Answer:
2x + [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
The like terms that you want to combine is 1/3 and 1/2. You need a common denominator which would be 6
[tex]\frac{1}{3}[/tex] = [tex]\frac{2}{6}[/tex]
[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{6}[/tex]
2x + [tex]\frac{2}{6}[/tex] + [tex]\frac{3}{6}[/tex]
2x + [tex]\frac{5}{6}[/tex] You cannot combine this with the 2 because the 2 is multiplied by x.
Helping in the name of Jesus.
how do i do this. please help thank you
Answer:
[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]
pls solve asap ..... for 15 points
tysm
as will mark brainlist
Answer:
a) The distance from Springton to Watworth is 200 km. Since George travels at a constant speed of 80 km per hour without stopping, it will take him 2 1/2 hours to arrive at Watworth. Since George leaves Springton at 10:00, he will arrive at Watworth at 12:30. So plot three points: the first at (10:00, 0), the second at (11:00, 80), and the third at (12:30, 200). Draw a line connecting the three points.
b) Karen arrived at Watworth at 13:50. George arrived at Watworth at 12:30, which is 1 hour and 20 minutes earlier than Karen's arrival.
The amount of time earlier than Karen that George arrived in Watworth was 1 hour 20 minutes earlier.
How to find the time taken ?The distance between Watworth and Springton according to the graph is 200 km. This means that George covered this distance in:
= 200 / 80
= 2.5 hours
He arrived at :
= 10 + 2.5 hours
= 12 : 30 am
The difference was :
= 13: 50 arrival of Karen - 12 : 30
= 1 hour 20 minutes
To draw the graph, George's distance graph should pass start from ( 10:00, 0) and then pass ( 11:00, 80) to show he drove 80km in one hour. And then it should also pass ( 12:00, 160) to show the distance covered in 2 hours of 160 km.
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You may need to use the appropriate technology to answer this question.
The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contains a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.
Company A
34 59 43 30 3
32 42 85 30 48
110 50 10 26 70
52 83 78 27 70
27 90 38 52 76
Company B
45 63 42 32 67
104 45 27 38 84
75 46 32 50 64
41 36 33 65 64
(a)
Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let 1 = population mean minutes late for delayed Company A flights and 2 = population mean minutes late for delayed Company B flights.)
H0: 1 − 2 < 0
Ha: 1 − 2 = 0
H0: 1 − 2 ≤ 0
Ha: 1 − 2 > 0
H0: 1 − 2 ≥ 0
Ha: 1 − 2 < 0
H0: 1 − 2 ≠ 0
Ha: 1 − 2 = 0
H0: 1 − 2 = 0
Ha: 1 − 2 ≠ 0
(b)
What is the sample mean number of minutes late for delayed flights for each of these two airlines?
Company A
min
Company B
min
(c)
Calculate the test statistic. (Round your answer to three decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
Using a 0.05 level of significance, what is your conclusion?
Do not Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.
Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
Reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0
(b) Means: Company A___50.6___ min.; Company B___52.75___ min.
c)The t-value is -0.30107., The p-value is 0 .764815.
What is a Hypothesis?A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon
A)H0: μ1 − μ2 = 0
i.e there is no difference between the means of delayed flight for two different airlines
Ha: μ1 − μ2 ≠ 0
i.e there is a difference between the means of delayed flight for two different airlines
(b)
Company A___50.6___ min.
Company B___52.75___ min.
Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25
= 1265/25= 50.6
Mean of Company B = x`2= ∑x/n =
=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20
= 1055/20= 52.75
Difference Scores Calculations
Company A
Sample size for Company A= n1= 25
Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24
Mean for Company A= x`1= 50.6
Total Squared Difference (x-x`1) for Company A= SS1: 16938
s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75
Company B
Sample size for Company B= n1= 20
Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19
Mean for Company B= x`2= 52.75
Total Squared Difference (x-x`2) for Company B= SS2=7427.75
s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93
T-value Calculation
Pooled Variance= Sp²
Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)
Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65
s2x`1 = s2p/n1 = 566.65/25 = 22.67
s2x`2 = s2p/n2 = 566.65/20 = 28.33
t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3
The t-value is -0.30107.
