The True statements are: b) -6 | 24, c) 11 | -33, and e) 5 | 126. The False statements are: a) 13|78 and d) 23 | 96.
The divisibility relationships in question can be evaluated as follows:
a) 13|78 - This statement is False. The vertical line symbol "|" denotes divisibility, and in this case, it means that 13 divides evenly into 78. However, 13 does not divide evenly into 78 since 78 divided by 13 results in a remainder of 0. Therefore, the statement is false.
b) -6 | 24 - This statement is True. The negative sign in front of the 6 indicates a negative number. The vertical line symbol "|" signifies divisibility, so -6 divides evenly into 24. When 24 is divided by -6, the result is -4, with no remainder. Hence, the statement is true.
c) 11 | -33 - This statement is True. Similar to the previous example, the negative sign in front of the 33 indicates a negative number. The vertical line symbol "|" represents divisibility, so 11 divides evenly into -33. When -33 is divided by 11, the result is -3, with no remainder. Therefore, the statement is true.
d) 23 | 96 - This statement is False. Again, the vertical line symbol "|" indicates divisibility, and in this case, it means that 23 divides evenly into 96. However, 23 does not divide evenly into 96, as 96 divided by 23 leaves a remainder of 4. Therefore, the statement is false.
e) 5 | 126 - This statement is True. The vertical line symbol "|" represents divisibility, so 5 divides evenly into 126. When 126 is divided by 5, the result is 25, with no remainder. Hence, the statement is true.
To summarize, the True statements are: b) -6 | 24, c) 11 | -33, and e) 5 | 126. The False statements are: a) 13|78 and d) 23 | 96.
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Let f be a function having derivatives of all orders for allreal numbers. The third-degree Taylor polynomial for f about x=2 isgiven by
T(x) = 7-9(x-2)2-3(x-2)3
a. find f(2) and f '' (2).
b. Is there enough information given to determine wheather fhas a critical point at x = 2?
If not, explain why not.
If so, determine whether f(2) is a relative maximum, arelative minimum, or neither, and justify your answer.
c. Use T(x) to find an approximation for f(0). Is there enoughinformation given to determine whether f has a critical point atx=0?
If not, explain why not.
If so, determine whether f (0) is a relative maximum, arelative minimum, or neither, and justify your answer.
d. The fourth derivative of f satisfies the inequality for all x in the closed interval [0,2]. Use thelagrange error bound on the approximation to f (0) found in part(c) to explain why f (0) is negative.
Solution :
Given : [tex]$T(x)=7-9(x-2)^2-3(x-2)^3$[/tex]
a). f(2) = T(2) = 7
[tex]$\frac{f""(2)}{2!} =-9$[/tex] , so f''(2) = [tex]$-18$[/tex]
b). Yes, since f'(2) = T'(2) [tex]$=$[/tex] 0, [tex]$f$[/tex] does have the critical point at [tex]$x=2.$[/tex]
Since f''(2) = [tex]$-18$[/tex] < 0, [tex]$f(2)$[/tex] is relative maximum value.
c). [tex]$f(0)=T(0)=-5$[/tex]
It is also not possible for determining if [tex]$f$[/tex] has a critical point at x = 0 because [tex]$T(x)$[/tex] gives exact information only at [tex]$x=2.$[/tex]
d). The Lagrange [tex]$\text{error}$[/tex] bound [tex]$=\frac{6}{4!}|0-2|^4= 4$[/tex]
[tex]$f(0) \leq T(0)+4 = -1$[/tex]
Therefore, [tex]$f(0)$[/tex] is negative.
b) A cubical water tank has 1.5m as the length of its each side. Find the volume of the tank.
Answer:
3.375
Step-by-step explanation:
To get the volume of a cube you need to multiply length width and height since the cube is similar in length width and height you need to multiply 1.5 by itself three times.
V=l×w×h
V=1.5×1.5×1.5
V=3.375
Note:you need to multiply it to itself three times not to the number three.
Also it is only used if one number is given if three numbers are given multiply those three numbers hope this helps have a good day
A food truck sells tacos, burritos, and drinks.
Let event A = A customer buys a taco.
Let event B= A customer buys a drink.
What does P(A or B) = 0.45 mean in terms of this problem?
