Step-by-step explanation:
To check Olivia's work, we can multiply the factors she obtained to see if they result in the original expression. Let's perform the multiplication:
(x + 3y)(x^2 - 1) = x(x^2 - 1) + 3y(x^2 - 1)
Distributing the terms:
= x * x^2 - x * 1 + 3y * x^2 - 3y * 1
= x^3 - x + 3yx^2 - 3y
As we compare this with the original expression:
x^3 - x + 3x^2y = 3y
We can see that Olivia's factored expression, (x + 3y)(x^2 - 1), does not match the original expression. Olivia made a mistake in the step where she distributed the terms.
To correct the mistake, we need to distribute the terms correctly. Let's go through the factoring process again:
Starting with the original expression: x^3 - x + 3x^2y = 3y
Rearranging the terms: x^3 + 3x^2y - x - 3y = 0
Now, we can factor by grouping:
x^2(x + 3y) - 1(x + 3y) = 0
Notice that we have a common factor of (x + 3y). Factoring it out:
(x + 3y)(x^2 - 1) = 0
Now we have the correct factored expression.
Answer:
Olivia's work is not correct.
The correct factorization of the expression is: (x-1)(x+1)(x+3y)
Step-by-step explanation:
In order to check Olivia's work, we can expand the two factors she gave:
x(x^2-1)+3y(x^2-1)
x^3-x+3x^2*y-3xy
This is not equal to the original expression, so Olivia's factorization is incorrect.
To help Olivia find the correct factorization, we can first factor out a common factor of x from the first two terms:
x(x^2-1)+3y(x^2-1)
x(x^2-1)+3y(x^2-1)
Now, we can factor the quadratic expression x^2-1:
x(x-1)(x+1)+3y(x-1)(x+1)
Finally, we can factor out a common factor of (x-1)(x+1) from the two terms:
(x-1)(x+1)(x+3y)
This is the correct complete factorization of the expression.
Write the inequality that is represented by the number line below use x as your variable
Answer:
-4 < x < 2
Step-by-step explanation:
-4 is where the first point begins.-4
since the point is "open", aka not shaded, it should be "<"-4 <
we now have to insert the given variable, x-4 < x
the second, ending point, is also "open"-4 < x <
the ending point lands on 2-4 < x < 2
hopefully this answers your question. but a little fyi, this is simply the way i learned it, so it may/may not be what you exactly need :)
3(-2p-1)=-6p -3
Need help for this equation immediately have to turn it in tomorrow it’s pre algebra
The list below shows the different taco shells, fillings, and toppings sold at Rico's Taco Bar.
Taco Shells
Fillings
Toppings
Soft
Chicken
Cheese
Hard
Beef
Lettuce
Bean
Sour Cream
Onions
Salsa
How many different types of tacos can Rico make using one taco shell, one filling, and one topping?
Answer:
30 different types of tacos can Rico make.
Step-by-step explanation:
Given - The list below shows the different taco shells, fillings, and toppings sold at Rico's Taco Bar.
Taco Shells Fillings Toppings
Soft Chicken Cheese
Hard Beef Lettuce
Bean Sour Cream
Onions
Salsa
To find - How many different types of tacos can Rico make using one taco shell, one filling, and one topping?
Proof -
Given that,
There are 2 different types of Taco shells, 3 different type of fillings and 5 different types of toppings.
So, by the fundamental principal of counting,
Total types of tacos Rico made = 2 × 3 ×5 = 30
When solving the equation x/5 - 12 = 10, what is your last step?
A. Multiply by 5 on each side.
B. Add 12 to each side.
C. Divide by 5 on each side.
D. Subtract 12 from each side.
+10 points!
Answer:
A multiply by 5
Step-by-step explanation:
x/5-12=10
x/5=10+12
x/5=22
multiple each side by 5
x=22*5
An archer la bete bathe buye 59% of the time Who shoots Barrows, what is the probability that she gets exactly 4 bulfs eyes? Assume each shot is independent of the others Round to three decimal places
A. 0.133
B. 0.003
C 0.240
D 0.121
The probability that the archer gets exactly 4 bullseyes is 0.133.
How do we calculate?The probability of an event is described as a number that indicates how likely the event is to occur and is expressed as a number in the range from 0 and 1.
P(X = k) = C(n, k) * [tex]P^k[/tex] * [tex](1 - p)^(^n^ - ^k^)[/tex]
C(n, k) = binomial coefficient
p= probability of success in a single trial
n = number of trials
The archer hits the bullseye 59% of the time,
p = 0.59
k = 4.
n = 8)
P(X = 4) = C(8, 4) *[tex]0.59^4[/tex] *[tex](1 - 0.59)^(^8^ -^ 4^)[/tex]
P(X = 4) = 0.133
Learn more about probability at:
https://brainly.com/question/24756209
#SPJ4
Pls hurry!! It’s a quick question
Answer:
3/2
Step-by-step explanation:
This problem is concerned with integrals of the form 1 = $* $(d, where f(x) = ln(x)h(x). Here, b>0 and h(0) exists but is not equal to zero, so that f(x) unbounded in the limit x + 0.
The integral of the given form 1 = $* $(d, where f(x) = ln(x)h(x) and b>0, where h(0) exists but is not equal to zero, is divergent.
This is because the function f(x) is unbounded in the limit x + 0.The integral 1 = $* $(d, where f(x) = ln(x)h(x) and b>0, is divergent because the function f(x) is unbounded in the limit x + 0. The integral of the given form can be represented as∫ba ln(x)h(x) dx, which can be evaluated by using integration by parts.Using u = ln(x), dv = h(x) dx, v = ∫h(x) dx, and du = dx/x, we get the integral as∫ba ln(x)h(x) dx = ln(x) ∫ba h(x) dx - ∫ba (∫ba h(x) dx/x) dx= ln(b) ∫ba h(x) dx - ∫ba (∫xba h(t) dt/x^2) dx.Since h(0) exists but is not equal to zero, ln(x)h(x) goes to infinity as x approaches 0. Therefore, the integral diverges as x approaches 0.
Know more about integral here:
https://brainly.com/question/31433890
#SPJ11
What is 2x+5g+7y+1.52x+32.6+5.1g+11.1+9y simplified?
Answer:
10.1g+3.52x+16y+43.7
Step-by-step explanation:
no i dont want to download ur answer.
the area is ___ square units
Answer: I think it’s 4
Step-by-step explanation: count the squares surrounding the triangle, 4 times 2 is eight 1/2 of that is 4
I'm confused math 7th grade pls help im confused
Answer:
10
Step-by-step explanation:
What type of test should be performed to test the following? Họ: H = 27 HA: μ< 27 X = 33 o= 2.5 n= 77
Explanation:
The type of test to be performed to test the hypothesis with the following data: Họ: H = 27, HA: μ< 27, X = 33, o= 2.5, and n= 77 is a left-tailed Z-test.
Hypothesis testing is a statistical technique that allows us to evaluate the validity of the hypothesis or assumptions regarding a population parameter. The hypothesis testing is based on several assumptions that must be met to test whether the null hypothesis is true or false.In this case, we will use the left-tailed Z-test since we have a sample size n > 30 and the population standard deviation is known as o= 2.5.Here are the steps for performing the left-tailed Z-test:
Step 1: State the null hypothesis and alternative hypothesis. H0: μ = 27 vs. Ha: μ < 27 (left-tailed test)
Step 2: Determine the level of significance (α). Assume α = 0.05
Step 3: Calculate the test statistic, which is given by: Z = (X - μ) / (o / √n)Where X is the sample mean, μ is the population mean, o is the population standard deviation, and n is the sample size.Z = (33 - 27) / (2.5 / √77)Z = 3.354
Step 4: Determine the p-value associated with the test statistic.Using a Z-distribution table or calculator, we find that the p-value is less than 0.001.
Step 5: Compare the p-value with the level of significance.Compare the p-value with α (0.05). Since the p-value is less than α, we reject the null hypothesis.Hence, the conclusion is that there is sufficient evidence to support the alternative hypothesis that the population mean is less than 27 at the 0.05 significance level.
Learn more about Hypothesis testing here https://brainly.in/question/39460466
#SPJ11
the points (-9,f) and (-10,5) has a slope of 3. What is the value of f?
Simplify each Equation
Answer:
a.37
b. 82
c.101
d.8
e.6
f.3
Step-by-step explanation:
hope this helps
Pls answer all of them or none of them! Tysm!
Answer:
18. $11
19. $1.40
20. 31
21. 4.05
22. 8.2
23. 31
24. 5.05
25. $14.99 per month
26. 3.7 oz
27. 16 miles ???
28. $6 each
Step-by-step explanation:
Hope that helps. That took a long time sorry. Also I am not a hundred percent sure on 27. If someone else has a different answer just check both
PLEASE HELP IM BEGGING YOU ITS EASY IM JUST SLOW
Answer:
6
Step-by-step explanation:
Formula for area A=0.5(bh)
12=0.5(4h)
12=2h
6=h
Answer:
6
Step-by-step explanation:
Area of triangle equation:
A=[tex]\frac{1}{2}[/tex] base * height
For this triangle...
12=[tex]\frac{1}{2}[/tex] (4) (x)
we need to figure out what x is to find the height.
To get x alone in this equation we can first divide both sides by 4
12/4=[tex]\frac{1}{2}[/tex] (x) ---> 3= [tex]\frac{1}{2}[/tex] (x) Then multiply by the reciprocal of 1/2 which is 2/1
x=6
Yes or no ?
Please help quick
Answer:
yes
Step-by-step explanation:
multiples of 11: 11,22,33,44,55,66,...
Answer:
No because multiples of 11 are 11,22,33,44,55 etc and multiples of 66 are 66,132,198,264,330 etc
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Step-by-step explanation:
A. Right
B. Acute
C. Right
D. Obtuse
there are 24 marbles in a bag: 2/16 of the marbles are red, 1/8 of the marbles are blue, 1/4 of the marbles are yellow, 1/3 of the marbles are black, 1/6 of the marbles are silver. how many of each type of marble is there?
Answer: 3 red marbles, 3 blue marbles, 6 yellow marbles, 8 black marbles, 4 silver marbles
Step-by-step explanation:
I know these are the correct number of marbles because I set up these numbers as fractions and solved for x.
For examples, 2/16 of the marbles are red. 2/16=x/24
You would do this because we are trying to find the number of marbles that are red out of the 24 marbles.
Next, we would do 24 divided by 16= 1.5 Then 1.5 times 2=3
You would follow this rule for each fraction of marbles in order to find the true number of marbles out of 24.
Question 1 5 pts When adjusting the cutoff threshold for a classification algorithm, it is always possible to simultaneously improve the specificity and sensitivity of the classifier. O True False
The statement as it has been written can be shown as false.
Is it true or false?There is often a trade-off between specificity and sensitivity when changing the cutoff criterion for a classification algorithm. Sensitivity relates to the classifier's capacity to accurately identify the positive cases, while specificity refers to the classifier's capacity to do so.
You can modify the ratio of true positive to false positive rates by setting the cutoff value. By identifying more occurrences as positive, lowering the threshold may boost sensitivity, but it can also result in an increase in false positives, which lowers specificity.
Learn more about algorithm:https://brainly.com/question/28724722
#SPJ4
17. Find the missing angle(s).
132
f
9
Answer:
34
Step-by-step explanation:
Answer:
angle f is 132..........
S2 are nonzero subspaces, with Si contained inside S2, and suppose that dim(S2) = 4 .(1) What are the possible dimensions of S1? (2) If S1 ≠S2, then what are the possible dimensions of S1 ?
The possible dimensions of S1, can range from 0 to 4, and if S1 ≠ S2, then the possible dimensions of S1 can range from 1 to 4, where the dimension of S1 is equal to the dimension of S2 plus 1 up to a maximum dimension of 4.
(1) The possible dimensions of S1, when S2 is a nonzero subspace contained inside it and dim(S2) = 4, can be any integer value from 0 to 4.
(2) If S1 ≠ S2, then the possible dimensions of S1 can range from 1 to 4. Since S1 ≠ S2, it means that S1 must have at least one additional vector that is not present in S2. Therefore, the dimension of S1 can be equal to the dimension of S2 plus 1 (dim(S2) + 1), up to the maximum possible dimension of 4.
To elaborate further, when S1 ≠ S2, it implies that there exists a vector in S1 that is not in S2. This additional vector increases the dimension of S1 by one. Hence, the possible dimensions of S1 can be 1, 2, 3, or 4, as long as it is greater than or equal to the dimension of S2 plus 1. However, it is important to note that the specific dimension of S1 depends on the specific vectors and subspaces involved in the given context.
To learn more about Subspaces, visit:
https://brainly.com/question/17517360
#SPJ11
Find the sum 1/2+1/4
Answer:
3/4
Step-by-step explanation:
Make a common denominator and multiply the many times the denominator had to get to the common denominator to the numerator.
A car drives at a constant rate of 60 miles per hour for a given period of time. 5. What is the independent variable? 6. What is the dependent variable?
5. The independent variable is the period of time.
6. The dependent variable is the distance traveled by the car.
5. The independent variable is the period of time because it is the variable that is controlled or manipulated in this scenario. The car's speed remains constant at 60 miles per hour, and the time is the factor that can be changed or adjusted.
6. The dependent variable is the distance travelled by car because it is the variable that is influenced or affected by the independent variable. In this case, the distance traveled depends on the period of time for which the car maintains a constant speed of 60 miles per hour.
The longer the period of time, the greater the distance traveled, and vice versa. The relationship between the independent variable (time) and the dependent variable (distance) is determined by the constant rate of 60 miles per hour. As time increases, the car covers more distance, while as time decreases, the car covers less distance.
Therefore, the distance traveled is dependent on the period of time for which the car maintains its constant speed.
Know more about the independent variable click here:
https://brainly.com/question/1479694
#SPJ11
able 29-4 Bank of Cheerton Assets Liabilities Reserves $4,200 Deposits 55,800 $60,000 Loans Refer to Table 29-4. If the Fed's reserve requirement is 5 percent, then what quantity of excess reserves does the Bank of Cheerton now hold? $1,200 $600 $2,090 $3,000
The Bank of Cheerton now holds $1,200 in excess reserves. So, correct option is A.
To determine the quantity of excess reserves that the Bank of Cheerton holds, we first need to calculate the required reserves. The required reserves are the portion of the deposits that the bank is required to hold as reserves based on the reserve requirement set by the Federal Reserve.
The reserve requirement is given as 5 percent, and the Bank of Cheerton has deposits of $60,000. Therefore, the required reserves can be calculated as follows:
Required Reserves = Deposits * Reserve Requirement
= $60,000 * 0.05
= $3,000
Next, we can calculate the excess reserves, which are the reserves held by the bank in excess of the required reserves. Excess reserves can be calculated as the difference between the total reserves (reserves held by the bank) and the required reserves:
Excess Reserves = Reserves - Required Reserves
= $4,200 - $3,000
= $1,200
Therefore, correct option is A.
To learn more about reserves click on,
https://brainly.com/question/31569505
#SPJ4
A feeder at the zoo in shape of a cone has a radius of 3 inches. It holds about 113.04 cubic inches of food. Approximate its height to the nearest inch. Use 3.14 to approximate the value of pie.
Answer:
12 inches
Step-by-step explanation:
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
People Entering Amusement Park
A graph titled People Entering Amusement Park has time (minutes) on the x-axis, and number of people on the y-axis. Points trend in a positive line.
Time (minutes)
a.
positive; as time passes, the number of people entering decreases.
b.
negative; as time passes, the number of people entering decreases.
c.
no correlation
d.
positive; as time passes, the number of people entering increases.
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
In a busy amusement park the number of people entering always increases as time goes on. I’m sure you know this if you ever been to one and had to wait in those long lines at the entrance or at any of the rides.
Answer:
D
Step-by-step explanation:
ifunny is dankreloaded
In the diagram of EHG below, JF || HG, EJ=3, JH=18, and FG=72. What is the length of EG
Answer:
EG = 84
Step-by-step explanation:
Here, we want to get the length of EG
Mathematically, we will be considering two triangles
these are EFJ and EHG
These two triangles are similar as can be seen
when two triangles are similar, the ratio of their corresponding sides are equal
Thus, we have it that;
EH/EG = EJ/EF
let us represent EF by x
so; EG is (x + 72)
EH = 3 + 18 = 21
Hence, we have it that;
21/x+ 72 = 3/x
21(x) = 3(x + 72)
21x = 3x + 216
21x-3x = 216
18x = 216
x = 216/18
x = 12
EG = 12 + 72 from EG = x + 72
EG = 84
Write a real world problem that can be represented by 10x-40=100
Answer:
10x - 40 = 100, x = 14
Step-by-step explanation:
At a flower shop, there are 10 bouquets with the same amount of flowers in each of them. In total, 40 flowers were purchased. Now, there are 100 flowers left in the shop. How many flowers are in a bouquet?
This situation can be represented by
10x
(the number represents the bouquets, while the variable x represents the amount of flowers in a bouquet)- 40
(this represents the flowers that were purchased)= 100
(this represents the flowers remaining)State the name of the property illustrated. (2+1) + (6 +5) = (V6 +5) +(2+1)
The property illustrated in (2 + 1) + (6 + 5) = (6 +5) +(2 + 1) is the commutative property of addition
How to determine the name of the propertyFrom the question, we have the following parameters that can be used in our computation:
(2 + 1) + (6 + 5) = (6 +5) +(2 + 1)
In the above expression, we can see that
The terms of the expression are swapped
This can be illustrated as
if a + b = b + a
The name of the property is the commutative property of addition
Hence, the name of the property illustrated in (2 + 1) + (6 + 5) = (6 +5) +(2 + 1) is the commutative property of addition
Read more about commutative property at
https://brainly.com/question/30517591
#SPJ4
I NEED HELP, WILL GIVE U BRAINLIEST IF U GIVE ME ANSWER <3
Answer:
It would be the last choice. Base= 8 in; height= 3 in
Step-by-step explanation:
It gives you the measurement for the height you just have to read what the ruler says at the bottom. When does the shape stop on the ruler? That number would be the answer in this case it would be the last choice.
Answer:
i dont know lol
Step-by-step explanation: