If x = 2, y = 6, and z = 4, which expression is equivalent to 4? à 54+0-3+2=4. D Xtra 4 ... A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby.
Enter the x,y value in the text box below for the following table of values where the x value is -2
y = 3x + 4
Answer:
x=-2
y = 3× -2 + 4
y= -6 + 4
y = -2
PLEASE HELP god bless you /Barak Allah fic A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
The required number of new boys in a sports team is 62.
As mentioned in the question, A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50
Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys
Thus, the required number of new boys in a sports team is 62.
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Solve for <1. (Will mark as brainiest!)
Answer:
< 1 = 64°
Step-by-step explanation:
First at all the sum of 2 angles should be 180°
< 3 + 116° = 180°
< 3 = 180 - 116
< 3 = 64°
Then, the sum of intern angles of a triangle must sum 180°, so:
< 1 + 52° + < 3 = 180°
< 1 +52 + 64 = 180
< 1 = 180 - 64 -52
< 1 = 64°
Can someone answer this for me. I NEED HELPPP
Find the value of y if m∠3 =65° and m∠1 =(15y+5)°
Answer: 4 i think
Step-by-step explanation:
65=15y+5
65 - 5 = 15y +5 -5
60 = 15y
60/15 = 15y/15
4 = y
A. Quantity A is greater B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. 0
No information is given for x and it can be fraction or real number, so option D is correct.
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator.
It tells how many equal parts of the whole or collection are taken.
No information is given for x and it can be fraction or real number, so option D is correct.
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What is the total area of the tiles Felix needs to buy?
By using the formula for area of parallelogram, it can be calculated that
Felix needs to buy 80 [tex]cm^2[/tex] of tiles
What is area of parallelogram?
Area of parallelogram is the total space taken by the parallelogram.
If b is the base of the parallelogram and h is the height of the parallelogram, then area of the parallelogram is calculated by the formula
Here,
Base of each parallelogram = 4cm
Height of each parallelogram = 2cm
Area of each parallelogram = 4 [tex]\times[/tex] 2 = 8 [tex]cm^2[/tex]
Area of 10 parallelograms = 8 [tex]\times[/tex] 10 = 80 [tex]cm^2[/tex]
Felix needs to buy 80 [tex]cm^2[/tex] of tiles
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Complete Question
The full diagram has been attached.
Match the metric units on the left with their
approximate equivalents on the right. Not all the
options on the right will be used.
1 meter
kilogram
1 liter
1 cup
I mile
2
pounds
1 quart
I yard
Answer:
meter - yard
kilogram - 2 pounds
liter - quart
3/4x + 2/3y - 3/8x + 1/2y
[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].
Step-by-step explanation:1. Write the expression.[tex]3/4x + 2/3y - 3/8x + 1/2y[/tex]
2. Operate with like terms.a) First, start by operating with the terms that contain the "x" variable.
[tex]3/4x- 3/8x\\ \\\frac{3}{4}x-\frac{3}{8}x\\ \\ \frac{3*2}{4*2}x-\frac{3}{8}x\\ \\\frac{6}{8}x-\frac{3}{8}x\\ \\x(\frac{6}{8} -\frac{3}{8} )\\ \\x(\frac{6-3}{8} )\\ \\x(\frac{3}{8} )\\ \\\frac{3}{8}x[/tex]
b) Start with terms containing "y".
[tex]2/3y+1/2y\\ \\\frac{2}{3}y +\frac{1}{2} y\\ \\\frac{2*2}{3*2}y +\frac{1*3}{2*3} y\\ \\\frac{4}{6}y +\frac{3}{6} y\\ \\y(\frac{4+3}{6})\\ \\y(\frac{7}{6})\\ \\\frac{7}{6} y[/tex]
3. Put the terms together.[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].
The mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $100. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? $1064 $1417 $1373 $856 $1250 $1102
Answer:
The empirical rule states that for a bell-shaped distribution, approximately 68% of the data values will fall within one standard deviation of the mean, 95% of the data values will fall within two standard deviations of the mean, and 99.7% of the data values will fall within three standard deviations of the mean.
Using this information, we can calculate the range of values that fall within two standard deviations of the mean for the given data set:
Mean: $1200
Standard deviation: $100
Two standard deviations: $200
Therefore, the range of values that fall within two standard deviations of the mean is $1200 - $200 = $1000 to $1200 + $200 = $1400.
With this information, we can determine which of the given data values are unusual (more than two standard deviations from the mean):
$1064 is within two standard deviations of the mean.
$1417 is outside of two standard deviations of the mean.
$1373 is within two standard deviations of the mean.
$856 is outside of two standard deviations of the mean.
$1250 is within two standard deviations of the mean.
$1102 is within two standard deviations of the mean.
Therefore, the data values $1417 and $856 are unusual (more than two standard deviations from the mean).
We can also determine which of the given data values are very unusual (more than three standard deviations from the mean) using the same process. The range of values that fall within three standard deviations of the mean is $1000 to $1600. With this information, we can see that none of the given data values are very unusual (more than three standard deviations from the mean).
A stage manager is trying to seat important guests in the front row of a theater. The row has seven seats, and she would like a diplomat in the first seat, a singer in the second seat, and a movie director in the third seat. After this, the remaining diplomats, singers, and movie directors will be seated in the last four seats, in no particular order. If there are 3 diplomats, 2 singers, and 2 directors attending the show, how many different front row plans are possible?
Answer: 12 row plans
The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.
Step-by-step explanation:
While hiking, Kurt ate 1/3 of a cup of nuts. Danielle ate 1/6 of a cup of nuts. How much more did Kurt eat than Danielle?
Kurt will eat 1/6 cups more than Danielle if Kurt ate 1/3 of a cup of nuts and Danielle ate 1/6 of a cup of nuts by using ratio and proportion concept.
What is ratio and proportion?When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.
A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written. A ratio in mathematics displays the multiplicative relationship between two numbers.
Given,
A cup of nuts ate by Kurt=1/3
A cup of nuts ate by Danielle=1/6
(1/3)-(1/6)
=1/6
Therefore, Kurt will eat 1/6 cups more than Danielle.
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Hello I have to develop that (x-1)(x+2) I know that it makes x²+x-2 but I don't understand why, can you explain me ?
Answer:
pls rate as brainliest it will go a long way
Step-by-step explanation:
(x–1)(x+2)
STEP 1
using the first bracket to expand the other
= x(x + 2) –1(x + 2)
= x² + 2x –x –2
= x² + x – 2
Step 2
or by using the other bracket to expand the other
(x – 1)(x + 2)
x(x – 1) + 2(x – 1)
= x² – x + 2x – 2
= x² + x – 2
Luis has 60 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 216 square meters. Solve for the dimensions (length and width) of the field. The dimensions are __ meters by __ meters .
The dimensions are 12 meter by 18 meter .
what is perimeter of rectangle ?perimeter of rectangle = 2(length + width)
length and width of the Luis plot by L and W, respectively.
We know that the perimeter, is 60 meters. So we can write:
2L + 2W = 60
Simplifying this equation, we can divide both sides by 2:
L + W = 30
now , area of the plot is 216 square meters:
L x W = 216
use substitution to solve for one of the variables. Let's solve for L in the first equation:
L = 30 - W
We can substitute this expression for L into the second equation:
(30 - W) x W = 216
[tex]W^2 - 30W + 216 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2
Simplifying:
W = [30 ± 6] / 2
So W = 18 or W = 12.
If W = 18, then L = 30 - 18 = 12.
If W = 12, then L = 30 - 12 = 18.
Therefore, the dimensions are 18 meters by 12 meters or 12 meters by 18 meters.
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Which equations have the same value of X as 5/6x + 2/3=-9? Select three options
The equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
What is equation?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation
3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Consider the given equation
5/6 x + 2/3 = -9
Subtract 2/3 from both sides,
5/6x + 2/3 - 2/3 = -9 - 2/3
5/6x = -29/3
[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]
The value of x is -11.6.
Hence, the equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
After solving above these equations we get the same value of x which is -11.6.
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Complete question:
Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9
6(5/6x + 2/3) = -9(6)
5 x + 4 = -54 5 x + 4 = -9
5 x = -13
5 x = negative 58
Edgar accumulated $9,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for
2 years, how much will he owe on this debt in 2 years for quarterly compounding? Round your answer to the nearest cent.
To calculate the total amount of interest that Edgar will owe on his credit card debt after 2 years of quarterly compounding at a 20% annual interest rate, we need to use the formula A = P(1 + r/n)^nt, where A is the total amount of money owed after t years, P is the initial principal (or amount borrowed), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the initial principal is $9,000, the annual interest rate is 20%, the number of times the interest is compounded per year is 4 (since the interest is compounded quarterly), and the number of years is 2. Plugging these values into the formula, we get A = $9,000(1 + 0.20/4)^4 * 2 = $9,000(1.05)^8 = $9,000 * 1.4064 = $12,658.40. Thus, after 2 years of quarterly compounding at a 20% annual interest rate, Edgar will owe approximately $12,658.40 on his credit card debt. This result should be rounded to the nearest cent, giving us $12,658.40.
A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
The firm has available to it on weekly basis, 480 hours of machining time, 400 hours of polishing time and 400 hours of assembling time. The unit profits on the product are Birr 360, Birr 240, Birr 360 and Birr 480, respectively.The firm has a contract with a distributor to provide 50 units of product I, and 100 units of any combination of products II and III each week. Through other customers the firm can sell each week as many units of products I, II and III as it can produce, but only a maximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Make a mathematical model for the given problem. Assume that any unfinished pieces can be finished the following week.
Step-by-step explanation:
The firm should manufacture 50 units of product I, 100 units of product II, and 100 units of product III each week to meet all contractual obligations and maximize its total profit.
To set up the mathematical model for this problem, we can use variables to represent the number of units of each product that the firm manufactures each week. Let x1 be the number of units of product I, x2 be the number of units of product II, x3 be the number of units of product III, and x4 be the number of units of product IV.
The first constraint is that the firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. This can be represented as:
x1 = 50
x2 + x3 = 100
The second constraint is that the firm has a maximum of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time each week. The time required for each product can be represented as:
x16 + x28 + x34 + x410 <= 480 (machining time)
x14 + x26 + x32 + x48 <= 400 (polishing time)
x14 + x24 + x34 + x46 <= 400 (assembling time)
The third constraint is that the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. This can be represented as:
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
The objective is to maximize the firm's total profit, which is the sum of the profits for each product. The unit profits for each product are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The total profit can be represented as:
360x1 + 240x2 + 360x3 + 480x4
The complete mathematical model for this problem is:
Maximize: 360x1 + 240x2 + 360x3 + 480x4
Subject to:
x1 = 50
x2 + x3 = 100
x16 + x28 + x34 + x410 <= 480
x14 + x26 + x32 + x48 <= 400
x14 + x24 + x34 + x46 <= 400
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
This model can be solved using linear programming techniques to find the values of x1, x2, x3, and x4 that maximize the total profit while satisfying all of the constraints. In this case, the optimal solution is x1 = 50, x2 = 100, x3 = 100, and x4 = 0, which corresponds to manufacturing 50 units of product I, 100 units of product II, and 100 units of product III each week. This meets all of the contractual obligations and maximizes the total profit.
The objective is to maximize total profit, which is given as
P = 360 [tex]x_1[/tex]+ 240[tex]x_2[/tex]+ 360[tex]x_3[/tex] + 480[tex]x_4[/tex]
What is Linear Programming Problem?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.
Let[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] and [tex]x_4[/tex] be the number of units of product I, II, III and IV to be produced, respectively.
The constraints are that the time requirements for each product should not exceed the available time, the firm is contractually obligated to produce 50 units of product I and 100 units of products II and III, and the firm can sell at most 25 units of product IV.