Answer:
b, the probability that a customer buys a taco, a drink, or both is 45%
P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.
In terms of this problem, P(A or B) = 0.45 represents the probability that a customer buys either a taco (event A) or a drink (event B).
When we say "P(A or B)," it refers to the probability of either event A or event B occurring. In this case, it means the probability of a customer buying a taco or a drink from the food truck.
The value of 0.45 indicates the numerical probability associated with the event A or B. It represents the likelihood that a randomly selected customer from the food truck will purchase either a taco or a drink.
Therefore, P(A or B) = 0.45 means that there is a 45% probability that a customer will buy a taco or a drink from the food truck.
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G(x)= x^2 + 5x
g(-3)=
Answer: The answer is g=x/16
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
g(-3) = (-3)^2 + 5(-3) [Take x value as -3]
= 9 -15
= -6
At a constant speed, a car travels 75 miles in 60 minutes. How far does
the car travel in 18 minutes? If you get stuck, consider using the table.
Answer:
22.5 miles
Step-by-step explanation:
75/60 = x/18
60x = 1350
x = 22.5
En san pedro de atacama, un dia de septiembre a las 7a.M., la temperatura fue de 6°c, la que fue aumentando 2,3°c en promedio por hora hasta que alcanzo su maxima de 30,15 °c ¿ a que hora alcanzo su temperatura maxima
Answer:
5:30 p.m.
Step-by-step explanation:
30.15 - 6 = 24.15
24.15 / 2.3 = 10.5 hrs
7 + 10.5 = 17.5 = 5:30 p.m.
Jackson has a table with a square top and he wants to buy a circular piece of lace
that will cover the entire top of the table. The top of the table has side lengths of 12
inches, as shown.
12 in
12 in
What is the area, in square inches, of the smallest circular piece of lace Jackson could
Answer:
144
Step-by-step explanation:
the area is 144 im prob wrong
Sasha had to run 1/3 of a mile. She decided to walk, jog, and run the 1/3 mile, in equal parts. What fraction of the mile will she run?
A.9
B.3/9
C.1/9
D.3/3
(Need help asap pls)
Answer:
C 1/9
Step-by-step explanation:
She needs to run 1/3 of a mile and is going to run/jog/walk that 1/3 mile
So she must do 1/9 of a mile running, 1/9 walking, and 1/9 jogging because 1/3 is equivalent to 3/9.
Since she is going to run/jog/walk the same amount of the 1/3 she is going to run 1/9 of the 1/3
Let me know if I'm wrong
Hope I helped :]
Purple paint is made of a ratio of
16 white : 3 blue : 1 red
how much white paint is needed to make one gallon of purple paint?
plz help its important
there are 16/20 x 1 gallon = 4/5 gallons of white paint in one gallon of purple paint (got it from safari)
whats 10x10+111-21x999/999+21-111/10?
Answer:
199.9
Step-by-step explanation:
TB
05-75 2/10,n/30 is interpreted as
The term "TB 05-75 2/10, n/30" represents the payment terms for a transaction.
The term "TB 05-75 2/10, n/30" provides specific information regarding the payment terms for a transaction. Here's a breakdown of its components:
1. "TB": This stands for "Trade Discount" and signifies that the terms are related to a discount offered for the transaction.
2. "05-75": The numbers indicate a cash discount percentage and a payment period. In this case, "05" represents a cash discount of 5%, and "75" indicates a payment period of 75 days.
3. "2/10, n/30": These terms further elaborate on the payment conditions. "2/10" means that a 2% cash discount can be taken if the payment is made within 10 days. The "n/30" portion implies that the net payment is due within 30 days from the date of the transaction.
In summary, "TB 05-75 2/10, n/30" signifies that a trade discount is offered, a cash discount of 5% is available if payment is made within 10 days, and the net payment is due within 30 days. It provides clear guidelines for the payment terms and discounts associated with the transaction.
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If ab=8 and a^2+b^2=16 then what is the valué of (a+b)^2 PLSS HELP NOW
I think that i got it but at the same time not sure but the value of a+b should be 14+20
12. Use Russian Peasant Multiplication to perform the following problem. Explicitly show your addition. 49 x 65
Using the Russian Peasant Multiplication, 49 x 65 is 3,185.
