Answer: probability of getting two 5s =0.04
probability of getting at least one 5 =0.36
probability of getting a total score greater than 5 =0.6
Step-by-step explanation:
Total outcomes on 1 spinner = 5
Then , total outcomes of spinning it 2 times= [tex]5\times5 = 25[/tex]
Number of outcomes for getting two 5's = 1
Then, the probability of getting two 5s [tex]=\dfrac{\text{Favorable outcomes of getting two 5's }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{25}=0.04[/tex]
Number of outcomes for getting at least one 5 [ {(1,5),(2,5),(3,5),(4,5),(5,5), (5,1), (5,2), (5,3), (5,4)} ] =9
Then, the probability of getting at least one 5[tex]=\dfrac{\text{Favorable outcomes of getting at least one 5 }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{9}{25}=0.36[/tex]
Number of outcomes for getting a total score of 5, [ {(1,4),(4,1),(2,3),(3,2)} ] =4
Then, the probability of getting a total score of 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score of 5 }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{4}{25}[/tex]
Number of outcomes for getting a total score greater than 5 [ {(1,5),(5,1),(2,4),(4,2),(2,5), (5,2), (3,4),(4,3), (3,5), (5,3), (3,3), (4,5), (5,4), (4,4), (5,5)} ] =15
Then, the probability of getting a total score greater than 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score greater than 5 }}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{15}{25}=\dfrac{3}{5}=0.6[/tex]
what is
5/14 mulitypled by 4 in simplest form
Answer:1 3/7
Step-by-step explanation:When you multiply the nominator and 4you get 20.So it would 20/14 but if you find the simplest form of fraction you would get 1 3/7
Write each function in standard form. Determine the x-intercepts of the function.
Y=-4(x+2)(x+3)
Answer:
X Intercept (-2,0), (-3,0) and Standard form y = -4x^2 - 20x - 24
Step-by-step explanation:
To write a polynomial in standard form, simplify, and then arrange the terms in descending order.
y = ax^2 + bx + c
y = (−4x−8) (x+3)
Expand (−4x−8) (x+3) using the FOIL Method
y = −4x ⋅ x − 4x ⋅ 3 − 8x−8 ⋅ 3
Simplify and combine like terms.
y = −4x^2 − 20x − 24
Hope this can help
Choose the equivalent system of linear equations that will produce the same solution as the one given below 4x-y=-11 2x+3y=5
Answer: x = -2 , y = 3
Step-by-step explanation:
4x-y=-11
2x+3y=5
Solve 4x-y=-11 for y
Add -4x to both sides
4x-y+-4x=-11+-4x
-y=-4x-11
Divide both sides by -1
-y/-1=-4x-11/-1
y=4x+11
Substitute 4x+11 for y in 2x +3y=5
2x+3y=5
2x+3(4x+11)=5
Simplify both sides of the equation
14x+33=5
Add -33 to both sides
14x+33+-33=5+-33
14x=-28
Divide both sides by 14
14x/14=-28/14
x=-2
Substitute -2 for x in y= 4x+11
y=4x+11
y=(4)(-2)+11
Simplify both sides of the equation
y=3
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answer:
73.2
Step-by-step explanation:
you can find the answer using trigonometry relationship
sin31°=41/x
x=41/sin31°. sin31° is approximately equal to 0.56
x=41/0.56
x=73.2
Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).
Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
[tex]|u|=\sqrt{14^2+9^2}[/tex] which is [tex]\sqrt{277}[/tex]
[tex]|v|=\sqrt{3^2+6^2}[/tex] which is [tex]\sqrt{45}[/tex]
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
[tex]cos\theta=\frac{uv}{|u||v|}[/tex] where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
[tex]cos^{-1}\theta=\frac{96}{111.64676}[/tex] which returns an angle measure of 30.7. Plugging that all into the dot product formula:
[tex]u*v=\sqrt{277}*\sqrt{45}cos(30.7)[/tex] gives you a dot product of 96
What is the volume of the following
rectangular prism?
Answer: 13.5 units³
Step-by-step explanation:
[tex]\dfrac{5}{2}\times \dfrac{27}{5}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5\ units^3}[/tex]
PLSSS HELPFind the next term of the sequence. 1, 8, 27, 64, ..
Answer:
125
Step-by-step explanation:
So you can see that the sequence is all of the perfect cubes so knowing that the next perfect cube we have to find is 5's perfect cube which is 125.
Answer:
192
Step-by-step explanation:
Helppppp❤️ Please please
Answer:
B and D
Step-by-step explanation:
I think this is the answer
What is the value of f(-1) ?
Answer:
f(-1) = 12
Step-by-step explanation:
Using the graph for f(x) let x=-1
Find the y value when x= -1
f(-1) = 12
Amanda is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges $111 and allows unlimited mileage. Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.
Answer:
For mileages higher than 80 miles Company A will charge less than Company B
Step-by-step explanation:
Hi, to answer this question we have to write an inequality:
Company A charges $111 and allows unlimited mileage.
Company A =111
Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven
Company B = 55+0.70m
Where m is the number of miles.
Company A has to charge less than Company B
a<b
111 < 55+0.70m
Solving for m
111-55 < 0.70 m
56 < 0.70m
56/0.70 < m
80 < m
For mileages higher than 80 miles Company A will charge less than Company B
PLEASE help me with this question!
Answer:
[tex]44^\circ[/tex]
Step-by-step explanation:
The angle measuring [tex]y^\circ[/tex] is formed by two secants intersecting at an exterior point.
The measure of that angle is half the difference between the big intercepted arc and the little intercepted arc.
y = 1/2 (m arc FKB - m arc CGJ)
Plug in the values you know.
56 = 1/2 (156 - m arc CGJ)
Multiply both sides by 2 to clear the fraction.
112 = 156 - m arc CGJ
Subtract 156.
-44 = - m arc CGJ
44 = m arc CGJ
The measure of the little intercepted arc is [tex]44^\circ[/tex].
pls answer asap i need this answer quick plus the full explanation #4
Answer:
Her Verticle ramp support was 5.5 ft tall.
Step-by-step explanation:
In this type of question, you would need to use the saying "soh cah toa".
Soh Cah Toa is a saying that people use for Sin, Cosine, and tagent. Each of those mean
Sine: opposite/hypotenuse Cosine: Adjacent/hypotenuse and Tagent: Opposite/Adjacent
In this specific question to figure out how tall or high her support is or needs to be have to 20 degree angle off the ground, you will need to use Sin which is opposite over Hypotenuse or x/16
To find the answer in your calculator you would do:
Sin(20)=x/16
First thing you do is the get the x on one side by itself so you would multiply 16 on both sides giving you:
16 × Sin(20)= x
You would then follow to put Sin(20) in your calculator giving you 0.34202014332
After that you multiply that number by 16
5.47232229321
Rounding to the nearest tenth you get answer:
5.5
Write as an equation: Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara? (Let b = Barbara)
a+b+c=68
b-3=a
c-5=b
now just solve the system of equations, substitue so that there are only b's in the equation:
a+b+c=68
(b-3) + b + (b+5) = 68
3b=66
b=22
Therefore Barbara is 22
The required age of barbar is 22 years.
Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Alice, Barbara and Carol are a, b and c.
Age Alice is 3 years younger than Barbara,
a = b - 3 - - - -(1)
Age Barbara is 5 years younger than Carol
b = c - 5
c = b + 5 - - - -(2)
Together the sisters are 68 years old i.e.
a + b +c =68
From equation 1 and 2
b - 3 + b + b +5 = 68
3b + 2 = 68
3b = 66
b = 33
Thus, the required age of barbar is 22 years.
Learn more about arithmetic here:
brainly.com/question/14753192
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In the standard coordinate plane, how many units separate the points (5, -1) and (5, 12).
Answer:
13
Step-by-step explanation:
Put -1 and 12 in the absolute value form and add them together. You'll get 13.
Number of units separate the points is 13 units.
Distance between two Coordinate:Given that;
Coordinate of first point = (5 , -1)
Coordinate of second point = (5 , 12)
Find:
Number of units separate the points
Computation:
Number of units separate the points = √(x1 - x2)² + (y1 - y2)²
Number of units separate the points = √(5 - 5)² + (-1 - 12)²
Number of units separate the points = √(-13)²
Number of units separate the points = 13 units
Find out more information about 'Coordinate'.
https://brainly.com/question/4399730?referrer=searchResults
A square has side length x and a triangle has a base (3x - 2) and height (2x + 4). At what value of x will the two figures have the same area?
Show work and explain all steps.
Answer:
0.73
Step-by-step explanation:
Data obtained from the question include the following:
Length (L) of square = x
Base (b) of triangle = (3x – 2)
Height (h) of triangle = (2x + 4)
Area of square = L²
Area of square = x²
Area of triangle = ½bh
Area of triangle = ½(3x – 2) (2x + 4)
Expand
½ [3x(2x + 4) –2(2x + 4)]
½[6x² + 12x – 4x – 8]
½[6x² + 8x – 8]
3x² + 4x – 4
Area of triangle = 3x² + 4x – 4
Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:
Area of triangle = area of square
Area of triangle = 3x² + 4x – 4
Area of square = x²
Area of triangle = area of square
3x² + 4x – 4 = x²
Rearrange
3x² – x² + 4x – 4 = 0
2x² + 4x – 4 = 0
Solving by formula method
a = 2, b = 4, c = –4
x = – b ± √(b² – 4ac) / 2a
x = – 4 ± √(4² – 4×2×–4) / 2×2
x = – 4 ± √(16 + 32) / 4
x = – 4 ± √(48) / 4
x = (– 4 ± 6.93)4
x = (– 4 + 6.93)4 or (– 4 – 6.93)4
x = 0.73 or –2.73
Since the measurement can not be negative, the value of x is 0.73.
