There are 8 possible outcomes when you throw a coin three times:
[tex]HHH,\ HHT,\ HTH,\ HTT,\ THH,\ THT,\ TTH,\ TTT[/tex]
Out of these combination, the ones with exactly two heads are
[tex]HHT,\ HTH,\ THH[/tex]
So, 3 combinations out of 8 have exactly two heads. This means that the probability of having two heads with three coin throws is 3/8
Answer: [tex]\bold{\dfrac{3}{8}}[/tex]
Step-by-step explanation:
Step 1: Numerator
You are looking for an outcome of getting exactly two heads out of a total of three tosses. This can be written as: ₃C₂
The formula for a combination problem is: [tex]\dfrac{n!}{r!(n-r)!}[/tex]
n is the total number of tossesr is the total number of successes (in this case, heads)[tex]_3C_2=\dfrac{3!}{2!(3-2)!}=\dfrac{3\times2\times1}{2\times1\times 1}=3[/tex]
There are 3 successes (heads)
Step 2: Denominator
You are looking for the total possible combinations of heads and tails for three tosses (2³)
1st toss and 2nd toss and 3rd toss
2 x 2 x 2 = 8 total possible outcomes
An athlete jumped 5.5 feet which was 1.1 times higher than the previous jumper how high did the previous athlete jump
Answer:
5 ft
Step-by-step explanation:
Let the height of the previous jump be represented by j. Then 1.1j = 5.5 ft.
Dividing both sides by 1.1, we get j = 5 ft. This was the height of the previous jump.
Answer:
5 ft
Step-by-step explanation:
The previous jumper jumped p
The new jumper jumped p*1.1 and that was 5.5 ft
1.1p = 5
Divide each side by 1.1
1.1p/1.1 = 5.5/1.1
p = 5
The previous jumper jumped 5 ft
coseca/4+cota/2=cota/8-coseca/2
It's not clear if this is a problem to solve or a problem to prove. Let's see where it goes.
We note the cotangent half angle formula is
[tex]\cot x = \dfrac{ 1 + \cos 2x}{\sin 2x}[/tex]
The tangent and cotangent half angle is expressible in terms of the full angle without any ambiguity, so let's set b=a/4 so a=4b.
It turns out to be true for all a (at least all a that don't make the any of the functions undefined). So it's a problem to prove.
Here's the proof. I actually did it from the bottom up, but it's better to present it this way as a proof.
We start with the cosine double angle formula:
[tex]\cos 2b = 2\cos^2 b- 1[/tex]
Multipy both sides by sin b:
[tex]\sin b \cos 2b = 2 \sin b \cos^2 b - \sin b[/tex]
Sine double angle formula:
[tex]\sin b \cos 2b = \sin 2b \cos b- \sin b[/tex]
Add sin 2b to both sides:
[tex] \sin 2b+ \sin b\cos 2b = \sin 2b + \sin 2b \cos b - \sin b[/tex]
Divide by sin b sin 2b
[tex] \dfrac{1}{\sin b} + \dfrac{\cos 2b}{\sin 2b} = \dfrac{1 + \cos b}{\sin b} - \dfrac{1}{\sin 2b}[/tex]
Turn to cosecants and cotangents. We use the cotangent half angle formula above.
[tex] \csc b + \cot 2b = \cot \frac b 2 - \csc 2b[/tex]
Substituting b=a/4:
[tex] \csc \frac a 4 + \cot \frac a 2 = \cot \frac a 8 - \csc \frac a 2 \quad\checkmark[/tex]
If ƒ (x ) = 2x 2 + 3, find ƒ (3).
Answer:
[tex]f(x) = 2 \times 2 + 3 \\ f(3) = 4 + 3 \\ 3f = 7 \\ f = \frac{7}{3} [/tex]
Hope it help youAnswer:
The answer is 15
Step-by-step explanation:
If ƒ (x ) = 2x 2 + 3, find ƒ (3).
2(3)^2 +3
6^2+3
= 15
Which characteristic is correct for the function
f(x) = -3x^4 + 7x^2?
odd
Neither even nor odd
Even
Both even and odd
Answer:
This is an even function.Step-by-step explanation:
[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]
======================================================
[tex]f(x)=-3x^4+7x^2\\\\f(-x)=-3(-x)^4+7(-x)^2=-3x^4+7x^2\\\\f(-x)=f(x)[/tex]
The function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) = -3x⁴ + 7x²
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = -3x⁴ + 7x²
To check whether the function is odd or even, plug x → -x in the function:
f(-x) = -3(-x)⁴ + 7(-x)²
f(-x ) = -3x⁴ + 7x²
f(-x) = f(x)
The function is even.
