Answer:
1/30
Step-by-step explanation:
When you multiply fractions, you just muliply across,
1*3= 3
9*10= 90
you now have 3/90 but you have to simplify, we know 3 goes into 3 and it also goes into 90 equally
3/3= 1
90/3= 30
So your answer is 1/30!!
I hope this helps!!!!!!!!!!!
I need help please with this question
The approximation of [tex]\sqrt{44}[/tex], to the hundredths place, is given as follows:
[tex]\sqrt{44} = 6.63[/tex]
How to estimate a non-exact square root?The estimate of a non-exact square root of x is done finding two numbers, as follows:
The greatest number less than x that is a perfect square, which we call a.The smallest number greater than x that is a perfect square, which we call b.For this problem, we want to estimate the root to the hundredth's place, hence the number that we must compare is:
44 x 10^4 = 440000.
(as each 10² is equivalent to the square root of a decimal digit).
Then the numbers are:
663² = 439569 < 440000.664² = 440896 > 440000.Hence the square root is approximated as follows:
663/100 = 6.63.
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NO LINKS!!!! URGENT HELP PLEASE!!!!!
Find the area of ΔABC
5. B= 141°, a = 7, c = 8
6. C=70°, a=30, b= 24
7. A = 100°, b = 20, c = 25
Answer:
5) 17.62 units² (2 d.p.)
6) 338.29 units² (2 d.p.)
7) 246.20 units² (2 d.p.)
Step-by-step explanation:
To find the area of a triangle given two sides and the included angle, use the Sine Rule (Area of a Triangle) formula:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Rule (Area of a triangle)}\\\\$A=\dfrac{1}{2}ab \sin C$\\\\\\where: \\ \phantom{ww}$\bullet$ $a$ and $b$ are adjacent sides. \\ \phantom{ww}$\bullet$ $C$ is the includ\:\!ed angle.\\\end{minipage}}[/tex]
[tex]\hrulefill[/tex]
Question 5Given values:
a = 7c = 8B = 141°The two sides of the triangle are 'a' and 'c', and the included angle is 'B'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ac \sin B\\\\&=\dfrac{1}{2} \cdot 7 \cdot 8 \cdot \sin 141^{\circ}\\\\&= 28 \sin 141^{\circ}\\\\& = 17.6209709...\\\\&= 17.62\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 6Given values:
a = 30b = 24C = 70°The two sides of the triangle are 'a' and 'b', and the included angle is 'C'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ab \sin C\\\\&=\dfrac{1}{2} \cdot 30\cdot 24 \cdot \sin 70^{\circ}\\\\&= 360\sin 70^{\circ}\\\\&= 338.289343...\\\\& = 338.29\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 7Given values:
b = 20c = 25A = 100°The two sides of the triangle are 'b' and 'c', and the included angle is 'A'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} bc \sin A\\\\&=\dfrac{1}{2} \cdot 20 \cdot 25 \cdot \sin 100^{\circ}\\\\&= 250 \sin 100^{\circ}\\\\&= 246.201938...\\\\& = 246.20\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
Exam the following data set.
{8,19,11,20,2,14,17,9,15}
Which answer shows the five number summary that could be used to create a box plot for this data?
The five number summary of the data set for the box plot would be :
Minimum value: 2Q1 : 9Median : 14Q3 : 19Maximum value: 20How to find the five number summary ?First, order the numbers in ascending order:
2, 8, 9, 11, 14, 15, 17, 19, 20
The minimum is the smallest number which is 2. The maximum is the largest number which is 20.
The median is the number in the middle which is 19. The Q1 is the number in the middle of the first half of the numbers which is 9. The Q3 is the number in the middle of the second half which is 19.
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Answer:
min=2
1st quartile= 8.5
median=14
3rd quartile=18
max=20
Step-by-step explanation:
PLEASE HELP!!!!!!
it’s a division equation
Answer:
x+1
Step-by-step explanation:
you have to rewrite the equestion, factor the expression, and than reduce it
Dana had to pay her friend $900, 3 months ago and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month, what single payment would settle both payments today?
Dana had to pay her friend $900, 3 months ago, and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month. $1499.45, single payment would settle both payments today.
Given:
The principal of a loan is the original sum borrowed.The interest rate per period is known as rate.The loan's duration is expressed in terms of time.Simple interest = Principal × Rate × Time
Simple interest = $900 × 0.015 × 3
Simple interest = $40.50
Present Value = Future Value / (1 + Rate x Time)
Present Value = $580 / (1 + 0.015 × 3)
Present Value = $580 / 1.045
Present Value = $558.95
Total amount $580 loan is $558.95.
Total amount owed = $940.50 + $558.95
Total amount owed = $1499.45
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A sales person starts working 40 hours per week at a job with 2 options for being paid . Option A is an hourly wage of $19. Option B is a commission rate of 8% on weekly sales.
How much does the sales person need to sell in a given week to earn the same amount with each option?
A. $9,500
B. $4,750
C. $760
D. $320
Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week [tex]\sf = 19 \times 40 = \$760[/tex]
Now, according to option b, he will get 8% commission on weekly sales.
Let. x = the amount of weekly sales.
To earn the same amount of option A, he will have to equal the 8% of x to $760
So, [tex]\sf \dfrac{8x}{100}=760[/tex]
Or, [tex]\sf 8x= 76000[/tex]
Or, [tex]\sf x= \dfrac{76000}{8}=9500[/tex]
the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.
An urn contains 11 red balls numbered 1 through 11, 11 yellow balls numbered 1 through 11, 11 green balls numbered 1 through 11, and 11 black balls numbered 1 through 11. If 4 balls are randomly selected, find the probability of getting
(a) a flush (i.e., all balls the same color).
(b) three of a kind. (Three of a kind is 3 balls of one denomination and a fourth ball of a different denomination. e.g., 5,5,5,2)
(c) two pairs. (A pair is two balls of the same denomination. e.g., 3,3. Two pairs is something like 3,3,5,5, i.e., a pair of one denomination and a second pair of a different denomination.)
please write the steps as well!! thank you so much
(a) Probability of getting a flush is 0.000546.
(b) Probability of getting three of a kind is 0.00451.
(c) Probability of getting two pairs is 0.0150.
We have,
(a)
To calculate the probability of getting a flush, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of balls = 11 (red) + 11 (yellow) + 11 (green) + 11 (black) = 44 balls
The number of ways to choose 4 balls (without replacement)
= 44C4 = 44! / (4! x (44 - 4)!) = 44! / (4! x 40!)
= 44 x 43 x 42 x 41 / (4 x 3 x 2 x 1)
= 7315
The number of favorable outcomes:
There are 4 different colors of balls, so we have 4 possible flushes (all red, all yellow, all green, all black).
Probability of getting a flush = Number of favorable outcomes / Total number of outcomes = 4 / 7315 ≈ 0.000546
(b)
To calculate the probability of getting three of a kind, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).
Number of ways to choose 3 balls of the same denomination: We have 11 denominations, so we can choose 3 balls of the same denomination in 11C1 = 11 ways.
Number of ways to choose the fourth ball of a different denomination: After choosing 3 balls of the same denomination, we have 3 denominations left from which we can choose the fourth ball. So, the number of ways to choose the fourth ball = 3.
Number of favorable outcomes = Number of ways to choose 3 balls of the same denomination x Number of ways to choose the fourth ball of a different denomination
= 11 x 3
= 33
Probability of getting three of a kind = Number of favorable outcomes / Total number of outcomes = 33 / 7315 ≈ 0.00451
(c)
To calculate the probability of getting two pairs, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).
Number of ways to choose the first pair: We have 11 denominations, so we can choose the first pair in 11C1 = 11 ways.
Number of ways to choose the second pair: After choosing the first pair, we have 10 denominations left from which we can choose the second pair. So, the number of ways to choose the second pair = 10.
Number of favorable outcomes
= Number of ways to choose the first pair x Number of ways to choose the second pair
= 11 x 10
= 110
Probability of getting two pairs = Number of favorable outcomes / Total number of outcomes = 110 / 7315 ≈ 0.0150
Thus,
(a) Probability of getting a flush = 4/7315 ≈ 0.000546
(b) Probability of getting three of a kind = 33/7315 ≈ 0.00451
(c) Probability of getting two pairs = 110/7315 ≈ 0.0150
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Suppose a website has about 1,500,000 users. When each member signs up,
he or she is assigned an account number.
A sample of users is to be chosen to take a survey. Using systematic
sampling of account numbers, which of these will result in the smallest
sample size?
OA. Choosing every 1500th account number
OB. Choosing every 15th account number
OC. Choosing every 150th account number
D. Choosing every 15,000th account number
Select the correct answer from each drop-down menu. A graph of quadrilateral 1 with the nodes of (minus 3, 7), (minus 4, 9), (minus 7, 9), and (minus 4, 5). Transformation of quadrilateral 2 with the nodes of (3, minus 4), (3, 6), (8, 2.8), and (7.2, minus 1.9). Quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations. The transformation that maps quadrilateral 1 onto quadrilateral 2 is a followed by a dilation with a scale factor of .
This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.
The coordinates are given as:
First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).
Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)
Calculate the distance AB and A'B' using:
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ AB = √ (-4 + 3)² + (9 - 7)²
⇒ AB = √1 + 4
⇒ AB = √5
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ A'B' = √ (3 - 3)² + (6 + 4)²
⇒ A'B' = 10
This gives, Divide A'B' by AB to determine the scale factor (k)
k = 10 / √5
k = 2√5
Hence, this transformation is a by a factor of 2√5
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Answer:
Reflection and 2
Step-by-step explanation:
for plato
What is the X intercepts of f(x) =-2x^2 + 10x - 7
Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.
a) The given symbolic logic statement can be translated into English as follows:
"Not exists x such that (P(x) and Q(x)), and for all y, if R(y) then P(y)."
b) Potential ambiguities in the translated statement:
The scope of the negation symbol "¬" is not explicitly defined. It can be interpreted as applying only to the first part of the statement or to the entire statement.
The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which parts of the statement they apply to.
c) To eliminate ambiguities while maintaining the original meaning, the statement can be rewritten as follows:
"(∀x)(¬(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y))"
How to explain the informationIn the revised statement: The negation symbol "¬" applies to the entire first part of the statement, indicating that there does not exist any x for which both P(x) and Q(x) are true.
The quantifiers (∀x) and (∀y) explicitly indicate that the following predicates apply universally to all values of x and y.
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a) The monthly basic salary of the married Chief of Army Staffs (COAS) General is Rs 79,200 with Rs 2,000 dearness allowance. He gets Dashain allowance which is equivalent to his basic salary of one month. He contributes 10% of his basic salary in Employee's Provident Fund (EPF) and he pays Rs 50,000 as the premium of his life insurance. Given that 1% social security tax is levied upon the income of Rs 6,00,000, 10% and 20% taxes are levied on the next incomes of Rs 2,00,000 and up to Rs 3,00,000 respectively. Answer the following questions. What is his monthly basic salary? (ii) Find his taxable income. (iii) Find the total income tax paid by him.
i) The monthly basic salary of the married COAS General is Rs 79,200.
ii. Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480
iii. The total income tax paid by him is Rs 24.8.
How to calculate the valueHis taxable income can be calculated as follows:
Total Monthly Income = Rs 79,200 + Rs 2,000 + Rs 79,200 = Rs 1,60,400
EPF Contribution = 10% of Basic Salary = 10% of Rs 79,200 = Rs 7,920
Life Insurance Premium = Rs 50,000
Total Deductions = EPF Contribution + Life Insurance Premium = Rs 7,920 + Rs 50,000 = Rs 57,920
Taxable Income = Total Monthly Income - Total Deductions
Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480
For income up to Rs 6,00,000: No income tax
For income between Rs 6,00,001 and Rs 8,00,000: 1% of the amount exceeding Rs 6,00,000
Taxable Income in this slab = Rs 2,480 (Rs 1,02,480 - Rs 6,00,000)
Income tax for this slab = 1% of Rs 2,480 = Rs 24.8
Therefore, the total income tax paid by him is Rs 24.8.
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10A34594-4103-466C-A0CC-22EBA
9EB47A6.jpeg
The total surface area of the cylinder is 414.7 cm².
What is the curved surface area of the cylinder?The curved surface area of the cylinder is calculated as follows;
C.S.A = 2πrh
where;
r is the radius of the cylinderh is the height of the cylinderThe curved surface area of the cylinder is calculated as;
C.S.A = 2π(6 cm) x (5 cm)
C.S.A = 188.5 cm²
The total surface area of the cylinder is calculated as follows;
T.S.A = 2πrh + 2πr²
circular area = 2πr² = 2π x (6cm)² = 226.2 cm²
The total surface area = 188.5 cm² + 226.2 cm² = 414.7 cm²
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Which graph represents the solution to the following problem? y < |x+3|
The graph that shows the solution set of the inequality is the second one.
