Answer: the correct option is (C) x - 1.
Step-by-step explanation: We are given to select the correct binomial that is a factor of the following trinomial :
[tex]T=4x^2+20x-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To select the factor, we need to factorize expression (i). To factorize, we need two integers with sum 20 and product -96.
From (i), we have
[tex]T\\\\=4x^2+20x-24\\\\=4x^2+24x-4x-24\\\\=4x(x+6)-4(x+6)\\\\=(x+6)(4x-4)\\\\=4(x+6)(x-1).[/tex]
So, the factors of the given trinomial are 4, (x + 6) and (x - 1).
Since 4 and ( x + 6) are not in the options, so (x - 1), is the correct binomial.
Thus, (C) is the correct option.
Which statements are true about thecordered pair (7,19) and the system of equations 2x-y=-5
what is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6
a. -6
b. 7
c. x+2
d. 2x-3
Final answer:
The greatest common factor (GCF) of the numerator and denominator in the rational expression (7x+14)/(2x²+x-6) is x+2. Thus, option C is correct.
Explanation:
To find the greatest common factor (GCF) of the numerator and denominator of the given rational expression (7x+14)/(2x²+x-6), we need to factor both the numerator and the denominator separately.
For the numerator 7x+14, we can factor out a 7:
7x + 14 = 7(x + 2)
For the denominator 2x² + x - 6, we need to factor it as a quadratic expression. This can be done by finding two numbers that multiply to give -12 (the product of the coefficient of x² and the constant term) and add up to 1 (the coefficient of x). These numbers are 3 and -4, so the denominator can be factored as:
2x² + x - 6 = (2x - 3)(x + 2)
Now we can see that the common factor between the numerator and the denominator is x + 2. Therefore, the GCF is x + 2, which corresponds to option (c).
If 36 sqrt2 - 24 sqrt2 = sqrtN, what is N?
How many three-letter codes can we make using only vowels, a, e, i, o, or u?
Answer and explanation:
Given : Vowels a,e,i,o or u.
To find : How many three-letter codes can we make using only vowels ?
Solution :
1) If we assume that repetition is allowed then
The three letter code can form
[tex]5\times 5\times 5=125[/tex] ways
Number of three-letter codes can we make using only vowels is 125.
2) If we assume that repetition is not allowed then
The three letter code can form
[tex]5\times 4\times 3=60[/tex] ways
Number of three-letter codes can we make using only vowels is 60.
Consider a game in which a coin will be flipped three times. for each heads you will be paid $100. assume that the coin comes up heads with probability 4/5.
Let x ∼ bin(9, 0.4). find
a. p(x > 6)
b. p(x ≥ 2)
c. p(2 ≤ x < 5)
d. p(2 < x ≤ 5)
e. p(x = 0) f. p(x = 7) g. μx h. σ2 x
The question involves the properties of a binomial distribution with parameters 9 and 0.4. The properties asked can be calculated using binomial theory, allowing the probability of certain outcomes, the mean and variance of the distribution to be found.
Explanation:The question involves a binomial distribution denoted as x ∼ bin(9, 0.4), where 9 is the total number of trials and 0.4 is the probability of success. The distribution properties desired are:
c. p(2 ≤ x < 5): The probability that x takes a value between 2 and 5, which is found by adding up the probabilities p(x = 2), p(x = 3) and p(x = 4) in the binomial distribution.e. p(x = 0): This is the probability that there are 0 successes, given by (0.6)^9 in this case.f. p(x = 7): The probability of having 7 successes which can be calculated using binomial formula.g. μx: This is the expected value or mean of the distribution, which in binomial distribution is np, so μx = 9 * 0.4 = 3.6.h. σ2 x: This is the variance, calculated as np(1-p), hence σ2x = 9 * 0.4 * (1 - 0.4) = 2.16.Learn more about Binomial Distribution here:https://brainly.com/question/33656163
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Melinda has shown that a function, f(x), increases by 4 for every unit in the domain. What does this prove?
The function f(x) is an arithmetic sequence.
The function f(x) is a geometric sequence.
The function f(x) is not a sequence.
This does not prove anything.
Answer:-The function f(x) is an arithmetic sequence.
Explanation:-
Let [tex]a_1[/tex] be the initial value
According to the question
[tex]a_2=a_1+4[/tex]
[tex]a_3=a_2+4\\\Rightarrow\ a_3=(a_1+4)+4\\\Rightarrow\ a_3=a_1+4+4\\\Rightarrow\ a_3=a_1+2(4)\\\Rightarrow\ a_3=a_1+2\times4\\\Rightarrow\ a_3=a_1+(3-1)4[/tex] and so on
Thus, we can write a formula for the term n of an arithmetic sequence in the form:
[tex]a_n=a_1+(n-1)4[/tex]
where, n=1,2,3,4,....
4= common difference
Therefore, the function f(x) is an arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which each term increases or decreases by a constant number.Jerry's strips of dry meat joint sells of these two types of dry meat. he sells twice as many bags of dried beef as he does bags of dried turkey . His profit from the dryed beef is a 1.50 per bag while his profit for dryed turkey is a $2 per bag how many bags of each must he sell to profit for $ 500. please help
Where is the point of concurrency of the angle bisectors of a triangle?
A) outside the triangle
B) inside the triangle
C) on the triangle
Answer:
B) inside the triangle
Step-by-step explanation:
That point of concurrency is called the "incenter" as it is the center of the largest circle that can be inscribed in the triangle. It is always located inside the triangle.
Each angle bisector must be inside the triangle, so their point of intersection must be inside the triangle.
Final answer:
The point of concurrency of the angle bisectors of a triangle called the incenter, is always located inside the triangle.
Explanation:
The point of concurrency of the angle bisectors of a triangle is known as the incenter. This point is where all three angle bisectors of a triangle intersect, and it is always inside the triangle.
No matter what type of triangle it is—scalene, isosceles, or equilateral—the incenter is always located within the interior of the triangle, serving as the center of the triangle's incircle, which is a circle that is tangent to all three sides of the triangle. Thus , the correct option is B.
Please help me with questions 26 and 27
Make a box-and-whisker plot for the data. What is the upper quartile value? 56 32 48 52 51 53 48 38 35 42 40 46 54 50
Answer:
Step-by-step explanation:
The given data is:
56 32 48 52 51 53 48 38 35 42 40 46 54 50
In order to get the value of the upper quartile, first arrange he given data in ascending form, we get
32, 35, 38, 40, 42, 46, 48, 48, 50, 52, 53, 54, 56
The upper quartile is:48, 50, 52, 53, 54, 56
The value of upper quartile is given as:
[tex]\frac{52+53}{2}[/tex]
=[tex]\frac{105}{2}[/tex]
=[tex]52.5[/tex]
Thus, the value of the upper quartile will be 52.5.
What set of reflections would carry triangle ABC onto itself?
H + 9.7 = -9.7 what is this answer
EXPERTS/ACE/GENIUSES HELP PLZ!!:)
( only #2 )
Explain as well!! Best answer will get brainlist... but make ur answer short and sweet plz.
(a) Volume of 1st cup = (1/3)pi *(4/2)^2 * 8 = 32/3 pi in^3
scoops = (2000/3)pi / ( 32/3) pi = 2000/32 = 62.5 = 63
(b) Volume of 2nd cup = (1/3)pi *(8/2)^2 * 8 = 128/3 pi in^3
scoops = (2000/3)pi / ( 128/3) pi = 2000/128 = 15.625 = 16
Two years ago Carol's living expenses were $ 1200 $ 1200 per month. This year the same items cost Carol $ 1400 $ 1400 per month. What was the annual inflation rate for the past two years?
I need help please I’m confused
The ratio of boys to girls at the beach cleanup was 7:8. If there are 42 boys, how many girls are there?
that ratio means for every 7 boys there are 8 girls
so 42 boys / 7 = 6
now 6*8 = 48
there are 48 girls
At a concession stand, one person purchased 3 drinks and 3 soft pretzels for a total of $9.00. Another person purchased 4 drinks and 2 soft pretzels for a total of 8.50. What was the price of one soft pretzel
A machine that fills bottles with a beverage has a fill volume whose mean is 25.01 ounces, with a standard deviation of 0.02 ounces. a case consists of 24 bottles randomly sampled from the output of the machine. find the standard deviation of the total volume of the beverage in the case.
The standard deviation of the total volume of beverage in a case of 24 bottles, each with a standard deviation of 0.02 ounces, is approximately 0.098 ounces. This is calculated by multiplying the standard deviation of one bottle by the square root of the number of bottles in the case.
Explanation:The question involves finding the standard deviation of the total volume of beverage in a case of 24 bottles, given that each bottle has a fill volume with a mean of 25.01 ounces and a standard deviation of 0.02 ounces. To calculate the standard deviation of the total volume in the case, we multiply the standard deviation of a single bottle by the square root of the number of bottles in the case. This is because the standard deviation of the sum of independent random variables (in this case, the volume of each bottle) is equal to the square root of the sum of their variances.
Step-by-step Solution:
Standard deviation of one bottle = 0.02 ounces.
Number of bottles in a case = 24.
Total standard deviation = 0.02 ounces * √24.
Calculate the square root of 24, which is approximately 4.898.
Multiply the standard deviation of one bottle by this value to get the total standard deviation of the case: 0.02 * 4.898 = 0.098 ounces (approximately).
Therefore, the standard deviation of the total volume of beverage in a case of 24 bottles is approximately 0.098 ounces.
A farmer wants to fence in a section of land for a horse pasture. Fencing costs $29 per yard. How much will it cost to fence the pasture?
Final answer:
To find the cost of fencing a horse pasture, calculate the total length needed and multiply it by the cost per yard.
Explanation:
A farmer wants to fence in a section of land for a horse pasture. Fencing costs $29 per yard. How much will it cost to fence the pasture?
To calculate the cost of fencing the pasture, you need to determine the total length of the fencing needed in yards. Once you have the total length, you can multiply it by the cost per yard to find the total cost.
Example:
Assuming the total length of fencing needed is 100 yards.Multiply the total length by the cost per yard: 100 yards x $29 = $2900.Therefore, it will cost $2900 to fence the pasture.A department store has average daily sales of $29,876.76. The standard deviation of sales is $1000. On Tuesday, the store sold $34,893.71 worth of goods. Find Tuesday's z score.
Answer with explanation:
Mean[tex]\Bar X[/tex] = $ 29,876.76
Standard Deviation[tex]\sigma[/tex] = $1000
[tex]\mu[/tex] =$34,893.71
Z-Score Formula
[tex]Z_{score}=\frac{\Bar X -\mu}{\sigma}\\\\Z_{score}=\frac{29876.76-34893.71}{1000}\\\\=\frac{-5016.95}{1000}\\\\=-5.01695\\\\=-5.02[/tex]
So, Tuesday Z-Score= -5.02
Two secant segments intersect outside a circle as shown. What is the value of x?
Please help me with questions 24, 25, 26
How many numbers must be selected from the set $\{1, 3, 5, 7, 9, 11, 13, 15\}$ to guarantee that at least one pair of these numbers add up to 16?
Find The Equation Of The Line below
the number of painters p employed to paint a building is inversely proportional to the time taken to paint the building b which equation best models the number of painters required to finish the painting
Answer:
C
Step-by-step explanation:
Hudson worked two jobs last summer to start saving for a car. He mowed lawns during the day and worked at a pizza place in the evenings. In one month, Hudson earned a total of $1,400. If he earned $360 more at the pizza place than mowing lawns how much did he earn at each job?
Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.
What is a system of linear equation?A System of Linear Equations is when we have two or more linear equations working together.
Given that, Hudson mowed lawns during the day and worked at a pizza place in the evenings. Hudson earned a total of $1,400. also he earned $360 more at the pizza place than mowing lawns
Let he earn x at deliveries and y at mowing,
Therefore, establishing a system of equations,
x+y = 1400
x-y = 360
Adding both the equations,
2x = 1760
x = 880
y = 1400-880
y = 520
Hence, Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.
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A basketball player makes 60% of his shots from the free throw line. suppose that each of his shots can be considered independent and that he throws 4 shots. let x = the number of shots that he makes. what is the probability that he makes all 4 shots?
Using the binomial distribution, it is found that there is a 0.1296 = 12.96% probability that he makes all 4 shots.
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For each throw, the player either makes it or misses it. The probability of making each throw is the same, independent of other throws, thus, the binomial distribution is used to solve this question.
Binomial probability distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, with X having two possible outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success on a single trial.
Makes 60% of the shots, thus [tex]p = 0.6[/tex]4 shots, thus [tex]n = 4[/tex].The probability of making all of them is P(X = 4), thus:[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]
0.1296 = 12.96% probability that he makes all 4 shots.
A similar problem is given at https://brainly.com/question/9000732
What are the solutions to the equation? x2−12x+36=4 Enter your answers in the boxes. x1= x2=
Answer:
4 and 8
Step-by-step explanation:
x1 = 4
x2 = 8
Which relation defined by a set of ordered pairs is a function?
A {(2, 6), (3, 6), (4, 5), (6, 6), (6, 7)}
B {(6, 2), (6, 3), (5, 4), (6, 6), (7, 6)}
C {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)}
D {(–2, 6), (3, –6), (–4, 5), (6, –6), (6, –7)}
Answer:
Step-by-step explanation: