Answer:
i. 13.23
ii. 20.58
iii. 76.77
iv. 84.48
Step-by-step explanation:
Here , we are to calculate the square root of we have of the decimal numbers and correct to two decimal places.
i. √(175.01) = 13.229 = 13.23
ii. √(423.74) = 20.5849 = 20.58
iii. √(5893.27) = 76.767 = 76.77
iv. √(7136.8) = 84.4795 = 84.48
Kindly note that the approximation to two decimal places are the figures after the equal to
find the value of X also show the process please
Answer: 36
Step-by-step explanation:
Someone Help? I am not too sure if I am right.
Answer:
You are right.
Step-by-step explanation:
The values corresponding to x = 3 is -5.
(Write each statement in function notation if you know what function notation is)
1. At 3 seconds, the toy rocket is higher than the drone.
2. At the start, the toy rocket is 25ft above the drone.
The statements that relate each function are given as follows:
1. At 3 seconds, the toy rocket is higher than the drone: f(3) > g(3).
2. At the start, the toy rocket is 25ft above the drone: f(0) - g(0) = 25.
What are the inequality symbols and what are the functions?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The functions for this problem are given as follows:
f(x): height of the toy rocket after x seconds.g(x): height of the drone after x seconds.At 3 seconds, we have that the toy rocket is higher than the drone, that is, f(3) is greater than g(3), hence the inequality is given as follows:
f(3) > g(3).
At the start, the heights are given as follows:
Toy rocket: f(0), as the start is equivalent to a time of 0 seconds.Drone: g(0).The difference is of 25 ft, hence the expression is given as follows:
f(0) - g(0) = 25.
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what is 24 divided by 8/15
Answer:
45
Step-by-step explanation:
put 24 over 1 to make it a fraction.
So now its:
24/1 divided by 8/15
Now cross multiply
So now its:
24*15/1*8
(24 times 15)
Over
(1 times 8)
=360/8
=45
24 divided by 8/15 is equal to 45.
To divide 24 by 8/15, we can simplify the problem by multiplying 24 by the reciprocal of 8/15, which is 15/8. Multiplying fractions involves multiplying the numerators and denominators.
So, 24 divided by 8/15 can be rewritten as 24 multiplied by 15/8:
24 * (15/8)
When we multiply the numerators (24 * 15) and the denominators (1 * 8), we get:
360/8
Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, which is 8:
45/1
Therefore, 24 divided by 8/15 is equal to 45.
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What is the value of 2.4 -(-3.6)?
Answer:
6 positive
Step-by-step explanation:
if u subtract a negative you are really just adding a positive. ok? ok.
Answer:
6
Step-by-step explanation:
2.4 - (-3.6) is as if it's addition. You're subtracting a negative number, so it becomes like addition.
It's as if someone had 10 apples and left and you got the apples, so the act of removing them got you more apples.
regarding the probability of type l error (a) and type ll error which statement is true
Type I error (also called a false positive) occurs when a null hypothesis is rejected when it is actually true. The probability of committing a Type I error is denoted by the symbol alpha (α), and is typically set at a certain level (e.g., 0.05 or 0.01) depending on the significance level desired for the hypothesis test.
Type II error (also called a false negative) occurs when a null hypothesis is not rejected when it is actually false. The probability of committing a Type II error is denoted by the symbol beta (β). The power of a statistical test is equal to 1 minus the probability of a Type II error (i.e., power = 1 - β).
Therefore, the statement that is true regarding the probability of Type I and Type II errors is that they are complementary to each other. That is, as the probability of a Type I error decreases (by setting a lower significance level), the probability of a Type II error generally increases (i.e., the power of the test decreases). Conversely, as the probability of a Type II error decreases (by increasing the sample size or effect size), the probability of a Type I error generally increases. It is important to strike a balance between controlling these two types of errors, depending on the specific goals and context of the research or hypothesis test.
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Solve 2x 10 = -4
X = ?
Type the correct answer in each box. Round your answers to two decimal places. Subtract vector v = <2, -3> from vector u = <5, 2>. The magnitude of the resulting vector, u – v, is approximately , and its angle of direction is approximately .
The magnitude of the resulting vector, u – v, is approximately 5.83, and its angle of direction is approximately 59.04°.
To solve the given problem, we are going to find the difference of two vectors u and v.
The vector u is <5,2> and the vector v is <2,-3>. So, u - v is <5,2> - <2,-3>.<5,2> - <2,-3> = <5 - 2, 2 - (-3)> = <3,5>
The magnitude of the resulting vector u – v is approximately √(3² + 5²) = √34 = 5.83 (rounded to two decimal places).
Now, to find the angle of direction of the resulting vector, we will use the formula:θ = tan⁻¹(y/x)θ = tan⁻¹(5/3) = 59.04° (rounded to two decimal places)
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Can someone please help me with this
Answer:
circumference of circular track =2πR
R = 50/2 = 25m
circumference = 2 × 22/7 × (25) = 157.14 ≈ 157m
No. of rounds made = 10
total distance covered = 157 × 10 = 1570m
Option 3) 1570 is correct
AMSWER ASAP PLEASE PLEASE PLEASE
Answer:
(2,14)
Step-by-step explanation:
so i solved this with substitution but there are other methods to solve this!
equation 1 : y = -x + 16
equation 2 : y = x + 12
solve for y in equation 1 !!
y = -x + 16
(add x on both sides)
y + x = 16
(subtract y on both sides)
x = -y + 16
equation 1 now equals : x = -y + 16
substitute equation 1 into equation 2 :)
y = (-y + 16) + 12
(add 16 + 12)
y = -y + 28
(add y on both sides)
2y = 28
(divide 2 on both sides)
y = 14
now to solve for x you can insert y !
you can use equation 1 or equation 2 to solve for x.
i'm using equation 2 :
y = x + 12
(14) = x + 12
(subtract 12 on both sides)
x = 2
therefore, the answer is (2, 14).
hope this helps :p
SS ZONE
Block 5> Topic 3> Applications of Percent
Dre is painting a mural for his school.
Each can of spray paint costs $5 before
sales tax. The sales tax rate is 10%.
Plot a point that represents how Dre can
spend money on spray paint.
Cost Including Sales Tax (5)
132
88
44
20
40
60
Cost Before Sales Tax ($)
A point that represents how Dre can spend money on spray paint is plotted on the proportional relationship graphed at the end of the answer.
How to model the money spent?The money spent after sales tax is obtained multiplying the money spent before sales tax by a constant, hence a proportional relationship models the situation.
The general format of a proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality.
In this problem, the sales tax rate is of 10%, meaning that the total amount paid is composed as follows:
Cost before sales tax.10% of the cost before sales tax.Considering x as the cost before sales tax, the equation is given as follows:
y = x + 0.1x
y = 1.1x.
Meaning that one point is given as follows:
(5,5.5).
Meaning that when the cost before sales tax is of $5, the cost including sales tax is of $5.5.
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in looking at a scatterplot of interrater reliability, why would a researcher want to see all the dots close to the line of agreement?
In looking at a scatter plot of inter-rater reliability, a researcher would want to see all the dots close to the line of agreement because it shows that there is a high level of agreement between the raters.
What is inter-rater reliability?Inter-rater reliability refers to the degree to which different raters or observers agree on their judgements or evaluations of a particular behavior, characteristic, or event. It is a measure of consistency between the observations of two or more raters. Inter-rater reliability is important because it ensures that the results obtained from the research are valid and reliable, which means that they are accurate and can be trusted.
In a scatterplot of interrater reliability, the dots represent the ratings or observations made by different raters. The line of agreement is a straight line that represents perfect agreement between the raters, i.e., all the raters make the same rating. If all the dots are close to the line of agreement, it means that the raters are in close agreement with each other, and there is a high level of inter-rater reliability.
If the dots are scattered far from the line of agreement, it means that the raters are not in agreement with each other, and there is a low level of inter-rater reliability. Thus, a researcher would want to see all the dots close to the line of agreement because it shows that there is a high level of agreement between the raters.
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Which side lengths form a right triangle?
Choose all answers that apply:
A 5,8,9
6, 8, 10
5,7,√/74
The side lengths that form a right triangle are given as follows:
6, 8, 105,7,√74What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.A right triangle is formed when the Pythagorean Theorem is respected, hence:
6² + 8² = 10²
36 + 64 = 100
100 = 100 -> right triangle with the side lengths 6, 8 and 10.
5² + 7² = [sqrt(74)]²
25 + 49 = 74
74 = 74 -> right triangle with the side lengths 5,7 and√74.
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3. A soft drink vendor at a popular beach analyzes his sales records and finds that if he sells xcans of soda pop in one day, his profit (in dollars) is given by P(x) 0.001x2 3x 1800 What is his maximum profit per day, and how many cans must he sell to reach the maximum profit?
The maximum profit per day is $600, and the soft-drink vendor must sell 1,500 cans to achieve this maximum profit.
The profit function for the soft-drink vendor is given by P(x) = -0.001x^2 + 3x - 1800. To find the maximum profit per day and the number of cans to sell for maximum profit, follow these steps:
1. Identify the quadratic function: In this case, it's P(x) = -0.001x^2 + 3x - 1800.
2. Find the vertex of the parabola, which represents the maximum profit point. The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a and b are the coefficients of the quadratic function (a = -0.001, b = 3).
3. Calculate the x-coordinate of the vertex: x = -3 / (2 * -0.001) = -3 / -0.002 = 1500.
4. Substitute the x-coordinate back into the profit function to find the maximum profit: P(1500) = -0.001(1500)^2 + 3(1500) - 1800 = $600.
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This graph shows the number of laps that Jan runs as her coach times her.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement.
The slope of the line is
Choose...
.
This means that Jan runs
Choose...
laps every
Choose...
.
trying to get my grade up please be the right answer
The slope of the line is 2 and Jan runs 2 laps for every minute.
The slope of the line:The slope of the line is defined as the change in the y-coordinate with respect to the x- coordinate and the formula for slope is given by
Slope (m) = (y₂ - y₁) / (x₂ - x)Where (x₁, y₁) and (x₂, y₂) are points where the line passes through.
Here we have
The graph shows the number of laps that Jan runs
From the graph,
The line that represents the situation will pass through (2, 4) and (5, 10)
Using the formula, Slope (m) = (y₂ - y₁) / (x₂ - x)
Slope of the line = [10 - 4]/[5 - 2 ] = 6/3 = 2
This means that Jan runs 2 laps for every 1 minute
Therefore,
The slope of the line is 2 and Jan runs 2 laps for every minute.
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you'll need to write an equation that relates x and y for points along the incline. what is this equation?
The equation whigh relates x and y points along the incline is: y = 2x - 3
We know that the general form of a slope - intercept form of equation of line is :
y = mx + c
m = slope
and c = y-intercept
We know that slope is nothing but angle of incline.
From figure we can observe that the line passes through points (3, 3) and (6, 9)
Using the formula of slope,
m = (9 - 3) / (6 - 3)
m = 6/3
m = 2
So the equation of line would be
y = 2x + c
As line passes though point (3, 3),
3 = 2(3) + c
3 = 6 + c
c = - 3
So, the equation that relates x and y for points along the incline is:
y = 2x - 3
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The complete question is:
All three points displayed are on the line. you'll need to write an equation that relates x and y for points along the incline. what is this equation?
A bleach and water solution with a 2:3 ratio means: A 1/3 part bleach and 2/3 part water B 2 cups of bleach and 3 cups of water C 3 cups of bleach and 2 cups of water
The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.
A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.
To understand this ratio, let's break it down using different units:
A. 1/3 part bleach and 2/3 part water:
If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.
B. 2 cups of bleach and 3 cups of water:
If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.
C. 3 cups of bleach and 2 cups of water:
If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.
Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.
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There are 210 concrete blocks available to make a retaining wall. The bottom three rows will all have the same number of blocks. The next six rows will each have two blocks fewer than the row below it. How many blocks are in each row?
The number of blocks in each row is 25 and 23.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
There are 210 concrete blocks available to make a retaining wall.
The bottom three rows will all have the same number of blocks.
The next six rows will each have two blocks fewer than the row below it.
Now, let the block in lower row be x
Then blocks in upper will be x-2
So,
3x+6(x-2)=210
3x+6x-12=210
9x=222
x=25
x-2=23
Therefore, by algebra the answer will be 25 and 23.
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A company uses a coding system to identify its clients. each code is made up of two letters and a sequence of digits, for example ad108 or rr45789. the letters are chosen from a, d, r, s and i. letters may be repeated in the code. the digits 0 to 9 are used , but no digit may be repeated in the code. how many different clients can be identified with a coding system that is made up of two letters and two digits?
The correct answer is option 3: 2250. To calculate the number of different clients that can be identified with a coding system we need to multiply the number of options for each component.
For the two-letter component, there are five options (A, D, R, S, U) that can be chosen for each letter. Since repetition is allowed, there are 5 choices for the first letter and 5 choices for the second letter. Therefore, there are 5 x 5 = 25 possible combinations of two letters.
For the two-digit component, there are 10 options (0-9) for the first digit. Since no digit can be repeated, there are 9 options for the second digit (one less than the available options). Therefore, there are 10 x 9 = 90 possible combinations of two digits.
To calculate the total number of different clients that can be identified, we multiply the number of options for the two-letter component (25) by the number of options for the two-digit component (90). This gives us a total of 25 x 90 = 2250 different clients that can be identified with the coding system.
#A company uses a coding system to identify its clients. Each code is made up of two letters and a sequence of digits, for example AD108 or RR45789 The letters are chosen from A;D; R; S and U. Letters may be repeated in the code. The digits 0 to 9 are used, but NO digit may be repeated in the code. The number of different clients that can be identified with a coding system that is made up of TWO letters and TWO digits is: 1. 2230 2. 2240 3. 2250 4. 2210 22
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A side of the triangle below has been extended to form an exterior of 65. Find the value of x.
Check the picture below.
Determine the smallest integer value of x in the solution of the following inequality.
- 3x + 10 < 5
Answer:
x > 5/3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
-3x + 10 < 5
Step 2: Solve for x
Subtract 10 on both sides: -3x < -5Divide -3 on both sides: x > 5/3Here we see that any value x greater than 5/3 would work as a solution.
1. Compare the statement using >, <, or =
-|-5| |-10|
Answer:
1st one, A
Step-by-step explanation:
Point Z is equidistant from the sides of ARST. C R Z A B S Which must be true? A. SZ&TZ
B. RZ =R BZ
C. CTZ = ASZ
D. ASZ=ZSB
Answer:
B. RZ =R BZ
Step-by-step explanation:
Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.
Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.
Answer: vv
Step-by-step explanation:
Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.
Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.
Now, let's examine the options:
A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.
B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.
C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.
D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.
Therefore, the only statement that must be true is option B: RZ = RB.
The figure below is made up of a square with height, h, units and a right triangle with height, h units, and a base length, b units.
The area of this figure is 80 square units.
Write an equation for the area of the shape below.
Answer:
Step-by-step explanation:
A = 12 × 16 + (1/2)(12 + 8)(10) = 292 units²
The Equation for Area of figure is area of Figure, h² + 1/2(h)(b) = 80
What is Area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given:
We have the figure consist of one rectangle and one right triangle.
Now, Area of Figure,
=Area of rectangle + area of Triangle
= length x width + / x base x height
= 16 x 12 + 1/2 x 10 x 20
= 192+ 100
=292 unit²
and, if the square with height, h, units and a right triangle with height, h units, and a base length, b units.
Then, area of Figure= h² + 1/2(h)(b) = 80 square units.
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Use the Central Limit Theorem to find the probability of the indicated event, assuming that the distribution of the population data is unknown. In a certain city, employees work an average of 18.9 hours of overtime every month, with a standard deviation of 7.8 hours. What is the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours? Provide a solution showing your calculations and submit your work for marking. Include a sketch as part of your complete solution. P(X > 20)=
The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.
To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.
Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).
For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.
To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.
In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.
Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.
Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.
Here's a sketch to visualize the calculation:
|
|
|
| **
| * *
| * *
| * *
| * *
| * *
| * *
-------------------|--------------------------
18.9 | 20
The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.
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how many ways can five numbers be drawn from a group of twelve numbers if the order does not matter?
The number of ways to draw five numbers from a group of twelve numbers without considering the order is 792. This can be calculated using the combination formula nCk = n!/((n-k)!k!).
The number of ways to draw five numbers from a group of twelve numbers without considering the order is given by the combination formula.
The formula is nCk = n!/((n-k)!k!), where n is the total number of items in the group and k is the number of items to be chosen. Applying this formula to the given problem, we get 12C5 = 792.
To understand this formula intuitively, imagine picking a team of five players from a group of twelve players. The number of possible teams is the number of combinations of five players that can be formed from the group of twelve players.
For the first player, we have twelve choices. For the second player, we have eleven choices (since one player has already been chosen). Continuing this process, we have 12111098 ways to choose a team of five players if order matters.
However, since the order does not matter, we need to divide this number by the number of ways the five players can be arranged, which is 54321. Therefore, the number of possible teams is (12111098)/(54321) = 792.
In summary, the number of ways to draw five numbers from a group of twelve numbers without considering the order is 792. This can be calculated using the combination formula nCk = n!/((n-k)!k!), where n is the total number of items in the group and k is the number of items to be chosen.
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The optimal amount of x1, x2, P1, P2 and income are given by the
following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I
=4189 The new price of P1 is the foll
The total change in the consumed quantity of x₁ as per given price and income is equal to 213.
x₁ = (21/7)P₁
x₂ = (51/7)P₂
P₁ = 10
P₂ = 5
P₁' = 81
To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',
The difference between the quantities consumed at the original price and the new price.
Let's calculate the quantity consumed at the original price,
x₁ orig
= (21/7)P₁
= (21/7) × 10
= 30
x₂ orig
= (51/7)P₂
= (51/7) × 5
= 36.4286 (approximated to 4 decimal places)
Now, let's calculate the quantity consumed at the new price,
x₁ new
= (21/7)P1'
= (21/7) × 81
= 243
x₂ new
= (51/7)P2
= (51/7) × 5
= 36.4286
The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,
Change in x₁
= x₁ new - x₁ original
= 243 - 30
= 213
Therefore, the total change in the quantity consumed of x₁ is 213.
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The above question is incomplete, the complete question is:
The optimal amount of x1, x2, P1, P2 and income are given by the following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?
Please answer step by step
what is the correct similarity statements?
The correct similarity statement is: ΔRSV ≈ ΔTUR
What is similar triangles?Similar triangles are the two triangles that have same shape but different sizes.
This means that corresponding angles of similar triangles are congruent, and corresponding sides are proportional.
More properly, two triangles are similar if and only if:
Their corresponding angles are congruent.
Their corresponding sides are proportional.
This statement represents the similarity between two triangles, where ΔRSV and ΔTUR are corresponding sides of the triangles. The symbol "≈" represents the "approximately equal to" relationship, which indicates that the ratios of the corresponding sides of the two triangles are equal, and thus they are similar.
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Find the distance between (5,3)and(9,7)
Answer:
wouldnt it be 4,4?
Step-by-step explanation:
Answer:
Step-by-step explanation:
Calculate the distance between two points by filling in the x and y values of both coordinates. How do you find the distance between two points? Distance Formula : Example: For two points, (3,2) and (15, 10) the distance is calculated as: Distance = 14.42 (rounded to the nearest 100th)
Estimate the value of each quotient. Drag each division problem to the correct category shown below. Do not find the actual quotient when solving this problem.
2,456÷122,456÷12 2 , 456 ÷ 12 returned to choices list.
2
,
456
÷
12
526
÷
26
3
,
012
÷
42
6
,
960
÷
57
1
,
590
÷
35
Quotients between 10 and 100
Quotients between 100 and 1,000
Quotientes invested $ 10,000 cash to start the pepair shop.