=(-5,8) \\ slope=\frac{3}{4} \\ Therefore, \\ \frac{y-8}{x--5}=\frac{3}{4} \end{gathered}[/tex][tex]\begin{gathered} \frac{y-8}{x+5}=\frac{3}{4} \\ y-8=\frac{3}{4}(x+5) \\ y-8=\frac{3}{4}x+\frac{15}{4} \\ y=\frac{3}{4}x+\frac{15}{4}+8 \end{gathered}[/tex][tex]\begin{gathered} y=\frac{3}{4}x+\frac{15+32}{4} \\ y=\frac{3}{4}x+\frac{47}{4} \end{gathered}[/tex]Hence, the equation of the line that passes through the point ( - 5, 8) and perpendicular to the given equation is
[tex]y=\frac{3}{4}x+\frac{47}{4}[/tex]This probability distribution shows thetypical distribution of the number of shoes
First, add the frequencies in order to obtain the total number of surveyed people,
[tex]T=12+20+38+20+10=100[/tex]Then, the condition 'a teenager has 4 or more pairs of shoes' is satisfied if the number of shoes is either 4 or 5; then,
[tex]P(4or5)=P(4)+P(5)=\frac{20}{100}+\frac{10}{100}=\frac{30}{100}=\frac{3}{10}[/tex]The exact answer is 3/10 or 0.3 (both are equivalent)JK bisects angle LJM, the measure of angle LJM=2x+15, and the measure of angle KJM=6x-5. Solve for x.
JK bisects angle LJM, the measure of angle LJM=2x+15, and the measure of angle KJM=6x-5. Solve for x.
In this problem we have that
because JK bisects angle LJM
substitute the given values
(2x+15)=2(6x-5)
solve for x
2x+15=12x-10
12x-2x=15+10
10x=25
x=25/10
x=2.5(837-700)-37+ 1419/33
Answer:
(837-700)-37+ 1419/33 = 143
Explanation:
We are given:
[tex]\left(837-700\right)-37+\frac{1419}{33}[/tex]First, we can solve the parentheses and the quotient:
[tex]137-37+43[/tex]Now we solve:
[tex]100+43=143[/tex]Thus, the answer is 143
What is the range of function gif 9(2) = /(=) + 3,O A (3, 00)O B. (-00, 00)O C. (-00, 3)O D. (-3, 3)
Step 1
Given;
[tex]\begin{gathered} f(x)=e^x \\ g(x)=f(x)+3 \end{gathered}[/tex]Required; To find the range of g(x)
Step 2
[tex]\mathrm{The\:set\:of\:values\:of\:the\:dependent\:variable\:for\:which\:a\:function\:is\:defined}[/tex][tex]\begin{gathered} k=3 \\ f\left(x\right)>3 \\ Range=\left(3,\:\infty\:\right) \end{gathered}[/tex]Answer;
[tex]Range=\left(3,\:\infty\:\right)[/tex]At the produce store you can buy 2 bags of bananas for $13.90. How muchwould it cost if you were to buy 7 bags?
ANSWER:
$ 48.65
STEP-BY-STEP EXPLANATION:
We can calculate the value of 7 bags with the help of the following proportion:
[tex]\frac{13.9}{2}=\frac{x}{7}[/tex]We solve for x, which would be the cost of the 7 bags, like this:
[tex]\begin{gathered} 13.9\cdot7=2\cdot x \\ x=\frac{97.3}{2} \\ x=48.65 \end{gathered}[/tex]The cost of 7 bags is $ 48.65
In a survey of 29 instructors, it was found that 22 liked white boards, 11 liked blackboards, and 7 liked both. How many instructors did not like white boards?
We need to find the number of instructors that did not like whiteboards.
In order to do so, notice that from the 11 instructors who liked blackboards, 7 also liked whiteboards.
Thus, among the instructors who liked at least one of the two types of boards, the number of them who didn't like whiteboards is:
[tex]11-7=4[/tex]Also, there were some instructors among the whole group of 29 that didn't like any of the two boards. Thus, those ones didn't like whiteboards.
The following image illustrates this problem:
So, we need to find x and add it to the other 4 instructors that didn't like whiteboards.
