Answer:
option 2
2x²- x - 1
Step-by-step explanation:
We are given points: (-1,2), (0,-1) and (2,5)
Substitute each point one by one in the quadratic equation to check if the quadratic equation contains all points mention.
2) f(x) = 2x²- x - 1
Point(-1,2)
f(-1) = 2(-1)² -(-1) -1
2 = 2 + 1 - 1
2 = 2
Point(0,-1)
f(0) = 2(0)² -(0) -1
-1 = 0 - 0 -1
-1 = -1
Point(2,5)
f(2) = 2(2)² -(2) -1
5 = 8 - 2 -1
5 = 6 - 1
5 = 5
Find all solutions of the given equation. (enter your answers as a comma-separated list. let k be any integer. round terms to two decimal places where appropriate.) cos θ + 1 = 0
Answer:
θ = 6.28k +3.14
Step-by-step explanation:
cos(θ) is -1 for θ = π and multiples of 2π added to that.
___
The answer above rounds π and 2π as requested by the problem statement. Those values are only valid for small values of k. (I suppose it might be reasonable to argue that no rounding is appropriate.)
Simplify −2√45+3√3+2√3 Question 4 options: A.−6√5+6√3 B.−2√5+6√3 C.−6√5+5√3 D.−18√5+5√3
Answer:
C
Step-by-step explanation:
You're probably stuck by this problem. Let's rewrite the problem.
-2√45 + 3√3 + 2√3The first part of simplifying the expression is to simply the radicals. Since 45 has a factor which is a square, let's simplify.
-2√45 = -2√5 × 9 = (-2 × 3)√5 = -6√5Let's just continue simplifying and dissect the 3√3 + 2√3.3√3 + 2√3 = 5√3...The answer is...5√3 - 6√5 or -6√5 + 5√3, CRewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)
Answer:
(sin^2 w + 1) / cos w.
Step-by-step explanation:
Note: sec w = 1 / cos w and csc w = 1/ sin w.
So we have:
(sec w(1 + csc^2 w)) / (csc^2 w)
= 1/cos w ( 1 + 1/ sin^2 w) / (1 / sin^2 w)
= ( 1/ cos w + 1 / sin^2 w cos w) * sin^2 w
= sin^2 w/ cos w + sin^2 w / (sin^2 w cos w)
= sin^2 w / cos w + 1 / cos w
= (sin^2 w + 1) / cos w.
WHICH OF THE FOLLOWING DESCRIBES THE FUNCTION -X^4+1?
Answer:
B
Step-by-step explanation:
The function -x^4 + 1 is a polynomial graph. As such it has specific characteristics or behavior you can expect to see:
It's leading coefficient is -1. This means the graph changes direction. Both ends of this graph face down into negative infinity.Its degree is 4 meaning it is an even graph. This means both ends end the same way and NOT opposite directions.In conclusion, this graphs has ends which end the same direction and both face down.
I need help with this problem
Answer:
h = 15Step-by-step explanation:
The formula of an area of a parallelogram:
[tex]A=bh[/tex]
b - side
h - height
We have b₁ = 18 and h₁ 10 and b₂ = 12.
[tex]b_1h_1=b_2h[/tex]
Substitute:
[tex]12h=(18)(10)[/tex]
[tex]12h=180[/tex] divide both sides by 12
[tex]h=15[/tex]
The Garcia family started the day with 2 gallons of milk. They drank 1 quart of milk for breakfast and 3 pints for lunch.How many pints of milk did the Garcia family have left after lunch.
Answer:
11 pt
Step-by-step explanation:
Convert all volumes to pints
Starting volume
2 gal × 4 qt/1 gal = 8 qt
8 qt × 2 pt/1 qt = 16 pt
Breakfast
1 qt × 2 pt/1 qt = 2 pt
Stating volume = 16 pt
Less breakfast = -2 pt
Less lunch = -3 pt
After lunch = 11 pt
The Garcia family had 11 pt of milk left after lunch.
Which of the following is the correct radical form of this expression
ANSWER
The correct answer is A.
EXPLANATION
The given expression is
[tex]( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) ^{ \frac{5}{6} } [/tex]
Recall that:
[tex] {a}^{ \frac{m}{n} } = (\sqrt[n]{a} ) ^{m} [/tex]
For the given expression,
[tex]m = 5[/tex]
[tex]n = 6[/tex]
and
[tex]a = \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} [/tex]
We substitute all these values to obtain the radical form:
[tex]( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) ^{ \frac{5}{6} } = ( \sqrt[6]{( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) })^{5} [/tex]
The correct choice is A.
Stretch your thinking.Rewrite this using the word fewer.Carey reads 10 more pages than lucey
Answer:
Lucy reads 10 fewer pages that Carey
Step-by-step explanation:
The first sentence reads as Carey having more, so Lucy has fewer,
Rewriting it using fewer means that Lucy will be the main subject of the sentence, so Lucy reads 10 fewer pages that Carey is the sentence you want
Evaluate the log without a calculator ( Show your work )
[tex]log_{2} \sqrt[5]{16}[/tex]
Answer: x = 1/5
//Hope it helps.
Answer:
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}[/tex]
Step-by-step explanation:
The given logarithmic expression is:
[tex]\log_2(\sqrt[5]{16} )[/tex]
We rewrite the radical as an exponent to obtain;
[tex]\log_2(\sqrt[5]{16} )=\log_2(16^{\frac{1}{5}} )[/tex]
Recall and use the power rule; [tex]\log_a(M^n)=n\log_a(M)[/tex]
[tex]\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(16 )[/tex]
We write 16 as an index number to base 2.
[tex]\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(2^4)[/tex]
We apply the power rule again;
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}\log_2(2)[/tex]
We simplify to get;
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}(1)[/tex]
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}[/tex]
plz help me
The table shows the change in the annual sales turnover of a company in millions of dollars, S(x), where x represents the years since the company was founded.
x S(x)
1 $495
3 $598.95
5 $724.73
7 $876.92
9 $1,061.08
What is the predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11]?
A.
$184.15 per year
B.
$111.42 per year
C.
$222.83 per year
D.
$92.08 per year
Answer:
its going to be d
Step-by-step explanation:
Answer:
The correct option is B.
Step-by-step explanation:
The general exponential regression model is
[tex]y=ab^x[/tex]
Using regression tool the exponential regression model for the given data is
[tex]S(x)=449.9999(1.09999)^x[/tex]
[tex]S(x)=450(1.1)^x[/tex]
The value of function at x=9 is
[tex]S(9)=450(1.1)^9=1061.07646[/tex]
The value of function at x=11 is
[tex]S(11)=450(1.1)^{11}=1283.90252[/tex]
The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is
[tex]m=\frac{S(11)-S(9)}{11-9}[/tex]
[tex]m=\frac{1283.90252-1061.07646-}{2}=111.413\approx 11.42[/tex]
The average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is 11.42. Therefore the correct option is B.
Tell which statement is the best estimate for the division problem 185 divide 61
Answer:
whichever is closest to 3.032787
Determine whether or not the given procedure results in a binomial distribution. if not, identify which condition is not met. spinning an american roulette wheel 74 times and recording the number the ball lands on.
Answer:
This procedure does not result in a Binomial distribution.
Step-by-step explanation:
In a Binomial distribution there are only 2 outcomes in each trial.. In the roulette experiment there are more than 2 possible outcomes for each trial so this condition is not met.
The spinning of an American roulette wheel 74 times doesn't result in a binomial distribution because there are more than two possible outcomes and thus the second condition - only two possible outcomes for each trial - for a binomial experiment is not met.
Explanation:The procedure of spinning an American roulette wheel 74 times and recording the number the ball lands on does not result in a binomial distribution. This is because it does not meet all the conditions necessary for a statistical experiment to be classified as a binomial experiment.
For an experiment to be classified as a binomial experiment, it must meet the following conditions:
There must be a fixed number of trials.There are only two possible outcomes for each trial, termed as success and failure.The trials are independent and must be repeated under identical conditions.Although the procedure meets the condition of having a fixed number of trials, it fails on the second and third conditions. On a roulette wheel, there are 38 possible outcomes, not two, so it fails the condition of only having two outcomes (success or failure). Moreover, the outcome of each spin is independent but the conditions are not identical, as the chance of landing on any particular number is not the same for every spin (if we consider landing on a specific number as 'success').
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For 1 and 2, state whether the numbers are parameters or statistics, and use the appropriate notation to describe each number. 1. a random sample of female college students has a mean height of 64.5 inches, which is greater than the 63-inch mean height of all adult american women.
Answer:
x-bar 64.5 is a statistic because it describes a sample.
Mu 63 is a parameter because it describes a population.
The symbol for mu is a Greek m
Step-by-step explanation:
Final answer:
A random sample mean, like the 64.5 inches height for female college students, is a statistic denoted as \( \bar{x} \), while the mean height of all adult American women is a parameter denoted as \( \mu \). Determining whether a number is a parameter or statistic informs how it is used in hypothesis testing and confidence interval construction.
Explanation:
When identifying whether the numbers are parameters or statistics, it's important to distinguish between data collected from a population or a sample. In the scenarios mentioned, such as when a random sample of female college students has a mean height of 64.5 inches, we are dealing with a statistic. This is because it is a measure obtained from a sample. The appropriate notation for this sample mean would be \( \bar{x} \). This contrasts with the information such as the mean height of all adult American women, which is a parameter because it relates to the entire population. The notation for a population mean is \( \mu \). Considering other examples provided, when we calculate a p-value or when we undertake a study and calculate the difference in mean heights between groups, we are dealing with statistics.
In practice, the difference between statistics and parameters is essential for hypothesis testing, constructing confidence intervals, and making inferences about the population based on sample data. For example, if the p-value is close to zero in a test related to the mean height of high school basketball players, it suggests that there is strong evidence against the null hypothesis \( H_0 \), which posits no effect or no difference. The alternative hypothesis \( H_1 \) would be that there is a significant difference.
Given a spherical weather balloon with a volume of 36π cubic feet. What is the diameter, in feet, of the weather balloon?
A) 3
B) 6
C) 9
D) 12
Answer:
option B [tex]D=6\ ft[/tex]
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]V=36\pi\ ft^{3}[/tex]
substitute and solve for r
[tex]36\pi=\frac{4}{3}\pi r^{3}[/tex]
simplify
[tex]27=r^{3}[/tex]
[tex]r=3\ ft[/tex]
Find the diameter
[tex]D=2r=2(3)=6\ ft[/tex]
Answer:
b)6
Step-by-step explanation:
A shampoo company begins selling a new bottle of shampoo that is advertised as 25% more shampoo than the old bottle. If the new bottle holds 15 ounces of shampoo, how much did the old bottle hold?
15 - 25% = 14.47 ounces of shampoo
The original shampoo bottle held 12 ounces before the 25% increase to 15 ounces. For the tile cleanser, the percent by mass of HCl is calculated to be 14.84%. Discussions of consumer product concentrations, like laundry detergent costs per ounce, often involve linear relationships and predictive models.
The question requires understanding percent increase and how to calculate the original amount given the increased quantity. To find the original volume of the shampoo bottle before the 25% increase, we set up the equation where the original volume (V) times 1.25 (to represent the 25% increase) equals the new volume of 15 ounces:
V x 1.25 = 15 ounces
To solve for V, we divide both sides of the equation by 1.25:
V = 15 ounces / 1.25
V = 12 ounces
Therefore, the old bottle held 12 ounces of shampoo.
To address another concept related to consumer products, the question on mass percentage, namely the percent by mass of HCl in a tile cleanser, also represents a common mathematical calculation in consumer product information. The calculation is as follows:
Percent by mass = (mass of solute / total mass of solution) x 100%
Percent by mass of HCl = (135 g / (135 g + 775 g)) x 100%
Percent by mass of HCl = (135 g / 910 g) x 100%
Percent by mass of HCl = 14.84%
Thus, the bottle of tile cleanser has 14.84% by mass of HCl.
When discussing the cost per ounce of laundry detergent in different sizes, such as a 40 oz. size or a 90 oz. size, the concept of linear relationships may be explored, as well as the possibility of identifying outliers or considering the validity of predictive models like the least-squares line.
A recipe calls for 4 cups of strawberries for every 6 cups of whipped topping. If gary uses 54 cups of whipped topping how many cups of strawberries does he need?
Answer:
36 cups
Step-by-step explanation:
If you notice, 6 times 9 is 54. So, 4 times 9 is 36. You need 36 cups of strawberries!
Hank and Debra each one two milking cows. One day, they Milked their cows and compared the amount of milk the cows produced in that day
Answer:
it would be great if you provided a question here..!
Step-by-step explanation:
There are 10 cards. Each card has one number between 1 and 10, so that every number from 1 to 10 appears once. In which distributions does the variable X have a binomial distribution? Select each correct answer. When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen. When a card is chosen at random without replacement three times, X is the number of times an even number is chosen. When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen. When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen.
Answer:
When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen; When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.
Step-by-step explanation:
In a binomial distribution, there are only two outcomes, or outcomes that can be reduced to 2. In the first choice, we either draw a prime number or do not draw a prime number. In the third choice, we either draw a 3 or do not draw a 3.
There must be a fixed number of trials. In the first choice, we have 5 trials; in the third option, we have 6 trials.
The trials must be independent of each other. Since the cards in the first and third options are drawn with replacement, the outcome of one trial does not influence the probability of the next trial.
The probability must be the same for every trial. This is true of the first and third options.
Answer:
Prime And 3 is choosen
Step-by-step explanation:
As an estimation we are told ?3 is €4. Convert €83.60 to pounds. Give your answer rounded to 2 DP.
Answer:
€83.60 = £62.70
Step-by-step explanation:
£3/€4 = £x/€ 83.60
¾ = x/83.60
Multiply each side by the lowest common denominator (4 × 83.60)
3 × 83.60 = 4x
Divide each side by 4
x = (3 × 83.60)/4 = £62.70
∴ €83.60 = £62.70
(The conversion factor is out of date. The current conversion factor is closer to £6 = €7.)
Using the given exchange rate, we set up a conversion equation and solve for the unknown variable. We find that €83.60 is roughly equivalent to 62.86 pounds.
Explanation:Based on the given exchange rate, 1 pound (£) is equivalent to 1.33 Euros (€). Therefore, to convert €83.60 to pounds, we should do the following:
Set up the conversion ratio: 1.33 €/£ = 83.60 €/x £To solve for x (the value in pounds), cross-multiply: 1.33x = 83.60Divide both sides by 1.33: x = 83.60/1.33Rounding off to two decimal places, x = 62.86 £Therefore, €83.60 is approximately equivalent to 62.86 pounds.
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Please answer this question, only if you know the answer! Will give brainliest!
Answer:
Because point P is not the midpoint of OQ.
Step-by-step explanation:
The circle center is found at the intersection of the perpendicular bisectors of any two chords. Segment PC is perpendicular to OQ, but does not bisect it. Hence, point C cannot be the circle center.
Jody practiced a piano piece for 500 seconds bill practiced a piano piece for 8 minutes who practiced longer explain
Answer:
Jody
Step-by-step explanation:
You can either convert 500 seconds to minutes or 8 minutes to seconds to compare. I'll do both.
There is 60 seconds in a minute. To find the total minutes of 500 seconds, divide 500 by 60 → 8.3, which means that Jody practiced for 8.3 minutes.
To find the total seconds of 8 minutes, multiply 60 seconds per minute by 8 minutes → 60 * 8 = 480 seconds which means that Bill practiced for 480 seconds.
Now you can compare. Jody practiced for 500 seconds, or 8.3 minutes. Bill practiced for 480 seconds, or 8 minutes. Jody practiced longer.
A betting company wishes to sell 5000 tickets 50 of which will win prizes. I.) A students decided to buy 200 tickets. Let X be the number of tickets that win a prize. Write the probability distribution of X and give its mean. Ii.) Using a Poisson approximation for the distribution of X find the probability of at least three tickets winning a prize. Iii.) Calculate the number of tickets that should be bought so as the probability of at least one winning a prize is 90%
Answer:45000,000,000,000
Step-by-step explanation:you just have to times it
A square pyramid and a cone have the same base area. The volume of the cone is 100cm^3 , and the height of the cone is 15 cm. The height of the square pyramid is 24 cm. Find the volume of the square pyramid to the nearest whole unit.
Answer:
160 cm³
Step-by-step explanation:
1. Calculate the base area of the cone
The volume for the volume (V) of a cone is
V = ⅓Ah
Data:
V = 100 cm³
h = 15 cm
Calculation:
100 = ⅓ A× 15
100 = 5A
A = 100/5 = 20 cm²
2. Volume of Pyramid.
The volume for the volume (V) of a square pyramid is
V = ⅓Ah
Data:
A = 20 cm²
h = 24 cm
Calculation:
V = ⅓× 20× 24 = 160 cm³
The volume of the square pyramid is 160 cm³.
Thirty Mercedes and Audi participated in a 30 mile race. The average driving speed of the Mercedes and Audi were recorded. A random sample (Sample 1) of the Mercedes's average driving speed (km/h) is: 120, 142, 142, 165, 132, 130, 156, 136, 167, 139, 144. A random sample (Sample 2) of the Audi's average driving speed (km/h) is: 112, 145, 146, 165, 163, 141, 112, 134, 113, 114, 125. What is the median of Sample 1? What is the median of Sample 2?
Answer:
Median for sample 1 = 142
Median for sample 2 = 134
Step-by-step explanation:
For Sample 1:
For finding median, the data is first arranged into ascending or descending order. We are arranging the data in ascending order.
120, 130, 132, 136, 139, 142, 142, 144, 156, 165, 167
The formula for calculating the term which will be median is:
Median= ((n+1)/2)
Here in sample 1, n=11
So, putting n=11 in the formula
= ((11+1)/2)
= (12/2)
=6th term
The sixth term is 142, so
Median of sample 1=142
For Sample 2:
For finding median, the data is first arranged into ascending or descending order. We are arranging the data in ascending order.
112, 112, 113, 114, 125, 134, 141, 145, 146, 163, 165
The formula for calculating the term which will be median is:
Median= ((n+1)/2)
Here in sample 2, n=11
So, putting n=11 in the formula
=((11+1)/2)
=(12/2)
=6th term
The sixth term is 134, so
Median of sample 2=134
Please answer this question, will give brainliest!
See the attached picture:
Solve for x.
x2−9=16
Enter the solutions for the equation in the boxes.
x = ___ or x = ___
The answer will be
x=5 or x=-5
hope this help
Please help me quickly!
Select all of the following true statements if R = real numbers, Z = rational numbers, and W = {0, 1, 2, ...}.
WZ
RZ
-1 W
R
{0, 1, 2, ...} W
0 Z
Answer:
We can start solving this problem by first identifying what the elements of the sets really are.
R is composed of real numbers. This means that all numbers, whether rational or not, are included in this set.
Z is composed of integers. Integers include all negative and positive numbers as well as zero (it is essentially a set of whole numbers as well as their negated values).
W on the other hand has 0,1,2, and onward as its elements. These numbers are known as whole numbers.
W ⊂ Z: TRUE. As mentioned earlier, Z includes all whole numbers thus W is a subset of it.
R ⊂ W: FALSE. Not all real numbers are whole numbers. Whole numbers must be rational and expressed without fractions. Some real numbers do not meet this criteria.
0 ∈ Z: TRUE. Zero is indeed an integer thus it is an element of Z.
∅ ⊂ R: TRUE. A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition (since NONE of its elements are not an element of R).
{0,1,2,...} ⊆ W: TRUE. The set on the left is exactly what is defined on the problem statement for W. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be equal to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).
-2 ∈ W: FALSE. W is just composed of whole numbers and not of its negated counterparts.
Step-by-step explanation:
Certain elements and sets are examined for their relationships with the sets of real numbers, integers, and whole numbers; identifying which elements belong to which sets and if one set is a subset of another.
When comparing different sets of numbers, we analyze whether one set is a subset of another and whether certain elements belong to specific sets. The given question involves the sets R (real numbers), Z (integers), and W = {0, 1, 2, ...}, also known as the set of whole numbers or non-negative integers.
→ W ⊂ Z: This is true because all elements of W are non-negative integers, which are a subset of Z, the set of all integers including negative, zero and positive whole numbers.
→ R ⊂ W: This is false because the set of real numbers includes irrational numbers as well as negative numbers, which are not included in W.
→ 0 ∈ Z: This is true because zero is an integer and, therefore, is an element of Z.
→ ∅ ⊂ R: This is true because the empty set is a subset of all sets, including the set of real numbers.
→ {0, 1, 2, ...} ⊆ W: This is true because this set is exactly W itself, and a set is always a subset of itself.
→ -2 ∈ W: This is false because W contains only non-negative integers, and -2 is a negative number.
Someone help me please
Answer:
P = 48A = 144Step-by-step explanation:
The formula of regular polygon with n sides of length b and apothem a:
[tex]A=\dfrac{nba}{2}[/tex]
We have:
n = 6
b = 8
a = 6
Substitute:
[tex]A=\dfrac{(6)(8)(6)}{2}=144[/tex]
The perimeter:
[tex]P=6b\to P=(6)(8)=48[/tex]
The sum of two integers is 23 and the positive difference of the same two integers is 13. What is the product of these two integers?
A) 90 B) 75
C) 46 D) 299
Answer:
A) 90
Step-by-step explanation:
"The sum of two integers is 23" becomes
a + b = 23
"the positive difference of the same two integers is 13" becomes
a - b = 13 (difference means subtract)
Now solve the system..
a + b = 23
a - b = 13 *use addition or elimination method, since b has opposite coefficients...
2a = 36 ( we add the two equations together)
a = 18 (divide by 2 on both sides)
Since a = 18, 18 + b = 23, gives us b = 5. (18 + 5 = 23)
ab = (18)(5) = 90
Answer: A) 90
Let one integer is = x.
Sum of them is 23. So the other integer is (23 - x).
Given: Difference = 13.
So,
[tex]x-(23-x)=13\\ x-23+x=13\\ 2x=36\\ x=18[/tex]
So the other number is = 23 - x = 23 - 18 = 5.
So the product = 18*5=90
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the area of the top face of a cube is 9 square meters. what is the volume of the cube
for a cube v=a^3, so 9^3= 729