The student question is about calculating the statistics and probabilities for two different sample sizes of adolescent girls who are developmentally delayed, reaching their adult height.
For the sample size of 29 girls, the estimated standard error is 1.6337, and the statistic is 1.10. For the larger sample size of 91 girls, the new estimated standard error is 0.9222, and the new statistic is 1.95. As the sample size increases, the statistic becomes smaller.
Using the Distributions tool to determine the probability of getting the statistic or something more extreme for each sample size, you can find the probabilities (p) for each case. For the sample size of[tex]29 (n=29),[/tex] you will obtain a specific probability (p).
Similarly, for the sample size of[tex]91 (n=91)[/tex], you will get another probability (p). The distribution will change with larger sample sizes (n).
To observe the distribution changes, you can use the Degrees of Freedom slider in the tool and move it from the smallest value to the largest value. This will help you see how the shape of the distribution changes as the sample size increases.
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QUESTION 1. Assume we are testing a function with 3 variables:
Variable A: has values 0 and 1
Variable B: has values 0 and 1
Variable C: has values 0 and 1
What is the total 2-way variable value configuration coverage achieved by the following tests:
A=0; B=0; C=1
A=0; B=1; C=1
A=1, B=0, C=0
The total 2-way variable achieved by the given tests is 6.
How to find 2-way variable?
There are three pairs of variables, and each pair can have two possible values, resulting in 2-way variable value configurations. Therefore, the total 2-way variable value configuration coverage achieved by the given tests is 6, as follows:
A=0, B=0
A=0, C=1
B=0, C=1
A=0, B=1
A=1, B=0
A=1, C=0
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Triangle TUV, with vertices T(-8,2), U(-2,8), and V(-9,9), is drawn inside a rectangle, as shown below.
The area of triangle TUV with vertices T(-8,2), U(-2,8), and V(-9,9) are 13.4 units.
What is triangle?A triangle is a closed two-dimensional plane figure that has three sides, three angles, and three vertices. The sum of the angles of a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles. Some common types of triangles include equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are a fundamental concept in geometry and are used in many areas of mathematics and science.
Here,
To find the area of triangle TUV, we can use the formula:
Area = 1/2 * base * height
We can choose any two sides of the triangle as the base and the corresponding height. Let's choose TU as the base and the perpendicular distance from V to TU as the height.
First, let's find the length of TU:
TU = √[(8 - 2)² + (-2 - (-8))²]
= √[6² + 6²]
= 6√(2)
Next, let's find the slope of TU:
mTU = (8 - 2) / (-2 - (-8))
= -3/2
The line perpendicular to TU passing through V has a slope equal to the negative reciprocal of mTU:
mVQ = 2/3
The equation of the line passing through V and perpendicular to TU is:
y - 9 = (2/3)(x + 9)
Solving for x and y at the point where this line intersects TU, we get:
y = (2/3)x + 19
(2/3)x + 19 = -3x/2 + 7
x = -8/7
y = 94/21
The perpendicular distance from V to TU is the absolute value of y - 8:
|94/21 - 8| = 2/21
So, the area of triangle TUV is:
Area = 1/2 * TU * (2/21)
= (1/21)√(2)
To find the area of rectangle QRS, we need to find the length and width. We can use the distance formula to find the length QR and the width QS:
QR = √[(9 - (-8))² + (9 - 2)²]
= √[289]
= 17
QS = √[(9 - (-9))² + (2 - 2)²]
= √[324]
= 18
So, the area of rectangle QRS is:
Area = QR * QS
= 17 * 18
= 306
Area of triangle QRS = Area of rectangle QRS - Area of triangle TUV
= 306 - (1/21)√(2)
≈ 13.4 units
So, the answer is (C) 13.
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Complete question:
Triangle TUV, with vertices T(-8,2), U(-2,8), and V(-9,9), is drawn inside a rectangle. What is the area, in square units, of the triangle TUV?
A. 7
B. 10
C. 13
D. 18
A house plan has concrete stairs leading down into the garage. How much concrete is needed to make the stairs? 3 ft 2 ft 8 ft 5 ft [? ] ft ³ 2 ft 8 ft 1 ft
The amount of concrete needed to make the stairs that leads to the garage is 64 cubic feet
Calculating the amount of concrete needed to make the stairs?The missing information is added as an attachment
The concrete needed to make the stairs is the volume of the stairs and this is calculated using
Volume = Base area * Height
Where
Base area = 3 * 2 + 2 * 1
Base area = 8
And
Height = 8
So, we have
Volume = 8 * 8
Evaluate
Volume = 64
Hence, the amount needed is 64 cubic feet
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-5x - 3y + 7x + 21y Simplify
Answer:
2x + 18y
Step-by-step explanation:
-5x - 3y + 7x + 21y ----> (combine like terms)
2x - 3y + 21 y ---> (combine like terms)
2x + 18y
Answer:
[tex]\huge\boxed{\sf 2(x + 9y)}[/tex]
Step-by-step explanation:
Given expression:= -5x - 3y + 7x + 21y
Combine like terms= -5x + 7x - 3y + 21y
= 2x + 18y
Common factor = 2So, take 2 as a common factor
= 2(x + 9y)[tex]\rule[225]{225}{2}[/tex]
the volume of a cube decreases at a rate of 6 m 3 / s . find the rate at which the side of the cube changes when the side of the cube is 4 m . answer exactly or round to 2 decimal places.
The rate at which the side of the cube changes when the side of the cube is 4 m is -1/8 m/s (or approximately -0.125 m/s).
Let's use the formula for the volume of a cube:
V = s³
where V is the volume and s is the length of one side of the cube. To find the rate of change of the side length, we need to differentiate this formula with respect to time t:
dV/dt = d/dt (s³) = 3s² ds/dt
We know that dV/dt = -6 m³/s (the negative sign indicates that the volume is decreasing), and when s = 4 m, we have:
-6 = 3(4²) ds/dt
Simplifying this equation gives us:
ds/dt = -6 / (3*4²) = -1/8 m/s
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26. In the given figure, OP || RS. ZPQR = 60° and QRS = 130°. Then what is the measure of ZOPQ? S P 60% R 130⁰
Answer: The answer is 60.
Step-by-step explanation:
Using the fact that OP || RS, we know that∠RWV = 180° − 130° 1. ∠RWV = 50° We know that,∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal) Also, for line OP∠OQP + θ = 180° θ = 180° − ∠OPQ = 180° − 110° 2. θ = 70°
Answer:
The measure of ∠OPQ is 110°.
Step-by-step explanation:
Draw a line parallel to OP from point Q. Label a point on the line T. (See attached diagram).
Angles SRQ and TQR are alternate interior angles, and so according to the Alternate Interior Angles Theorem, they are congruent.
⇒ m∠TQR = m∠SRQ = 130°
Given m∠PQR = 60° and m∠TQR = 130° then:
⇒ m∠TQP + m∠PQR = m∠TQR
⇒ m∠TQP + 60° = 130°
⇒ m∠TQP = 70°
Angles OPQ and TQP are same-side interior angles, and so according to the Same-side Interior Angles Theorem, they are supplementary (sum to 180°).
⇒ m∠OPQ + m∠TQP = 180°
⇒ m∠OPQ + 70° = 180°
⇒ m∠OPQ = 110°
Therefore, the measure of ∠OPQ is 110°.
help i need help with this its very hard
Answer:
3a + 2b
Step-by-step explanation:
Let the unknown side have length X.
X + X + 5a - b + 5a - b = 16a + 2b
2X + 10a - 2b = 16a + 2b
2X = 6a + 4b
X = 3a + 2b
Answer: 3a + 2b
Solve for x 8 x + 3 ≥ 19
Answer:
x ≥ 2
Step-by-step explanation:
8x + 3 ≥ 19
8x ≥ 19 - 3
8x / 8 ≥ 16 / 8
x ≥ 2
Answer:
Sure, I can solve for x:8x + 3 ≥ 19Subtracting 3 from both sides:8x ≥ 16Dividing both sides by 8:x ≥ 2Therefore, the solution is x ≥ 2.
if one flag pole is y feet tall and casts a shadow x feet long, then how tall is another nearby flag pole that casts a shadow p feet long at the same time of day?
If one flag pole is y feet tall and casts a shadow x feet long, and another nearby flag pole casts a shadow p feet long at the same time of day, we can use similar triangles to determine the shadow of the second flag pole.
In this scenario, the two flag poles and the ground form two similar right triangles. The height of the first flag pole (y) corresponds to one leg of the first triangle, and the length of its shadow (x) corresponds to the other leg.
Similarly, the height of the second flag pole (h) corresponds to one leg of the second triangle, and the length of its shadow (p) corresponds to the other leg.
Therefore, the height of the second flag pole is equal to the product of the height of the first flag pole and the length of the shadow of the second flag pole, divided by the length of the shadow of the first flag pole.
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Debra’s rectangular vegetable garden measures 9 1/3 yards by 12 yards. A bottle of garden fertilizer costs $14.79. If Debra needs to mix 1/8 cup of fertilizer with water for each square yard of her garden, how many cups of fertilizer does she need?
She needs 14 cups of fertiliser.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area = length * width
Find the area of the garden:
Area = 9 1/3 * 12
= 28/3 * 12
= 112 yards²
Find the amount of the fertiliser needed:
1 yards² = 1/8 cup
112 yards² = 1/8 * 112 = 14 cups
She needs 14 cups of fertiliser.
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What is the value of k?
127.3°
Pls just say a b c or d
A triangle with side lengths 7, 6, 4 is
Acute
Right
Obtuse
Right
so 7 is the hypotenuse because it is the biggest. so you have to use 6 and 4 in the formula to see if they equal 7.
(a)²+(b)²=c²
(6)²+(4)²=c²
36+16=c²
(square root) 52=c²
the square root of 52 is 7
so therefore it is a right triangle.
During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon? _____ gallons
Answer:30 gallons
Step-by-step explanation:
Answer:
30 gallons of tea
Step-by-step explanation:
Step 1:
First, before we do anything, let's convert 2 hours into minutes. There are 60 minutes in an hour, so we would multiply 60 and 2 to get 120 minutes.
Step 2:
Since we know that 4 cups of tea are poured every minute, we must multiply 4 by 120 because it is poured every 1 minute, and 4 × 120 = 480.
Step 3:
We also know that there are 16 cups of tea in one gallon, so we would divide 480 by 16 because we are trying to get how many gallons there are. 480 ÷ 16 = 30, so there are 30 gallons of tea poured in two hours.
When the temperature drops below 15°C in a building, the furnace turns on.
At what temperatures will the heater turn on? Write an inequality to represent
this situation, and graph the solution on a number line.
The inequality to represent this situation is T < 15°C, where T is the temperature.
What is inequality?Inequality is a statement that two values, expressions, or quantities are not equal. Inequality is usually represented by the symbols ">", "<", "≥", or "≤".
This inequality can be graphed on the number line by representing 15°C as a point on the number line. Any values to the left of 15°C, such as 14°C, 13°C, and so on, would be represented as points to the left of 15°C on the number line.
Less than inequality is used to compare two values to see if one is less than the other. In this case, the inequality T < 15°C states that the temperature T must be less than 15°C in order for the furnace to turn on.
Graphically, the solution to this inequality is represented by a number line with a point at 15°C and all points to the left of 15°C represented in the solution set.
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if you're good at quadratics...
Therefore, the correct answer is: [tex](x+10)^2=82[/tex]. ( right hand side of the equation).
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically contains variables, which are represented by letters, and may also include constants and operators. The general format of an equation is:
expression = expression
For example, the equation x + 2 = 6 means that the expression x + 2 is equal to the expression 6. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.
To solve the quadratic equation by completing the square, Jamie needs to follow the steps:
Move the constant term to the right-hand side of the equation:
[tex]x^2 + 20x = -18[/tex]
Add and subtract the square of half the coefficient of x to the left-hand side of the equation:
[tex]x^2 + 20x + (20/2)^2 - (20/2)^2 = -18[/tex]
[tex](x+10)^2 - 100 = -18[/tex]
Simplify the right-hand side of the equation:
[tex](x+10)^2 = 82[/tex]
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What is the endpoint of a line segment with these points? Endpoint: Z(–21, 15) Midpoint: M(–13, 29) (–5, 43) (–17, 22) (–27, 21) (–29, 1)
Answer: A - (-5, 43)
Step-by-step explanation:
during a one-month promotional campaign, tiger films gave either a free dvd rental or a 12-serving box of microwave popcorn to new members. it cost the store $1 for each free rental and $2 for each box of popcorn. a total of 89 new members were signed up and the store's cost for the incentives was $135. how many of each incentive were given away?
By using system of equations, there are 43 free DVD rentals and 46 boxes of microwave popcorn were given away during the promotional campaign.
Let's use the following variables
x: the number of free DVD rentals given away
y: the number of boxes of microwave popcorn given away
We can set up a system of equations to represent the given information:
x + y = 89 (total number of new members signed up)
1x + 2y = 135 (total cost of the incentives)
We can solve for x or y in the first equation and substitute into the second equation
x = 89 - y
1(89 - y) + 2y = 135
89 - y + 2y = 135
y = 46
Substituting y = 46 into the first equation:
x + 46 = 89
x = 43
Therefore, 43 free DVD rentals and 46 boxes of microwave popcorn.
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Prove that the following statement is false. There exists an integer n such that 6n2 + 27 is prime. To prove the statement is false, prove the negation is true. Write the negation of the statement. For every integer n, 6n² + 27 is prime. For every integer n, 6n2 + 27 is not prime. There exists an integer n, such that 6n2 + 27 is not prime. There exists a composite number q = 6n2 + 27, such that n is an integer. There exists an integer n, such that 6n2 + 27 is prime. Now prove the negation. Suppose n is any integer. Express 6n2 + 27 as the following product: 6n2 + 2 Now is an integer because sums and products of integers are integers. Thus, 6n2 + 27 is not prime because it is a
The negation of the statement "There exists an integer n such that 6n2 + 27 is prime" is "For every integer n, 6n2 + 27 is not prime."
To prove the negation, we can use algebraic manipulation to show that 6n2 + 27 is always composite.
Suppose n is any integer. We can factor out 3 from 6n2 + 27 to get 3(2n2 + 9). Since 2n2 + 9 is always odd (2 times any integer is even, and adding 9 makes it odd), we can further factor it as (2n2 + 9) = (2n2 + 6n + 9 - 6n) = [(2n+3)(n+3)] - 6n.
Substituting this expression back into 3(2n2 + 9), we get 3[(2n+3)(n+3) - 6n]. Since (2n+3)(n+3) - 6n is an integer, 3[(2n+3)(n+3) - 6n] is composite for every integer n. Therefore, 6n2 + 27 is not prime for any integer n.
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(-3m+3d):3 пожалуйста срочноооооо!!!!!!!!!
Answer:
-m + d
Step-by-step explanation:
(-3m + 3d) : 3 =
(-3m + 3d) x 1/3 =
-m + d
ASAP
Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:
a. A’
b. A∩B
c. A∪B
Answer:
a. A' = {3, 5, 7, 9} (complement of A)
b. A∩B = {2} (intersection of A and B, which contains only the even prime number 2)
c. A∪B = {2, 4, 6, 8, 3, 5, 7} (union of A and B, which contains all even numbers and all prime numbers between 2 and 9)
A business owner applies for a credit card to cover $14,000 in emergency expenses. The credit card charges 16.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?
Credit card charges $19665.33 will the balance on the card be, rounded to the nearest penny.
What is interest in simple words?
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The interest rate for the loan is denoted by this proportion.
Interest is the cost of borrowing money and is typically stated as a percentage, such an annual percentage rate (APR). Lenders may charge interest to borrowers for the use of their funds, or borrowers may charge interest to lenders for the use of their funds.
amount applied for = $14,000
interest rate = 16.99%
the balance after 2 years
P₀ = $1400
r = 16.99% = 0.1699
t = 2
[tex]P_{0} = P_{0}e^{rt}[/tex]
[tex]P_{2} = 1400e^{0.1699 * 2}[/tex]
≈ $19665.33
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Is r=4q-5 a linear function ?
Answer:
yes
Step-by-step explanation:
replace r and q with y and x:
y = 4x - 5
It is a line.
when is it appropriate to take a pulse by counting the heart rate for 30 seconds and multiplying by two?
It is appropriate to take a pulse by counting the heart rate for 30 seconds and multiplying by two when a rapid or irregular pulse is suspected, or when it is difficult to count the pulse for a full minute.
Counting the heart rate for a full minute is the most accurate way to determine the heart rate. However, there are situations when it may be more appropriate to count the heart rate for 30 seconds and multiply by two.
For example, if a person's pulse is rapid or irregular, it may be difficult to accurately count the pulse for a full minute. In such cases, it may be more appropriate to count the pulse for 30 seconds and multiply by two to get an estimate of the heart rate.
Another situation where it may be appropriate to count the pulse for 30 seconds is when time is limited, such as in an emergency situation. In such cases, counting the pulse for 30 seconds and multiplying by two can provide a quick estimate of the heart rate.
However, it is important to note that counting the pulse for 30 seconds and multiplying by two may not be as accurate as counting the pulse for a full minute.
Therefore, if possible, it is recommended to count the pulse for a full minute to obtain the most accurate measurement of the heart rate.
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Hi does anyone know how to do problem 2 and 3 on the worksheet?
2. Using percentage, we can find that Melissa needs to save $34500 in order to purchase the house.
3. The project was worth 97 points.
Define percentage?The denominator of a percentage (also known as a ratio or fraction) is always 100.
As a percentage, "%" is read as "percent" or "percentage" in this context.
You may always "divide by 100" this percent symbol to make it into a fraction or decimal equivalent.
Here we can see that Melissa has already $2500 in her savings account.
Total cost of house = $185000
Now for the loan she needs to have 20% of the mortgage as savings.
20% of $185000
20/100 × 185000
= 37000
Now she already has $2500.
So, the amount she need to save is= $37000 - $2500
= $34500
Now, total grade Brooke received = 87.
10 points have been taken off for her mistakes.
Total worth of test = 87+10 =97points.
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a high school baseball player has a 0.253 batting average. in one game, he gets 8 at bats. what is the probability he will get at least 6 hits in the game?
The probability of a high school baseball player getting at least 6 hits in one game, given a 0.253 batting average, when he gets 8 at-bats, is 0.0197 or approximately 2%.
Given, the high school baseball player's batting average is 0.253, which means in 100 times he hits the ball, he will make 25.3 hits on average. We need to find the probability of getting at least 6 hits in a game when he gets 8 at-bats.
We will calculate the probability using the Binomial Probability formula. Here, the number of trials is 8, and the probability of success is 0.253. We need to find the probability of getting at least 6 hits.
P(X≥6) = 1 - P(X<6)
P(X<6) = ∑P(X=i), i=0 to 5
We can use the Binomial Probability Table to find these probabilities or use the Binomial Probability formula.
P(X<6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)
= C(8,0) (0.253)^0 (1 - 0.253)^8 + C(8,1) (0.253)^1 (1 - 0.253)^7 + C(8,2) (0.253)^2 (1 - 0.253)^6 + C(8,3) (0.253)^3 (1 - 0.253)^5 + C(8,4) (0.253)^4 (1 - 0.253)^4 + C(8,5) (0.253)^5 (1 - 0.253)^3
≈ 0.9799
Therefore, P(X≥6) = 1 - 0.9799
= 0.0201 or approximately 2%.
Hence, approximately 0.0197 or 1.97% is the probability of a high school baseball player, who has a batting average of 0.253, obtaining at least 6 hits when given 8 at-bats during a single game.
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given the following frequency table of values, is the mean, median, or mode likely to be the best measure of the center for the data set? valuefrequency 351 364 376 386 395 631
For the given following frequency table of values 351, 362, 373, 381, 391, The mode is likely to be the best measure of the center for the data set.
The given frequency table is as follows:
Value frequency 351, 362, 373, 381, 391.
To find the most appropriate measure of central tendency for a dataset, we need to analyze the spread of data.
The mean, median, and mode are measures of central tendency in statistics.
We can find the following measures from the given data set:
Mean: It is calculated by summing up all the values and then dividing the result by the total number of values. This measure of central tendency is appropriate when the data are symmetrical.
Median: It is the middle value of the data set when arranged in order. It is suitable for skewed data.
Mode: It is the most common value in the data set. It is appropriate when data is discrete. The data in the frequency table appear to be discrete.
Because the data are discrete, the most appropriate measure of central tendency is the mode. So, the mode is likely to be the best measure of the center for the given value frequency data set.
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what is the value of t?
Answer:
t=36°
Step-by-step explanation:
90-54=36
opposite angles are equal so t=36°
a sample of test scores is normally distributed with a mean of 120 and a standard deviation of 10. what score is located 2 standard deviations below the mean? g
The score located 2 standard deviations below the mean is 100. This score can be found by subtracting 2 standard deviations (20) from the mean (120).
The normal distribution is a bell-shaped curve that is symmetrical around the mean. This means that if you calculate the number of standard deviations away from the mean, you can use the same number to calculate how many standard deviations away from the mean the score is.
For example, in this question, the mean is 120 and the standard deviation is 10. To find the score located 2 standard deviations below the mean, subtract 2 standard deviations from the mean. This means the score is 120 - 20 = 100.
In general, the formula for calculating the score located x standard deviations away from the mean is:
Score = Mean + (x * Standard Deviation)
For example, to find the score located 4 standard deviations away from the mean, the formula is:
Score = Mean + (4 * Standard Deviation)
In this example, the score is 120 + (4 * 10) = 160.
In summary, to find the score located x standard deviations away from the mean, use the formula:
Score = Mean + (x * Standard Deviation)
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PLEASE HURRY !! I NEED HELP!!!
Answer:$10
Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?
He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.