Answer:
3:4
Step-by-step explanation:
It's males to females. so we make 42:56 simplify that we get 3:4
A recent survey suggests that 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus. What is the probability that a randomly chosen college student either has a job or lives on campus
[tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability that a randomly chosen college student either has a job or lives on campus:
Given: 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus.
So, out of 100 students, 42 students either has a job or live on campus.
43 college students have a job and 12 live on campus.
So, 43 + 42 + 12 = 85 + 54 - 42
85 + 12 = 139 - 42
97 = 97
Therefore, [tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
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In general, the arithmetic average return is probably too _____ (low/high) for longer periods and the geometric average is probably too _____ (low/high) for shorter periods.
The arithmetic average return is probably too high for longer periods and the geometric average is probably too low for shorter periods.
What is Arithmetic Average Return?
When we look at historical returns, the difference between the geometric and arithmetic average returns isn't too hard to understand.
To put it slightly differently, the geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered. A somewhat trickier question concerns forecasting the future, and there's a lot of confusion about this point among analysts and financial planners.
Now, If we have estimates of both the arithmetic and geometric average returns, then the arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.
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Determine whether the relationship is an inverse variation or not. Explain.
The relationship is not an inverse variation because the product xy is not a constant.
What is Inverse variation?Inverse variation is the relationship between two quantities whereby an increase in one quantity cause a decrease in the other quantity.
In this type of variation the product of the two quantities is constant.
Analysis:
if x is one quantity and y is the other,
Mathematically, x = [tex]\frac{k}{y}[/tex]
Where, k is a constant,
it means k = xy
from the table, when, x =2, y = 409, xy = 2 x 409 = 818
Also, x = 3, y = 240, xy = 3 x 240 = 720
Therefore, 720 not equal to 818.
In conclusion, The product xy is not a constant, so the relationship is not an inverse variation.
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A chemist has three different acid solutions. the first acid solution contains 20 % acid, the second contains 30 % and the third contains 60 % . he wants to use all three solutions to obtain a mixture of 54 liters containing 45 % acid, using 2 times as much of the 60 % solution as the 30 % solution. how many liters of each solution should be used? the chemist should use liters of 20 % solution, liters of 30 % solution, and liters of 60 % solution.
Let [tex]a,b,c[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% acid solutions, respectively. These quantities then contain [tex]0.20a[/tex], [tex]0.30b[/tex], and [tex]0.60c[/tex] liters of acid.
The chemist wants to end up with a total volume of 54 liters, so
[tex]a + b + c = 54[/tex]
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
[tex]0.20a + 0.30b + 0.60c = 24.3[/tex]
He will also use twice as much of the 60% solution as the 30% solution, so
[tex]c = 2b[/tex]
Substitute this into the first two equations and solve for [tex]a,b[/tex].
[tex]\begin{cases} a + 3b = 54 \\ 0.20a + 1.50b = 24.3 \end{cases}[/tex]
Eliminating [tex]b[/tex], we have
[tex](a + 3b) - 2 (0.20a + 1.50b) = 54 - 2(24.3) \implies 0.60a = 5.4 \implies \boxed{a = 9}[/tex]
Solve for [tex]b[/tex].
[tex]9+3b=54 \implies 3b=45 \implies \boxed{b=15}[/tex]
Solve for [tex]c[/tex].
[tex]c = 2(15) \implies \boxed{c=30}[/tex]
a = 9, b = 15 and c = 30 liters of each solution should be used.
What liter means?According to the metric system, a liter is a unit for measuring volume. A bottle of Coke that holds 33.76 ounces, or 1.0567 quarters, is an example of a liter. 2. The fundamental metric unit of liquid volume or capacity, which is equivalent to 1.06 quarts or 2.12 pints.What is a liter of water?Let's examine this with the help of the following justification. Despite the fact that there is no established standard size for glasses, their capacity varies. In contrast, we estimate that a glass of water holds 8 ounces, and a liter holds 32 ounces.According to the question:
Let a, b, and c stand for the relative volumes (in liters) of the 20 percent, 30 percent, and 60 percent acid solutions. The amount of acid in these amounts is 0.20a, 0.30b, and 0.60c liters.
a+b+c = 54 because the chemist wishes to have a final volume of 54 liters.
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
0.20a + 0.30b + 0.60c = 24.3
Additionally, he will consume twice as much of the 60% solution as the 30% solution, thus c = 2b.
Substitute this into the first two equations and solve for a,b
a + 3b = 54
0.20a + 1.50b = 24.3
Eliminating b, we have[tex](a+3 b)-2(0.20 a+1.50 b)=54-2(24.3) \\0.60 a=5.4[/tex]
a = 9.
Solve for b.9+3b = 54
3b = 45
b = 15.
Solve for c.c = 2(15)
c = 30.
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HELP!!!!!!QUICK!!!!!!!
Use the Law of Sines to solve (if possible) the triangle for the value of c. Round answers to the nearest tenths. A = 27.5°, a = 15.0 cm, b = 36.4 cm
The law of sines cannot be used to calculate the side c.
How to solve for side c?The given parameters are:
A = 27.5°, a = 15.0 cm, b = 36.4 cm
Based on the above values,
The law of sines cannot be used to calculate the side c.
This is so because the angle C is not given
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What is the simplified form of startroot startfraction 2,160 x superscript 8 baseline over 60 x squared endfraction endroot? assume x ≠ 0.
The simplified form is [tex]6x^{3}[/tex].
What are indices in maths?
An index, or a power, is the small floating number that goes next to a number or letter.The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.The equation is -
[tex]\sqrt{\frac{2160x^{3} }{60x^{2} } }[/tex]
We can rewrite this using property of multiplication to obtain
[tex]\sqrt{\frac{2160}{60} * \frac{x^{8} }{x^{2} } }[/tex]
We simplify variable expression in the radicand using
[tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]
[tex]\sqrt{36 * x^{8 - 2} }[/tex]
[tex]\sqrt{36 * x^{6} }[/tex]
[tex]\sqrt{36 * (x^{3})^{2} }[/tex]
[tex]\sqrt{36} * \sqrt{(x^{3})^{2} }[/tex]
[tex]6 * x^{3}[/tex]
Therefore, the simplified form is [tex]6x^{3}[/tex]
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Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative three and negative four.
The equation of the graphed parabola is y=a[tex](x+3)^{2}[/tex]-4.
Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).
We are required to find the equation of the graphed parabola.
The equation of a quadratic function of vertex (h,k) is given by:
y=a[tex](x-h)^{2}[/tex]+k
In the above equation a is the leading coefficient.
We have been given point (-3,-4).
We have to just put the value of h=-3 and k=-4 and the required equation will be as under:
y=a[tex](x+3)^{2}[/tex]-4
Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a[tex](x+3)^{2}[/tex]-4.
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2 quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!
Answer:
t = 60/n
Step-by-step explanation:
The original equation we know is y = k/n
Since 12 people can assemble the set in 5 hours, when y is 5, n will be 12.
We can now input that value into the equation.
--> 5 = k/12
--> 5(12) = k/12 (12)
--> 60 = k
--> k = 60
The equation to represent the situation can be written as:
t = 60/n
and that is our final answer!
12 people can assemble in 5hours
So
y=k/x12=k/5k=60Equation
y=60/xOr
t=60/nDetermine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
Step-by-step explanation:
Finding the third angle in triangle XYZ,
[tex]m\angle YXZ=180^{\circ}-77^{\circ}-48^{\circ}=55^{\circ}[/tex],
Thus, [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
What is the area of the shape?
Answer: 21 units²
Step-by-step explanation:
Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where a and b are the parallel sides and h is the height.
Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.
[tex]A=\frac{1}{2}(5+9)*3[/tex]
[tex]A=\frac{1}{2}(14)*3[/tex] [Adding in the parentheses]
[tex]A=7*3[/tex] [Multiplying one-half by 14]
[tex]A=21[/tex] [Multiplying 7 and 3]
The area is 21 units².
There is a 40% probability that a student PASSES their first statistics exam. Using a Binomial Distribution, if we randomly select 7 students: What is the probability that more than 5 PASS their first statistics exam
The probability that more than 5 students will pass their exam is 0.0188416.
How to find the probability?The probability that a student passes their examination = 40% = 0.4
The probability that more than 5 students pass their statistics exam = Probability that 6 students pass their exam + Probability that 7 students pass their exam
The probability that 6 students pass their exam =
[tex]7C_{6} (0.4)^{6} (0.6)^{1}\\=7(0.4)^6(0.6)\\=0.0172032[/tex]
The probability that 7 students pass their exam =
[tex]7C_{7} (0.4)^{7} (0.6)^{0}\\=(0.4)^7\\=0.0016384[/tex]
The probability that more than 5 students pass their statistics exam = 0.0172032 + 0.0016384
= 0.0188416
Therefore, we have found the probability that more than 5 students will pass their exam to be 0.0188416.
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On purchasing a cell phone, Tia got an offer and got the cell phone for $35\%$ less than the tag price. If she saved $\$140$ on that cell phone. Then price on the tag must be $\$$
On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.
Since, the cell pone is sold with 35% discount on it.
Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.
Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.
Hence,
35% discount on tag price=Saved amount
(35/100)×T=140
where T is the tag price.
T=(140×100)35
T=14000/34
T=400
Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.
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If a truck traveled 75 miles in 3 hours, how many miles would the truck have traveled per minute?
The truck travelled 0.42 miles per minute
How to determine the miles per minute?The given parameters are:
Distance = 75 miles
Time = 3 hours
Convert time to minutes
Time = 3 * 60 minutes
Time = 180 minutes
The speed is calculated as:
Speed = Distance/Time
This gives
Speed = 75 miles/180 minutes
Evaluate
Speed = 0.42 miles per minutes
Hence, the truck travelled 0.42 miles per minute
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three decreased by eleven times a number
Step-by-step explanation:
3 - 11x
x is "a number".
so, the request is to multiply it by 11 and subtract the result from 3.
Which type of arc requires another entity to specify its start point?
Slope-intercept form?
Answer:
y=3x+4
Step-by-step explanation:
The original formula for slope-intercept is y=mx+b.
b is your y-intercept (where the line crosses the y-axis).
m is your slope which is 3/1 or just 3.
Question 14 of 23
Which of the following describes a compound event?
OA. spinning a 3 on a spinner
OB. rolling a 3 on a die
OC. getting tails on a coin toss
OD. rolling a 5 on a die and drawing a 10 from a deck of cards
SUBMIT
Answer:
B
Step-by-step explanation:
NEED HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
A
Step-by-step explanation:
The function has vertical asymptotes at x=7 and x=-3, so the denominator needs to have factors (x-7) and (x+3).
This eliminates all the options except for A.
A student missed 45 problems on a mathematics test and received a grade of 39%. If all the problems were of equal value, how many problems were on the test
There were 74 problems in the test.
Rounding-off percentageLet the student got total number of problems in the test to be X.
Percentage of correct answer = 39 %
⇒ 61% of X were incorrect
⇒61/100 x X = 45
⇒61X = 45x100
⇒X = 4500/61
⇒X=73.77
After rounding off 73.77, we get 74.
Hence, we can say that there were total of 74 problems in the test.
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If there are fifty raffle tickets in a jar, and only two will be drawn out, and you own two of them, what chance do you have of owning both winning tickets?
Answer:
1/25
Step-by-step explanation:
Answer:
I think it may be 1/1225
Step-by-step explanation:
first chance is 2/50 and second chance is 1/49 as one card decrease at first. So multiplying it we get 1/1225.
What equation is parallel to 3y = 6x-10 and passes through A(4,5)?
Answer:
57?
Step-by-step explanation:
A piece of plexiglass is in the shape of a semicircle with radius 2m. determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass
The dimensions of the rectangle having greatest area in the piece of plexiglass which is a semicircle is [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex].
Given radius of piece of plexiglass which is a semi circle equal to 2m.
We have to find the dimensions of the rectangle which is inscribed in the semi circle.
Draw a rectangle in a semicircle.
Suppose the length of rectangle be x and width be y.
Draw a line from the center to the vertex of the rectangle which forms a right angled triangle with sides x,y and 2.
[tex](x/2)^{2} +y^{2} =2^{2}[/tex]
y=[tex]\sqrt{16-x^{2} }/2[/tex]
Area of rectangle=2xy
=x[tex]\sqrt{16-x^{2} }[/tex]/2
Finding the derivative of area
d A/dx=1/2[x(-2x)/2[tex]\sqrt{16-x^{2} }[/tex]+[tex]\sqrt{16-x^{2} }[/tex]]
d A/dx=0
1/2[[tex]-2x^{2} /2\sqrt{16-x^{2} }+\sqrt{16-x^{2} } ][/tex]=0
Solving for x
[tex]\sqrt{16-x^{2}[/tex]=[tex]x^{2} /\sqrt{16-x^{2} }[/tex]
16-[tex]x^{2}[/tex]=[tex]x^{2}[/tex]
16=2[tex]x^{2}[/tex]
[tex]x^{2}[/tex]=8
x=2[tex]\sqrt{2}[/tex]
put the value of x in y=[tex]\sqrt{16-x^{2} }/2[/tex] to get the value of y
y=[tex]\sqrt{16-8} /2[/tex]
=[tex]\sqrt{8} /2[/tex]
= 2[tex]\sqrt{2} /2[/tex]
=[tex]\sqrt{2}[/tex]
Hence the dimensions of rectangle which is in a semi circle of radius 2 is [tex]\sqrt{2} and 2\sqrt{2}[/tex].
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help quick, it's based on polynomials .
Find the area of the shape
Answer:
Step-by-step explanation:
I got you first you want to get some little ceasers
What is equilibrium if autonomous expenditures are $2,000 and the mpe is 0. 5?
The equilibrium level if autonomous expenditures are $2,000 and the mpe is 0. 5 is $4000.
How to calculate the equilibrium?From the information given, the autonomous expenditures are $2,000 and the mpe is 0. 5.
Here, the equilibrium level will be:
= 2000/(1 - 0.5)
= 2000/0.5
= 4000
In conclusion, the correct option is $4000.
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Identify the scale of measurement for the following variable: The weight of a group of dieters. Group of answer choices nominal ratio ordinal interval
Ratio scale of measurement for the following variable, The weight of a group of dieters.
What scale of measurement is the variable of weight?Ratio measurement scale of ratio variables include height, weight, and distance. The ratio scale allows for the addition, subtraction, division, and multiplication of data. Additionally, ratio scales have a "real zero," which sets them apart from interval scales. The ratio scale is used to determine weight. The ratio is identical to the interval scale, with the exception that 0 on the scale denotes the absence of anything. serval scales can depict values lower than zero and do not hold a true zero. For instance, you can gauge temperatures as low as -10 degrees Celsius. Contrarily, ratio variables are always greater than zero. Height and weight are measured starting at 0 and never below it. Because they are numbers as we typically think of them, ratio scales are the simplest to comprehend. On a ratio scale, the distance between consecutive numbers is equal, and a score of zero indicates that there is no presence of the thing being measured. The majority of ratio scales are counts of items.
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find area and perimeter show your work
Answer:
A= 16
P=16
Step-by-step explanation:
A=h^bxb/ 2
P= side+base+side
The length of a rectangle is 5 5/3 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68
(question and answers attached)
The perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The perimeter of any object is the total sum length of its boundary.
The perimeter of a rectangle with length l units and width w units is given as:
Perimeter = 2(l + w) units.
In the question, we are given that the length of a rectangle is 5 3/5 inches and its width is half of its length. We are asked to find the perimeter of the rectangle.
The length of the given rectangle (l) = 5 3/5 inches = 28/5 inches.
The width of the given rectangle (w) = Half of length = 1/2 * 28/5 inches = 14/5 inches.
Thus, the perimeter of the rectangle = 2(l + b) = 2(28/5 + 14/5) inches,
or, the perimeter = 2(42/5) inches,
or, the perimeter = 84/5 inches,
or, the perimeter = 16.8 inches.
Thus, the perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.
The given question is incorrect. The correct question is:
"The length of a rectangle is 5 3/5 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?
(a) 16.8 inches
(b) 8.4 inches
(c) 2.8 inches
(d) 15.68"
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What is a Turned triangle?
Please tell me QUICKLY.
like the place where you are applying TURNED TRIANGLE.
coz literrally it means that if the trianlge has for example angle a on its right side then we turn the triangle as a whole and make the turn such that angle a is anywhere else but not on our right side....
I believe the explanation is clear, if not do contact me
Genevieve wants to verify that negative x is the simplified expression of one-fifth (5 x minus 20) minus one-half (4 x minus 8). which procedure can genevieve follow to verify this? add one-fifth (5 x minus 20) minus one-half (4 x minus 8) and negative x. put an equal sign between one-fifth (5 x minus 20) minus one-half (4 x minus 8) and one-fifth (5 x minus 20) minus one-half (4 x minus 8) and then solve for x. substitute 5 into the first expression, substitute 4 into the second expression, and evaluate them. substitute 5 into each expression and evaluate them.
Answer: -x
Apply Multiplicative Distribution Law:- 1/5 * 5x - 1/5 * 20 - 1/2 * 4x - 1/2 *(-8)
Determine the sign for multiplication or division: 1/5 * 5x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 1/5 * 20 - 1/2 * 4x + 1/2 * 8
Cross out the common factor: x - 4 - 1/2 * 4x + 1/2 * 8 - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 1/2 * 8
Cross out the common factor: x - 4 - 2x + 4
Reorder and gather like terms: (x - 2x) + (- 4 + 4)
Collect coefficients for the like terms: (1 - 2) * x + (- 4 + 4)
Calculate the sum or difference : - x + (- 4 + 4)
The sum of two opposites equals 0: -x
Answer: -x
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Answer:
D) Substitute 5 into each expression and evaluate them.
Step-by-step explanation: