Answer:
(a) 6 x (21 ÷ 3) + 8
Step-by-step explanation:
The first step in translating English to math is to understand the English.
Parsing itThe quotient of 21 and 3 is written (21 ÷ 3). Six times that quotient is ...
6×(21÷3)
When 8 is added to this, it becomes ...
6 × (21 ÷ 3) + 8
A person draws a card from a hat. Each card is one color, with the following
probabilities of being drawn: 1/25 for blue, 1/15 for yellow, 1/10 for green, and
1/20 for white. What is the probability of pulling a green or yellow card, written
as a reduced fraction?
FU
Answer:
1/6
Step-by-step explanation:
1/15 yellow, 1/10 green, and 1/20 white
1/15 + 1/10 is the probability for yellow or green.
2/30 + 3/30 = 5/30 = 1/6
Brainliest, please :)
if f x is a linear function, f(-1)=3, and f(1)=5, find an equation for f(x)
The equation of f(x) is f(x) = x + 4
How to determine the equation?The given parameters are
f(-1) = 3 and f(1) = 5
Start by calculating the slope (m) using:
[tex]m = \frac{f(1) - f(-1)}{1 - -1}[/tex]
This gives
[tex]m = \frac{5 - 3}{1 + 1}[/tex]
Evaluate
m = 1
The equation is then calculated as;
f(x) = m(x - x1) + f(-1)
This gives
f(x) = 1(x + 1) + 3
Expand
f(x) = x + 4
Hence, the equation of f(x) is f(x) = x + 4
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Find the equation of a line with a slope of 13/2
that passes through the point (−2, — 10).
Answer: [tex]y=\frac{13}{2} x+3[/tex]
Step-by-step explanation:
Remember the point-slope equation which is [tex]y-y_{1} = m(x-x_{1} )[/tex] where[tex](x_{1} , y_{1} )[/tex] is your point and [tex]m[/tex] is your slope.
Given that we substitute what you have:
[tex]y-(-10) =\frac{13}{2} (x - (-2))[/tex]
Minus and minus give us positive:
[tex]y+10 =\frac{13}{2} (x +2)[/tex]
Multiply slope into the parenthesis:
[tex]y+10= \frac{13}{2}x + \frac{13}{2}*2\\[/tex]
Calculate it:
[tex]y+10= \frac{13}{2}x +13[/tex]
Isolate the [tex]y[/tex] by subtracting 10 from both sides:
[tex]y=\frac{13}{2} x + 13 -10[/tex]
Your final equation is:
[tex]y=\frac{13}{2} x +3[/tex]
Hope this makes sense!
And here's the graph to prove that the line actually goes through the point [tex](-2,-10)[/tex]:
Hi I would like to know how I can solve this problem.
The [tex]n[/tex]-th term is
[tex]U_n = \dfrac14 n^2 (n+1)^2[/tex]
so the 39th term is
[tex]U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}[/tex]
Observe that
[tex]2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)[/tex]
which suggests that
[tex]V_n = 8U_n = \boxed{2n^2(n+1)^2}[/tex]
Calculate the following ratios, correct to 3 decimal places. a. sin 58 = b. cos 26 = c. tan 63=.
Answer: sin(58) = 0.848, cos(26) = 0.898, and tan(63) = 1.962
Step-by-step explanation:
2 qts for every 50 gal of water i just want to use 15 gal of water so how much do i use
The amount of qts to use for 15 gals is 0.6qts
Proportion and ratio
Ratio are written as quotient of 2 integers
Given that 2 qts for every 50 gal of water, this is written as;
2qts = 50 gals
In order to calculate for 15gal, we will have:
x = 15gals
Take the ratio
2/x = 50/15
50x = 30
x = 3/5
x = 0.6qts
Hence the amount of qts to use for 15 gals is 0.6qts
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What is the values of x?
Answer:
x = 34
Step-by-step explanation:
complementary angle sum to 90°
sum the 2 angles and equate to 90
x + x + 22 = 90
2x + 22 = 90 ( subtract 22 from both sides )
2x = 68 ( divide both sides by 2 )
x = 34
Deondra has 57 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 340 square meters. List each set of possible dimensions
(length and width) of the field.
