Answer:
48 feet
Step-by-step explanation:
So first find the amount of fence they would need in terms of x, which would be (x - 2) + (3x - 1) + (5x + 8) + (3x - 1) + (x - 2). Then, you know these add up to 106 so you get the equation:
\(x-2+3x-1+5x+8+3x-1+x-2 = 106\)
Now, you just have to solve.
First, combine like terms
\(13x + 2 = 106\)
Then, subtract 2 from both sides
\(13x = 104\)
Next, divide both sides by 13.
\(x = 8\)
The last step is to find the length of 5x + 8 by substituting x = 8 in
\(5*8+8=40+8=48\)
To buy a car, Jason makes a down payment of $1500 and pays $350 per month in installments. The equation =350+1500 represents the total amount he will spend on his car.
How much has Jason paid at the end of one year? $
Answer:
if nth term of the AP 3,10,17.... is same as the nth term of the AP 63,65,67.... find n.
Step-by-step explanation:
please solve this also it's hard for me
What is the area of a trapezoid with base lengths 8 in and 10 in and a
height of 9 in?
Answer: 81 inches
Step-by-step explanation:
Area of a trapezoid is … Area= 1/2(b1+b2)h
So if we plug it in
Area = 1/2(8+10)9
= 1/2(18)9
= 9(9) = 81
The purchased cost of a 5-m3 stainless steel tank in 1995 was $10,900. The 2-m-diameter tank is cylindrical with a flat top and bottom. If the entire outer surface of the tank is to be covered with 0.05-m-thickness of magnesia block, estimate the current total cost for the installed and insulated tank. The 1995 cost for the 0.05-m-thick magnesia block was $40 per square meter while the labor for installing the insulation was $95 per square meter.
The estimated current total cost for the installed and insulated tank is $12,065.73.
The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:
surface_area = 2 * pi * r * h + 2 * pi * r^2
where:
r is the radius of the cylinder
h is the height of the cylinder
In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:
surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586
The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:
surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293
The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:
cost = 6.806032934459293 * (40 + 95) = $1,165.73
The original cost of the tank was $10,900, so the total cost of the insulated tank is:
cost = 10900 + 1165.73 = $12,065.73
Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.
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Can you please help me
since its an isosceles triangle, which is divided at the centre,
the remaining length of the given right angle triangle is 5
using pythagoras theorem to find x
x^2 = 8^2 - 5^2
x^2 = 64 - 25
x^2 = 39
x = square root of 39
x = 6.25
therfore the answer is:
A. 6.25
For any string w = w1w2 · · ·wn, the reverse of w, written wR, is the string w in reverse order, wn · · ·w2w1. For any language A, let AR = {wR|). Show that if A is regular, so is AR
To show that AR if A is regular, we can use the fact that regular languages are closed under reversal.
This means that if A is regular, then A reversed (written as A^R) is also regular.
Now, to show that AR is regular, we can start by noting that AR is the set of all reversals of strings in A.
We can define a function f: A → AR that takes a string w in A and returns its reversal wR in AR. This function is well-defined since the reversal of a string is unique.
Since A is regular, there exists a regular expression or a DFA that recognizes A.
We can use this to construct a DFA that recognizes AR as follows:
1. Reverse all transitions in the original DFA of A, so that transitions from state q to state r on input symbol a become transitions from r to q on input symbol a.
2. Make the start state of the new DFA the accepting state of the original DFA of A, and vice versa.
3. Add a new start state that has transitions to all accepting states of the original DFA of A.
The resulting DFA recognizes AR, since it accepts a string in AR if and only if it accepts the reversal of that string in A. Therefore, AR is regular if A is regular, as desired.
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Let R be the region in the first quadrant bounded by the x-axis, the graph of x=y2+2, and the line x=4. What is a the interval for the area of R?
A region in the first quadrant defined by the x-axis, the graph of x=y2+2, and the line x=4 is called R then the area of R be \($-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$\)
What is meant by parabola ?A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. A parabola is a U-shaped curve that represents the graph of a quadratic function.
Students are able to fill in the gap between the mathematics they learn in class and the things they see in real life by drawing a comparison between the equation of a parabola and a shape found in the real world (the parabaloid). They can conceive difficult ideas that they might otherwise find repugnant by doing this.
Sketch the graph of \($x=y^2+2$\) by sketching the sideways parabola \($x=y^2$\) then adding 2 to the x coordinates (translate 2 to the right).
Add the x axis and the vertical line x = 4.
The area can be found by either
\($\int_2^4 \sqrt{x-2} d x$$\) or \($\int_0^{\sqrt{2}}\left(4-\left(y^2+2\right)\right) d x$$\)
\($=\int_0^{\sqrt{2}}-x^2+2 d x$$\)
Apply the Sum Rule: \($\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$\)
\($=-\int_0^{\sqrt{2}} x^2 d x+\int_0^{\sqrt{2}} 2 d x$$\)
simplifying the equation, we get
\($\int_0^{\sqrt{2}} x^2 d x=\frac{2 \sqrt{2}}{3}$$\)
\($\int_0^{\sqrt{2}} 2 d x=2 \sqrt{2}$$\)
\($=-\frac{2 \sqrt{2}}{3}+2 \sqrt{2}$$\)
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A sample of 16 values is taken from a normal distribution with mean µ. The sample mean is 13.25 and true variance 2 is 0.81. Calculate a 99% confidence interval for µ and explain the interpretation of the interval.
The interpretation of the confidence interval is that we are 99% confident that the true population mean (µ) falls within the range of [12.808, 13.692].
To calculate a 99% confidence interval for the population mean (µ), we can use the formula:
Confidence interval = sample mean ± (critical value * standard error)
Given that the sample mean (\(\bar{X}\)) is 13.25 and the true variance (σ²) is 0.81, we can calculate the standard error using the formula:
Standard error (SE) = √(σ²/n)
n represents the sample size, which is 16 in this case. Plugging in the values:
SE = √(0.81 / 16) ≈ 0.15
The critical value corresponds to the desired confidence level, which is 99%. Since we have a sample size of 16, we need to use the t-distribution instead of the standard normal distribution. With a 99% confidence level and 15 degrees of freedom (n-1), the critical value is approximately 2.947.
Calculating the confidence interval:
Confidence interval = 13.25 ± (2.947 * 0.15) ≈ 13.25 ± 0.442 ≈ [12.808, 13.692]
The interpretation of the confidence interval is that we are 99% confident that the true population mean (µ) falls within the range of [12.808, 13.692]. This means that if we were to repeat the sampling process many times and calculate the confidence intervals, approximately 99% of those intervals would contain the true population mean.
In conclusion, based on the given data and calculations, we can be 99% confident that the true population mean (µ) lies within the range of [12.808, 13.692].
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Moe painted the lid of the barrel. The circumference of the barrel is 32*3.14 inches. What is the area of the lid in square inches?
Answer: 803.84 inch²
Step-by-step explanation:
The lid will take the appearance of a circle so the area of the lid is the same as the area of a circle:
Area of a circle = π * radius²
The circumference of a circle is:
= π * diameter
Looking at the above, the diameter is 32inches because this is the figure to be multiplied with π = 3.14 to find the circumference.
Since diameter is 32, radius will be:
= 32 / 2
= 16 inches
Area = 3.14 * 16 * 16
= 803.84 inch²
Jim is asked how many solutions there will be for the following system of equations: y=x²-5 y=3(x-1)² Jim argues that because both parabolas are facing upwards, they must intersect at some point, even if it's very high up. Evaluate his reasoning. (Note, you do not need to solve the system - only evaluate Jim's reasoning)
Jim's reasoning is sound because the two equations given represent parabolas that are both facing upwards. This means that their graphs will have a minimum point and therefore will intersect at least once.
To understand why this is the case, it is helpful to visualize the graphs of both equations. The quadratic function y = x^2 - 5 has a vertex at (0, -5) and opens upward. This means that as we move away from the vertex in either direction, the value of y increases indefinitely. Similarly, the quadratic function y = 3(x - 1)^2 also has a vertex at (1, 0) and opens upward. However, since the leading coefficient is greater than 1, this parabola will be narrower and its minimum point will be higher up than that of the first equation.
Because both parabolas have a minimum point, they will intersect at least once. If we imagine moving one of the parabolas vertically or horizontally, we can see that they will always intersect unless they are completely separate from each other. Since the two parabolas in the system of equations given are not completely separate, they must intersect at some point.
Therefore, Jim's reasoning is correct in concluding that the system of equations must have exactly one solution.
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336,765=3,14×0.55×(l+0.55) please help
Answer:
l = 194999.45
Step-by-step explanation:
I'm going to assume that you meant 3.14 by 3,14.
336,765 = 3.14 × 0.55 × (l + 0.55)
336,765 ÷ (3.14 × 0.55) = l + 0.55
(336,765 ÷ (3.14 × 0.55)) - 0.55 = l
l = 194999.45
. Determine the instantaneous rate of change at x=−1. b. Determine the average rate of change on the interval −1≤x≤2
a.) The instantaneous rate of change at x = -1 for the function f(x) = 2x² - 3x + 1 is -7.
b.) The average rate of change on the interval [-1, 2] for the function f(x) = 2x² - 3x + 1 is -4/3.
a)
Instantaneous rate of change of a function can be defined as the rate of change of a function at a particular point.
It is also called the derivative of a function.
The instantaneous rate of change at x = -1 is given by:
f'(-1) = (d/dx) f(x)|x=-1
Given the function f(x) = 2x² - 3x + 1,
Using the power rule of differentiation, we get
f'(x) = d/dx (2x² - 3x + 1) = 4x - 3 At x = -1,
we have f'(-1) = 4(-1) - 3 = -7
Therefore, the instantaneous rate of change at x = -1 is -7.
b)
The average rate of change of a function over a given interval [a, b] is the ratio of the change in y-values (Δy) to the change in x-values (Δx) over the interval. It is given by:
(f(b) - f(a))/(b - a)
For the function f(x) = 2x² - 3x + 1,
evaluate (f(2) - f(-1))/(2 - (-1)) = (8 - 12)/(3) = -4/3
Therefore, the average rate of change on the interval [-1, 2] is -4/3.
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In an experiment, the control variable is rand the response variable is s.
Which variable is not manipulated, but measured, and represents the data
being recorded?
A. Both r and s
B. s
C. Neither r nor s
D. r
Answer:
S.
Control variables are kept constant between experiments.
Step-by-step explanation:
Control variable r is not manipulated, but measured and represents the data being recorded.
What is mean by Variables?A variable is a value that can change, depending on information.
Given that;
In an experiment, the control variable is r and the response variable is s.
Now,
Control variable is a variable that's always constant in an experiment.
It is not a variable of interest in the study, but its controlled because it could influences the outcomes.
Thus, Control variable r is not manipulated, but measured and represents the data being recorded.
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Fill in the blanks.
Complete the table. Write each percent as a percent of 1.
Answer:
1/10, 0.1, 10%
3/4, 0.75, 75% of 1
1/5, 0.2, 20%
Step-by-step explanation:
i hope this helped : )
The critical F value with 6 numerator and 60 denominator degrees of freedom at a = .05 is 3.74. 1.96. 2.25. O 2.37.
The critical F value with 6 numerator and 60 denominator degrees of freedom at a = .05 is 2.37.
This means that if the calculated F value is greater than 2.37, we can reject the null hypothesis at the 5% level of significance. The other values given (3.74, 1.96, and 2.25) are critical values for different degrees of freedom and different levels of significance, but they are not relevant to this specific question.
How can you determine F's crucial value?
Start by locating the table that matches your degree of relevance. The junction of the column and rows that corresponds to your numerator and denominator DF should then be located.
For your test, the crucial values are shown in the F-table cell at that junction.
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The width of a rectangle is 3 feet less than twice the length. Find the length if the
perimeter is 84
Answer:
Your width is 5 feet and your length is 7!!!!!
Step-by-step explanation:
MARK AS BRAINLIEST
Question 4
5 pts
A football team gained 6 yards on a first down,
lost 15 yards on the second down, and gained 12
yards on the third down. How many yards did the
team gain or lose?
-50
-
21 yards
o 9 yards
033 yards
03 yards
Answer:
they have gained 3 yards
Step-by-step explanation:
they went foward 6 but went back 15 leaving them at -9 then gained 12 putting them at 3
Ernest works in the shipping department at Wal-Mart. Each
Empty crate weighs 150 lbs. How many boxes, each weighing 35
lbs. can Ernest put in the crate if the total weight is to be at most 850
Ibs?
3 + 2x = y Given x = 4 y =
Answer:
\(y = 9\)
Step-by-step explanation:
\(3 + 2x = y\)
\(y = 3 + 6\)
\(y = 9\)
Hope it is helpful...A Normality Check was conducted for a data set. The conclusion is that the data are from a normal distribution. The equation of the straight line that are closest to the data is given as
y=0.918x-0.175.
Find the estimated population mean.
a) 0
b) -0.175
c) 0.918
d) sqrt(0.918)
To find the estimated population mean from the given equation, we will use the fact that the data are normally distributed. The equation provided is a linear equation that represents the best-fit line for the data:
y = 0.918x - 0.175. The correct option is B.
Since the data follows a normal distribution, the mean will be located at the point where the line is at its highest. In a normal distribution, the peak (or the highest point) occurs when the probability density is the greatest. In the case of the given linear equation, this peak corresponds to the y-intercept, which is the point where the line crosses the y-axis (when x = 0).
Plugging x = 0 into the equation:
y = 0.918(0) - 0.175
y = -0.175
Thus, the estimated population mean is -0.175.
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6. From the menu, select the correct
approximation.
If the expression
√24 × √10
represents the area of a rectangle, then
the approximate area of the rectangle is
60 square units
15 square units
8 square units
120 square units
The approximate area of the rectangle as per the options will be equal to 15 square units. Hence, option B is correct.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure.
The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given information in the question,
Let the length is given as, l = √24 and,
The width is given as, w = √10
Use the formula of area of rectangle,
A = lw
A = √24 × √10
A = 4.89 × 3.16
A = 15.45 ≈ 15 square units.
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Determine the WVC on for each day presented below. Day 1: Air Temperature= 86°F and RH= 60% Day 2: Air Temperature= 41°F and RH=90% At what point during the day would you expect outside relative humidity values to be the lowest? …to be the highest? Explain/justify your response.
Relative humidity tends to be highest during the early morning hours, shortly before sunrise.
To determine the Wet-Bulb Temperature (WBT) and Wet-Bulb Depression (WBD), we need the dry-bulb temperature (DBT) and relative humidity (RH) values.
The Wet-Bulb Temperature (WBT) is the lowest temperature that can be achieved by evaporating water into the air at constant pressure, while the Wet-Bulb Depression (WBD) is the difference between the dry-bulb temperature (DBT) and the wet-bulb temperature (WBT). These values are useful in determining the potential for evaporative cooling and assessing heat stress conditions.
Day 1: Air Temperature= 86°F and RH= 60%
To calculate the WBT and WBD for Day 1, we would need additional information such as the barometric pressure or the dew point temperature. Without these values, we cannot determine the specific WBT or WBD for this day.
Day 2: Air Temperature= 41°F and RH= 90%
Similarly, without the necessary additional information, we cannot calculate the WBT or WBD for Day 2.
Regarding your question about the point during the day with the lowest and highest outside relative humidity values, it is generally observed that the relative humidity tends to be highest during the early morning hours, shortly before sunrise. This is because the air temperature often reaches its lowest point overnight, and as the air cools, its capacity to hold moisture decreases, leading to higher relative humidity values.
Conversely, the outside relative humidity tends to be lowest during the late afternoon, typically around the hottest time of the day. As the air temperature rises, its capacity to hold moisture increases, resulting in lower relative humidity values.
It's important to note that these patterns can vary depending on the local climate, weather conditions, and geographical location. Other factors such as wind patterns and nearby bodies of water can also influence relative humidity throughout the day.
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how to solve 2+(n-1)3
Answer:
3n - 1
Step-by-step explanation:
2+(n-1)3
=> 2 + 3*n -3*1
=> 2 + 3n - 3
=> 3n - 1
Hope you understand!!
pls help with geometry
Answer:
Step-by-step explanation:
4) Corresponding part of congruent figures are congruent.
ΔABC ≅ ΔDEF
∠B = ∠E
∠B = 93°
∠F = ∠C = 73°
AC = DF = 7.6 cm
DE = AB = 5.4 cm
5)∠M = ∠A = 112
∠C =∠O = 81
OP = CD
AD = MP
Find the distance between each pair of points. Round when needed to the nearest tenth. P (2, -1), Q (10, – 7)
Answer:
10
Step-by-step explanation:
Please tell me if it’s a right triangle or not ( ಥ _ ಥ )
6, 7, 8
10,20,30
16,18,82
22,42,60
Were the empty years of Charles II's reign a good time to live in london?
The "Empty Years" was a phrase used to describe the period of the reign of King Charles II from 1660 to 1685. It was a time when London underwent significant transformations, both culturally and politically.
This period was characterized by a lack of major events or significant changes, hence the term "Empty Years." The term may have been misleading, though. Charles II's reign was an exciting time to live in London, with the restoration of the monarchy and the subsequent rebuilding of the city.
The period was also characterized by significant political developments, including the establishment of the two-party system and the rise of political satire. The London Gazette, the first regular newspaper in the city, was also established during Charles II's reign. The growth of political satire and the press helped to shape public opinion and influence political events in the city. Overall, the "Empty Years" of Charles II's reign were an exciting time to live in London, with a growing economy, cultural and political developments, and a sense of renewed hope for the future.
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Elizabeth Oliver sells luxury cars. She earns a 4 percent straight commission. Lastmonth her sales totaled $128,000. What was her commission?
$128,000 represents 100%
To find how much is 4% we can use the next proportion:
\(\frac{128,000\text{ \$}}{x\text{ \$}}=\frac{100\text{ \%}}{4\text{ \%}}\)Solving for x:
\(\begin{gathered} 128,000\cdot4=100\cdot x \\ \frac{512,000}{100}=x \\ 5,120=x \end{gathered}\)Her commission is $5,120
Here is a linear equation: y = 1/4x + 2. What is the x-intercept of the graph of the equation? Submit and Explain
pls help
i need help does anyone know this question
Answer:
The third answer is correct.
Step-by-step explanation:
You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral. Then you need the scale factor from the smaller figure to the larger.
Side EF times the scale factor will give you side AB. Let's call the scale factor s then our equation would be:
EF x s = AB To find s divide both sides by EF
\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)
s = \(\frac{AB}{EF}\) This is our scale factor.
Helping in the name of Jesus.
The probability density function of the random variable X whose moment generating function (1/2)(1+e^t) is: (a) x/3,x=0,1,2 (b) 1/2,x=0,1 (c) 1/3,x=0,1,2 (d) x+1/3,x=0,1
The probability density function (pdf) of the random variable X, whose moment generating function is (1/2)(1+e^t), is given by (c) 1/3, x=0,1,2.
The moment generating function (MGF) of a random variable X is defined as the expected value of \(e^{tX}\), where t is a real number. In this case, the given MGF is (1/2)(1+\(e^t\)).
To find the pdf, we need to calculate the probabilities for each possible value of X. The pdf is obtained by taking the derivative of the MGF with respect to t and evaluating it at t=0.
Differentiating the MGF with respect to t, we get d/dt[(1/2)(1+\(e^t\))] = (1/2)\(e^t\). Evaluating this at t=0, we obtain (1/2)\(e^0\) = 1/2.
Since the pdf represents probabilities, the sum of probabilities for all possible values of X must be equal to 1. In this case, we have three possible values for X: 0, 1, and 2. Therefore, we divide the total probability (1) equally among these three values, resulting in (c) 1/3, x=0,1,2.
Hence, the correct answer is (c) 1/3, x=0,1,2.
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