The sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt
How to create the sample space?The given parameters are
Stuffed toys, n = 3
Toys to arrange, r = 3 i.e. teddy bear (t), a kitten (k), and an elephant (e).
The number of arrangement is calculated as;
Ways = nPr
Substitute the known values in the above equation
Ways = 3Pr
Apply the permutation formula
Ways = 3!/0!
0! =1
So, we have
Ways = 3!/1
This gives
Ways = 3!
Expand
Ways = 3 * 2 * 1
Evaluate
Ways = 6
This means that the sample size is 6
Hence, the sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt
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help needed with this one
Based on the given parameters, the length of the missing length in the triangle is 12 units
How to determine the length of the missing side?The given triangle is an scalene triangle
Scalene triangles are triangles that have unequal three sides
The missing side is x, and the value of x is calculated using the following equivalent ratios
We have
4 : 8 = 6 : x
Express the above equation as a fraction
4/8 = 6/x
Evaluate the quotient
0.5 = 6/x
Solve for x
x = 6/0.5
Evaluate the quotient
x = 12
Hence, the length of the missing length is 12 units
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(06.04) it costs $100 to rent the bowling alley, plus $4 per person. the cost for any number (n) of people can be found using the expression 100 4n. the cost for 15 people equals $ ___. (input whole number only.) numerical answers expected! answer for blank 1:
The cost for 10 people equals to $ 140.
What is cost simple word?
Cost is a value of money that a company had to spend to produce its goods or services. It is calculated as the amount that company spends in order to produce a certain unit of a product. In simple words – it is the money that a company spends on things such as labor, services, raw materials, and more.Cost of renting bowling alley = $ 100
Additional cost of renting bowling alley per person = $ 4
⇒ Total Cost for n no. of people = 100 + 4 × n
So, Cost for 10 people = Fix $100 for bowling alley + $4 for each 10
people
= 100 + 4 × 10
= 100 + 40
= 140
Therefore, The cost for 10 people equals to $ 140.
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PLease helppppppppp!!!
Answer:
437.068 28.019
Step-by-step explanation:
Not sure how to explain this one....it is what it is
7 ones = 7
3 tens = 30
4 hundreds = 400 added = 437
No tenths = 0
6 hudredths = .06
8 thousandths = .008 added to = 437.068
280 tenths = 280 * 1/10 = 28
19 thousandths = .019 summed = 28.019
Ashley has two equations that she found to be valuable models for her research. She thinks that if she can find the intersection of the two graphs, she will be able to identify a key point to her studies. At what point do these equations intersect?
4y –x = 9
y = 2x − 3
(3,3)
(3,-3)
(-3,-3)
(-3,3)
The equations intersect at the point (3 ,3 ).
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
4y –x = 9 (1)
y = 2x − 3 (2)
You should replace the variable y of equation 1 to equation 2. Then, you will have:
4*(2x-3)-x=9
8x-12-x=9
8x-x=9+12
7x=21
x=3
If x=3, from equation 2 you can find the value of y. Thus, y=2*3-3=6-3=3
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If the graph of y = |x| is translated so that the point (1, 1) is moved to (4, 1), what is the equation of the new graph?
a.) y = | x - 3|
b.) y = | x + 3|
c.) y = | x| - 3
d.) y = | x| + 3
Answer:
A
Step-by-step explanation:
the answer is A because it is absolute so it would actually be x + 3
A container contains 20 liters of milk and another container contains 20 liters of syrup. One liter was taken from each vessel and poured into another vessel. After doing this twice, determine the ratio of milk and syrup in the two types of mixture.
Answer:
Step-by-step explanation:
20 liters -1 liter = 19 liters of milk
20 liters -1 liter = 19 liters of syrup
This was done twice so therefore;
19 liters -1 liter = 18 liters of milk
19 liters -1 liter = 18 liters of syrup
Therefore the ratio comes to 18:18
18 goes into 18 1 and the same for the other 18. Therefore the ratio comes to ;
1:1
Your final answer is 1:1
In the expansion of (2a + 3b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5
The possible variable terms are a^5b^3, b^8, a^4b^4, a^8, ab^7
How to determine the possible variable term?The expression is given as:
(2a + 3b)^8
The power of the above expression is 8
When expanded, the sum of powers on each variable must be 8.