Thus, the function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) = -3x⁴ + 7x²
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7. Noreen needs to ship 9,480
candles. If 15 candles are shipped
in each box, how many boxes of
candles will she ship?
Noreen can ship 632 boxes of candles
because 9480 divided by 15 is 632
Tell whether the two figures are similar. Explain your reasoning
Answer:
See below.
Step-by-step explanation:
If they were similar corresponding sides would be in the same ratio.
Testing: 5/4 = 1.25
8/6 = 4/3 = 1.333...
They are not in the same ratio so they are not similar.
Two figures are similar if their corresponding angles are congruent and their corresponding side lengths are proportional. We can determine if two figures are similar by comparing the ratios of their corresponding side lengths.
Determining whether two figures are similar involves a thorough examination of their corresponding angles and side lengths. Two figures are considered similar if their corresponding angles are congruent (equal) and their corresponding sides are in proportion, meaning that the ratios of the lengths of corresponding sides are the same throughout the figures.
First, we examine the angles. If all corresponding angles in the two figures are equal, then it's a strong indication of similarity. Similar figures have the same shape, and equal angles ensure that the shapes are the same when scaled up or down.
Next, we analyze the side lengths. For figures to be similar, the ratios of corresponding side lengths must be constant. This means that if you were to take any two sides from the first figure and divide their lengths, and then do the same for the corresponding sides in the second figure, the ratios should be equal.
In summary, similarity between two figures is established by the equality of corresponding angles and the constancy of ratios between corresponding side lengths. If both conditions are met, the figures are indeed similar, which means they have the same shape, and one can be obtained from the other through uniform scaling (enlarging or shrinking).
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What is the value of b in the equation 3b + 2(b - 1) =8
Answer:
b = 2
Step-by-step explanation:
In order to find the value of b, we have to isolate b on one side of equation first
So,
[tex]3b+2(b-1)=8[/tex]
Multiplying 2 with b-1
[tex]3b+2b-2=8\\5b-2=8[/tex]
Adding 2 on both sides
[tex]5b-2+2=8+2\\5b=10[/tex]
Dividing by 5 on both sides
[tex]\frac{5b}{5}=\frac{10}{5} \\b=2[/tex]
So the value of b is 2 ..
ANSWER
The value of b is 2
EXPLANATION
The given linear equation in b is
[tex]3b + 2(b - 1) = 8[/tex]
We expand to get:
[tex]3b + 2b - 2= 8[/tex]
We now group similar terms to obtain:
[tex]3b + 2b = 8 + 2[/tex]
Combine the similar terms now to obtain:
[tex]5b = 10[/tex]
Divide both sides by 5 to get:
[tex]b = \frac{10}{5} [/tex]
This simplifies to:
[tex]b = 2[/tex]
A golf course in Phoenix, Arizona, uses an average of 80 million gallons of water daily for irrigation. An average family of four (also living in Phoenix, AZ) uses 325,851 gallons of water per year. Rounded to the nearest ten, how many families of four can one golf course provide water for? 89,610 families 250 families 896,120 families 245 families
The golf course can provide water for approximately 89,610 families of four.
Explanation:To find out how many families of four the golf course can provide water for, we need to compare the average water usage of the golf course with the average water usage of a family of four.
The golf course uses an average of 80 million gallons of water daily for irrigation.
To convert this to gallons per year, we multiply by 365:
80 million gallons/day * 365 days/year = 29.2 billion gallons/year.
Now, we divide the total water usage of the golf course by the water usage of one family of four:
29.2 billion gallons/year / 325,851 gallons/year = approximately 89,610 families of four.
The golf course can therefore provide water for approximately 89,610 families of four.
The system of equations y = –2x + 1 and y = x + 5 is shown on the graph below.Which statement is true about the solution to the system of equations? The x-value is between –1 and –2, and the y-value is between 3 and 4. The x-value is between 3 and 4 , and the y-value is between –1 and –2. The x-value is between 1 and 2, and the y-value is between –3 and –4. The x-value is between –3 and –4, and the y-value is between 1 and 2.
