The value after simplifying the number 10^3(10)^4 is 10⁷.
The simplification of given number can be done through the rule of exponent -
[tex] {a}^{m} [/tex] × [tex] {a}^{n} [/tex] = [tex] {a}^{m+n} [/tex], where m and n are the powers of a.
Now, keeping the values in formula -
Value = [tex] {10}^{3} [/tex] × [tex] {10}^{4} [/tex]
Based on the rule, the simplified for these powers will be
Value = [tex] {10}^{3+4} [/tex]
Performing addition of powers on Right Hand Side of the equation
Value = [tex] {10}^{7} [/tex]
Alternatively, the numbers can be expanded and multiplied. Further write the result in scientific notation as above. However, it will a long method which is not practical for very large numbers.
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Find the domain and range.
The domain of the given function is (-∞, ∞), the rage of the function is (-∞, 1).
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The lowest to highest value of x-coordinate is the domain of the function.
The lowest to highest value of y-coordinate is the range of the function.
The highest point of the function is (2.5, 1).
The highest value of y-coordinate is 1.
Since the graph function can be expended to infinity, the lowest value of y-coordinate is -∞.
The range of the function is (-∞, 1).
Both ends of graph can be extended -∞ to ∞ for x-coordinate.
The domain of the function is (-∞, ∞).
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Write a quadratic inequality to represent the area of a stained-glass mosaic that sits under a parabolic arch 10 feet tall and 8 feet wide at the base, if the left side of the base is the origin.
Answer:
To represent the area of a stained-glass mosaic that sits under a parabolic arch, we can use the equation for a parabolic arch, which is of the form
y = a(x - h)^2 + k
where (h,k) is the vertex of the parabola. The width of the parabolic arch at the base is 8 feet, so the vertex of the parabola is located at (4,0). Therefore, the equation for the parabolic arch is
y = a(x - 4)^2
The height of the parabolic arch is 10 feet, so we can represent the area of the stained-glass mosaic as the region where y is between 0 and 10. This can be expressed as the inequality
0 ≤ a(x - 4)^2 ≤ 10
Solving this inequality for x gives us the solution
-2 ≤ x - 4 ≤ 2
which simplifies to
2 ≤ x ≤ 6
Therefore, the quadratic inequality that represents the area of the stained-glass mosaic is
2 ≤ x ≤ 6
Step-by-step explanation:
Answer:
y ≤- 5/8(x - 4)² + 10 andy ≥ 0-------------------------------------------------------
According to given details we have:
The vertex at (8/2, 10) = (4, 10),The parabola opens down,It passes through the origin.The equation for the parabola is y = a(x - h)² + k, where (h, k) is vertex.
Substitute h = 4, k = 10:
y = a(x - 4)² + 10We know y = 0 at x = 0, substitute to find the value of a:
0 = a(0 - 4)² + 100 = a(16) + 1016a = - 10a = - 10/16 = - 5/8So the parabola is:
y = - 5/8(x - 4)² + 10We are looking for the area between the parabola and the x-axis, therefore we need two inequalities:
y ≤- 5/8(x - 4)² + 10 andy ≥ 0See attached for reference.
(1 point) in the 6/51 lottery game, a player picks six numbers from 1 to 51. how many different choices does the player have if repetition is not allowed? note that the order of the numbers is not important. your answer is :
There are 18 million different choices for a player to pick six numbers from 1 to 51. By using the combinations formula, the required value is obtained.
What is the formula for finding the number of combinations?The combinations formula is as follows:
ⁿCₓ = n!/(n - x)!x!
Where n is the total number of things and x is the required number of things.
Calculation:It is given that,
In a 6/51 lottery game, a player picks six numbers from 1 to 51.
So, the number of different choices the player has if repetition is not allowed is
ⁿCₓ = n!/(n - x)!x!
Here, n = 51 and x = 6
On substituting the values, we get
⁵¹C₆ = 51!/(51 - 6)!6!
⇒ ⁵¹C₆ = 51!/45!6!
⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46 × 45!)/45! × 6!
⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46)/6 × 5 × 4 × 3 × 2 × 1
⇒ ⁵¹C₆ = 17 × 10 × 49 × 47 × 46 = 170 × 105938 = 18,009,460
Therefore, there are 18 million choices for the player to pick six numbers from a set of 51 numbers.
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The equation and table show the cost, y, of different sports programs as a function of the number of classes x
Based on the provided table and equation when the class size is 1, gymnastics is less expensive, and when the class size is 3 or 4, ice skating is less expensive.
Given that y denotes the price and x denotes the number of classes, the gymnastics programmed is completed by the table, whereas the ice skating program is concluded by the equation y = 18x + 20.
Find the cost of the ice skating programmed for classes 1, 2, 3, and 4 as the table already lists the price for each specified number of gymnastics courses.
For 1 class, substitute x = 1 into y = 18x + 20:
y = 18(1) + 20
y = $38
For 2 class, substitute x = 2 into y = 18x + 20:
y = 18(2) + 20
y = $56
For 3 class, substitute x = 3 into y = 18x + 20:
y = 18(3) + 20
y = $74
For 4 class, substitute x = 4 into the equation y = 18x + 20:
y = 18(4) + 20
y = $92
We may infer from the foregoing that gymnastics is less expensive when the number of lessons is 1. When there are three or four courses, ice skating is less expensive.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
Mr. Lincoln is making slime for his kindergarten class. He has 3 cups
of glue. Each batch of slime uses 2/3 cup of glue. How many batches
of slime can Mr. Lincoln make? Show your work
In linear equation, 5 batches of slime can Mr. Lincoln make.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Based on the given conditions, formulate = 3 ÷ 2/3
= 3 * 3/2
= 3 * 3/2
= 9/2
the smallest integer greater than or equal to = 9/2 : 5
= 5
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3. The Alvarez family bought a car for $2,000. They made a down
payment of $500. If they want to pay the balance in 5 equal
payments, how much will each of these payments be?
The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.
Each payment will have to be $300
What is static electricity?
Build up of electrical charges on the surface of an object
Build up of light energy that causes electrical charges to move
The flow of electrical charges in a conductor
The movement of electrical charges through an insulator
Static electricity is an imbalance of electric charges within or on the surface of a material.
What is a charge? What is current?Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field.Electric charge can be positive or negative. Like charges repel each other and unlike charges attract each otherRate of flow of charge per unit time is called current.We have static electricity.
Static electricity is an imbalance of electric charges within or on the surface of a material or between materials. The charge remains until it is able to move away by means of an electric current or electrical discharge.
Therefore, Static electricity is an imbalance of electric charges within or on the surface of a material.
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What effect does decreasing the sample size have on a distribution of sample means? a) It will have more variation b) It will not make any difference cIt will have less variation
c) It will have less variation.
Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.
For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.
In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.
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Answer this question:
Your friend thinks that the triangles shown below are congruent by SAS. Is your friend correct? Explain.
Choose the correct answer below.
A.
Yes, the figure indicates that three corresponding sides are congruent.
B.
No, the congruent angles are not the included angles.
C.
Yes, the figure indicates that two corresponding sides and their included angle are all congruent.
D.
No, the congruent sides are not the included sides.
E.
Yes, the figure indicates that two corresponding angles and their included side are all congruent.
F.
No, the figure only indicates that two corresponding sides are congruent, not three as required by the SAS Postulate.
Answer:
B. No, the congruent angles are not the included angles.
Step-by-step explanation:
The SAS (Side-Angle-Side) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
In the given figure, we can see that two sides of the two triangles are congruent: side AB is congruent to side DE, and side AC is congruent to side DF. However, the included angles, which are the angles formed by these sides, are not congruent. Angle BAC is not congruent to angle EDF.
Since the included angles are not congruent, we cannot use the SAS Postulate to conclude that the two triangles are congruent. Therefore, the correct answer is B: No, the congruent angles are not the included angles.
Answer:
B. No, the congruent angles are not the included angles.
Step-by-step explanation:
You want to know if the triangles shown are congruent by SAS.
SASThe SAS congruence postulate tells you that two triangles are congruent if the angles between corresponding congruent sides are congruent. (The A=angle is between the S=side in SAS.)
In the diagrams, the marked angles are not between the marked sides. The SAS postulate cannot be used with these triangles.
In short, ...
No, the congruent angles are not the included angles
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JRB has been looking for a longboard for a while now. She found one for 80% of the original price. She paid $720 for it. What was the original price?
Answer:900
Step-by-step explanation:
720=.80x
720/.80=900
to check it
900*.20=720
Provide the missing statement and reasons for the following proof:
The missing statements and reasons in the proof are:
R3: Alternate Interior ∠s theorem
S4: Reflexive property
R5: ASA
How to Provide the Missing Statement and Reason of a Proof?A proof involves statements that are stated on one column, then followed by reasons that justify the statements stated, on another column.
The missing statements and reasons in the given proof above are explained below:
Statement Reason
1. Parallelogram ABCD with diagonal AC 1. Given
2. AB║CD and AD║BC 2. Def. of parallelogram
3. ∠1 ≅ ∠2 and ∠3 ≅ ∠4 3. Alternate Interior ∠s theorem
4. AC ≅ AC 4. Reflexive property
5. ΔABC ≅ ΔCDA 5. ASA
6. AB ≅ CD and AD ≅ BC 6. CPCTC
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is there a regualr polygon with an interior angle sum of 9000 degrees? if so, what is it
Answer:
Yes, there is. It's called a regular 52-gon.
please help me :( If you traveled 6,000,000,000 miles into outer space, you would be about one-fourth of the way to Venus. Write this measurement in scientific notation.
A. 6 x 106 miles
B. 60 x 106 miles
C. 6 x 109 miles
D. 60 x 109 miles
The given measurement in scientific notation as [tex]6\times10^9[/tex]. Therefore, option D is the correct answer.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].
The given distance is 6,000,000,000 miles.
There are 9 zeros in the given number
So, scientific notation is [tex]6\times10^9[/tex]
Therefore, the number in scientific notation is [tex]6\times10^9[/tex].
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Ruby biked a trail that is 3/5 mile each way. After biking 1/4 of the trail, she stopped to rets. What fraction of a mile did Ruby bike before she stopped to rest?
Answer:
7/20 miles
Step-by-step explanation:
get a common denominator
subtract the numerators
then you have the fraction she biked
Compute The Following. (A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9
The Computation results of given combination and permutation expression,
(A) P(9, 3) = 504
(B) C(9, 3) = 84
(C) P(8,8) = 40,320
(D)P(9,9) = 1
What is Permutations and Combination ?A permutation is an arrangment of arranging objects or numbers in order.
The formula for permutations is
ⁿPᵣ = n!/(n-r)!
Combinations are the way of selecting objects or numbers from a group of objects, in such a way that the order of the objects does not matter.
The formula for combinations is,
ⁿCᵣ = n!/[r! (n-r)!]
ⁿCᵣ represents the number of combinations from “n” objects taken “r” at a time.
We have given some expressions and we shall compute these.
(A) P(9, 3) , here n = 9 and r = 3
=> P(9, 3) = 9!/(9-3)! = 9!/6! = 9×8×7×6!/6!
P(9, 3) = 9×8×7 = 504
(B) C(9, 3) = 9!/3!(9-3)! = 9!/6!×3!
= 9×8×7×6!/6!(3×2×1) = 9×8×7/6 = 84
(C) P(8, 8) = 8!/(8-8)!
= 8!/0! = 8! = 8×7×6×5×4×3×2×1 = 40,320
(D) C (9, 9) = 9!/9!(9-9)!
= 9!/9! 0! = 1
Hence ,we get all the values of given expression.
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there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random, what is the probability they have an average weight of greater than 10 pounds and less than 15 pounds?
