As our determined t-score (2.77) is larger than the critical t-value (2.262), we disregard the null hypothesis in favor of the alternative one
How to solve
Given data:
The 1980 mean weight (μ) was 180.4 pounds, while the 2023 sample mean weight (x) was 197.9 pounds;
additionally, the sample size (n) was 10 and the sample standard deviation (σ) was 20 pounds.
At a significance level of 0.05, we calculate the t-score by first dividing (x-μ)/(σ/sqrt(n)).
This gives us the value 17.5/6.32 or 2.77 for the t-score.
Afterward, it is necessary to find the critical t-value with a two-tailed test at a significance level α=0.05 in respect to having 9 degrees of freedom (df = n – 1 = 10 – 1 = 9).
This can be located through either a t-distribution table or an online calculator; the result displays the calculated critical t-value being approximately ±2.262.
As our determined t-score (2.77) is larger than the critical t-value (2.262), we disregard the null hypothesis in favor of the alternative one, signifying there is a glaringly significant disparity between the average mass of grown male adults from 1980 and 2023 which upholds the researcher's statement that since 1980, males in the U.S. have gotten heavier.
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8. A graph represents the proportional relationship between the number of pages printed, y, and the time in minutes, x. If there is a point on the graph at (4, 720), how many pages can be printed in half a minute?
The number of pages that can be printed in half a minute is 90 pages
How many pages can be printed in half a minute?From the question, we have the following parameters that can be used in our computation:
The graph represents a proportional relationship
Where
x = minutes
y = pages
When the time is half a minute, we have
x = 0.5
So, we have the following ordered pair
(0.5, y)
From the question. we have
(4, 720)
So, we have
(0.5, y) = (4, 720)
Express as an equation
So, we have
y/0.5 = 720/4
This gives
y = 0.5 * 720/4
Evaluate
y = 90
Hence, the number of pages is 90
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digit shows a number written in words 2. expanded form shows a number written using digits 3. period one of the numerals from 0 to 9 4. place value the position of a digit in a number, which determines its value 5. standard form each three-digit part of a whole number, separated by commas 6. word form shows a number written as an addition statement
The statements can be arranged correctly as follows:
1. Word Form shows a number written in words.
2. Standard form shows a number written using digits.
3. Digit is one of the numerals from 0 to 9
4. Place value the position of a digit in a number, which determines its value.
5. Period each three-digit part of a whole number, separated by commas
6. Expanded form shows a number written as an addition statement
How to determine the termsWe can determine the terms by first understanding the mathematical meanings. Word form is a term used in math to denote expressions written in word B.
Also, the standard form is a way of shortening large numerical values using digits. Digits are single numbers that run between 0 to 9 and they make up the higher values of numbers.
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please help i need this done
The value of f(j) when
1. j = -1 is 11
2. j = 0 is 10
3. j = 1 is 11
4 . j = 2 is 14
What is a function?A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
For example, here j is a variable and f(j) is the function of 'j'.
f(j) = j²+10
Therefore , when j = -1
f(j) = -1)² + 10
f(j) = 1+10 = 11
When j = 0
f(j) = 0²+10
= 0+10 = 10
when j = 1
f(j) = 1²+10
= 1+10 = 11
When j= 2
f(j) = 2²+10
= 4+10
= 14
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If RS = ST 81, QR = v + 33, and QT = 3v 19, what is QT
The requried measure of the side QT in triangle SQT is 59 units.
A figure is shown with two triangles, SQT and SQR.
Since in the question we are given to RS = ST 81, QR = v + 33, and QT = 3v 19,
As RS = St and SQ is a common side both the triangle are congruent, QT = QR
v + 33 = 3v - 19
52 = 2v
v = 26
Now,
QT = 3(26) - 19
QT = 59
Thus, the requried measure of the side QT in triangle SQT is 59 units.
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15 points!!!! Carefully look at the relationship between altitude and
temperature in the atmosphere. Describe how temperature
changes when moving from sea level upward in the
atmosphere.
From the data given, we can see that as you move upward in the atmosphere from sea level, the temperature generally decreases such as from 28 degree to negative degree.
