Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:
C) 2
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion between a and b is given by:
a/b = 2.
Then:
a = 2b.
The expression is:
[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]
Hence option C is correct.
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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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A college currently has 600 students enrolled
full time. Of these students, 400 are science
majors while 200 are liberal arts majors. If
350 of the students are male, and 250 of the
males are science majors, how many female
students are liberal arts majors?
(A) 200
(B) 150
(C) 100
(D) 50
Answer:
C) 100
Step-by-step explanation:
250+600-350-400
850-350-400
500-400=100
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
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Number line with closed circle on 5 and shading to the left
Number line with closed circle on 5 and shading to the right.
Number line with open circle on 5 and shading to the left.
Number line with open circle on 5 and shading to the right.
The graph that includes the possible values for the number of people who still need to sign up for the team is:
Number line with closed circle on 5 and shading to the right.
What is the situation and which inequality models it?Researching this problem on the internet, a team currently has 4 players, and needs at least 9.
When x players are signed, the number of players will be of 4 + x. Since the team needs at least 9 players, the inequality is:
[tex]4 + x \geq 9[/tex]
The solution is:
[tex]x \geq 9 - 4[/tex]
[tex]x \geq 5[/tex]
Which is represented as follows:
Number line with closed circle on 5 and shading to the right.
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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 :)
Q3 The grade-point averages of 20 college seniors selected at random from the graduating class are as follows:
3.2 1.9 2.7 2.4 2.8 2.9 3.8 3.0 2.5 3.3
1.8 2.5 3.7 2.8 2.0 3.2 2.3 2.1 2.5 1.9
a) Evaluate the Median of grade point
b) Calculate the highest marks of bottom 30% students
d) Calculate Q1 & Q3.
Answer:
Step-by-step explanation:
A) The median number is just the middle number so it should be 2.8
B) Bottom 30% are the six lowest amounts. The highest of the bottom six numbers is 2.3. Not sure what it means by calculating them. 1.8, 1.9, 1.9, 2.0, 2.1, and 2.3 are the lowest six. If you need to add them up the answer is 12.
C) I don’t know what your Q1 is.
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
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 _____
An American roulette wheel contains 38 slots. Eighteen of the slots are colored red and eighteen are colored
black. The remaining two slots are colored green. A ball is spun on the wheel and comes to rest in one of the
38 slots. If you bet $1 on the the number 32 and win, the house pays you $36.
What is the expected value of betting on 32?
$1
O-$1
4
O-$5.30
O-$0.053
The expected value of betting 32 is -$0.053, making the 4th option the right choice.
In the question, we are asked for the expected value of betting on 32, given that if we bet $1 on the number 32 and win, the house pays $36, and there are 38 slots.
The probability distribution can be shown as:
x $35 -$1
p(x) 1/38 37/38
as, if we get 32, which has the probability of 1/38, the winning number, we gain $35, and for the rest, having a probability of 37/38, the losing number, we lose -$1.
Thus, the expected value can be calculated as E(x) = ∑x.p(x).
Thus, the expected value = $35(1/38) + (-$1)(37/38) = -$2/38 = -$0.05263 ≈ -40.053.
Hence, the expected value of betting 32 is -$0.053, making the 4th option the right choice.
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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]:
f(x) =4x2 + 8x -5 factor completely
The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)
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.
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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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]
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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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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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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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:
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]
A ship leaves port on a bearing of 36.0° and travels 12.1 mi. The ship then turns due east and travels 6.1 mi. How far is the ship from port, and what is its bearing
The bearing angle exists 53.49°.
How to estimate the bearing angle of a ship?A bearing of 36° corresponds to the corresponding angle of
θ = 90 -36 = 54°
The (x, y) values for the position of the ship after achieving its first heading exist:
[tex]x_1[/tex] = 12.1 Cos 54° = 7.11 m
[tex]y_1[/tex] = 12.1 Sin 54° = 9.78 m
Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore
[tex]x_2[/tex] = 6.1 mi
[tex]y_2[/tex] = 0 mi
To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:
Δx [tex]= x_1+x_2[/tex]
= 7.11 mi + 6.1 mi = 13.21 mi
Δy [tex]=y_1+y_2[/tex]
= 9.78 mi + 0 mi = 9.78 mi
[tex]$r=\sqrt{(x_{total})^2+(y_{total})^2}[/tex]
[tex]=\sqrt{(13.21mi)^2+(9.78mi)^2}[/tex]
= 16.43 mi
The direction of the displacement vector exists given by
tan θ = Δy/Δx
θ = arc tan (Δy/Δx)
= arc tan (9.78/13.21)
= 36.51°
The question requested for the bearing angle, which exists just this angle subtracted from 90°:
90° - 36.51° = 53.49°.
Therefore, the bearing angle exists 53.49°.
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The graph of the discrete probability to the right represents
the number of live births by a mother 40 to 44 years old
who had a live birth in 2015. Complete parts (a) through (d)
below.
0.30-
0.25-
0.20
0.15
0.10
0.05
0.00
0
0.235
1
0.270
2
0784
113 0101
-4426-0004 0.045
3
6
Number of Live Births
(a) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth live birth in that year?
(Type an integer or a decimal)
(b) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year?
(Type an integer or a decimal.)
(c) What is the probability that a randomly selected 40- to 44-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year?
(Type an integer or a decimal)
(d) If a 40-to 44-year-old mother who had a live birth in 2015 is randomly selected, how many live births would you expect the mother to have had?
The values of the probabilities are
The probabilities are 0.109, 0.202, 0.106The expected number of births is 3How to determine the probabilities?The image that completes the question is added as an attachment
The probability of having her fourth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
Hence, the probability is 0.109
The probability of having a live birth in her fourth or fifth live birth in that year?From the attached graph, we have:
P(x) = 0.109 when x = 4
P(x) = 0.093 when x = 5
So, we have:
P(4 or 5) = 0.109 + 0.093
Evaluate
P(4 or 5) = 0.202
Hence, the probability is 0.202
The probability of having a live birth in her sixth or more live birth in that year?This is represented as:
P(x >= 6)
From the attached graph, we have:
P(x) = 0.022 when x = 6
P(x) = 0.036 when x = 7
P(x) = 0.048 when x = 8
So, we have:
P(x >= 6) = 0.022 + 0.036 + 0.048
Evaluate
P(x >= 6) = 0.106
Hence, the probability is 0.106
How many live births would you expect the mother to have had?This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = 0.234 * 1 + 0.291 * 2 + 0.167 * 3 + 0.109 * 4 + 0.093 * 5 + 0.022 * 6 + 0.036 * 7 + 0.048 * 8
Evaluate
E(x) = 2.986
Approximate
E(x) = 3
Hence, the expected number of births is 3
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Super confused need help
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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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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your restaurant serves 50 bowls of French onion soup daily and each serving has 8 ounces of onion per portion. Do you think it would be better to purchase whole onions at $1.99 per pound, and cut them yourself, or purchase pre-sliced onions at $2.99 per pound?
I would be better to purchase whole onions at $1.99 per pound, and cut them yourself
Optimization of costNumber of bowls = 50
Weight of each bowl = 8
Total weight of the onion soup = 8 x 50 = 400 ounces
Note that:
1 pound = 16 ounces
Total weight in pounds = 400/16
Total weight in pounds = 25 pounds
If you buy the whole onions and purchase at $1.99 per pound
Total cost = 25 x 1.99 = $49.75
If you purchase pre-sliced onions at $2.99 per pound
Total cost = 25 x $2.99 = $74.75
Since it is cheaper to purchase whole onions at $1.99 per pound, it is the better choice
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The ratio of the weight of an object
The weighing of the man on the earth given the ratio is 174 pounds
Ratioratio of the weight of an object on the earth to the moon = 6:1Weight of a man on the moon = 29 poundsWeight of the man on Earth = xEquate the ratio
6 : 1 = x : 29
6/1 = x/29
cross product6 × 29 = 1 × x
174 = x
x = 174 pounds
Complete question:
The ratio of the weight of an object on the earth to the moon is 6:1. If a man weighs 29 pounds on the moon, calculate his weighing on the earth.
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the sum of two numbers is 55. the greater number is seventeen times the smaller number plus one. Find the numbers
Answer:
52 and 3
Step-by-step explanation:
17x+1 + 1x =55
18x+1=55
18x=54
x=3
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:
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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