Answer:
0.56
Step-by-step explanation:
125 in total.
Let x be the number of those who passed both tests.
85 passed English, then 85-x passed only English;95 passed statistics, then 95-x passed only statistics;15 failed both.Thus,
x+(85-x)+(95-x)+15=125,
195-x=125,
x=70.
Thus, the probability that they passed both tests is
[tex]Pr=\dfrac{70}{125}=\dfrac{14}{25}=0.56.[/tex]
need help asap need it thenext few minutes
Answer:
Correct Option is d [tex](x+3)^2 = 11[/tex]
Step-by-step explanation:
For completing the square our equation should be in the form of [tex]a^2 +2ab + b^2 = (a+b)^2[/tex]
In the given equation we have:
[tex]x^2 +6x -2\\x^2 + 2(x) (?) +(?)^2 = 2\\for\,\, making\,\, 6x\,\, 2*x*3=6x \\so, \,\,we\,\, can\,\, add\,\, and\,\, subtract\,\, (3)^2 \,\,on\,\, both\,\, sides\\x^2 + 2(x) (3) +(3)^2 -(3)^2= 2\\(x+3)^2 -9 =2\\(x+3)^2 =2+9\\(x+3)^2 = 11[/tex]
Correct Option is d [tex](x+3)^2 = 11[/tex]
Which situation describes DEPENDENT events?
A) A student is chosen from Classroom A, then that student flips a coin.
B) One student is chosen from Classroom A, then a student is chosen from Classroom B.
C) One student is chosen from Classroom A, then a second student is chosen from Classroom A.
D) A student is chosen from Classroom A, then that student chooses a card from a standard 52-card deck.
Answer:
C) One student is chosen from Classroom A, then a second student is chosen from Classroom A.
Step-by-step explanation:
The choice of each student being chosen is dependent on the first one, as there will be one less person to choose from, leading to a higher chance of the another being chosen.
Answer:
i wanna say the answer is B
Step-by-step explanation:
Coach Kent brings 3 quarts of sports drink to soccer practice. He gives the same amount of the drink to each of his 16 players . How many ounces does each player get
Step-by-step explanation:
Hi there! The answer is,6 ounces of sports drink for each player. Pay attention to the following steps:
1 quart= 32 ounces
3 quarts= 32×3 =96 ounces
96÷16= 6 ounces
what is the y coordinate in the solution for the system of linear equations below
-3x+2y=6
and 4x-y=2
please show work :)
Answer:
y=6
Step-by-step explanation:
use elimination by making the ys opposite in value and eliminating them from the equation so there is only variable:
-3x+2y=6
2(4x-y=2)
-3x+2y=6
8x-2y=4
Combine like terms and divide by 5 on both sides.
5x=10
x=2
Plug x in to find y:
4(2)-y=2
8-y=2
y=6
The y-coordinate in the system of equations, we can use the elimination method. After manipulating the equations, we find that the y-coordinate of the solution is 6.
The y-coordinate of the solution for the given system of linear equations:
-3x + 2y = 6
4x - y = 2
We can use the method of substitution or elimination. Let's use elimination for this example:
Multiply the second equation by 2 to make the coefficients of y equal but opposite: -3x + 2y = 6 becomes -3x + 2y = 6 (unchanged) and 4x - y = 2 becomes 8x - 2y = 4.
Add the modified equations together: (-3x + 2y) + (8x - 2y) = 6 + 4, which simplifies to 5x = 10.
Divide by 5 to solve for x: x = 10 / 5, so x = 2.
Substitute x = 2 into one of the original equations to find y: -3(2) + 2y = 6, which simplifies to -6 + 2y = 6.
Add 6 to both sides to isolate 2y: 2y = 12.
Divide by 2 to solve for y: y = 12 / 2, so y = 6.
Therefore, the y-coordinate of the solution is 6.
The populations and areas of four states are shown. Which statement regarding these four states is true? The state with the lowest population has the greatest population density. The state with the second lowest population has the lowest population density. The state with the lowest population has the lowest population density. The state with the second greatest population has the lowest population density.
The state with the second lowest population has the lowest population density.
The correct statement from the given option is The state with the second-lowest population has the lowest population density.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The population density of a state is the ratio of the population of the state and the area of the state. Therefore, the population density of the states can be written as,
[tex]\text{Population density of state}=\dfrac{\text{Population of the state}}{\text{Area of the state}}\\\\\\\text{Population density of state A}=\dfrac{1,055,173}{2,677} = 394.163[/tex]
[tex]\text{Population density of state B}=\dfrac{1,333,089}{36,418} = 36.6\\\\\\\text{Population density of state C}=\dfrac{3,596,677}{5,543} = 648.87\\\\\\\text{Population density of state D}=\dfrac{6,745,408}{10,555} = 639.073[/tex]
Thus, the correct statement from the given option is The state with the second-lowest population has the lowest population density.
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Two sides of a triangle have measures of 6 inches and 12 inches. Which measure could be the length of the third side?
Final answer:
The third side of a triangle with sides of 6 inches and 12 inches must be greater than 6 inches and less than 18 inches in length, without being exactly 6 or 18 inches.
Explanation:
The length of the third side of a triangle with two sides measuring 6 inches and 12 inches must adhere to the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Consequently, for the given triangle, the possible range for the length of the third side, denoted as x, is between 6 inches and 18 inches (exclusive), that is: 12 - 6 < x < 12 + 6. The value of x cannot be exactly 6 or 18 inches because the triangle would collapse into a straight line. Therefore, the permissible length can be any real number greater than 6 inches but less than 18 inches.
Tell whether or not f(x) = 3 sin 2 - cos x is a sinusoid.
Answer
b. No
Step-by-step explanation:
We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is a sinusoid.
The function is
f(x) = 3*sin(2*x) - 5*cos(x)
Which can be seen in the picture below
We can notice that f(x) is a not sinusoid. It has periodic amplitudes, and the function has a period T = 2π
The maximum and minimum values are
Max = 6.937
Min = -6.937
Answer:
B
Step-by-step explanation:
No
Create/Write a direct variation word problem. Create a table of values representing the word problem. Write the equation representing the direct variation word problem. Graph the equation.
The word problem is Royal works part-time at a local store and earns $12 per hour.
The equation is y = 12x, the graph is attached and the table is
Hours Worked | Earnings ($)
1 | 12
2 | 24
3 | 36
4 | 48
5 | 60
Create/Write a direct variation word problem
A direct variation word problem is as follows
Royal works part-time at a local store and earns $12 per hour.
The above is a direct variation word problem and the equation can be represented as
y = 12x
Where
x is the number of hoursy is the total earning12 is the earning per hourSo, we have the table of values to be
Hours Worked | Earnings ($)
1 | 12 i.e. 12 * 1
2 | 24 i.e. 12 * 2
3 | 36 i.e. 12 * 3
4 | 48 i.e. 12 * 4
5 | 60 i.e. 12 * 5
The graph of the function is added as an attachment
A company is creating a box without a top from a piece of cardboard, but cutting out square corners with side length x.
Which expression can be used to determine the greatest possible volume of the cardboard box?
(15−x)(22−x)x
(x−15)(x−22)x
(15−2x)(22−2x)x
(22x−15)(15x−22)
Answer:
(15−2x)(22−2x)x
Answer:
Volume of box = (15−2x)(22−2x)x
C is correct.
Step-by-step explanation:
A company is creating a box without a top from a piece of cardboard, but cutting out square corners with side length x.
The dimension of the cardboard must be 15 x 22 because all options has same value.
We have rectangle cardboard with 15 x 22. We cut square from each corner of the board with dimension x.
New length of box = 22 - 2x
New Width of box = 15 - 2x
Height of the box = x
Volume of box is equal to volume of cuboid.
Volume of box = LBH
= (15-2x)(22-2x)(x)
Hence, The correct volume of the box is (15-2x)(22-2x)(x)
if a right circular cone is intersected by a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone, as the picture below, what shape is produced?
Answer:
C. An ellipse
Step-by-step explanation:
If you cut a cone on the side with an angle that will produce an ellipse-shaped plane.
if you were to cut the cone perpendicularly to its height (as if the double cone on the picture was straight up), you would get a circle as the plane, because it would be a transversal cut of a circular cone.
If you cut it with an angle, you're stretching the circle... so you'll have an ellipse.
It is NOT a parabola NOR a hyperbola, since both would require the cross-section to go through the base... which it does not in this problem. Please refer to the image below.
Answer:
An ellipse
Step-by-step explanation:
A p e x
If -798 degrees is in standard position, determine a coterminal angle that is between 0 degrees & 360 degrees and state the quadrant in which the terminal side lies.