What is the Russian Peasant Multiplication?The Russian Peasant Multiplication method converts the problem into binary (base 2) multiplication from base 10 by halving the numbers on the first column repeatedly till the second number doesn't become 1 and doubling the numbers on the second column.
Then, add up the numbers in the second column that correspond to odd numbers in the first column to get the result.
49 65
÷ 2 24 130 x 2
12 260
6 520
3 1,040
1 2,080
Add:
65, because we ignored 1 when we divided 49 by 2
1,040, because we ignored 1 when we divided 3 by 2
2,080
= 3,185
Check:
49 x 65 = 3,185
Based on the Russian Peasant Multiplication method, the product of 49 x 65 is 3,185.
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Which of the following properties is represented by the calculations in the photo?
A) multiplication property of equality
B) zero sum property
C) addition property of equality
D) zero product property
Answer:
D. zero product property
Step-by-step explanation:
Base on the Zero Product Property, if the product of factors gives us 0, either of the factors or both would equal 0.
Thus,
xy = 0, therefore,
x = 0 or y = 0
Therefore, the property that is represented by the calculation given in the photo is Zero Product Property.
A random sample of n_1 = 555 individuals results in x_1 = 451 successes. An independent sample of n_2 = 600 individuals results in x_2 = 510 successes. Does this represent sufficient evidence to conclude that p_1≠ p_2 at the α = 0.05 level of significance?
There is no sufficient evidence to conclude that p₁ ≠ p₂
How to determine if the conclusion is sufficientFrom the question, we have the following parameters that can be used in our computation:
n₁ = 555
x₁ = 451
n₂ = 600
x₂ = 510
Calculate the pooled sample proportion using
p = sum of x/sum of n
So, we have
p = (451 + 510)/(555 + 600)
p = 0.832
Calculate the test statistic using
[tex]z = (\frac{x_1}{n_1} - \frac{x_2}{n_2}) \div (\sqrt{(p * (1 - p) / n_1) + (p * (1 - p) / n_2)}}[/tex]
So, we have
[tex]z = (\frac{451}{555} - \frac{510}{600}) \div (\sqrt{(0.832 * (1 - 0.832) / 555) + (0.832 * (1 - 0.832) / 600)}})[/tex]
When solved, we have
z = -1.699
The critical value at α = 0.05 level of significance is 1.645
The z = -1.699 is less than this value
This means that we fail to reject the null hypothesis
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100 - x2 + 15, cuando x = 9
What is the sum of 2 with exponent of 4 and 7 with an exponent of 2. please write in standard form.
Answer:
I think the answer would be 65 , because :
2^4 + 7^2 = 16 + 49 = 65 .
hope it helps u ^.^
Answer:
65
Step-by-step explanation:
First you would solve the exponent and then you would add them
2 to the power of 4 = 16
7 to the power of 2 = 49
16 + 49 = 65
2 to the power of 4 + 7 to the power of 2 = 65
The equations y = 5x and y = –1∕5x + 4 represent what types of lines?
Answer:
It might be perpendicular lines
Step-by-step explanation:
If dy /dx is undefined for a given value of x, then the line tangent to the curve y f(x) at that value does not exist Select one:
a. true b. false
The statement "If dy/dx is undefined for a given value of x, then the line tangent to the curve y = f(x) at that value does not exist" is false.
If the derivative dy/dx is undefined at a given value of x, it means that the slope of the tangent line is undefined at that point.
However, the tangent line can still exist.
For example, consider the curve y = |x| at x = 0.
The derivative dy/dx is undefined at x = 0 since the slope changes abruptly at that point. However, we can still draw a tangent line at x = 0, which is the y-axis itself.
Therefore, even if the derivative is undefined, it does not necessarily mean that the tangent line does not exist.
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20. An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth
Answer:
2.88 mi
Step-by-step explanation:
please help thank u alot going to put pictures!
multiple 2y(6y2+4y-3)
Answer:
Step-by-step explanation:
Y- intercepts (-3 = 2 3, 0) , (-3 - 2 3, 0)
a string runs up and to the left in the x-y plane, making an angle of 29◦ to the vertical. determine each component of the unit vector that points along the string, beginning with ˆrx.
To determine the components of the unit vector that points along the string, we need to break down the vector into its x and y components.
Given that the string makes an angle of 29 degrees to the vertical, we can define the unit vector as follows:
ˆr = ˆrx + ˆry
To find the x-component (ˆrx) of the unit vector, we can use the cosine of the angle:
cos(29°) = ˆrx
To find the y-component (ˆry) of the unit vector, we can use the sine of the angle:
sin(29°) = ˆry
Let's calculate the values:
ˆrx = cos(29°)
ˆry = sin(29°)
Using a calculator or mathematical software, we can find the numerical values of ˆrx and ˆry:
ˆrx ≈ 0.8829
ˆry ≈ 0.4695
Therefore, the components of the unit vector that points along the string are approximately:
ˆrx ≈ 0.8829
ˆry ≈ 0.4695
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Sarah donated $920 for a new park. Sarah's brother donated $850. How much more money did Sarah donate?
please answer ASAP AFAP PLEASE PLEASE ANSWER RIGHT OR I'LL REPORT YOU TO BRAINLY . but on the other hand if you answer correctly I'll just give you brainliest, and go to your profile and thank you and give you a 5 star rating!
Answer:
The answer is B. 4.4 oz.
Step-by-step explanation:
What do we know? We have the 6-pack of 12-ounce bottles and they cost $2.99, we also know that the other bottle 67.6 ounces that also costs $2.99.
Forgot the money, we're just going to be looking at the ounces.
First, we take the 6-pack and multiply by 12 because we want the size as one, rather than seperate. 6 x 12 = 72
The question is asking how many more ounces are you getting if you purchase the 6-pack. In order to do this, we take the 72 ounces that we got and subtract that 67.6 ounces of the other drink. 72 - 67.6 = 4.4
The ounces saved are 4.4 ounces.
Convert each of the following implicitly quantified statements
to their formally quantified statement equivalent.
Implicitly quantified statements can be converted into formally quantified statements by specifying the quantifiers and the domain of discourse.
To convert an implicitly quantified statement to its formally quantified statement equivalent, we need to determine the quantifiers and the domain of discourse.
1. For universally quantified statements, we use the universal quantifier (∀). It indicates that the statement holds for all elements in the domain of discourse. For example, if the statement is "All cats have tails," we can convert it to the formally quantified statement ∀x(Cat(x) → HasTail(x)), where Cat(x) represents "x is a cat" and HasTail(x) represents "x has a tail."
2. For existentially quantified statements, we use the existential quantifier (∃). It indicates that there exists at least one element in the domain of discourse for which the statement is true. For example, if the statement is "There is a red apple," we can convert it to the formally quantified statement ∃x(Red(x) ∧ Apple(x)), where Red(x) represents "x is red" and Apple(x) represents "x is an apple."
By explicitly stating the quantifiers and defining the predicates in the statement, we can convert implicitly quantified statements into their formally quantified statement equivalents, making the meaning and scope of the statement clear within a specific domain of discourse.
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Use the following picture to find the measure of angles 3 and 4. (picture)
A cylinder has a base radius of 6ft and a height of 18ft. What is its volume in cubic ft, round to the nearest tenth?
Answer: 2035.8
Step-by-step explanation:
The volume of the cylinder is 2034.72 cubic ft
What is the volume of the cylinder?The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold or we can say the volume of a cylinder is the number of unit cubes that can be fit into it. The formula for volume of cylinder is V = A × h
Assuming the given cylinder is Right Circular Cylinder
Then the formula is V = πr²h
From the question radius (r)= 6ft
height (h)=18ft
volume (V)= π× 6² × 18
=2034.72 cubic ft
Thus the volume of the cylinder is 2034.72 cubic ft
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What is the slope of the line that
passes through these two points?
(1, 2)
(2, 8)
(x1.yı) Slope =
rise (y2-yı)
Remember, given two points,
(x2:y2) run (x2-x1)
Answer:
6
Step-by-step explanation:
8 - 2 / 2 - 1
6 / 1
6
which of the following fractions converts to a repeating decimal? a. 7/16 B.5/8 C. 2/3 D.4/10
Answer:
B
Step-by-step explanation: