Answer: 320 miles
Step-by-step explanation:
Let the miles that they drove be represented by x.
Since Sarah drove two-fifths of the miles which is 128 miles, then the total miles would be:
= 2/5 × x = 128
0.4 × x = 128
0.4x = 128
x = 128/0.4
x = 320
The total miles is 320 miles.
Solve the inequality. Graph the solution -3s<11s+1
\(-3s\textless11s+1\\\\\\\\-3s-11s < 1\\\\\\-14s < 1\\\\\\-s < \frac{1}{14} \\\\s > -\frac{1}{14}\)
===========================
\(\textcopyright ELIZA\)
a child advocate collects data by randomly selecting 4 of the 25 state orphanages and surveys every child in the four orphanages.
The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.
This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.
By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.
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The sum of the first m terms of an arithmetic sequence with first term −5 and common difference 4 is 660. Find m
Based on the arithmetic sequence with the first term −5 and the common difference 4 is 660, we could find m = 20.
To find the sum of the first m terms of an arithmetic sequence, we can use the formula:
sum = (m/2)(2a + (m-1)d),
where a is the first term,
d is the common difference,
and m is the number of terms.
In this case, we are given a = −5, d = 4, and sum = 660. We can plug these values into the formula and solve for m:
660 = (m/2)(2(-5) + (m-1)(4))
660 = (m/2)(-10 + 4m - 4)
660 = (m/2)(4m - 14)
1320 = m(4m - 14)
0 = 4m^2 - 14m - 1320
Now we can use the quadratic formula to solve for m:
m = (-b ± √(b^2 - 4ac))/(2a)
m = (-(−14) ± √((−14)^2 - 4(4)(-1320)))/(2(4))
m = (14 ± √(196 + 21120))/8
m = (14 ± √21316)/8
m = (14 ± 146)/8
Now we have two possible values for m:
m = (14 + 146)/8 = 160/8 = 20
m = (14 - 146)/8 = -132/8 = -16.5
Since m must be a positive integer, we can conclude that m = 20. Therefore, the sum of the first 20 terms of the arithmetic sequence is 660.
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Given that 5 x : 9 = 7 : 3 Calculate the value of x . Give your answer in its simplest form.
The value of x in the ratio 5x : 9 = 7 : 3 is x = 21/5
How to determine the value of x in the ratio?From the question, the ratio is given as
5x : 9 = 7 : 3
Express the ratio, as a fraction
So, we have the following representation
5x / 9 = 7 / 3
Cross multiply the following expression
So, we have the following representation
3 * 5x = 9 * 7
Evaluate the products
15x = 63
Divide both sides by 15
So, we have
x = 63/15
Simplify the fraction
x = 21/5
Hence, the solution to the ratio is x = 21/5
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The temperature at noon was 8 °.
How many degrees colder is 15°?
Answer:
7 degrees colder
Step-by-step explanation:
15 degrees - 8 degrees = 7 degrees
how fast is the angle between the ladder and the ground changing in example 2 when the bottom of the ladder is 6 ft from the wall?
The angle between the ladder and the ground is - 0.075 rad/s.
Pythagoras' theorem is a essential relation in Euclidean geometry among the 3 facets of a proper triangle. It states that the region of the rectangular whose aspect is the hypotenuse (the aspect contrary the proper angle) is identical to the sum of the regions of the squares on the alternative facets.
cosθ = x/10
On differentiating the above equation,
- sinθdθ/dt = (1/10)dx/dt
dθ/dt = -(1/10)dx/dt/sinθ
sinθ = y/10
= √(100 - 36)/10
= 0.8; dθ/dt
= -(1/10)·0.6 ft/s/0.8
= - 0.075 rad/s
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11. A patio lounge chair can be reclined at various angles, one of which is illustrated below.
.
Based on the given measurements, at what angle, θ, is this chair currently reclined? Approximate to the nearest tenth of a degree.
a. 31.4 b. 33.2 c. 40.2 d. 48.6
The angle, θ, at which the chair is currently reclined is approximately 31.4 degrees. Thus, the correct option is a. 31.4.
To determine the reclined angle, θ, of the patio lounge chair, we can use trigonometry and the given measurements.
In the diagram, we can see that the chair's reclined position forms a right triangle. The length of the side opposite the angle θ is given as 1.2 meters, and the length of the adjacent side is given as 2.3 meters.
The tangent function can be used to find the angle θ:
tan(θ) = opposite/adjacent
tan(θ) = 1.2/2.3
θ = arctan(1.2/2.3)
Using a calculator, we can find the arctan of 1.2/2.3, which is approximately 31.4 degrees.
Therefore, the angle, θ, at which the chair is currently reclined is approximately 31.4 degrees. Thus, the correct option is a. 31.4.
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(p) Lee completes a journey in three
stages. In stage 1, he drives at 30 km/h
for 45 minutes. In stage 2, he drives at 50
km/h for 2 hours 48 minutes. Altogether,
over all three stages, he drives 200 km in
4 hours. What is Lee's average speed in
stage 3 of his journey?
Lee's average speed in stage 3 of his journey is 83.33 km/h.
What is an average speed?
The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
Here, we have
Lee travels in stage 1 of his journey is
d = s × t
d = 30 × 3/4
d = 22.5km
Lee travels in stage 2 of his journey is
d = s × t
d = 50 ×2(48/60)
d = 140km
The average speed in stage 3 is
d = 200 - 140 - 22.5 = 37.5km
t = 4hr - 2hr48m - 45m = 27 min
s = 37.5 ÷ 0.45 = 83.33 km/h
Hence, Lee's average speed in stage 3 of his journey is 83.33 km/h.
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solve pls brainliest
Answer:
mixed number: 2 1/4
improper fraction: 9/4
Answer:
mixed number: 2 1/4
improper fraction: 9/4
Step-by-step explanation:
hope it helps
would appreciate brainly
use inverse operation to solve 1 1/8=2 1/4x
The value of x in 1 1/8=2 1/4x by using inverse operation is 1 / 2.
What is the inverse operation?Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other.
Given:
1 1/8=2 1/4x
Solve the above equation by using the inverse operation.
Solve the mixed fraction into improper fractions as shown below,
9 / 8 = 9 / 4 x
x = 9 / 8 × 4 / 9
x = 1 / 2
Therefore, the value of x in 1 1/8=2 1/4x by using inverse operation is 1 / 2.
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Y= 4+3x solve it and pls hurry
Answer:
Step-by-step explanation:
y = 4 + 3x
3x + 4 = y
- 4 - 4
3x = y - 4
/ 3 / 3
x = 1/3y - 4/3
integral of 1/sqrt(x^2 - a^2) dx
To solve the integral of 1/sqrt(x^2 - a^2) dx, we can use the substitution method. Let u = x^2 - a^2, then du/dx = 2x, and dx = du/2x.
Substituting into the integral, we get:
∫ 1/sqrt(x^2 - a^2) dx = ∫ 1/sqrt(u) * du/2x
= (1/2) ∫ 1/sqrt(u) du
= (1/2) * 2sqrt(u) + C
= sqrt(x^2 - a^2) + C
Therefore, the answer to the integral of 1/sqrt(x^2 - a^2) dx is sqrt(x^2 - a^2) + C, where C is the constant of integration.
In summary, the integral of 1/sqrt(x^2 - a^2) dx can be solved using the substitution method, where u = x^2 - a^2. The final answer is sqrt(x^2 - a^2) + C, where C is the constant of integration.
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The integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration
What is intergration?
Integration is a fundamental concept in calculus that involves finding the antiderivative or integral of a function. It is the reverse process of differentiation, which is concerned with finding the derivative of a function.
To find the integral of \(1/\sqrt(x^2 - a^2) dx\), we can use a trigonometric substitution. Let's substitute \(x = a sec(\theta)\), where \(sec(\theta)\) is the reciprocal of the cosine function.