The total degrees of freedom is = n1+n2- 2= 25+20-2=43
The critical region for two tailed test at significance level ∝ =0.05 is
t(0.025) (43) = t > ±2.017
Since the calculated value of t= -0.30107. does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.
The p-value is 0 .764815. The result is not significant at p < 0.05.
C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.
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can someone please help me+explain how to do this step by step, im so confused
Your gross income is $4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in a regular savings account at a 3.8% APR. What is the total amount of your emergency fund? How much is in the CD and savings account? How much is the total interest earned between both accounts in 60 days?
1. The total amount of your emergency fund will be $11,403.75.
2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.
What is the total amount of your emergency fund?Your FICA deduction is 7.65% of your gross income:
7.65% of $4,520.00 = $345.98
Your federal tax withholding is 11.75% of your gross income:
11.75% of $4,520.00 = $531.40
Your state tax withholding is 8.5% of your gross income:
8.5% of $4,520.00 = $384.40
Your total deductions are:
= $345.98 + $531.40 + $384.40
= $1,261.78
Your monthly income after deductions is:
= $4,520.00 - $1,261.78
= $3,258.22
Your fixed expenses are 30% of your realized income:
= 30% of $3,258.22
= $977.47
Your monthly savings amount is:
= $3,258.22 - $977.47
= $2,280.75
You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:
= 5 x $2,280.75
= $11,403.75
Regenerate response
How much is in the CD and savings account?You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:
= 75% of $11,403.75 = $8,552.81
You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:
= 25% of $11,403.75
= $2,850.94.
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I need help with this problem it's is
8x+5+3x+8=90
Answer:
x = 7
Step-by-step explanation:
8x + 5 + 3x + 8 = 90
11x + 5 + 8 = 90
11x + 13 = 90
11x = 77
x = 7
Let's Check
8(7) + 5 + 3(7) + 8 = 90
56 + 5 + 21 + 8 = 90
61 + 21 + 8 = 90
82 + 8 = 90
90 = 90
So, x = 7 is the correct answer!
Answer:
7
Step-by-step explanation:
First, collect common factors. This means put the x's together and the regular numbers together.
8x+3x=11x
5+8=13
11x+13=90
Subtract 13 from both sides
11x+13=90
-13 -13
11x=77
Divide 77 by 11
x=7
Hope this helps! :)
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The shaded area covers around 0.8664 square feet of space.
What is the typical normal distribution where the standard deviation is 0 and the mean 1?The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.
Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.
Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:
0.9332 - 0.0668 = 0.8664
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A pipe is made of 1cm thick, has a radius of 11cm. Find the volume of the metal used in making 2.4cm of pipe
Question 6(Multiple Choice Worth 5 points) (Statistical Measurements LC) Which of the following is a statistical question that can result in numerical data? What is the name of your favorite pizza store? How many hours this week did you spend on homework? O How many times did you go swimming this year? How many pink erasers do the students in your class have?
The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
Identifying the statistical question that can result in numerical data?The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"
This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.
"What is the name of your favorite pizza store?" is a question that asks for a categorical response, "How many times did you go swimming this year?" is a question that asks for a countable response, And "How many pink erasers do the students in your class have?" is a question that asks for a discrete numerical response.Read more about statistical question at
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The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $75,000 10-year term policy for a 25-year-old male. Round your answer to the nearest cent. A 5-column table with 6 rows titled Term Insurance. Column 1 is labeled Age with entries 20, 21, 22, 23, 24, 25. Column 2 is labeled 5-year term male with entries 2 dollars and 43 cents, 2.49, 2.55, 2.62, 2.69, 2.77. Column 3 is labeled 5-year term female with entries 2.07, 2.15, 2.22, 2.30, 2.37, 2.45. Column 4 is labeled 10-year term male with entries 4.49, 4.57, 4.64, 4.70, 4.79, 4.85. Column 5 is labeled 10-year term female with entries 4.20, 4.36, 4.42, 4.47, 4.51. a. $363.75 c. $183.75 b. $207.75 d. $338.25
The answer is $359.25, which is closest to option A: $363.75.