(L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters. This can be obtained by forming quadratic equation for the data.
Calculate the set of possible dimensions (length and width) of the field:
Let length be L and width be W.
Given that,
three sided fence has a length of 57m,
⇒ 2W + L = 57 m ⇒ L = 57 - 2W
the area of the land is 340 square meters
length × width = 340 ⇒ L × W = 340
(57 - 2W)W = 340
57W - 2W² = 340
2W² - 57W + 340 = 0
Solve for W using quadratic formula,
a = 2, b = -57, c = 340
W = (-b±√b²-4ac)/2a
= (57±√3249-2720)/4
= (57±√529)/4
= (57±23)/4
W = 20 m and W = 8.5 m
For W=20, L=57-2(20) = 17
For W=8.5, L=57-2(8.5) = 40
Hence (L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters.
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Simplify the following fractions.
Please Slove this 2 question
Answer:
b)14/3 or 4 2/3 C) 256/15 or 14 1/15
Step-by-step explanation:
In the second fraction, the "of" means to multiply
Answer:
#b
[tex] \displaystyle{ \pmb{ \pink{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }}}[/tex]
[tex]\frak{SOLUTION:}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex]\displaystyle{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }[/tex]
Convert mixed fractions into improper fractions:[tex] = \displaystyle{ \frac{16}{5} \times \frac{7}{2} \div \frac{12}{5} }[/tex]
[tex]=\displaystyle{ \frac{16}{5} \times \frac{7}{2} \times \frac{5}{12} \frak{(Performing division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel{16} \: {}^{2} \times 7 \times \cancel5}{ \cancel5 \times \cancel 2 \times 12} }[/tex]
[tex]\displaystyle{ = \frac{8 \times 7}{12} }[/tex]
[tex] =\displaystyle{} \frac{56}{12} [/tex]
[tex]\displaystyle{ = \frac{ \cancel2 \times \cancel2 \times 2 \times 7}{ \cancel2 \times \cancel 2 \times 3} }[/tex]
[tex]\displaystyle{ = \frac{14}{3} \frak {\: or} \: 4 \frac{2}{3} } [/tex]
#c
[tex]\displaystyle{\pmb{ \pink{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }}}[/tex]
[tex]\displaystyle{ \frak{SOLUTION:}}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex] \displaystyle{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \left( \frac{1}{2} \times \frac{16}{5} \right)\frak{(Performing "of")}}[/tex]
[tex] = \displaystyle{ \frac{8}{3} \div \left( \frac{1 \times \cancel{16} \: {}^{8} }{ \cancel2 \times 5} \right) }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \frac{8}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \times \frac{5}{8} \frak{(Performing \: division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel8}{3} \times \frac{5}{ \cancel8} }[/tex]
[tex] = \displaystyle{ \frac{5}{3} \frak{ \: or \: }1 \frac{2}{3} }[/tex]
Answered by :
[tex]\frak{\pink{seolleaphrodite}}[/tex]
Super confused need help
f(x) =4x2 + 8x -5 factor completely
The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)
There are some 1-dollar bills, some 5-dollar bills, and a 20-dollar bill in an envelope. The number of 1-dollar bills is five times the number of the 5-dollar bills. We randomly pull a bill from the envelope. How many 1-dollar bills are in this envelope if the expected value of the bill pulled is $2.00?
Answer:
the number of 1 dollars bills was 5 si make 1 more 5 dollars so 8n total it is 10 dollars.
If m4 = 108°, what is the measure of 26?
Answer:
108
Step-by-step explanation:
When the lines cut through by a transversal are parallel, alternate interior angles are congruent. angle 4 = angle 6 = 108
Solve the system of equations by substitution.
2x + y = 3z
x + y = 6z
What is the value for y from the first equation, that could be substituted into the second equation?
A. -2x +3z
B. 3z + 2x
C. -2x - 3z
D. 2x + 3z
Consider the following figure:
What is the value of x + y?
The value of the sum of the angles x + y of the given triangle is; 220°
How to find the angles in a triangle?We know that the sum of angles in a straight line is equal to 180°. Thus;
∠CFE + ∠OFE = 180
140 + ∠OFE = 180
∠OFE = 180 - 140
∠OFE = 40°
Similarly, we can use the same principle to get;
∠OEF + ∠BEF = 180°
∠OEF + y = 180°
∠OEF = 180 - y
Similarly,
∠AOF + ∠EOF = 180°
x + ∠EOF = 180°
∠EOF = 180 - x
Sum of angles in a triangle is equal to 180°. Thus;
40 + 180 - y + 180 - x = 180
Rearranging gives;
x + y = 180 + 180 + 40 - 180
x + y = 220°
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Explain the difference between using the trigonometric ratios (sin, cos, tan) to solve for a
missing angle in a right triangle versus using the reciprocal ratios (sec, csc, cot). You must
use complete sentences and any evidence needed (such as an example) to prove your
point of view. (10 points)
Answer:
ok
this called f to do
Step-by-step explanation:
1. take a _____
Which statement is true about the function f(x) = 6x7?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = –f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
Answer: The function is odd because f(–x) = –f(x).
Step-by-step explanation:
[tex]f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)[/tex]
The function is odd because f(–x) = –f(x).
How to determine the true statement?The function is given as:
f(x) = 6x^7
A function is odd if the following is true
f(-x) = -f(x)
Calculate f(-x)
f(-x) = 6(-x)^7
f(-x) = -6x^7
Calculate -f(x)
-f(x) = -6x^7
By comparison;
f(-x) = -f(x) = -6x^7
Hence, the function is odd because f(–x) = –f(x).
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where a=8a=8a, equals, 8 is a solution.
Answer:
a=0
Step-by-step explanation:
If this is what you are asking, and if I understand it correctly, 8*8=64 and not 8, but 8*0=0, therefore 0 is a solution.
3. Make a conjecture about the sum of two even numbers based on the following pattern:
12 = 4 + 8
26 = 6 + 20
48 = 16 + 32
72 = 24 + 48
88 = 36 x 52
and so on.
The conjecture we can use is that the sum of all even numbers is an even number.
How to write Mathematical Conjectures?We are given the sum of two even numbers as follows;
12 = 4 + 8
26 = 6 + 20
48 = 16 + 32
72 = 24 + 48
88 = 36 x 52
From the above, we see that they are all even numbers and as such the conjecture we can use is that the sum of all even numbers is an even number.
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look at the pictures
The function is increasing on the interval (3, ∞)
Interval of a functionGiven the rational function shown below
g(x) = -2√x-3
For the function to be a positive function, the value in the square root must be positive such that;
x - 3 = 0
Add 3 to both sides
x = 0 + 3
x = 3
Hence the interval where the function is increasing is (3, ∞)
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( WILL GIVE BRAINLIEST ) a dog trainer compared the mean numbers of lessons for two groups of dogs which statement is true about the data?
Answer:
Answer number 1
......................
Given the graph of g(x), describes the transformation of the parent function f(x)=2^x.
If the parent function is transformed by:
Shifting 1 unit to the right, the image function is given by g(x) = (x - 1)²Shifting 1 unit to the left, the image function is given by g(x) = (x + 1)².Shifting 1 unit downward, the image function is given by g(x) = x² - 1.Transformation of the parent function.The graph of the parent function is a parabolic curve which opens in the y-axis direction and with its vertex at the origin on a cartesian coordinate.
By critically observing the graph of this parent function [f(x) = x²], we can infer and logically deduce that the transformed curve is a downward opening parabola which has a vertex at (-5, -2).
Thus, if the parent function is transformed by:
Shifting 1 unit to the right, the image function is given by g(x) = (x - 1)²Shifting 1 unit to the left, the image function is given by g(x) = (x + 1)².Shifting 1 unit downward, the image function is given by g(x) = x² - 1.Read more on transformation here: https://brainly.com/question/17586310
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The image of the point (-7, 8) under a translation is (-11, 6). Find the coordinates
of the image of the point (8, -3) under the same translation.
Answer:
(4,-5)
Step-by-step explanation:
1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off
at 4°. Can Brooke walk out to bring the boat back without getting water over the
tops of her hip boots which are 1 m tall? Explain your reasoning.
