three of the 15 people in the Latin club are chosen at random to wear togas to school to promote the club. What is the probability that Joseph, Heldi, and Katy are chosen
The probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that three of the 15 people in the Latin club are chosen at random to wear togas to school to promote the club. Therefore, the number of ways 3 people can be chosen out of 15 is,
Number of ways to choose 3 people = ¹⁵C₃ = 455
Now, the number of ways Joseph, Heidi, and Katy can be chosen in only one way. Therefore, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is,
Probability = 1 /455 = 0.002197
Hence, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.
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Help please!
x=
4
9
16
Answer:
16
Step-by-step explanation:
cos60°=8/x
x=8/cos60°
Which statements describe a parabola? Check all that apply.
A parabola is the set of all points equidistant from the directrix and focus.
The fixed line is called the vertex of a parabola.
The focus is a fixed point inside the parabola.
The line of symmetry intersects the focus and directrix.
The line of symmetry and the directrix are perpendicular.
The parabola intersects the directrix.
Answer:
First, third, fourth and fifth statements describe a parabola
Step-by-step explanation:
The correct statements are:
A parabola is the set of all points equidistant from the directrix and focus.
The focus is a fixed point inside the parabola.
The line of symmetry intersects the focus and directrix.
The line of symmetry and the directrix are perpendicular.
Answer:
1, 3, 4, and 5 are the correct answers.
2 and 6 are not.
Find the length of each side of the polygon for the given perimeter
Answer:
choice number 2) 10 in, 18.5 in 31.5 in
Step-by-step explanation:
we collect and evaluate the like terms.like terms means the ones that can be evaluated. like 2y and 7y are like terms. they either can be added or subtracted to get an answer . 7y-2y =5y. but you cant subtrac or add 7y with 5 because they are not like terms.
2y +1 + 7y + 3y + 5 = 60
(2y+7y+3y)+(1+5) = 60
12y + 6 = 60
The 6 crosses the equal sign to the other side because of like terms.And becomes a minus
12y = 60 - 6
12y = 54
y = 4.5
so,
2y +1= 2 x 4.5 + 1 =10
7y = 7 x 4.5 = 31.5
3y + 5= 3 x 4.5 + 5 =18.5
Answer is 10 in, 18.5 in, 31.5 in
If you need any clarification or more explanation pls do mention at the comment section so that i can help more thx
Hope this helps and if it does pls mark as branliest answer thx
(Do not use spaces. Use to represent exponents. Example 2^3 is 22.)
Answer: y=6^x-3
It is a exponent form of graph, so first:
y=a^x-b
When b=0, the asymptote is y=0 but as the asymptote given is y=-3, b=-3
Second:
the y value increases 6, when x changes 0 to 1, so a=6
If n2 = 1/16, then n could be which of the following?
-8
-1/4
1/4
[tex]n^2=\dfrac{1}{16}\\\\n=-\dfrac{1}{4} \vee n=\dfrac{1}{4}[/tex]
Please answer the question from the picture above:)
Answer:
It's the red figure. This is because it is rotated 180 degrees.
Step-by-step explanation:
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
The model represents x2 – 9x + 14. Which is a factor of x2 – 9x + 14?
Answer:
(x-2)(x-7)
Step-by-step explanation:
x2 – 9x + 14 = x² - 2x - 7x + 14
= x(x-2) - 7(x-2)
= (x-2)(x-7)
Answer:
Factor of x² – 9x + 14 is:
(x-2)(x-7)
Step-by-step explanation:
We have to find the factors of:
x² – 9x + 14
On splitting the middle term, we get
x² -7x -2x +14
which could also be written as:
x(x-7)-2(x-7)
which is equivalent to:
(x-2)(x-7)
Hence, Factor of x² – 9x + 14 is:
(x-2)(x-7)
write 3/5 with denominator 10 and 20
Answer:
Answer is 6/10 and 12/20
Step-by-step explanation:
Let the numerator be x.
3/5=x/10
x=30/5
x=6
The required fraction is 6/10
Now same method applies for taking 20 as denominator
3/5=x/20
x=60/5
x=12
The required fraction is 12/20
Choose the Domain & Range of the Relation shown in the graph:
Domain: -1, 0, 1, 2, 3
Range: -3, -1, 0, 3
Domain: -3, -1, 0, 3
Range: -3, -1, 0, 3
Domain: -3, -1, 0, 3
Range: -1, 0, 1, 2, 3
Domain: 3, 1, 0, 3
Range: -1, 0, 1, 2, 3
Answer:
C) Domain: -3, -1, 0, 3
Range: -1, 0, 1, 2, 3
Step-by-step explanation:
Domain is using x values
Range is using y values
some one help me pleaseeeeeeeeeee
Answer:
slope = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 4) ← 2 points on the line
m = [tex]\frac{4+1}{2-0}[/tex] = [tex]\frac{5}{2}[/tex]
solve the system of linear equations separate the x- and y- values with a comma. -13x = -54 - 20y and -10x= 60 + 20y
[tex]\bf \begin{cases} -13x=-54-20y\\ -10x=60+20y \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{-13x=-54-20y}\implies -13x+20y=-54\implies \boxed{20y}=13x-54 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 2nd equation}}{-10x=60+\left( \boxed{13x-54} \right)}\implies -10x=6+13x\implies -10x-6=13x[/tex]
[tex]\bf -6=23x\implies \blacktriangleright -\cfrac{6}{23}=x \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{-13\left( -\cfrac{6}{23} \right)=-54-20y}\implies \cfrac{78}{23}=-54-20y[/tex]
[tex]\bf \stackrel{\textit{multipying both sides by }\stackrel{LCD}{23}}{23\left( \cfrac{78}{23} \right)=23(-54-20y)}\implies 78=-1242-460y\implies 1320=-460y \\\\\\ \cfrac{1320}{-460}=y\implies \blacktriangleright -\cfrac{66}{23}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( -\frac{6}{23}~,~-\frac{66}{23} \right)~\hfill[/tex]
find missing term w+9/6=12
Answer: The missing term for W is 10.5.
Step-by-step explanation:
W + 9/6 = 12
W +9/6 - 9/6 = 12- 9/6
W = 12 - 1.5
W = 10.5
A flock of 200 birds were flying south for the winter. Every day, the amount of birds in the flock increased by an average of 4%.
The amount of birds in the flock, b, can be represented by an exponential function, where d represents the number of days since the 200 birds started. What is the equation of this exponential function?
b = 1.04 · 200d
Answer:
[tex]b=200(1.04)^{d}[/tex]
Step-by-step explanation:
we know that
The exponential function is of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
In this problem we have
a=200 birds
b=100%+4%=104%=104/100=1.04
substitute
[tex]y=200(1.04)^{x}[/tex]
Let change of variables
[tex]b=200(1.04)^{d}[/tex]
where
b is the amount of birds in the flock
d is the number of days since the 200 birds started
Find the cube root of x^54.
hope this helps. goodluck
A survey asked people if they prefer to read books or e-books. The results are shown in the table below. What is the
marginal relative frequency of the number of people who prefer to read books?
Male Female Total
Read books
Read e-books
D
0.57
0.49
0.43
0.42
The marginal relative frequency of the number of people who prefer to read books is 0.42
Answer:
.42
Step-by-step explanation:
If the sum of n terms of a G.P series is 225, the common ratio is 2 and the last term
(nth term) is 128.
Answer:
Step-by-step explanation:
what is the finance charge?
Answer:
n = 8.
Step-by-step explanation:
I am assuming that the sum is 255.
The last term is 128 and the common ratio is 2 so we can work backwards until we reach a sum of 255.
Term n = 128 so the previous term must be 128/2 = 64.
So following this pattern we have:
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
So we see that n = 8.
The equation has no solution.
A. 13y + 2 - 2y = 10y + 3 - y
B. 9(3y +7) - 2 = 3(-9y + 9)
C. 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
D. 5(2.2y + 3.4) = 5(y - 2) + 6y
Option D which simplifies to 11y +17 = 11y -10 has no solution since the left and right sides of the equations aren't equal after simplifying.
