The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.
Step 1: Calculate the z-scores for the given values using the formula:
z = (x - μ) / σ
For 189.7:
z1 = (189.7 - 189.7) / 96.7 = 0
For 213:
z2 = (213 - 189.7) / 96.7 ≈ 0.2417
Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.
P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939
Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.
To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance
Step 1: Calculate the standard error of the mean (σ_m) using the formula:
σ_m = σ / sqrt(n)
σ_m = 96.7 / sqrt(62) ≈ 12.2878
Step 2: Convert the given qualities to z-scores utilizing the equation:
z = (x - μ) / σ_m
For 189.7:
z1 = (189.7 - 189.7) / 12.2878 = 0
For 213:
z2 = (213 - 189.7) / 12.2878 ≈ 1.8967
Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.
P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702
Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
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What is the meaning of "[tex] \left \{ (x,y):\varphi(x,y) \right \}[/tex]"?
The given set is defined as the cartesian product of two sets X and Y.
In the given set,
We have to explain the meaning of {(x,y) : Ψ(x,y)}
Since we know,
The Cartesian product AxB of two sets A and B is the set of all feasible ordered pairs with A as the first element and B as the second element
Then,
AxB ={ (p,q): p ∈ A and q ∈ B}
The typical Cartesian coordinates of the plane,
Where A is the set of points on the x -axis, B is the collection of points on the y -axis, and AxB is the xy -plane, are one example.
And we also know that,
A function of two variables is a function in the sense that each input has precisely one output.
The inputs are ordered pairs of letters (x,y). Real numbers (each output is a single real number) are the outputs.
A function's domain is the set of all possible inputs (ordered pairs), but its range is the set of all possible outputs (real numbers).
The function is expressed as z = f(x,y)
Hence,
The set {(x,y) : Ψ(x,y)} is defined as the set of cartesian product of X and Y in which the cartesian product is defined by the function Ψ(x,y), which is a function of two variables.
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Given the vector u equal to 2 (cos 325°, sin 325°) and vector v equal to
6 (cos 155°, sin 155°), find the sum u + v and write your answer in
magnitude and direction form with the magnitude rounded to the nearest
tenth and the direction rounded to the nearest degree, 0° ≤ 0 < 360°.
Answer:
[tex]u+v=4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]
Step-by-step explanation:
When adding two vectors, we add their horizontal components, and then their vertical components:
[tex]u=2\langle\cos325^\circ,\sin325^\circ\rangle=\langle2\cos325^\circ,2\sin325^\circ\rangle\\v=6\langle\cos155^\circ,\sin155^\circ\rangle=\langle6\cos155^\circ,6\sin155^\circ\rangle\\\\u+v=\langle2\cos325^\circ+6\cos155^\circ,2\sin325^\circ+6\sin155^\circ\rangle\\u+v\approx\langle-3.8,1.39\rangle[/tex]
We are not done however as we need to now calculate the magnitude and the direction of the resultant vector:
Magnitude:
[tex]||u+v||=\sqrt{(-3.8)^2+1.39^2}\approx4.1[/tex]
Direction:
[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{1.39}{-3.8}\biggr)\approx-20^\circ=180-20^\circ=160^\circ[/tex]
Therefore, the resultant vector is about [tex]4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]
The assets and liabilities of a 22-year-old recent college graduate are listed below.
Furniture $4,091
Car Loan $6,060
Credit Card Balances $3,940
Savings Account Balance $2,143
Student Loans $29,400
Car Value $21,500
Equipment $4,805
The college graduate is hired at a law firm with a $10,000 signing bonus, that will be deposited into the savings account. The firm also agrees to immediately pay off $25,000 in student loan debt. What is the college graduate's new net worth?
$11,309
$14,400
$23,643
$28,139
Record Examination) are normally distributed with a mean of 555 and a standard
deviation of 110. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score below 335.
The percentage of people taking the test who score below 335 is
Answer:
2.5%
Step-by-step explanation:
You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.
