Step-by-step explanation:
4x² + 12x + 8 = 0
this has the same solutions as
x² + 3x + 2 = 0
as we simply divided everything by 4. 0/4 = 0.
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case that is
x = (-3 ± sqrt(3² - 4×1×2))/(2×1) =
= (-3 ± sqrt(9 - 8))/2 = (-3 ± sqrt(1))/2
x1 = (-3 + 1)/2 = -2/2 = -1
x2 = (-3 - 1)/2 = -4/2 = -2
so, the 2 solutions are
x = -1
or
x = -2
Which of the following is the formula for the solutions of a quadratic equation ax2 + bx + c = 0?
You owe $46,212.35 on a student loan that carries an APR of 6.9%. You place the loan into forbearance for 5 years. How much do you owe on the loan when it comes out of forbearance?
You owe on the loan is $64512.90
Given,
In the question:
You owe $46,212.35 on a student loan that carries an APR of 6.9%. You place the loan into forbearance for 5 years.
To find the how much do you owe on the loan when it comes out of forbearance?
Now, According to the question:
Based on the given conditions,
Formulate;
You owe $46,212.35 on a student
Interest is 6.9%
46212.35 x (6.9% +1)^5
Evaluate the equation/expression:
64512.90
Hence, You owe on the loan is $64512.90
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Seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary. Find the measures of these three angles.
The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.
How to find angles of a decagon?A decagon simony means a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.
Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.
Therefore,
1440 - 1220 = 220
Let the angles be a, b and c.
Therefore,
a + b + c =220
a + b = 90
b + c = 180
Hence,
a = 220 - 180
a = 40°
b = 90 - 40
b = 50°
c = 180 - 50
c = 130°
The angles are 40°, 50° and 130°.
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Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
The proportions of the total rooms that were occupied each year are:
The current year is 84%.The previous year is 81%.What is the proportion?Proportion is the fractional value of a variable when compared to the whole.
Proportions show the ratio or relative relationship between two or more values set as equal.
Like ratios, proportions are depicted in fractions, decimals, or percentages to show how two values compare.
Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
Proportion of occupied rooms = 84% 81%
(1,512/1,800 x 100) (1,458/1,800 x 100)
Thus, on average, room occupancy for the two years is 82.5%, and proportionately for each year, it is 84% for the current year, while the previous year recorded 81%.
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Question Completion:What proportion of the total rooms were occupied each year?
can anyone help with this
Answer:
bla blablablablabla
Step-by-step explanation:
blablablablablabla
Examine the worked examples. Then, answer the questions.
Alessa's car uses 2 gallons of gas to drive 45 miles.How many miles can
Alessa's car drive using 15 gallons of
Answer:
Alessa's car would be able to drive 337.5 miles with 15 gallons of gas.
A telephone exchange operator assumes that 8% of the phone calls are wrong numbers.
If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 494 phone calls would differ from the population proportion by more than 3%? Round your answer to four decimal places.
The probability that the phone calls would differ from the population proportion by more than 3% is 0
How to determine the probability value?From the question, the given parameters about the distribution are
Proportion, p = 8%Sample size, n = 494The actual proportion, x = greater than 3%The mean is calculated as
Mean = np
So, we have
Mean = 8% * 494 = 39.52
The standard deviation is calculated as
Standard deviation = √np(1 - p)
So, we have
Standard deviation = √494 * 8% (1 - 8%) = 0.77
The z-score is calculated using the following formula
[tex]z = \frac{\bar p - p}{\sqrt{p(1 - p)}/n}[/tex]
Substitute the given parameters in the above equation
[tex]z = \frac{8\% - 3\%}{\sqrt{8\% * (1 - 8\%)}/494}[/tex]
Evaluate
z = 90.9
The probability is then calculated as:
P(x > 3%) = P(z > 90.9)
From the z table of probabilities, we have;
P(x > 3%) = 0
Hence, the probability is 0
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I can determine if a relation is a
function.
1. Use vertical line test to determine if
the graph is a function. Why or why not?
71
(
7
2
Z
2
4
Answer:
1st Graph : Function
2nd Graph : Not a Function
Step-by-step explanation:
For the 1st Graph , any Vertical Line will not pass the Graph in more than one Point , So it represents a Function
For the 2nd Graph , many Vertical Line will pass the Graph in two Points , So it is not a Function
Pixel A is located 80 km from the Jacksonville radar. How many seconds did it take for the radar pulse to travel to the target at Pixel A and return to the radar? (It will be a very small answer!)