The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134
In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.
We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.
Given, μ = 12, σ = 8, n = 4
P(X > 8)
= P(z > (8 - 12 / 8/√4))
= P(z > -1)
= 1 - P(z ≤ -1)
= 1 - [1 - P(z ≤ 1)]
= P(z ≤ 1)
= 0.84134
Therefore, the required probability is 0.84134
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The graph of the equation y = 3x + 1 is shown below.
If the graph is reflected across the y-axis, what will be the equation of the new graph?
Answer:
y = -3x + 1
Step-by-step explanation:
A quarter of a year is 1/4 of a year. There are 12 months in a year. How many months are in a quarter of a year? Draw a diagram to illustrate the problem.
There are Three months in a quarter of a year.
To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:
1 year = 4 quarters
1 quarter= [tex]\frac{1}{4}[/tex] year
1 year = 12 months
Thus,
1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)
1 quarter = [tex]\frac{12}{4}=3[/tex]
So, There are Three months in a quarter of a year.
One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).
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There are Three months in a quarter of a year.
To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:
1 year = 4 quarters
1 quarter= [tex]\frac{1}{4}[/tex] year
1 year = 12 months
Thus,
1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)
1 quarter = [tex]\frac{12}{4} =3[/tex]
So, There are Three months in a quarter of a year.
One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).
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Find the smallest positive integer which has the same number of factors as 2022.
Using HCF to determine the integer with smallest number of factors, the value is 24
What is LCMHCF stands for Highest Common Factor. It is the largest positive integer that divides two or more given numbers without leaving a remainder.
In this problem, we are asked to find number that will have the same number of factors as 2022, we can start by listing all factors of 2022.
The HCF of 2022 are
2022 : 1, 2, 3, 6, 337, 674, 1011, 2022
The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24
24 has 8 factors, which is the same number of factors as 2022. 24 is the smallest positive integer with 8 factors.
From the explanation above, the smallest integer with same number of factors as 2022 is 24.
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Janet is shopping for silver as an investment. At her local silver shop she is presented with two options: round coins and rectangular bars. She looks at the
prices for each.
●
The silver shop will sell her round silver coins according to the equation p=
27s which shows the relationship between s, the number of ounces of silver
she buys, and p. what she will pay for the round coins.
The silver shop will sell her rectangular silver bars but they are more popular
so she has to pay a premium to acquire the rectangular bars. The equation p
= 27.5s +50 shows the relationship between s, the number of ounces of
silver she buys, and p, what she will pay for the rectangular bars.
Janet intends to buy 40 ounces of silver at the silver shop. How much money will
she save by purchasing only round coins instead of rectangular bars?
Answer:
To determine how much money Janet will save by purchasing round coins instead of rectangular bars, we need to find the difference in cost between the two options.
First, we can find the cost of the round coins by plugging 40 ounces into the equation p=27s:
p = 27 * 40 = 1080
Next, we can find the cost of the rectangular bars by plugging 40 ounces into the equation p = 27.5s + 50:
p = 27.5 * 40 + 50 = 1100
The difference in cost between the two options is 1100 - 1080 = $<<1100-1080=20>>20. Therefore, Janet will save $20 by purchasing round coins instead of rectangular bars.
Step-by-step explanation:
SELF EXPLANATORY
Is a origin on a graph proportional relationship?
Answer: Yes
Step-by-step explanation:
Most of the time, if a graph passes through the origin it is a proportional relationship!
se the given information to prove that m
By using the given information we can prove that m ∠ABC = m ∠EDC.
What are similar angles?
Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.
Given:
m ∠1 = m ∠2
m ∠2 = m ∠4
We have to prove that m ∠ABC = m ∠EDC
Let, ∠ABC = ∠1 + ∠2
and ∠EDC = ∠3 + ∠4
So, m ∠ABC = m ∠1 + m ∠2
and m ∠EDC = m ∠3 + m ∠4
From the given information,
m ∠1 + m ∠2 = m ∠3 + m ∠4 (Since m ∠1 = m ∠3, m ∠2 = m ∠4)
⇒ m ∠ABC = m ∠EDC
Hence, by using the given information we can prove that
m ∠ABC = m ∠EDC.
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What is the solution to the equation1 over the square root of 8 = 4(m + 3)? (1 point)
m = − 15 over 4
m = − 11 over 4
m = 5 over 4
m = 9 over 4
Answer:
A) m = − 15 over 4-------------------------------------------------
The equation should read:
[tex]1/\sqrt{8}=4^{m+3}[/tex]Solve it in below steps:
[tex]1/\sqrt{2^3}=(2^2)^{m+3}[/tex][tex]1/2^{3/2}=2^{2(m+3)}[/tex][tex]2^{-3/2}=2^{2m+6}[/tex][tex]-3/2=2m+6[/tex][tex]-3=4m+12[/tex][tex]4m=-15[/tex][tex]m=-15/4[/tex]Correct choice is A.
Which one is an undefined term?(A) Point
(B) Line
(C) Plane
(D) All of the above
Answer:
all the above
Step-by-step explanation:
examples of undefined term are point line and plane
Jessica starts skiing 1.2 miles East of the ski lodge, at an elevation of 1.8 miles above sea level. She finishes 0.3 miles East of the ski lodge, at an elevation of 1.2 miles above sea level.
What is the slope of the ski slope
Therefore , the slope of the ski slope is 39.197°.
What is slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Here ,
Given:
She begins her skiing at an elevation of 1.8 miles above sea level, 1.2 miles east of the ski lodge. At an altitude of 1.2 miles above sea level, she comes to an end 0.3 miles to the east of the ski lodge.
a = 1.2 miles
b = 1.8 miles
x = 1.2 miles
y= a-b = 1.8-1.2 = 0.6 miles
=>y tan A = A1
=> arctan(-) = arctan( 0.6 )
=> 0.68413 radian
A = A1 → degree= 0.68413 * 180 /π = 39.197°
Therefore, the slope of the ski slope is 39.197°.
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What equal the number eighteen?
Answer:
1 + 17 = 18
2 + 16 = 18
3 + 15 = 18
4 + 14 = 18
5 + 13 = 18
6 + 12 = 18
7 + 11 = 18
8 + 10 = 18
9 + 9 = 18
Step-by-step explanation:
Answer:
0+18=18
1+17=18
2+16=18
3+15=18
4+14=18
5+13=18
6+12=18
7+11=18
8+10=18
9+9=18
10+8=18
11+7=18
12+6=18
13+5=18
14+4=18
15+3=18
16+2=18
17+1=18
18+0=18
if my overall grade is 44 percent and a test is worth 60 percent of that grade and i get 50 percent on a test what would my overall grade be now?
(1 point) standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers. how many different standard plates are possible in this system? (assume repetition of letters and numbers is allowed.) your answer is :
Therefore ,there are 158,184,000 ways to create a license plate in this system.
What is combination ?A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.
According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.
The first number (the digits 1 through 9) can be obtained in nine different ways.
There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).
There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.
How many ways are there to get the next number? 10 ways\s.
Thus ,total options for obtaining a license plate:
9 x 26 x 26 x 26 x 10 x 10=158184000
Therefore ,there are 158,184,000 ways to create a license plate in this system.
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Taylor Swift is having 2 concerts at the same venue on Friday and
Saturday nights. On Friday, the ratio of the number of tickets sold to the
number of tickets still available is 5 to 3. On Saturday night, the ratio of the
number of tickets that were sold to the number of tickets available was
7:1. If 1,300 tickets were still available for the Saturday night concert, How
many tickets were sold for the Friday night concert?
Answer:
When using raitos you want to do P=2 +2+2+2
P=8
when L equals Ochoa
what will the answer be?
B2 + 62 + 25 gives us 169 - 25 and that gives us C Ronaldo
Step-by-step explanation:
Hope this helped! :)