We have:
[tex]\begin{gathered} 15+7+4+x=29 \\ \\ 26+x=29 \\ \\ x=29-26 \\ \\ x=3 \end{gathered}[/tex]Thus, another 3 instructors didn't like whiteboards.
Therefore, the total number of instructors who didn't like whiteboards is
[tex]4+3=7[/tex]Notice that we can find the same result in a faster way: since 22 instructors liked whiteboards from a total of 29 instructors, it means that 29 - 22 = 7 didn't like whiteboards.
Therefore, the answer is 7.
Solve for: A = a b= Round to the nearest tenth.
We have the following triangle:
First, we start from the fact that we have an internal angle of 72 degrees and a right angle i.e. a 90-degree angle.
Second, having two internal angles, we solve and find the last internal angle.
[tex]180-90-72=18[/tex]Third, we find "a" and "b" with the law of sines, the equation of this law is:
[tex]\frac{a}{\sin(A)}=\frac{b}{\sin (B)}=\frac{c}{sn(C)}[/tex]Where we have these values:
[tex]\begin{gathered} a=a \\ b=b \\ c=11 \\ \sin (A)=\sin (18) \\ \sin (B)=\sin (72) \\ \sin (C)=\sin (90)=1 \end{gathered}[/tex]Now we solve "a"
[tex]\begin{gathered} \frac{a}{\sin (18)}=\frac{11}{\sin (90)} \\ a=11\cdot\sin (18) \\ a=3.3991\cong3.4 \end{gathered}[/tex]Now we solve "b"
[tex]\begin{gathered} \frac{b}{\sin (72)}=\frac{11}{\sin (90)} \\ b=11\cdot\sin (72) \\ b=10.4646\cong10.46 \end{gathered}[/tex]In conclusion, the answers are approximate:
[tex]\begin{gathered} a\cong3.4 \\ b\cong10.46 \end{gathered}[/tex]At the fair 220 balloons are given to 40 children, 3/4 of whom are girls. Each boy receives twice as many balloons as each girl. How many more balloons do all the girl receive than all the boys
We have the following:
3/4 of 40 = 30 girls, therefore 10 boys
Due each boy receives twice as many balloons as each girl
boys get a multiple of 20 balloons (10 * 2), girls get the same multiple of 30 (30 * 1) balloons.
so
x * (30 + 20) = 220 balloons
x * 50 = 220 balloons
x = 220/50
so the number is 4.4
Boys receive 20 * 4.4 = 88 balloons.
Girls receive 30 * 4.4 = 132 balloons.
This is algebra 2 I’m confused a little bit, I remember the format but it’s a little wonky I guess!
1)
Given:
The objective is to find the transformation of the graph which contians the equation y = √x.
Explanation:
The graph of the equation y = √x is,
1. a)
First, rotate the graph of the function around x axis by multiplying the whole function by (-1).
[tex]y=-\sqrt[]{x}[/tex]By moving 2 units to the left, the transformation will be,
[tex]y=-\sqrt[]{x+2}[/tex]Further transformation of 1 unit to the down side, the equation will be,
[tex]y=-(\sqrt[]{x+2}+1)[/tex]Hence, the required equation of transformation is obtained.
1. b)
First, rotate the graph of the function around y axis by multiplying only the x values of the function by (-1).
[tex]y=\sqrt[]{-x}[/tex]Further transformation of 3 units to the right side, the equation will be,
[tex]y=\sqrt[]{-x+3}[/tex]Hence, the required equation of transformation is obtained.
which of the following values is the solution of x divided by 32 equals 8?A. 24B.40C.256 D.4
If the domain of f(x) = 3x + 5 is {-1, 0, 1, 2, 3}, what is the range?
The domain is the set of values that are allowed to plug into our function and it is represented by the variabel x.. In our case, the domaini s {-1,0,1,2,3}. On the other hand, the range is the set of values that the function assumes after we plug an x value in.
Then, we need to substitute each x value into the given function f(x). So, for x=-1, we have
[tex]\begin{gathered} f(-1)=3(-1)+5 \\ f(-1)=-3+5 \\ f(-1)=2 \end{gathered}[/tex]Similarly, for x=0, we get
[tex]\begin{gathered} f(0)=3(0)+5 \\ f(0)=5 \end{gathered}[/tex]For x=1, we obtain
[tex]\begin{gathered} f(1)=3(1)+5 \\ f(1)=8 \end{gathered}[/tex]Now, for x=2, we have
[tex]\begin{gathered} f(2)=3(2)+5 \\ f(2)=11 \end{gathered}[/tex]and finally, for x=3 we get
[tex]\begin{gathered} f(3)=3(3)+5 \\ f(3)=14 \end{gathered}[/tex]Therefore, the range is the following set:
[tex]{}\lbrace2,5,8,11,14\rbrace[/tex]Given the following table with selected values of f (x) and g(x), evaluate f (g(1)).x–6–4134f (x)4–1–613g(x)143–4–6A. –4B.–1C.1 D.4
[tex]f[g(1)][/tex]
The function is a composite function
Let us first find g(1)
[tex]g(1)=3[/tex]The problem now reduces to f(3)
[tex]f(3)=1[/tex]The final answer is 1 .
The right choice is OPTION C
14V + 25 − 5V = 4(V + 25)
Step 1
Given; 14V + 25 − 5V = 4(V + 25)
Required; Find V
Step 2
[tex]\begin{gathered} 14V+25-5V=4(V+25) \\ \mathrm{Group\:like\:terms} \\ 14V-5V+25=4\left(V+25\right) \end{gathered}[/tex][tex]\begin{gathered} Add\:similar\:elements \\ 9V+25=4\left(V+25\right) \\ Expand\text{ the bracket} \\ 9V+25=4V=100 \end{gathered}[/tex][tex]\begin{gathered} 9V-4V=100-25 \\ 5V=75 \\ \frac{5V}{5}=\frac{75}{5} \\ V=15 \end{gathered}[/tex]Answer;
[tex]V=15[/tex]A. Graph Cubas population and describe what pattern you can see. B. Explain why a logistic model would be a better choice for Cubas population growth than an exponential model. C. Find a logistic function f(t)= L/1+C(e^-bt), that models Cubas population growth. - Assume that .039 is a good value for b. Do not change this value - Graph f(t) = 11,000/1+15(e^-.039t) on top of your points (so starting value L=11,000 and the starting value for C=15) - experiment with values for L and C until you have a good model for the graphed points. Limit yourself to L-values between 11,000 and 15,000 and C-values between 11 and 15
A. We have to graph the data (years in the horizontal axis, population in the vertical axis):
B. The shape of the time series match the logisti model: it has an exponential growth in the first stage and then it flattens.
C. We have a logistic model with b=0.039.
We have to plot the function:
[tex]f\mleft(t\mright)=\frac{11000}{1+15\cdot e^{-0.039t}}[/tex]If we add it to the data plot we get:
This parameters do not fit the actual population. So we have to change L between 11000 and 15000 and C between 11 and 15.
If we change them to C=14 and L=13000, we get:
which is a significant better fit than the original model.
8 as a radical to the 10 power
The correct answer is:
[tex]\sqrt[8]{10\text{ = 1.33}35\text{ }}[/tex]In our solution, we are calculating the 8th root of 10
A company is designing a label for a new cylindrical container. The container and some of its dimensions are shown. The label will be the same height as the container and will not overlap itself and will cover the entire side of the cylinder. What will be the area of the label 2 A) 31(8.75) cm? B) 61(875) cm? 91(8.75) cm D) 127(8.75) cm2 E) 157t(8.75) cm?
The base area, B, of a cylinder with radius, r, is as given below
[tex]B=\pi r^2[/tex][tex]\begin{gathered} \text{ Since B = 9}\pi cm^2 \\ \text{then we must have that} \\ \pi r^2=9\pi \end{gathered}[/tex]Hence,
[tex]\begin{gathered} r^2=9 \\ \Rightarrow r=\sqrt[]{9}=3 \\ r=3\operatorname{cm} \end{gathered}[/tex]Since the label will only cover the entire side of the cylinder without overlapping, then the area of the label is the curved surface area of the cylinder.
Given a cylinder with radius,r, and height, we must have that
[tex]\text{the curved surface area = 2}\pi rh[/tex]In this case, h = 8.75cm,
Therefore,
[tex]\text{area of the label = 2}\pi\times3\times8.75=6\pi(8.75)cm^2[/tex]Hence the right choice is B
The line is parallel to the line y = 1/2x-3, and contains the point (6,5)
Given: Equation of a line
[tex]y=\frac{1}{2}x-3[/tex]Required: To find the equation of the line that is parallel to the given line and contains the point (6,5).
Explanation: The slopes of the parallel lines are equal. Moreover, the general equation of a line is
[tex]y=mx+c[/tex]Comparing the equation of the given line with the general equation of the line, we get,
[tex]Slope,m=\frac{1}{2}[/tex]Hence, the required line has a slope of 1/2. It is given that this line contains the point (6,5).
Using the slope point equation of a line-
[tex]y-y_0=m(x-x_0)[/tex]Putting the values, we get,
[tex]\begin{gathered} y-5=\frac{1}{2}(x-6) \\ 2y-10=x-6 \\ 2y=x+4 \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]Final Equation: The equation of the line is
[tex]y=\frac{1}{2}x+2[/tex],
A man purchased a magazine at the airport for $2.39. The tax on the purchase was $0.17. What is the tax rate at the airport? Raund to the nearest percentThe tax rate is ? Round to the nearest percent as needed.
In order to find the percent corresponding to the tax rate, we divide the tax over the cost of the magazine and multiply it by 100
[tex]\frac{0.17}{2..39}\cdot100=7.11\text{\%}\approx7\text{\%}[/tex]A salesman earns a commission of $350 for selling $2500 in merchandise. Find the commission rate. Write your answer as a percentage.
14%
Explanation
we can solve this by using a rule of three
let x represents the rate commision( in percentage)
so
if
[tex]2500\rightarrow100\text{ \%}[/tex]then
[tex]350\rightarrow x[/tex]now, set the proportion and solve for x
[tex]\begin{gathered} \frac{2500}{100}=\frac{350}{x} \\ \text{cross multiply} \\ 2500x=350\cdot100 \\ 2500x=35000 \\ \text{divide both sides by 2500} \\ \frac{2500x}{2500}=\frac{35000}{2500} \\ x=14 \end{gathered}[/tex]it means, the rate is 14%
I hope this helps you
Answer:
13%
Step-by-step explanation:
4. In a geometric sequence, ag = 64 and a 10 = 0.25.Use the geometric mean to find the value of ag.3216
We are asked to determine the term between the 8th and 10th terms of the geometric sequence. To do that we need to have into account that in a geometric sequence the term between two given terms is equivalent to the geometric mean of the two terms. The geometric terms between the two terms is given by:
[tex]G_m=\sqrt[]{a_1a_2}[/tex]Replacing the values:
[tex]\begin{gathered} G_m=\sqrt[]{(64)(0.25)}_{} \\ G_m=\sqrt[]{16} \\ G_m=4 \end{gathered}[/tex]Therefore, the 9th term is 4.
Simplify the ratio 15 to 21 is?
Given the ratio;
[tex]15\colon21[/tex]To simplify the above ratio, we would change the ratio to a fraction then divide the numerator and the denominator by the same value, and till we get to the lowest possible term.
This gives,
[tex]\begin{gathered} \frac{15}{21}\mleft\lbrace\text{Divide numerator and denominator by 3}\mright\rbrace \\ =\frac{5}{7} \\ \therefore5\colon7 \end{gathered}[/tex]Therefore, the answer is
Answer: 5:7
-TB +6r) = 14-1 .1+(3), GREMOR -R=17 3-18R=14.R 190 3-18 R&R=14-RAR Ral -3-172314 -3-178+3=1443 -4k + 2(5k - 6) = -3k - 39 n 1=-212
We need to find k, so we have that
[tex]\begin{gathered} -4k+2(k-6)=-3k-39_{} \\ -4k+2k-12=-3k-39_{} \\ -4k+2k+3k=-39+12_{} \\ k=-27_{} \end{gathered}[/tex]So the answer is k=-27.
Jonah's restaurant bill comes to $25.65 and he leaves a 15% tip. What is Jonah's total restaurant bill?
Given
Restaurante bill $ 25.65
Tip 15%
Total
Procedure
Total = 25.65 + 25.65*15%
Total = 25.65+3.847
Total = 29.4975
Hello! The Question is included in the picture. I’m having a hard time understanding this. Please help!
Answer:
A. The sidewalk length: 24.9'
B. The sidewalk width: 21.6'
C. The garden length: 11.7'
D. The garden width: 8.4'
E. Total garden area: 98.3 square inches
Step-by-step explanation:
We have two rectangles (R). Let's define:
R₁ = the biggest rectangle = sidewalk + garden
R₂ = the smallest rectangle = garden
The area of the rectangle R₁ (AR₁) can be calculated as follows:
AR₁ = l₁.w₁
AR₁ = (1.87x+5+x+3+x+3)(1.5x+3+x+3+x+3)
AR₁ = (3.87x + 11)(3.5x + 9)
Also,
AR₁ = area of sidewalk + area of garden
Area of the sidewalk = 64875 square inches = 450.5 square feet
AR₁ = 450.5 + (1.87x + 5)(1.5x + 3)
We can equal both equations to find the value of x:
(3.87x + 11)(3.5x + 9) = 450.5 + (1.87x + 5)(1.5x + 3)
13.5x² + 34.8x + 38.5x + 99 = 450.5 + (2.8x² + 5.6x + 7.5x + 15)
13.5x² + 73.3x + 99 = 2.8x² + 13.1x + 450.5
13.5x² -2.8 x² + 73.3x - 13.1x + 99 - 450.5 = 0
10.7x² + 60.2x - 351.5 = 0
Now, we can use the quadratic formula to the value of x.
According to the quadratic formula:
For a equation:
ax²+ bx + c = 0,
x = (-b ± √Δ)/2a
and
Δ = b² - 4ac
So, in this exercise:
Δ = 60.2² - 4(10.7)(-351.5)
Δ = 3624 + 15044.2
Δ = 18668.2
x = (-60.2 ± √18668.2)/(2*10.7)
x = (-60.2 ± 136.6)/21.4
x₁ = (-60.2 + 136.3)/21.4
x₁ = 3.6'
x₂ = (-60.2 - 136.3)/21.4
x₂ = -9.2'
Since the sides of the rectangle can not be negative, we will use the value of x₁ = 3.6'.
Now, let's calculate the sides of the garden:
lenght: 1.87x + 5
length: 1.87*3.6 + 5
length: 11.7'
width: 1.5x + 3
width: 1.5*3.6 + 3
width: 8.4'
And the area of the garden AR₂:
AR₂ = 11.7*8.4
AR₂ = 98.3 square inches
Finally, let's calculate the sides of the biggest rectangle:
lenght: 11.7 + x + 3 + x + 3
lenght: 11.7 + 3.6 + 3 + 3.6 +3
lenght: 24.9'
width: 8.4 + x + 3 x + 3
width: 8.4 + 3.6 + 3 + 3.6 +3
width: 21.6'
indicate me answer choice The spinner shown is spun once. Find each probability. Write each answer as a fraction, a decimal, and a percent. B E M C A P P(not M) Oa. 2 3 Da Į, N0.7,8 67% Ob. 0,17,8 17 Oc. 5, N 0.3, 33% Od. 3 0.83, 83%
When the spinner is spun,
4. What is the profit the restaurant makes from selling 100 burritos? Does the restaurant make money o lose money? Explain.
if the restauran sells 100 burritos, it obtains $550 dollars.
Then, when the restauran sells 100 burritos it makes money, because the earnings are greater than zero dollars.
Which answer choice correctly represents 0.513333… ?A) 0.513 _B) 0.513 __C) 0.513 ___D) 0.513
Explanation
The given question is an example of a recurring decimal
The decimal number given:
[tex]0.513333\ldots\text{..}[/tex]This shows that 3 continues indefinitely
A good way to write this will be to put a sign on 3 to show that it continues
This will be
Thus, the answer is option B
If i could just get help with part A please. i have part B right
We can rewrite the fraction inside the square root as:
[tex]\frac{5\cdot3}{3\cdot3}=\frac{15}{9}\text{.}[/tex]Therefore:
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