C= 3 × 10^8 m s−1
R= 80,000
R= CT/2
[tex]C=3\times 10^8~\frac{m}{s}\hspace{5em}R=80000\implies R=8\times 10^4 \\\\[-0.35em] ~\dotfill\\\\ R=\cfrac{CT}{2}\implies 2R=CT\implies \cfrac{2R}{C}=T\implies \cfrac{2(8\times 10^4)}{3\times 10^8}=T \\\\\\ \cfrac{16\times 10^4}{3\times 10^8}=T \implies \cfrac{16}{3}\times\cfrac{10^4}{10^8}=T\implies \cfrac{16}{3}\times\cfrac{1}{10^8\cdot 10^{-4}}=T \\\\\\ \cfrac{16}{3}\times\cfrac{1}{10^{8-4}}=T \implies \cfrac{16}{3\times 10^4}=T\implies \cfrac{16}{30000}=T\implies \cfrac{1}{1875}=T[/tex]
Gavin deposited money into his savings account that is compounded annually at an interest rate of 9% Gavin thought the equivalent quarterly interest rate would be 2.25% is Gavin correct?
The quarterly interest rate is equal to 2.25%. This implies that Gavin is correct.
How to determine the value of equivalent quarterly interest rate?Mathematically, the compound interest on an investment can be calculated by using this formula:A(t) = P(1 + r/n)^{nt}
Where:A represents the future value.
r represents the interest rate.
n represents the number of times compounded.
P represents the principal.
T represents the time measured in years.
In this scenario, Gavin's savings account is compounded annually at an interest rate of 9%. This ultimately implies that, the equivalent quarterly interest rate would be calculated by dividing the annual interest rate of 9% by 4 as follows:
Quarterly interest rate = 9/4
Quarterly interest rate = 2.25%
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Hank rents 9 cases of plates.He has 250 guests attending the banquet. There are 30 plates in each case. Did Hank rent enough plates? Explain
Answer:
yup
Step-by-step explanation:
so to find the amount of plates he has we :
30*9 = 270
How many guests :
250
Hank has 20 extra plates,
hope this helps :)
Find the quotient.
2.4)7.68
Answer:0.3125
Step-by-step explanation:
none sry
what the area and pelase explain give brainly points
Answer: 10 squares
Step-by-step explanation:
The answer for the area is 10 squares but I’m not sure that’s what they’re asking for.
Hayley's fuel bills for her house increased from £76 a month in 2021
to £89 a month in 2022. Calculate the percentage increase in Hayley's
fuel bills from 2021 to 2022.
Give your answer correct to three significant figures.
The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.
What is a Percentage Increase?
The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.
Steps to Calculate Percentage Increase?
The formula to calculate Increase (I) is given by, [tex]I=Y-X[/tex], where [tex]X[/tex] is the original value and [tex]Y[/tex] is the new value.The percentage increase formula is given by, [tex]\%I=\frac{I}{X} \times 100[/tex]Here, in the question, it is given that,
The original amount (X) or the fuel bill in 2021 is £76.
The new amount (Y) or the fuel bill in 2022 is £89.
So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,
[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]
Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,
[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]
Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.
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manuel wishes to purchase 25cent and 30 cent stamps. he decides to buy 10 fewer 30 cent stamps. How many of each can he buy for no more than $19.00
Using the simplification, Manuel buy 15 stamps of 25 cents and 5 stamps of 30 cent.
In the given question,
Manuel wishes to purchase 25 cent and 30 cent stamps.
He decides to buy 10 fewer 30 cent stamps.
We have to find how many of each can he buy for no more than $19.00.
Let he buy x stamps of 25 cent.
He want to buy 10 fewer 30 cent stamps.
So he buy x−10 stamps of 30 cent.
But he have to buy total stamps of $19.
So the equation is
x+x−10 = 19
Simplifying
2x−10=19
Add 10 on both side
2x−10+10=19+10
2x=29
Divide by 2 on both side
2/2 x =29/2
x=14.5
x≈15
Hence, he buy 15 stamps of 25 cent.
Now finding the number of 30 cent.
he buy x−10 stamps of 30 cent.
So 15−10=5.
So he buy 5 stamps of 30 cent.
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What is the mean of these numbers? 53 29 47 36 65
What line is perpendicular to the line y= -1/2x + 8
Answer: y=2x+8
Step-by-step explanation:
you take the reverse of the slope being 2 including the negative.
Which equation below represents the Exponent Property of Logs?
The only equation given that represents the Exponent Property of Logs is; Option A: log(A^r) = r*log(A)
How to find the exponent property of logarithm?The exponent property of logarithm says that the log of a power is the exponent times the logarithm of the base of the power. For example;
logₐ(MN) = logₐM + logₐN
logₐ(M/N) = logₐM - logₐN
logₐ(3²) = 2logₐ3
The first example above shows the product rule of logarithms
The second example shows the quotient rule of logarithms
The third rule shows the power rule
Now, looking at the options, the only one that shows the correct pattern of exponent property of logarithm is;
Option A: log(A^r) = r*log(A)
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3x ≥5 or -3/5x-3>7 solve the compound inequality
By using the concept of linear inequation, the required solution is
[tex]x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here the given linear inequation is
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7[/tex]
Now
[tex]3x \geq 5 \ or \ \frac{-3}{5}x -3 > 7\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5} x > 7 + 3\\\\x \geq \frac{5}{3} \ or \ \frac{-3}{5}x > 10\\\\x > \frac{5}{3} \ or \ x < \frac{10 \times 5}{-3}\\\\x > \frac{5}{3} \ or \ x < -\frac{50}{3}[/tex]
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Amount Desired at End of Period
$17,600.00
Length of Time
7
1. Period Used
2. Rate Used
23. PV factor used
3 4. PV of amount desired at end of period
Rate
2%
Compounded
Quarterly
Required:
Complete the following using the information above and the present value Table 12.3
or the present value table in the Business Math Handbook or the present value
formula to answer the following:
Note: Use cells A2 to D3 from the given information to complete this question.
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%" and PV factor used is 0.62026 .
Hence,
The amount desired at end of a period is $9400.
The length of time is 4 years .
The rate is 2%.
Compounded is monthly.
The period used is 48.
The rate used is 1%.
The PV factor used is 0.62026 .
The PV of the amount desired at the end of the period is $5830.45
What is the percentage?
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%".
Here from the question,
PV factor = (1 + i) ----(1)
where, i = 12/12 % , i =1
and
n = 4(12)
n = 48
Substituting the values in the equation , we get
PV factor = (1 + 0.01)^ -48
PV factor = 0.62026
Hence,
the amount desired at end of a period is $9400.
The length of time is 4 years.
The rate is %.
Compounded is monthly.
The period used is 48 .
The rate used is 1%.
The PV factor used is 0.62026.
The PV of the amount desired at the end of the period is $5830.45
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I need help with this Question.
The number of quarts in 12 L is 12.684 qt.
Given that, 12 L to qt.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
Here,
There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.
Now, 12 L=12×1.057
= 12.684 qt
Therefore, the number of quarts in 12 L is 12.684 qt.
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Neema bought appliances costing $3725 at a store charging 5% add-on interest. She made a $700 down payment and agreed to monthly payments over four years. Find the total cost, for the appliances plus
interest.
The total cost for the appliances plus interest is $
(Type an integer or decimal.)
The total cost for the appliances plus interest is 4330.
What is an interest rate?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR.
Here, we
Cost of the appliance = $3725
Neema paid $700 so amount financed = $3725 - $700 = $3025
Interest rate on the loan = 3025*0.05*4 = $605
Total cost of the appliance = $3725 + 605 = $4330
Hence, the total cost for the appliances plus interest is 4330.
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How will the mode be affected if the outlier is removed from the data set below? 58, 60, 53, 54, 60, 35, 58, 60
will the mode decrease?
will the mode not change?
is there not enough information?
will the mode increase?
The mode will not change.
Given data,
58,60,53,54,60,35,58,60
Outlier is the value in a set of data that much higher or lower than other values in data.
from given data, outlier is 35.
Mode is the value in a set of data that occurs more frequently in set of data.
from given data, 60 occurs more frequently.
Hence, 60 is the mode of data.
If outlier is removed from the data set then it will not affect the mode of the data
Thus, the mode will not change.
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A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 170 feet. To cover the lawn bags of fertilizer are required
Answer: The correct answer is 17 bags of fertilizer to cover the lawn
Step-by-step explanation:
1 bag of fertilizer covers 3000 SF of lawn
How many bags are needed for an area of 290 feet x 170 feet
Calculate the Square Feet:
290 x 170 = 49,300 SF
Divide space (SF) by bag coverage (SF):
49,300 / 3,000 = 16.43 bags of fertilizer
Round up answer to 17 bags of fertilizer
Select the values that make the inequality
The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.
Given,
In the question:
To see the figure:
To select the values that makes the inequality s ≤ 4 true.
Number table are given in figure.
To see the figure and analysis.
Now, According to the question;
To make the inequality s ≤ 4 true.
The selected value must be less than 4 {Properties of Inequality}
The values are sorted from small to large:
So, The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.
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one serving of a certain brand of yogurt contains 7g of fat. the low fat version contains 45.75% less fat per serving. how many grams of fat does one serving of the low fat yogurt contain?
The grams of fat that are contained in one serving of the low-fat yogurt are: 3.7968g.
How do we obtain the grams of fat for one serving of low-fat yogurt?To obtain the number of grams of fat that is contained in one serving of the low-fat yogurt, we need to first note the percentage content of the low-fat version of yogurt.
100 - 45.75% = 54.25% or 0.5425
Since one serving of the yogurt contains 7g of fat, then the low-fat serving will be equal to:
7g × 0.5425 = 3.7968
So, the total gram of fat for one serving of the low-fat yogurt is equal to:
3.7968g
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-4x=76 x equals _-____________________________________________________________________________________________________________________________________________________________--
The value of x in the equation -4x = 76 is 19.
What is equation?The equals sign is used in equations to indicate the equality of two expressions in a formula.
Given:
-4x = 76,
-x = 76 / 4,
x = -19
Therefore, the value of x in the equation -4x = 76 is 19.
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Classify the polynomial by its degree: 4m³-9x² + 10
A) 0
B) 1st
C) 2nd
D) 3rd
E) 4th
A company that most adults would erase all of their personal data online if they could. In order to test this claim, a GFI Software Survey of 565 randomly selected adults showed that 59% of them would erase all of their personal information online if they could.
A. State the null and alternative hypotheses (in symbols).
B. Explain what a Type 1 and a Type 2 error would be in this case.
C. State the conclusion if the null hypothesis is rejected.
D. State the conclusion if the null hypothesis is not rejected.
a) The null and alternative hypothesis are given as follows:
Null: [tex]H_0: p \leq 0.5[/tex]Alternative: [tex]H_1: p > 0.5[/tex]b) The errors are given as follows:
Type I: A sample which gives enough evidence that most people would erase the data, if in reality they wouldn't.Type II: A sample in which the proportion of people that would erase their data isn't significantly above 50%, when in fact it is.c) The conclusion of a rejected null hypothesis is: There is enough evidence that most adults would erase their data if they could.
d) The conclusion of a not rejected null hypothesis is: There is not enough evidence that most adults would erase their data if they could.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that most adults would erase all of their personal data online if they could, that is, if the proportion is not greater than 50%, hence:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that they would erase the information, that is, if the proportion is greater than 50%, hence:
[tex]H_1: p > 0.5[/tex]
A rejected null hypothesis means that the alternative hypothesis is accepted, that is, there is enough evidence that most adults would erase their data if they could.
A not rejected null hypothesis, conversely, means that there is not enough evidence that most adults would erase their data if they could.
What are type I and type II errors?Type I errors are when a true null hypothesis is rejected. Hence, the context of this problem, it would mean a sample which gives enough evidence that most people would erase the data, if in reality they wouldn't.
Type II errors are when a false null hypothesis is not rejected. Hence, the context of this problem, it would mean a sample in which the proportion of people that would erase their data isn't significantly above 50%, when in fact it is.
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Essay for operation of sets
What is Set Theory Formula?
The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
In a set theory, there are three major types of operations performed on sets, such as: Union of sets (∪) Intersection of sets (∩) Difference of sets (–)
Set Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product of Set
Set Union
The union of sets A and B (denoted by A ∪ B) is the set of elements that are in A, in B, or in both A and B. Hence, A ∪ B = { x | x ∈ A OR x ∈ B }.
n(A∪B) = n(A) + n(B) − n(A∩B)
Set Intersection
The intersection of sets A and B (denoted by A ∩ B) is the set of elements which are in both A and B. Hence, A ∩ B = { x | x ∈ A AND x ∈ B }.
n(A∩B) = n(A)+n(B)−n(A∪B)
Set Difference
The set difference of sets A and B (denoted by A - B) is the set of elements that are only in A but not in B. Hence, A - B = { x | x ∈ A AND x ∉ B }.
Complement of a Set
The complement of a set A (denoted by A’) is the set of elements which are not in set A. Hence, A' = { x | x ∉ A }. More specifically, A'= (U - A) where U is a universal set that contains all objects.
The complement of a universal set is an empty set U′ = ϕ. The complement of an empty set is a universal set ϕ′ = U.
Cartesian Product / Cross Product
The Cartesian product of n number of sets A1, A2, ... An denoted as
A1 × A2 ... × An can be defined as all possible ordered pairs
De-Morgan's Law - The De Morgan's law states that for any two sets A and B, we have (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'
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