Given the statement: The square of the difference between a number n and eighty.
we need to write the algebraic expression for the statement.
The difference between the number n and 80 will be:
[tex]n-80[/tex]The square of the difference will be:
[tex](n-80)^2[/tex]Use Cramer's Rule to solve the system. You may use the calculator for computations only - do not use any matrix functions. Show all work
Solution
Therefore the value of
[tex]\begin{gathered} x=-1 \\ y=\frac{5}{2}=2.5 \end{gathered}[/tex]One friend claims that to find the height of the platform, you need to use the tangent ratio. Explain why her approach is or is not a reasonable approach to finding the height of the platform.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the trigonometric ratios
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotensue} \\ \cos\theta=\frac{adjacent}{hypotenuse} \\ \tan\theta=\frac{opposite}{adjacent} \end{gathered}[/tex]STEP 2: Analyze the given scenario to get the details given
We were given the length of the piece of wood needed to make the ramp as 3.5m long, this implies that the length of the side is 3.5m. From the given image, this is the hypotenuse.
[tex]hypotenuse=3.5m[/tex]The angle of elevation is 28 degrees,
[tex]\theta=28\degree[/tex]The height of the platform from the image will be opposite since it is the side that is facing the angle 28 degrees.
[tex]opposite=height\text{ }of\text{ }platform[/tex]Joining all these together, we have a right-angled triangle given below:
From the given ratios in step 1, since we know tha hypotenuse and the opposite and also the theta, therefore the correct ratio to use is:
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotenuse} \\ \\ \sin28=\frac{height}{3.5} \\ height=3.5\times\sin28 \end{gathered}[/tex]Therefore, the given claim of needing tangent ratio to find the height of the platform is not a reasonable approach because the adjacent which is the base is not given.
Fergus gets paid $5.25 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 48hours?a. $63.04b. $190.90c. $210d. $273.04
The correct answer is d. $273
Fergus worked 48 hours in the week. This means that for 40 hours he was paid $5.25 per hour; And for 8 hours he was paid 150% of the normal (150% is one and a half time)
Then for the regular paid hours:
$5.25 per hour by 40 hours => 5.25*40= $210
Now for the 8 remaining hours we need to calculate how much Fergus is paid by hour.
Then 50% of $5.25 is the same as 5.25 divided by 2: 5.25/2 = $2.625
Then the 150% is equal to 100% + 50%. The 100% is $5.25 and the 50% is $2.625
5.25 + 2.625 = $7.875
This is what Fergus gets paid for every overtime hour. This week he worked 8 overtime hours.
Then, $7.875 * 8 = $63
Now the total earning of the week is equal to $210 + $63 = $273 and that's option D.
Find the number of CDs that will produce maximum revenue.
Given data:
Price of CD is,
[tex]p(x)=90-\frac{x}{6}[/tex]The total revenue is,
[tex]R(x)=90x-\frac{x^2}{6}[/tex]First find the derivative of revenue function and then equate it to zero we have,
[tex]\begin{gathered} R^{\prime}(x)=0 \\ 90-\frac{2x}{6}=0 \end{gathered}[/tex][tex]\begin{gathered} \frac{x}{3}=90 \\ x=90\times3 \\ x=270 \end{gathered}[/tex]Now, to prove the maximize find the double derivative of revenue function
[tex]\begin{gathered} R^{\doubleprime}(x)<0 \\ \frac{-2}{6}=\frac{-1}{3}<0 \end{gathered}[/tex]Thus, 270 CD's will produce maximum revenue.
Answer: Option (c) that is 270.
If tan A = 21/20 and cos B = 28/53 and angles A and B are in Quadrant I, find the valueof tan(A - B).
Does the function f(x) or g(x) have a greater value at x=2? f(x)=4∙2^x
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph: g(x)
function: f(x) = 4 * 2 ^ x
Step 02:
greater value ==> x = 2:
graph: g(x)
x = 2 , y = 18
g(2) = 18
function: f(x) = 4 * 2 ^ x
[tex]f(2)\text{ = 4 }\cdot2^2=\text{ 4 }\cdot\text{ 4 = 16}[/tex]The answer is:
g(x) has a greater value at x = 2
Consider the following random sample of data: 12, 24, 30, 15, 22, 5, 9, 3, 101, 20
SOLUTION
The given data in desending order is:
[tex]3,5,9,12,15,20,22,24,30,101[/tex]Recall that the median is the middle number of set of numbers arranged in ascending or descending order.
Notice that there are 10 data values Hence the area two middle value
The median is the average of the middle values:
[tex]\frac{15+20}{2}=17.5[/tex]Hence the median is 17.5
Recall that an outlier is a data point that differs significantly from other observations
Hence the outlier is 101.
Note that new data will become:
[tex]\begin{equation*} 3,5,9,12,15,20,22,24,30 \end{equation*}[/tex]Therefore the median is 15
What is the speed of a jet plane that flies 8100 km in 9 hours (in km/hr)
V = d/t
Speed = distance/time
V = 8100km/9hr = 900Km/hr
Answer:
V = 900 km/h
Susan's television was damaged during her move and she decides to replace it. She finds the television she wants at the BigBox Store. She can buy the television on consignment for $982 with a 14% down payment. How much must Susan pay as down payment? Round your answer to the nearest cent. Do not include a dollar sign in your answer.
ANSWER
$137.48
EXPLANATION
We have to find the 14% of $982,
[tex]982\cdot\frac{14}{100}=982\cdot0.14=137.48[/tex]Hence, she must pay
$137.48
I took a screenshot I didn’t want to type it again
You have a 52 standard deck.
There are 4 suites on the deck: diamonds, hearts, spades, and clubs.
Each suite has 13 ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, Jack, Queen, and King → This means that there are 4 cards with each rank on the deck.
The "9 of clubs is missing on your deck"
This means that:
1) Your deck has one less card, the total number of cards is 51.
2) Your deck has one less club, instead of 13 club cards, you have 12.
3) Your deck has one 9 less, which means that there are 3 nines on your deck.
a) You have to select one event, whose probability decreased due to the missing 9 of clubs.
For example, the event "you draw a card at random and it's a 9"
The expected probability of drawing a 9 of the deck can be determined as the number of nines divided by the number of cards on the deck:
[tex]\begin{gathered} P(9)=\frac{4}{52} \\ P(9)=\frac{1}{13} \\ P(9)=0.076\approx7.6\% \end{gathered}[/tex]But in reality, there is one 9 is missing from the deck, so you have 3 nines and 51 cards on the deck, its probability is:
[tex]\begin{gathered} P(9)=\frac{3}{51} \\ P(9)=\frac{1}{17} \\ P(9)=0.059\approx5.9\% \end{gathered}[/tex]The expected probability of drawing a card at random and the card being a 9 is 7.6%, but due to the missing card, the probability dropped to 5.9%.
This means that drawing a card at random and selecting a 9 is less likely than expected.
b) You have to select one event whose probability increased due to the missing card.
For example, the probability of drawing an Ace, knowing that the card is a club:
On a normal deck there are 13 clubs and "one Ace of clubs", the expected probability of drawing the ace, given that the card is a club can be determined as follows:
[tex]\begin{gathered} P(\text{Ace}|\text{Club)}=\frac{1}{13} \\ P(\text{Ace}|\text{Club)}=0.076\approx7.6\% \end{gathered}[/tex]But we are missing one club, which means that the total number of clubs is missing, so instead of having 13 clubs, we have twelve. The probability can be determined as follows:
[tex]\begin{gathered} P(\text{Ace}|\text{Club)}=\frac{1}{12} \\ P(\text{Ace}|\text{Club)}=0.083\approx8.3\% \end{gathered}[/tex]The expected probability of drawing the Ace, given that the card is a club, on a normal deck is 7.6%, but due to the missing 9 of clubs, this probability has increased to 8.3%.
So this event is more likely due to the missing card.
c) You have to select an event whose probability hasn't changed due to the missing card.
For example, the event "draw a card at random and is a Heart"
The expected probability of drawing a heart from the deck is equal to the quotient between the number of hearts and the total number of cards on the deck:
[tex]\begin{gathered} P(H)=\frac{13}{52} \\ P(H)=\frac{1}{4} \\ P(H)=0.25\approx25\% \end{gathered}[/tex]Your deck is missing one card, so there are 13 Hearts and a total of 51 cards, the probability can be determined as follows:
[tex]\begin{gathered} P(H)=\frac{13}{51} \\ P(H)\approx0.254\approx25.4\% \end{gathered}[/tex]The probability of drawing a heart is around 25% when the deck is complete or missing one card.
Drag and drop a phrase to make the statement true. TrianglesABC and DEF are Response area.similar or not similar
Solution:
Given two triangles;
Triangle ABC and DEF are similar only if;
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} \angle A=180^o-80^o-60^o \\ \angle A=40^o=\angle D \end{gathered}[/tex]Also,
[tex]\angle B=\angle E=80^o[/tex]Also,
[tex]\begin{gathered} \angle F=180^o-80^o-40^o \\ \angle F=60^o=\angle C \end{gathered}[/tex]FINAL ANSWER: Triangle ABC and DEF are similar triangles
Factor the following difference of squares. *Check for a GCF.
ANSWER
(x + 15)(x - 15)
EXPLANATION
The difference of squares is equivalent to the product of the sum and subtraction of the bases,
[tex]a^2-b^2=(a+b)(a-b)[/tex]So, to factor this difference of squares, we have to find the principal square roots of each term,
[tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{225}=15 \end{gathered}[/tex]So this is,
[tex]x^2-225=x^2-15^2=(x+15)(x-15)[/tex]Hence, the factored form is (x + 15)(x - 15).
Find the remaining zer Degree 3; zeros: 5, 7- i The remaining zero(s) of f is
Answer:
The remaining zero is;
[tex]7+i[/tex]Explanation:
Given that two of the zeros of a polynomial are;
[tex]\begin{gathered} 5 \\ 7-i \end{gathered}[/tex]to get the remaining zero.
Recall that according to complex conjugates, complex roots/zeros comes in pairs;
[tex]\begin{gathered} a+bi \\ \text{and} \\ a-bi \end{gathered}[/tex]where a and b are real numbers.
Applying the rule to the given roots.
Since we have a complex root;
[tex]7-i[/tex]we must also have the other pair of the complex root;
[tex]7+i[/tex]Therefore, the remaining zero is;
[tex]7+i[/tex]Find the reference angle for a rotation of 297º.
We have the following angle:
We know that the reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis. In this case, we have the following reference angle:
To find the value of the reference angle, we substract 297 from 360:
[tex]x=360-297=63[/tex]therefore, the reference angle for a rotation of 297° is 63°
Draw the image of a triangle after a dilation with a scale factor of 2.
Let's begin by listing out the information given to us:
The vertices of the triangle is given as:
[tex](0,0),(0,5),(-4,2)[/tex]Dilation by a scale factor of 2 means the triangle will be enlarged, the coordinate of the vertices become:
[tex]\begin{gathered} (0,0)\rightarrow2(0,0)=(0,0) \\ (0,5)\rightarrow2(0,5)=(0,10) \\ (-4,2)\rightarrow2(-4,2)=(-8,4)_{} \end{gathered}[/tex]We will then graph this
can you please help me solve this? i can't solve this question.
To solve this question, we have to relate period (seconds to make a cycle) and its length.
We can relate them as:
[tex]T=2\pi\sqrt[]{\frac{L}{g}}[/tex]where g is the acceleration due to gravity and L the length of the pendulum.
If T1=2.00 and T2=1.99, we can relate them as:
[tex]\begin{gathered} \frac{T_2}{T_1}=\sqrt[]{\frac{L_2}{L_1}} \\ \frac{L_2}{L_1}=(\frac{T_2}{T_1})^2=(\frac{1.99}{2.00})^2=0.995^2=0.990025 \\ L_1=\frac{L_2}{0.990025}\approx1.01L_2 \end{gathered}[/tex]Then, we know that the length of should be 1% larger than it actually is.
As we do not know the actual length, we will use the first equation to calculate the actual length first and then the correct length for a period of 2 seconds.
[tex]\begin{gathered} T=2\pi\sqrt[]{\frac{L}{g}} \\ \frac{T}{2\pi}=\sqrt[]{\frac{L}{g}} \\ L=g(\frac{T}{2\pi})^2 \\ L=9.81\cdot(\frac{1.99}{2\cdot3.14})^2=9.81\cdot0.3167^2=9.81\cdot0.1=0.981\text{ m} \end{gathered}[/tex]NOTE: all the variables and constants are in meters and seconds.
As the correct length is 1% larger than 0.981 m, we can calculate the increase in length as:
[tex]\Delta L=0.01\cdot L_2=0.01\cdot0.981m=0.00981\text{ m}[/tex]Answer: 0.00981 m
your freezer should be kept at -18 C. One day you woke up and noticed the door was left open and the temperature is now -4 degrees C. How many degrees warmer is the freezer now?
where are given that the reference temperature of a freezer is -18 C, if the temperature is -4 C. the difference in temperature will give us how many degrees warmer the freezer is:
[tex]\Delta T=-4-(-18)[/tex]To solve the operations we need first change the sing inside the parenthesis since it is preceded by a minus sing.
[tex]\Delta T=-4+18[/tex]Solving the operations:
[tex]\Delta T=14[/tex]Therefore, the freezer is 14C warmer.
How many ounces are in 10 1/2 pounds?1 pound = 16 ounces
hello
to solve this question, we simply need to equate this
[tex]\begin{gathered} 1\text{pound}=16\text{ounces} \\ 10\frac{1}{2}=x\text{ ounces} \\ \text{cross multiply both sides } \\ x\times1=10.5\times16 \\ x=168\text{ounces} \end{gathered}[/tex]from the calculation above, 10.5 pounds would be equal to 168 ounces
Write the correct system of inequalities, by first defining x and y, that correctly models the situation. Then write the inequalities and then graph the situation stated below. For your stock portfolio, you have at most $4000 that you want to use to buy stock in two companies. One is a construction company, the other is a biotech company. You want to have at least 2 times as much in the construction company as you do in the biotech company. System of inequalities:
SOLUTION
Let x be a construction company,
Let y be a biotech company
From the question, we have that :
[tex]\begin{gathered} x\text{ + y }\leq\text{ 4000}\ldots\ldots..\ldots\ldots\ldots\ldots..equ\text{ 1 } \\ x\text{ }\ge\text{ 2y}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots equ\text{ 2} \end{gathered}[/tex]
Statistics and probil
we know that
Minimum value=838
Maximum value=1443
Difference=1443-838=605
we have that
Lower Class Limit Upper-Class Limit
838 838+x
838+x 838+2x
838+2x 838+3x
838+3x 838+4x
838+4x 838+5x
838+5x 838+6x=1443
Find out the value of x
838+6x=1443
6x=1443-838
6x=605
x=100.83
therefore
the answer is
Lower Class Limit Upper-Class Limit
838 838+100.83=938.83
938.83 1039.66
1039.66 1140.49
1140.49 1241.32
1241.32 1342.15
1342.15 1443
Find out the frequency for each class
838-938.83 ----> (838,842) ---------> frequency=2 ok
938.83- 1039.66 -----> (945,1034,1025) --------> frequency=3 ok
1039.66-1140.49 -----> (1124,1136,1057,1130) ----> frequency=4 ok
1140.49-1241.32 -----> (1184) ----> frequency=1 ok
1241.32-1342.15 ----> (1247, 1249,1256) -----> frequency=3 ok
1342.15- 1443 -----> (1352,1439,1439,1368,1381,1342,1395) -----> frequency=7
f(x)=x^3-4x^2+x+6 find all the real zeros of the function
The zeroes of the polynomial f(x)= x³ - 4x² + x + 6 = 0 are x - 1, x = 2
and x = 3.
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, f(x)= x³ - 4x² + x + 6 = 0.
Now, zeroes of the polynomial should be factors of 6 they are ±1, ±2. ±3, ±6.
Now at x = 1 f(x) = 4 so not a zero, at x = - 1, f(x) = 0 so x = - 1 a zero
at x = 2 f(x) = 0 so x = 2 is a zero,
at x = 2 f(x) = so x = 3 is a zero.
learn more about polynomials here :
https://brainly.com/question/20121808
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does any know how to find the variance using n=122 p= 0.64
The formula to find the variance of a binomial distribution given the values n and p is:
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \text{ Where} \\ q=1-p \end{gathered}[/tex]In this case, you have:
[tex]\begin{gathered} n=122 \\ p=0.64 \\ q=1-p \\ q=1-0.64 \\ q=0.36 \end{gathered}[/tex]Then
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \sigma^2=122\cdot0.64\cdot0.36 \\ \sigma^2=28.11 \\ \text{ Rounding to the nearest tenth} \\ \sigma^2=28.1 \end{gathered}[/tex]Now, the standard deviation is the square root of the variance. So, you have
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{28.1} \\ \sigma=5.3 \end{gathered}[/tex]Therefore, the variance and standard deviation of the binomial distribution with the given values n y p are
[tex]\begin{gathered} \sigma^2=28.1\Rightarrow\text{ Variance} \\ \sigma=5.3\Rightarrow\text{ Standard deviation} \end{gathered}[/tex]how many 1/5s are in 20?
there are 100 1/5s in 20
TASK 8 Michael has made a scale drawing of his classroom. The scale for his drawing is 0.5 in.: 3 ft. a. The length of the classroom is 30 ft. The length of the room on the scale drawing is 6 in. Is this correct? Explain why or why not. b. One of the student tables is 6 ft long. How long should it be on the drawing? Explain how you got your answer. c. Write your own problem concerning Michael's drawing. Solve and explain your answers.
The scale drawing is
Inches : Feet
0.5 : 3
We need to find the length of the classroom on the drawing if it is 30 feet
Let us use the ratio above to find it
Inches : Feet
0.5 : 3
x : 30
by using cross multiplication
[tex]x\times3=0.5\times30[/tex]3x = 15
Divide both sides by 3 to find x
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]x = 5
The length on the drawing must be 5 inches
a) 6 inches is incorrect because the length on the drawing must be 5 inches
b) The student is 6 ft long
let us use the ratio above to find his length on the drawing
Inches : Feet
0.5 : 3
y : 6
By using cross multiplication
[tex]\begin{gathered} y\times3=0.5\times6 \\ 3y=3 \end{gathered}[/tex]Divide both sides by 3 to find y
[tex]\begin{gathered} \frac{3y}{3}=\frac{3}{3} \\ y=1 \end{gathered}[/tex]b) his length on the drawing is 1 inch
for number c) choose any length by feet and use the ratio to find its length on the drawing
Your height is 8 feet
Let us find it in the drawing
Inches : Feet
0.5 : 3
h : 8
By using cross multiplication
[tex]\begin{gathered} h\times3=0.5\times8 \\ 3h=4 \end{gathered}[/tex]Divide both sides by 3 to find h
[tex]\begin{gathered} \frac{3h}{3}=\frac{4}{3} \\ h=\frac{4}{3} \end{gathered}[/tex]c) Your height on the drawing is 4/3 inches
To determine whether or not it is sensible to do a regression analysis, look atQuestion 20 options: the slope y-intercept scatter plot correlation
Explanation
Regression analysis is a set of statistical methods used to estimate relationships between a dependent variable and one or more independent variables.
Before one determines if one will do a regression analysis, we will have to check for the scatter plot
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.
Thus, the answer is a scatter plot
20. Connie's pool has 50 cubic yards of water in it and is draining at a rate of 3 cubic yards per second. Paula's pool has 9 cubic yards of water currently in it and is filling at a rate of 4 cubic yards per second. After how many seconds will Connie's pool have less water than Paula's?
write the equation for the Connie's pool and Paula's pool
Connie's
[tex]y=50-3x[/tex]y=cubic yards of water remaining in the pool
x=time in seconds
Paula's
[tex]y=9+4x[/tex]y=cubic yards of water in the pool
x=time in seconds
write the inequality in order for connie's pool to have less water
[tex]\begin{gathered} 50-3x<9+4x \\ \end{gathered}[/tex]solve the inequality for x
[tex]\begin{gathered} 50-9<3x+4x \\ 41<7x \\ x>\frac{41}{7} \end{gathered}[/tex]After 41/7 seconds Connie's pool will have less water than Paula's.
A company charges (c) a flat fee of $4 for shipping plus $0.85 per pound (p). Which equation expresses this relatioship?
The cost of shipping is the flat rate plus the cost per pound times the number of pounds
c = flat rate + rate* pounds
c = 4 + 0.85*p
The write the second part in the opposite order
c = 0.85p +4
When we add the order doesn't matter
Answer B c = 0.85p + 4
Our university consists of three colleges: business, engineering, and fine arts. There are 2,900 students in the business college, 1,500 students in the engineering college, and 1,000 students in the fine arts college. What percent of the total number of students are in the fine arts college. Round your answer to the nearest percent.
Given data:
The numbers of students in business college is B=2,900.
The numbers of students in engineering college is E=1,500.
The numbers of students in fine arts is A=1,000.
The percentage of total number of students in fine arts is,
[tex]\begin{gathered} P=\frac{A}{B+E+A}\times100 \\ =\frac{1,000}{2,900+1,500+1,000}\times100 \\ =18.52\text{ percent} \\ \approx18\text{ percent} \end{gathered}[/tex]Thus, the percentage of the students in fine arts is 18 %.
Can I please get someone to help me with this?
First, notice that the line intersects the y-axis at the point (0,5), and that it also passes through the point (2,4). Then, we can use the equation for the slope given two points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we get the following:
[tex]\begin{gathered} (x_1,y_1)=(2,4)_{} \\ (x_2,y_2)=(0,5) \\ \Rightarrow m=\frac{5-4}{0-2}=-\frac{1}{2} \\ m=-\frac{1}{2} \end{gathered}[/tex]now that we have that the slope is m = -1/2 and that the y-intercept is 5 (since the intersection is the point (0,5)), then, the equation of the line in slope intercept form is:
[tex]y=-\frac{1}{2}x+5[/tex]the doll collector store has an inventory of 420 dolls a total of 70 dogs are made of porcelain and the remainder are made of plastic which of the following is the ratio of the plastic dolls to the total number of dolls in store inventory
let:
P = Number of plastic dolls = 420 - 70 = 350
N = total number of dolls in store inventory
[tex]\begin{gathered} P\colon N \\ 350\colon420=\frac{350}{420}=\frac{5}{6} \end{gathered}[/tex]