Why does temperature change with altitude in atmosphere?This is because earth atmosphere is heated from bottom-up by the Earth's surface, so, the nearest air to the ground is warmer than the air at higher altitudes. When we climb higher, the air pressure decreases and this causes the air to expand and cool.
This decrease in temperature with increasing altitude is known as the adiabatic lapse rate, but this is known to vary depending on factors such as humidity and atmospheric conditions.
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Tyrone is saving up money to buy a car. Tyrone puts $10,000.00 into an account which earns 5% interest, compounded monthly. How much will he have in the account after 5 years?
Round your answer to the nearest cent.
The solution is, $ 12833 .59 will he have in the account after 5 years.
Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on any interest that has previously accrued. In other words, it is interest that is earned on both the initial principal and any interest that has been added to it over time.
by the question.
We can use the formula for compound interest to solve the problem:
A = P
where:
A = final amount (x in this case)
P = principal or initial amount ($10,000.00)
r = annual interest rate (5% in this case)
n = number of times the interest is compounded per year (12, since it's compounded monthly)
t = time in years (5, since Tyrone opened the account 5 years ago)
Substituting the values given, we get:
A = $ 12833 .59
The solution is, $ 12833 .59 will he have in the account after 5 years.
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If there were 20 dogs and 60 cats at a pet daycare, how many cats would there be if there were 40 dogs and the ratio stayed the same?
The quantity of cats that will be in the pet daycare when there are 40 dogs would be = 120 cats.
How to calculate the ratio of cats to dogs in the pet daycare?Ratio can be defined as the comparison of two values that shows the amount of one value that can be found in the other value.
The initial amount of dogs = 20
The initial amount of cats = 60
The final amount of dog = 40
The final amount of cats = ?
That is;
20 dogs = 60 cats
40 dogs = X cats
make X the subject of formula;
X = 40×60/20
= 2400/20
= 120 cats
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PLEASE I NEED AN ANSWER QUICKLY
Let c = children's and a = adults.
Mathland Theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250. How many of each type of ticket were sold?
Answer:
90 children's tickets and 200 adult tickets were sold.
Step-by-step explanation:
Let's use the variables c and a to represent the number of children's and adult tickets sold, respectively.
From the problem, we know that:
The total number of tickets sold is 290: c + a = 290
The total revenue from ticket sales is $2250: 5c + 9a = 2250
We now have two equations with two unknowns. We can use substitution or elimination to solve for c and a. Here's one way to use elimination:
Multiply the first equation by 5 to get 5c + 5a = 1450
Subtract the above equation from the second equation to eliminate c: 5c + 9a - (5c + 5a) = 2250 - 1450
Simplify: 4a = 800
Solve for a: a = 200
Substitute a = 200 into the first equation to solve for c: c + 200 = 290
Simplify: c = 90
Therefore, 90 children's tickets and 200 adult tickets were sold.
Rita earns $30 for each hour that she works.
Use this information to fill in the table. Then plot the ordered pairs given by the table.
Answer:
Hii^^ Here's your answers:
5 hrs=$150 earned
7 hrs=$210 earned
9 hrs=$270 earned
Step-by-step explanation:
30x = amount earned
x = hours
Answer:(5,150) (7,210) (9,270)
Step-by-step explanation: For each hour she works, she earns 30 dollars.
Number of hours: Money she earns
1:30
X stands for the amount of money she earns. So for 5 hours, we can write this:
5:X
To get from 1:30 to 5:x, you multiply by 5. 1x5=5. So you multiply 30x5 and get 150. Do the same for the other situations, and you get:
5:150
7:210
9:270
To plot them on the graph, the number of hours she works is x, and the money she earns is y.
So, put these on the graph:
(5,150)
(7,210)
(9,270)
CAN SOMEONE HELP WITH THIS PROBLEM?
The value of the infinite series expression [tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] is -30.
Given information:
[tex]\sum^{124}_{i = 1}a_i = -10[/tex] and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].
The required series form can be rearranged as,
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) &= 29\sum^{124}_{i = 1}a_i - 13\sum^{124}_{i = 1}b_i[/tex]
Substitute the provided values of [tex]\sum^{124}_{i = 1}a_i = -10[/tex] and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].
We get,
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = 29(-10) - 13(-20)
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -290+ 260
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -30.
As a result, the required value is -30.
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Find the area of the shaded region
Area= 69π or 216.77 square units.
Step-by-step explanation:1. Find the area of the white circle.Remember that the formula for the area of a circle is the following:
[tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
Hence, the area of the white circle is:
[tex]A_{WC} =\pi (10)^{2} =100\pi[/tex]
2. Find the area of the red circle.Here you can use the same formula, just need to change the value of the radius:
[tex]A_{RC} =\pi (13)^{2} =169\pi[/tex]
3. Find the difference between the 2 areas.[tex]A_{RC} -A_{WC} =169\pi -100\pi =69\pi[/tex]
4. Express the final result.The area of the shaded region is 69π or 216.77 square units, approximately.
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which expression uess exactly terms and is equivalent to 6(2 + x + x + y)
The equivalent value of the expression is A = 12 + 6x + 6x + 6y
Given data ,
Let the expression be represented as A
Now , the value of A is
A = 6(2 + x + x + y)
On simplifying the equation , we get
A = 6 ( 2 ) + 6x + 6x + 6y
On further simplification , we get
A = 12 + 6x + 6x + 6y
Hence , the expression is A = 12 + 6x + 6x + 6y
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The complete question is attached below :
which expression uess exactly terms and is equivalent to 6(2 + x + x + y)
which function has the greatest rate or change
Suppose we have data about a three-stock financial market that satisfies the single-index model as below: (the standard deviation of the market-index portfolio is 18%)
Capitalization Beta Excess Return Std Dev
A $3,000 0.15 10% 40%
B $2,000 0.95 2% 30%
C $1,500 1.7 17% 50%
What is the mean excess return of the value-weighted index portfolio?
Express your answer in percent and round it to 2 decimal places. For example, if your answer is 0.25456, then please write down 25.46 (without the percent sign).
The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:
Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500
Next, we can calculate the weight of each stock in the index portfolio as follows:
Weight of Stock A = $3,000 / $6,500 = 0.4615
Weight of Stock B = $2,000 / $6,500 = 0.3077
Weight of Stock C = $1,500 / $6,500 = 0.2308
The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:
Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081
The mean excess return of the index portfolio can be calculated using the single-index model as:
Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio
= 1.081 x 18%
= 19.458%
Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:
Mean Return = Mean Excess Return + Risk-Free Rate
= 19.458% + 2%
= 21.458%
Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
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3. Han thinks that since the arc length in circle A is longer, its central angle is larger. Do
you agree with Han? Show or explain your reasoning.
Yes , Han is correct as the a circle with a longer arc length has a larger central angle
Given data ,
Let the arc length of the circle A = 6π units
Let the radius of the circle A = 15 units
Let the arc length of circle B = 2π units
Let the radius of the circle B = 5 units
Now , The length of an arc in a circle is determined by both the radius of the circle and the central angle that subtends the arc. The formula for calculating the length of an arc in a circle is given by:
Arc length = (Central angle / 360 degrees) x (2πr)
Though two circles' radii differ, they may nevertheless have distinct arc lengths even though their centre angles are the same. Similar to this, if the radii of two circles are adjusted properly, two circles with differing central angles can nevertheless have the same arc length.
Hence , the central angle is solved
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PLEASE HELP
the pattern for representing a triangular number
The pattern that can be used to represent a triangular number is T(n) = 1 + 2 + 3 + ... + n.
What is a triangular number ?A number that can take the form of an equilateral triangle is called a triangular number. By definition, it represents the sum of positive integers up to n consecutive natural numbers. The pattern for such a calculation is expressed as follows:
T(n) = 1 + 2 + 3 + ... + n.
Triangular numbers exhibit many engaging properties and are applicable across various mathematical and real-world contexts.
In conclusion, the pattern used to represent a triangular number is T (n) = 1 + 2 + 3 + ... + n.
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what is the ratio of apple oranges and bananas when 48 are in the basket all together
not each
The ratio of apple oranges and bananas cannot be calculated with the given information
Calculating the ratio of apple oranges and bananasFrom the question, we have the following parameters that can be used in our computation:
Fruits = Orange, Bananas and Apple
Total number of fruits = 48
The available parameters is not enough to determine the ratio
Assuming that we have
Banana = 10
Orange = 20
Apple = 18
Then the ratio would be:
Apple : oranges : bananas = 18 : 20 : 10
Simplify
Apple : oranges : bananas = 9 : 10 : 5
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4. What is Probability?
(ii) State the axioms of probability
(iii)Two fair dice are thrown, what is the probability of getting
(a) the sum of 9
(b) two odd numbers
(c) two prime numbers
(d) two factors of 12
4c. What is Statistics?
(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.
(ii) The axioms of probability are:
the non-negativity (that the probability of an event is greater than or equal to zero), and
the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).
(iii) When two fair dice are thrown the probability of getting:
a) The sum of 9 = 1/9
b) Two odd numbers = 1/4
c) two prime numbers = 1/9
d) two factors of 12 = 1/9
(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.
How to find probability when two dice are thrown?To find probability when two dice are thrown, we have:
(a) The sum of 9:
We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways
A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.
(b) Two odd numbers:
We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).
possible outcomes = 9,
So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.
(c) Two prime numbers
We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)
possible outcomes = 4,
So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.
(d) Two factors of 12:
We count the number of ways and divide by the total possible outcomes.
The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways
possible outcomes = 6
Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12
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What is the surface area of the
triangular prism shown?
14 m
10 m
A. 558 m²
B. 976 m²
25 m
24 m
25 m
C. 1,680 m²
D. 1,750 m²
10
The calculated surface area of the triangular prism is 976 square meters
Calculating the surface area of the triangular prism?From the question, we have the following parameters that can be used in our computation:
The dimensions of the triangular prism
The surface area of the triangular prism is the sum of the individual shapes
So, we have the following formula
Surface area = Area of rectangle + Area of the 2 triangles + Area of the 2 rectangles
Using the dimensions, we have
Surface area = 10 * 14 + 2 * 1/2 * 24 * 14 + 2 * 25 * 10
Evaluate
Surface area = 976
Hence, the surface area is 976
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2. The base of the model pyramid shown in this diagram is a 40cm by
20cm rectangle and its height is 35cm. Calculate is volume in cubic
centimetres to the nearest cubic centimetre.
35 cm
40 cm
20 cm
The volume of the pyramid is 9333 cubic centimetres
Calculating the volume in cubic centimetresFrom the question, we have the following parameters that can be used in our computation:
Base dimensions = 40 cm by 20 cm
Height = 35 cm
The volume of the pyramid is calculated as
Volume = Product of Base dimensions and Height/3
substitute the known values in the above equation, so, we have the following representation
Volume = 40 * 20 * 35/3
Evaluate
Volume = 9333
Hence, the volume is 9333
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Which is the correct form of q (x) +
O A.
14
7³ +7 + = +2
OB.
c.
OD.
14
7 + 2 + 14
(7³ - 14x² + 28x
(7³
7x³ + 7 +
-
-
for the expression
55) +1242
14x² + 28x − 55) +
124
7z¹+z+14
726 +2+147
Answer:
The correct answer is C
Step-by-step explanation:
pleaseee help with mathhhh.
The value of the expression is 2x³ + 3x² - 27x + 40
How to determine the productIt is important we know that algebraic expressions are described as expressions that are composed of factors, constants, variables, coefficients and terms.
Algebraic expressions are also made up of arithmetic operations, such as;
AdditionBracketParenthesesSubtractionMultiplicationDivisionFrom the information given, we have;
1. (x + 5)(2x² -7x + 8)
expand the bracket
2x³ - 7x² + 8x + 10x² -35x + 40
collect like terms
2x³ - 7x² + 10x² + 8x - 35x + 40
Add the like terms
2x³ + 3x² - 27x + 40
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Five more than the product of a number and six is equal to nine
Answer:
Think about the PEMDAS rules for order of operations.
Multiplication comes before addition or subtraction, so first we have "the product of a number and 5" - that's 5x. Then "six more" than that would be 5x + 6. "Equals" means the "=" sign, so the final answer is 5x + 6 = 8.
El profesor de educación física tenía 12 balones y ahora tiene 96 por cuanto se multiplicó la cantidad de los balones
may i have the different proofs for this thank you
The proof for AB ≅ CD is:
Step Statement Reason
1 ∠B ≅ ∠D, BC || AD Given
2 ∠BCA ≅ ∠CAD Alternate Interior angles
3 AC ≅ AC common side
4 ΔABC ≅ ΔADC Angle-Angle-Side rule of congruency
5 AB ≅ CD Corresponding sides of congruent triangle
Consider triangle ABC and triangle ADC.
Here, side BC is parallel to side AD.
From the attached figure we can observe that AC is a transversal.
so, ∠BCA and ∠CAD would be alternate angles formed by two parallel lines and transversal.
By property of Alternate Interior angles,
∠BCA ≅ ∠CAD
Also, we can observe that side AC is common side to ΔABC and ΔADC.
We rewrite this proof as,
Step Statement Reason
1 ∠B ≅ ∠D, BC || AD Given
2 ∠BCA ≅ ∠CAD Alternate Interior angles
3 AC ≅ AC common side
4 ΔABC ≅ ΔADC Angle-Angle-Side rule of congruency
5 AB ≅ CD Corresponding sides of congruent triangle
This is the required proof.
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PLS HELP MARKING AS BRAINLIST
The value of c as per the law of cosines, to the nearest tenth, is 5.1 units.
Given information:
a = 8, b = 9 C = 34°.
To find the value of C:
According to the Law of Cosines, for any triangle ABC:
c² = a² + b² - 2ab cos(C)
Substituting the given values:
c² = 8² + 9² - 2(8)(9) cos(34°)
c² = 64 + 81 - 144 cos(34°)
c² = 145 - 144 cos(34°)
Taking the square root of both sides:
c = √(145 - 144 cos(34°))
Using a calculator:
c ≈ 5.1 units (rounded to the nearest tenth)
Therefore, the value of c is approximately 5.1 units.
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How many ml are needed to prepare 750 mg from 1:250
187, 500 ml are needed to prepare 750 mg from 1:250.
We have to find amount in ml to prepare 750 mg from 1:250.
let the amount needed in ml be x.
Using proportion
1/750 = 250 / x
x= 750 . 250
x= 187, 500 ml
Thus, to prepare 750 mg 187,500 ml is needed.
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for the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. x|y
2|5
6|15
18|45
Yes , y varies directly with x as a proportion of k = 2.5
Given data ,
Let the values of x = { 2 , 6 , 18 }
Let the values of y = { 5 , 15 , 45 }
Now , the proportion equation is y = kx
On simplifying , we get
k = 5/2
k = 2.5
Therefore , the proportionality constant is k = 2.5
Hence , the proportion is y = 2.5 ( x )
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The neighbor of 1250 people has 30 city blocks. Each block is 1/16 mile long by 1/8 mile wide. Find the population density of the neighborhood in people per square mile.
Answer:
Step-by-step explanation:
The population density of the neighborhood is 12000 people per square mile.
Total number of people = 1250
Number of city blocks = 30
Length of the block, l = 1/16 mile
Width of the city block, w = 1/18 mile
Area of one block, A = l x w
A = (1/16) x (1/18)
A = 1/288 square mile
Total area of all the 30 blocks, A' = 30 x A
A' = 30/288 square mile
So, the population density,
D = Total no.of people/A'
D = 1250/(30/288)
D = 1250 x 288/30
D = 12000 people per square mile.
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i dont know how to subtract: 8-4 1/2.
Answer:
The answer would be 3.5 in decimal form.
Answer:
The answer is 55/12
Step-by-step explanation:
8-41/12
(8×12+1×(-41))/12
(96-41)/12
55/12