For
[tex]\begin{gathered} \sin 61=\cos \theta \\ \theta=\cos ^{-1}(\sin 61) \\ \end{gathered}[/tex]For
[tex]\begin{gathered} \cos 17=\sin \theta \\ \theta=\sin ^{-1}(\cos 17) \\ \end{gathered}[/tex]Which of the following is an equation of a line that is parallel to y = 4x - 5 and has a y-intercept of (0, 7)?
Answer:
Step-by-step explanation:
To start your equation is in the format y=mx+b.
For a line to be parallel it must have the same slope (m) so we know 4 must remain the same. x & y will not change since they represent the variables. y=4x (so far) then the point (0,7) as stated is the y intercept. 0 is the x value and 7 is the y we need to add 7 to our equation.
final equation y=4x+7
event a is the event that randomly selected students from your school is make event b is the event that randomly selected students from your school owns a bicycle which of the following do we know for certain correctly represents the probability of selecting a male students or selecting a student who owns a bicycle
The or probability in the context of this problem is represented as follows:
P(A U B).
Or probabilityThe or probability between two events A and B is the probability that at least one of the events happen.
The symbol of the or probability is given as follows:
U
In the context of this problem, the events are given as follows:
Event A: a randomly selected student is male.Event B: a randomly selected student owns a bike.Hence the probability of selecting a male students or selecting a student who owns a bicycle is represented as follows:
P(A or B) = P(A U B).
The other options are as follows:
P(A ∩ B): both male and own bike, representing the intersection operation of the events.P(A): male.P(B): own bike.Missing informationThe complete problem is given by the image at the end of the answer.
More can be learned about probabilities at https://brainly.com/question/14398287
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What is the area of this trapezoid? Enter your answer in the box. ft2
Given the figure, we can deduce the following information:
Upper base = 15 ft
Lower base = 37 ft
Height = 18 ft
To determine the area of a trapezoid, we use the formula:
[tex]A=\frac{a+b}{2}h[/tex]where:
A=Area
a=upper base
b=lower base
h=height
We plug in what we know:
[tex]\begin{gathered} A=\frac{a+b}{2}h \\ =\frac{15+37}{2}(18) \\ \text{Simplify} \\ A=\frac{52}{2}(18) \\ =\frac{936}{2} \\ A=468ft^2 \end{gathered}[/tex]Therefore, the area of the trapezoid is 468 ft^2.
What 3D shape will be formed when the following are rotated around the axis
a)
A washer will be formed
b)
A cone will be formed
C)
A sphere will be formed
Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.
Given:
Sara's age is represented by S and Ronaldo's age is represented by R.
Since,
Sara is 33 years younger than Ronaldo, then;
S= R - 33
Now, the sum of ages of Sara and Ronaldo is 105 then
[tex]R+S=105[/tex]Hence, from above,
[tex]\begin{gathered} S+R=105 \\ S=R-33 \end{gathered}[/tex]Therefore, second option is correct.
Hey everybody! Can somebody help me solve this problem? I don't need a big explanation just the answer and a brief explanation on how you get it! Look at photo for problem.
Given the ordered pairs:
(-12, -16), (-3, -4), (0, 0), (9, 12)
Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:
[tex]y=k\cdot x[/tex]Using the ordered pairs:
[tex]\begin{gathered} -16=-12k\Rightarrow k=\frac{4}{3} \\ -4=-3k\Rightarrow k=\frac{4}{3} \\ 0=0\cdot k\text{ (this means that it is correct)} \\ 12=9k\Rightarrow k=\frac{4}{3} \end{gathered}[/tex]We conclude that the constant of variation is:
[tex]k=\frac{4}{3}[/tex]the length of a screwdriver is 0.75 cm is how many screws can be placed to the end to make a road that's 18 cm long show yours
Length of screwdriver = 0.75
Length of road = 18cm
Number of screws that can be placed on a road
[tex]\begin{gathered} =\text{ }\frac{18}{0.75} \\ =\text{ 24} \end{gathered}[/tex]The graph below shows the length of Jutta's hair over 6 months period. Each month point represents a measurement at the beginning of a month. How many inches did her hair grow between the beginning of February and the beginning of July?
Given:
Length of hair at the beginning of february is 4.1''
Length of hair at the beginning of July is 7.7''
[tex]\begin{gathered} \text{Hair grown between beginning of February an beginning of July=7.7''-4.1''} \\ =3.6^{\doubleprime} \end{gathered}[/tex]please help me ASAP!!!
substitute x = 5 in the above function
[tex]f(5)=\sqrt[]{2(5)^2-3(5)+1}[/tex][tex]=\sqrt[]{2(25)-15+1}[/tex][tex]=\sqrt[]{50-15+1}[/tex][tex]=\sqrt[]{36}=\text{ 6}[/tex]f(5) = 6
Do you know anything about dilation!?
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Problem
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Solution
for this case we can do the following proportional rule:
4/144 = x/100
And solving for x we got:
x= 100 (4/144)= 2.77
So between 2 and 3 grape fruits are expected
Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured, and the scientists realize that the gas is leaking over time in a linear way. Nine minutes since the experiment started, the gas had a mass of 68.4 grams. Thirteen minutes since the experiment started, the gas had a mass of 61.2 grams. At what rate is the gas leaking? Use g for grams and min for minutes.
the rate is:
[tex]m=\frac{61.2-68.4}{13-9}=-\frac{7.2}{4}=-1.8\frac{g}{\min }[/tex]discriminant for 2n^2+8n+1=-7
The given equation is
[tex]\begin{gathered} 2n^2+8n+1=-7 \\ 2n^2+8n+1+7=0 \\ 2n^2+8n+8=0 \end{gathered}[/tex]Where a = 2, b = 8, and c = 8.
The discriminant formula is
[tex]D=b^2-4ac[/tex]Let's replace the values
[tex]D=(8)^2-4(2)(8)=64-64=0[/tex]The equation has one real solution.During a baseball game, Diego thought his team would get 4 runs, and they actually got 7 runs. What was Diego's percent error? Make sure to include a percent sign. (Round to two decimal places)
Answer:
11 percent
Step-by-step explanation:
No idea to explain
Section 5.2-4 Graph the following system of equations and find the solution. Plot the solution on the graph. Enter your answer as (x,y). -2x-3y = 0 x+3y = 3 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Clear All Draw: LineDot Solution =
For finding y, we can replace the value of x in any equations.
Solution (-3,2)
Plot graphs
27. Ava surveys teachers for how long it takes them to drive to school eachmorning. She records each response in the dot plot shown.5 10 15 20 25 30 35 40 45 50 55 60Length of Drive (minutes)Ava considers drives of 55 minutes or more as not typical. Given this,which measure of the entire data set represents the most typicaldriving time?meanrangemedianmean absolute deviation
EXPLANATION
The measure that represent the most typical driving time is the mean.
Corbie earns $2750 paid once a month after taxes.
James gets paid every other week for tutoring at the
local library, and his smallest paycheck in the past six
months was $280.
Their monthly rent for their home is $925 and their most
expensive month for combined utilities last year cost
$325. Their smartphones cost $180 per month. They
spend $120 per week on groceries, $45 per week on
gas,and $620 per month for their car's payment,
insurance, and maintenance savings. James spends
$600 per semester (twice a year) for college tuition.
They each give themselves a $100 per week allowance
for personal expenses such as clothes, haircuts, dining
out, and entertainment.
Calculate their prorated monthly amounts, their monthly
totals, and their cash flow.
1. Corbie and James' total prorated monthly incomes are Corbie's $2,750 and James' $606.
2. Their combined monthly totals are:
Income = $3,356.
Expenses = $3,111.
3. Their monthly net cash flow is $245.
What is the net cash flow?The net cash flow is the cash surplus after paying all operating costs.
The net cash flow for Corbie and James is the difference between their total earnings per month and their total expenses per month.
For some income and expenses, there is a proration. Since 52 weeks make up the typical year, each month is considered 4.33 weeks.
1 year = 52 weeks
1 month = 4.33 weeks (52/12)
Monthly Income:
Corbie = $2,750
James = $606 ($280 x 26/52 x 4.333)
Total income = $3,356
Monthly Expenses:
Rent = $925
Utilities = $325
Phones = $180
Groceries = $520 ($120 x 4.33)
Gas = $195 ($45 x 4.33)
Tuition = $100 ($600 x 2)/12
Incidentals = $866 (200 x 4.33)
Total expenses = $3,111
Net Cash Flow = $245 ($3,356 - $3,111)
Thus, whereas, Corbie and James earn a combined and prorated monthly income of $3,356, their total monthly expenses of $3,111 leave them with a net cash flow of $245.
Learn more about the net cash flow at https://brainly.com/question/2804189
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8You are asked to draw a triangle withside lengths of 10 inches, 7 inches, and2 inches. How many triangles like thiscan you draw?A. OneB. ThreeC. TwoD. Zero
ANSWER
D. Zero
EXPLANATION
The triangle inequality states that the sum of any two sides of a triangle is greater than the third side,
All these inequalities must be true to be able to form a triangle with the given sides,
[tex]\begin{gathered} 7+10>2\Rightarrow17>2\Rightarrow true \\ 2+10>7\Rightarrow12>7\Rightarrow true \\ 7+2>10\Rightarrow9>10\Rightarrow false \end{gathered}[/tex]Hence, no triangle can be formed with these side lengths.