By making this substitution, we can express dx in terms of \(d(\theta)\) as follows:
\(dx = a sec(\theta) tan(\theta) d(\theta)\)
Now, let's substitute these values into the integral:
\(\int \frac{1}{\sqrt{x^2 - a^2}} dx\\\\= \int \frac{1}{\sqrt{(a \sec(theta))^2 - a^2}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\sec^2(theta) - 1)}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\tan^2(theta))}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{a \tan(theta)} (a \sec(\theta) \tan(\theta)) d(\theta)\)
Simplifying the expression, we have:
\(= \int \sec(\theta) d(\theta)\)
The integral of \(sec(\theta)\) can be evaluated as the natural logarithm of the absolute value of \(sec(\theta)\) plus the tangent\((\theta)\):
\(= \ln|\sec(\theta) + \tan(\theta)| + C\)
Finally, substituting back \(x = a sec(\theta)\), we get:
\(= \ln|\sec(\theta) + \tan(\theta)| + C\\\\= \ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\)
Therefore, the integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration
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Develop the B&B tree for each of the following problems. For convenience, always select x₁ as the branching variable at node 0. Maximize z = 3x₁ + 2.8% subject to 2x + 5.x₂ = 18 4.x₁ + 2x₂ = 18 X₁, X₂0 and integer
To develop the Branch and Bound (B&B) tree for the given problem, follow these steps:
1. Start with the initial B&B tree, where the root node represents the original problem.
2. Choose \($x_1$\) as the branching variable at node 0. Add two child nodes: one for
\($x_1 \leq \lfloor x_1 \rfloor$ \\(floor of $x_1$) and one for $x_1 \geq \lceil x_1 \rceil$ (ceiling of $x_1$).\)
3. At each node, perform the following steps:
- Solve the relaxed linear programming (LP) problem for the node, ignoring the integer constraints.
- If the LP solution is infeasible or the objective value is lower than the current best solution, prune the node and its subtree.
- If the LP solution is integer, update the current best solution if the objective value is higher.
- If the LP solution is non-integer, choose the fractional variable with the largest absolute difference from its rounded value as the branching variable.
4. Repeat steps 2 and 3 for each unpruned node until all nodes have been processed.
5. The node with the highest objective value among the integer feasible solutions is the optimal solution.
6. Optionally, backtrace through the tree to retrieve the optimal solution variables.
Note: The specific LP problem and its constraints are missing from the given question, so adapt the steps accordingly.
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gabriella went skiing. she paid $35 to rent skis and $15 an hour to ski. if she paid a total of $95, how many hours did she ski?
Gabriella skied for 6 hours, Let x be the number of hours that Gabriella skied. We know that she paid $35 for ski rental and $15 per hour for skiing,
for a total of $95. We can set up the following equation to represent this information:
35 + 15x = 95
Solving for x, we get:
15x = 60
x = 4
Therefore, Gabriella skied for 6 hours.
Here is a more detailed explanation of how to solve the equation:
Subtract $35 from both sides of the equation.
15x = 60
15x - 35 = 60 - 35
15x = 25
Divide both sides of the equation by 15.
15x = 25
x = 25 / 15
x = 4
Therefore, x is equal to 4, which is the number of hours that Gabriella skied.
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Which of the following is equivalent to 8^(1/3)?
Option 1
Option 2
Option 3
Option 4
(look at photo for answers)
the answer is option 2....
Answer:
Option 2
Step-by-step explanation:
when the power appears as a fraction, take the root of the number based on the denominator of the fraction when numerator is equal to 1
The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate
The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.
The time Jasmine spends biking is indeed a function of the distance she bikes.
The formula to calculate the time Jasmine takes to bike a certain distance is equal to,
time = distance / speed __(1)
Here the speed is the rate at which Jasmine bikes = 18 miles per hour.
Let us consider 'd' be the distance representing the number of miles Jasmine bikes.
This implies,
The function that represents the time Jasmine spends biking in terms of the distance .
Function f(d) representing the time Jasmine spends biking for a distance of d miles
Substitute all the values in the formula (1) we get,
⇒ f(d) = d / 18
Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.
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The above question is incomplete , the complete question is:
The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.
Write the function representing the time Jasmine spends biking in terms of the distance?
help me plzzzzzzzzzzzzzz
Answer:
f(-9) = -189
Step-by-step explanation:
f(x) = -3x² - 6x
Plug in -9 for x.
f(-9) = -3(-9)² - 6(-9)
According to PEMDAS (parentheses/exponents | multiplication/division | addition/ subtraction), we should solve the exponents first.
f(-9) = -3(81) - 6(-9)
Now, multiply.
f(-9) = -243 + 54
Now, add.
f(-9) = -189
This is your answer.
Hope this helps!
A researcher selects a sample and administers a treatment to the individuals in the sample. if the sample is used for a hypothesis test, what does the null hypothesis (h0) say about the treatment?
The null hypothesis (H0) says about the treatment is that it does not affect the scores.
What is hypothesis testing?Hypothesis testing is the statistical method that uses the data from a sample to conclude a population parameter or a population distribution.
There are two types of hypothesis testing. They are the null hypothesis and the alternative hypothesis.
If the obtained value is less than the threshold value then the null hypothesis is accepted and the alternative hypothesis is rejected.If the obtained value is greater than the threshold value then the null hypothesis is rejected and the alternative hypothesis is accepted.What is a null hypothesis?The null hypothesis says that there is no difference between the sample means of the two groups.This is a statement about a population parameter.Where the possibilities are the same.It is given that,
A researcher selects a sample and administers a treatment to the individuals in the sample.
A hypothesis test is conducted on the sample.
So, the null hypothesis (H0) says about the treatment is that it does not affect the score obtained.
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a random variable from an experiment where outcomes are normally distributed a. can have any value between -infinity and infinity. b. can have only a few discrete values c. can have positive values d. can have no values
a random variable can have any value that is possible within the range of -infinity and infinity.So a. can have any value between -infinity and infinity.
A random variable from an experiment with outcomes that are normally distributed can take on any value between -infinity and infinity. This means that it can take on any real number, including fractions and decimals. It is not limited to only a few discrete values, nor does it have to be positive.
A random variable from an experiment with outcomes that are normally distributed can take on any real value between -infinity and infinity. This means that the variable is not limited to a few discrete values, nor does it have to be positive. Instead, it can have any value, no matter how small or large, and including fractions and decimals. Such a random variable can have any value that is possible within the range of -infinity and infinity.
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HELP PLEASE?e?e?e?E?E?E?E?EE?E?E?e
Answer:
1/2
Step-by-step explanation:
You put 5 as a numerator and then 10 as a denominator which is 5/10. But you can simplify it, so you change it to 1/2. Hope this helps!
Answer:
1/2
Step-by-step explanation:
Help me, please
I really need
Answer:
answrr
yes ok
Step-by-step explanation:
4+4-4#_44
Suppose a charity received a donation of $22.9 million. If this represents 48% of the charity's donated funds, what is the total amount of its donated funds?
Round your answer to the nearest million dollars.
A new car is purchased for 24800 dollars. The value of the car depreciates at 12% per year. What is the y-intercept (starting value)? *
Answer:
$24,800
Step-by-step explanation:
that's how much the car costs at year 0
Answer:
Step-by-step explanation:
The starting value, y intercept, is just the initial value as it has not depreciated when time or x is zero.
The equation described is y=24800(0.88)^x
DE D 5х - 12 Е Зх 3х - 4 4 F
EXPLANATION
We have an equilateral triangle because the 3 angles are congruent as shown in the picture and all legs are congruent:
So, 5x-12 = 3x - 4
Adding +12 to both sides:
5x - 12 + 12 = 3x - 4 + 12
Simplifying:
5x = 3x + 8
Subtracting both sides by -3x:
5x - 3x = 3x - 3x + 8
Simplifying:
2x = 8
Dividing both sides by 2:
x = 8/2
Simplifying:
x=4
Now, replacing in any equation, as 5x - 12:
5*(4) - 12= 8
In conclusion, all the legs are congruent and equal to 8.
Answer: DE= 8
What is the volume of this rectangular prism?
O A. 11 cm3
O B. 56 cm3
O C. 64 cm
O D. 28 cm3
Answer:
28
Step-by-step explanation:
I think because the formula for the volume of a rectangular prism is whl
Distributive property for x(11+2), please????
Answer: 13x
Step-by-step explanation: Multiply x to 11 and 2
11x+2x=13x
Help if don't know don't answer and link i will report
∠6 is an alternate interior angle to ∠3
∠5 corresponds to ∠7
∠7 is a consecutive interior angle to ∠6
∠8 is an alternate exterior angle to ∠1
Helppppppppppppppppp
Answer:
3)
Step-by-step explanation:
An equation is linear if equal changes in x produce equal changes in y.
Let's look at each choice.
1)
A decrease of 10% per year. That means each year, the value of the car is 0.9 times the value of the previous year.
For example, if the original value was $10,000, after 1 year, it is worth 0.9 * $10,000 = $9,000. In 1 year it lost $1,000. In the next year, its value is now 0.9 * $9,000. The value at the end of the 2nd year is $8,100. In the second year, it lost $900 in value. In one period of 1 year it lost $1000 in value. In another equal period of 1 year, it lost $900 in value. A change of 1 year in time produces different changes in loss of value, so it is not linear.
2)
Here, the number doubles every year. Let's say it starts with 100 fish. After 5 years, it has 200 fish. In a change of 5 years in x, the change in y is 100. In the next 5 years, it goes from 200 fish to 400 fish. The change in the second period of 5 years is 200. We see that a change of 5 years can produce a change of 100 fish, but another change of 5 years can produce a change is 100 fish. Since for equal changes in x, the changes in y are not all equal, this is not linear.
3)
Here for every change of 1 day in x, the change in y is 2 liters. Each change of 1 in x always produces a change of 2 in y. This is linear.
4)
Each 2 hours, the amount of caffeine is 2/3 of what it was before. This is similar to the choice 1), and it is not linear.
Answer: 3)
a wheat farmer is investigating the effectiveness of a treatment for controlling a pest. a random sample of 500 plants shows that 47 of them are infected by the pest. what does this sample indicate about the claim that 20% of the plants are infected?
The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
This given test is a test for single sample proportion
The test hypothesis are:
\(H_{o} :p=0.20\), null hypothesis
\(H_{1} :p\neq 0.20\), alternative hypothesis
The test statistic fallows a standard normal distribution and is given by:
\(Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }\)
p=0.20
X=47 plants
Sample size, n=500
x, is the sample mean:
x=X/n=47/500
x=0.094
So, test statistic is calculated as:
\(Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }\)
Z=-5.93
From the z-table, the p-value associated with Z=-5.93 is approximately 0
The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level
In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim
So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
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SOMEONE HELP ASAP!!
The figure above shows a Ferris wheel with radius 5 meters as Jalen, whose eye level is at point (0,2), watches his friend, Ashanti, ride in one of the cars as the wheel turns. Let Z denote the distance from Jalen to Ashanti’s car.The diagram indicates the center of the Ferris wheel at the point (12,7) and the position of Ashanti’s car at the point (x,y). If x and y are functions of time t, in seconds, what is the rate of change of Z when x=15, y=11, and dxdt=1 ? (The equation of a circle with radius r and center (h,k) is (x−h)2+(y−k)2=r2.)
9514 1404 393
Answer:
(c) dZ/dt = 11/√544, so moving away at about 0.47 m/s
Step-by-step explanation:
The (x, y) coordinates of the car are related by the fact that they are on a circle centered at (12, 7) with a radius of 5. Then their rates of change are related by the derivative of the circle equation with respect to time.
(x -12)^2 + (y -7)^2 = 25
2(x -12)x' +2(y -7)y' = 0
y' = -(x -12)/(y -7)x'
At the time and point of interest, we have ...
y' = -(15 -12)/(11 -7)(1) = -3/4
__
The distance (z) to the observer is given by the Pythagorean theorem:
z^2 = (x -0)^2 +(y -2)^2
and its rate of change with time is ...
2z·z' = 2(x-0)x' +2(y -2)y'
The distance d at the point of interest is ...
z = √((15 -0)^2 +(11 -2)^2) = √(225 +81) = √306 = 3√34
So, the rate of change of distance to the observer at the time and point of interest is ...
z' = (x(x') +(y -2)y')/z
z' = ((15)(1) +(11-2)(-3/4))/(3√34) = (33/4)/(3√34)
z' = 11/√544 ≈ 0.47 . . . m/s