2. are the engineer who designed a new branch for the Mountain Railroad
Company. You sent your plans calling for 100 km of track up Bixby Mountain
taking trains 99 km east of the city of Bixby, to the City Council for approval.
But before the Council got around to looking at your plans, they passed a
regulation that no railroad tracks could go up their mountain at an angle of more
than 8°. Will your plans be approved? Why or why not?
3. The residents of Quietville, a little town 9 km from the San Francisco Airport,
insist that any plane flying over their town disturbs them if it is lower than 3 km.
Will a plane that took off at a 21° angle disturb them? Why?
4. You are an air pollution inspector, checking that factories in your city have
chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s
chimney, you find the angle from the ground to the chimney top is 51°. Can the
company use that chimney legally? Explain.
6. River City is offering a $3 million contract to build a bridge between points A and
C on opposite sides of City River. Along the side of the river that makes a right
angle with the line of the bridge at point C, a surveyor walked 72 m to point B
where she measured the 55° angle form B to A. Long Company will build the
bridge for $3 million if it is not more than 103 m from point A to point C. Short
Company agrees to build it if it is no more the 100 m. Which contracting firm
will be awarded the contract? Why?
7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach
her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s
greenhouse under her window? Explain your reasoning.
8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take
skiers all of the way up to the top of the mountain where there is a snack bar at
the 500 m elevation? Explain your reasoning.
9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km
from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s
plane as it flies over their new home for the first time today, but there is a layer of
clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes
off at a 9° angle? Explain.
10.You are the cost control expert for an engineering firm designing a giant
television tower having several metal braces, each built in 21 m from the base at a
73° angle with the ground. Part of your job is to decide which standard length of
metal brace wastes less metal: the brace that comes 71 m long, or the one that is
73 m long. What is your decision?
The correct responses found using trigonometric ratios are as follows;
Brooke's cannot bring the boat back without getting water over her boots.The plan will not be approvedThe plane will not disturbThe company can not use the chimney legallyThe Long company will build the bridgeThe fireman can reach her.The lift does not take the skiers up to the bar.Eric will be able to see his Dad's plane.The 73 m. braceHow can trigonometric ratios be used to find the right responses?1. The depth of the water = 15 × tan(4°) = 1.049 m
The height of Brooke's boot = 1 m
Therefore;
Brooke's cannot bring the boat back without getting water over her boots.2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°
Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;
The plan will not be approved.3. Height reached by the plane = 9 × tan(21°) = 3.455
Therefore;
The plane will not disturb.4. Height of the chimney at the factory = 50 × tan(51°) = 61.745
The minimum chimney height = 65 m.
Therefore;
The company can not use the chimney legally.6. Length of the bridge = 72 × tan(55°) ≈ 102.83
Therefore;
The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7
Therefore;
The fireman can reach her.8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8
Therefore;
The lift does not take the skiers up to the bar.9. Height reached by plane = 26 × tan(9°) ≈ 4.12
The plane flies under the cloud therefore;
Eric will be able to see his Dad's plane.10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83
Therefore;
The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.Learn more about trigonometric ratios here:
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The mean date is 1985.67 and standard deviation 9.2 is greater than 2005?
Answer:
Step-by-step explanation:
Use the mean and the standard deviation obtained from the last discussion and test the claim that the mean age of all books in the library is greater than 2005.
This is the last discussion:
The science portion of my library has roughly 400 books.
They are arranged, on shelves, in order of their Library of Congress
code and, within equal codes, by alphabetical order of author.
Sections Q and QA have a total of 108 books.
The bulk of the library was established in the early 1990s.
I used a deck of cards, removing the jokers and face cards, keeping
only aces (1) and "non-paints" (2 to 10). Starting from the start of
the first shelf, I would turn a card (revealing its number N) and I
would go to the Nth book. This uses ordinal numbers (1 would means the
"first" book, not a gap of 1).
The cards were shuffled sufficiently to assume that the cards have a
random order.
I sampled only the LC subsections Q and QA (therefore, not a true
sample of the entire library, as this classification is not purely
random).