Using the above explanation, we have the following possible variable terms:
a^5b^3, b^8, a^4b^4, a^8, ab^7
This is because the sum of powers equals 8
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Which statement describes independent events?
A. You write the numbers 1 through 10 on
index cards. You randomly draw two
cards without replacement: a 6 and an 8.
C. You randomly draw a blue marble from a
bag, return the marble, and then
randomly draw a yellow marble.
B. A President and Vice President are
randomly selected from a group of 24
students.
D. You randomly draw four cards from a
standard deck of cards without
replacement. You draw a King, then a
Queen, then a Jack, and then an Ace.
The statement that describes independent events is:
C. You randomly draw a blue marble from a bag, return the marble, and then randomly draw a yellow marble.
How to determine the statement describes independent eventsIn this case, the events of drawing a blue marble and drawing a yellow marble are independent because the first draw does not affect the probability or outcome of the second draw.
Returning the marble to the bag ensures that each draw is independent of the previous one.
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Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).
4x − y = −6
x + 4y = 7
x − 4y = −9
4x + y = 2
Answer:
x + 4y = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )
m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 2 )
2 = [tex]\frac{1}{4}[/tex] + c ⇒ c = 2 - [tex]\frac{1}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex]x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form
multiply through by 4 to clear the fractions
4y = - x + 7 ( add x to both sides )
x + 4y = 7 ← equation in standard form
equation of line in two point form is needed here.
(y - y1) = [ (y2 - y1)/(x2-x1) ] (x - x1)y - (2) = [ (1 - 2)/(3 - (-1)) ] (x - (-1))y - 2 = [ -1/4 ] (x + 1)y = -(x/4) -1/4 + 2y = -x/4 + 7/44y = -x + 7x + 4y = 7from your scale drawing, find the actual distance between the opposite corners of the school ball
The actual distance between the opposite corners of the school hall is; 10√34 m
How to use a Scale Drawing?The scale drawing showing the corners of the hall has been drawn and attached.
Now, from the attached scale drawing it was drawn with the scale;
1 cm to represent 5 m.
Now, the distance between the opposite corners of the hall measuring 50 m and 30 m is indicated as D on the scale drawing. Thus, to find the distance between the opposite corners, we will use Pythagoras theorem to get;
D² = 30² + 50²
D² = 900 + 3500
D² = 4400
D = √4400
D = 10√34 m
Thus, the actual distance between the opposite corners of the school hall is; 10√34 m
Complete question is;
Make a scale drawing of a rectangular school hall which is 50 m long and 30 m wide using a scale of 1 cm to 5 m. From your scale drawing, find the actual distance between the opposite corners of the hall.
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Find sin() and cos(), tan() and cot(), and sec() and csc(). webassign plot (a) sin() and cos() (b) tan() and cot() (c) sec() and
The values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
How to evaluate the trigonometry functions?The figure that completes the question is added as an attachment
From the figure, we have the third side of the triangle to be
Third = √(7^2 - 4^2)
Evaluate
Third = √33
The sin(α) is calculated as:
sin(α) = Opposite/Hypotenuse
This gives
sin(α) = 4/7
The cos(β) is calculated as:
cos(β) = Adjacent/Hypotenuse
This gives
cos(β) = 4/7
The tan(α) is calculated as:
tan(α) = Opposite/Adjacent
This gives
tan(α) = 4/√33
The cot(β) is calculated as:
cot(β) = Adjacent/Opposite
This gives
cot(β) = 4/√33
The sec(α) is calculated as:
sec(α) = Hypotenuse/Adjacent
This gives
sec(α) = 7/√33
The csc(β) is calculated as:
sec(β) = Hypotenuse/Opposite
This gives
sec(β) = 7/√4
Hence, the values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
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simplify (b^9)^3
A b^9
B b^6
C b^24
D b^27
Apply the exponent rule (x^a)^b= x^ab.