The total capacity of a water bottle and a mug is 7/8 litre. The capacity of the mug is 1/4 litre. How much greater is the capacity of the water bottle than the mug.
Answer:
The capacity of the water bottle is 2.5 times greater than the mug.
Step-by-step explanation:
We know that the capacity of a water bottle and a mug is 7/8 litre:
[tex]bottle+mug=\frac{7}{8}[/tex]
But we also now that the mug's capacity is 1/4 litre, so the equation above becomes:
[tex]bottle + \frac{1}{4}=\frac{7}{8}[/tex]
Now we want to know how much greater the capacity of the bottle than the mug is. To do this we need to know first what's the capacity of the bottle.
So, we would have:
[tex]bottle=\frac{7}{8}-\frac{1}{4} \\\\bottle=\frac{7}{8}-\frac{2}{8}\\\\\\bottle=\frac{5}{8}[/tex]
Therefore the bottle has a capacity of 5/8 liter while the mug has a 2/8 liter one.
To know how much greater is the capacity of the water bottle than the mug we need to divide these two quantities, so we have:
[tex]\frac{5}{8}[/tex]÷[tex]\frac{2}{8}[/tex][tex]=\frac{5}{8}[/tex]×[tex]\frac{8}{2}[/tex][tex]=\frac{5}{2}=2.5[/tex]
Therefore the capacity of the water bottle is 2.5 times greater than the mug.
A doctor recommends a two-step process to treat a rare form of pancreatic cancer. The first method is successful 80% of the time. If the first method is successful, the second method is successful 90% of the time. If the first treatment is not a success, the second is 25% of the time. What is the probability that both treatments are unsuccessful?
Answer:
The answer is 15%.
Step-by-step explanation:
The probability that:
Both treatments are successful:80% x 90% = 72%
The first method is a success, but the second one is not:80% x (1 - 90%) = 8%
The first method is not successful, but the second one is:(1 - 80%) x 25% = 5%
Both treatments are unsuccessful:1 - (72% + 8% + 5%) = 15%
HELPPPPP PLEASEEEE!!!!
Which system of inequalities represents region Z?
Answer:
Hey there!
The two lines in this graph are: y=-1/5x+2, and y=3x-2
Since y=-1/5x+2 is a dotted line, we know that we use the < or > symbols.
Since y=3x-2 is a straight line, we use the ≤ and ≥ symbols.
Thus, for area z, we have y<-1/5x+2, and y≥3x-2
Hope this helps :)
Given a graph for the transformation of f(x) in the format g(x) = f(kx), determine the k value.
ту
g(x)
f(x)
k= -4
k= -1/4
k= 1/4
k= 4
ASAP!!!!
Answer: C
1/4
Step-by-step explanation:
Given a graph for the transformation of f(x) in the format g(x) = f(kx),
This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.
Therefore, the value of k will be 1/4.
Answer:
k=4
Step-by-step explanation:
The area of a rectangular deck, in square meters, is given by the polynomial 40p2 + 24p.
The deck is 8p meters wide.
a) Find the polynomial that represents the length of the deck.
b) Find the polynomial that represents the perimeter of the deck. PLEASE HELP ASAP
Answer:
a. 5p+3
b. 26p + 6
Step-by-step explanation:
a.
Area = length × width
40p² + 24p = length × 8p
Factorise out 8p from both sides
8p(5p + 3) = length × 8p
Divide both sides by 8p
5p + 3 = length
b.
Perimeter = 2(length + width)
"" = 2(5p+3 + 8p)
"" = 2(13p + 3)
"" = 26p + 6
A data-entry clerk spends $86 per week for food. This is 20% of his weekly income. What is the weekly income? Show work please :
Answer:
$430
Step-by-step explanation:
Let the weekly income be x
Money spent on food= $86
% of weekly income spent on food = 20
20% of weekly income in terms = 20/100 * x = x/5
This, income is equal to $86 as given
thus,
x/5 = 86
x = 86*5 = 430
Thus, weekly income is $430.
Can someone help me on this finance problem?
what is the equation of the following line (10 -2) (0 0) a. y= -5x b. -x c. y= 5x d. -1/5x e. y= x f. y= 1/5x
Answer:
Step-by-step explanation:
(0+2)/(0-10)= 2/-10 = -1/5
y - 0 = -1/5(x - 0)
y = -1/5x
solution is D
Help! Pls pls pls! Fast!
it is transformed [tex]|x|[/tex] function. moved down by and right by 1 unit,
so $y=|x-1|-1$
the length of diagonal of a rectangular field is 23.7 m and one of its sides is 18.8 m. find the perimeter of the field.
Answer:
Approximately 66.4 Meters
Step-by-step explanation:
So we have a rectangle with a width of 18.8 meters and a diagonal with 23.7 meters. To find the perimeter, we need to find the length first. Since a rectangle has four right angles, we can use the Pythagorean Theorem, where the diagonal is the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
Plug in 18.8 for either a or b. Plug in the diagonal 23.7 for c.
[tex](18.8)^2+b^2=23.7^2\\b^2=23.7^2-18.8^2\\b=\sqrt{23.7^2-18.8^2} \\b\approx14.4 \text{ meters}[/tex]
Therefore, the length is 14.4 meters. Now, find the perimeter:
[tex]P=2l+2w\\P=2(14.4)+2(18.8)\\P=66.4\text{ meters}[/tex]
What is the effect of the graph of the equation y=3/7x + 6 is changed to y=3/7x -2?
A. The line is shifted right 8 units
B. The line is shifted down 8 units
C. The line is shifted left 8 units
D. The line is shifted up 8 unit
Answer:
down 8 units
Step-by-step explanation:
going from +6 to -2 goes down 8 units
Answer:
B. The line is shifted down 8 unitsStep-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units to the left
f(x - n) - shift the graph n units to the right
==============================================
We have y = 3/7x + 6. It has been changed to y = 3/7x - 2.
y = 3/7x + 6 → f(x) = 3/7x + 6
f(x) - 8 = (3/7x + 6) - 8 = 3/7x + 6 - 8 = 3/7x - 2
A Pythagorean spiral is constructed by drawing right triangles on the hypotenuse of the other right triangles. Start with a right triangle in which each leg is 1 unit long. Use the hypotenuse of that triangle as one leg of a new triangle and draw the other leg 1 unit long. A spiral has been started below, continue the pattern until a spiral with 12 triangles is formed. 1. Determine the Tangent of the angle at the centre of the spiral for each of the first five triangles. 2. Use this pattern to predict the tangent of the 100th triangle.
Answer:
The angle is determined by dividing 360 by the number of vertexes that it took to complete the circle. The tangent of the 100th triangle would be the same respectively.
Step-by-step explanation:
I remember learning this in kindergarten.
given the equation below which of the following shows the quadratic formula correctly applied? 3x^2-4x-12=0
[tex] {3x}^{2} - 4x - 12 = 0[/tex]
[tex]a = 3[/tex]
[tex]b = - 4[/tex]
[tex]c = - 12[/tex]
Formula:
[tex] \boxed{x = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]
Replacing:
[tex]x = \dfrac{ -( - 4) \pm \sqrt{ { (- 4)}^{2} - 4(3)( - 12)} }{2(3)} [/tex]
Option: C).
Solve the system of equations below x - y = 5 2x - 3y = 4
Answer:
x=11 y=6
Step-by-step explanation:
making x the subject in the first equation we get
x=y+5 put that in the second equation we also get
2(y+5)-3y=4
2y+10-3y=4
-y=4-10
-y=-6
y=6 use that to also find x from the equation x=y+5 we get
x=6+5
x=11
therefore x=11 y=6
If f(x) = |x| + 9 and g(x) = –6, which describes the value of (f + g)(x)? (f+g)(x)≥3 for all values of x (f+g)(x)≤3 for all values of x (f+g)(x)≤6 for all values of x (f+g)(x)≥6 for all values of x
Answer:
(f + g)(x)≥3 for all values of xStep-by-step explanation:
Given the expressions f(x) = |x| + 9 and g(x) = –6, sine f(x) contains the absolute value of a variable x, this absolute value can be negative and positive. Therefore f(x) can be expressed in two forms as shown;
f(x) = x+9 and f(x) = -x+9
If f(x) = x+ 9 and g(x) = -6
(f + g)(x) = f(x)+ g(x)
(f + g)(x) = x+9+(-6)
(f + g)(x) = x+9-6
(f + g)(x) = x+3
Similarly, if f(x) = -x+ 9 and g(x) = -6
(f + g)(x) = f(x)+ g(x)
(f + g)(x) = -x+9+(-6)
(f + g)(x) = -x+9-6
(f + g)(x) = -x+3
(f + g)(x) = 3-x
In both expresson, we have bith x to be positive and negative, hence we can write the value of resulting x as an absolute value as shown;
(f + g)(x) = |x|+3
This shows that (f + g)(x)≥3 for all values of x