Thus, I picked 21 books (the expected number being 108/5.5 = 19.6 --> 20 books)
The sampled dates of publication were (presented as an ordered set):
1967, 1968, 1969, 1975, 1979, 1983, 1984,
1984, 1985, 1989, 1990, 1990, 1991, 1991,
1991, 1991, 1992, 1992, 1992, 1997, 1999
The median date is 1990
The mean date is 1985.67
Variance = 84.93 ( Sum of (date-mean)^2 )
SQRT of variance = 9.2 (sample standard deviation)
The "sigma-one" confidence interval (containing 68% of the books), if
the sample were NOT skewed, and if the distribution were "normal"
would contain dates from "mean - 9.2" to "mean + 9.2"
Sigma-2 (95%) would have mean - 2(9.2) to mean + 2(9.2)
Sigma-3(99.7%) from "1985.67 - 3(9.2)" to "1985.67 + 3(9.2)"
1958.07 to 2012.6
There, you see one reason why the distribution is skewed (it is
possible to have books older than 1958, but it is impossible to have
book newer than 2012), but it still represents a usable model for the
library. If it applies to the entire library of 400 books, you would
expect one book (0.3% of 400) to fall outside the 3-sigma interval.
Your students have been working on algebra equations involving inequalities. The rule for learning the > sign is:
The rule for learning the > sign is demonstrating eating with the right hand.
InequalityThe inequality signs are;
Greater than >Let was than <Equal to =Greater than or equal to ≥Less than or equal to ≤The rule for teaching your students the greater than > sign is by imagining eating with their right hand. The shape of the hand when taking food into the mouth is the greater than sign.
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9
What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%?
97.51
102.53
101.78
105.25
The price of a two-year bond is 101.78 and the correct option is C.
Given that a 9% annual coupon and a yield to maturity of 8%.
Simple yield is the amount of interest received by a bond issuer divided by the current market price of the associated bond.
Implicit Face value, FV=$100
Time, N=2 years
Coupon, C=(9/100)×$100=9
The yield of maturity, r=8%=0.08
Now, we will find the bond price using the formula
Price of bond = C× [1-{1/ (1+r)ⁿ}/r] +M/ (1+r)ⁿ
Substitute the values in this formula, we get
Price of bond=9×[1-{1/(1+0.08)²}/0.08]+100/(1+0.08)²
Price of bond=9×[1-{1/(1.08)²}/0.08]+100/(1.08)²
Price of bond=9×[1-{1/1.1664}/0.08]+100/1.1664
Price of bond=9×[(1-0.857)/0.08]+85.73
Price of bond=9×[0.143/0.08]+85.73
Price of bond=9×1.7875+85.73
Price of bond=16.0875+85.73
Price of bond=101.78
Hence, the price of a two-year bond with a 9% annual coupon and a yield to maturity of 8% is 101.78.
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round 14.81 to the nearest tenth
Answer: 14.8
Step-by-step explanation: If the number in the hundredths place is less than 5, you must round down. On the contrary, if that number is 5 or greater, you must round up. This applies for rounding to any place not just the tenths place. For example, if you were to round it to the ones place, the answer would be 15.
Answer:
14.8
Step-by-step explanation:
The hundredth is smaller than 5, therefore you have to round down.
hope it helps
2. Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Grades are weighted according to credit hours. If a student receives one A in three-credit class, one D in three-credit class, three B in three-credit class and two C in one-credit class, what is the student’s grade point average?
Based on the student's grades, and the credit hours, their grade point average is 2.60.
What does the student get as their GPA?First, find the grade points earned:
= (4 x 3) + (1 x 3) + (3 x 3) + (2 x 1)
= 12 + 3 + 9 + 2
= 26
The GPA is:
=Grade points earned / total number of credits
= 26 / (3 + 3 + 3 + 1)
= 26 / 10
= 2.6
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What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?
What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?
(3, 13)
(9/3, 13)
(2, 12)
(3, 19)
Answer: (3, 13)
Step-by-step explanation:
If we let the point be P, then AP:BP=2:1.
[tex]P=\left(\frac{(2)(3)+(1)(3)}{2+1}, \frac{(2)(19)+(1)(1)}{2+1} \right)=(3, 13)[/tex]