A. 146 degrees; IV
B. 282 degrees; IV
C. 146 degrees; II
D. 282 degrees; II
Answer:
4
Step-by-step explanation:
What is the midpoint of the segment show below
Answer:
Your answer is B. (3, 5/2)
Step-by-step explanation:
The formula to find the midpoint of a segment is
(x1 + x2) / 2 to find the x value
and (y1 + y2) / 2 to find the y value of the midpoint.
To find the midpoint of the segment in the photo, you would do...
-1 + 3 divided by 2, giving you 3 for your x
and then 2+3 divided by 2, giving you 5/2 for your y.
Hope this helps!
Answer:
B
Step-by-step explanation:
the midpoint is based on the average of the two pair of point X1 and X2 as Y1 and Y1 divided by 2, each one. So, if we settle X1 and Y1 as (-1,2) and X2 and Y1 as (7,3)
(X1 + X2)/2 = (-1+7)/2 = 6/2= 3
(Y1 + Y2)/2 = (2+3)/2 = 5/2
so, we get the Answer B (3 , 5/2)
which number line shows the solution 1/2x-2>0
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]\frac{1}{2}x-2>0[/tex]
Solve for x
[tex]\frac{1}{2}x>2[/tex]
[tex]x>4[/tex]
The solution is the interval ------> (4,∞)
All real numbers greater than 4
In a number line, the solution is the shaded area at right of x=4 (open circle, the number 4 is not included in the solution)
see the attached figure
Answer
On 4 there is a circle and the line goes to the right
Step-by-step explanation:
Barb walked 1.3 miles to her friend's house and then 3/4 mile to the library. How far did Barb walk in all?
Answer:
1.78 miles
Step-by-step explanation:
3/4 = .75 of a mile + 1.3 = 1.78
The answer is 2.05.
you can make the fraction into a decimal, 3/4=0.75, then you just add 0.75 to 1.3.
What is the least number that has 4 odd factors that are all the same? each factor is greater than 1, and can have only 1 and itself as factors. explain how you found the number?
Answer:
81
Step-by-step explanation:
We need to have 4 odd factors not including 1 that are the same
Listing the odd numbers
1,3,5,7,9,11,13,.....
3 is the smallest odd number that is not 1
The factors of 3 are 1 and 3
The number is 3*3*3*3
81
If sin Θ = 2/3 and tan Θ < 0, what is the value of cos Θ?
Answer:If sin Θ is positive and tan Θ is negative, then the angle should be in the second quadrant using the rule of thumb. In this case, cos Θ is expected to be negative.
Step-by-step explanation:If sin Θ is positive and tan Θ is negative, then the angle should be in the second quadrant using the rule of thumb. In this case, cos Θ is expected to be negative.
Answer:
cos Ф = adj / hyp = √5 / 3
Step-by-step explanation:
If sin Ф is +, then Ф must be in either Quadrant 1 or Quadrant 2.
If tan Ф < 0, then Ф must be in either Quadrant 2 or Quadrant 3.
So we conclude that Ф is in Quadrant 2.
If sin Ф = opp / hyp = 2/3, then opp = 2 and hyp = 3, and adj is found using the Pythagorean Theorem:
adj = √( 3² - 2² ) = √( 5 )
With adj = √5 and hyp = 3, cos Ф = adj / hyp = √5 / 3
Each week you deposit money in a savings account. The first week you deposit $8 in the account. Each week you deposit $2 more than you deposited the week before. How much do you save after 12 weeks?
Answer:
228
Step-by-step explanation:
I would have saved $228 after 12 weeks if in the first week I deposit $8 in the account, and each week I deposit $2 more than deposited the week before
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The savings account can be represented by an arithmetic sequence in which the first term (a) = 8, and common difference (d) = 2. Hence, money saved after 12 weeks is:
[tex]S_{n}=\frac{n}{2}(2a+(n-1)d) \\\\S_{12}=\frac{12}{2}(2(8)+(12-1)2) = 228[/tex]
I would have saved $228 after 12 weeks if in the first week I deposit $8 in the account, and each week I deposit $2 more than deposited the week before
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blank x blank x blank = 27
Can someone fill in the blanks for me.
Let's assume your "blanks" are letters x.
[tex]x\times x \times x=27[/tex]
Can be also written:
[tex]x^3=27[/tex]
Now we solve for x using cubic root.
[tex]x=\sqrt[3]{27}=\boxed{3}[/tex]
The blanks are all equal to number 3.
But that is not the only solution.
Hope this helps.
r3t40
Answer: 3
The question is, what numbers multiplied 3 times will get 27?
[tex]\sqrt[3]{27}[/tex] = 3
Hope this helps and have a great day!!!
Describe different ways in which a plane might intersect the cylinder and the cross section that results?
Answer : If it is perpendicular to the axis, then a circle. If it is at an angle to the axis, then an ellipse. If it is parallel to the axis, then two parallel lines. Those are the only 3 cases that I can think of.
Hope this helps.
Help help! 50+ points plus Brainlist answer if work is shown!
Answer:
4 sqrt(5)
-----------------
5
83 +12 sqrt(35)
Step-by-step explanation:
1. 4 sqrt(6)
--------------------
sqrt(30)
Multiply the top and bottom by sqrt(30) to rationalize the denominator
4 sqrt(6) *sqrt(30)
--------------------
sqrt(30)*sqrt(30)
4 sqrt(180)
--------------------
30
Simplify
2 sqrt(36 *5)
--------------------
15
We know that sqrt(ab) = sqrt(a) sqrt(b)
2 sqrt(36)sqrt(5)
--------------------------
15
2 *6*sqrt(5)
-------------------
15
Simplify
2 * 2 sqrt(5)
---------------------
5
4 sqrt(5)
-----------------
5
2. (2 sqrt(5) + 3 sqrt(7))^2
(2 sqrt(5) + 3 sqrt(7)) (2 sqrt(5) + 3 sqrt(7))
FOIL
first 2sqrt(5)*2sqrt(5)=4*5=20
outer 2 sqrt(5) * 3 sqrt(7) = 6 sqrt(35)
inner 3 sqrt(7) *2 sqrt(5) = 6 sqrt(35)
last 3sqrt(7) 3sqrt(7) = 9*7 = 63
Add them together = 20 + 6 sqrt(35)+ 6 sqrt(35) +63 = 83 +12 sqrt(35)
Help me out here please! Thanks.
Answer:
A. [tex]\frac{1}{5} log_{3}x +log_{3}y[/tex]
Step-by-step explanation:
We have the expression
[tex]log_{3} (\sqrt[5]{x} *y)[/tex]
As these two values are being multiplied, we can separate the two and the sum of them will be equal to the multiplied version
[tex]log_{3}\sqrt[5]{x} +log_{3}y[/tex]
The [tex]\sqrt[5]{x}[/tex] can be rewritten as [tex]x^{\frac{1}{5} }[/tex]. This allows us to use the exponent rule. This means that it can be written as
[tex]\frac{1}{5} log_{3}x +log_{3}y[/tex]
Answer:
A. [tex] \dfrac{1}{5} \log_3 x + \log_3 y [/tex]
Step-by-step explanation:
[tex] \log_3(\sqrt[5]{x} \cdot y) = [/tex]
The log of a product is the sum of the logs.
[tex] = \log_3 \sqrt[5]{x} + \log_3 y [/tex]
Now, write the root as a rational power.
[tex] = \log_3 x^\frac{1}{5} + \log_3 y [/tex]
The log of a power is the the exponent times the log of the base.
[tex] = \dfrac{1}{5} \log_3 x + \log_3 y [/tex]
Help me out here please!
Answer:
c
Step-by-step explanation:
Investment in new issues (the stock of newly formed companies) can be both suicidal and rewarding. suppose that of 400 newly formed companies in 2010, only 11 appeared to have outstanding prospects. suppose that an investor had selected two of these 400 companies back in 2010. find the probability that at least one of the investor's companies had outstanding prospects. round to seven decimal places.
Final answer:
To find the probability that at least one of the investor's companies had outstanding prospects out of 400 newly formed companies, we can use the complement rule. The rounded probability is 0.0067747.
Explanation:
To find the probability that at least one of the investor's companies had outstanding prospects, we can use the complement rule. The complement of at least one company having outstanding prospects is that none of the companies have outstanding prospects. Since there are 400 companies in total and only 11 have outstanding prospects, the probability that a single company does not have outstanding prospects is 389/400. Therefore, the probability that both companies do not have outstanding prospects is (389/400)^2. The probability that at least one company has outstanding prospects is 1 - (389/400)^2.
Rounding this to seven decimal places, the probability that at least one of the investor's companies had outstanding prospects is 0.0067747.
The following graph shows the amount of snow that fell in Denver, Colorado in the winter of 1888-1889. How many inches of snow did Denver receive during this period?
21 inches
21.3 inches
21.7 inches
22 inches
The answer is:
The second option, Denver received 21.3 inches of snow during the period from 1888 to 1889.
Why?To know how many inches of snow did Denver receive, we need to sum each the number of inches received per year from 1888 to 1889.
So, from the graph, we have:
For Nov '88, 3 inches.
For Dec '88, 0.8 inches.
For Jan '89, 5.5 inches.
For Feb '89, 8.4 inches.
For Mar '89, 3.6 inches.
Now, adding the number of inches for each month/year, we have:
[tex]Total=3in+0.8in+5.5in+8.4in+3.6in=21.3inches[/tex]
Hence, we have that Denver received a total of 21.3 inches for the 1888-1889 year period.
Have a nice day!
Ok so the equation d=70t represents the distance in miles covered after traveling at 70 miles per hour for t hours... What is D when T is 2.25
d= 157.5 when t is 2.25. all you need to do is plug in 2.25 for t which gives us: d=70(2.25) = 157.7
Multiply the rate, 70 miles per hour, by the given time, 2.25 hours, to find that the distance d is 157.5 miles when t is 2.25 hours.
Explanation:The question asks for the value of d when t is 2.25 in the equation d = 70t, where d represents the distance in miles and t represents the time in hours. To find the value of d, simply multiply the rate (70 miles per hour) by the given time (2.25 hours).
Solution: d = 70×2.25 = 157.5 miles
Therefore, the distance d when t is 2.25 hours is 157.5 miles.
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dion flips a coin 20 times and records if it comes up heads. if getting heads is a success, what is the probability of a success on each roll?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The probability of success (getting heads) on one roll DOESNT affect other rolls, so we need to find probability of getting a head in a roll.
Probability is defined as the number of favorable outcomes divided by the total number of outcomes.
Here, favorable outcome is getting a head. So, on one roll, getting a head is 1. Also, the total number of outcomes is either a head or a tail. So total number of outcomes is 2.
Thus,
P(Heads) = 1/2
(3Q) Find the amplitude and period of f(t)= -tan.0t
Answer:
option b
amplitude none ; period 5π/2
Step-by-step explanation:
Given in the question a function,
f(t)=-tan(0.4t)
The tangent function does not have an amplitude because it has no maximum or minimum value. The period of a tangent function, y=atan(bx),is the distance between any two consecutive vertical asymptotes.
Period = π/|b|
= π/2/5
= 5π/2
Olivia is cutting a 1 \dfrac12 \text{ m}1 2 1 ? m1, start fraction, 1, divided by, 2, end fraction, space, m by \dfrac34\text{ m} 4 3 ? mstart fraction, 3, divided by, 4, end fraction, space, m piece of rectangular paper into two pieces along its diagonal. Find the area of each of the pieces.
"169 A" is answer than k y o u
Answer:
9/16
Step-by-step explanation:
If you horizontally stretch the linear parent function f(x) = x by a factor of 2, what is the equation of the new function?
A. g(x) = 1/2x
B. g(x) = x-2
C. g(x) = 2x
D. g(x) = 2-x
To horizontally stretch the linear parent function f(x) = x by a factor of 2, we replace 'x' in the original function with 'x/2'. Therefore, g(x) = x becomes g(x) = x/2 or g(x) = 1/2x.
Explanation:When we talk about stretching the "linear parent function" f(x) = x horizontally by a factor of 2, we are essentially changing the 'x' values of the function, and the equation of the function changes accordingly. When a function is stretched horizontally by a factor of 'b', the new function becomes f(x/b). So, in this case, as the stretch factor is 2, the new function will be f(x/2).
This means that wherever you see 'x' in the original function, you replace it with 'x/2'. So, f(x) = x becomes g(x) = x/2. Therefore, the correct answer to your question is g(x) = 1/2x.
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An object falls 9 m in the first second, another 27 m in the second second, and then 108 m more in the third second. If this pattern continues, how far will the object fall during the first 4 seconds?
360 m
684 m
426 m
117 m
Answer: B) 684m
Step-by-step explanation:
From 9 to 27 is a 3 times increase, from 27 to 108 is a 4 times increase. So following the pattern, we can determine that it will increase 5 times, and fall another 540m in second 4. Then, we simply add all the numbers together to get the answer!