Z scoreThe z-score of 335 is ...
Z = (X -µ)/σ
Z = (335 -555)/110 = -220/110 = -2
DistributionThe empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.
P(X < 335) = 5%/2 = 2.5%
The percentage of people taking the test who score below 335 is 2.5%.
<95141404393>
QUESTION 1 Below is a recipe for baking brown bread. Ingredients O O 0 0 ● 1 package (ounce) active dry yeast 2 cups warm water (110°F to 115°F) 3 tablespoons sugar 1 tablespoon salt 2 tablespoons canola oil Note that you may use the following conversions: 1 ounce = 28 grams 1 cup = 250ml °C (°F 32) ÷ 1,8 6-to 6 cups all-purpose flour 4 1.1 How many grams of active dry yeast must be used for the bread recipe? 1.2 Calculate the maximum temperature of the water in degree celsius that must be used to make the bread. 1.3 Convert 2 cups of warm water to millilitres. 4 1,4 1 tablespoon= 15 ml, determine the ratio of warm water to canola oil. Give the ratio in (2) (3) (2)
Answer:
Step-by-step explanation:how many grams of active dry yeast must be used for bread recipe
Find the arithmetic means in the given sequence. 175, ?, ?, ?, 235 a. 185, 195, 205 c. 220, 205, 190 b. 195, 215, 225 d. 190, 205, 220 Please select the best answer from the choices provided A B C D
Answer:
Step-by-step explanation:
To find the arithmetic means in the given sequence, we need to determine the missing numbers between 175 and 235.
Let's calculate the differences between consecutive terms:
1st difference: 235 - 175 = 60
2nd difference: (Next number) - (Previous number) = (Next number) - 235
Since the differences are constant, we can add the same value to each term to find the missing numbers.
Let's calculate the missing numbers using the 1st difference:
175 + 60 = 235
175 + 60 + 60 = 295
175 + 60 + 60 + 60 = 355
Now we have the complete sequence: 175, 235, 295, 355.
To find the arithmetic means, we take the average of consecutive terms:
1st arithmetic mean: (175 + 235) / 2 = 205
2nd arithmetic mean: (235 + 295) / 2 = 265
3rd arithmetic mean: (295 + 355) / 2 = 325
Among the given choices, the correct answer is:
c. 220, 205, 190
This answer represents the correct sequence of arithmetic means between 175 and 235.
Emma runs 12km
Cycles 26km
Running speed X km/m
Cycling speed 10km/hr faster than running speed
Total time taken 22 hrs and 48 minutes
An expression for time in hrs he takes to run 12km is 12/x
Show time of x for the total time he takes in hrs
The value of x in the expression is 66/114.
Let's begin by addressing the issue in detail:
Emma runs 12 km, hence the time it takes her to complete that distance is 12/x hours.
Emma cycles 26 kilometers at a speed that is 10 kilometers per hour faster than she runs.
Her cycling pace is therefore (x + 10) km/hr. Her cycle distance is 26 kilometers, which can be calculated as 26/(x + 10) hours.
Emma's total time spent cycling and running is 22 hours and 48 minutes. By dividing 48 minutes by 60, we can translate it to hours: 48/60 = 0.8 hours.
We can now formulate an equation to express the entire amount of time spent:
12/x + 26/(x + 10) = 22.8
To get rid of the denominators and solve this equation, multiply both sides by x(x + 10).
12(x + 10) + 26x = 22.8x(x + 10)
To make the calculation easier:
12x + 120 + 26x = 22.8x² + 228x
Combining comparable phrases
38x + 120 = 22.8x² + 228x
Changing the equation's order:
22.8x² + 228x - 38x - 120 = 0
22.8x² + 190x - 120 = 0
By dividing the equation by 0.4, the coefficients are made simpler:
57x² + 475x - 300 = 0
Solving the equation by x = (-b ± √(b² - 4ac)) / (2a),
x = (-475 ± √(475² - 4 * 57 * -300)) / (2 * 57)
Simplifying further:
x = (-475 ± √(225625 + 68400)) / 114
x = (-475 ± √293025) / 114
x = (-475 ± 541) / 114
Now, we can calculate the two possible solutions:
x₁ = (-475 + 541) / 114
x₁ = 66 / 114
x₁ ≈ 0.579
x₂ = (-475 - 541) / 114
x₂ = -1016 / 114
x₂ ≈ -8.912
Take x = 66/114
Hence the value of x in the expression is 66/114.
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A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below:
8.5 ft height
4 ft length
13 ft width
The conical base of the silo provides stability and structural integrity, enabling the company to offer reliable storage solutions for grains. It optimizes space utilization and supports easy handling and retrieval of stored grains.
The silo manufactured by the company features a conical base, as depicted in the drawing. The given dimensions are as follows: the height is 8.5 feet, the length measures 4 feet, and the width is 13 feet.
The height of 8.5 feet refers to the vertical distance from the base of the silo to the top of the conical base. It represents the overall height of the silo structure.
The length of 4 feet represents the measurement from one side of the conical base to the other. This dimension determines the diameter of the circular base of the silo.
The width of 13 feet signifies the measurement from the front to the back of the conical base. It determines the circumference of the circular base of the silo.
With these dimensions, the silo exhibits a conical shape, where the circular base gradually tapers towards the top. This design is well-suited for storing grains, as it allows for efficient distribution of pressure and facilitates the flow of grains during loading and unloading processes.
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a circular feild has a diameter of 32 meters.
A farmer wants to build a fence around the edge of the feild.
Each metre of fence will cost £15.95
Work out the total cost of the fence
The circumference of a circle = pi x diameter
Circumference = 3.14 x 32 = 100.48 meters (rounded to two decimal places)
The farmer needs to build a fence around the edge of the field, which has a circumference of 100.48 meters. So the total length of fence needed is 100.48 meters.
Each meter of fence cost £15.95, therefore the cost of building the entire fence can be calculated as:
Total Cost = Length of fence x Cost per meter of fence Total Cost = 100.48 x £15.95 Total Cost = £1601.08
Therefore, it would cost the farmer a total of £1601.08 to build a fence around the edge of the circular field.
Answer:
$1603.47
Step-by-step explanation:
To borrow money, you pawn your guitar Based on the value of the guitar, the paunbroker loans you $720. One month later, you get the guitar back by paying the paunbroker $1272. What annual interest rate did you pay?
You will pay a simple interest rate of
(Round to the nearest whole number as needed)
To determine the annual interest rate paid, we need to calculate the simple interest for one month and then convert it to an annual rate.
The formula for simple interest is:
Simple Interest = Principal × Rate × Time
In this case, the principal amount is $720, and after one month, you pay back a total of $1272. Therefore, the interest paid is:
Interest = $1272 - $720 = $552
We can now calculate the monthly interest rate:
Rate = Interest / Principal = $552 / $720 ≈ 0.7667
To convert the monthly interest rate to an annual rate, we multiply it by 12:
Annual Rate = Monthly Rate × 12 = 0.7667 × 12 ≈ 9.20
Therefore, you paid an annual interest rate of approximately 9.20%.
Solve the inequality for w.
w+7<20
Simplify your answer as much as possible.
0
Answer:
w<13
Step-by-step explanation:
Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.
Answer:
w < 1`3
Step-by-step explanation:
Isolate the variable w on one side of the inequality sign.
w+7<20
w<20 - 7
w<13.
The number of people attending a football match as audience is stated as 31200,
correct to 3 significant figures. What could be largest and the smallest possible number
of people attending the match?
The largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.
To determine the largest and smallest possible number of people attending the football match, given that the figure is stated as 31,200 with 3 significant figures, we need to consider the range of values that can be represented within that significant figures constraint.
For a number to be stated with 3 significant figures, the last significant figure is uncertain and can be either rounded up or down.
To find the largest and smallest possible numbers, we'll consider the cases where the last significant figure is rounded up and rounded down.
Rounding up:
If we round up the last significant figure, the possible range of values is from 31,150 to 31,249.
So the largest possible number of people attending the match would be 31,249.
Rounding down:
If we round down the last significant figure, the possible range of values is from 31,100 to 31,199.
So the smallest possible number of people attending the match would be 31,100.
Therefore, the largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.
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Jim is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random.
This game is this: Jim rolls the number cube once. He wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. He loses $6.50 if a 5or 6 is rolled.
(a) Find the expected value of playing the game.
(b) What can Jim expect in the long run, after playing the game many times?
Jim can expect to gain money.
Jim can expect to lose money.
Jim can expect to break even (neither gain nor lose money).
part a.
the expected value of playing the game is found as -$0.50.
part b.)
Jim can expect to lose money in the long run if he plays the game many times because the expected value is negative.
How do we calculate?The expected outcomes and their corresponding values are:
If we roll a 1 = Jim wins $1.
If we roll a 2 =Jim wins $2.
If we roll a 3 = Jim wins $3.
If we roll a 4 = Jim wins $4.
If we roll a 5 or 6 = Jim loses $6.50.
We then calculate the value:
Expected value = (Probability of rolling a 1) × (Value of rolling a 1) + (Probability of rolling a 2) × (Value of rolling a 2) + (Probability of rolling a 3) × (Value of rolling a 3) + (Probability of rolling a 4) × (Value of rolling a 4) + (Probability of rolling a 5 or 6) × (Value of rolling a 5 or 6)
Expected value = (1/6) × $1 + (1/6) × $2 + (1/6) × $3 + (1/6) × $4 + (2/6) × (-$6.50)
EV = $1/6 + $2/6 + $3/6 + $4/6 - $13/6
EV = ($1 + $2 + $3 + $4 - $13)/6
EV = -$3/6
Expected value = -$0.50
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A curve C and a straight-line L have respective equations.
y = 2x^2 - 6x + 5
and
2y + x = 4
Find the coordinates of the points of intersection between C and L. Given that the line L is parallel to the line P passing through the points of intersection. Find the equation of line P.
The equation of line P passing through the points of intersection is y = -1/2x + 2.
To find the coordinates of the points of intersection between curve C and line L, we need to solve the system of equations formed by their respective equations.
The equations are:
C: y = 2x^2 - 6x + 5 ...(1)
L: 2y + x = 4 ...(2)
We can solve this system by substituting the value of y from equation (1) into equation (2):
2(2x^2 - 6x + 5) + x = 4
4x^2 - 12x + 10 + x = 4
4x^2 - 11x + 6 = 0
To solve this quadratic equation, we can factorize it:
(4x - 3)(x - 2) = 0
Setting each factor to zero, we get:
4x - 3 = 0 --> x = 3/4
x - 2 = 0 --> x = 2
Now, substitute these x-values back into equation (1) to find the corresponding y-values:
For x = 3/4:
y = 2(3/4)^2 - 6(3/4) + 5
y = 9/8 - 18/4 + 5
y = 9/8 - 9/2 + 5
y = 9/8 - 36/8 + 40/8
y = 13/8
For x = 2:
y = 2(2)^2 - 6(2) + 5
y = 8 - 12 + 5
y = 1
Therefore, the coordinates of the points of intersection between C and L are (3/4, 13/8) and (2, 1).
Now, we need to find the equation of line P passing through the points of intersection.
We have two points on line P: (3/4, 13/8) and (2, 1).