Answer:
The x-value is between –1 and –2, and the y-value is between 3 and 4
Step-by-step explanation:
we have
y=-2x+1 ----> equation A
y=x+5 ----> equation B
Solve the system of equations by elimination
Multiply the equation B by 2 both sides
2y=2x+10 ----> equation C
Adds equation A and equation C
y=-2x+1
2y=2x+10
---------------
y+2y=1+10
3y=11
y=11/3
Find the value of x
y=x+5
11/3=x+5
x=(11/3)-5
x=-4/3
therefore
x=-1.33, y=3.67
The x-value is between –1 and –2, and the y-value is between 3 and 4
The x-value is between –1 and –2, and the y-value is between 3 and 4
Step-by-step explanation:
2 3 + x = 3 what is X solved for
Answer:
Obviously its x=3-23=-20.
Hi there! My name is Zalgo and I am here to help you out on this wonderful day. "23+x=3", it seems that we need to find the "X value". That would be "-20". In order to test that it is the correct answer, just input it into the equation. "23+-20=3".
I hope that this helps! :)
"Stay Brainly and stay proud!" - Zalgo
(By the way, do you mind marking me as Brainliest? I'd greatly appreciate it! Thank you! XP)
Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + 2y = 12 –x = –y – 6
A. (9, 3)
B. (7, 1)
C. (6, 0)
D. (8, 2)
Answer:
(8,2)
Please make sure I interpreted your system correctly below.
x+2y=12
-x=-y-6
Step-by-step explanation:
I assume the system is
x+2y=12
-x=-y-6
-----------
I'm going to multiply both sides of equation 2 by -1 giving me
x+2y=12
x=y+6
I'm now going to plug equation 2 into equation 1.
(y+6)+2y=12 I replaced x with y+6 in the first equation
y+6+2y=12
3y+6=12
3y=6
y=2
So
x=y+6
x=2+6
x=8
The solution is (8,2)
Which values for A and B will create infinitely many solutions for this system of equations? ax-y=8 2x+y=b
Answer:
a = -2 , b = -8
Step-by-step explanation:
* Lets talk about the solution of the linear equations
- There are three types of the solutions of the system of linear equations
# If the two lines intersect each other, then there is one solution
- The equations are ax+ by = c , dx + ey = f
# If the two lines parallel to each other, then there is no solution
- The equations are ax+ by = c , ax + by = d in its simplest form ,
where a is the coefficient of x , b is the coefficient of y and
c , d are the numerical terms
# If the two lines coincide (over each other), then there are infinite
solutions
- The equations are ax+ by = c , ax + by = c in its simplest form, where
a is the coefficient of x , b is the coefficient of y and c is the
numerical term
* Lets solve the problem
∵ The system of equation is:
ax - y = 8 ⇒ (1)
2x + y = b ⇒ (2)
∵ The system create infinitely many solutions
∴ The lines are coincide
- The equations must be equal, then multiply equation(1) or (2) by -1 to
make the coefficient of y in the two equations equal
∴ -ax + y = -8
∴ 2x + y = b
∵ Their coefficients of x are equal
∵ Their coefficients of y are equal
∵ Their numerical terms are equal
∵ The coefficient of x in equation (1) is -a and in equation (2) is 2
∴ -a = 2 ⇒ multiply both sides by -1
∴ a = 2
∵ The numerical term in equation (1) is -8 and in equation (2) is b
∴ b = -8
* The values for a and b will create infinitely many solutions are -2 , -8
60 POINTS
Simplify square root of 5(10-4 square root of 2 attached to the 4)
Please explain how you got your answer. Answer choices:14, 15 with square root of 2 attached, 5 with square root of 2 attached - 4 with 10 being attached to -4, none of the above.
Answer:
[tex] 10\sqrt{5} - 4 \sqrt{10} [/tex]
Step-by-step explanation:
[tex] \sqrt{5} (10 - 4 \sqrt{2} )[/tex]
Multiply
[tex] \sqrt{5} [/tex]
with each term within the bracket
[tex] = \sqrt{5} + \times 10 - \sqrt{5} \times 4 \sqrt{2} [/tex]
[tex] = 10 \sqrt{5} - 4 \sqrt{10} [/tex]
What are the coordinates for the imagine of point N, when the figure is translated3 units to the right and 3 units up
A) (3,2)
B (6,5)
C (3,3)
D (-6,-5)
point N is at (3,2)
3units to the right and 3units up = x+3, y+3
3+3=6; 2+3=5
new coordinate: (6,5)
Given the following triangles, what additional information is required in order to know that the triangles are congruent because of the ASA congruence criteria?