Using the order of operations, which operation should you perform last to evaluate the expression below?(7*4)+(10 ÷ 2)*(14.7 - 9)A.multiplicationB.divisionC.additionD.subtractionHELP! A.P.S
Explanation
Given (7*4)+(10 ÷ 2)*(14.7 - 9), we can see that only two operations occur outside of the parenthesis which is multiplication and addition.
In the order of evaluation of expressions, the parenthesis comes first before multiplication and then addition. Therefore,
Answer: Option C (Addition)
What is the value of 7C4?A). 35B). 840C). 2,520D). 5,040
Answer:
A) 35
Explanation:
The combination nCx can be calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]Where n! = n(n-1)(n-2)...(2)(1)
So, to find 7C4, we need to replace n by 7 and x by 4 to get:
[tex]7C4=\frac{7!}{4!(7-4)!}=\frac{7!}{4!(3)!}[/tex]Therefore, 7C4 is equal to:
[tex]7C4=\frac{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(4\cdot3\cdot2\cdot1)(3\cdot2\cdot1)}=\frac{5040}{24(6)}=\frac{5040}{144}=35[/tex]So, the answer is:
A) 35
If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.
Radius of the circle : Radius is the distance from the center outwards.
With the help of radius we can determine the following terms:
1. Diameter : Diameter is the twice of radius and it is teh staright line that passes through the center. Expression for the diameter is :
[tex]\text{ Diameter= 2}\times Radius[/tex]2. Circumference: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It express as:
[tex]\begin{gathered} \text{ Circumference of Circle=2}\Pi(Radius) \\ \text{ where }\Pi=3.14 \end{gathered}[/tex]3. Area of Circle: Area of a circle is the region occupied by the circle in a two-dimensional plane. It express as:
[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{where : }\Pi=3.14 \end{gathered}[/tex]4. Center Angle of the Sector: Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. It express as :
[tex]\text{ Central Angle of sector=}\frac{Area\text{ of Sector}}{\Pi(radius)^2}\times360[/tex]5. Arc length : An arc of a circle is any portion of the circumference of a circle. It express as :
[tex]\text{ Arc Length = }Radius(\text{ Angle Substended by the arc from the centerof crircle)}[/tex]In the given figure the radius is AO & BO
can you help me with key attributes of quadratic function
The shape of a quadratic function is a parabola.
The domain of a quadratic function is the set of all real numbers.
The range of the quadratic function is the set of all y values at or above the vertex for a parabola open upwards.
In the given parabola, y=0 is the y coordinate of the vertex of the parabola.
Therefore, the range is R=[0, ∞).
The domain is (-∞, ∞).
Kuta Software Infinie Algebra ? Absolute Value Inequalities Salve each inequality and graph its solution. 61 1 laulsis * -36043 3) m-2/
Prob 22
7 + | 6v + 7| ≤ 60
then
| 6v + 7| ≤ 53
now eliminate lines ||
6v + 7 ≤ 53
and
6v + 7 ≤ - 53,. 6v ≤ -60
Now solve for x
6v ≤ 47,. v≤ 46/6
also
6v ≥ -47,. v≥ -46/6
Then answer is
-10 ≤ v ≤ -46/6
Graph for problem 22
10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work.
SOLUTION
A.
To solve this question, we will use the compound interest formula.
Which is:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ Since\text{ we are dealing with a yearly statistics, n = 1} \end{gathered}[/tex][tex]\begin{gathered} \text{From 1989 to 2007, there is a year difference of 18 years} \\ t=18 \\ A=109,185 \\ P=125,500 \\ We\text{ are looking for the continuous growth rate (r)} \\ \text{Now, we will substitute all these given parameters into the formula } \\ \text{above.} \end{gathered}[/tex][tex]\begin{gathered} 109,185=\text{ 125,500(1-}\frac{r}{100})^{18} \\ \frac{195185}{125500}=\frac{125500}{125500}(1-\frac{r}{100})^{18} \\ 0.87=(1-\frac{r}{100})^{18} \\ \text{take the natural logarithm of both sides:} \\ \ln 0.87=18\ln (1-\frac{r}{100}) \\ -0.1393=18\ln (1-\frac{r}{100}) \\ \frac{-0.1393}{18}=\ln (1-\frac{r}{100})_{}_{}_{}_{}_{} \\ -0.007737=\ln (1-\frac{r}{100}) \\ \end{gathered}[/tex][tex]\begin{gathered} e^{-0.007737}=(1-\frac{r}{100}) \\ 0.9922=1-\frac{r}{100} \\ \frac{r}{100}=1-0.9922 \\ \frac{r}{100}=0.007707 \\ r=100\times0.007707 \\ r=0.771\text{ \%} \end{gathered}[/tex]The continuous decay rate is 0.771%
B.