What is multiplication?Calculating the sum of two or more numbers is the procedure of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.
The premium for a $75,000 10-year term policy for a 25-year-old male will be $75 times the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. From the table, the premium per $1,000 face value for a 10-year term policy for a 25-year-old male is $4.79. Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male will be:
$75 × $4.79 = $359.25
Rounding to the nearest cent, the answer is $359.25, which is closest to option A: $363.75. Therefore, the answer is (a) $363.75.
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find g(x+4): g(x)=-5+2x/1+x
2x + 3/x + 5 is the value of expression .
What is an expression in mathematics?
A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:
The expression is (number/variable, arithmetic operator, number/variable). For example, x + y is an expression whose term has an addition operator between x and y. There are two kinds of formulas in mathematics. Numeric expression - contains only numeric values. An algebraic expression containing both numbers and variables.
g(x) = -5+2x/1+x
g(x+4) = -5+2(x + 4)/1+(x + 4 )
= -5 + 2X + 8/1 + X + 4
= 2x + 3/x + 5
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In the year 2000, the population of Mexico was about 100 million, and it was growing by 1.53% per year. At this growth rate, the function f(x) = 100(1.0153)x gives the population, in millions, x years after 2000. Using this model, in what year would the population reach 106 million? Round your answer to the nearest year.
Answer:
2004
Step-by-step explanation:
if g(x)= 3x²+7x-1, then f'(x)=?
Answer:
Step-by-step explanation:
Answer: The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.
To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).
Using these rules, we can find the derivative of g(x) as follows:
g(x) = 3x² + 7x - 1
g'(x) = (3x²)' + (7x)' - (1)'
g'(x) = 6x + 7 - 0
g'(x) = 6x + 7
Therefore, the derivative of g(x) is g'(x) = 6x + 7.
Step-by-step explanation:
An African mousebird is 2 feet tall. A camel is 4 times as tall as the mousebird. How tall is the camel in inches?
The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 84 square inches. Solve for the dimensions (length and width) of the poster.
Step-by-step explanation:
w = width
2w + 2 = Length
Area = W x L = 84 = w (2w+2)
84 = 2w^2 + 2w
0 = 2w^2 + 2w - 84 Use Quadratic Formula
a = 2 b=2 c = -84
to find
W = 6 then L = 14 inches
The sum of a number and 2 is 6 less than twice that number.
Answer:
8
Step-by-step explanation:
Let's use algebra to solve the problem.
Let x be the number we're looking for.
The problem states that "the sum of a number and 2 is 6 less than twice that number", which can be written as:
x + 2 = 2x - 6
To solve for x, we need to isolate it on one side of the equation. We can start by subtracting x from both sides:
x + 2 - x = 2x - 6 - x
Simplifying:
2 = x - 6
Now we can isolate x by adding 6 to both sides:
2 + 6 = x - 6 + 6
Simplifying:
8 = x
Therefore, the number we're looking for is 8.
Answer:
8
Step-by-step explanation:
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment. A 5-column table with 2 rows. Column 1 is labeled Bond with entries A B C 7 and one-half 15, X Y Z 7 and three-fourths 15. Column 2 is labeled current yield with entries 7.5, 8.4. Column 3 is labeled volume with entries 128, 17. Column 4 is labeled Close with entries 104 and three-fourths, 100 and one-half. Column 5 is labeled Net change with entries blank, + one-fourth. If you buy three of the ABC bonds with $10 commission for each, how much will it cost? a. $3142.50 b. $1047.50 c. $3172.50 d. $1077.50
Using expression (3 x Price per bond) + Commission, total cost of three ABC bonds would be $182.70.
What exactly are expressions?
In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated or simplified to produce a value. Expressions can be as simple as a single number or variable, or they can be complex, involving multiple operations and functions.
Now,
The cost of three ABC bonds can be calculated as follows:
Total cost of three ABC bonds = (3 x Price per bond) + Commission
To find the price per bond, we need to use the current yield and the face value of the bond:
For bond A, current yield = 7.5, face value = 100, so price per bond = 100 x (7.5/100) = 7.50
For bond B, current yield = 8.4, face value = 100, so price per bond = 100 x (8.4/100) = 8.40
For bond C, current yield = 7.75, face value = 100, so price per bond = 100 x (7.75/100) = 7.75
So the total cost of three ABC bonds would be:
(3 x 7.50) + (3 x 8.40) + (3 x 7.75) + (3 x 10) = $104.25 + $25.20 + $23.25 + $30 = $182.70
Therefore, the correct answer is not listed.
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Determine the amount of taxes owed on a taxable income of $51, 100.
A) $5,310.00
B) $6,919.00
C) $11,682.00
D) $12,744.40
The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.
What is the taxable amount?To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.
For the tax year 2021, the federal income tax brackets and rates for single filers are:
10% on taxable income from $0 to $9,950
12% on taxable income from $9,951 to $40,525
22% on taxable income from $40,526 to $86,375
24% on taxable income from $86,376 to $164,925
32% on taxable income from $164,926 to $209,425
35% on taxable income from $209,426 to $523,600
37% on taxable income over $523,600
To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.
Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.
Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.
Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.
Adding these three amounts together, we get the total tax owed:
$995 + $3,384.48 + $2,312.72 = $6,692.20
Therefore, the closest answer choice is B) $6,919.00.
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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).
What is an income?An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.
Define tax?Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.
=$51100* 22/100
=$11242
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Suppose fhat F(x) = x^2 and G(x) = -1/4 (x+7)^2 . Which statement best compares the graph of G(x) with the graph if F(x)?
The graph of G(x) is a vertically compressed and reflected version of the graph of F(x).
What is a graph?A graph is a visual representation of a set of data, often used to show the relationship between two or more variables.
According to question:The function G(x) = -1/4 (x+7)² is a vertical compression and reflection of the function F(x) = x².
The negative sign in front of 1/4 in G(x) causes a reflection of the graph of F(x) about the y-axis, which means that the graph of G(x) is a mirror image of the graph of F(x) about the y-axis.
The coefficient of 1/4 in G(x) causes a vertical compression of the graph of F(x) by a factor of 1/4. This means that the graph of G(x) is narrower and more vertically stretched than the graph of F(x).
Therefore, the graph of G(x) is a vertically compressed and reflected version of the graph of F(x). In other words, G(x) is a transformation of F(x).
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If P(x,y) is the point on the unit circle defined by real number 8, then cscg =
OA.
OB.
y
B. 1
O C.
-|X
y
OD. V
X
The value of Cscθ is 1/y.
What is a trigonometric function?
The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here, we have
Given: if p(x,y) is the point on the unit circle defined by the real number theta.
We have to find the value of the csc theta.
P(x,y) is the point on the unit circle (the unit circle has a radius of 1 and center (0,0))
Now in a diagram, we can see that
OA= x
AP= y
radius OP =1
∠POA =θ
Now in ΔAOP
Cscθ = hypotenuse/opposite side
Cscθ = OP/AP
Cscθ = 1/y
Hence, the value of Cscθ is 1/y.
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I need help with this
Answer:
1500
Step-by-step explanation:
Number of boxes = 12
Number of pencils in each box = 125
Total number of pencils
= 12 × 125
= 1500 pencils
How can I solve this math problem within 5 minutes
The equation a² + b² = c² represents the Pythagorean theorem.
What is the Pythagorean theorem?This is a theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.
To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:
If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):
Plug in the known values for a and b into the equation and solve for c.
Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.
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Problem 3: Find the diameter of a semicircle with an area of 76.97 square yards.
The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.
What is the diameter of a semicircle with an area of 76.97Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²
Where r radius and π is constant pi.
Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:
76.97 = 1/2 × (πr²)
Multiplying both sides by 2, we get:
153.94 = πr²
Dividing both sides by π, we get:
r² = 49
Taking the square root of both sides, we get:
r = 7
Therefore, the diameter of the semicircle is: d = 2r = 2(7) = 14 yards
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In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
A) 20%
B) 24%
C) 25%
D) 28%
thought i would leave this but ⇒ty to whoever answers this, have an amazing day <3
The percentage of females with brown eyes as follows is 25%.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".
According to question:Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:
Population Males Females
Total 60 40
Brown eyes 18 ?
From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.
We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.
Finally, we can calculate the percentage of females with brown eyes as follows:
% of females with brown eyes = (10 / 40) x 100% = 25%
Therefore, the answer is (C) 25%.
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Evelyn sells 4 bags of popcorn. Her teammate Sidney sells 5 bags of popcorn. How much money do they raise in all?
A farmer counted the number of apples on each tree in his orchard. How many trees have at least 21 apples but fewer than 80 apples?
Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.
Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:
n1 - n2
To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.
Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:
- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.
- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.
- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.
Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:
The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.
The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.
Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:
n1 - n2 = 0.16T - 0.025T = 0.135T
Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.
Step-by-step explanation:
A new theater is being built for the city ballet. The balcony has 90 seats. The
floor has 15 rows with x seats in each row. The number of people in the
theater must be under 240 to meet fire safety regulations.
What is the solution of this inequality, and what is its meaning?
The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.
What is inequality?
In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.
To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.
Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)
Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240
Now we can solve for x by first subtracting 90 from both sides of the inequality,
15 × x ≤ 150
Next, we can divide both sides of the inequality by 15,
x ≤ 10
Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.
To check this solution, we can plug x = 10 into our expression for the total number of seats,
Total number of seats = 90 + (15 × 10) = 240
This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.
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The length of a side of an equilateral triangle is 14 centimeters.
What is the length of the altitude of the triangle?
2√ 7cm
3√ 7 cm
7√ 2 cm
7√ 3 cm
Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]
Step-by-step explanation:
Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.
Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:
[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]
Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]
solve the equation x^2+4x-11=0 by completing the square
To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:
Move the constant term to the right side of the equation:
x^2 + 4x = 11
Complete the square by adding the square of half the coefficient of x to both sides of the equation:
x^2 + 4x + (4/2)^2 = 11 + (4/2)^2
Simplifying the left side:
x^2 + 4x + 4 = 11 + 4
Factor the perfect square on the left side of the equation:
(x + 2)^2 = 15
Take the square root of both sides of the equation:
x + 2 = ±√15
Solve for x by subtracting 2 from both sides:
x = -2 ± √15
Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.
1) What is the equation of the trend line in the scatter plot?
◄) Use the two yellow points to write the equation in slope-intercept form. Write any
coefficients as integers, proper fractions, or improper fractions in simplest form.
8 9 10
X
An equation of the trend line in the scatter plot is equal to y = -4x/9 + 9.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 9)/(9 - 0)
Slope (m) = -4/9
At data point (0, 9) and a slope of -4/9, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 9 = -4/9(x - 0)
y - 9 = -4x/9
y = -4x/9 + 9
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PLEASE HELP QUICK IM CONFUSEDDD
Answer:
x = 2.16228, -4.16228
Step-by-step explanation:
(2x² - 2x) - 5 = (x - 2)²
2x² - 2x - 5 = x² - 4x + 4
x² + 2x - 9 = 0
Use quadradic equation to find the roots of x: a=1 , b=2, c=-9
x = 1 ± √10
x = 2.16228, -4.16228