Answer:
27/10
Step-by-step explanation:
x/2-1/5 = x/3+1/4
x/2-x/3 = 1/4+1/5
(30x-20x)/60 = (15+12)60
10x = 27
=> x = 27/10
Answer: x= 27/10
decimal form is 2.7
Step-by-step explanation:
simplify both side of equation then isolate the variable
:)
Stat 0,-10 and -6,-8
The midpoint of the given coordinates of points (0,-10) and (-6,-8) is ( -3,-9 )
How determine the midpoint between two point?A midpoint is simply a point that divides a line segment into two equal halves.
The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point 1( 0,-10 )
x₁ = 0y₁ = -10Point 2( -6,-8 )
x₂ = -6y₂ = -8Midpoint = ?
To determine the midpoint, plug the given points into the midpoint formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( ( 0 + (-6) )/2, ( (-10) + (-8) )/2 )
M = ( ( 0 - 6) )/2, ( -10 - 8 )/2 )
M = ( ( -6 )/2, (-18 )/2 )
Midpoint M = ( -3,-9 )
Therefore, the midpoint of the coordinates is ( -3,-9 ).
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A pyramid with a rectangular base has a volume of 60 cubic feet and a height of 6 feet. The width of the rectangular base is 4 feet. Find the length of the rectangular base.
Answer:
length=2.5feet
Step-by-step explanation:
Volume =Base area * height
6/60=(4*length) * 6/6
10=4length
length=10÷4
=2.5feet
The length of the pyramid is 7.5 feet.
What is a pyramid with rectangular base?'A rectangular pyramid is a type of pyramid with the base shaped like a rectangle but the sides are shaped like a triangle. A pyramid usually has triangular sides but with different bases.'
According to the given problem,
Volume = 60 cubic feet
Height = 6 feet
Width of rectangular base = 4 feet
Let the length be x,
Volume =\(\frac{L * W * H}{3}\)
⇒ 60 = \(\frac{x*6*4}{3}\)
⇒ 180 = 24x
⇒ x = \(\frac{180}{24}\)
⇒ x =\(\frac{45}{6}\) = 7.5
Hence, we can conclude that the value of the length of the rectangular base is 7.5 feet.
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Quadrilateral ABCD is shown on the coordinate plane.
What needs to be proven to conclude that quadrilateral ABCD is a parallelogram?
A
-6 -4 -2
B.
C.
O A. slope of AB = slope of CD and slope of BC = slope of DA
slope of AB= slope of BC and slope of CD= slope of DA
side length of BC= side length of DA and slope of DA x slope of AB = -1
OD. side length of AB= side length of CD and slope of BC x slope of CD=-1
6
4-
2+
-2-
4-
-6-
D
B
6
C
X
Answer:
The slope of AB = slope of CD and slope of BC = slope of DA
Hope this helps!
Step-by-step explanation:
Liz is using the distributive property to evaluate the expression 27 (36) by using friendlier numbers. Her work is shown below.
Liz’s Work
27(36)
Step 1
27 (3 + 12)
Step 2
27 (3) + 27 (12)
Step 3
81 + 324
Step 4
405
What was the first error that Liz made?
Step 1 should have been 27(6 + 30).
Step 2 should have been 27(3) + 12.
Step 3 should have been 27(30)(12).
Step 4 should have been 16,244.
Answer:
in step one
Step-by-step explanation:
it looks wrong
Answer:
step 1
Step-by-step explanation:
i took the test
(a) What is the present value of $25,000 due 9 periods from now, discounted at 10%? (Round answer to 2 decimal places, e.g. 25.25.) Present value $ (b) What is the present value of $25,000 to be received at the end of each of 6 periods, discounted at 9%?
a) The present value of $25,000 due 9 periods from now, discounted at 10%, is approximately $10,593.22.
b) The present value of $25,000 to be received at the end of each of 6 periods, discounted at 9%, is approximately $22,935.35.
(a) Present Value of $25,000 due 9 periods from now, discounted at 10%:
To calculate the present value, we need to discount the future cash flow of $25,000 back to its current value using the given discount rate of 10%. The formula to calculate the present value is:
Present Value = Future Value / (1 + Discount Rate)ⁿ
Where:
Future Value is the amount to be received in the future ($25,000).
Discount Rate is the rate at which we discount the future cash flow (10%).
'n' is the number of periods or years until the future cash flow is received (9 periods in this case).
Let's plug in the values into the formula and calculate the present value:
Present Value = $25,000 / (1 + 0.10)⁹
Calculating the denominator:
(1 + 0.10)⁹ = 1.10⁹ ≈ 2.36
Present Value = $25,000 / 2.36 ≈ $10,593.22
(b) Present Value of $25,000 to be received at the end of each of 6 periods, discounted at 9%:
In this case, we have a cash flow of $25,000 to be received at the end of each of 6 periods, discounted at 9%. Let's calculate the present value:
Present Value = $25,000 / (1 + 0.09)¹ + $25,000 / (1 + 0.09)² + ... + $25,000 / (1 + 0.09)^6
Calculating each discount factor:
(1 + 0.09)¹ ≈ 1.09
(1 + 0.09)² ≈ 1.1881
(1 + 0.09)³ ≈ 1.2950
(1 + 0.09)⁴ ≈ 1.4116
(1 + 0.09)⁵ ≈ 1.5386
(1 + 0.09)⁶ ≈ 1.6765
Plugging in the values and summing them up:
Present Value = $25,000 / 1.09 + $25,000 / 1.1881 + $25,000 / 1.2950 + $25,000 / 1.4116 + $25,000 / 1.5386 + $25,000 / 1.6765
Present Value ≈ $22,935.35
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for each pair of numbers determine by what percent the second number is greater than the first.also determine by what percent the first numberis less than the secon. 100 and 110
The first number, 100, is about 9.09% less than the second number, 110. Note that we obtain a negative value for the percent decrease because the first number is smaller than the second.
What is the percent decrease?
Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.
To determine the percent by which the second number is greater than the first, we can use the formula:
(percent increase) = [(new value - old value) / old value] x 100%
Substituting the given values, we get:
(percent increase) = [(110 - 100) / 100] x 100% = 10%
This means that the second number, 110, is 10% greater than the first number, 100.
To determine the percent by which the first number is less than the second, we can use the formula:
(percent decrease) = [(old value - new value) / old value] x 100%
Substituting the given values, we get:
(percent decrease) = [(100 - 110) / 110] x 100% = -9.09...%
Therefore, This means that the first number, 100, is about 9.09% less than the second number, 110. Note that we obtain a negative value for the percent decrease because the first number is smaller than the second.
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URGENT pleaseee help me ill send you 20 dollars plus 50 points and brainlist if right!!!!
use the sohcahtoa method!
Answer:
A. 22°
E. 15
I. 39°
F. 71°
C. 25.6
H.12.9
K.55°
23 kg to lbs is how many pounds?
23 kg is equivalent to 50.7098 pounds.
When converting between units of weight, it is important to understand the relationship between the units. Kilograms (kg) and pounds (lbs) are both units of weight, but they are not equivalent. One kilogram is equal to 2.20462 pounds.
To convert kilograms (kg) to pounds (lbs), you can use the conversion factor of 2.20462. The formula to convert kg to lbs is:
lbs = kg x 2.20462
So, to convert 23 kg to pounds, we can plug in the value of 23 for kg and multiply it by 2.20462:
lbs = 23 x 2.20462
lbs = 50.7098
It's worth noting that when dealing with such calculations, you need to take care of the precision of the result.
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use a triple integral to find the volume of the solid bounded by the parabolic cylinder y=4x2 and the planes z=0,z=8 and y=6.
The volume of the solid bounded by the parabolic cylinder \(y=4x^2\) and the planes z=0,z=8, and y=6 is 16π cubic units.
How to find the volume of the solid bounded by the parabolic cylinder ?To find the volume of the solid bounded by the parabolic cylinder \(y=4x^2\) and the planes z=0,z=8, and y=6, we can set up a triple integral using cylindrical coordinates.
First, we need to find the bounds for the variables in our integral.
Since the solid is bounded by the plane y=6, we know that the maximum value for y is 6. For z, we know that the solid is bounded between the planes z=0 and z=8.
For x, we need to find the bounds in terms of y and z.
The equation of the parabolic cylinder is \(y=4x^2\), which can be rewritten as\(x^2=y/4.\) Since we are using cylindrical coordinates,
we know that x=rcosθ and y=rsinθ, so we can rewrite \(x^2\) as \((rcos\theta)^2=(rsin\theta)/4\). Solving for r, we get \(r=\sqrt((y/4)/cos^2\theta+sin^2\theta).\)
Using this equation, we can find the bounds for r in terms of y and θ.
We want to find the maximum and minimum values of r for a given y, so we can take the derivative of r with respect to θ and set it equal to 0:
\(dr/d\theta = (-y/4)sin\thetacos\theta/(cos^2\theta+sin^2\theta)^(3/2)\)
This derivative is equal to 0 when sinθ=0 or cosθ=0, which means θ=0 or θ=π/2. So the bounds for θ are 0 to π/2.
When θ=0 or θ=π/2,\(r=\sqrt(y/4)\), so the maximum and minimum values of r for a given y are 0 and sqrt(y/4), respectively.
Finally, we need to find the bounds for z. Since the solid is bounded between z=0 and z=8, we know that the maximum and minimum values of z are 8 and 0, respectively.
Putting it all together, the triple integral for the volume of the solid is:
V = ∫∫∫ (r dz dy dθ)
With the following bounds:
θ: 0 to π/2
y: 0 to 6
z: 0 to 8
\(r: 0 to\sqrt(y/4)\)
So the integral becomes:
V = ∫[0,π/2]∫[0,6]∫[0,8] (r dz dy dθ)
= ∫[0,π/2]∫[0,6]∫[0,8] (r) dz dy dθ
= ∫[0,π/2]∫[0,6] (4r) dy dθ
= ∫[0,π/2] 48/3 dθ
= 16π
Therefore, the volume of the solid bounded by the parabolic cylinder \(y=4x^2\) and the planes z=0,z=8, and y=6 is 16π cubic units.
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How many minutes are required for 175 gpm to pass the entire 1500-foot length of a 12-inch diameter pipeline? a. 6.73 minutes b. 8.57 minutes c. 50.3 minutes d. 64 minutes e. 125 minutes
The time required for 175 gpm to pass through a 1500-foot length of 12-inch diameter pipeline is d) 8.57 minutes.
To solve this problem, we can use the following formula:
Time = Distance / Velocity
where Velocity = Flow rate / Cross-sectional area
We are given the flow rate (175 gpm) and the dimensions of the pipeline (12-inch diameter), so we can calculate the cross-sectional area:
Area = π x (diameter/2)^2
Area = π x (12/2)^2
Area = π x 36
Area = 113.1 square inches
Next, we can calculate the velocity:
Velocity = Flow rate / Cross-sectional area
Velocity = 175 / 113.1
Velocity = 1.55 feet per second
Finally, we can use the time formula to calculate the time required:
Time = Distance / Velocity
Time = 1500 / (1.55 x 60)
Time = 8.57 minutes (rounded to two decimal places)
Therefore, the answer is option (b) 8.57 minutes.
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2) The representative agent lives for infinite periods (0,1,2,…) and receives exogenous incomes of y0,y1,y2,…, respectively. The lifetime present discounted value of utility is given by: ∑t=0[infinity]βtln(ct) with β(<1) being the discount factor and ct is consumption at time t. The agent is allowed to save or borrow at the real interest rate r, but she cannot die with debt or wealth. Assume also that the initial wealth is zero. a. Solve the optimization problem of the agent using the period-by-period budget constraints. In particular, show the Euler equation. b. Using the given functional form, write the Euler equation between time 1 and time 3 . In other words, show how c1 and c3 are related. c. Write the present discounted value of optimal lifetime consumption as a function of c0 (and, potentially, other parameters or exogenous variables). d. Write the present discounted value of optimal lifetime utility as a function of c0 (and, potentially, other parameters or exogenous variables). e. Find the present discounted value of lifetime income as a function of y0 (and, potentially, other parameters or exogenous variables) when income is growing each period at the rate of γ, where 0<γ0 ? Explain!
a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. U0 = ∑t=0[infinity](β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.
a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:
At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.
Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin
d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity](β(1 + r))^tln(ct).
This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.
This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.
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Help. Step By Step Explanation. Ron and two of his friends ate one fourth each of an eight slice pizza. Find remaining slice of the pizza
Answer:
2 remaining slices
Step-by-step explanation:
It sounds complicated so firstly, let's break it down.
Ron and two of his friends
There are three people involved in this question.
ate one fourth each
These three people ate one fourth of the pizza each
of an eight slice pizza.
From a pizza with eight slices
Find remaining slice of the pizza
The main question : remaining slice of the pizza
So since there were three people and they ate one fourth of the pizza
( One fourth's \(\frac{1}{4}\) by the way )
We need to find out how much have they ate.
Simply multiply 3 with \(\frac{1}{4}\) .
3 × \(\frac{1}{4}\) = \(\frac{12}{4}\) × \(\frac{1}{4}\)
= \(\frac{3}{4}\)
And there you go! Ron and his friends ate \(\frac{3}{4}\) of the pizza.
But that's not the end.
The main question : Remaining slice of the pizza
It's an eight slice pizza, so a slice would be : \(\frac{1}{8}\)
A full eight slice pizza would be one.
So, to find the remaining slice of pizza, simply subtract \(\frac{3}{4}\) from 1.
1 - \(\frac{3}{4}\) = \(\frac{4}{4}\) - \(\frac{3}{4}\)
= \(\frac{1}{4}\)
Now there's a remainding of \(\frac{1}{4}\) of the pizza.
But the question asked for remaining slices.
So, simply convert the denominator into 8!
( Just in case you don't know what's a denominator )
\(\frac{numerator}{denominator}\)
So, simply multiply the denominator by 2 to turn 4 into 8!
And also, whenever the denominator is multiplied/ divided by any number, so do the numerator.
\(\frac{1 times 2}{4 times 2}\) = \(\frac{2}{8}\)
Your answer's the numerator, 2!
So your final answer should be 2 remaining slices out of the eight sliced pizza.
HOPE THIS ANSWER HELPED :)Andrea ordered a computer on the Internet. The computer cost $1399 plus 6 1/2% sales tax. What was the total amount Andrea paid for her computer?
Answer:
$1,489.94
Step-by-step explanation:
Answer:
1,489.94
Step-by-step explanation:
6.5% = 0.065
1399x 0.065= 90.935
1399 + 90.935 = 1,489.94
Actual demand for the past 16 periods is shown below. Prepare a trend adjusted exponential smoothing forecast using the following parameters: a = 4, B = .3, TAF5 = 652.67, and T5 = -33. (Round all you
To forecast future demand using trend adjusted exponential smoothing, the given information includes actual demand for the past 16 periods and the parameters required for the forecast. The parameters include the smoothing constant (α), the trend smoothing constant (β), the trend-adjusted forecast for period 5 (TAF5), and the trend for period 5 (T5).
The question asks to prepare a trend-adjusted exponential smoothing forecast based on these parameters.
Trend adjusted exponential smoothing combines exponential smoothing with a trend component to forecast future values. The formula for calculating the forecast is:
Ft+1 = Ft + Tt + α * (At - Ft) + β * (Tt - Tt-1)
Where:
Ft is the forecast for period t
Tt is the trend component for period t
At is the actual demand for period t
α is the smoothing constant
β is the trend smoothing constant
To start, we need to initialize the forecast and trend values. In this case, we are given the trend-adjusted forecast for period 5 (TAF5) and the trend for period 5 (T5). So, we set F5 = TAF5 and T5 = T5.
Next, we can use the formula to calculate the forecast and trend values for the remaining periods.
We iterate through the periods from t = 6 to t = 16, applying the formula to update the forecast and trend values based on the actual demand for each period.
Finally, we round the forecast values to the desired precision.
By following this procedure and applying the given parameters, we can prepare a trend-adjusted exponential smoothing forecast for the future demand.
The forecast values will reflect the trend in the historical data while incorporating the smoothing constants for better accuracy.
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find the x and y intercepts of the graph calculator
The x-intercept is (-0.67, 0), which means that when y = 0, x = -0.67. The y-intercept is (0, 2), which means that when x = 0, y = 2.
To find the x and y-intercepts of the graph on a calculator, follow the steps given below:
First, we need to graph the equation in the calculator to obtain its graph. Then, we can read off the x and y-intercepts from the graph. Here are the steps:
Step 1: Press the ‘Y=’ button on the calculator to enter the equation in the calculator. For example, if the equation is y = 3x + 2, type this equation in the calculator.
Step 2: Press the ‘Graph’ button on the calculator. This will show the graph of the equation on the screen. The graph will show the x and y-intercepts of the equation.
Step 3: To find the x-intercept, look for the point where the graph crosses the x-axis. The x-coordinate of this point is the x-intercept. To find the y-intercept, look for the point where the graph crosses the y-axis. The y-coordinate of this point is the y-intercept. For example, consider the equation y = 3x + 2. The graph of this equation looks like this: Graph of y = 3x + 2
The x-intercept is (-0.67, 0), which means that when y = 0, x = -0.67.
The y-intercept is (0, 2), which means that when x = 0, y = 2.
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the cost of a car rental is $35 per day plus 18 cents per mile. you are on a daily budget of $71.
Answer:
1024
Step-by-step explanation:
35 x 18 x 71 = I dont know
Jennifer has $3955 in her retirement account, and Reggie has $3935 in his. Jennifer is adding
$8 per day, whereas Reggie is contributing $18 per day. Eventually, the two accounts will
contain the same amount. What balance will each account have? How long will that take?
Jennifer and Reggie will each have a retirement account balance of $
days.
Answer:
3955, 3963, 3971,
that's jennifer's
3935, 3953, 3971,
that's Reggie's
so Jennifer would have 3971 on the third day, and so would reggie. the amount would be 3971
When the declaration/// int y = 5; /// is followed by the
assignment /// y += 3.7; /// the value of y is _______.
Answer:
y = 8.7
Step-by-step explanation:
Assuming we can use decimal places, y is equal to 8.7.
In programming, += is often used as a substitute for y = y + x (example)
Therefore, y = y + 3.7, and since y = 5, y = 5 + 3.7, y = 8.7
can 22.75 be rounded off to 23.5?
(im not smart pfft)
Answer:
No
Step-by-step explanation:
22.75 can be rounded to:
22.8
23
20
Answer:
no only 22.8
Step-by-step explanation:
QUESTION 11 Determine the critical value of chi square with 3 degree of freedom for alpha=0.05 7.815 9.348 0.004 3.841 1.5 points Save Answer QUESTION 12 If a random sample of size 64 is drawn from a
The formula for the standard error of the mean is as follows:Standard error of the mean (SEM) = σ/√nWhere, σ is the population standard deviation and n is the sample size. As the sample size increases, the standard error of the mean decreases. The correct answer is standard error of the mean decreases.
Critical value of chi-square with 3 degrees of freedom for alpha = 0.05The correct option is 7.815.Chi-square distribution: The chi-square distribution is a continuous probability distribution that has one parameter known as degrees of freedom.
Chi-square distribution arises when the square of a standard normal random variable follows this distribution and it is one of the widely used probability distributions in hypothesis testing and statistics. When the sample size increases, the chi-square distribution looks more like a normal distribution. Critical value of chi-square: It is the cutoff value used to determine whether to reject or fail to reject the null hypothesis in the chi-square test.
The critical value depends on the degrees of freedom and the level of significance of the test. For a given alpha (α) value and degrees of freedom, we can obtain the critical value from the chi-square table. If the test statistic calculated from the sample data exceeds the critical value, we reject the null hypothesis and accept the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
The critical value of chi-square with 3 degrees of freedom for alpha = 0.05 is 7.815.Answer: The correct option is 7.815.Question 12: Sampling distributionThe sampling distribution is a probability distribution that shows the probability of different outcomes that could be obtained from a given sample size drawn from a population. The distribution of a statistic (mean, proportion, variance) from all possible samples of a fixed size (n) is known as the sampling distribution of that statistic. Central Limit Theorem:
According to the Central Limit Theorem, the sampling distribution of the sample mean is approximately normally distributed if the sample size is large enough (n ≥ 30) or if the population is normally distributed. This theorem states that the distribution of the sample mean approaches a normal distribution with mean μ and standard deviation σ/√n as the sample size increases, regardless of the population distribution. The standard error of the mean is the standard deviation of the sampling distribution of the mean.
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What are angles for Grade 6?
In Grade 6, students typically learn about angles and their properties. Some of the key concepts that students may study include:
Understanding that an angle is formed by two rays with a common endpoint called the vertex.Identifying and labeling angles, using the vertex and the two rays that form the angle.Understanding that angles can be measured in degrees (°).Measuring angles with a protractor.Classifying angles as acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), or straight (exactly 180°).Identifying and drawing complementary and supplementary angles.Understanding the relationship between adjacent angles formed by parallel lines and transversals.Using angle properties to solve problems and prove geometric theorems.These are some of the key concepts that students may learn about angles in Grade 6, but the specific curriculum can vary depending on the school district and state.
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(-15)2 equals ? This has got me stuck for a few minutes.
Answer:
225
Step-by-step explanation:
(- 15)² = - 15 × - 15 = 225
What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?
y minus 4 = 3 (x minus 1)
1 minus y = 3 (x minus 4)
y 1 minus 4 = 3 (1 minus x 1)
1 minus y 1 = 3 (4 minus x 1)
what is the y intercept of the points (2,72) and (5,162)
Answer:
12
Step-by-step explanation:
Type Into Calculator:
SAT-EDIT-TYPE IN X VALUES AND Y VALUES (FROM ORDERED PAIR)-STAT-CALC-4-ENTER
(ii) If M is proximinal, ((x
n
,y
n
))
n=1
[infinity]
is a sequence in X×X such that y
n
∈P
M
(x
n
) and lim
n→[infinity]
((x
n
,y
n
))=(x,y) then y∈P
M
(x).
If M is a proximinal set and we have a sequence ((x_n, y_n)) in X×X such that y_n belongs to the projection of x_n onto M, and the limit of the sequence approaches (x, y), then y also belongs to the projection of x onto M.
We will use the definition of a proximinal set and the properties of limits to support this claim.
Let's assume that M is a proximinal set in X. Given a sequence ((x_n, y_n)) in XX such that y_n P_M(x_n) for all n N, where P_M(x_n) represents the projection of x_n onto the set M, we are also given that lim_n((x_n, y_n)) = (x, y
Consider the distance function d((x, y), M) = infd((x, y), m): Now, we must demonstrate that y P_M(x), or that y is the projection of x onto the set M. Since y_n P_M(x_n) for all n, we have d((x_n, y_n), M) = d(x_n, y_n), P_M(x_n)) = 0 for all n. If we take the limit as n approaches infinity, we get d(x, y), M) = d(x, y), P_M(x)) = 0.
As a result, we can deduce that y is a point in M that satisfies the minimum, i.e., y P_M(x).
As a result, we have demonstrated that y is P_M(x) if M is proximal and ((x_n, y_n)) is a sequence in XX such that y_n = P_M(x_n) and lim_n = (x, y).
According to the definition of proximinality and the properties of limits, if M is a proximinal set and we have a sequence ((x_n, y_n)) in XX such that y_n belongs to the projection of x_n onto M, and the limit of the sequence approaches (x, y), then y also belongs to the projection of x onto M.
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How do you find the base height and volume if you know the area?
We can determine the value of height (h) by 2x of area gives the value of base height and the volume can be determined by dividing the base area by the height.
The product of the length and width of the rectangle forming the base of a cuboid would yield the area of the base.
Any solid's capacity is represented by its volume. It is the measurement of the interior volume of a particular shape and is only calculable for three-dimensional shapes.
The cuboid's base area is (l × b) sq. units, and its volume is (l × b × h) cu. units.
It is simple to determine the value of height (h) by taking the ratio of these two quantities. As the result of length and width would no longer be the standard term.
If you know the area and you have to find the volume:
Since the base area is known, the volume can be determined by dividing the base area by the height. (Remember that volume is expressed in cubic units.)
If you know the area and you have to find the base height:
Now that you know the area of the triangle
Area=1/2*base*height
Then if we want to know base height so 2x of area gives the value of base height.
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Suppose the physics club is going on a field trip. Members will be riding in vans that will hold 7 people each including the driver. At least 24 people will be going on the field trip. What is the least number of vans needed to make the trip?
Answer:
4
Step-by-step explanation:
24/7 = 3.xxxx
Which is more than 3 and there is no such thing as a 0.xxx bus then you round the van value to the next whole number.
Keep practicing, this is basic stuff
Answer:
4
Step-by-step explanation
24 people going on the field trip and each bus seats 7 people
so 24/7 = 3 R3 + there will be 3 extra people because there will be 3 drivers so in total there will be 27 people so there will be 4 buses needed
I hope this helped : )
You are setting up a study area where you will do your home work each evening. It is triangular with an entrance on one side. You want to put your computer in the corner with the largest angle and the bookshelf on the longest side. 1. Where should you place your computer? 2. On which side should you place the bookshelf? Explain If the measure of one angle of the triangle is 90°. 3. What type of triangle is your study room? (PLEASE HELP ME WITH THIS QUESTION)
You should place the computer at corner with 90°, you should place the bookshelf on the opposite side of the computer and the triangle is a right triangle.
Given that you are setting up a study area which is triangular with an entrance on one side.
You want to put your computer in the corner with the largest angle and the bookshelf on the longest side.
Also, one angle of the triangle is 90°.
So, since one angle is right angle, so the triangle is a right triangle,
We know that the largest angle in a right triangle is 90°.
So, you should place your computer in the corner which is measuring 90°.
Also, the largest angle is opposite of the largest side, so you should place the bookshelf on the side which is opposite to the computer.
Hence you should place the computer at corner with 90°, you should place the bookshelf on the opposite side of the computer and the triangle is a right triangle.
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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 4 large boxes and 8 small boxes has a total weight of 169 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 71 kilograms. How much does each type of box weigh?
Answer:
weight of large box=15.250 kgm
wight of box=13.500 kgm.
Step-by-step explanation:
let weight of large box=x kgm
and weight of small box=y kgm.
4x+8y=169
2x+3y=71
multiply by 2
4x+6y=142
subtract from first
2y=27
y=27/2=13.500 kgm
4x+8(27/2)=169
4x+108=169
4x=169-108
4x=61
x=61/4=15.250 kgm
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