Answer:
Step-by-step explanation: The expected loss is 50 cents, we know that it is more likely to lose than win. It is therefore difficult to get-50, so the overall difference between the two possibilities is 2, 50/200=1/4, and the probability to win is 1/4, and the probability to lose is 3/4. Since (1/4)*3=3/4, the number of black balls is 3 times the number of white balls, so k=15.
Natasha, Mark and Henry share some sweets in the ratio 7:3:2. Natasha gets 75 more sweets than Henry. How many sweets are there altogether?
Answer:
180
Step-by-step explanation:
Given the ratio = 7 : 3 : 2 = 7x : 3x : 2x ( x is a multiplier ), then
7x = 2x + 75 ( Natasha gets 75 more sweets than Henry )
Subtract 2x from both sides
5x = 75 ( divide both sides by 5 )
x = 15
Thus
total number of sweets = 7x + 3x + 2x = 12x = 12 × 15 = 180
Please help...........
Answer:
315.1° (1 d.p.)
Step-by-step explanation:
Please see the attached picture for the full solution.
what is 11.52/128 show your work
Answer:
0.09
Step-by-step explanation:
11.52 / 128
First, divide both numerator and denominator by 2:
2.88 / 32
Divide both numerator and denominator by 4:
0.72 / 8
Divide 0.72 by 8, you get 0.09.
Which of the following shows the division problem below in synthetic division form?
Answer: D
Step-by-step explanation:
In synthetic division, if the divisor is an expression like x+3, you should always switch it to if x+3 were equal to 0.
[tex]x+3=0\\x=-3[/tex]
So, you should use -3. The only options with -3 are B and D.
The coefficients for the dividend are 7, -2, and 4, so D is the correct answer.
Hope this helps! If you still have questions, please ask.
Please help me with this question... I can't seem to understand
Answer:
d is 83.2 metersStep-by-step explanation:
To calculate the horizontal distance d we use cosine
cos ∅ = adjacent / hypotenuse
From the question
d is the adjacent
the hypotenuse is 145m
So we have
cos 55 = d / 145
d = 145 cos 55
d = 83.16
d is 83.2 meters to 3 significant figures
Hope this helps you
A chemist whishes to prepare 100 liters of 45% purity of sulphuric acid .He has two kinds of acid solutions in stock ,one is 55% pure and the other is 30% pure .How many leters of each kind should be used for the mixture?
Answer:
the chemist should use 60 liters of 55% solution and 40 litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.
Step-by-step explanation:
From the given information,
Let x be the litres of 55% pure solution
Let y be the litres of 30% pure solution
Also;
Given that our total volume of solution is 100 litres
x+y =100 ---- (1)
The total solution of pure by related by the sum of the individual pure concentrations to make up the concentration of final solution.
(0.55)(x)+(0.30)(y) = 0.45(100) ---- (2)
From equation (1)
Let ; y = 100 - x
Replacing the value for y = 100 - x into equation (2)
(0.55)(x)+(0.30)(100-x) = 0.45(100)
0.55x + 30 - 0.30x = 45
0.55x - 0.30x = 45 - 30
0.25x = 15
x = 15/0.25
x = 60 liters of 55% solution
From ; y = 100 - x
y = 100 - 60
y = 40 litres of 30% solution.
Therefore, the chemist should use 60 liters of 55% solution and 40 litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.
Suppose that the market research department of a famous bakery has determined that the most aesthetically pleasing donut has a thickness that is twice the inner radius of the donut (that is, the radius of the donut’s hole). The formula for the inner radius of the donut is given by the equation , where V is the volume of the donut in cubic centimeters. Use the table of values to help you answer the questions about r(v). -30 -0.80 -20 -0.70 -10 -0.55 0 0 10 0.55 20 0.70 30 0.80
Answer:
The information given are;
[tex]r(V)=\sqrt[3]{\dfrac{V}{6\cdot \pi ^{2}}}[/tex]
Where;
r(V) = The radius of the doughnut (cm)
V = The volume of the doughnut (cm³)
The data are;
V, r(V)
-30, -0.8
-20, -0.7
-10, -0.55
0, 0
10, 0.55
20, 0.7
30, 0.8
From the table of values, the identified key features are;
a) There is a direct relationship between the radius and the volume of the doughnut
b) The correlation between the data increases to direct proportionality from the volume of 20 cm³ and above
c) The data values are symmetric and continuous about the y and x-axis
2) There is a direct linear relationship between radius, r and the volume V at end ends of the data between r and V where V = -30 and-20 at one end and 20 and 30 at the other end
b) The x and y-intercept are
The x -intercept = (0, 0)
The x -intercept = (0, 0)
c) The pivot point is the point about which change occurs, therefore, the pivot point is the (10, 0.55)
d) The domain is a member of the set of real numbers, R while the range is also a member of the set of real numbers, R
Step-by-step explanation:
Which set of events is an example of dependent events?
A. Rolling an odd number, and then rolling an even number.
B. You choose a number from 1 to 50 from a hat, replace it, and then draw a second number.
C. You choose a marble from a bag, don't replace it, and then choose another marble.
D. You roll a 4, and then spin yellow on a spinner.
C.
Because the marble is not replaced and that affects the next event where another marble is chosen.
Dependent events:
It is the event where one event outcome is dependent on the other event outcome.
Independent events:
It is the event where one event outcome is not dependent on the other event outcome.
You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
Option C is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Dependent events:
It is the event where one event outcome is dependent on the other event outcome.
Independent events:
It is the event where one event outcome is not dependent on the other event outcome.
Now,
A. Rolling an odd number, and then rolling an even number.
This is an independent event.
B. You choose a number from 1 to 50 from a hat, replace it, and then draw a second number.
This is an independent event.
C. You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
D. You roll a 4 and then spin yellow on a spinner.
This is an independent event.
Thus,
You choose a marble from a bag, don't replace it, and then choose another marble.
This is a dependent event.
Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.
Option C is the correct answer.
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Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square. Need help quick Plz!!!
Answer:
The answer is below
Step-by-step explanation:
The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).
From the sector, AB = AC = radius of the sector (r) = 12. Therefore:
[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]
From the triangle: AC² = AB² + BC²
AC² = 12² + 12² = 144 + 144
AC² = 288
AC=√288 = 12√2
[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]
How does the graph of g(x) = (x + 4)^3-6 compare to the parent function f(x)=x^3 Choices:
Explanation:
f(x) = x^3
f(x+4) = (x+4)^3 .... shifts graph 4 units to the left
f(x+4) - 6 = (x+4)^3 - 6 ... shifts 6 units down
The change from x to x+4 means the xy axis has moved four units to the right (since each input is now 4 units larger). If we hold the curve y = x^3 to be completely still while the xy axis moves 4 units to the right, then the illusion of the curve moving 4 units to the left happens.
The -6 at the end does what you'd expect it to do, and there is no opposites going on here. Whatever the y value is, subtract 6 from it to get the new y value. Effectively this moves the graph down 6 units.
Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer.
Answer: Degree of polynomial (highest degree) =4
Maximum possible terms =9
Number of terms in the product = 5
Step-by-step explanation:
A trinomial is a polynomial with 3 terms.
The given product of trinomial: [tex](x^2 + x + 2)(x^2 - 2x + 3)[/tex]
By using distributive property: a(b+c+d)= ab+ac+ad
[tex](x^2 + x + 2)(x^2 - 2x + 3)=(x^2 + x + 2) x^2+(x^2 + x + 2) (-2x)+(x^2 + x + 2)(3)\\\\=x^2(x^2)+x(x^2)+2(x^2)+x^2 (-2x)+x (-2x)+2 (-2x)+x^2 (3)+x (3)+2 (3)\\\\\\=x^4+x^3+2x^2-2x^3-2x^2-4x+3x^2+3x+6[/tex]
Maximum possible terms =9
Combine like terms
[tex]x^4+x^3-2x^3+3x^2-4x+3x+6\\\\=x^4-x^3+3x^2-x+6[/tex]
Hence, [tex]\left(x^2\:+\:x\:+\:2\right)\left(x^2\:-\:2x\:+\:3\right)=x^4-x^3+3x^2-x+6[/tex]
Degree of polynomial (highest degree) =4
Number of terms = 5
Answer:
Sample Response: To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x2 by x2, you add the exponents to get x4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.
The degree of the product of the trinomials is 4 because the degree of each trinomial is 2.
The maximum number of terms in the product of the trinomials is 5.
There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.
Explanation:
This is the response on Edge 2020-21. Hope this helps, have a great day!
Please answer this question now
Answer:
[tex] r = 17.5 [/tex]
Step-by-step explanation:
Given ∆TRS,
Where,
m < R = 105°
TR = s = 15
RS = t = 6
ST = r = ?
Find r using the Law of Cosines.
[tex] r^2 = s^2 + t^2 - 2*s*t*cos(R) [/tex]
Plug in the values stated above into the formula
[tex] r^2 = 15^2 + 6^2 - 2*15*6*cos(105) [/tex]
[tex] r^2 = 225 + 36 - 180*(-0.2588)[/tex]
[tex] r^2 = 261 + 46.584 [/tex]
[tex] r^2 = 307.584 [/tex]
[tex] r = \sqrt{307.584} [/tex]
[tex] r = 17.5 [/tex] (to the nearest tenth)
Q7-8 PLEASE HELP ME
Answer:
(-4,-7)
Step-by-step explanation:
Use the online graphing calculator called Desmos. That's what I did. Just input the two equations and it'll show you the completed graph. I hope this help you:)
what is angle and how would you know
Answer:
Angle:
When two lines/rays intersect at a point, they form an angle.
=> Angles may be in radians and degrees.
See the attached file in which two rays intersect to form an angle.
Answer:
[tex]\boxed{\mathrm{view \: explanation \: and \: attachment}}[/tex]
Step-by-step explanation:
Two lines (arms/rays) intersect at one point (vertex) creating an angle.
Which is the simplified form of x Superscript negative 12?
Answer:
1/x^12
Step-by-step explanation:
X^-12....simply move x^-12 to the other side of the division and change the sign of the exponent.
The simplified form of the expression x Superscript negative 12 is 1/ x¹².
What is the rule of exponent?The rule of the exponent is defined as the simplified form of the exponents
(aᵇ)ⁿ = aᵇⁿa⁻ⁿ = 1/aⁿaᵇ * aⁿ = aᵇ⁺ⁿaᵇ / aⁿ = aᵇ⁻ⁿwhere a is the base and b and n are the exponent.
Here given in the question is the expression that x superscript negative 12.
As we now superscript is to write the number in exponent position.
here -12 is written in the superscript of x.
then the mathematical expression will be converted as
x superscript negative 12 = x⁻¹²
As we know from the rule of exponent that a⁻ⁿ = 1/aⁿ where a is the base and n is the exponent.
x⁻¹² can be rewritten as x⁻¹² = 1/ x¹²
Therefore the simplified form of the expression x Superscript negative 12 is 1/ x¹².
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PLEASE HELP ASAP IM REALLY TRING TO FINISH A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
__♥__♥_____♥__♥___ Put This
_♥_____♥_♥_____♥__ Heart
_♥______♥______♥__ On Your
__♥_____/______♥__ Page If
___♥____\_____♥___ You Had
____♥___/___♥_____ Your Heart
______♥_\_♥_______ Broken
________♥_________…………….
99 students choose to attend one of three after school activities: football, tennis or running.
There are 61 boys.
19 students choose football, of which 5 are girls.
31 students choose tennis.
28 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answer: [tex]\dfrac{49}{99}[/tex]
Step-by-step explanation:
There are 61 boys --> 38 girls
A) 19 chose football: 5 are girls --> 14 are boys
B) 38 girls: 28 chose running, 5 chose football --> 5 girls chose tennis
C) 31 students chose tennis: 5 are girls --> 26 are boys.
D) 61 boys: 14 chose football, 26 chose tennis --> 21 boys chose running.
[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&14&5&19\\Tennis&26&5&31\\\underline{Running}&\underline{\quad 21\quad}&\underline{\quad 28\quad}&\underline{\quad 29\quad}\\Total&61&38&99\end{array}}[/tex]
Total running = 21 boys + 28 girls = 49
Total students = 99
[tex]\dfrac{\text{Total running}}{\text{Total students}}=\large\boxed{\dfrac{49}{99}}[/tex]
John has 9 boxes of apples. Each box holds 16 apples. If 7 boxes are full, and 2 of the boxes are half full, how many apples does john have?
Answer:
128 Apples
Step-by-step explanation:
Answer:
128 apples
Elaborated:
Your first multiple 16 and 7 which is 112. Your than multiply 2 and 8 since the remaining boxes are half full which is 16. 112+16 is 128. Hope this helps!
A rectangular piece of wood is 12 centimeters longer than it is wide. A strip 1 centimeter wide is cut off all around. This decreases the area by 120 square centimeters. What were the original dimensions?
Answer:
Length 37 cm, width 25 cm.
Step-by-step explanation:
Let the original dimensions be length x and width x - 12 cms.
The new dimensions will be length (x - 2) and width (x - 12 - 2) = x-14 cm.
So , from the areas, we have:
x(x - 12) - (x - 2)(x - 14) = 120
x^2 - 12x - (x^2 - 16x + 28) = 120
-12x + 16x - 28 = 120
4x = 148
x = 37 cms
So the length was 37 cm and the width was 37-12 = 25 cm.
BRAINLIEST! ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answer:
20 km/hr
Step-by-step explanation:
The boat's still-water speed is the average of its speeds against and with the current:
(15 +25)/2 = 20 . . . km/hr
__
If you want to write equations, you can let b and c represent the speeds of the boat and current in km/hr.
b - c = 15 . . . . upstream speed
b + c = 25 . . . . downstream speed
Add these two equations, and you get ...
(b -c) +(b +c) = (15) +(25)
2b = 40
b = 20 . . . . divide by 2
The speed of the boat in still water is 20 km/hr.
Answer:
20 km/hr
Step-by-step explanation:
To solve this, you have to find the average speed it is going. To find this, you just add up all of the speeds mentioned and divide it by the number of speeds you added.
15 +25=40
40/2=20
20km/hr!!!
Good luck on what you are doing I hope you do well! Brainliest would be great :)
CAN ANYONE HELP ME! WILL GIVE OUT BRAINLIEST!!
Answer:
C
Step-by-step explanation:
4:10 ≠ 6:8
I really need help please
Answer:
1. 2.997
2. 29.93
Step-by-step explanation:
1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.
2. Same thing, gotta multiply all given values
Solve this one 0.2=x/5-1.4
Answer:
x = 8[tex]0.2 = \frac{x}{5} - 1.4[/tex]
Move 1.4 to the left side of the equation
That's
[tex]0.2 + 1.4 = \frac{x}{5} \\ \\ \frac{x}{5} = 1.6[/tex]
Convert the decimal to fraction
That's
1.6 = 8/5
[tex] \frac{x}{5} = \frac{8}{5} [/tex]
Multiply through by 5
We have
[tex] \frac{x}{5} \times 5 = \frac{8}{5} \times 5 \\ \\ \\ x = 8[/tex]
Hope this helps you
What the answer to this question
Answer:
44
Step-by-step explanation:
Eric completed 1/3 of his homework before dinner and then 2/7 after dinner. How much homework did Eric complete?
The homework completed by Eric will be equal to 13/21.
What is the fraction?
The fraction is defined as the division of the whole part into an equal number of parts.
To add fractions, you first have to set the denominators equal to each other. To do this, you find the LCD (least common denominator) of the two fractions until you find a shared number.
To do this, list out the multiples of each number (3x1=3,3x2=6,3x3=9, and so on. Do this also with 7) The LCD for 3 and 7 is 21. 3x7=21, and 7x3=21. You want to set each fraction’s denominator equal to 21.
You want to multiply each side of 1/3 by 7. 1/3 would become 7/21. You’d do this because 3x7=21, and if you multiply the bottom by you need to multiply the top by. 7x3=21 so you multiply both sides by 3 to get 6/21.
Now you have 7/21 and 6/21 and can add them. Now that they are equal, you can ignore the denominator and just add the numerators. 7+6=13 so Eric completed 13/21 of his homework.
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can anyone help me solve this function?
f-g means to subtract g from f:
(4^x - 8) - (5x+6)
Remove the parenthesis and change the equations sings for g:
4^x-8 -5x -6
Combine like terms:
4^x - 5x - 14
The answer is A.
What is the slope of the line?
O slope = 1/3
O slope = -3
O slope = 3
Answer:
Slope = 3
Step-by-step explanation:
Slope is rise (vertical distance) over run (horizontal distance).
Our rise is equal to 3
Our run is equal to 1
So, slope = 3/1 = 3
US
Find the value of x.
80
93
112
y
Z
x = [?]
Answer:
x = 74°
Step-by-step explanation:
The diagram shown in this question, is a Quadrilateral inscribed in a circle
It is important to note that
The sum of opposite angles in a Quadrilateral = 180°
93° + z = 180°
z = 180° - 93°
z = 87°
In a cyclic quadrilateral,
Intercepted angle = 1/2(Intercepted arc)
Intercepted angle = 93°
Intercepted arc = x + 112°
Hence,
93° = 1/2(x + 112)°
93° × 2 = x + 112°
186° = x + 112°
x = 186° - 112°
x = 74°
Answer:
It’s 87° for mine
Step-by-step explanation:
Find the product.
(6xyz4)(5xy3)
PLEASE HELP!!! ASAP!!
Answer:
[tex]30x^2y^4z^4[/tex]
Step-by-step explanation:
If we multiply 6x by 5x, we get [tex]30x^2[/tex].
If we multiply y by [tex]y^{3}[/tex], we get [tex]y^{4}[/tex].
z stays the same, since it's not being multiplied by anything.
Hope this helped!
Answer:
Step-by-step explanation:
Multiply each term:
30x^2y^4z^4
Plz mark me brainliest!!
HELPPPPPPPPPPPPPPPPPPPPPPP
Answer:
1) A'(8, -10)
B'(10, -8)
C'(2, -4)
2) A''(8, -4)
B''(10, -6)
C''(10, -10)
Step-by-step explanation:
1) For reflection across the line y = -1, given that the lowest point is of ABC which is point C with coordinates (2, 2), we have;
The vertical distance from the point C to the line y = -1 is 3 units down, therefore, the coordinate of the reflection of C will be 3 units below the line y = -1 at C'(2, -4)
The coordinates of the point A(8, 8) will be A'(8, -10)
The coordinate of the point B(10, 6) will be B'(10, -8)
2) Given that we have A'(8, -10), B'(10, -8), and C'(2, -4), we have reflection over y = -7, we have;
The coordinates of the point A'(8, -10) will be A''(8, -4)
The coordinate of the point B'(10, -8) will be B''(10, -6)
The coordinate of the point C'(2, -4)will be C''(10, -10)
Which gives, a total translation of -12 units down as follows;
A''(8, -4) - A(8, 8) = (0, -12)
B(10, 6) - B''(10, -6) = (0, -12)
C(2, 2) - C''(10, -10) = (0, -12).