First, let's find the slope of line P using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - 13/8) / (2 - 3/4)
m = (-5/8) / (5/4)
m = -1/2
Now, we have the slope of line P, -1/2. We can use one of the points, let's say (3/4, 13/8), and the slope to find the equation of line P using the point-slope form:
y - y1 = m(x - x1)
Substituting the values:
y - 13/8 = -1/2(x - 3/4)
Simplifying:
y - 13/8 = -1/2x + 3/8
y = -1/2x + 3/8 + 13/8
y = -1/2x + 16/8
y = -1/2x + 2
Therefore, the equation of line P passing through the points of intersection is y = -1/2x + 2.
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Michelle’s robotics club plans to sell reusable water bottles with their logo as a fundraiser. They buy 75 water bottles for $443.25. They agree to sell each water bottle for 25% more than the price at which they were purchased. At what price should they sell each water bottle?
The required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.
Given that number of water bottles purchased is 75 and cost price (C,P) of the 75 water bottles is $443.25. The increase % on the purchase price is profit % = 25%.
To calculate the selling price when cost price and profit % is given by following steps:
Step 1 - Calculate the 25% of the cost price which gives profit.
Step 2 - Calculate SP, Selling price = Cost price + profit.
That implies, Profit = 25% of C.P.
Profit = 25/100 × 443.25.
Therefore, Profit = $110.81.
That implies, Selling price(S.P) = Cost price + profit.
S.P = 443.25 + 110.81.
Thus, S.P = $554.06.
Hence, the required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.
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2. The area of a figure is 207 m². If the
dimensions are multiplied by what will
3'
be the area of the new figure?
Answer:
Step-by-step explanation:
If the dimensions of a figure are multiplied by 1/3, then the area of the new figure will be 1/9 of the original area.
Therefore, if the area of the original figure is 207 m², then the area of the new figure will be 23 m² (207 m² * 1/9).
I hope this helps!
Answer:
23 m^2
Step-by-step explanation:
As all of the dimensions have been multiplied by a constant, the two figures are similar to one another.
The ratio between the areas of two similar figures is given by the ratio of similarity (= the ratio between two similar sides between the two figures) squared.
In our case, the ratio of similarity is 1/3.
Therefore, the ratio between the two areas is (1/3)^2 = 1/9.
[tex]207 \times \frac19 = 23 \left[\text{m}^2\right][/tex]
Find the equation of the regression line for the data in the table.
X
y
25 6
44 13
46 14
52 10
57 13
Round your answers to the nearest tenth.
x + =
y
Submit
The equation for the regression line from the data is y = -0.98x + 56.8
Given data ,
To find the equation of the regression line, we will use the method of least squares. The regression line is represented by the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
We need to calculate the values of m and b. Let's begin by finding the mean values of x and y:
Mean of x (x₁) = (6 + 13 + 14 + 10 + 13) / 5 = 12.2
Mean of y (y₁) = (25 + 44 + 46 + 52 + 57) / 5 = 44.8
Next, we calculate the deviations from the mean for both x and y:
Deviation from the mean of x (Δx) = x - x₁
Deviation from the mean of y (Δy) = y - y₁
Now, we calculate the sum of the products of the deviations from the mean:
Σ(Δx * Δy) = (6 - 12.2) * (25 - 44.8) + (13 - 12.2) * (44 - 44.8) + (14 - 12.2) * (46 - 44.8) + (10 - 12.2) * (52 - 44.8) + (13 - 12.2) * (57 - 44.8)
Σ(Δx * Δy) ≈ -51.6
Next, we calculate the sum of the squared deviations from the mean of x:
Σ(Δx²) = (6 - 12.2)² + (13 - 12.2)² + (14 - 12.2)² + (10 - 12.2)² + (13 - 12.2)²
Σ(Δx²) ≈ 52.8
Now, we can calculate the slope (m) using the formula:
m = Σ(Δx * Δy) / Σ(Δx²)
m ≈ -51.6 / 52.8 ≈ -0.98
Finally, we can calculate the y-intercept (b) using the formula:
b = y₁ - m * x₁
b ≈ 44.8 - (-0.98) * 12.2 ≈ 56.8
Hence , the equation of the regression line for the given data is:
y = -0.98x + 56.8
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What are the approximate coordinates in the rectangular plane that represent the polar coordinates (4, 110 degrees).? Round values to the nearest thousandth.
