Answer:
Number of girls shorter than [tex]60[/tex] inches are [tex]301[/tex].
Step-by-step explanation:
Given: The heights of the population of girls in an Arlington, NY school follows a normal distribution.
Mean[tex]=63[/tex]
Standard deviation[tex]=2[/tex]
Total number of girls[tex]=450[/tex]
Now using the formula,
Standard normal variant, [tex]z=\frac{x-mean}{standard deviation}[/tex]
Now, substitute the values and replace [tex]x[/tex] by [tex]60[/tex]
So. [tex]z=\frac{60-63}{2}[/tex]
[tex]z=-\frac{3}{2}[/tex] or [tex]-1.5[/tex]
Now, probability of girls shorter than [tex]60[/tex] inches
[tex]p(z>-1.5)=0.668[/tex] look up the value in the normal distribution table
Therefore, number of girls shorter than [tex]60[/tex] inches
[tex]=0.668[/tex]×[tex]450[/tex]
[tex]=301[/tex]
Two players are stand on a basketball court. The angles of elevation from the foot of each player to the 3.5 meters high basket are 40° and 50°. How far apart are the players from each other?
Please try to answer it with a trigonometric function
Therefore, the players are 6.84 meters apart from each other.
What is a projectile?An item that is propelled by the application of an external force and then travels freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and combat, despite the fact that every item traveling through space is a projectile.
What is tangent?The straight line that traverses a point with a slope equal to the derivative of the curve at that location is said to be the tangent line to a plane curve at that point in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
If we let x be the distance between the players, then we can use the tangent function to relate the angle of elevation to the distance between the player and the basket:
tan(40°) = 3.5/x
tan(50°) = 3.5/(x+1)
We can solve for x in both equations, and set them equal to each other, we get x= 6.84m
Therefore, the players are 6.84 meters apart from each other.
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Solve each system by elimination.
1) -3х – бу = -3
5x + 5y = 0
Answer: look at the picture
Step-by-step explanation: Hope this help :D
the supplement of an angle is 30 degrees more than the measure of the angle, what is the measure of the angle smaller angle = degrees Greater arogle = degrees
Two supplementary angles equal 180 degrees.
Let the first angle = x
The second angle is 30 degrees more so this would be x + 30
Now add the two angles together to equal 180:
X + x+ 30 = 100
Combine like terms:
2x + 30 = 180
Subtract 30 from both sides:
2x = 150
Divide both sides by 2:
X = 75
One angle = x = 75
The other angle is x + 30 = 75 + 30 = 105
The smaller angle is 75 degrees.
Tell you
Try It!
Write an inequality to represent each situation.
a. Harry is taller than 60 inches.
b. Sherry is not 4 years old.
c. Hank has at least $7. 50.
The inequality to represent each situation is Harry > 60 inches, Sherry ≠ 4 years, and Hank ≥ $7.50.
a) Harry: This inequality states that Harry is taller than 60 inches. This is likely referring to Harry's height, as most people measure height in inches. This inequality can also be written as Harry ≥ 60 inches, emphasizing that Harry is at least 60 inches tall.
b) Sherry: This inequality states that Sherry is not equal to 4 years. This could be referring to Sherry's age, as it is common to measure age in years. This inequality can also be written as Sherry ≠ 4 years, emphasizing that Sherry is not exactly 4 years old.
c) Hank: This inequality states that Hank is greater than or equal to $7.50. This is likely referring to Hank's amount of money, as it is common to measure money in dollars. This inequality can also be written as Hank ≥ $7.50, emphasizing that Hank has at least $7.50.
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Please answer this math question
Answer:
[tex] \frac{-5}{28} [/tex]
Step-by-step explanation:
Given:
[tex] \frac{-1}{5} * (\frac{3}{4} + \frac{1}{7}) [/tex]
Required:
Solve
Solution:
[tex] \frac{-1}{5} * (\frac{3}{4} + \frac{1}{7}) [/tex]
Apply distributive property by multiplying each reaction in the box by -⅕
[tex] (\frac{-1}{5} * \frac{3}{4}) + (\frac{-1}{5} * \frac{1}{7}) [/tex]
[tex] \frac{-3}{20} + \frac{-1}{35} [/tex]
Add together. Common denominator is 140. Therefore:
[tex] \frac{-21 + (-4)}{140} [/tex]
[tex] \frac{-25}{140} [/tex]
Simplify further
[tex] \frac{-5}{28} [/tex]
Two alien pacehip tart traveling toward each other from pace tation that are 710,000 km apart. The firt pacehip tarted an hour before the econd pacehip and i traveling at 110,000 km/hr. In how many hour will the two pacehip meet if the econd pacehip i traveling at 90. 000 km/hr?