Explanation:We are tasked with determining which equation has no solution among the given options: A) 13y + 2 - 2y = 10y + 3 - y, B) 9(3y +7) - 2 = 3(-9y + 9), C) 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1 and D) 5(2.2y + 3.4) = 5(y - 2) + 6y. The equation without a solution will be the one in which the variables cancel out and the remaining numbers are not equal.
Solving the equations, starting with A, by combining like terms, we have 11y + 2 = 9y + 3, this eventually gives us y = 0.5. Option B, simplifying gives us 27y + 63 = -27y + 27, therefore y = -1.33. For C, we simplify to 34.5y + 3.1 = 34.5y - 5.1. Because both sides of the equation have equal coefficients for y, this results in 34.5y = 34.5y, which holds true for any value of y. Hence, the equation has infinitely many solutions. Option D simplifies to 11y +17 = 11y -10. Here, we see that 11y = 11y is true, however, the constants are not equal (i.e. 17 does not equal -10). Thus, option D is the equation with no solution.
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A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live
for one week without producing any additional offspring. Each replicated organism also replicates at the same rate. At hour one,
there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven?
2,801
19,531
19,607
97.655
Answer:
B. 19,531
Step-by-step explanation:
Answer:
The correct answer is option (2) 19,531
Step-by-step explanation:
Given Data;
a = 1 (first term)
r = 5 (five offspring)
n = 7 ( number of hours)
Using the formula of a geometric progression, we have
S₇ = [tex]\frac{a(r^{n} - 1) }{r -1}[/tex]
Substituting, we have
S₇ = [tex]\frac{1(5^{7} -1) }{5-1}[/tex]
S₇ = 78124/4
= 19531
Therefore, there are 19531 number of organisms at hour seven.
Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?
Answer:
20000*(0.85)^x
Step-by-step explanation:
Answer:
The function f(x) representing the value of car after x years is given by
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
Step-by-step explanation:
Since value of car depreciates by 15% each year
Value of car after 1 year
[tex]f(1)=value of new car \times(1-\frac{15}{100})[/tex]
=>[tex]f(1)=\$ 20,000\times(1-\frac{15}{100})[/tex]
Value of car after 2 year
[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})^{2}[/tex]
Value of car after 3 year
[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})^{3}[/tex]
Similarly value of car after x years is
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
write the product using exponents
(-2) x (-2) x (-2)
Answer:
(-2)3 = -8
-2 × -2 = 4
4 × -2 = -8
Step-by-step explanation:
-2 multiply 3 times
negative times a negative equals a positive
negative times positive equals a negative
see results below
-2 × -2 = 4
4 × -2 = -8
50 points?with explanation
Answer:
a = b
b = c
So they're all equal, therefore a would be the same as c
Step-by-step explanation:
Answer: True
Step-by-step explanation: Since a||b and b||c, a||c is correct a is b and b is c.
Louise calculated the height of a cylinder that has a volume of 486 x cubic centimeters and a radius of 9 centimeters. Her work
is shown below
V=Bh
Step 1: 486x - R9?h
Step 2: 486 181 sch
486% 81
Step 3: 812 813
Step 4: h=6x cm
What error did Louise make when calculating the height of the cylinder?
In step 1, she substituted into the volume formula incorrectly.
In step 2, she calculated g2 incorrectly.
In step 4, the should have canceled, making the correct answer 6 cm.
Louise correctly calculated the height of the cylinder.
Answer:
Option C.
Step-by-step explanation:
we have that
The correct question is
Louis calculated the height of a cylinder that has a volume of 486pie cubic centimeters and a radius of 9 centimeters her work is shows below
V=BH
STEP 1: 486pie=pie9^2h
STEP 2: 486pie=81pieh
STEP 3: 486pie/81pie=81pie/81pie h
STEP 4: h=6pie cm
what error did Louise make when calculating the height of the cylinder
A. in step 1 she substituted into the volume formula incorrectly
B. in step 2 she calculated 9^2 incorrectly
C. in step 4 the pie should have canceled making the correct answer 6 cm
D. Louise correctly calculated the height of the cylinder
we know that
The volume of the cylinder is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the cylinder
we have
[tex]V=486\pi\ cm^{3}[/tex]
[tex]r=9\ cm[/tex]
Find the area of the base B
[tex]B=\pi r^{2}[/tex]
substitute
[tex]B=\pi (9)^{2}[/tex]
step 1
substitute the values in the formula of volume
[tex]486\pi=\pi (9)^{2}h[/tex]
step 2
[tex]486\pi=81\pi h[/tex]
step 3
Divide both sides by 81π
[tex]486\pi/81\pi=81\pi h/81\pi[/tex]
step 4
Simplify
[tex]6=h[/tex]
rewrite
[tex]h=6\ cm[/tex]
therefore
In step 4 the pie should have canceled making the correct answer 6 cm
Answer:
In step 4, the x should have canceled, making the correct answer 6 cm.
A square sign has an area of approximately 158 feet .What is the approximate length of one side of the sign?
Answer:
12.5698 (approximately 12.5, rounding to the nearest half)
Step-by-step explanation:
The area of a square is represented by the following equation:
[tex]A=a^2[/tex]
Whereas "a" represents the length of any one of the sides.
Since all sides of a square are equal in length, we can reverse engineer this formula to find the length of one side.
[tex]158=a^2[/tex]
Simply take the square root of both sides and you will have your answer.
[tex]12.5698=a[/tex]
To determine the length of one side of a square sign with an area of 158 feet, calculate the square root of the area which is approximately 12.57 feet.
A square sign has an area of approximately 158 feet. To find the length of one side of the sign, you need to calculate the square root of the area:
Side length = √(Area)
Side length = √(158) = 12.57 feet
for each figure, find the missing side lengths. leave your answer as radicals in simplest form.
Answer:
4
Step-by-step explanation:
I'm not sure what question you are asking about but the one you had answer is incorrect.
You are given the long side which is 2sqrt(3).
Compare this to xsqrt(3) and hopefully you see x is 2 and is the short side.
The hypotenuse is twice the short side measurement so 2(2)=4.
Answer: 4
Answer:
Step-by-step explanation:
48
This is a 30-60-90 triangle, and we are given the [tex]x[/tex] value for the triangle, which makes it easier.
The hypotenuse for a 30-60-90 triangle will always be [tex]2x[/tex], while the adjacent side for a 30-60-90 triangle will always be [tex]x*\sqrt{3}[/tex].
So the hypotenuse is 14, and the adjacent side is [tex]7*\sqrt{3}[/tex]/
49
This is also a 30-60-90 triangle, and we can use the rules explained above.
The x value is [tex]5*\sqrt{3}[/tex] so the hypotenuse is [tex]10*\sqrt{3}[/tex] and the adjacent side is 15.
51
This is also a 30-60-90 triangle, and the root three value is [tex]2*\sqrt{3}[/tex], making the x value 2 and the hypotenuse 4.
52
This is a 45-45-90 triangle, and the same side value is [tex]4*\sqrt{2}[/tex].
This means that the adjacent side is also [tex]4*\sqrt{2}[/tex] and the hypotenuse is 8.
what two values of x are roots of this equation x^2+2x-5=0
Answer:
x = 1 + √6
x = 1 - √6
The two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]
From the question,
We are to determine the values of x that are roots to the quadratic equation x² +2x -5=0
Using the quadratic formula
[tex]x= \frac{-b \pm \sqrt{b^{2} -4ac} }{2a}[/tex]
From the given equation x² +2x -5=0
[tex]a = 1, \ b = 2, \ and \ c=-5[/tex]
Putting the values into the equation, we get
[tex]x= \frac{-(2) \pm \sqrt{(2)^{2} -4(1)(-5)} }{2(1)}[/tex]
This becomes
[tex]x= \frac{-2 \pm \sqrt{4 --20} }{2}[/tex]
[tex]x= \frac{-2 \pm \sqrt{4+20} }{2}[/tex]
[tex]x= \frac{-2 \pm \sqrt{24} }{2}[/tex]
Then,
[tex]x= \frac{-2 \pm 2\sqrt{6} }{2}[/tex]
∴ [tex]x= -1 \pm \sqrt{6}[/tex]
[tex]x= -1 + \sqrt{6} \ OR \ x= -1 - \sqrt{6}[/tex]
Hence, the two values of x that are roots to the given equation are [tex]x= -1 + \sqrt{6}[/tex] and [tex]x= -1 - \sqrt{6}[/tex]
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The amount of blueberries picked, in pounds, varies directly as the number of hours worked. After
10
hours,
30
pounds were picked.
What is the constant of proportionality
k
? Do not include units in your answer.
Answer:
3
Step-by-step explanation:
3 pounds were picked per hour
Answer: Hello there!
We know that the number of blueberries picked varies directly as the number of hours worked.
Direct variation means that: b = kh
where b is the number of blueberries, k is a constant of proportionality and h is the number of hours worked.
we know that in 10 hours there are 30 pounds of blueberries collected, then we can replace these numbers in the equation and solve it for k. And you want that I don't include units in the answer, so I will not include them.
30 = k*10
k = 30/10 = 3
Then the constant of proportionality is 3, whit is the amount of punds of blueberrys collected in one hour.
Write a formula to help Jaheed determine the
number of cartons of juice he needs to
buy to make the punch.
Let's let
n = number of cartons of juice
m = number of liters in each carton
Enter the correct answer.
Answer:
n=m(x)
Step-by-step explanation:
n is the dependent variable m is the independent variable.
how many cartons, depends on how many liters are in a carton.
how many he needs to buy= the amount in carton× how ever much is in his recipe
for example
if they're are let's say 1.5 liters per carton than m=1.5. and if he needs 15 liters than n= 15
than the equation is
[tex]15 = 1.5 \times x[/tex]
x is how many cartons he needs to buy
solve for x by dividing both sides of the equation by 1.5
[tex]15 \div 1.5 = x[/tex]
and x=10 in this scenario
Which is a correct first step in solving 5- 2x < 8x - 3?
Answer:
Isolating the x.
Step-by-step explanation:
The first step to solving this problem is to isolate the variable, x.
To do so, subtract 8x and 5 from both sides.
Step #1)
5 - 2x < 8x - 3
5 (-5) - 2x (-8x) < 8x (-8x) - 3 (-5)
-2x - 8x < -3 - 5
-10x < -8
~
Answer:
x>4/5
Step-by-step explanation:
Subtract by 5 from both sides of equation.
5-2x-5<8x-3-5
Simplify.
-2x<8x-8
Subtract by 8x from both sides of equation.
-2x-8x<8x-8-8x
Simplify.
-10x<-8
Multiply by -1 from both sides of equation.
(-10x)(-1)>(-8)(-1)
Simplify.
10x>8
Divide by 10 from both sides of equation.
10x/10>8/10
Simplify, to find the answer.
8/10=4/5
x>4/5 is the correct answer.
I hope this helps you, and have a wonderful day!
Find the product of (4x + 3y)(4x − 3y).
16x2 − 24xy + 9y2
16x2 − 9y2
16x2 + 24xy + 9y2
16x2 + 9y2
Answer:
It's B
Step-by-step explanation:
B, 16x2-9y2
Answer: The correct option is (B) [tex]16x^2-9y^2.[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=(4x+3y)(4x-3y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the given product, we will be using the following formula :
[tex](a+b)(a-b)=a^2-b^2.[/tex]
The product (i) can be calculated as follows :
[tex]P\\\\=(4x+3y)(4x-3y)\\\\=(4x)^2-(3y)^2\\\\=16x^2-9y^2.[/tex]
Thus, the required product is [tex]16x^2-9y^2.[/tex]
Option (B) is CORRECT.