Answer: [tex]\bold{\dfrac{1}{36}}[/tex]
Step-by-step explanation:
The first die can be any number: [tex]P = (\dfrac{6}{6}) = 1[/tex]
The second die must match the first die: [tex]P = \dfrac{1}{6}[/tex]
The third die must also match the first die: [tex]P = \dfrac{1}{6}[/tex]
1st die and 2nd die and 3rd die = Probability of success
1 x [tex]\dfrac{1}{6}[/tex] x [tex]\dfrac{1}{6}[/tex] = [tex]\dfrac{1}{36}[/tex]
Which equation has no real roots? a. x2 – 6x + 12= 0 b. x2 – 25 = 0 c. x2 + 11x = 0 d. x2 + 12x + 11= 0
Answer:
A
Step-by-step explanation:
To find the number of real roots for a quadratic, we apply the discriminate. The discriminate is the inside portion of the square root from the quadratic formula.
[tex]b^2-4ac>0[/tex] yields 2 real roots[tex]b^2-4ac=0[/tex] yields 1 real root[tx]b^2-4ac<0[/tex] yields no real rootsa. [tex]x^2-6x+12=0[/tex] where a=1, b=-6, and c=12
[tex]b^2-4ac=(-6)^2-4(1)(12)=36-48=-12<0)[/tex] has no real roots
b. [tex]x^2-25=0[/tex] where a=1, b=0, and c=-25
[tex]b^2-4ac=(0)^2-4(1)(-25)=0+100=100>0)[/tex] has 2 real roots
c. [tex]x^2+11x=0[/tex] where a=1, b=11, and c=0
[tex]b^2-4ac=(11)^2-4(1)(0)=121-0=-121>0)[/tex] has 2 real roots
d. [tex]x^2+12x+11=0[/tex] where a=1, b=12, and c=11
[tex]b^2-4ac=(12)^2-4(1)(11)=144-44=100>0)[/tex] has 2 real roots
Point O is the center of the circle. What is the value of x?
a. 8
b. 9
c. 15
d. 17
Jose has scored 562 points on his math test so far this this semester. To get an A for the semester, he must score at least 650 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests in order to get an A
Answer:
562 + x ≥ 650
x ≥ 88
Step-by-step explanation:
He has 562 points. He needs x points to get an A. He must get at least 60 points to get an A.
562 + x ≥ 650
To solve this, we subtract 562 from each side
562-562 + x ≥ 650-562
x ≥ 650-562
x ≥ 88
m x 5 = 30
m = ?
A) 3
B) 4
C) 5
D) 6 what the answer
Answer: The correct option is D.
Step-by-step explanation: We are given a linear equation:
[tex]m\times 5=30[/tex]
To calculate the value of , we need to separate m from the constant '5' which is done when 5 goes to the other side of the equation and gets divided there:
[tex]m=\frac{30}{5}\\\\m=6[/tex]
Conclusion: Hence, the value of m is 6 for the given equation.
1.)What number needs to be added to both sides of the equation in order to complete the square? x2+16x=18
answer is 64
x^2+16x+64=18+64
2.)Solve for x over the complex numbers.
x2+10x+41=0
answer is x=-5+4i and -5-4i
3.)What is the factored form of the expression over the complex numbers?
16x2+9y2
answer is (4x+3iy)(4x-3iy)
Answer:
all of your answers are correct
1.) 64
2.) x= -5+4i and x= -5-4i
3.) (4x+3iy)(4x-3iy)
Answer:
1.When we are completing squares, we need to divide by 2 the linear term and then find its square power, that's the term we need to add on both sides of the equality, as follows
[tex](\frac{16}{2})^{2} =(8)^{2}=64[/tex]
Basically, we need to add the number 64 both sides
[tex]x^{2} +16x+64=18+64[/tex]
2.The given equation is
[tex]x^{2} +10x+41=0[/tex]
We need to apply the quadratic formula to solve this equation
[tex]x_{1,2} =\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Where [tex]a=1[/tex], [tex]b=10[/tex] and [tex]c=41[/tex]. Replacing these values, we have
[tex]x_{1,2} =\frac{-10(+-)\sqrt{10^{2}-4(1)(41) } }{2(1)}\\x_{1,2} =\frac{-10(+-)\sqrt{100-164 } }{2}=\frac{-10(+-)\sqrt{-64} }{2}[/tex]
There we need to use complex number, to transform the subradical number in a positive number
[tex]x_{1,2}=\frac{-10(+-)\sqrt{64}i }{2}=\frac{-10(+-)8i}{2}\\ x_{1,2}=-5(+-)4i[/tex]
Therefore, the complex solutions are
[tex]x_{1}=-5+4i\\ x_{1}=-5-4i[/tex]
3.The given expression is
[tex]16x^{2} +9y^{2}[/tex]
To solve this expression, remember that [tex]i=\sqrt{-1}[/tex]
First, we expresse both squares uniformly,
[tex]16x^{2} +9y^{2}=(4x)^{2}+(3y)^{2}[/tex]
But, we know that [tex]-(-1)=1[/tex], so
[tex](4x)^{2}+(3y)^{2}=(4x)^{2}-(-1)(3y)^{2}[/tex]
Then,
[tex](4x)^{2}-(-1)(3y)^{2}=(4x)^{2}-(3y)^{2}i^{2}[/tex], because [tex]i^{2}=-1[/tex]
Therefore, the expression with complex numbers is
[tex](4x)^{2}-(3iy)^{2}\\\therefore (4x+3iy)(4x-3iy)[/tex]
(: (: (: (: (: (: (: (: (: (: (: (: (:
Answer:
3
Step-by-step explanation:
I can see it in the demonstration graph
Answer:
3
Step-by-step explanation:
Male: 12
Female: 9
12 - 9 = 3
Hopes this helps
Celeste wants to have her hair cut and permed and also go to lunch she knows she will need $50 the perm cos twice as much as her haircut and she needs $5 for lunch how much does the permcost
Roxanne bought a 40-inch television that measures 24 inches in height. What is the width of the television?
Answer:
The width is 32 inches
Step-by-step explanation:
The angle of depression from the top of a lighthouse to a boat in the water is 30°. If the lighthouse is 89 feet tall how far is the boat from the lighthouse to the nearest foot?
A) 45 feet
B) 51 feet
C) 63 feet
D) 154 feet
Answer:
D) 154 feet
Step-by-step explanation:
The angle is less than 45°, so you know the distance will be more than 89 feet. There is only one choice in that range.
_____
The mnemonic SOH CAH TOA reminds you ...
... Tan = Opposite/Adjacent
so ...
... tan(30°) = (89 ft)/(distance to boat)
Then ...
... distance to boat = (89 ft)/tan(30°) ≈ 154 ft
what is the value of x?
Angle G and Angle F are the same, which means that HF = GH
This means that x = 15
Answer:x=15
Step-by-step explanation:
for an experiment you need to dissolve 0.05 moles of NaCl in one liter of water. how much NaCl must you weigh out?
for an experiment you need to dissolve 0.05 moles of NaCl in one liter of water. how much NaCl must you weigh out?
2.9 i just took the test
To find the amount of NaCl required, multiply the number of moles by the molar mass of NaCl. Hence, you need approximately 2.922 g of NaCl to get 0.05 moles.
Explanation:To find out how much NaCl you would need to weigh out, we need to convert moles to grams using the molar mass of NaCl. Knowing that the molar mass of NaCl is 58.44 g/mol, we could get the mass by multiplying the number of moles by the molar mass.
So, it would be 0.05 moles * 58.44 g/mol = 2.922 g of NaCl. You would need to weigh out approximately 2.922 grams of NaCl (assuming precision up to three decimal places) to get the required 0.05 moles needed for the experiment.