Which graph represents the solution set of the inequality?Here we have the following inequality:
y < |x + 3|
Notice that we have the symbol "<", then we know that the graph of the absolute value must be with dashed lines (because the points that lie on the graph aren't solutions).
Also, y is smaller than that, then the shaded region must be below the graph.
With that in mind, we conclude that the correct option is the second one.
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Pls help I’m stuck Tysm I really thankful
Answer:
23/41
Step-by-step explanation:
You want to know the fraction who failed, given they predicted they would fail.
StatsThe attached 2-way table shows the given numbers (black) and the numbers that make the totals correct (blue).
It shows 23 of the 41 who thought they would fail actually did. That fraction is ...
23/41 . . . . failed who thought they would
<95141404393>
Based on the picture above, what is the solution to the system of equations?
Type a response
Step-by-step explanation:
The 'solution ' is the point where the two lines intersect : ( 0,-1)
This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =[tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = [tex]$36.34 + $26.03[/tex]
= [tex]$62.37[/tex]
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Hii please answer i would appreciate it thankssss
a) The triangles are congruent by the AAA criterion.
b) The triangles are congruent by the SAS criterion.
a) In the first triangle the interior angles are 40 degrees and 30 degrees.
The other interior angle would be 180 - (40 + 30) = 110 degrees.
As per the diagram, the triangles have equal proportionate-sized side lengths.
Therefore, the triangles are congruent by the AAA criterion.
b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.
Therefore, the triangles are congruent by the SAS criterion.
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HELP PLS !% POINTS!!
Answer:
149 sq. ft
Step-by-step explanation:
For the triangle:
Base = 16-9 = 7 ft
Area of Triangle = 1/2 of b.h
= 1/2 of 7 * 6
= 21 sq. ft
Area of Rectangle = l.b
= 5 * 16
= 128 sq. ft
Total Area = 149 sq. ft
Kenya wants to open a savings account at a bank. The bank offers a savings account that pays
out 8% annual interest. If Kenya wants at least $7,000 in his account after 15 years, how much does
Kenya need to put in the account initially?
Kenya needs to initially put in the amount of $2,208.2in the account to have at least $7,000 after 15 years.
We can use the formula for compound interest:
A = P(1 + r/n)ⁿ
where A is the amount of money in the account after t years, P is the initial principal, r is the annual interest rate (as a decimal), and n is the number of times per year the interest is compounded.
Here, we want to find P, so we can rearrange the formula as:
P = A / (1 + r/n)ⁿ
We are given that r = 0.08 (8% interest) and n = 1 (interest is compounded annually).
We also know that A = $7,000 and t = 15 years.
So we can plug in these values and solve for P:
P = 7000 / (1 + 0.08/1)¹⁵
P = 7000 / (1.08)¹⁵
P ≈ $2,208.2
Therefore, Kenya needs to initially put in approximately $2,208.2in the account to have at least $7,000 after 15 years.
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Which point would be a solution to the system of linear inequalities shown below?
Answer:
(-2, 10)
Step-by-step explanation:
You want the point that would be a solution to the inequalities ...
y ≥ 5/2x +2y ≥ -4x -7GraphIt can be useful to graph the inequalities, or develop a mental picture of what the graph would look like. Both boundary line slopes are fairly steep, and the lines cross in the third quadrant. The V-shaped space above that intersection is the solution space.
The attachment shows the point (-2, 10) is a solution.
Try the answersFrom the shape and location of the solution space, we can eliminate the choices ...
(-8, 2) — too close to the x-axis in the far left part of the 2nd quadrant
(10, -3) — no part of the 4th quadrant is in the solution space
General formIt can work nicely to rewrite the inequalities as a comparison to zero.
5x -2y +4 ≤ 0 . . . . . the first inequality in general form
point (-2, 10): 5(-2) -2(10) +4 = -10 -20 +4 = -26 ≤ 0 . . . a solution
point (4, 9): 5(4) -2(9) +4 = 20 -18 +4 = 6 > 0 . . . . . . . not a solution
4x +y +7 ≥ 0 . . . . . . the second inequality in general form
point (-2, 10): 4(-2) +(10) +7 = -8 +10 +7 = 9 ≥ 0 . . . . . . a solution
point (4, 9): don't need to test (already known not a solution)
Point (-2, 10) is a solution.
__
Additional comment
We chose the use of "general form" inequalities for evaluating answer choices because ...
the arithmetic is mainly with positive integers (no fractions)the comparison to zero does not require a lot of mental effort<95141404393>
3. How does the percentage of people who would borrow from some financial institution compare to
the percentage of people who would borrow from friends or family?
The percentage of people borrowing from financial institutions generally exceeds borrowing from friends or family due to formality, legal protection, larger loan amounts, privacy, expertise, and long-term implications.
The percentage of people who would borrow from a financial institution compared to the percentage of people who would borrow from friends or family can vary depending on various factors such as cultural norms, economic conditions, individual preferences, and access to financial services. However, in general, borrowing from financial institutions is often more common and prevalent than borrowing from friends or family for several reasons.
Formality and Legal Protection: Borrowing from financial institutions offers a more formal and legally protected process. When individuals borrow from a financial institution, they enter into a contractual agreement that outlines the terms and conditions of the loan. This agreement provides a legal framework that protects both the borrower and the lender. In contrast, borrowing from friends or family often lacks the same level of formality and legal protection, which can lead to ambiguity and strain personal relationships.
Access to Larger Loan Amounts: Financial institutions typically have more capital and resources to lend larger amounts of money compared to friends or family members. If someone requires a substantial loan, such as for purchasing a home or starting a business, they are more likely to turn to a financial institution. These institutions have processes in place to evaluate creditworthiness, collateral, and other factors, allowing them to provide loans that meet the borrower's specific needs.
Privacy and Independence: Borrowing from a financial institution offers a level of privacy and independence that may be preferred by individuals. Some people might feel uncomfortable disclosing personal financial details or discussing their financial challenges with friends or family. Financial institutions provide a professional environment where individuals can maintain privacy and retain control over their financial matters.
Expertise and Financial Advice: Financial institutions employ professionals with expertise in lending and financial management. When borrowing from a financial institution, borrowers can benefit from the advice and guidance of these professionals. They can help borrowers understand the terms of the loan, explore different options, and make informed financial decisions. Friends and family members may not possess the same level of financial knowledge or experience, limiting their ability to provide comprehensive advice.
Long-Term Implications: Borrowing from friends or family can have long-term implications for personal relationships. Financial transactions have the potential to create tension, conflicts, or misunderstandings among individuals, especially if there are difficulties in repaying the borrowed amount. Relying on financial institutions can help maintain healthy personal relationships, as the borrowing and lending processes are conducted on a professional level, minimizing the emotional and relational strain that can arise from borrowing from loved ones.
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Find the simple interest owed if $340 is borrowed at 6.6% for 9 years
The simple interest owed on a $340 loan at 6.6% interest for 9 years is $201.96.
How to find simple interest?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given that:
Principal P = $340
Interest Rate r = 6.6%
Time t = 9 years
First convert the interest rate from percent to decimal:
Rate = r/100
Rate = 6.6/100
Rate = 0.066
Now, plug the values into the above formula and solve for interest.
I = P × r × t
I = $340 × 0.066 × 9
I = $201.96
Therefore, the simple interest is $201.96.
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At Chairs and More, assemblers are paid according to the following differential piece rate scale: 1−25 chairs in a week, $10 each; 26−40 chairs, $13 each; and $17.50 each for every chair over 40. Salina Grant assembled 47 chairs in one week. Find her gross pay.
Answer:
To find Salina Grant's gross pay, we need to calculate the pay for each range and add them together.
For the first 25 chairs, Salina will be paid $10 for each chair, so her pay for this range is:
25 chairs x $10 per chair = $250
For the next 15 chairs (26-40), Salina will be paid $13 for each chair, so her pay for this range is:
15 chairs x $13 per chair = $195
For the remaining 7 chairs (over 40), Salina will be paid $17.50 for each chair, so her pay for this range is:
7 chairs x $17.50 per chair = $122.50
Adding up all three ranges, Salina's gross pay is:
$250 + $195 + $122.50 = $567.50
Therefore, Salina Grant's gross pay for assembling 47 chairs in one week is $567.50.
Step-by-step explanation:
The mean of three test is 74 what must be the the 4th score to get a mean of 78?
To achieve a mean of 78 with four scores, the fourth score must be 90.
We need to consider the current mean, the number of tests, and the desired mean in order to find the fourth score needed to achieve a mean of 78
Let's assume the three test scores are x1, x2, and x3.
We know that the mean of these three scores is 74. So we can assume that
The sum of these numbers is 74 or
(x1 + x2 + x3)/3 = 74
Let's denote it as x4 ,to find the fourth score we will use the formula to calculate the mean:
(x1 + x2 + x3 + x4)/4 = 78
To solve for x4, we can rewrite it as:
x1 + x2 + x3 + x4 = 78 * 4
Now, we can substitute the value of the mean of the first three scores into the equation:
(x1 + x2 + x3) + x4 = 312
we know that,
(x1 + x2 + x3) = 3 * 74
or,
3 * 74 + x4 = 312
Simplifying this, we get:
222 + x4 = 312
Subtracting 222 from both sides:
x4 = 312 - 222
x4 = 90
Therefore, to achieve a mean of 78 with four scores, the fourth score must be 90.
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are the side lengths of triangle Graph shows a triangle plotted on a coordinate plane. The triangle is at A(minus 7, 3), B(minus 3, 6), and C(5, 0). Type the correct answer in each box. If necessary, round any decimal to the nearest tenth. units units units
The side lengths for the triangle are given as follows:
AC = 12.4.AB = 5.BC = 10.How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Then the length AC is given as follows:
[tex]AC = \sqrt{(5 - (-7))^2 + (0 - 3)^2}[/tex]
AC = 12.4.
The length AB is given as follows:
[tex]AB = \sqrt{(-3 - (-7))^2 + (6 - 3)^2}[/tex]
AB = 5.
The length BC is given as follows:
[tex]BC = \sqrt{(5 - (-3))^2 + (6 - 0)^2}[/tex]
BC = 10.
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Bill checked out 5 books from the library. Hazel checked out b fewer books than Bill. Choose the expression that shows the number of books Hazel checked out.
The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
Here, we have,
given that,
Bill checked out 5 books from the library.
Hazel checked out b fewer books than Bill.
now, we have to find the expression that shows the number of books Hazel checked out.
let,
that shows the number of books Hazel checked out = x
so, we have,
that shows the number of books Hazel checked out = b fewer books than Bill.
as, Bill checked out 5 books from the library.
so, we get,
the number of books Hazel checked out = 5 - b
so, we have,
x = 5-b
Hence, The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
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Fractions such as
12 in.
1 ft
and
1 yd
3 ft
are called
fractions.
Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called unit conversion fractions
Unit conversion fractions are used to convert between different units of measurement within the same quantity.
The fraction 12 in/1 ft represents the conversion factor from inches to feet, where 12 inches is equivalent to 1 foot.
This fraction allows us to convert a certain length measured in inches to an equivalent length in feet.
Similarly, the fraction 1 yd/3 ft represents the conversion factor from yards to feet, where 1 yard is equivalent to 3 feet.
This fraction allows us to convert a certain length measured in yards to an equivalent length in feet.
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Fill in each blank so that the resulting statement is true
Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called _________fractions
#1 Write a positive or negative integer that represents the situation.
You run up 24 steps.
© 24
0-24
The integer number that represents the situation running up 24 steps is given as follows:
+24.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For altitudes, the signs are given as follows:
Gain of altitude: positive integer.Loss of altitude: negative integer.In this problem, we have an increase of altitude of 24 steps, hence the integer number is given as follows:
+24.
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This exercise uses the normal probability density function and requires the use of either technology or a table of values of the standard normal distribution. The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.96 per access line per month, with a standard deviation of $2.25. Company A's operating expenses were $28.00 per access line per month. Assuming a normal distribution of operating expenses, estimate the percentage of regional phone companies whose operating expenses were closer to the mean than the operating expenses of Company A were to the mean. (Round your answer to two decimal places.)
The probability of the values of X that are less than 21 is 0.97725.
We have,
The term "standard deviation" refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
u = 20
and SD = 2.25
To find P(X < 21)
So, P(X < 21 )
= 1 - P(X > 21)
Now, P(X > 21)
= P(Z > [(21–20)/2.25]
= P( Z > 1/2.25)
= P(Z > 0.444)
= 0.02275
So, the required probability = P(Z < 21) = 1 - 0.02275= 0.97725
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complete question:
Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.