Using the normal distribution, it is found that there are 68 students with scores between 72 and 82.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are given, respectively, by:
\(\mu = 72, \sigma = 10\)
The proportion of students with scores between 72 and 82 is the p-value of Z when X = 82 subtracted by the p-value of Z when X = 72.
X = 82:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{82 - 72}{10}\)
Z = 1
Z = 1 has a p-value of 0.84.
X = 72:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{72 - 72}{10}\)
Z = 0
Z = 0 has a p-value of 0.5.
0.84 - 0.5 = 0.34.
Out of 200 students, the number is given by:
0.34 x 200 = 68 students with scores between 72 and 82.
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If x-2=2^(2/3) + 2^(1/3), show that x3 - 6x3 + 6x-2=0
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Complete the following proof.
Given: Two concentric circles with AB tangent to smaller circle at R
Prove: AR = RB
Step-by-step explanation:
The statements are
1.Draw Oa,Ob
2.OR is perpendicular to AB
3.OR is congruent to OR
4.OA is congruent to OB
5.Triangle AOR is congruent to BOR.
6.AR is congruent to AB.
The reasons are
1.Auxalaritly lines
2 Radius are perpendicular to tangent
3.Reflexitive
4.Radii of same circle are equal
5.HL theorem, (since we know hypotenuse and a leg)
6.CPCTC
What is 2/3 ➗ 1/6?
2
3
4
6
Answer:
12/3=4
Step-by-step explanation:
it's 4, 2/3's stay the same. do the reciprocal on 1/6 which will be 6/1 and multiply
2/3(6/1)=12/3
and turn it to a mixed fractions and you would get 4
A bug hits the windshield of a moving car. Which statement describes the forces?
Group of answer choices
D. The force on the bug and the force on the car remains at zero.
A. The force on the car is equal to the force on the bug.
C. The force on the bug is greater than the force on the car.
B. The force on the car is greater than the force on the bug.
Answer: B: the force on the car is greater than the force on the bug
Step-by-step explanation:
The force on the car is greater because it is travelling at a faster speed.
Marco went to the cafeteria to buy chicken sandwiches, C, worth $2.00, and hamburgers, h, worth $2.50.
He bought a total of 9 items and spent a total of $20.50. How many hamburgers and chicken sandwiches
did Marco buy?
HELP
Answer:
5 Hamburgers = $12.50 4 Chicken sandwiches $8.00( $12.50 + $8.00 = $20.50
Step-by-step explanation:
Answer:
Marco bought 5 hamburgers and 4 chicken sandwiches.
Step-by-step explanation:
Set up a system of equations:
2c + 2.5h = 20.5
c + h = 9
Solve by elimination by multiplying the bottom equation by -2:
2c + 2.5h = 20.5
-2c - 2h = -18
Add the equations together and solve for h:
0.5h = 2.5
h = 5
So, he bought 5 hamburgers. Plug in 5 as h into the second equation to solve for c:
c + h = 9
c + 5 = 9
c = 4
So, Marco bought 5 hamburgers and 4 chicken sandwiches.
A garden table and a bench cost $783 combined. The garden table costs $83 more than the bench. What is the cost of the bench?
Answer:
$557.5
Step-by-step explanation:
783/2
391.5 + 83 (more) =
557.5
A store sells grape jelly in 15-ounce jars for $13.59. Find the price per ounce
Answer:
91 cents per ounce
Step-by-step explanation:
Divide 13.59 by 15
Answer: $0.91
Step-by-step explanation:
Take $13.59 divided by 15 = $0.91 per ounce
If you can, please give me a Brainliest, I need 2 more to get to the highest rank, thank you!
A box of oranges weighs 4 kg. If one orange weighs 80 g, how many oranges are in the box?
Answer:
50 oranges
Step-by-step explanation:
Convert the measurements for them to be the same ie 4kg to g
1kg=1000g. 4kgx1000=4000g
4000g is the mass of all oranges
1 orange=80g
? =4000g that is 4000/80
=50 oranges
Answer:
50 oranges
Step-by-step explanation:
Since each orange is measured in grams, we convert the 4 kg to g to start.
4 kg is equal to 4000 g.
Each orange weighs 80 g, so we divide 80g into 4000g.
80 divided by 4000 equals 50.
50 oranges are in the box.
I Hope This Helps!
PLS HELP ME I ONLY HAV 2 MINS PLSSSSS
Answer:
- 8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
3x(x+x)−6x^2+2^2−12
=6x^2+−6x^2+4+−12
Combine Like Terms:
=6x^2+−6x^2+4+−12
=(6x^2+−6^2)+(4+−12)
=−8
Help please i don't want to get held back
Let total data be x GB
then
4% of x = 1.2GB
4% × x = 1.2
0.04 x = 1.2
x = 1.2 / 0.04
x = 120 ÷ 4 = 30 GB
A new Lexus sells for $56,000. Use 2 depreciation models and desmos to answer the following questions.
Model A: The car depreciates 12% per year.
Model B. Use straight line depreciation - the car has a value of $0 in 12 years.
Use desmos and attach a screenshot to show the following.
1. Use the wrench tool to label your x an y-values, change your x and y-value to appropriate numbers. Remember to lock the viewpoint.
2. Write on your screenshot and label the point where the linear model and the exponential model are equal.
3. Attach a screenshot to this ssignment.
Justgive me the equations
The time in years for which the values are the same is given as follows:
7.25 years.
How to obtain the models?A decaying exponential model is given as follows:
y = a(1 - r)^t.
For which:
a is the initial value.r is the decay rate, as a decimal.The parameters for this problem are given as follows:
a = 56000, r = 0.12.
Hence the exponential model is given as follows:
y = 56000(0.88)^x.
The linear model is given as follows:
y = b - mx.
In which:
b is the initial value.m is the yearly depreciation rate.The parameter values for this problem are given as follows:
b = 56000, m = 56000/12 = 4666.67.
Hence the linear model is:
y = 56000 - 4666.67.
The point of intersection of the two graphs is at a time of 7.25 years.
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What is a equivlant expresion for 4(2x+7)
Annual revenue from McDonald's restaurants worldwide between 2015 and 2019 can be estimated by R = 25.44 - 1.22t, where Ris in billion dollars and tis in years since January 1, 2015
The estimated annual revenue for McDonald's restaurants worldwide in 2019 is $20.56 billion.
The annual revenue from McDonald's restaurants worldwide between 2015 and 2019 can be estimated by the equation R = 25.44 - 1.22t, where R is in billion dollars and t is in years since January 1, 2015. To find the estimated annual revenue for a specific year, we can substitute the value of t into the equation and solve for R.
For example, to find the estimated annual revenue for the year 2017, we can substitute t = 2 (since 2017 is 2 years after January 1, 2015) into the equation:
R = 25.44 - 1.22(2)
R = 25.44 - 2.44
R = 23
Therefore, the estimated annual revenue for McDonald's restaurants worldwide in 2017 is $23 billion.
Similarly, we can find the estimated annual revenue for other years by substituting the corresponding value of t into the equation and solving for R. For example, for the year 2019, t = 4, so we can substitute t = 4 into the equation and solve for R:
R = 25.44 - 1.22(4)
R = 25.44 - 4.88
R = 20.56
Therefore, the estimated annual revenue for McDonald's restaurants worldwide in 2019 is $20.56 billion.
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Which three values are greater than 1/2?
1/3
45%
0.62
59%
0.315
3/4
Answer:
value 315 3/4 value 59 1/3
each of two persons tosses three gair coincs. what is the probability that they obtain the same numbre of heads
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
1/8
The probability of getting a head or a tail when flipping a coin is 1/2.
Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.
The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.
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what is the answer to
5x
2
+20x−60
1990
that my answer please follow for help this
Given f(x)=x*-x³-6x², for what values of x will f(x) > 0?
The values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.
To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².
First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).
Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.
Next, we analyze the signs of the factors:
1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.
2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.
3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.
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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y=√x (a) Find dy/dt, given x = 16 and dx/dt = 3. dy/dt (b) Find dx/dt, given x=25 and dy/d
The value of dy/dt is 0 units per second.
a) Given: y= √x Differentiating with respect to t, we get; \(dy/dt = 1/2√x * dx/dt\)
On substituting the values of x and dx/dt in the above equation, we get; dy/dt = 1/2 * √16 * 3= 1.5 units per second
Therefore, the value of dy/dt is 1.5 units per second.
b) Given: \(y= √x\)
Differentiating with respect to t, we get;
\(dy/dt = 1/2√x * dx/dt\)
Let us assume that y = k, where k is a constant that can be determined by the given value of x.
Substituting the values of x and y in the equation, we get; 25 = √x
Therefore, x = 625dx/dt
= 0
(Given)\(dy/dt = 1/2√x * dx/dt\)
dy/dt = 1/2√625 * 0
= 0
Therefore, the value of dy/dt is 0 units per second.
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How does a domain restriction placed on a non-invertible function affect its inverse? drag a function or an interval into each box to correctly complete the statement.
A domain restriction placed on a non-invertible function affect its inverse.
Using inverse function concepts, it is found that:
The inverse of the function is \(y = \sqrt{x+3}-1\), and the domain of the inverse function is \(\left[-3,\infty ]\)
A function will have an inverse if for each output, there is only one respective input.
The domain of the inverse is the range of the original function.
The function given is:
\(f(x) = (x+1)^{2} -3\)
It's range is \(\left[-3, \infty]\), which will be the domain of the inverse.
To find the inverse, we exchange x and y, and isolate y, then:
\(y = (x+1)^{2} - 3\\ \\x = (y+1)^{2} - 3\\\\(y+1)^{2} = x+3\\ \\\sqrt{((y+1)^{2}} = \sqrt{x+3} \\\\y+1 = \sqrt{x+3}\\\\y = \sqrt{x+3} -1\)
The inverse of the function is \(y = \sqrt{x+3} -1\), and the domain of the inverse function is \(\left[-3, \infty]\).
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
(2,3)
Step-by-step explanation:
answer this correctly for brainlist
A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
Answer:
45.5
Step-by-step explanation:
i passed
27, Two of the smallest mammals on Earth
are the bumblebee bat and the Etruscan
pygmy shrew. How much shorter is the
bat than the shrew?
Therefore, the bumblebee bat is 0.5 centimeters shorter than the Etruscan pygmy shrew.
What is inequality?Inequalities are used in many areas of mathematics, including algebra, calculus, and geometry. They are also used in other fields such as economics, physics, and engineering to model real-world situations where values can vary within certain bounds. Solving inequalities involves finding the set of values that satisfy the inequality. This can be done using algebraic techniques such as adding or subtracting the same quantity from both sides of the inequality, multiplying or dividing both sides of the inequality by a positive number, or using the properties of absolute value. The solution to an inequality is often expressed as an interval or a set of numbers that satisfy the inequality.
Here,
According to the Guinness World Records, the bumblebee bat is the smallest mammal in the world, measuring only about 3 centimeters in length, while the Etruscan pygmy shrew measures about 3.5 centimeters in length.
To find out how much shorter the bat is than the shrew, we can subtract the length of the bat from the length of the shrew:
3.5 cm - 3 cm = 0.5 cm
The bumblebee bat and the Etruscan pygmy shrew are both very small mammals, but the bumblebee bat is actually shorter than the Etruscan pygmy shrew.
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Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
2, 5, 8, ...
What is two and one-fourth subtracted by one-eighth?
Given f(x) = x2 - 2x + 3, find the value(s) for x such that f(x) = 18. The solution set is o
Answer:
0
Step-by-step explanation:
Since f(x)=18 you would do:
f(x)= 18(2)-2(18)+3
f(x)=36-36+3
Final Answer: 0
Step-by-step explanation:
f(x) = x^2 - 2x + 3
f(x) = 18
x^2 - 2x + 3 = 18
x^2 - 2x + - 15 = 0
(x-5) (x+3) = 0
x = 5 (or) x = -3
not sure of the answer^^
What is the measure of
Natalle is a softball coach. She has a pitching private lesson with Kasey. Kasey's mom pays Natalle $11 per hour plus a $6 tip. Write an equation that represents this scenario if the total cost was $39.
where t is the number of hours worked by Natalle
Here, we want to write an equation that will represent the given scenario
Let the number of hours for which she earned the pay be t
From the question, she earns $11 per hour
So for t hours, the amount earned excluding the tip will be;
\((11\times t)\text{ = \$11t}\)Now, let us add the tip and equate to the total amount earned
We have this as;
\(11t\text{ + 6 = 39}\)Adding and subtracting polynomials
Answer:
The expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 21
Step-by-step explanation:
The perimeter is the sum of all side lengths for a 2d shape, such as this triangle. Our perimeter is thus
4x² - 3 + 4x² - 2 + 4x² - 1
We can then separate our variables and constants to make it
4x² + 4x² + 4x² - 3 - 2 - 1
Add the constants to get
4x²+4x²+4x² - 6
To add variables, we must first make sure that they are the same variable/letter as well as to the same degree. The coefficient only affects the result. Because all of our variables are the same letter (x) and are all to the second degree, we can add them. To do this, we simply add the coefficients together to make one big coefficient, and multiply that by the variable. Thus,
4x² + 4x² + 4x² = (4+4+4)x² = 12x²
4x²+4x²+4x² - 6 = 12x² - 6
Another way of looking at it is that 4x² = 4(x²) = x²+x²+x²+x²
Therefore, the expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 12 * 1.5² - 6 = 21
Solve the quadratic equation. x2+x−6=0
Answer:
The value of x is -3 and 2.
Step-by-step explanation:
First, you have to elaborate the equation :
\( {x}^{2} + x - 6 = 0\)
\( {x}^{2} - 2x + 3x - 6 = 0\)
Next, you can factorize it by taking out the like-terms :
\(x(x - 2) + 3(x - 2) = 0\)
\((x + 3)(x - 2) = 0\)
Lastly you have to solve it :
\(x + 3 = 0\)
\(x = - 3\)
\(x - 2 = 0\)
\(x = 2\)
Answer:
\(x = 2\) or (look down)
Step-by-step explanation:
\(x^{2}\)+\(x\)−\(60\) \(=\) \(0\)
Answer:
\(x = -3\)
on a test consisting of 250 questions, jassi answered 40% of the first 125 questions correctly. what percent of the other 125 questions does she need to answer correctly for her grade on the entire exam to be 60%
test of 250 questions
40% of the fist 125 are ok, this means that 125(0.4) = 50 questions of the first 125 are ok
If jassi needs 60% of the 250 ok, that is 250(0.6) = 150
If of the first half she already has 50 questions ok, and needs 150, she needs to have 100 questions our of the second 125
If she needs 100 out of 125, this percent is 100/125 = 0.8, this means 80%
Answer:
Jassi needs 80% of the second 125 questions to be ok