See below for the explanation on how discriminant be used to determine the number of solutions
How can the discriminant be used to determine the number of solutions?Let a trinomial in standard form be represented as
y = ax^2 + bx + c
The discriminant (d) is calculated as
d = b^2 - 4ac
The solutions are dependent on the following conditions
If d = 0, the trinomial has 1 real solutionIf d < 0, the trinomial has imaginary solutionsIf d > 0, the trinomial has 2 different real solutionsRead more about discriminant at
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A computer user has downloaded 21 songs using an online file-sharing program and wants to create a CD-R with
11 songs to use in his portable CD player. If the order that the songs are placed on the CD-R is not important to
him, how many different CD-Rs could he make from the 21 songs available to him?
Answer:
If to create a CD 9 songs are needed and user have 19 songs then he can create 33522128640 such CD's if solving through permutations.
What is permutations?
It is basically an arrangement of objects in a certain order.It is expressed as n and it is equal to n!/(n-r)!.
How to calculate ways?
We have been given that user have 19 songs and 1 CD is made from 9 songs so the number of CD's which can be made is basically the number of ways these 9 songs are arranged from 19 songs in CD's. So, the number of CD's will be 19=19!/(19-9)!
=19!/10!
=19*18*17*16*15*14*13*12*11*10!/10!
=19*18*17*16*15*14*13*12*11
=335322128640 CD's
Hence 335322128640 CD's can be made from 19 songs by the user.
HELP WITH ALLL PLEASE LABEL THE NUMBERS :))
Answer:
18. in imge
19. is D
20. 10/3 (just divided by 5)
21. 8/7 bc negtive reciprocal
22. (0,8) y-int
Step-by-step explanation:
1. For infant girls, the mean body length at 10 months is 72 centimeters with a standard deviation of 3 centimeters. The 75th percentile for a 10 month-old girl is ____ centimeters? (Round to one decimal place)
Using the normal distribution, the 75th percentile for a 10 month-old girl is 74 centimeters.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 72, \sigma = 3[/tex]
The 75th percentile is X when Z = 0.675, hence:
0.675 = (X - 72)/3
X - 72 = 3 x 0.675
X = 74.
The 75th percentile for a 10 month-old girl is 74 centimeters.
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Real-World Application
al-World Application0231651561065
Fractions and mixed numbers
A real estate company is interested in the ages of home buyers. They examined the ages of thousands of home buyers and found that the mean age was 45 years old, with a standard deviation of 10 years. Suppose that these measures are valid for the population of all home buyers. Complete the following statements about the distribution of all ages of home buyers.
According to Chebyshev's theorem, at least 56% of the home buyer's ages lie between __ years and __ years. (Round your answer to the nearest whole number)
According to Chevyshev's theorem, at least what percent of the home buyers' age lie between 25 years and 65 years.
Using Chebyshev's Theorem, it is found that:
At least 56% of the home buyer's ages lie between 30 years and 60 years.At least 75% of the home buyers' age lie between 25 years and 65 years.What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]P = 100(1 - \frac{1}{k^{2}})[/tex].For the first item, we first have to find k when P = 56, hence:
[tex]56 = 100\left(1 - \frac{1}{k^{2}}\right)[/tex]
[tex]1 - \frac{1}{k^{2}} = 0.56[/tex]
[tex]\frac{1}{k^2} = 0.44[/tex]
k² = 1/0.44
k = sqrt(1/0.44)
k = 1.5.
Within 1.5 standard deviations, hence the bounds are:
45 - 1.5 x 10 = 30 years old.45 + 1.5 x 10 = 60 yards old.Hence:
According to Chebyshev's theorem, at least 56% of the home buyer's ages lie between 30 years and 60 years.
25 and 65 years are both 2 standard deviations from the mean, hence:
At least 75% of the home buyers' age lie between 25 years and 65 years.
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Find the length of the missing side. Leave your answer in the simplest radical form.
The length of the missing side is √69
How to find the length of the missing side?The triangle is a right triangle with the following parameters
Hypotenuse = 13
Leg = 10
Represent the missing side with x
By the Pythagoras theorem, we have
x = √Hypotenuse² - Leg²
This gives
x = √13² - 10²
Evaluate
x = √69
Hence, the length of the missing side is √69
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Answer quick I will mark brainlist
Answer:
Step-by-step explanation:
The Red circles have a probability of 1/2 of getting chosen, The red and blue circles together have an 100% chance of getting chosen because they are the total of circles. Np
How do you write 2.74 x 10 to the negative 3rd power in standard notation?
Answer:
The exponent is -3, making it 10 to the power of negative 3. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 3 times:
2.74 ->0.00274
Step-by-step explanation:
Final Answer 0.00274
54. The cone in the diagram has radius x cm and height 2x cm. The volume of the cone is 500 cm³. Find the value of x.
Value of x is 6.2 cm when x is the radius of cone.
What is Volume of cone?
The amount of space occupied by a cone is referred to as the volume of a cone. The volume of the cone depends on the base radius of the cone and the height of the cone. It can also be expressed in terms of its slant height wherever necessary.
Volume of cone formula, V= 1/3*[tex]\pi[/tex]*r∧2*h
given,
Height h= 2x
radius = x
Volume V= 500cm3
V= 1/3*[tex]\pi[/tex]*r∧2*h
500 = 1/3 *22/7*x2*2x
x∧3 = 5*3*5*5*2*2*7/11*4
x∧3 = 5*3*5*5*7/11
x = ∛(5*3*5*5*7/11)
x = 5(∛21/11)
x = 6.2 cm
Therefore, the radius of the cone x is 6.2 cm
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The Smiths went to the Cape for a wedding. They left at 11 a.m. They traveled 180 miles and drove at 60 miles per hour. What time did they reach their destination"
O 1:00 p.m.
Answer:
I think it should be 1 pm
Step-by-step explanation:
The Smiths left at 11 am and traveled 180 miles. If they drive at 60 miles per hour, that means that they traveled for 2 hours because 180 divided by 60 is two. That means they traveled for 2 hours and arrived at 1 pm.
What is 2,443,802,280 rounded to the nearest ten million
Answer:2,440,000,000
Step-by-step explanation:
(69 1/3)-(45 14/15)=
Answer:
-19
Step-by-step explanation:
1/3 of 69=23
14/15 of 45=42
23-42=-19
Answer:
23 2/5
Step-by-step explanation:
69 1/3 - 45 14/15
= (69 - 45) + (1/3 - 14/15)
= 24 + 1 x 5/3 x 5 - 14/15
= 24 + 5/15 - 14/15
= 24 + 5 - 14/15
= 24 + -9/15
= 24 + -9 ÷ 3/15 ÷ 3
= 24 + -3/5
= 23 2/5
What is the value of 6×10 to the 15th power divided by 4×10 to the 12th power
Step-by-step explanation:
Click photo to look ans
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At 6 AM, the temperature in New Crampton, California was 64℉. By 4 PM, the temperature had risen to 76℉. What was the change in temperature over the 10-hour period?
The change in temperature over the 10 hours using a mathematical operation, is 12℉.
What is a mathematical operation?A mathematical operation uses input values (variables, numbers, mathematical operators, and operands) to determine an output value.
Some of the mathematical operators include addition, subtraction, division, and multiplication.
For instance, we can subtract the temperature in New Crampton at 6 A.M. from the temperature at 4 P.M. to determine the temperature change.
Data and Calculations:The temperature at 6 A.M. in New Crampton = 64℉
The temperature at 4 P.M in the same city = 76℉
Change in temperature over 10 hours = 12℉ (76℉ - 64℉)
Thus, the change in temperature over the 10 hours using a mathematical operation, is 12℉.
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Give an example of a real-life situation where it might make sense to round a number and a different situation where it probably does not make sense to round a number.
Answer:
when dealing with money
50 points
A finance magazine did a survey and found that the average American family spends $1,600 on a summer vacation. If the distribution is normal with standard deviation $411, find the amount a family would have spent to be the 80th percentile.
Answer:
$1,945.91
Step-by-step explanation:
To find the amount a family would have spent to be at the 80th percentile, we can use the normal distribution.
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given that the average spending on a summer vacation is $1,600 and the standard deviation is $411:
Mean μ = $1,600Standard deviation σ = $411We need to convert the problem to the standard normal distribution by calculating the z-score.
The z-score represents the number of standard deviations a data point is away from the mean. To find the z-score corresponding to the 80th percentile, we need to find the critical value or z-score that corresponds to an area of 0.80 under the standard normal curve.
Using a standard normal distribution table or a calculator, the z-score corresponding to an area of 0.80 is 0.84162084...
Next, we use the formula for the z-score:
[tex]\boxed{z = \dfrac{x - \mu}{\sigma}}[/tex]
where z is the z-score, x is the data point, μ is the mean, and σ is the standard deviation.
Substitute z = 0.84162084..., μ = 1600, σ = 411 into the z-score formula:
[tex]0.84162084... = \dfrac{x - 1600}{411}[/tex]
Solving for x:
[tex]x=1945.90616...[/tex]
Therefore, a family would have spent approximately $1,945.91 to be at the 80th percentile of spending on a summer vacation.
Answer:
$1,945.03
Step-by-step explanation:
To find the amount a family would have spent to be at the 80th percentile, we need to find the z-score that corresponds to the 80th percentile and then use that z-score to calculate the corresponding amount.
First, we find the z-score using the standard normal distribution table or a calculator:
z = InvNorm(0.8) ≈ 0.8416
Next, we use the formula for transforming a z-score to a raw score:
z = (x - μ) / σ
where x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values and solving for x, we get:
0.8416 = (x - 1600) / 411
x - 1600 = 0.8416 * 411
x - 1600 = 345.0256
x = 1945.0256
Therefore, a family would have spent about $1,945.03 to be at the 80th percentile.
Complete the process of solving the equation.
Fill in all the missing terms and select all missing descriptions.
4(-3d+14) = -17d + 16
-12d +56 = -17d + 16
+56 = 16
5d = -40
d=
Add 17d to both sides
Divide both sides by 5
Answer:
d = -8
Step-by-step explanation:
4(-3d+14) = -17d + 16
-12d + 56 = -17d + 16
+17d +17d
5d + 56 = 16
-56 -56
5d = -40
÷5 ÷5
d= -8
I hope this helps!
Across
Down
1. animal that eats only plants
2. warm-blooded animals with hair or fur
3. animal that is hunted and eaten
4. animals who hunt other animals
5. back teeth
8. sharp. curved nails on an animal's foot 6. animal that eats meat and plants
9. animal that eats only meat
7. front teeth
Answer:
1. Herbivores
2. Mammals
3. Prey
4. Predators
5. Molars
6. Omnivores
8. Claws
9. Carnivores
What was the overall percent increase in the stadium capacity between 1920 and 2000
The overall percent increase in the stadium capacity between 1920 and 2000 considering the capacity was "x" in 1920 and "y" in 2000 is [tex][\frac{(y-x)}{x}*100][/tex].
As per the question statement, we are required to calculate the overall percent increase in the stadium capacity between the time period of 1920 and 2000. But no data about the stadium capacity is mentioned in the question statement. Hence, we will assume the capacity was "x" in 1920 and "y" in 2000. Assigning two variables to solve the question produces a generalized form of our required answer, in which, we can substitute any data to get the desired output.
Since Percentage change is calculated as
[{(Change from original)/(Original Value)}*100],
Our change in seating capacity of the stadium in 2000 from the year 1920 is [tex](y-x)[/tex] and original value being "x",
Overall percent increase in the stadium capacity between 1920 and 2000 is [tex][\frac{(y-x)}{x}*100][/tex].
Percent Increase: It is a measure of the difference (Increment) between the final value and the initial value, expressed in the form of a percentage.To learn more about Percent Increase, click on the link below.
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*HELP*
Henrich is a single taxpayer. In 2021, his taxable income is $455,000. What is his income tax and net investment income tax liability in each of the following alternative scenarios? Use Tax Rate Schedule, Dividends and Capital Gains Tax Rates for reference. (Do not round intermediate calculations. Leave no answer blank. Enter zero if applicable. Round your final answers to 2 decimal places.)
a. All of his income is salary from his employer.
Income tax _______
Net investment income tax ______
Total tax liability __________
b. His $455,000 of taxable income includes $2,000 of long-term capital gain that is taxed at preferential rates.
Income tax _______
Net investment income tax ______
Total tax liability __________
c. His $455,000 of taxable income includes $49,000 of long-term capital gain that is taxed at preferential rates.
Income tax _______
Net investment income tax ______
Total tax liability __________
d. Henrich has $197,500 of taxable income, which includes $51,000 of long-term capital gain that is taxed at preferential rates. Assume his modified AGI is $210,000.
Income tax _______
Net investment income tax ______
Total tax liability __________
The Investment Income, if any (g) $380 and The Net Income tax payable is $41,516.75
How to find the Total Income tax?A. The Taxable Income (a) $425,000
The Prefrentially taxed income (b) $0
The Income taxed at ordinary rates ( c) $425,000
The Tax on c above (d)
$124,469.95 = $120,529.75 + [($425,000 - $415,050) x 39.6%]
The Tax on b above ( e) is $0
Thus, the Total Income tax (f) is $124,469.95 (d + e)
The Investment Income, if any is $0 No Investment Income
The Net Income tax payable is $124,469.95
B. The Taxable Income (a) $425,000
The Prefrentially taxed income (b) $2,000
The Income taxed at ordinary rates ( c) $423,000
The Tax on c above (d);
$123,677.95 = $120,529.75 + [($423,000 - $415,050) x 39.6%]
The Tax on b above ( e) ;
$400 = $2,000 x 20%, Since marginal rate is 39.6%
The Total Income tax (f) $124,077.95 (d + e)
The Investment Income, if any (g) $76
($2,000 x 3.8% = $76)
The Net Income tax payable is $124,153.95 (f + g)
C. The Taxable Income (a) $425,000
The Prefrentially taxed income (b) $55,000
The Income taxed at ordinary rates ( c) $370,000
The Tax on c above (d);
$105,629.25 = $46,278.75 + [($370,000 - $190,150) x 33%]
The Tax on b above ( e);
$8,747.50 [($45,050 x 15%) + ($9,950 x 20%)]
The Total Income tax (f) $114,376.75 (d + e)
The Investment Income, if any (g) $2,090
($55,000 x 3.8% = $2,090)
The Net Income tax payable $116,466.75 (f + g)
D. The Taxable Income (a) $195,000
The Prefrentially taxed income (b) $50,000
The Income taxed at ordinary rates is ( c) $145,000
The Tax on c above (d);
$33,636.75 = $18,558.75 + [($145,000 - $91,150) x 28%]
The Tax on b above ( e);
$7,500.00 = $50,000 x 15%
The Total Income tax (f) is $41,136.75 (d + e)
The Investment Income, if any (g) $380
The Net Income tax payable is $41,516.75 (f + g)
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William Smith is choosing artisan bonsai trees. She has 15 different variants of bonsai trees and would like
to use 7 of them. How many different selections of the 7 bonsai trees are possible?
There are 6,435 different selections of 7 bonsais that William Smith can choose.
How many different selections of the 7 bonsai trees are possible?If we have a set of N elements, the number of different combinations of K elements (such that K is equal to or smaller than N) of those N elements is given by:
C(N, K) = N!/( (N - K)!*K!)
In this case, we know that she has 15 different variants of bonsai and she wants to use 7, then:
N = 15
K = 7
Replacing these values in the above formula we will get the possible combinations of bonsais.
C(15, 7) = 15!/( (15 - 7)!*7!) = 15!/( 8!*7!) = (15*14*13*12*11*10*9)/(7*6*5*4*3*2*1) = 6,435
There are 6,435 different selections of 7 bonsais.
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Given 9.05(−13.2), find the product.
The value of the product 9.05(-13.2) is -119.46
How to determine the product?The product expression is given as
9.05(-13.2)
Rewrite the product expression as
9.05(-13.2) = 9.05 * (-13.2)
Using a calculator, we have
9.05(-13.2) = -119.46
Hence, the value of the product 9.05(-13.2) is -119.46
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help like now and immediate
Answer: x=30
Step-by-step explanation:
6x-5+z-25=180
7x+210
x=30
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum equals 13, maximum equals 94, 6 classes
The minimum and maximum data entries is the to arrive at the values as follows:
The class width is solved to be 13lower class limits = 13, 26, 39, 52, 65, 78, 91upper class limits = 25, 38, 51, 64, 77, 90, 94How to find the class width, the lower class limits, and the upper class limitsGiven data
minimum equals 13, maximum equals 94, 6 classes
The class width
= ( maximum - minimum ) / 6
= ( 94 - 13 ) / 6
= 13.5
The class width is solved to be 13
Lower class limit
From the lowest 13,repeated addition of the class width gives the lower class limits as follows:
lower class limits = 13, 26, 39, 52, 65, 78, 91
Upper class limits
The upper class limit is gotten from the lower class limit by reducing one from the class width to get 13 - 1 = 12. This value is added to the lower class limits to get the upper class limits.
upper class limits = 25, 38, 51, 64, 77, 90, 94
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Help please, I need this done for extra credit
The value of 'x' in the given equation - 8 = - (x + 4) is 4.
What are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equivalent. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are 2 different expressions separated by a 'equal' sign.So, value of 'x' in - 8 = - (x + 4):
- 8 = - (x + 4)- 8 = - x - 4- 8 + 4 = -x-4 = -xSo, x = 4Therefore, the value of 'x' in the given equation - 8 = - (x + 4) is 4.
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The complete question is given below:
Find the value of x in the equation - 8 = - (x + 4).
PLEASE HURRY AND HELP. PLEASE AND THANK YOU
Answer:
Step-by-step explanation:
For each one you would take the Q1 and the Q3 value of the box and whisker plot and subtract them
Q3 - Q1 = IQR(interquartile range)
45 - 20 = 25
40 - 10 = 30
10 - 6 = 4
20 - 8 = 12
A company reported total equity of $185,000 at the beginning of the year. The company reported $250,000 in revenues and $185,000 in expenses for the year. Liabilities at the end of the year totaled $112,000. What are the total assets of the company at the end of the year?
Based on the revenue, total equity, and the ending liabilities, the total assets at the end of the year is $362,000.
What is the total assets?First, find the ending equity:
= Opening equity + Revenue - expenses
= 185,000 + 250,000 - 185,000
= $250,000
The total assets by the accounting equation is:
Assets = Liabilities + Equity
= 112,000 + 250,000
= $362,000
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The rectangular coordinate system shows the graph of the equations in a system of equations. Use the graph to determine the number of solutions for the system. If the system has only one solution, give its coordinates.
Answer:
A. The only solution is (-2, 1).
Step-by-step explanation:
Given a graph of two lines, you want the number of solutions to the system of equations the lines represent.
SolutionThe graph of an equation represents all of the points that satisfy that equation. When a system of equations has more than one equation, the set of points that satisfies all of the equations is the set of points where the graphs intersect (overlap) each other.
Here, the two straight lines intersect at exactly one point: (-2, 1). That one point represents the only solution to the system of equations.
The only solution is (-2, 1).
Maria uses 2/3 cup of powdered mix for every 2 gallons of water. Franco uses 1 1/4 cups of powdered mix for every 5 gallons of water. What is the strength of each sports drink?
The strength ratio of each sports drink is 4:3.
What is ratio ?Ratio can be defined as comparison of two or more similar quantities.
According to the given question Maria uses 2/3 cup of powdered mix for every 2 gallons of water.
Therefore the no. of cups of powdered mix per gallon in Maria's sports drink is
= (2/3)÷2
= (2/3)×(1/2)
= 2/6.
= 1/3 cups per gallon of sport drink.
In case of Franco the no. of cups of mix in his sport drink per gallon is
=(5/4)÷5
= 5/4×1/5
= 5/20
= 1/4 cups per gallon of sport drink.
∴ The strength of each sport drink is
= 1/3:1/4
= 12/3:12/4 ( LCM of 3,4 is 12 to remove the fractions)
= 4:3.
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