A.(3.759, –1.368)
B.(–3.996, –0.177)
C.(–1.368, 3.759)
D.(–0.342, 0.940)
Twenty-five psychology instructors have formed a committee to pick next year's textbook, and they have narrowed their decision down to two equally good books, one with a better bibliography and references, and the other with a better format and illustrations. Since the books are considered to be equally good, we will assume the probability an instructor chooses either book is 0.5 and the instructors' decisions are made independently. Using the binomial distribution, find the probability 15 or more instructors choose the book with the better format and illustrations.
To find the probability that 15 or more instructors choose the book with the better format and illustrations, we can use the binomial distribution formula.
Let's denote the event of an instructor choosing the book with the better format and illustrations as "success" (S), and the event of an instructor choosing the other book as "failure" (F). The probability of success is p = 0.5, and the probability of failure is q = 1 - p = 0.5.
We want to find the probability of 15 or more successes in a sample of 25 instructors. We can calculate this probability by summing the probabilities of exactly 15, 16, 17, ..., 25 successes.
P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)
Using the binomial distribution formula, the probability of exactly k successes in a sample of n trials is:
P(X = k) = C(n, k) * p^k * q^(n-k)
where C(n, k) is the binomial coefficient "n choose k," given by:
C(n, k) = n! / (k! * (n-k)!)
Applying this to our problem, we can calculate the probability as follows:
P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)
= Σ[ k = 15 to 25 ] ( C(25, k) * p^k * q^(25-k) )
Let's calculate this probability using the binomial distribution formula:
P(X ≥ 15) = Σ[ k = 15 to 25 ] ( C(25, k) * (0.5)^k * (0.5)^(25-k) )
Calculating this sum gives us the probability that 15 or more instructors choose the book with the better format and illustrations.
The amount of fast fashion waste (w) produced by city with a population (x)
is given by W=f(x). Waste is measured in tons per season (autumn/winter,
or spring/summer) and population is measured in thousand of people. The
city of Dunwoody, Georgia has a population of 53,300 and produces 5 tons
of waste fashion during the autumn/winter season. Express this in terms of
(f) and write a statement explaining what the means
The function implies that a city with a population of 53.3 thousand people produces 5 tons of fast fashion waste during the autumn/winter season.
How to explain the functionThe city of Dunwoody, Georgia has a population of 53,300, which is equal to 53.3 thousand people. So, we can express this in terms of f as follows:
W = f(53.3) = 5
This means that the function f(x) gives the amount of fast fashion waste produced by a city with a population of x thousand people. In this case, f(53.3) = 5, which means that a city with a population of 53.3 thousand people produces 5 tons of fast fashion waste during the autumn/winter season.
This is a significant amount of waste, and it is important to be aware of the environmental impact of fast fashion. Fast fashion is a term used to describe the rapid production of cheap, trendy clothing.
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what is the Euclid math contest and when can you take it
The Euclid math contest is the annual contest held by the University of Waterloo. The students from grade-11 to grade-12 can participate in the Euclid math contest.
Euclid contest is a Mathematics contest for senior-level high school students. This contest was participated by nearly 22000 students worldwide every year. This contest allows the students to demonstrate their knowledge of secondary school mathematics. This competition was held by the University of Waterloo.
The senior-grade students will participate in this contest and it takes 2 and a half hours to complete the contest. It has 10 questions and the total mark for the contest is 100. The University of Waterloo values the results from the Euclid math contest when it comes to admission and scholarship offers.
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Warm-Up
Jug
Use the diagram below to answer the questions.
Intro
K
P
M
Which are shown on the diagram? Check all that apply.
O
OKM
Ojk
OPK
OLJK
COM
Dong
KM, JK, PK, and MJ are shown on the diagram.
Then the correct options are B, C, D, and F.
Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
A line segment in mathematics has two different points on it that define its boundaries.
All the line segments will be
JK, JM, KM, MP, PK, and KL
The triangle KPM.
And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.
Then the correct options are B, C, D, and F.
Learn More about the coordinate geometry visit:
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12 out of 50 girls like shoes. what % of girls like shoes
Ms. Baker has a class of 15 students. She can spend $21 on each student to buy math supplies for the year. She first buys all of her students calculators, which
costs a total of $67.65, After buying the calculators, how much does she have left to spend on each student?
help i need the answer asap please
Answer:
664
Step-by-step explanation:
6x17
6x17
10x6
10x6
10x17
10x17
add them all up and u get 664
Can someone please explain how to get a and b step by step?
[tex]3a-2b=13\\4a+b=21|\cdot2\\\\3a-2b=13\\\underline{8a+2b=42}\\11a=55\\a=5\\\\3\cdot5-2b=13\\2b=2\\b=1[/tex]
Answer:
a = 5, b = 1
Step-by-step explanation:
We need to realize that in a parallelogram, opposite sides are congruent. Therfore, the length of NO and MP must be the same if we assume that Quadrilateral MNOP is a parallelogram.
Length of NO = 21
Length of MP = 4a + b
Therfore, we can get this equation: 4a + b = 21
We can do the same with the other 2 sides to get: 3a - 2b = 13
As you can see, this is a systems of equations! Lets solve it!
To find the values of "a" and "b" in the given system of equations:
Equation 1: 4a + b = 21
Equation 2: 3a - 2b = 13
We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method:
Multiply Equation 1 by 2:
2(4a + b) = 2(21)
8a + 2b = 42
Now, we can add Equation 2 and the modified Equation 1 to eliminate the "b" term:
(3a - 2b) + (8a + 2b) = 13 + 42
3a + 8a - 2b + 2b = 55
11a = 55
Divide both sides of the equation by 11:
a = 55 / 11
a = 5
Substitute the value of "a" into Equation 1 to find "b":
4(5) + b = 21
20 + b = 21
b = 21 - 20
b = 1
Therefore, the solution to the system of equations is a = 5 and b = 1.
Therfore, the answer is B, which is what you got as well! Good job!
~~~Harsha~~~
Which graph shows the image of the triangle reflected across the line of reflection shown? On a coordinate plane, a triangle has points (2, 4), (4, 2), (9, 6). A line of reflection is at y = 3. On a coordinate plane, a triangle has points (negative 1, negative 3), (2, 4), (4, 2). On a coordinate plane, a triangle has points (1, 4), (4, 2), (2, 0). On a coordinate plane, a triangle has points (2, 0), (4, 2), (9, negative 2). On a coordinate plane, a triangle has points (2, 2), (4, 4), (9, 0). Mark this and return
The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)
Thus, option (D) is correct.
Find out more on transformation at: https://brainly.com/question/19040905
How do I find the value of x?
[tex]\cfrac{x}{4}-\cfrac{x+10}{2}=3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{x}{4}-\cfrac{x+10}{2} \right)=4(3)}\implies x-(2x+20)=12 \\\\\\ x-2x-20=12-x-20=12\implies -20=12+x\implies \boxed{-32=x} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{2x+1}{5}-\cfrac{x-3}{7}=-2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{2x+1}{5}-\cfrac{x-3}{7} \right)}=35(-2) \\\\\\ 14x+7-(5x-15)=-70\implies 14x+7-5x+15=-70 \\\\\\ 9x+22=-70\implies 9x=-92\implies \boxed{x=-\cfrac{92}{9}}[/tex]
PLS HELP THANK YOUUUUUUU
7 1 /4 x − x =9 3/ 8
Answer:
1.5 is the correct answer