(b^9)^3= b^9*3= b^27
HELPPP There are 30 pencils in a box (15 pairs). 2 pair(s) are yellow,
3 pairs are brown, and the rest are tan. What is the probability of
pulling out a brown pencil on the first draw?
Write your answer as a reduced fraction.
Answer:
1/10
Step-by-step explanation:
Probability= number of brown pencil/number of pencil in the box
3/30
=1/10
Answer: 1/5
Step-by-step explanation:
30/15 pairs is 2 pencils per pair. That means there are 4 yellow pencils, 6 brown pencils, and the rest are tan.
30-10=20. There are 20 tan pencils.
6/30 is the probability of a brown pencil being pulled out.
This simplifies to 1/5.
help with math and explain plsss
Step-by-step explanation:
cotθcosθ=1tanθ⋅1cosθ
The square below has an area of x2 + 4x + 4 square meters.
What expression represents the length of one side of the square?
Perfect Squares
Write your answer without any spaces. Ex. x+3
Answer:
The side length of a square is the square root of its area. We know that:
x2 + 4x + 4 = (x + 2)2
Therefore, the side length of the square is x + 2
quien me hace una canción de ley de los cosenos de C por favor le doy 100 estrellas y corona
Answer:
Step-by-step explanation: all oof it equals to = 2c c2 = b1
A model train has a scale of 1 in : 3in. if the real train is 12ft tall then how tall is the model train
If the ratio of a model train to a real train exists 1:3 and the real train exists 12 feet then the model train exists 3 feet long.
How to estimate the ratio of the model train?Given that the model train contains a scale of 1: 3 and the real train exists 12 feet tall.
The ratio indicates how many times one number has another number.
A ratio exists as the relationship in quantity between two things.
It conveys the quantity of one thing in words of another.
The ratio of a model train to a real train exists at 1 inch :3 inches.
Height of model train = 12 [tex]*[/tex] 1/4
Height of model train = 3 inches
Therefore, the ratio of a model train to a real train exists 1: 3 and if the real train exists 12 feet then the model train exists 3 feet long.
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In a grade 11 class there are 30 learners. 16 of them are girls. there are 7 girls and 6 boys with blue eyes. a student is selected at random tone the class monitor what is the probability that the class monitor is a girl
Answer:
8/15
Step-by-step explanation:
possibilities/ sample size=16 girls/30 "learners"=8/15
30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?
6
8
12
10
Using the binomial distribution, you would expected to draw a face card 8 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
For this problem, the parameters are given as follows:
n = 35, as the experiment will be repeated 35 times.p = 12/52, as of the 52 cards, there are 12 faces, hence this is the probability of a success on a single trial.Then the expected value is found as follows:
E(X) = np = 35 x 12/52 = 420/52 = 8.
Thus, you would expected to draw a face card 8 times.
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What's the circumference of a
circle with a diameter of 31 inches?
Use 3.14 for I.
C = [?] inches
Enter the number that belongs in the green
box. Do not round your answer.
Hint: C = nd
Answer: C = 97.34 inches
Step-by-step explanation:
C = πd
= 3.14(31)
= 97.34
Please help me solve this problem with work
Answer:
m∠B ≈ 51.5°
Step-by-step explanation:
A triangle solver can find this answer simply by entering the data. If you do this "by hand," you need to first find length BC using the Law of Cosines. Then angle B can be found using the Law of Sines.
Length BCThe Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
a² = 21² +13² -2(21)(13)cos(91°) ≈ 619.529
a ≈ 24.8903
Angle BThe Law of Sines tells us ...
sin(B)/b = sin(A)/a
B = arcsin(sin(A)×b/a) = arcsin(sin(91°)×21/24.8903)
B ≈ 57.519°
The measure of angle B is about 57.5°.
please help!!! i just need this one
Answer:
[tex]p = x \\ r = 6\% \\ t = 2yrs[/tex]
[tex]p = 1600[/tex]
please see the attachment
Answer:
P = $1600
Step-by-step explanation:
We have to use the equation:
[tex]\boxed{I = Prt}[/tex] .
We know that:
• I = $192
• P = ?
• r = 6% = 0.06
• t = 2 years
Substituting these values into the equation:
[tex]192 = P \times 0.06 \times 2[/tex]
Solving for P:
[tex]P = \frac{192}{0.06 \times 2}[/tex]
[tex]P = \bf \$1600[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
ABIs parallel to CD, and EFis perpendicular to AB.
The number of 90° angles formed by the intersections of EFand the two parallel lines ABand CDis
Answer:
8
Step-by-step explanation:
The four angles formed at each intersection of lines are all 90°.
The total number of 90° angles at the two intersections is 2×4 = 8 90° angles.
Simplify: 7^x+1 + 7^x / 2×7^x
The simplified form of the expression 7^x+1 + 7^x / 2×7^x as given in the task content follows from the laws of indices and is equal to; 4.
What is the simplified form of the expression 7^x+1 + 7^x / 2×7^x?It follows from the task content that the expression whose simplified form is to be determined is given as; 7^x+1 + 7^x / 2×7^x.
On this note, it follows from the law of indices that; 7^x+1 = 7× 7^x.
Hence, we have; 7^x(7+1 ) / 2×7^x.
And upon simplification, we have; 8/2 = 4.
Consequently, we may conclude that the simplified form of the expression as given in the task content is; 4.
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What is the simplified form of the following expression?
2√27+√12-3√3-2√12
O√3
O 9√3
O 11 √3
O 15√3
Answer:
[tex] \sqrt{3} [/tex]
Step-by-step explanation:
27 is 3×3×3 from square root we can take 3 out as 3^2 elimate square root and remaining 3 is under root
Solve for P : p/10 = 7.2/3
P/10 = 7.2/3
P = 7.2x10/3
P=72/3
P= 24
Please help me urgently
Answer:
A=36°
B=54°
C=90°
a=7
b=9.6
c=11.9
Step-by-step explanation:
Upper case A,B,C are angles. B and C are given. Calculate A because the three angles in a triangle add up to 180°. See image.
Lower case a,b, and c are side lengths.
a is given. You need to use trigonometry and a calculator to find b or c or both. Or you can find one and use the Pythagorean Theorem to find the other. See image.
What is the quotient of the rational expression below?
3x+1 x-7
x+8 5x
O A.
O B.
O C.
O D.
3x² + x
x²+x-56
15x² +5x
x² +15x-56
15x² +5x
x²+x-56
15x² +1
x²+x-56
Answer: C
Step-by-step explanation:
[tex]\frac{3x+1}{x+8} \div \frac{x-7}{5x}\\\\=\frac{3x+1}{x+8} \times \frac{5x}{x-7}\\\\=\frac{5x(3x+1)}{(x+8)(x-7)}\\\\=\frac{15x^2 +5x}{x^2 +x-56}[/tex]
Jan has $30. Brenda has $66. How many DVDs can they buy with their total amount if one DVD costs $12?
Answer: they can buy about 8 dvds
Step-by-step explanation:
this is because 30 + 66 = 96 and if you do 96 divided by 12 it gives you 8
In 2021, the Internal Revenue Service (IRS) decreased the deductible mileage cost to 56 cents from 57.5 cents. Find the percent decrease. (Round to the nearest hundredth of a percent)
The deductible mileage cost has reduced by 2.16%
What is a percentage change?
A percentage change compares the difference between the new amount and the old amount to the old amount.
I mean the percentage change is the new deductible mileage cost minus the old deductible mileage cost divided by the old deductible mileage cost
New deductible mileage cost= 57.5 cents
Old deductible mileage cost= 56 cents
percentage decrease=(56-57.5)/57.5
percentage decrease=-2.61%
The negative sign in -2.61% means that there was a percentage decrease in deductible mileage cost by 2.61%
In essence, the deductible mileage cost has been reduced by 2.16%
Hundredth of a percent means two decimal places.
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