complete the steps to solve the polynomial equation x3-21x=-20 according to the rational root theorem, which number is a potential root of the polynomial?
What is the solution to this equation? -4x + 2 = 26 A. x = 7 B. x = 6 C. x = -7 D. x = -6
George has $23 to spend on art supplies he wants to buy markers papers and glue if the total cost of markers and papers is more than $14 which inequality represents the dollar amount P George can spend on glue
What is the probability of flipping a coin six times in a row and getting three heads and three tails?
Final answer:
The probability of flipping a coin six times and getting exactly three heads and three tails is calculated using the binomial formula and is found to be 31.25%.
Explanation:
The probability of flipping a coin six times and getting exactly three heads and three tails can be calculated using the binomial probability formula, which is P(x; n, p) = (n choose x) * p^x * (1-p)^(n-x), where 'n' is the number of trials, 'x' is the number of successes, and 'p' is the probability of success on any given trial.
In this instance, since we are flipping a fair coin, the probability 'p' of getting heads (success) on any single flip is 0.5. We want to find the likelihood of getting 'x' = 3 heads out of 'n' = 6 flips. Therefore, the equation becomes:
P(3; 6, 0.5) = (6 choose 3) * 0.5^3 * 0.5^(6-3)
The combination (6 choose 3) calculates the number of ways to choose 3 successes (heads) from 6 trials, which is 20. Plugging these values into the equation gives:
P(3; 6, 0.5) = 20 * (0.5^3) * (0.5^3) = 20 * (0.125) * (0.125) = 20 * 0.015625
This results in a probability of 0.3125, or 31.25%.
Therefore, the chance of flipping a coin six times and getting three heads and three tails is 31.25%.
If you earn 30K a year and are taxed 10% what's your gross income and net income
A scientific journal recently reported that there are currently 2,400 black rhinos in the world. The population of black rhinos is declining at a rate of 10% each year. Which of the following graphs represents the population of black rhinos, y, after x years?
Answer: the answer is B
Step-by-step explanation:
Answer:
The answer would be B
Step-by-step explanation:
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Elias purchases a home for $38,900. The value of the home, in thousands of dollars, since his purchase is shown in the table. Find an exponential function that models the data. Round numerical values to the nearest hundredth. Let x be the number of years since the purchase. The function f(x) =()x models the data. Use the model to predict the home’s value. After 12 years, the home’s value will be about $thousand. After 35 years, the home’s value will be about $thousand.
Answer:
f(x)=39.59
(1.09)
After 12 years: 111
After 35 years: 808
The exponential function models the data would be f(x) = 39.59 (1.09). After 12 years, the home’s value will be about $111 thousand and After 35 years, it will be about $808 thousand.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Elias purchases a home for $38,900.
Let x be the number of years since the purchase. The function f(x) =()x models the data.
f(x) = 39.59 (1.09)
by using the model to predict the home’s value.
After 12 years, the home’s value will be about $
111 thousand.
After 35 years, the home’s value will be about $
808 thousand.
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Party favors are on sale for $2.40 each. You have $380 to spend on the decorations and gifts, and you have already spent $270 on decorating. Write and solve an inequality to find the number of party favors you can buy.
Hence, the number of party favors you can buy is $[tex]45[/tex].
What is inequality?
An inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Here given that,
Party favors are on sale for $[tex]2.40[/tex] each. You have $[tex]380[/tex] to spend on the decorations and gifts, and you have already spent $[tex]270[/tex] on decorating.
So,
[tex]380-270=[/tex] $[tex]110[/tex]
To find the number of party favors you can buy, we divide $[tex]110[/tex] by the favors that are on sale for $[tex]2.40[/tex] is
[tex]\frac{110}{2.40}[/tex] = $[tex]45[/tex]
Hence, the number of party favors we can buy is $[tex]45[/tex].
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Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 10% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female. The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is . NextReset
Answer: There is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.
Step-by-step explanation:
Let E₁ be the event that members prefer swimming on weekends.
Let E₂ be the event that members prefer swimming on weekdays.
Let A be the event that the members are female.
Probability that members prefer swimming on weekends P(E₁) = 25%
Probability that members prefer swimming on weekdays P(E₂)= 75%
Probability that members prefer swimming on weekends and are female PA∩E₁)= 10%
Probability that members prefer swimming on weekdays and are female P(A∩E₂) = 55%
Using Conditional theorem, we will find the probability that a member is female given that the the person prefers swimming on weekends.
[tex]P(A\mid E_1)=\dfrac{P(A\cap E_1)}{P(E_1)}\\\\P(A\mid E_1)=\dfrac{10}{25}\\\\P(A\mid E_1)=0.4\\\\P(A\mid E_1)=0.4\times 100\%=40\%[/tex]
Hence, there is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.
The volume v of a right circular cone of radius r and height h is given by v = 1/3 pi r^2 h. suppose that the height decreases from 20 in to 19.95 in and the radius increases from 4 in to 4.05 in. compare the change in volume of the cone with an approximation of this change using a total differential.
Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that's also compounded semiannually at 10%. At the end of six years, what's the balance in Merle's account?
Answer:
93,600.16
Step-by-step explanation:
Find the annual interest rate.
I = $54, P = $900, t = 18 months
We have been given that
[tex]I = $54, P = $900, t = 18 \text{ months
}[/tex]
We know the formula,
[tex]I=Prt[/tex]
On substituting the given values, we get
[tex]54=900\cdot r\cdot \frac{18}{12}\\\\r=\frac{54\cdot 12}{900\cdot 18}\\\\r=\frac{1}{25}\\\\r=0.04\\\\r=4\%[/tex]
The annual rate interest is 4%
Mrs. Hicks has 35 students in her chemistry class. The ratio of girls to boys is 3:4. How many girls does she have in her class? Let both antecedents represent girls and let both consequence represent total students.
im having trouble with this word problem. A train travels 160 km in the same time that a plane covers 720 km. if the speed of the plane is 20 km per hour less than 5 times the speed of the train, find both speeds. Not sure how to solve.
The speed of the train is 40 km/h, and the speed of the plane is 180 km/h.
To solve the word problem regarding the speeds of a train and a plane, we first let the speed of the train be x km/h. According to the problem, the plane's speed is 20 km/h less than 5 times the speed of the train, which can be expressed as 5x - 20 km/h. Since they both travel the same amount of time, we can set up an equation based on their speeds and distances traveled:
Time taken by the train = Distance / Speed of the train = 160 / x
Time taken by the plane = Distance / Speed of the plane = 720 / (5x - 20)
Since the time is the same for both:
160 / x = 720 / (5x - 20)
Cross-multiply to solve for x:
160(5x - 20) = 720x
800x - 3200 = 720x
80x = 3200
x = 40
A helicopter is hovering 110 feet in the air over a landing pad. If a man sees the helecopter at an angle of elevation of 29°, which of the following shows how far the man is from the helicopter landing pad?
Answer:
198.44 feet
Step-by-step explanation:
a juice can is shaped like a cylinder ]. it is 12 centimeters wide and 16 centimeters tall. find its volume to the nearest whole number . use 3.14
To find the volume of the cylinder-shaped juice can, calculate using the formula V = π r² h with the radius being half of the can's width and the given height. The volume is found to be approximately 1804 cm³ when rounded to the nearest whole number.
Calculating the Volume of a Cylinder:
To calculate the volume of a cylinder, you should use the formula V = π r² h. First, we need to determine the radius of the juice can. Since it is given that the can is 12 centimeters wide, that means the diameter is 12 centimeters, and therefore, the radius (r) is half of that, which is 6 centimeters. We also have the height (h) of the can, which is 16 centimeters. Plugging these values into the formula gives us:
V = 3.14 × 6² × 16
Now, we calculate:
V = 3.14 × 36 × 16
V = 3.14 × 576
V = 1803.84 centimeters cubed (cm³)
When we round this to the nearest whole number, the volume of the juice can is approximately 1804 cm³.
use multiplication to create an equivalent fraction 6/5
In mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? Explain.
The factorization of x2 + 3x – 4 is modeled with algebra tiles.What are the factors of x2 + 3x – 4?
The factors of x^2 + 3x – 4 are (x + 4) and (x - 1), found by determining the factors of -4 that add up to 3.
Explanation:The factors of x2 + 3x – 4 can be found using the method of factoring quadratics. To factor this quadratic expression, we look for two numbers that multiply to give the constant term (-4) and add to give the coefficient of the middle term (3). Those numbers are 4 and -1, as 4 × -1 = -4 and 4 + (-1) = 3. Therefore, the expression can be factored into (x + 4)(x - 1).
Visualizing with algebra tiles or drawing on the concepts of geometric representation of polynomials, we can understand that this factoring corresponds to breaking down the area of a rectangle (represented by x2 + 3x – 4) into two smaller rectangles whose dimensions give the factors (x + 4) and (x - 1).
what is domain of g(x)= square root plus one
How much fruit juice (100%) is equivalent to 1 cup of fresh fruit?
a. 1/4 cup
b. 1 cup
c. 1 1/2 cups
d. 2 cups
e. 1/2 cup?
1 cup of fruit juice is equivalent to 1 cup of fresh fruit.
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 cup of fresh juice.
Fresh juice and 1 cup of fresh fruit are the same.
So,
Fresh juice = 1 cup
Thus,
1 cup of fruit juice is equivalent to 1 cup of fresh fruit.
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Tamar is thinking of a number in the hundredths. Her number is greater than 0.8 and less than 0.9. The greatest digit in the number is in the hundredths place. What number is Tamar thinking of? Explain.
Answer:
Therefore, Tamar is thinking of the number 0.89.
Step-by-step explanation:
Let x be the number Tamar is thinking of.
0.8 < x < 0.9
Since the greatest digits in the hundreths is greater digit, and there's an "8" in the tenths, the number can described as:
0.88< x < 0.9
There is only a single number in the hundredths that would fit the expression above, and that is 0.89.
Therefore, Tamar is thinking of the number 0.89.
Answer:
Let the be the number Tamar is thinking of. So from the above question,
0.8 < t < 0.9
Note that the greatest digits in the hundreths is greater digit, and there's an "8" in the tenths, the number can described as:
0.88< x < 0.9
There is only a number in the hundredths that would fit and that is 0.89.
Therefore, t = 0.89.
Step-by-step explanation:
Which function has a simplified base of 4 ^3 sqrt 4?
Final answer:
The function in question involves simplifying the base 4^3 multiplied by the square root of 4. Through understanding exponent rules and square root operations, this simplifies to 128, demonstrating the importance of algebraic fundamentals.
Explanation:
Understanding the Simplified Base of 4^3 \sqrt{4}
The question asks which function has a simplified base of 4^3 \sqrt{4}. Simplifying this expression requires understanding of exponent rules and square roots. The cube of 4, or 4^3, equals 64. The square root of 4 is 2, hence \(\sqrt{4}\) simplifies to 2. Combining these, we see that 4^3 multiplied by \(\sqrt{4}\) equals 64 * 2 = 128.
To put this into perspective, we would express the original operation as 4 raised to the power of 3 and then multiplied by the square root of 4, which can also be depicted as 4^3 * 2 since \(\sqrt{4} = 2\). Thus, the simplified base is not a direct function but rather an arithmetic operation resulting in 128.
It's crucial to note that while operations like these involve basic principles of exponents and roots, each step must be carefully followed to ensure accuracy. The concept behind these operations is grounded in the mathematical principles of handling integers, powers, and roots, highlighting the importance of solid fundamentals in algebra.
What is the fractional notation for 0.097
I'm barely on question 13 out of 25, need to speed up can someone help out
Two boxes contained 155 lb of flour. If you take 20 lb from the first and add it to the second, the first box will contain 12/19 of what is now in the second. What amount of flour was originally in each box?
Answer:
it is 80 and 75
Step-by-step explanation:
I go to RSM and when I answered this answer it said that it was correct
if f(x) = 2x+1/x-4, what is the value of f^-1 (3)?
As per the inverse of a function, the value of [tex]f^{-1}(3)[/tex] is 13.
What is the inverse of a function?"An inverse function is defined as a function, which can reverse into another function."
The given function is
[tex]f(x) = \frac{2x+1}{x-4}[/tex]
⇒ [tex]y = f(x) = \frac{2x+1}{x-4}[/tex]
⇒ [tex]xy - 4y = 2x + 1[/tex]
⇒ [tex]xy - 2x = 4y + 1[/tex]
⇒ [tex]x(y - 2)= 4y + 1[/tex]
⇒ [tex]x = \frac{4y+1}{y-2}[/tex]
⇒ [tex]f^{-1}(x) = \frac{4y+1}{y-2}[/tex]
Now, [tex]f^{-1}(3) = \frac{4(3)+1}{3-2} = (12+1) = 13[/tex]
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[1] seven conference calls are scheduled this morning between 10 and 11
a.m. [2] as a general rule, the company limits the number of conference calls to three per hour. [3] in the future, we should be more careful about scheduling calls. which sentence contains a flabby expression
Final answer:
The flabby expression is found in the sentence 'In the future, we should be more careful about scheduling calls,' which can be more concisely stated as 'In the future, we should schedule calls more carefully.'
Explanation:
The sentence that contains a flabby expression is: "In the future, we should be more careful about scheduling calls."
Flabby expressions are phrases or sentences that are wordy and can be expressed more concisely without losing their meaning. The sentence could be more directly stated as "In the future, we should schedule calls more carefully." By removing unnecessary words, the sentence becomes clearer and more to the point. Flabby expressions are usually considered poor writing style because they can make sentences needlessly long and obscure the main point.
The circumference of a circle is 10π cm. What is the Radius of the circle? A) 4 cm B) 5 cm C) 10 cm D) 20 cm
ASAP
Find the difference 51/4 - 2 3/4