These constraints can be written mathematically as:
3[tex]x_1[/tex] + 2 [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + 4[tex]x_4[/tex] ≤ 480 (Machining)
[tex]x_1[/tex] + [tex]x_2[/tex] + [tex]x_3[/tex] + 3[tex]x_4[/tex] ≤ 400 (Polishing)
2[tex]x_1[/tex] + [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + [tex]x_4[/tex] ≤ 400 (Assembling)
and, [tex]x_1[/tex] ≥ 50 (Product I)
[tex]x_2[/tex] + [tex]x_3[/tex] ≥ 100 (Products II and III)
[tex]x_4[/tex] ≤ 25 (Product IV)
[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] , [tex]x_4[/tex] ≥ 0
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30 POINTS. The county rummage sale arranges 250 tables in three groups. The group on the left has 75 tables. The group on the right has 80 tables. Write an equation to find the number of tables in the middle group. Then sovle your equation.
Answer: There are 95 tables in the middle group
Step-by-step explanation:
There are a total number of 250 tables.
There are three groups.
We know how many tables the left and right groups have
let x be the number of tables in the middle
75+80+x=250
155+x=250
x=95
piecewise function.
Express the function graphed on the axes below as a
Please help me
The piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
How to express the function graphed?On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).
On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).
That line passes through (-1, 0) and (0, 1), then the slope is:
a = (1 - 0)/(0 -(-1)) = 1
And the y-intercept is y = 1, then the equation of the line is:
y = x + 1
The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)
The slope is:
a = (0 - 7)/(6 -5) = -7
Then the line is something like:
y = -7*x + b
To find b, we use the point (6, 0)
0 = -7*6 + b
7*6 = 42 = b
Then this line is:
y = -7x + 42
Concluding, the piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.
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In square ABCD, m∠BCE=(5x+9)∘.
What is the value of x?
Enter your answer, as a decimal, in the box.
x =
Answer:
x = 7.2
Step-by-step explanation:
You want the value of x that makes ∠BCE = 45° = (5x +9)°.
SolutionDivide by ° and subtract 9 to get ...
36 = 5x
Divide by 5, and you have the value of x:
7.2 = x
The value of x is 7.2.
__
Additional comment
You know that the corner angles of a square are 90°, and that the diagonals bisect the corner angles. Each half is 45°.
CAN SOMEONE HELP WITH THIS QUESTION?✨
The time required to grow $5000 to $8300, if the rate of interest is 7.5 %, is 7 years.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The principal amount, p = $5000,
The amount, A = $8300
The rate of interest, r = 7.5 %,
Calculate the time as shown below,
[tex]A = p(1 + r / 400)^{4n}[/tex]
8300 = 5000 (1 + 7.5 / 400)⁴ⁿ
8300 / 5000 = (1 + 0.01875)⁴ⁿ
1.66 = (1.0188)⁴ⁿ
1.66 = (1.077)ⁿ
(1.077)⁷ = (1.077)ⁿ
n = 7
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Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles. Similar Not Similar A and B Similar – A and B Not Similar – A and B B and C Similar – B and C Not Similar – B and C A and C Similar – A and C Not Similar – A and C Three rectangles labeled A, B, and C. The length of rectangle A is labeled as 100 centimeters and the width is labeled as 80 centimeters. The length of rectangle B is labeled as 120 centimeters and the width is labeled as 100 centimeters. The length of rectangle C is labeled as 90 centimeters and the width is labeled as 72 centimeters.
A polygon is a plane shape with a minimum of three straight sides. Thus the appropriate answer are:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Polygons are majorly plane shapes which have straight sides. They are named with respect to the number of their sides, and the minimum sides is three. Some common examples are: trigon (3 sides), octagon (8 sides), hexagon (6 sides), pentagon (5 sides) , etc.
Two or more shapes are said to be similar if and only if they have some common properties with respect to their sides or internal angles.
Considering the ratios of the sides of the given polygons, it can be deduced that:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Thus none of the polygons are similar.
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Please help me with my question step by step
give brainliest.help
The required, team 3, tower garden donation shows the proportional relationship between weeks and donation,
What is proportionality?Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.
here,
From the table,
The ratio of a week to the donation of the individual team must be the same as the ratio of the preceding week and the donation of the respective team,
So,
Team 1,
1 / 1 = 2 / 3[1/4], false
Similarly, team 2 and team 4's relationship is also not proportional,
Now, team 3
1 / [2 1 / 3] = 2 / [4 2/3 ]
3 / 7 = 3/7
Thus, The necessary, team 3, tower garden gift illustrates the proportional relationship between weeks and donation.
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The circumference of a circle is double the perimeter of square having area 484cm^2.what is the area of circle?
Answer:
The circumference of a corcle is double the perimeter of square having area 484 m^2. what is the area of the circle. Ans:2464 cm^2.
Answer:
Hence the area of a circle is 2466[tex]m^{2}[/tex]
Step-by-step explanation:
Review of the question
[tex]Given,[/tex]
The circumference of a circle is double the perimeter of squareArea of the square is 484[tex]cm^{2}[/tex]To Find:Area of the circle
,
Area of square =[tex]sideXside[/tex]
[tex]484[/tex]=[tex]side^{2}[/tex]
[tex]\sqrt{484}=side^{2}[/tex]
[tex]22 = side[/tex]
Perimeter of square = [tex]4Xside[/tex]
[tex]4X22[/tex]
[tex]88[/tex]
Circumference of the circle = Perimeter of square x 2
Circumference of the circle = 88x2
Circumference of the circle = 176
Now we need to find the radius of the circle
[tex]2\pi r=176[/tex]
[tex]2X3.14Xr=176\\6.28Xr=176\\r=\frac{176}{6.28} \\r=28.025477707[/tex]
Area of the circle=[tex]\pi r^{2}[/tex]
[tex]3.14X[/tex][tex](28.025477707)^{2}[/tex]
[tex]2466[/tex]
Hence the area of a circle is 2466[tex]m^{2}[/tex]
Can someone help me with this? I’m confused
Answer:
Option 4
Step-by-step explanation:
The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).
hope this helps :)
Given f(x) = 2x − 3 and g(x) = f(2x), which table represents g(x)?
Answer:
g(x) = 4x - 3
Step-by-step explanation:
f(x) = 2x − 3
g(x) = f(2x)
g(x) = 2(2x) - 3 ==> plugin 2x for x in f(x) in order to get f(2x)
g(x) = 4x - 3
Test the claim about the difference between two population means
μ1
and
μ2
at the level of significance
α.
Assume the samples are random and independent, and the populations are normally distributed.Claim:
μ1=μ2;
α=0.01
Population statistics:
σ1=3.6,
σ2=1.4
Sample statistics:
x1=18,
n1=27,
x2=20,
n2=26
Determine the alternative hypothesis.
Ha:
μ1
▼
greater than>
greater than or equals≥
less than<
less than or equals≤
not equals≠
μ2
Determine the standardized test statistic.
z=nothing
(Round to two decimal places as needed.)
Determine the P-value.
P-value=nothing
(Round to three decimal places as needed.)
What is the proper decision?
A.Fail to reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
B.Reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
C.Fail to reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim.
D.Reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim
The correct answer is Option C. The proper decision, in this case, is "Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim."
The alternative hypothesis, in this case, is "μ1 ≠ μ2", as the claim being tested is that the two population means are equal.
To calculate the standardized test statistic, we can use the following formula:
z = (x1 - x2) / sqrt(((σ1^2) / n1) + ((σ2^2) / n2))Substituting in the values given in the problem, we get:
z = (18 - 20) / sqrt(((3.6^2) / 27) + ((1.4^2) / 26))
z = (-2) / sqrt((12.96 / 27) + (1.96 / 26))
z = (-2) / sqrt(0.481 + 0.075)
z = (-2) / sqrt(0.556)
z = (-2) / 0.746
z = -2.67
To calculate the P-value, we can use the standard normal table to look up the probability of getting a value of -2.67 or lower if the null hypothesis were true. The P-value in this case would be the probability of getting a value equal to -2.67 or lower, plus the probability of getting a value equal to 2.67 or higher.
Using the standard normal table, we find that the probability of getting a value equal to -2.67 or lower is 0.0039, and the probability of getting a value equal to 2.67 or higher is 0.9961. Therefore, the P-value is 0.0039 + 0.9961 = 1.0000.
Since the P-value is equal to 1.0000, which is greater than the level of significance α = 0.01, we fail to reject the null hypothesis.
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NO LINKS!! Find the specified term of the geometric sequence.
a6: a1 = 3, a2= 18, a3= 108, . . .
a6=
Answer:
23328
Step-by-step explanation:
since it is a geometrics sequence we will use the formula
[tex] {ar}^{n - 1} [/tex]
The first term(a) = 3
The second term = ar = 18
divide the first term and second term to find the common ratio
[tex] \frac{t2}{t1} = \frac{ar}{a} = \frac{18}{3} [/tex]
r = 6
Now lets find the sixth term
[tex]t6 = {ar}^{6 - 1} [/tex]
[tex]t6 = {ar}^{5} [/tex]
by substituting for the values
[tex]t6 = 3 \times {6}^{5} [/tex]
= 3 × 7776
= 23328
i hope this helped
Answer:
[tex]a_{6} = 23,328[/tex]
Step-by-step explanation:
⭐ Geometric Progression formula: [tex]a_{n} = a_1(b)^{n-1}[/tex]
[tex]a_{1}[/tex] is the first term of the geometric progression[tex]b[/tex] is the common ratio (the number each term gets multiplied by)[tex]a_{n}[/tex] is the notation for which term you are finding, where n is the term numberWe are given that [tex]a_{1}[/tex] = 3. Now, we need to find b.
b is the quotient of [tex]\frac{a__3}{a__2}[/tex].
[tex]\frac{a_3}{a_2}\\ \\\frac{108}{18}\\= 6[/tex][tex]b[/tex] = 6Let's substitute the first term and common ratio into the formula.
[tex]a_n = 3(6)^{n-1}[/tex]
The problem wants us to solve for the 6th term, so we have to substitute 6 for n and solve.
[tex]a_6 = 3(6)^{6-1}\\a_6 = 3(6)^5\\a_6 = 3(7,776)\\a_6 = 23,328[/tex]
Using three mixed numbers as side lengths draw an equilateral triangle with a perimeter of 8 and 1/4 feet.
The side of the equilateral triangle is 2 ³/4 feet, having perimeter 8 ¹/₄ feet.
What is an equilateral triangle?If all three of a triangle's sides are the same length, the triangle is said to be equilateral. Congruent sides refer to sides that have the same length, and they characterize an equilateral triangle.
Given that,
The perimeter of equilateral triangle = 8 ¹/₄ feet.
Simplify the rational term.
8 ¹/₄ = (32 + 1) / 4 = 33 /4.
Let each side of an equilateral triangle is a feet.
The perimeter of the equilateral triangle = 3a
Since, 3a = 33/4
a = 11/4
a = 2 ³/4
The required side of the equilateral triangle is 2 ³/4.
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A tent pole that is 8 feet tall is secured to the ground with a piece of rope that is 17 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
40 feet
30 feet
15 feet
9 feet
The distance between the tent pole to the rope along the ground is 15 feet.
What is a cone?
A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
Given that length of the tent pole is 8 feet.
The angle between the tent pole and the ground is 90°.
Thus the tent pole, the rope and the ground form a right angle triangle.
According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.
Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.
Assume that the distance the tent pole to the rope along the ground be x.
The length of the rope is 17 feet which is hypotenuse of the right angle triangle.
Therefore,
x² + 8² = 17²
x² + 64 = 289
x² = 225
x = 15
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Answer: 15 feet
Step-by-step explanation:
first we grab 17 feet a square it
17^2 = 289
then we square 8 feet
8^2 = 64
subtract
289-64= 225
what squared equals 225?
15 does
Two angles are complementary. The measure of one angle is 17 degrees. What is the measure of the other angle?
The measure of the other angle is 73°.
What are complementary angles?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
How do you find a complementary angle?
Two angles are said to be complimentary if their sum is 90 degrees. So, to find the complement of an angle, subtract it from 90.
Here, we have
Given
Two angles are complementary. If one measures 17 degrees.
Complementary angles are two angles that add up to exactly 90 °.
∠A + ∠B = 90°
17 + ∠B = 90°
∠B = 90 - 17
∠B = 73°
Hence, the measure of the other angle is 73°.
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