QD and ED are congruent
DCQDCE
QC and DE are congruent
CDEDCQ
Answer:
The correct answer is : DCQ ( angle) = DCE (angle)
Answer: DCQ=DCE
Step-by-step explanation:
Simplify 4 to the power of 2 and 4 to the power of 8
Answer:
The second option.
Step-by-step explanation:
4^2 × 4^8
(4 × 4)(4 × 4 × 4 × 4 × 4 × 4 × 4 × 4) = 4^10
Or
4^2 × 4^8
=4^2+8
4^10
When solve an exponential with the same constant, you ga no problem. Just take one of those and and the exponent, you are good to go.
Please mark as brainliest.
-2x^2-6x-8=0 what is the solution using the quadratic equation
Answer:
x=-4, x=1
Step-by-step explanation:
[tex]x=\frac{-(-6)+\sqrt{(-6)^{2}-4(-2) 8 } }{2(-2)} : -4\\x=\frac{-(-6)-\sqrt{(-6)^{2} -4(-2) 8} }{2(-2)} : 1\\[/tex]
May I have help on number 7 please
Answer:
its A
Step-by-step explanation:
you do 28 x 66 :)
Two parallel lines are crossed by a transversal.
Answer:
Value of x is 37.
Step-by-step explanation:
Given:
line y and line z are parallel.
line x is traversal line.
To find: value of x.
∠( 3x + 4 )° and ∠ 115° are alternate interior angle in the given figure.
We know that Alternate interior angles of parallel lines are equal.
So,
3x + 4 = 115
3x = 115 - 4
3x = 111
x = 37
Therefore, Value of x is 37.
Two parallel lines are crossed by a transversal then the value of x is 37.
Given that line y and line z are parallel and line x is a traversal line.
To find that value of x.
We have ∠( 3x + 4 )° and ∠ 115° are alternate interior angles in the given figure.
We know that Alternate interior angles of parallel lines are equal So,
3x + 4 = 115
3x = 115 - 4
3x = 111
x = 37
Therefore, the Value of x is 37.
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Select one:
a. 4
b.5
c. 6
d. 7
Answer:
C
Step-by-step explanation:
Given 2 secants intersect a circle from a point outside the circle, then
The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
x(x + 10 + x) = 6(6 + 10 + x)
x(2x + 10) = 6(16 + x) ← distribute parenthesis on both sides
2x² + 10x = 96 + 6x ← subtract 96 + 6x from both sides
2x² + 4x - 96 = 0 ← in standard form
Divide through by 2
x² + 2x - 48 = 0 ← factor the left side
(x + 8)(x - 6) = 0
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 6 = 0 ⇒ x = 6
However x > 0 ⇒ x = 6 → C
Please help me geometry
Answer:
B
Step-by-step explanation:
The volume (V) of a pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] area of base × height, hence
V= [tex]\frac{1}{3}[/tex] × 64 × 8 ≈ 170.7 ( to 1 dec. place )
For this case we have that by definition, the volume of a pyramid is given by:
[tex]V = \frac {1} {3} * A_ {b} * h[/tex]
Where:
[tex]A_ {b}:[/tex] It is the area of the base
h: It's the height
According to the data we have:
[tex]A_ {b} = 64mm ^ 2\\h = 8mm[/tex]
Substituting:
[tex]V = \frac {1} {3} * 64 * 8\\V = \frac {512} {3}\\V = 170.666666667[/tex]
If we round up we have that the volume is[tex]170.7 \ mm ^ 3[/tex]
Answer:
Option B
In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box. x = yd A right triangle with one leg labeled x and the other leg labeled 40 yards. The angle that is opposite the leg labeled x yards is labeled 62 degrees.
The value of x is 75.2292.
what is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
given: a right triangle with base 40 yard.
Also, angle of elevation 62° .
and one of the side is 'x'.
Using trigonometry
tan 62= x/40
1.88073= x/40
x= 40*1.88073
x= 75.2292
Hence, value of x is 75.2292.
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The point of tangency of line s to circle B is
Answer: FIrst option.
Step-by-step explanation:
We need to remember that a tangent is a line that touches a circle at one point. This point is the "Point of tangency".
We can observe in the figure that the line "s" touches the circle A at a point identified as "J" and it also touches the circle B at a point identified as "K". Therefore, we can make the following conclusion:
The point of tangency of line "s" to circle B is: The point K.
This matches with the first option.
Which equation is not a linear equation?
Question 7 options:
a)
–4v + 2w = 7
b)
2
x
+
3
y
= 5
2x + 3y = 5 {"version":"1.1","math":"2x + 3y = 5"}
c)
x = -5
d)
x
4
= y
Answer:
-4v + 2w = 7 is not a linear equation.
Step-by-step explanation:
A linear equation is one in the form:
y = mx + x
-4v + 2w = 7 is not a linear equation since it has v and w instead of y and x.
A linear equation is any equation in the form Ax + By = C, with the degree of each variable being 1 and the exponents strictly positive. Hence x^4 = y is not a linear equation because the exponent of x is 4.
Explanation:In mathematics, a linear equation is any equation that can be written in the form Ax + By = C, where A, B, and C are constants, and x and y are variables. The degree of each variable in all the terms should be 1 and the exponents of the variables should be strictly positive integers. For example, an equation like ‘2x + 3y = 5’ would be considered linear. Looking at the provided options:
–4v + 2w = 7 is a linear equation2x + 3y = 5 is also a linear equationx = -5 is a linear equationHowever, x^4 = y is not a linear equation because the exponent of x is 4, not 1.Therefore, the answer is x4 = y.
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At which values of X does the function F(x) have a vertical asymptote? Check all that apply.
ANSWER
A. 1
D. 8
EXPLANATION
The vertical asymptote occurs at where the denominator of a rational function in its simplest form is equal to zero.
The rational function given is
[tex]p(x) = \frac{9}{(x - 1)(x - 8)} [/tex]
This rational function is in it's simplest form.
The vertical asymptotes occurs at
[tex](x - 1)(x - 8) = 0[/tex]
By the zero product principle, we must have either
[tex](x - 1) = 0 \: \: or \: \: (x - 8) = 0[/tex]
This implies that
[tex]x =1\: \: or \: \: x = 8[/tex]
Options A and D are correct.
A bag contains 10 marbles. Four of them are red, three blue, two white, and one yellow. A marble is drawn at random. What is the probability that it is not red? Be sure to reduce.
Answer:
6/10 but can be reduced to 3/5
Step-by-step explanation:
take every number exept red add them toget her and theres your answer.
The probability that it is not red is 0.6.
What is Probability?It is the ratio of total favorable outcome to the total number of outcomes.The value of probability lies between 0 and 1.Given: A bag contains 10 marbles.
Number of red marbles = 4
Number of blue marbles = 3
Number of white marbles = 2
Number of yellow marble = 1
A marble is drawn at random.
We have to find the probability that the marble is not red.
Hence, the marble can be blue, white and yellow.
∴ Apart from red marbles there are total of 6 marbles in the bag.
⇒ Total favorable outcomes = 6
⇒ Total number of outcomes = 10
Probability = (Total number of favorable outcomes) / (Total number of outcomes)
⇒ Probability = 6/10
⇒ Probability = 0.6
Therefore, the probability that it is not red is 0.6.
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Kates, Ratios, and proportions
A company is hosting a fundraising dinner and selling tickets to attend. The table below shows the total amount raised in relation to
the number of tickets sold.
Tickets Sold 2
Total Raised $36.00
3
$54.00
4
$72.00
5
$90.00
6
$108.00
What is the rate of change for the information in the table?
$9.00 per ticket
A.
B.
$27.00 per ticket
C.
$36.00 per ticket
D
$18.00 per ticket
Reset
Submit
O of 10 Answered
Session Timer: 1:04
Session Score: 0% (0/0)
61:3 odds pays out how much if you bet $25. I think $1550
Answer:
$508.33
Step-by-step explanation:
If I bet $25 (And I win, of course), I will win:
If I win $61 per every $3 bet, then:
61/3 = x/25 ⇒ Solving for 'x':
61*25/3 = $508.33
Finally, if you bet $25 you will win $508.33.
Identify the parent function that can be used to graph the function f(x)=3(x-9)2
Answer:
f(x) = x²
Step-by-step explanation:
what is the inverse of the function below? f(x)=x/3-2
Answer:it’s actually 3(x+2)
Step-by-step explanation: