The graph of the piecewise function f(x) is added as an attachment
How to graph the piecewise functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2 if 0 ≤ x ≤ 2
3 if 2 ≤ x < 4
-4 if 4 ≤ x ≤ 8
To graph the piecewise function, we plot each function according to its domain
Using the above as a guide, we have the following:
Plot f(x) = -1 in the domain -1 ≤ x < 0 Plot f(x) = -2 in the domain 0 ≤ x < 1 Plot f(x) = -3 in the domain 1 ≤ x < 2The graph of the piecewise function is added as an attachment
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Question
Graph the following
f(x) = 2 if 0 ≤ x ≤ 2
3 if 2 ≤ x < 4
-4 if 4 ≤ x ≤ 8
You can plot this function is Demos pretty easily. To do so enter the function as shown
drop down menu 5x – 2x + 7 –x = x+
Answer:
x=-7
Step-by-step explanation:
5x - 2x + 7 - x = x
2x - x = x - 7 - x
x = - 7
2x = x - 7
2x + 7 = x
2x + 7 - 7 =x7
A window is being replaced with tinted glass. The plan below shows the design of the window. Each unit length represents 1 foot. The glass costs $16 per square foot. How much will it cost to replace the glass? Use 3.14 fo
Which situation CANNOT be represented by the equation x + 12 = 30?
Total snowfall for the winter was 30 inches. In January, it snowed 12 inches. What is x, the amount of snow that fell during
the other winter months?
Maria had $12. When she combined her money with Sarah, they had $30. What is x, the amount of money Sarah had?
Juanita spent $30 at the store buying a shirt and shorts. She bought a shirt for $12. What is the cost, x, of the shorts?
James 12 miles on Monday and 30 miles on Tuesday. What is, x, the total number of miles James ran all together?
Answer: D IS THE CORRECT ANSWER
Step-by-step explanation: MARK BRAINLIEST PLS
Answer:
I took the test ._.
T/F A truth table for p V ~q requires four possible combinations of truth values.
False. A truth table for p V ~q requires only two possible combinations of truth values.
False. A truth table for p V ~q requires a total of two possible combinations of truth values.
The statement "p V ~q" is a logical disjunction, meaning it is true if either p is true or ~q is true (or both). There are only two possible truth values for each of these propositions: true or false. Therefore, there are only two possible combinations of truth values for the statement "p V ~q," which are:
- p is true, ~q is false (i.e., q is true)
- p is true, ~q is true (i.e., q is false)
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Will mark Brainliest
Computer A: A graph has programs on the x-axis and megabytes on the y-axis. A line goes through (0, 32) and (2, 176). Computer B: A 2-column table with 3 rows. Column 1 is labeled Programs: x with entries 2, 4, 6. Column 2 is labeled Megabytes: y with entries 198, 370, 542.
Devonne compared the memory usage of two computers as various programs were run. She concluded that Computer A uses more megabytes for each additional program than Computer B. Is she correct?
Yes. Computer A has the greater slope.
Yes. Computer A has greater initial value.
No. Computer B has the greater slope.
No. Computer B has the greater initial value.
Answer:
c
Step-by-step explanation:
Suppose that N is known and only success probability p is unknown. Compute the method of moment estimator and the maximum likelihood estimator for p.
The maximum likelihood estimator for p is: X/N
Let X1, X2, ..., Xn be n independent Bernoulli trials with success probability p and let N be a known positive integer. The number of successes observed is denoted by X = X1 + X2 + ... + Xn, and we want to estimate p.
Suppose that N is known and only success probability p is unknown. Compute the method of moment estimator and the maximum likelihood estimator for p.
The sample mean is a method-of-moments estimator of the population mean. This is one way of defining the method of moments. In this particular case, the population mean is equal to p, which is what we want to estimate.
The sample mean is equal to X / N.
Therefore, the method of moments estimator for p is:X/N
Maximum likelihood estimator
The probability mass function of X is given by:
\(P(X = k) = C(N,k) * pk * (1 - p) {}^{(N-k)} \)
where C(N,k) is the binomial coefficient (N choose k).
The log-likelihood function is given by:
\(ln(L(p)) = ln[C(N,X) * px * (1 - p) {}^{(N-X} ]\)
where X is a constant. Taking the derivative of this function with respect to p and setting it equal to zero, we get:
p = X / N
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What is the equation of this line in slope-intercept form?
y=-2/3x+1 y=2/3x+1 y=3/2x+1
to get the equation of any straight line all we need is two points from it, let's use those ones in the picture.
\((\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{2}{3}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{2}{3}}(x-\stackrel{x_1}{0})\implies y=\cfrac{2}{3}x+1\)
Given integer vector x has 5 elements with values 4, 7, 3, 0, 8. what are the ending values in x? int i; for (i = 0; i < x.size() - 1; i) { x.at(i) = x.at(i 1); }
The ending values in vector `x` after executing the given code snippet would be `7 3 0 8 8`.
The given code snippet appears to be incorrect and incomplete. There are a few issues:
1. The loop condition is not properly defined. Instead of `i < x.size() - 1`, it should be `i < x.size() - 1` to ensure that `i` does not exceed the valid index range of the vector `x`.
2. The increment expression `i` is missing in the loop statement, causing an infinite loop since `i` never changes.
Assuming the correct loop condition is `i < x.size() - 1` and the missing increment expression is `i++`, let's correct the code:
cpp
#include <iostream>
#include <vector>
int main() {
std::vector<int> x = {4, 7, 3, 0, 8};
int i;
for (i = 0; i < x.size() - 1; i++) {
x.at(i) = x.at(i + 1);
}
// Printing the modified vector x
for (int element : x) {
std::cout << element << " ";
}
std::cout << std::endl;
return 0;
}
Now, running this corrected code will give the following output:
7 3 0 8 8
After executing the loop, the vector `x` will have the ending values `7, 3, 0, 8, 8`. The last element `x.at(4)` is assigned the value of `x.at(4 + 1)`, which is `8`.
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Write an equation of a line that passes through the point T ( − 2, − 5 ) and is parallel to the line y = 5 x + 7 .
Answer:
y = 5x + 5
Step-by-step explanation:
the slope to be parallel y = 5x + 7 must still be 5. To make the line pass through T, the given point, you plug (-2, -5) into the y= mx + b formula. This becomes( -5 )= 5 (-2) + B, and you solve for b. In this equation, b = 5.
please help me? or if you could explain to me how can I get my answer.
Answer:
The Answere is 3 centimeters
Step-by-step explanation:
Google is an amazing professer
1)
cos^4 = 3/8+1/2cos2x+1/8cos4x
2) Cos^6 theta +sin^6 theta = 1-3/4sin^22theta
Please prove both I will appreciate you
\(\qquad\) \(\purple{\twoheadrightarrow\bf 2cos^2A = 1 + cos2A }\)
\(\qquad\) \(\purple{\twoheadrightarrow\bf a^3 +b^3 = (a+b)^3 -3ab(a+b)}\)
\(\qquad\) \(\purple{\twoheadrightarrow\bf 2 sinA cosA = sin2A}\)
________________________________________
1)
\(\qquad\) \(\twoheadrightarrow\bf L.H.S\)
\(\qquad\) \(\pink{\twoheadrightarrow\bf cos^4 x}\)
\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4} (2cos^2x)^2\)
\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}(1+cos2x)^2\)
\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}(1+2cos2x+cos^22x)\)
\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}+\dfrac{1}{2}cos2x+\dfrac{1}{8}\times 2cos^22x\)
\(\qquad\) \(\twoheadrightarrow\sf \dfrac{1}{4}+\dfrac{1}{2}cos2x+\dfrac{1}{8}\times(1+cos4x)\)
\(\qquad\) \(\pink{\twoheadrightarrow\bf \dfrac{1}{4}+\dfrac{1}{2}cos2x+\dfrac{1}{8}\times cos4x} \)
\(\qquad\) \(\twoheadrightarrow\bf R.H.S\)
______________________________________
2)
\(\qquad\) \(\twoheadrightarrow\bf L.H.S\)
\(\qquad\) \(\pink{\twoheadrightarrow\bf cos^6\theta +sin^6\theta }\)
\(\qquad\) \(\twoheadrightarrow\sf (cos^2\theta)^3 +(sin^2\theta)^3\)
\(\twoheadrightarrow\sf (cos^2\theta +sin^2\theta)^3 -3cos^2\theta sin^2\theta (cos^2\theta +sin^2\theta)\)
\(\qquad\) \(\twoheadrightarrow\sf 1-3\times \dfrac{1}{4}\times 4(sin\theta cos\theta) ^2\)
\(\qquad\) \(\twoheadrightarrow\sf 1-\dfrac{3}{4}(2sin\theta cos\theta) ^2\)
\(\qquad\) \(\pink{\twoheadrightarrow\sf 1-\dfrac{3}{4}sin^22\theta}\)
\(\qquad\) \(\twoheadrightarrow\bf R.H.S\)
X: -6. -2. 2. 6
Y: 8. 5. 2. -1
The slope of the line is ??????
Please help
Step-by-step explanation:
the slope = (8-5)/(-6+2) = 3/-4 = -¾
a pole that is 2.8m tall casts a shadow that is 1.49m long. at the same time, a nearby building casts a shadow that is 37.5m long. how tall is the building? round your answer to the nearest meter.
The height of the building is 71 meters.
We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:
(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)
Substituting the given values:
2.8 / 1.49 = (height of building) / 37.5
To find the height of the building, we can cross-multiply and solve for it:
(2.8 * 37.5) / 1.49 = height of building
Calculating the expression on the right side:
(2.8 * 37.5) / 1.49 ≈ 70.7013
Rounding to the nearest meter, the height of the building is approximately 71 meters.
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Dominick is training for a race. He spends 0.75 hours running each time he runs and 1.5 hours swimming each time
he swims. This week, he spent more than 6 hours training for the race. Which graph represents his possible training
times this week?
Answer:
The possible graph is "A". A further explanation is given below.
Step-by-step explanation:
The given values are:
Dominick spends on running
= 0.70 hours
He spends on swimming
= 1.5 hours
This week,
Dominick spends more than six hours.
If,
Number of runs be "x".
Number of swimming be "y".
then,
⇒ \(0.75x+1.5y>6\)
⇒ \(75x+150y>600\)
⇒ \(x+2y>8\)
Therefore, \(x+2y=8\)
x = 0
y = 4
So the above is the correct answer.
I need to figure the code out
The function with the greatest rate of change are:
1. C = 3
2. A = 5
3. A = 1
4. B = 3
What is the Rate of Change of a Linear Function?The rate of change of a linear function, also known as the slope of the line, represents the amount by which the output (y) changes for a given change in the input (x). In other words, it is the measure of how steep the line is.
The formula for the rate of change, or slope, of a linear function is:
slope = (change in y) / (change in x)
1. Rate of change for function A = change in y / change in x = 4/3
For B = 1/2
For C = 3/1 = 3
The function with the greatest rate of change is C = 3
2. Rate of change for function A = change in y / change in x = (10 - 5)/(1 - 0) = 5
For B = (12 - 8) / (3 - 1) = 2
For C = (6 - 3)/(1 - 0) = 3
The function with the greatest rate of change is A = 5
3. Rate of change for function A = change in y / change in x = 2/2 = 1
For B = (3 - 2)/(2 - 0) = 1/2
For C = 1/3
The function with the greatest rate of change is A = 1
4. Rate of change for function A = change in y / change in x = -1/3
For B = (10 - 1)/(4 - 1) = 3
For C = 2
The function with the greatest rate of change is B = 3
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Gary is thinking of a number he says my number is prime and it is a factor of 36 what is the.2 Number he could be thinking of
Answer:
3
Step-by-step explanation:
needed to write more but it's still 3
Evaluate the expression.
2.15(3)2=
Answer:
12.9
Step-by-step explanation:
assume that the random variable x is normally distributed, with mean μ = 70 and standard deviation σ = 12. compute the probability p(37 < x < 85).
Therefore, the probability that the random variable X falls between 37 and 85 is approximately 0.8916 or 89.16%.
To compute the probability P(37 < X < 85) for a normally distributed random variable X with a mean μ = 70 and standard deviation σ = 12, we need to standardize the values and use the standard normal distribution.
First, we calculate the z-scores for the given values:
z1 = (37 - μ) / σ = (37 - 70) / 12 ≈ -2.75
z2 = (85 - μ) / σ = (85 - 70) / 12 ≈ 1.25
Next, we use a standard normal distribution table or a calculator to find the probabilities associated with the z-scores.
Using a standard normal distribution table, we find:
P(Z < -2.75) ≈ 0.0028 (probability corresponding to z1)
P(Z < 1.25) ≈ 0.8944 (probability corresponding to z2)
To find the probability of the interval (37 < X < 85), we subtract the probability associated with the lower value from the probability associated with the upper value:
P(37 < X < 85) = P(-2.75 < Z < 1.25) = P(Z < 1.25) - P(Z < -2.75) ≈ 0.8944 - 0.0028 ≈ 0.8916
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calculate the volume when the area completely enclosed by the graphs y=x^2 and y= (3/(1 x^3)) is revolved about the x-axis
The volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\) To find the volume when the area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we can use the method of cylindrical shells.
First, let's find the points of intersection between the two curves by setting them equal to each other:
\(\[x^2 = \frac{3}{x^3}\]\)
To simplify this equation, we can multiply both sides by \(\(x^3\)\):
\(\[x^5 = 3\]\)
Now, taking the fifth root of both sides:
\(\[x = \sqrt[5]{3}\]\)
So the two curves intersect at \(\(x = \sqrt[5]{3}\)\).
To calculate the volume area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we need to integrate the circumference of each cylindrical shell multiplied by its height. The height of each shell is the difference in the y-values of the two curves, and the circumference is\(\(2\pi x\)\).
Let's integrate from \(\(x = 0\)\) to \(\(x = \sqrt[5]{3}\)\):
\(\[V = \int_0^{\sqrt[5]{3}} 2\pi x \left(\frac{3}{x^3} - x^2\right) \, dx\]\)
Simplifying this expression:
\(\[V = 2\pi \int_0^{\sqrt[5]{3}} \left(\frac{3}{x} - x^3\right) \, dx\]\)
Integrating each term separately:
\(\[V = 2\pi \left[3 \ln|x| - \frac{x^4}{4}\right]_0^{\sqrt[5]{3}}\]\)
Plugging in the limits of integration:
\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right] - 2\pi \left[3 \ln|0| - \frac{0^4}{4}\right]\]\)
Since \(\(\ln|0|\)\)is undefined, the second term on the right side is zero:
\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right]\]\)
Simplifying further:
\(\[V = 2\pi \left[3 \ln 3^{\frac{1}{5}} - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)
Using the properties of logarithms, we can simplify the first term:
\(\[V = 2\pi \left[3 \cdot \frac{1}{5} \ln 3 - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)
\(\[V = \frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\]\)
So the volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\)
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Applying PL, construct a symbolicmodel of the logical structure of the following argument. Construct a truth table to determine if the argument is valid. Be sure to state whether the argument is valid or invalid. If the argument is invalid then indicate a row that shows this. (4 points)
Jayco qualifies as a small business if and only if it has sales that are not large enough to influence its environment and it is privately owned by a small group of individuals. Jayco does not qualify as a small business. Therefore, Jayco must not be privately owned by a small group of individuals.
Please use these symbols: ~, v, • , ⊃, ≡
We can see that there is at least one row where all premises are true (row 7), but the conclusion is false. Therefore, the argument is invalid.
To construct a symbolic model of the argument, let's define the following symbols:
P: Jayco qualifies as a small business.
Q: Jayco has sales that are not large enough to influence its environment.
R: Jayco is privately owned by a small group of individuals.
Now we can represent the statements in symbolic form:
Premise 1: P ≡ (Q • R)
Premise 2: ~P
Conclusion: ~R
To determine if the argument is valid or invalid, we can construct a truth table:
| P | Q | R | P ≡ (Q • R) | ~P | ~R |
|---|---|---|-------------|----|----|
| T | T | T | T | F | F |
| T | T | F | F | F | T |
| T | F | T | T | F | F |
| T | F | F | F | F | T |
| F | T | T | F | T | F |
| F | T | F | T | T | T |
| F | F | T | F | T | F |
| F | F | F | T | T | T |
From the truth table, we can see that there is at least one row where all premises are true (row 7), but the conclusion is false. Therefore, the argument is invalid.
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5 x ?= 5 x (4 + ?) =( ? x 4) + (5 x ?)
Answer:
6/5
Step-by-step explanation:
2. 1: How Big Can the Garden Be? A homeowner wants to build a garden with concrete tiles around the outside. He has room for the garden to vary in length but not width. He’s not sure what size he wants the garden to be. Here are sketches of gardens that are 1, 2, and 3 meters long. The homeowner needs to know how many concrete tiles will be needed for different possible garden lengths. 3 by 3 grided rectangle, center rectangle shaded. 3 by 4 grided rectangle, center 2 rectangles shaded. 3 by 5 grided rectangle, center 3 rectangles shaded. Create a table to show how many tiles will be needed if the garden is 1, 2, 3, 4, or 5 meters long. Describe the way the pattern is growing
The length of the garden can be squared to determine the number of concrete tiles required for a garden of any length. We would want 6 x 6 = 36 tiles, for instance, if the garden was 6 meters long.
We can count the number of concrete tiles required for each length using the accompanying sketches to generate a table for gardens of various lengths.
We can see from this table that the quantity of tiles required for each length is equal to the length squared. For a garden that is 3 meters long, for instance, we would want 3 x 3 = 9 tiles for each of the 3 rows, for a total of 27 tiles.
The number of tiles required for longer gardens is equal to the length of the garden squared, and this pattern is maintained.
Therefore, The length of the garden can be squared to determine the number of concrete tiles required for a garden of any length. We would want 6 x 6 = 36 tiles, for instance, if the garden was 6 meters long.
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Solve the system of equations :-6x - y = -16-6x -5y = -8
The given system of equation are :
-6x - y = -16
-6x -5y = -8
On subtracting both the equation we get :
-6x -y -(-6x -5y) = -16 -(-8)
-6x -y +6x +5y = -16 +8
-6x + 6x +5y -y = -8
4y = -8
4y = -8
Divide both side by 4:
4y/4 = -8/4
y = -2
Substitute the value of y =- 2 in the any one equation:
-6x - y = -16
-6x - (-2)= -16
-6x + 2 = -16
-6x = -16 -2
-6x = -18
x = 3
Answer : x = 3, y = -2
what does infinite=/mean
Answer:
Infinite describes things that are endless
Step-by-step explanation:
Alice is willing to spend $30 on a pair of jeans, and has a coupon for $10 off she found online. She selects and purchases a $35 pair of jeans, pre-discount. Jeff finds some steaks for $16 for which he would have been willing to pay $20. The butcher notices the meat is near the expiration Jeffs surplus: date and gives him an extra 75% off.
Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.
Let's calculate the final amount paid by Alice and Jeff for their purchases.
Alice:
Alice has a budget of $30 for a pair of jeans, and a coupon for $10 off.The price of the jeans she selects is $35 before the coupon.To find the final price she paid, we need to subtract the coupon discount from the original price of the jeans: $35 - $10 = $25.So Alice paid $25 for her pair of jeans.Jeff:
Jeff finds a pack of steaks for $16 and is willing to pay up to $20.This means he has a surplus of $20 - $16 = $4 that he is willing to spend on the steaks.The butcher notices the meat is near the expiration date and gives Jeff an extra 75% off.To calculate the discount, we first need to find 75% of the original price: 0.75 * $16 = $12.So Jeff gets a discount of $12, and the final price he paid is the original price minus the discount: $16 - $12 = $4.Therefore, Jeff paid $4 for the steaks.So, Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.
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A circle has a circumference of 20π meters. If a sector has a central angle of 45°, what is the arc length of the sector? Use pi = 3.14
the arc length of the sector is 7.85 meters.
Define circumferenceThe circumference is define for a circle is given by the formula:
C = 2πr
where C is the circumference, π is the value of pi, and r is the radius of the circle.
In this case, the circumference of the circle is given as 20π meters. So we can write:
20π = 2πr
Dividing both sides by 2π, we get:
r = 10 meters
The arc length of a sector of a circle with central angle θ and radius r is given by the formula:
Arc length = (θ/360°) x 2πr
where θ is the central angle in degrees.
