Step 1: To tell the null and alternative hypotheses for the test:
Null hypothesis (H0): The mean ACT score of first-born children is equal to or greater than the mean ACT score of second-born children. μ1 ≥ μ2Alternative hypothesis (Ha): The mean ACT score of first-born children is lower than the mean ACT score of second-born children. μ1 < μ2What are the other stepsStep 2: The test statistic for this scenario is the z-score, calculated as:
Step 3 involves comparing the chosen significance level (1% in this instance) with the test statistic to decide whether to reject or accept the null hypothesis. In case the test statistic falls within the critical region, the null hypothesis is rejected, but if it doesn't, the null hypothesis is not rejected.
We can also determine the p-value related to the test statistic and assess its compatibility with the selected level of significance. If the significance level exceeds the p-value, we do not reject the null hypothesis, but if the p-value is lower, then we reject the null hypothesis.
Learn more about hypothesis from
https://brainly.com/question/606806
#SPJ4
By how much could the largest sample observation be decreased without affecting the value of the median?
Largest value can decreased by 49 without affecting the value of median.
How to find Median in a given stats?The median is the middle score in the set. To find the median, you take these steps:
Step 1: Arrange the scores in numerical order
Step 2: Count how many scores you have
Step 3: Divide the total scores by 2
Step 4: If you have an odd number of total scores, round up to get the position of the median number. If you have an even number of total scores, go to the number in that position and average it with the number in the next higher position to get the median.
For example:
given sets: 5, 4, 3, 6, 8
now rearrange the sets in increasing order: 3, 4, 5, 6, 8
median = ( n + 1 ) / 2 = ( 5 + 1) / 2 = 3
here median = 5
We have given that:
384, 350, 354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.
when we arrange it in increasing order.
here n = 26
median = ( n + 1 ) / 2
median = average of 13th and 14th element
median = 371
larger value can be decreased by 420 - 371 = 49
Hence,
Largest value can decreased by 49 without affecting the value of median.
Learn more about "Median and Statistics" from here: https://brainly.com/question/28060453
#SPJ4
Disclaimer: The question given was incomplete on the portal. Here is the complete question.
Question: A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape:
384, 350, 354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.
By how much could the largest sample observation be decreased without affecting the value of the median?
The largest sample observation could be decreased by 54.5 without affecting the value of the median.
We have given the data:
384, 350, 354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.
Now, we arrange it in increasing order.
321, 329, 330, 339, 350, 354, 354, 359, 361, 363, 365, 366, 369, 370, 374, 376, 376,378, 384, 393, 394, 396, 398,404, 424
Here n = 26
median = ( n + 1 ) / 2
median = 369 + 370 / 2
median = 369.5
Larger value can be decreased by 424 - 369.5= 54.5
Therefore, the largest sample observation could be decreased by 54.5 without affecting the value of the median.
Learn more about median here:
brainly.com/question/28060453
#SPJ4
The question given was incomplete on the portal. Here is the complete question.
A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape:
384, 350, 354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.
By how much could the largest sample observation be decreased without affecting the value of the median?
Please help need done by 2:00 pm
Based on the instructions given, the next step would be to subtract 40 to the current number.
How to explain the informationInitial number: 5.
Subtract 40: Assuming we start with the number 5, subtracting 40 would give us -35.
Subtract 5: If we take the result from step 2 (-35) and subtract 5, we would have -40.
At this point, the current number is -40. The next step you provided is "A - Subtract 40
Learn more about numbers on
https://brainly.com/question/25734188
#SPJ1
2/3 of 27 equal 25% of a number
Answer:
The number is 72
Step-by-step explanation:
2/3*27 = 2*9 = 18
so 18 = 25%
25% = 1/4
so 1/4 = 18/?
so ? = 18*4 = 72
Answer:
x=72
Step-by-step explanation:
This is an easy equation.
2/3*27=25/100x
solve.
2/3 * 27 is 18
18=25/100x
Divide. (25/100 can be converted to 1/4
Divide 18 by 1/4x
x=72!
Cheers, I hope you can understand.
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
to determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
The correlation coefficient between the student's height and the distance they were able to jump is 0.86.
What is the correlation coefficient?The correlation coefficient is a number that ranges from -1 to 1. It shows the strength of the relationship between two variables. It also shows the direction of the relationship.
Positive correlation is when the two variables move in the same direction. If one variable increases, the other variable also increases. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases. Zero correlation is when there is no relationship between the variables.
The correlation coefficient is calculated using a financial calculator.
Here is the complete question:
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
To learn more about correlation, please check: https://brainly.com/question/27246345
#SPJ1
Answer:
It's 0.92
Step-by-step explanation:
I took the test already
Help me please it’s the last question and I’m stuck
Answer:
Step 3 i think because 10-7+7=13 because if u do that problem u actually get 10 instead of 13
Step-by-step explanation:
because 10-7+7=13 because if u do that problem u actually get 10 instead of 13
The curve C is given parametrically by : = cost, y=sint. Se up an integral but do not evaluate to find the arc length of the curve within the interval of 0 sts = Os=fo Vsin’t - 4sin’t : cos?idt Os = lof v1+ 4sin’t • cos?tdt Os = so sin’t + cositat Os = l. Vsin’t + 4sin’t · cos?tdt =
The arc length of the curve C between t=0 and t=2π is 2π units.
The formula for finding arc length for a curve parameterized by x = f(t), y = g(t) between t=a and t=b is:
L = ∫a^b √[f'(t)^2 + g'(t)^2] dt
In this case, we have x = cos(t) and y = sin(t). Therefore, we have:
dx/dt = -sin(t)
dy/dt = cos(t)
Using these derivatives, we can calculate the integrand:
√[(-sin(t))^2 + (cos(t))^2] = √[1] = 1
So the integral for finding arc length becomes:
L = ∫0^2π 1 dt
Simplifying this integral, we get:
L = [t]0^2π = 2π
Therefore, the arc length of the curve C between t=0 and t=2π is 2π units.
To learn more about units visit:
https://brainly.com/question/19244145
#SPJ11
I will give you a Brainliest
Answer:
B isa the answer for me it might be wrong for you or switch them
Step-by-step explanation:
In Alaska, the coldest temperature ever recorded is -80°F. That is much colder than in
Hawaii, where the coldest recorded temperature is 15°F.
How many degrees warmer is Hawaii's coldest recorded temperature than Alaska's?
Hawaii's coldest recorded temperature is 95°F warmer than Alaska's coldest recorded temperature. This is primarily because Hawaii is closer to the equator and has a tropical climate that is warm and humid throughout the year. The coldest temperature ever recorded in Alaska is -80°F, while the coldest recorded temperature in Hawaii is 15°F.
Temperature is a measure of the amount of heat in an object. It's typically measured in Fahrenheit, Celsius, or Kelvin. The coldest temperature ever recorded in Alaska is -80°F, whereas the coldest temperature ever recorded in Hawaii is 15°F. This implies that Hawaii's coldest temperature is 95°F warmer than Alaska's coldest.
Because of its location, Alaska's temperature can be very harsh. In the winter, temperatures frequently drop below freezing, making it difficult for people and animals to live there. In contrast, Hawaii has a tropical climate that is warm and humid throughout the year. It's also located closer to the equator, where the sun's rays are stronger, and the temperature is higher.
Hawaii's coldest recorded temperature is 95°F warmer than Alaska's coldest recorded temperature. This is primarily because Hawaii is closer to the equator and has a tropical climate that is warm and humid throughout the year. Therefore, Hawaii's coldest recorded temperature is 95°F warmer than Alaska's coldest recorded temperature.
To know more about the tropical climate, visit:
brainly.com/question/885982
#SPJ11
WHAT IS 0.5/1.5 SQUARED
Step-by-step explanation:
.5 / 1.5 is 1/3 (1/3)^2 = 1/9
Answer: 0.09
Step-by-step explanation:
0.5 ÷ 1.5 = 0.3 0.3squared = 0.09
Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
t = 10.296 sin 60.945°i + 10.296 cos 60.945°j
t = 10.296 sin 240.945°i + 10.296 cos 240.945°j
t = 10.296 cos 60.945°i + 10.296 sin 60.945°j
t = 10.296 cos 240.945°i + 10.296 sin 240.945°j
The correct answer is option (C).