The two spaceships will meet in 8 hours if the second spaceship is traveling at 90. 000 km/hr.
To calculate the time it will take for the two spaceships to meet, you must use the equation Distance = Rate x Time. Since the first spaceship has a higher rate of speed, it will reach the second spaceship in less time than it would take the second spaceship to reach the first.
This means that the time it takes for the two spaceships to meet will be equal to the time it takes for the first spaceship to travel the distance between the two space stations. We can use the equation to solve for time: Time = Distance/Rate. In this case, the distance is 710,000 km and the rate is 110,000 km/hr, so the time is 6.45 hours.
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Which of these is a solution to the equation 1/8=2/5•x 2/40, 5/16, 17/40, 11/40
Answer:
Simple, [tex]1/8=2/5x[/tex] so [tex]1/8/2/5=x[/tex] would become [tex]x=1/20[/tex], which is equal to 2/40 :)
Step-by-step explanation:
Xavier ran 13 miles in 182 minutes. Assume Xavier maintains a constant speed.
Enter the number of minutes it takes Xavier to run 1 mile
Answer:
14 minutes
Step-by-step explanation:
We can represent Xavier's running in the following ratio using the given information:
distance : time
13 miles : 182 minutes
To get the answer to this problem, all we have to do is divide both sides of the ratio by 13, so that the left side is 1 mile.
[tex]13 \textrm{ miles} : 182\textrm{ minutes}\\\overline{\ \ \ \ 13 \ \ \ \: } \ \ \: \overline{\ \ \ \ \ \ \, 13 \ \ \ \ \ \ }[/tex]
1 mile : 14 minutes
It takes Xavier 14 minutes to run 1 mile.
a ball is dropped from a height of 600 feet. the height of the ball, H, after t seconds can be modeled by the function rule, H(t)=-4.9t^2 + 600. what would be the independent quantity
Answer:
the independent quantity is "t" (time in seconds)
Step-by-step explanation:
The problem statement tells you the function rule gives you H (the dependent quantity) as a function of t seconds. "t seconds" is the independent quantity.
14
The knob of a baseball bat is circular, as shown. The knob of this baseball bat has a
diameter of 3 inches.
Knob of -
baseball bat
Which measurement is closest to the area of the knob of the baseball bat in square inches?
F
28.26 in?
G
7.06 in
H
9.42 in?
J
21.02 in?
Answer:
its G
Step-by-step explanation:
How do you solve composite functions examples?
The composite function is the result of first applying the function (x^2 - 1) to the input and then applying the function (5x + 2) to the result. The final result of the composite function is 5x^3 + 2x - 3.
Step 1: Apply (x^2 - 1) to the input:
(x^2 - 1) = x^2 - 1
Step 2: Apply (5x + 2) to the result:
(5x + 2)(x^2 - 1)
= 5x^3 - 5x + 2x - 2
Step 3: Simplify:
5x^3 - 5x + 2x - 2
= 5x^3 + 2x - 3
A composite function is the result of applying two or more functions in succession. The order of operations for a composite function is to first apply the first function, then apply the second function to the result of the first, and so on. In the example given, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function
(x^2 - 1)
to the input and then applying the function (5x + 2) to the result. The calculation can be broken down into three steps: Step 1 is to apply (x^2 - 1) to the input to get x^2 - 1, Step 2 is to apply (5x + 2) to the result to get 5x^3 - 5x + 2x - 2,
and Step 3 is to simplify the result to get the final answer of
5x^3 + 2x - 3.
To summarize, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function (x^2 - 1) to the input, and then applying the function (5x + 2) to the
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In the formula P = 2L + 2W, what does the P represent? What does the L represent? and what does the W represent?
What is always true about the interquartile range of a data set? Select all that apply.
A.
The interquartile range is greater than the range.
B.
The interquartile range contains the median of the data set.
C.
The interquartile range is less than the range.
D.
The interquartile range contains about 50% of the data set.
The interquartile range is.....
Answer:
Our goal is to understand how range and interquartile range describe data. To do this, we have to define the range and interquartile range of a given set of data, we have to be able to calculate the range and interquartile a range of a given set of data, and then we want to be able to determine how range and interquartile range are impacted by outliers.
So how can you describe data with range and interquartile range? Range tells us if data is grouped closely together or spread far apart. Interquartile range tells us if data is grouped closely around the median. The key concepts. Range is the difference of the maximum and minimum values.
So if we wanted to calculate the range of this particular data set here, we would say 20 minus 1 and get a range of 19. Interquartile range is the difference of the upper and lower quartiles. In order to do this, we first have to find the median to find those upper and lower quartiles. The median of this data set, the value in the middle, is 6. The lower quartile is the median of the lower half, the middle value then of these three data points being 3.
The upper quartile would be the middle of this data set, and that would be 8. So if we wanted to find the interquartile range, we'd subtract those values. 8 minus 3 gives us an interquartile range of 5. Interquartile range describes the spread of data around the median.
A small interquartile range means that most of the data, the middle half, is clustered tightly around the median, whereas a large interquartile range would mean that that data that's in the middle is more spread out. And finally, outliers impact the range, but have little impact on the interquartile range. If we consider our data set here, we see that we have an outlier of 20, but it really only impacts the range.
It does not play a significant role on the interquartile range.
Step-by-step explanation: also brainleist
Hence your answer will be D
A, B & C form a triangle where
∠
BAC = 90°.
AB = 12.2 mm and CA = 8.3 mm.
Find the length of BC, giving your answer rounded to 1 DP.
Answer:
[tex]Pythagoras \ theorem,\\BC^2 = AB^2 + AC^2 = 12.2^2 +8.3^2 =217.73\\\\BC =14.8mm[/tex]
What is the rule for translations?
Answer:
A translation is a type of transformation that moves each point in a figure the same distance in the same direction.
Step-by-step explanation:
Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.
Sara’s English test had 90 questions and she got 18 questions wrong. What percent of the questions did she get correct?
Answer:
80%
Step-by-step explanation:
First we find the percentage she got wrong:
[tex]\frac{18}{90}[/tex] Is the fraction she got wrong, now we convert this into a percentage by divding 18 by 90 and multiplying by 100
18÷90×100=20
so to find the remaining percent we subtract 20 from 100
100-20=80
And our answer is 80
Answer:
80%
Step-by-step explanation:
10%= 9
20%= 18
18= how many they got wrong
90=total questions
90= 100%
18= 20%
100%=20%=80%
does the order of the quantities in an inequality matter
The order of the quantities in an inequality matters. Therefore, it is true.
How to illustrate the inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
When resolving an inequality, you can do one of the following: Add the same amount to each side; Subtract the same amount from each side; Multiply or divide each side by the same positive amount. You must flip the inequality symbol if you multiply or divide each side by a negative number.
Therefore, the order matters.
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Please help I beg of you
WILL MARK BRAINLIST
Answer:
A ≈ 25.1 cm²
Step-by-step explanation:
The area (A) of the shaded region is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]
= π × 6² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex] ← cancel π and 2π by π
= 36 × [tex]\frac{\frac{4\pi }{9} }{2}[/tex]
= 18 × [tex]\frac{4\pi }{9}[/tex]
= 2 × 4π
= 8π ≈ 25.1 cm² ( to 1 dec. place )
If you were carrying a credit card balance of $2,000 at a 24% interest rate, what is the interest charge per month on that balance?
4. Two of the angles in a triangle have measure of 79° and 81°. Which of the angle measures below
could belong to a triangle that is similar to this triangle?
A) 81 and 80°
B) 81 and 20°
C)79° and 90°
D)79° and 21°
Answer:
B) 81 and 20°
Step-by-step explanation:
In any triangle, the sum of the measures of the three angles is 180°. Therefore, if two angles in a triangle have measures of 79° and 81°, the third angle must have a measure of 180 - 79 - 81 = 20°. Therefore, the answer is B) 81 and 20°.
Answer:
B
Step-by-step explanation:
A circle with center O has radius 25. Chord AB of length 30 and chord CD of length 14 intersect at point P . The distance between the midpoints of the two chords is 12. The quantity OP^2 can be represented as m/n, where and are relatively prime positive integers. Find the remainder when m+n is divided by 1000.
Therefore after using the Pythagorean Theorem and the properties of chords in a circle we got 626 when m+n is divided by 1000.
What is Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Define hypotenuse.The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.
Let M and N be the midpoints of chords AB and CD, respectively.
Let X and Y be the foot of the perpendicular from P to chord AB and CD respectively.
Since X,Y are on the circle and P is the midpoint of XY,
OP = PX = PY = radius = 25
Now, using the Distance Formula:
(XM)^2 + (YN)^2 = (12)^2
By the Pythagorean Theorem, on triangle PXN and PYM,
(25)^2 + (YN)^2 = (PN)^2 = (14/2)^2 and
(25)^2 + (XM)^2 = (PX)^2 = (30/2)^2
OP^2 = 625 = 25^2
thus m+n = 625 + 1 = 626
and remainder when m+n is divided by 1000 is 626 % 1000 = 626
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Charlotte is a customer-satisfaction expert at a large pizza company. She took a random sample of 1{,}0001,0001, comma, 000 delivery orders and constructed a one-sample zzz interval to estimate the proportion of delivery orders that take more than an hour to arrive. She decides to repeat this process, but this time she'll use a sample of 4{,}0004,0004, comma, 000 orders. Assume that the point estimates from each sample are approximately equal.What is true about the margins of error from these two samples
The smaller sample's margin of error will be almost twice as great as the larger sample's margin of error.
Calculating the margin of error for a given sample from a population:
Let the level of significance be and the standard deviation of the population be σ and the sample size be n, then we have:
MOE(Margin of Error)= [tex]z_{a/2}\times\frac{\sigma}{\sqrt n}[/tex]
Using the above formula to calculate the margin of errors for two specified samples
For first sample:
Sample size = n(1) = 1000
MOE(1) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {1000}}[/tex]
For second sample:
Sample size = n(2) = 4000
MOE(2) = [tex]z_{a/2}\times\frac{\sigma}{\sqrt {4000}}[/tex]
(since it was given that they have same point estimates, so same standard deviation)
Their ratios are given by
MOE(2)/MOE(1) = [tex]\frac{z_{a/2}\times\frac{\sigma}{\sqrt {4000}}}{z_{a/2}\times\frac{\sigma}{\sqrt {1000}}}[/tex]
MOE(2)/MOE(1) = [tex]\sqrt{\frac{1000}{4000}}[/tex]
MOE(2)/MOE(1) = 1/2
MOE(1) = 2*MOE(2)
Thus, the margin of error from the smaller sample will be about double of the margin of error from the larger sample.
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Please, help meee. Please
Answer:
Hope it helps you!...............
1/2% in decimal
please give me my answer Also
I AM NOT ASKING for 1/2 in decimal
I am asking for 1/2 percent in decimal
Answer:
Step-by-step explanation:
We know that : Percentage means 'divided by 100'
therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005
Neil work a a conultant at a oftware company. The amount of hi annual bonu i baed upon the number of hour he work. B = the amount of Neil' bonu
h = the number of hour Neil work
Which of the variable i independent and which i dependent?
The independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).
In this scenario, the amount of Neil's bonus (B) is dependent on the number of hours he works (h). The number of hours he works is the input or independent variable, while the amount of bonus he receives is the output or dependent variable. It can be said that the number of hours he works is the cause and the amount of bonus is the effect.
The equation is B = f(h) where f is the function that relates the two variables.
Thus, the independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).
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Complete Question is-
Neil works as a consultant at a software company and the amount of his annual bonus is based on the number of hours he works, which variable is independent and which is dependent? With B as the amount of Neil's bonus, and h as the number of hours Neil works.
What is the domain of g?
Answer:
of g(x) is the set of all real numbers
Please help me with my hw
Answer:
9m^8 n^2
Step-by-step explanation:
Open up the parenthesis and simplify to find your answer.
is my answer correct or is it wrong
Answer:
Your answer is wrong, H is the correct answer.
Step-by-step explanation:
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Note: This rule must be satisfied for all 3 conditions of the sides.
What's 2x to the third
Answer:
8x^3
Step-by-step explanation:
(2x)^3
=(2x)^3
=2x*2x*2x
=8x^3
Why is halting problem undecidable?
Therefore , the solution of the given problem of tractable problem comes out to be the halting problem is undecidable for Turing machines.
Tractable problem: what is it?a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.
Here,
Alan Turing proved in 1936 that a general algorithm running on a Turing
machine that solves the halting problem for all possible program-input
pairs necessarily cannot exist.
the halting problem is undecidable for Turing machines.
Therefore , the solution of the given problem of probability comes out to be the halting problem is undecidable for Turing machines.
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