In this case, the central angle of the sector is 45°, and the radius of the circle is 10 meters. So we can substitute these values into the formula:
Arc length = (45/360) x 2π(10) = (1/8) x 20π = 2.5π
Using the value of pi as 3.14, we can calculate the arc length as:
2.5π = 2.5 x 3.14 = 7.85 meters
Therefore, the arc length of the sector is 7.85 meters.
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Please help with these word problems!!!
The speed of the plane in still air is 87 mph and the speed of the wind is 29 mph.
The cost of one package of tulip bulbs is $10.8 and the cost of one bag of daffodil bulbs is $8.5.
A van can carry 14 students and a bus can carry 62 students.
There are 13 students in each van and 59 students in each bus.
How to calculate the speedLet the speed of the plane be p and the speed of the wind be w. Then we have the following system of equations:
p + w = d/t1 = 580/5 = 116
p - w = d/t2 = 580/10 = 58
Adding the two equations, we get:
2p = 174
p = 87 mph
Substituting this value into either equation, we get:
w = 29 mph
Therefore, the speed of the plane in still air is 87 mph and the speed of the wind is 29 mph.
Let the cost of one package of tulip bulbs be x and the cost of one bag of daffodil bulbs be y. Then we have the following system of equations:
6x + 12y = 198
7x + 6y = 127
Multiplying the second equation by 2 and subtracting it from the first equation, we get:
5x = 54
x = 10.8
Substituting this value into either equation, we get:
y = 8.5
Therefore, the cost of one package of tulip bulbs is $10.8 and the cost of one bag of daffodil bulbs is $8.5.
Let the number of students a van can carry be x and the number of students a bus can carry be y. Then we have the following system of equations:
16x + 8y = 752
5x + 5y = 380
Simplifying the second equation, we get:
x + y = 76
Multiplying this equation by 8 and subtracting it from the first equation, we get:
8x = 112
x = 14
Substituting this value into either equation, we get:
y = 62
Therefore, a van can carry 14 students and a bus can carry 62 students.
Let the number of students a van can carry be x and the number of students a bus can carry be y. Then we have the following system of equations:
16x + 5y = 417
10x + 8y = 480
Multiplying the first equation by 2 and subtracting it from the second equation, we get:
6x = 42
x = 7
Substituting this value into either equation, we get:
y = 51
Therefore, a van can carry 7 students and a bus can carry 51 students.
Let the number of students in each van be x and the number of students in each bus be y. Then we have the following system of equations:
14x + 16y = 1086
10x + 13y = 870
Multiplying the first equation by 13 and subtracting it from the second equation multiplied by 16, we get:
2x = 26
x = 13
Substituting this value into either equation, we get:
y = 59
Therefore, there are 13 students in each van and 59 students in each bus.
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7) A plane traveled 580 miles to Ankara and back. The trip there was with the wind. It took 5 hours. The trip back was into the wind. The trip back took 10 hours. Find the speed of the plane in still air and the speed of the wind.
8) Amanda and Ndiba are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and bags of daffodil bulbs. Amanda sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. Ndiba sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of $127. Find the cost each of one package of tulips bulbs and one bag of daffodil bulbs.
9) The local amusement park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 16 vans and 8 buses with 752 students. High School B rented and filled 5 vans and 5 buses with 380 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
10) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 16 vans and 5 buses with 417 students. High School B rented and filled 10 vans and 8 buses with 480 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
11) The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 14 vans and 16 buses with 1086 students. High School B rented and filled 10 vans and 13 buses with 870 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
7. What value of c will make x2 – 20x + c
a perfect square trinomial?
In a circle, an angle measuring 2.4 radians intercepts an arc of length 24.4. Find the radius of the circle to the nearest
The radius of the circle is approximately 10.17 units (rounded to two decimal places).
To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:
arc length = radius x central angle
In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:
24.4 = r x 2.4
Solving for r, we get:
r = 24.4 / 2.4
r ≈ 10.17
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c. Explain why 32 percent is equivalent to
32/100
by
using your answers to parts (a) and (b).
Answer: 32% is equal to 32/100.
Step-by-step explanation: This is because 32% is also equal to 0.32. Percents are evaluted with the fraction denominator 100. 32/100 is also 32 parts out of 100 parts. This expression represents 32%.