Using the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ t=2021-2007=14 \\ P=109,185 \\ n=1 \\ A=\text{?} \\ r=0.771 \\ \text{Substitute all the parameters into the formula above:} \end{gathered}[/tex][tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=109,185(1-\frac{0.771}{100})^{1\times14} \\ A=109,185\times0.89730607 \\ A=97,972.36 \\ A=97,972\text{ (to the nearest person)} \end{gathered}[/tex]The population of the city in the year 2021 is 97,972.
C.
We will use the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=97,890 \\ P=125,500 \\ r=0.771 \\ t=\text{?} \\ \text{Substitute all these parameters into the formula above:} \\ \end{gathered}[/tex][tex]\begin{gathered} 97890=125,500(1-\frac{0.771}{100})^t^{} \\ \frac{97890}{125500}=\frac{125500}{125500}(0.99229)^t \\ 0.78=0.99229^t \\ \ln 0.78=t\ln 0.99229 \\ -\frac{0.2485}{\ln 0.99229}=t \\ t=32.101 \\ SO\text{ the year that the population will reach 97,890 will be:} \\ 1989+32.101=2021.101 \\ \text{Which is approximately year 2021.} \end{gathered}[/tex]The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 10. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 62.
we are given
mean=42
Std=10
if the mean=42 + std =10 42+10=52
if the mean=42 - std=10 42-10=32
Rule -- 68-95-99.7
68% of the measures are within 1 standard deviation of the mean.
42+10=52
95% are within 2.
42+20=62
99.7% are within 3.
42+30=72
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
we are ask for the porcentage of request between 42-62 (between the mean and 2+std)
62 is two standard deviations above the mean.
Of the 50% of the measures below the mean, 95% are between 42 and 62, so
0.95(50)=47.5
The approximate percentage of light bulb replacement requests numbering between 42 and 62 is of 47.5%
Which sequence of transformations will map AABC onto AA' B'C'?A- reflection and translationB- rotation and reflectionC- translation and dilation D- dilation and rotation
For the given problem, we can observe that the image is bigger than the original diagram.
We can also observe that the image is rotated counterclockwise.
Hence, the sequence of transformation that maps triangle ABC onto triangle A'B'C' is a dilation and a rotation.
Answer: Option D
2. (02.01 LC)While researching the industry she is interested in, Charlize sees that the average employment rate is 97.3%. How many people, out of every 250, are employed? (1point)24.33O 234.66Ο Ο243.25O 256.93
EXPLANATION
We can compute the average by multiplying the average by 0.973, as shown follows:
[tex]\text{Amount of people}=250\cdot0.973=243.25[/tex]In conclusion, the amount of people is equal to 243.25
In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t= 0.0588s^(1.125) where s is the distance in meters and t is the time to run thatdistance in seconds.a. Find Kennelly's estimate for the fastest a human could possibly run 1609 meters.t= seconds (Round to the nearest thousandth as needed.)
For this problem, we are given a formula that predicts the fastest a human can run a certain distance. We need to determine the time a human can run 1609 meters.
The formula is:
[tex]t=0.0588s^{1.125}[/tex]We need to replace s with 1609 and solve for t.
[tex]\begin{gathered} t=0.0588(1609)^{1.125}\\ \\ t=0.0588\cdot4049.26\\ \\ t=238.096 \end{gathered}[/tex]The fastest a human can run 1609 meters is 238.096 seconds.
The points −−5, 11 and r, 9 lie on a line with slope 2. Find the missing coordinate r.
Solution
[tex]\begin{gathered} Let\text{ }(x_1,y_1),\text{ }(x_2,y_2) \\ Let\text{ }m=slope \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} If(-5,-11)=\text{ }(x_1,y_1),then\text{ }x_1=-5,\text{ }y_1=-11 \\ (r,9)=\text{ }(x_2,y_2),then\text{ }x_2=r,\text{ }y_1=9 \end{gathered}[/tex]Using the Slope formula written above;
[tex]\begin{gathered} 2=\frac{9-(-11)}{r-(-5)} \\ 2=\frac{20}{r+5} \\ Cross\text{ }multiply \\ 2(r+5)=20 \\ Expansion\text{ }of\text{ }bracket \\ 2r+10=20 \\ 2r=20-10 \\ 2r=10 \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \frac{2r}{2}=\frac{10}{5} \\ r=5 \end{gathered}[/tex]Therefore, the missing co-ordinate r is 5.
HighByte Entertainment sells four types of products: video games, DVDs, CDs, and radios. The numbers sold for 2020 and 2021 are shown in the double bargraph below. Use this graph to answer the questions.
Solution
Use this graph to answer the questions below:
The numbers sold for 2020 and 2021 are shown in the double bar above
1. The number of radio sold in 2021 = 440
2. Which products sold more in 2021 than in 2020 :
The only products that sold more in 2021 than in 2020 is video games
3. Which products sold the least over the two years
The products that sold the least = DVDS