What are the fundamental forms of trigonometry?Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).
The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:
t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)
The vector's magnitude is given by:
|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296
The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.
θ = tan⁻¹ (–9/–5) ≈ 60.945°
In trigonometric form, the vector t is thus represented as follows:
t = [t|cos|i] + [t|sin|j]
We get the following by altering the values of |t| and:
t = 10.296 cos I + 10.296 sin j of angle 60.945
As a result, the following is the proper trigonometric representation of the vector t:
t = 10.296 cos I + 10.296 sin j of angle 60.945
Thus, alternative is the right response (C).
To know more about Trignometric visit:
https://brainly.com/question/29076920
#SPJ1
nine increased by a number....Turned into a mathematical expression
The mathematical expression for "nine increased by a number" is,
9 + x, ∀x>0
Use the concept of inequality defined as:
An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.
It signifies that the expression on the left should be more or smaller than the expression on the right, or vice versa. Literal inequalities occur when the relationship between two algebraic expressions is defined using inequality symbols.
The given statement is: "Nine increased by a number"
Consider a number x which is greater than 0.
If nine is increased by a number then the number 9 will be 9 + x.
As 9 + x > 9 for every x > 0,
Therefore, the given statement can be written as,
9 + x, ∀x>0
Hence the mathematical expression for the given statement is,
9 + x, ∀x>0
To learn more about inequality visit:
https://brainly.com/question/30231190
#SPJ6
(L1) Given: CM↔ is a perpendicular bisector of AB¯ at point MProve: AC=BC
CM is the perpendicular bisector of AB at M, it means that CM is perpendicular to AB, and AM=BM. Therefore, we have two right triangles, triangle AMC and triangle BMC, with a shared side CM, and AM=BM.
By the Pythagorean theorem, we know that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Applying this to triangles AMC and BMC, we have:
AC² = AM² + CM²
BC² = BM² + CM²
Since AM=BM, we can substitute AM for BM in the second equation, giving:
BC² = AM² + CM²
Since the left-hand sides of these two equations are equal (by the given that CM is the perpendicular bisector of AB), we can set their right-hand sides equal to each other and simplify:
AC² = BC²
Taking the square root of both sides gives us:
AC = BC
for such more question on perpendicular bisector
https://brainly.com/question/18991632
#SPJ11
the depth of water in tank a in inches is modeled by a differentiable and increasing function h for
The depth of water in tank A is modeled by a differentiable and increasing function h.
This means that the function h describes how the depth of water changes as time passes.
The fact that it is differentiable means that the function has a well-defined slope at every point, which indicates how quickly the depth is changing. This means that the function is continuous and smooth, with no sharp turns or corners.
Furthermore, the fact that the function is increasing means that the depth is always getting higher over time.
This makes sense since water is constantly being added to the tank.
Hence, the depth of water in tank A is described by a differentiable and increasing function h, which means that the function has a well-defined slope at every point and that the depth is always getting higher over time.
learn more about function click here:
https://brainly.com/question/11624077
#SPJ11
if marked price = 1,540 during the off season a discount was given and it was sold for 1,463. find the discount and the discount percent
Answer:
The discount is $77, and the discount percent is 5%
Step-by-step explanation:
Discount: $1,540 - $1,463 = $77
Discount percent: $1,463 / $1,540 = 0.95, 1.00 - 0.95 = 0.05, 0.05 = 5%
x - 9 = 1/4x + (1/4x + 12) +(1/4x - 3)
Answer:
x=72
Step-by-step explanation:
x-9=3/4 ⋅ x+9
1/4 ⋅ x -9=9
1/4⋅x=18
x=72
What are the different ways you can solve a system of linear equations in two variables? What is the process for solving a system using each method?
19. The range of the graph of y = cos x is 0 ≤ y ≤ 2 -1≤y≤1 a. b. C. d. -2x ≤ x ≤ 21 YER
The range of the graph of y = cos x is -1 ≤ y ≤ 1.
Option (b) -1 ≤ y ≤ 1 is the correct answer.
The range of a function refers to the set of all possible output values that the function can take. For the function y = cos x, the cosine function oscillates between -1 and 1 as the input x varies.
When x is at its maximum value (such as x = 0, 2π, 4π, etc.), the cosine function evaluates to 1. Similarly, when x is at its minimum value (such as x = π, 3π, 5π, etc.), the cosine function evaluates to -1.
Therefore, the range of the graph of y = cos x is -1 ≤ y ≤ 1, which means that y can take any value between -1 and 1, inclusive. This is option (b) in the given choices.
Learn more about graph from
https://brainly.com/question/19040584
#SPJ11
What are the MRSs? Determine if there is a diminishing MRS
a. U(x,y)=3x+y
b. U(x,y)=x.y
c. U(x,y)=x⋅y
d. U(x,y)=x2−y2
e. U(x,y)=x+yx.y 3.
Consider each of a. U(x,y)=x0.1y0.4 b. U(x,y)=min(αx,βy) c. U(x,y)=αx+βy calculate the following i. Demand curves for x and y ii. Indirect utility function iii. (Indirect) expenditure function iv. Show that the demand curve is homogeneous in degree zero in terms of income and prices
a. The MRS is constant (not diminishing) at 1/3.
U(x,y) = 3x + y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / 3
The MRS is constant (not diminishing) at 1/3.
b. The MRS is diminishing because as y increases, the MRS decreases.
U(x,y) = x * y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / y
The MRS is diminishing because as y increases, the MRS decreases.
c. The MRS is diminishing because as y increases, the MRS decreases.
U(x,y) = x * y
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = 1 / y
Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.
d. The MRS depends on the ratio of y to x and can vary.
U(x,y) = x^2 - y^2
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x
The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.
e. The MRS depends on the values of x and y and can vary.
U(x,y) = x + y / (x * y)
The MRS for this utility function can be found by taking the partial derivative of x concerning y:
MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)
The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.
Now let's move on to the second part of the question:
For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.
To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.
To know more about partial derivative:
https://brainly.com/question/32387059
#SPJ11
The difference of 13 and the product of 3 and a number a is equal to 5.
Answer:
a=8/3
Step-by-step explanation:
Ok, so first, we are gonna make this an equation
13-3a=5
Now, we will subtract 13 from 5
Now we have -3a=-8
Now, divide -8 by -3 and we get...
a=8/3
Theorem 7.1.2 (Calculations with the Fourier transform)
Given f € L¹(R), the following hold:
(i) If f is an even function, then
f(y) = 2 [infinity]J0 f(x) cos(2πxy)dx.
(ii) If f is an odd function, then
f(y) = -2i [infinity]J0 f(x) sin(2πxy)dx.
(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.
(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.
The Fourier transform pair for a function f(x) is defined as follows:
F(k) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx
f(x) = (1/2π) ∫[-∞,∞] F(k) \(e^{2\pi iyx}\) dk
Now let's prove the given properties:
(i) If f is an even function, then f(y) = 2∫[0,∞] f(x) cos(2πxy) dx.
To prove this, we start with the Fourier transform pair and substitute y for k in the Fourier transform of f(x):
F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx
Since f(x) is even, we can rewrite the integral as follows:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[-∞,0] f(x) \(e^{2\pi iyx}\) dx
Since f(x) is even, f(x) = f(-x), and by substituting -x for x in the second integral, we get:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[0,∞] f(-x) \(e^{2\pi iyx}\)dx
Using the property that cos(x) = (\(e^{ ix}\) + \(e^{- ix}\))/2, we can rewrite the above expression as:
F(y) = ∫[0,∞] f(x) (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dx
Now, using the definition of the inverse Fourier transform, we can write f(y) as follows:
f(y) = (1/2π) ∫[-∞,∞] F(y) \(e^{2\pi iyx}\) dy
Substituting F(y) with the expression derived above:
f(y) = (1/2π) ∫[-∞,∞] ∫[0,∞] f(x) \(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\)/2 dx dy
Interchanging the order of integration and evaluating the integral with respect to y, we get:
f(y) = (1/2π) ∫[0,∞] f(x) ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy dx
Since ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy = 2πδ(x), where δ(x) is the Dirac delta function, we have:
f(y) = (1/2) ∫[0,∞] f(x) 2πδ(x) dx
f(y) = 2 ∫[0,∞] f(x) δ(x) dx
f(y) = 2f(0) (since the Dirac delta function evaluates to 1 at x=0)
Therefore, f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx, which proves property (i).
(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.
The proof for this property follows a similar approach as the one for even functions.
Starting with the Fourier transform pair and substituting y for k in the Fourier transform of f(x):
F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx
Since f(x) is odd, we can rewrite the integral as follows:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx - ∫[-∞,0] f(x) \(e^{-2\pi iyx}\) dx
Using the property that sin(x) = (\(e^{ ix}\) - \(e^{-ix}\))/2i, we can rewrite the above expression as:
F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) - \(e^{2\pi iyx}\)/2i dx
Now, following the same steps as in the proof for even functions, we can show that
f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx
This completes the proof of property (ii).
In summary:
(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.
(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.
To know more about even function click here :
https://brainly.com/question/32608607
#SPJ4
(a) An angle measures 83°. What is the measure of its supplement?
(b) An angle measures 65°. What is the measure of its complement?
Rocky Mountain Tire Center sells 10,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 40% of the purchase price of the tires per year. The purchase price is $25 per tire if fewer than 200 tires are ordered,$17 per tire if 200 or more, but fewer than 8,000, tires are ordered, and $13 per tire if 8,000 or more tires are ordered.
a) How many tires should Rocky Mountain order each time it places an order?
b) What is the total cost of this policy?
a) Rocky Mountain should order 200 tires each time it places an order.
b) The total cost of this policy is $17,160.
a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:
If fewer than 200 tires are ordered: The purchase price is $25 per tire.
If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.
If 8,000 or more tires are ordered: The purchase price is $13 per tire.
Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.
b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:
Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200
Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950
Therefore, the total cost of this policy is $40,950.
Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.
To know more about time, visit
https://brainly.com/question/27792043
#SPJ11
How do you translate an entire triangle?
To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points
Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.
There are some steps of translating the triangle:
Step 1: Find the coordinates of each of the triangle's vertices in step one.
Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.
Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.
To learn more about translation of triangle link is here
brainly.com/question/17052587
#SPJ4
solve for x -2 (1-4x) = 3x + 8
Answer:
x = 2Step-by-step explanation:
\(-2 (1-4x) = 3x + 8\\\\Expand\: -2(1-4x) \: :-2+8x\\-2+8x=3x+8\\\\\mathrm{Add\:}2\mathrm{\:to\:both\:sides}\\-2+8x+2=3x+8+2\\\\Simplify\\8x=3x+10\\\\\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}\\8x-3x=3x+10-3x\\\\Simplify\\5x =10\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\frac{5x}{5}=\frac{10}{5}\\\\Simplify\\\\x =2\)
Answer:
2
Step-by-step explanation:
-2 (1-4x) = 3x + 8
-2 × 1 - -2 × 4x = 3x + 8
-2 + 8x = 3x + 8
8x - 3x = 8 + 2
5x = 10
x = 10/5
x = 2
hope this helps you!
A certain number of special spells must be cast to protect the secret hiding place of the Order of the Phoenix. Each member of the Order is capable of casting the same number of these spells per hour. If two wizards were to join the Order, casting the protection spells can be completed in three hours instead of four hours. How many wizards are in the Order?
Answer: There are 6 wizards in the order.
Step-by-step explanation:
Let's suppose that:
Let's define S as the rate at which each wizard casts the spells.
Let's suppose also that there are N wizards in the order.
We know that the N wizards can complete the task in 4 hours, then:
(N*S)*4h = 1
(the 1 represents the completed task)
And we know that if 2 more wizards joined, the total task would be completed in 3 hours, then we have the equation:
(N+2)*S*3h = 1
Then we have the system of equations:
(N*S)*4h = 1
(N+2)*S*3h = 1
And we want to find the value of N.
To start, we need to isolate S in one of the equations, i will isolate S in the first equation:
S = (1/N*4h)
Now we can replace this in the second equation, to get:
(N+2)*(1/N*4h)*3h = 1
(N + 2)*3/(4*N) = 1
Now we can solve this for N.
(3/4) + 6/(4N) = 1
Now we can multiply by N in both sides to get:
(3/4)*N + 6/4 = N
6/4 = N - (3/4)*N = (1/4)*N
(6/4)*4 = N
6 = N
There are 6 wizards in the order.
If the given ΔXYZ is rotated by 180 degrees around point X in a clockwise direction, what are the new coordinates of the Y and Z vertices? Select the two correct answers.
Answer:
Options C and D
Step-by-step explanation:
From the graph attached,
Coordinates of the vertices,
X → (0, 0)
Y → (-1, -2)
Z → (0, -2)
Rule for the rotation of a point (h, k) by 180° about the origin is given by,
(h, k) → (-h, -k)
By this rule,
Coordinates of the image points will be,
X(0, 0) → X'(0, 0)
Y(-1, -2) → Y'(1, 2)
Z(0, -2) → Z'(0, 2)
Therefore, Option (C) and Option (D) are the correct options.
Answer
C/D
Step-by-step explanation:
show that an 2 n − 5 n is also a solution to the recurrence relation an 7an−1 − 10an−2. what would the initial conditions need to be for this to be the closed formula for the sequence?
The expression 2^n - 5^n is indeed a solution to the recurrence relation an = 7an-1 - 10an-2. To use it as the closed formula for the sequence, the initial conditions need to be specified. The initial values for a0 and a1 would need to be determined based on the sequence being generated. Once the initial conditions are established, the expression 2^n - 5^n can be used to find the nth term of the sequence directly without having to rely on the recurrence relation.
To demonstrate that 2^n - 5^n satisfies the given recurrence relation, we need to substitute it into the relation and verify that it holds true for all n.
Given recurrence relation: an = 7an-1 - 10an-2
Substituting 2^n - 5^n into the recurrence relation:
7(2^(n-1) - 5^(n-1)) - 10(2^(n-2) - 5^(n-2))
Expanding and simplifying the expression:
7 * 2^(n-1) - 7 * 5^(n-1) - 10 * 2^(n-2) + 10 * 5^(n-2)
Rearranging the terms:
2 * 7 * 2^(n-2) - 2 * 7 * 5^(n-2) - 10 * 2^(n-2) + 10 * 5^(n-2)
Combining like terms:
2(7 * 2^(n-2) - 7 * 5^(n-2) - 5 * 2^(n-2) + 5 * 5^(n-2))
Factoring out 2 from the expression:
2(7 * 2^(n-2) - 5 * 2^(n-2) - 7 * 5^(n-2) + 5 * 5^(n-2))
Simplifying further:
2(2^(n-2)(7 - 5) - 5^(n-2)(7 - 5))
The expression simplifies to:
2(2^(n-2)(2) - 5^(n-2)(2))
2 * 2^(n-1) - 2 * 5^(n-1)
Which is equal to 2^n - 5^n.
To know more about recurrence relation, visit
https://brainly.com/question/4082048
#SPJ11
Find the slope and reduce.
P = (-4, -1) Q = (-3, -3)
Slope = [?]
Enter
Answer:
-2Step-by-step explanation:
The formula of a slope:
\(m=\dfrac{y_2-y_1}{x_2-x_1}\)
We have two points
P(-4, -1) and Q(3-3)
Substitute:
\(m=\dfrac{-3-(-1)}{-3-(-4)}=\dfrac{-3+1}{-3+4}=\dfrac{-2}{1}=-2\)
Solve for x. Round to the nearest tenth, if necessary.
K
X
J
69
400
I
Answer:
44.4
Step-by-step explanation:
sin(40)= x/69
x=69(sin40)
x= 44.4
I need help on this question I’m in the middle of a quiz please answer if you know the answer.
Answer:
y-2=0
Step-by-step explanation:
okk
simple
y-2=0
okk
Answer:
second one
Step-by-step explanation: