The probabilities of drawing all hearts, face cards, or even cards are calculated with the formula: [tex](n/52) * ((n-1)/51) * ((n-2)/50)[/tex] where n is the total number of cards that match the desired outcome.
Explanation:The subject here is probability, specifically, how to determine the likelihood of a particular outcome when drawing cards from a standard deck. Let's deal with each probability one at a time.
The probability that all the cards are hearts: There are 13 hearts in a deck of 52 cards. So the probability that the first card is a heart is 13/52, the second is 12/51 (because one heart is already drawn), and the third is 11/50. So, the overall probability is [tex](13/52) * (12/51) * (11/50).[/tex]The probability that all the cards are face cards: There are 12 face cards (kings, queens, and jacks) in a deck. Using the same principle, the probability is [tex](12/52) * (11/51) * (10/50).[/tex]The probability that all the cards are even: The 'even' cards are 2, 4, 6, 8, 10, which have 4 of each (hearts, diamonds, spades, clubs) totaling 20 cards. So, the probability is [tex](20/52) * (19/51) * (18/50).[/tex]Learn more about Probability here:
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If a right circular cone is intersected by a plane that goes through both napped of the cone but not through the vertex, as in the picture below, what shape is produced?
Answer:
F. Hyperbola
Step-by-step explanation:
In each napped, you'll have a parabola, combined they form an hyperbola.
It's one of the various shapes that can be produced by a plane intercepting a right circular cone, as you can see in the attached picture.
Each plane intersection is different, based on the angle and the position it passes through.
I hope that helps.
Answer:
hyperbola
Step-by-step explanation:
apeex
You have a total of 45 dimes and quarters. You have 3 more quarters than dimes. Which system of equations can you use to find the number x of quarters and number y of dimes you have? Use the system to determine how much money you have in quarters and dimes.
Let's call dimes x and the quarters x+3 since we have 3 more of them.
x+x+3=45
2x=42
x=21
we have 21 dimes and 23 quarters
21*0.10=2.1
23*0,25=5.98
if we add those together it equals 8.08
Answer:
$8.10
Step-by-step explanation:
Let d and q represent the # of dimes and quarters, respectively. Then write equations reflecting this story:
q = d + 3, and d + q = 45. Substitute d + 3 for q in the second equation, obtaining:
d + d + 3 = 45, or 2d = 42, or d = 21. Then there are 21 dimes and 24 quarters. That comes to $2.10 + $6.00, or $8.10.
What is the value of x? Enter your answer in the box x=
Answer: 45°
Step-by-step explanation:
There are 180 degrees in a triangle so
180-80=100-55=45°
One day at lunch, the cafeteria sold thirty-four 1-pint containers of milk. The cafeteria also sold forty-eight 12-fl-oz bottles of water. Did the cafeteria sell more fluid ounces or milk? How many more?
Fluid ounces, 47 more
Simplify 3ab + 4ab + 5
12ab
7ab + 5
not possible
Answer:
7ab+5
Step-by-step explanation:
add like terms (3ab+4ab=7ab)
5 doesn't have a like term so it stays by itself
Hey there! :)
3ab + 4ab + 5
In order to simplify this, we must add like terms. In addition, when simplifying, you can ONLY add like terms.
Since both "3ab" & "4ab" contain "ab," you are able to combine them together!
When combining like terms, you only add the numerical value, not the letters.
This leaves us with : 7ab + 5
Therefore, your answer is 7ab + 5
~Hope I helped!~
Which expression represents the area of the triangle drawn below (4x-3) (2x-1) (4x-2) (3x-3)?
Answer:
option C
Step-by-step explanation:
Area of the triangle=4x²+4x+1
Fred's dog groomer charges $25 to give his dog a haircut. The groomer is increasing the price for a haircut by 35%. What will Fred pay the groomer the next time his dog has a haircut?
Answer:
33.75
Step-by-step explanation:
Step 1- Find the decimal form of 35%
Step 2- When you find that multiply that by 25
Step 3- When you find the answer to step 2 add that to 25
That is your answer
Final answer:
The price that Fred will pay the groomer the next time when his dog has a haircut is $33.75.
Explanation:
The question asks us to calculate the new price Fred will pay for his dog's haircut after the groomer increases the price by 35%. To find the new price, we'll use the formula for calculating percentage increase, which is: New Price = Original Price + (Original Price * Percentage Increase).
First, convert the percentage increase to a decimal by dividing it by 100, so 35% becomes 0.35. Then, multiply the original price of $25 by 0.35 to find the amount of the increase, which is $8.75.Finally, add the increase to the original price to find the new price, which is $25 + $8.75 = $33.75. So, Fred will pay $33.75 the next time his dog has a haircut.
Which graph shows a car traveling at 50 miles per hour?
Answer:
If you could insert a picture of the graphs that would help! thank you!
Step-by-step explanation:
Three friends buy one pack of 80 stickers. T hey divide the stickers equally and give the remainder to their teacher. How many will each friend get?
Answer:
26
Step-by-step explanation:
80 divided by three = 26.666666
26 times 3 = 78
2 leftover
The number sticker each student get is 26 and the number stickers teacher got is 2.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, three friends buy one pack of 80 stickers.
Now, number of stickers each friend = 80/3
3|80|26
78
_____
2
Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.
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Identify the volume and surface area of the sphere in terms of π. HELP PLEASE!!
Answer:
the third one.
Answer: C) V = 562.5π [tex]in^{3}[/tex] ; S = 225π [tex]in^{2}[/tex]
Step-by-step explanation: Please see the image below!
A line passes through (1, –5) and (–3, 7). a. Write an equation for the line in point-slope form. b. Rewrite the equation in slope-intercept form. y – 5 = 3(x + 1); y = 3x + 8 y + 5 = –3(x – 1); y = –3x – 2
see picture attached.
i hope this helped !!
ANSWER
Point-slope form:
[tex]y + 5 = -3(x - 1)[/tex]
Slope-intercept form;
[tex]y = - 3x - 2[/tex]
EXPLANATION
The point-slope form of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We need to find the slope using the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Let us substitute the point (1, –5) and (–3, 7).
This implies that,
[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]
[tex]m = \frac{12}{ - 4} = - 3[/tex]
The point slope form now becomes,
[tex]y - - 5 = - 3(x - 1)[/tex]
[tex]y + 5 = -3(x - 1)[/tex]
To find the slope intercept form, we expand to obtain;
[tex]y = - 3x + 3 - 5[/tex]
[tex]y = - 3x - 2[/tex]
Which choice is equivalent to the fraction below when x is greater than or equal to 2?
Answer:
D. 2(√{x} + √{x - 2})
Step-by-step explanation:
As hinted in the question, we have to simplify the denominator.
To understand it easier, let's imagine we have x - y in the denominator. If we multiply it with x + y we'll get x² - y², right? Check the next line:
(x - y) (x + y) = x² + xy -xy - y² = x² - y²
If we have the square of those nasty square roots, it will be much simpler to deal with. So, let's multiply the initial fraction using x+y, but with the real values:
[tex]\frac{4}{\sqrt{x} - \sqrt{x - 2} } * \frac{\sqrt{x} + \sqrt{x - 2}}{\sqrt{x} - \sqrt{x - 2}} = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} }[/tex]
Then we simplify:
[tex]\frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(x) - (x - 2) } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{ 2 } = 2(\sqrt{x} + \sqrt{x - 2})[/tex]
Answer is D. 2(√{x} + √{x - 2})
The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii.
Answer:
6√2.
Step-by-step explanation:
The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90. Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.
A totem pole casts a 20 meter shadow when the angle of elevation of the sum is 45what is the distance from the top of the totem pole to the end of the shadow
Answer:
20√2 meters (approximately 28.28 m)
Step-by-step explanation:
It may help to make a diagram. Because this is a 45 45 90 triangle, you can use those rules to help solve.
Final answer:
The distance from the top of a totem pole to the end of its shadow, when the angle of elevation of the sun is 45 degrees, is approximately 28.28 meters.
Explanation:
The student has presented a problem that involves using trigonometry to calculate the distance from the top of a totem pole to the end of its shadow when the angle of elevation of the sun is 45 degrees. To solve this, we can use the concept of right-angled triangles and the properties of special triangles, specifically a 45-45-90 triangle where the two legs are congruent. Since the angle of elevation is 45 degrees and the length of the shadow is given as 20 meters, we know that in this special right triangle, the lengths of the two legs are equal. Therefore, the distance from the top of the totem pole to the end of the shadow (the hypotenuse of the triangle) is the length of the shadow times the square root of 2, based on the Pythagorean theorem.
Using the formula hypotenuse = leg × √2, we substitute the leg length of 20 meters to get hypotenuse = 20 m × √2, which equals approximately 28.28 meters.
What is the solution to the equation below?
Please show work.
Answer:
x = -9
Step-by-step explanation:
Multiply both sides by √(x - 6) to eliminate the fraction:
√(3x) = 3√(x - 6)
Now square both sides:
3x = 9(x - 6), or 3x = 9x - 54.
Combining the x terms results in -6x = -54, and thus x = 9.
Answer:
The correct answer is option D. x = 9
Step-by-step explanation:
From the attached question we get an expression,
√3x/√(x - 6) = 3
To find the solution of given expression
√3x/√(x - 6) = 3
Squaring both side we get,
3x/(x - 6) = 9
3x = 9 * (x - 6)
3x = 9x - 54
9x - 3x = 54
6x = 54
x = 54/6 = 9
Therefore the correct option is D. x = 9
Write an explicit rule and recursive rule for a geometric sequence with a second term of 6 and a third term of 12.
Step-by-step answer:
Given:
Geometric sequence with
second term, T2 = 6
third term, T3 = 12
Wants to have the explicit and recursive rules.
Solution:
common ratio, r = 12/6 = 2
Therefore the first term, T1
= second term /r
= 6/2
=3
Thus the absolute rule is
Tn = T1 *r^(n-1) where T1 = 3, r=2. Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good
The recursive rule (depending on the previous term)
Tn = Tn-1*r = 2*Tn-1
The explicit rule for the sequence is a_n = 3 * 2^(n-1), and the recursive rule is a_n = a_(n-1) * 2. These were determined by identifying the common ratio of the sequence as 2.
Explanation:In a geometric sequence, each term is generated by multiplying the previous term by a common ratio. Given the second term (6) and third term (12) in the sequence, we can identify the common ratio by dividing the third term by the second term. So, 12 divided by 6 equals 2. Therefore, the common ratio is 2.
So, the explicit rule (the nth term) of this sequence would be: a_n = a_1 * r^(n-1) = 6 / 2 * 2^(n-1) = 3 * 2^(n-1).
The recursive rule for the sequence would be: a_n = a_(n-1) * r = a_(n-1) * 2.
To summarize, we determined the common ratio to be 2 by dividing the third term by the second term. We then used this ratio to create the explicit and recursive rules for the geometric sequence.
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In the figure, AB ||CD and m3=130. What is
m<6 = 180° - m<3
m<6 = 180° - 130°
m<6 = 50°
Answer: m6 equals 50 degrees
Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50
PLEASE HELP ASAP
30 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
d. 3x³ and 2x³
Step-by-step explanation:
In standard form, the terms of a polynomial expression are written in order of descending powers of the variable. There will be only one term for any given power of the variable.
Here, there are two terms that have x to the third power. These terms must be combined to write the expression in standard form. They are the only terms that can be combined: 3x³ + 2x³ = 5x³.
Celia and Jake bought 4 pizzas that cost $7 each and bread sticks that cost $3 they spilt the cost between them. Which equations could be used to find how much each paid? Let T stand for the total coat and E stand for the amount each paid.
Answer:
E = (3b+28)/2
T=3b+28
E= t/2
Step-by-step explanation:
The coat of the 4 pizzas would be $28, and an unknown amount of breadsticks that cost 3 dollars each.
Im going to use B as the amount of breadsticks bc i dont know what its supposed to be but that should be the correct answer.
T=3b+28
E= t/2
in order to solve he following system of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them? 4x-2y=7, 3x-3y=15
Answer:
To eliminate x multiply the first equation by 3 and the second equation by 4
To eliminate y multiply the first equation by 3 and the second equation by 2
Step-by-step explanation:
We are given a system of linear equations;
4x-2y=7
3x-3y=15
solving by elimination means that we shall be getting rid of one of the variables in order to determine the other. In this case we can either eliminate x or y. In order to eliminate any of these variables, we first must make their coefficients equal in both equations. To eliminate x;
Multiply the first equation by 3 and the second equation by 4.
To eliminate y;
Multiply the first equation by 3 and the second equation by 2.
NEED MATH HELP!!!!
( with the 2 problems I missed)
Answer:
[tex]t=7.4years[/tex]
Step-by-step explanation:
Let's clear t from the equation [tex]N=16.10^{0.15t}[/tex]. In order to clear t, we have to apply [tex]log_{10} (x)[/tex] in both side of the equations.
[tex]log_{10}N=log_{10}(16.10)^{0.15t}[/tex]
By using properties of the logarithm
[tex]log_{10} (a.b)}= log_{10}a+log_{10}b[/tex]
We obtain:
[tex]log_{10}N=log_{10}(16)+log_{10} (10^{0.15t})[/tex]
Ordering using the logarithm property [tex]log_{10}a^{n} =nlog_{10}a[/tex] and [tex]log_{10} 10=1[/tex]
[tex]log_{10}N=log_{10}(16)+0.15tlog_{10}10[/tex]
[tex]log_{10}N=log_{10}(16)+0.15t[/tex]
Clearing t
[tex]t=\frac{log_{10}N-log_{10}(16)}{0.15}[/tex] using the logarith property [tex]log_{10}a-log_{10}b=log_{10}\frac{a}{b}[/tex]
we obtain:
[tex]t=\frac{log_{10}\frac{N}{16} }{0.15}[/tex]
The number of Elm trees is N = 204
Solving
[tex]t=\frac{log_{10}\frac{204}{16} }{0.15}\\t=\frac{log_{10}12.75}{0.15}=7.370[/tex]
Round to the nearest tenths place [tex]t=7.4years[/tex]
A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle. (x + 5)x = 104 x2 + 5x – 104 = 0 Determine the solutions of the equation. What solution makes sense for the situation? x = What are the dimensions of the rectangle? width = inches length = inches
Answer:
Step-by-step explanation:
x² + 5x – 104 = 0
Factor using the AC method. Here, a = 1 and c = -104. Multiplied together, ac = -104. Factors of -104 that add up to +5 are +13 and -8.
(x + 13) (x - 8) = 0
x = -13, 8
A negative width doesn't make sense, so x = 8. Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.
Answer:
width = 8
length = 13
Step-by-step explanation:
All that is left to do is factor the results that you have
x^2 + 5x - 104 = 0
You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.
The two numbers are 8 and 13
More formally stated, the quadratic can be factored to
(x + 13)(x - 8) = 0
x - 8 =0
x - 8 + 8 = 8 + 0
x = 8
x + 13 = 0 has no meaning.
That means that the width ( a positive number ) = 8
The length is 5 more = 13
Please help me please
Answer:
b = 17
Step-by-step explanation:
Since PQ = RQ then ΔPQR is isosceles and QS is a perpendicular bisector
Hence PS = RS = 17 ⇒ b = 17
Write the equation of the quadratic function with roots 6 and 10 and a vertex at (8, 2).
Answer:
https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Given the roots are x = 6 and x = 10, then
the factors are (x - 6) and (x - 10)
The quadratic is then the product of the roots
y = a(x - 6)(x - 10) ← a is a multiplier
To find a substitute (8, 2) into the equation
2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )
a = - [tex]\frac{1}{2}[/tex]
Hence
y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors
y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute
y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30
Please help me out please!! :)
Starting from the Pythagorean identity, we deduce
[tex]\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}[/tex]
If we plug in the value 7/10 for sin(x), we have
[tex]\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}[/tex]
Use the domain and range of each of the following relations to determine which is a function.
Answer:
a) Function
b) Not a function
c) Function
d) Not a function
Step-by-step explanation:
a) Domain = { 7,-6,2}
Range = {5,0,3}
It is a function as every value in domain has some and unique value mapped to it in Range
b)
Domain = { 7,-6,2}
Range = {5,0,-2,3}
It is not a function as -6 value in domain has two values mapped to it in Range
c)
Domain = { 7,2}
Range = {-6,-7}
It is a function as every value in domain has some and unique value mapped to it in Range
d)
Domain = { 7,-6}
Range = {5,0,3}
It is not a function as 7 value in domain has two values 3 and 5 mapped to it in Range
The scores of a psychology exam were normally distributed with a mean of 70 and a standard deviation of 5 a failing grade on the exam was anything two or more standard deviations below the mean what was the cutoff for a failing score
Answer:
The Answer is likely 60.
Step-by-step explanation:
Two standard deviations from 70 is 60, because the actual deviation is 5, so 2 of those equals 10. 10 - 70 = 60.
Answer:
60
Step-by-step explanation:
Two standard deviations below the mean is:
70 - 2(5) = 60
Mary Beth and her family ate a meal in a restaurant the cost of the meal was $34.50 the sales tax was 8% of the cost of the meal
Which explanation best describes how to solve this problem? Marcia covered her kitchen floor with twice as much tile as her bathroom floor. She tiled 15 square feet of her bathroom floor. She also tiled a 9-square-foot area by her front door. How many square feet of her house did Marcia tile altogether?
Answer:
54 ft^2
Step-by-step explanation:
Bathroom area is 15 ft^2
The kitchen is twice the bathroom
2*15 = 30 ft^2
Kitchen: 30 ft^2
Front door: 9ft^2
The total is all the areas added together
Total = bathroom + kitchen + front door
= 15 ft^2 + 30 ft^2 + 9 ft^2
= 54 ft^2
The average age three people running for election is 42. A fourth person joins the race and the average drops to 40. What is the fourth person's age?
Let [tex]a_1,\ldots,a_4[/tex] denote the ages of the 4 candidates. Then
[tex]\dfrac{a_1+a_2+a_3+a_4}4=40[/tex]
[tex]a_1+a_2+a_3+a_4=160[/tex]
[tex]\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3[/tex]
The average age of the first 3 candidates is 42, so
[tex]\dfrac{a_4}3=\dfrac{160}3-42[/tex]
[tex]\implies\boxed{a_4=160-3\cdot42=34}[/tex]