This is a typical example of applying concepts of molality and molarity in chemical solutions, where you need to accurately determine the amount of solute to use to achieve a precise molar concentration.
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What is the 20th term of the arithmetic sequence?
A printer prints 75 pages in 5 minutes. At the same rate, how many pages does the printer print in 7 minutes? Solve and show your work. • Explain how you solved using the words "first," "next," and "last."
Answer:
105
Step-by-step explanation:
first, the printer print 15 (75/5) pages per minutes,
next, 7×15=105
Millicent filled out an order for $179.10 worth of items. If the sales tax is 3 1/2% and the shipping is listed below, what was the total amount of her order?
Shipping and Handling Charges
Up to $25 $4.50
$25.01 to $75 $6.95
$75.01 to $125 $8.95
$125.01 and above $10.95
Question 6 options:
$194.52
$195.62
$196.32
$197.42
Answer:
(179.10 * 0.035) =6.2685 185.3685 = $196.32
Step-by-step explanation:
First we add 3.5% to the total.
Second we see that the total is over $125.01 thus we add another 10.95 and get 196.3185, rounded to 196.32
Answer:
Option C., $196.32 is the answer.
Step-by-step explanation:
Millicent filled out an order, worth of items = $179.10
The sales tax on that item = [tex]3\frac{1}{2}[/tex]% = 3.5%
total price of the item = 179.10 + ( 3.5% of 179.10)
179.10 + (0.035 × 179.10)
179.10 + 6.2685 = $185.3685 ≈ $185.37
Shipping and handling charges up to $125.01 and above is $10.95
Total price + shipping = 185.37 + 10.95 = $196.32
The total amount of her order is $196.32
Start at 39 and create a pattern with the rule subtract 5. What is the third number in the pattern,,?
Answer:
24
Step-by-step explanation:
39-5= 34, 34-5= 29, 29-5= 24
Answer:
3rd to last? 29
Step-by-step explanation:
If the square ABCD is dilated by a scale factor of 2 to form A'B'C'D', what is the ratio of the area of A'B'C'D' to the area of ABCD
Answer:
4:1
Step-by-step explanation:
If the side length x is dilated to 2x, the area x² will dilate to (2x)² = 4x², which is 4 times the original x².
Answer:
1:4 C
Step-by-step explanation:
Can someone please explain how to do these?
Answer:
First question answer: The limit is 69
Second question answer: The limit is 5
Step-by-step explanation:
For the first limit, plug in [tex]x=8[/tex] in the expression [tex](9x-3)[/tex], that's the answer for linear equations and limits.
So we have:
[tex]9x-3\\9(8)-3\\72-3\\69[/tex]
The answer is 69
For the second limit, if we do same thing as the first, we will get division by 0. Also indeterminate form, 0 divided by 0. Thus we would think that the limit does not exist. But if we do some algebra, we can easily simplify it and thus plug in the value [tex]x=1[/tex] into the simplified expression to get the correct answer. Shown below:
[tex]\frac{x^2+8x-9}{x^2-1}\\\frac{(x+9)(x-1)}{(x-1)(x+1)}\\\frac{x+9}{x+1}[/tex]
Now putting 1 in [tex]x[/tex] gives us the limit:
[tex]\frac{x+9}{x+1}\\\frac{1+9}{1+1}=\frac{10}{2}=5[/tex]
So the answer is 5
Julie and Eric row their boat (at a constant speed) downstream for 40 miles in 4 hours, helped by the current. Rowing at the same rate the trip back, against the current, takes 10 hours. Find the rate of the current.
Final answer:
The rate of the boat is 7 mph and the rate of the current is 3 mph.
Explanation:
To find the rate of the current in this problem, we can use the equation:
Rate of downstream trip = Rate of boat + Rate of current
Rate of upstream trip = Rate of boat - Rate of current
Let's assign variables to the rate of the boat and the rate of the current. Let B represent the rate of the boat and C represent the rate of the current.
From the information given, we know that:
40 miles = (B + C) x 4 hours
40 miles = (B - C) x 10 hours
Now we can solve these equations to find B and C. Let's start by simplifying the equations:
40 = 4B + 4C
40 = 10B - 10C
Divide both sides of the equations by 4 and 10 respectively:
10 = B + C
4 = B - C
Add the two equations together:
10 + 4 = 2B
14 = 2B
Divide both sides by 2:
7 = B
Substitute the value of B back into one of the equations to solve for C:
10 = 7 + C
Subtract 7 from both sides:
3 = C
Therefore, the rate of the boat is 7 mph and the rate of the current is 3 mph.
Which measurement represents the largest volume?
A) 999mL
B) .99L
C) 998cm³
D) 1.02L
Answer:
B
Step-by-step explanation:
The measurement representing the largest volume among the options is D) 1.02 L, as it is larger than .99 L, 0.999 L and 0.998 L, which are the rest of the options converted into the same unit (liters).
Explanation:In order to determine which of these measurements represents the largest volume, we need to make sure we're comparing them using the same units of measure. So, we'll convert everything to liters (L), as this is the most common unit among the options.
First of all, A) 999 milliliters (mL) is equal to 0.999 Liters (L) because 1 L = 1000 mL. B) .99L is just .99L. For C) 998 cubic centimeters (cm³), we need to know that 1 cm³ is equal to 1 mL, so 998 cm³ equals 0.998 L. Finally, D) 1.02 L is already in liters.
Looking at these conversions, D) 1.02 L represents the largest volume among the given choices.
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You earned $34,000 and your total tax due was $6,200. What was your average tax rate? a) 8% b) 10% c) 18% d) 20%
Answer is C 18%
Step-by-step explanation:
Solve this system of linear equations. Separate the x- and y- values with a coma. 3x=36-15y. 11x =-78+15y
Answer:
(-3,3)
Step-by-step explanation:
3x=36-15y and 11x =-78+15y
We move all x and y terms to the left hand side of the equation , so that we can apply elimination method
3x=36-15y , Add 15 y on both sides , 3x + 15y = 36
11x =-78+15y, subtract 15y on both sides, 11x -15y = -78
Now we add both equations
3x + 15y = 36
11x -15y = -78
------------------------
14x = -42
divide both sides by 14
x= -3
Now Plug in -3 for x in any one of the given equation
3x=36-15y
3(-3) = 36 - 15y
-9 = 36 - 15y
Subtract 36 on both sides
-45 = -15y
Divide both sides by -15
So y= 3
Answer is (-3,3)
Nikki spent $59.29 on clothing. She bought 3 shirts and a pair of pants. The pair of pants cost $21.79. If each shirt cost the same amount, how much did each shirt cost?
The daily cost of hiring a plumber,y,to work x hours on a repair project can be modeled using the linear function y=55x +75. The plumber charges a fixed cost of $75 plus sn additional cost of 55 per hour.The plumber works a maximum of 50 hours per week. For one week of work what is the domain of the function for this situation
The domain of the function for one week of work is all values of x that are less than or equal to 50.
The domain of a function represents the set of all possible input values for that function. In this situation, the function represents the daily cost of hiring a plumber for x hours of work, and the maximum number of hours the plumber works per week is 50. Therefore, for one week of work, the domain of the function is the set of all values of x that are less than or equal to 50.
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A geologist had to rocks on a scale that weighed 3.3 kg together the first rock was 0.3 of the total weight how much did each Rock weigh
Answer:
A geologist had to rocks on a scale that weighed 3.3 kg together the first rock was 0.3 of the total weight how much did each Rock weigh?
First thing you have to do is take 3.3 and multiply it by 0.3, that gives you 0.99. And just take the 0.99 and subtract 3.3 by 0.99. that gives you your ANSWER(2.31 kg) Hope that helps!
Step-by-step explanation:
To solve the problem, we first find the weight of the first rock by multiplying the total weight of the rocks by 0.3, then subtract the weight of the first rock from the total weight to find the weight of the second rock. The first rock weighs 0.99 kg and the second rock weighs 2.31 kg.
Explanation:The problem involves understanding proportions since the first rock weighs 0.3 of the total weight. First, let us find the weight of the first rock. Multiply the total weight of the rocks, which is 3.3 kg, by 0.3 to find the weight of the first rock. That is 3.3 kg * 0.3 = 0.99 kg.
Next, subtract the weight of the first rock from the total weight to find the weight of the second rock. That is 3.3 kg - 0.99 kg = 2.31 kg. So, the first rock weighs 0.99 kg while the second rock weighs 2.31 kg.
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Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 18 miles per hour faster than the eastbound train. If the two trains are 800 miles apart after 4 hours, what is the rate of the westbound train?
Do not do any rounding.
This has to be right, the first time because it will force me to start over
Answer:
The combined speeds of the trains equals 800 miles per 4 hours or
200 miles per hour.
This averages out to 100 miles per hour for each train.
Westbound train is 18 mph faster so
109 mph = Westbound
91 mph = Eastbound
That seems to be right except trains speeds of 91 mph and 109 mph seem to be VERY fast.
Step-by-step explanation:
Factor 18 out of 18x−498 ( THIS IS 7th GRADE MATH BTWWWW <3)
The factored form of the expression 18x - 498 when 18 is factored out is 'x - 27.67'
Explanation:To factor out 18 from 18x-498, you divide each term in the expression by 18. That would look like this: 18x / 18 - 498 / 18. This simplifies to x - 27.67.
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To factor 18 out of 18x - 498, divide each term by 18. The factored form is 18(x - 27.67).
Explanation:Factoring in mathematics involves breaking down an algebraic expression into its constituent factors. Factoring is crucial for solving equations, simplifying expressions, and understanding the underlying structure of mathematical relationships.
To factor 18 out of 18x - 498, divide each term by 18:
18x / 18 = x
498 / 18 = 27.67
So, the factored form is: 18(x - 27.67)
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A farmer plants apple, pear, and cherry trees in an orchard. The number of apple trees is 8 more than twice the number of pear trees. The number of cherry and pear trees combined is 11 more than the number of apple trees. The farmer plants 143 trees total. How many of each type of tree did the farmer plant in the orchard?
Answer:
Let x represents the number of apple tree and y represents the number of pear tree and z represents the number of cherry tree in an orchard.
From the given statement: The number of apple trees is 8 more than twice the number of pear trees.
⇒ [tex]x = 2y + 8[/tex] .....[1]
Also, It is given that the number of cherry and pear trees combined is 11 more than the number of apple trees.
⇒[tex]y + z = x + 11[/tex] ......[2]
The farmer plants 143 trees total.
⇒[tex]x +y +z =143[/tex] .....[3]
Substitute equation [2] into [3] we get;
[tex]x + x + 11 = 143[/tex]
Combine like terms;
[tex]2x +11 = 143[/tex]
Subtract 11 on both sides we get;
2x + 11 -11 =143 -11
Simplify:
2x = 132
Divide both sides by 2 we get;
x = 66
Substitute the value of x in equation [1];
66 = 2y + 8
Subtract 8 on both sides we get;
[tex]66 -8 =2y + 8 -8[/tex]
Simplify:
58 = 2y
Divide by 2 on both sides we get;
y = 29
Substitute the value of x and y in equation [3];
we have;
29 + 66 + z = 143
95 + z =143
Subtract 95 on both sides, we get;
95+ z -95 = 143- 95
Simplify:
z = 48
The framer plant in the orchard = 66 apple trees , 29 pear trees and 48 cherry trees
Select all that apply. Solve for x, 0 < x < 2 pie. 2 sin x - sqrt 3 = 0
< is actually less than or equal to sign.
sqrt means square root.
answer choices (select all that apply)
pie/3
2pie/3
4pie/3
5pie/3
Answer: A and B
pi/3 and 2pi/3
=========================================
Work Shown:
2*sin(x) - sqrt(3) = 0
2sin(x) = sqrt(3)
sin(x) = sqrt(3)/2
Using the unit circle, we see that sin(theta) is equal to sqrt(3)/2 when theta is theta = pi/3 in quadrant I, and when theta = 2pi/3 in quadrant II.
So sin(pi/3) = sqrt(3)/2 and sin(2pi/3) = sqrt(3)/2
--------------------
You can check these answers by replacing x with the value in question and seeing if you get zero. Make sure your calculator is in radian mode
Plug in x = pi/3
2*sin(x) - sqrt(3) = 0
2*sin(pi/3) - sqrt(3) = 0
0 = 0 .................... this is a true equation, x = pi/3 is confirmed as a solution
Plug in x = 2pi/3
2*sin(x) - sqrt(3) = 0
2*sin(2pi/3) - sqrt(3) = 0
0 = 0 .................... true equation, x = 2pi/3 is confirmed as a solution
Plug in x = 4pi/3
2*sin(x) - sqrt(3) = 0
2*sin(4pi/3) - sqrt(3) = 0
-3.4641016 = 0 ............ false equation, x = 4pi/3 is a nonsolution
Plug in x = 5pi/3
2*sin(x) - sqrt(3) = 0
2*sin(5pi/3) - sqrt(3) = 0
-3.4641016 = 0 ............ false equation, x = 5pi/3 is a nonsolution
Final answer:
To solve the trigonometric equation 2 sin x - √(3) = 0 within the interval 0 ≤ x < 2π, we find that sin x = √(3)/2 at x = π/3 and 2π/3, which are the correct answer choices.
Explanation:
To solve for x in the given trigonometric equation 2 sin x - √(3) = 0, we first isolate the sine function by adding √3 to both sides and then divide by 2, giving us sin x = √(3)/2. Now, we seek the angles x within the interval 0 ≤ x < 2π (where π is pi) that satisfy this equation. We know that sin x is √(3)/2 at the angles π/3 and 2π/3 in the first and second quadrants, respectively. These are the two angles where the sine function takes the value of √(3)/2 between 0 and 2π. Therefore, the correct answer choices are π/3 and 2π/3.
It is important to consider that the sine function is positive in the first and second quadrants, and given the range for x, we don't need to consider the third or fourth quadrants where sine is negative. Additionally, the angles 4π/3 and 5π/3 correspond to a negative value of the sine function, thus they do not satisfy the equation.
Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.
the length is 3 yd, the base is 7 yd, and the width is 6 yd
Answer:
The surface area is 162 yards
Step-by-step explanation:
A = 2(w l + h l + h w)
A = 2(7 (3) + 6 (3) + 6 (7))
7 x 3 = 21
6 x 3 = 18
6 x 7 = 42
21 + 18 +42 = 81
81 x 2 = 162
I need help on this. Please
Answer: choice C, y = 0.014x+0.85
==============================
Explanation:
Each column of the table represents an (x,y) pair of values
x = number of pages
y = cost
If we look at the first two columns, we see the two points (50,1.55) and (100,2.25). The x value is listed first. Let's compute the slope of the line through these two points
m = (y2-y1)/(x2-x1)
m = (2.25-1.55)/(100-50)
m = 0.7/50
m = 0.014
So far, we see the answer is between A,B or C as they have the slope of 0.014
Use this slope value, and one of the points -- say (x,y) = (50,1.55) -- to find the y intercept b
y = mx+b
y = 0.014x+b .... plug in the slope found earlier
1.55 = 0.014*50+b ... plug in the point (x,y) = (50,1.55)
1.55 = 0.7+b
1.55-0.7 = 0.7+b-0.7 ... subtract 0.7 from both sides
0.85 = b
b = 0.85
With m = 0.014 as the slope and b = 0.85 as the y intercept, we can say that y = mx+b turns into y = 0.014x+0.85. That narrows the answer down to choice C.