Answer:
a) ∀x∃y ¬∀zT(x, y, z)
∀x∃y ∃z ¬T(x, y, z)
b) ∀x¬[∃y (P(x, y) ∨ Q(x, y))]
∀x∀y ¬ [P(x, y) ∨ Q(x, y)]
∀x∀y [¬P(x, y) ^ ¬Q(x, y)]
c) ∀x ¬∃y (P(x, y) ^ ∃zR(x, y, z))
∀x ∀y ¬(P(x, y) ^ ∃zR(x, y, z))
∀x ∀y (¬P(x, y) v ¬∃zR(x, y, z))
∀x ∀y (¬P(x, y) v ∀z¬R(x, y, z))
d) ∀x¬∃y (P(x, y) → Q(x, y))
∀x∀y ¬(P(x, y) → Q(x, y))
∀x∀y (¬P(x, y) ^ Q(x, y))
Answer:
a) ∃x∀y∃z~T(x, y, z)
b) ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)
c) ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))
d) ∃x∀y(P(x, y) → ~Q(x, y))
Step-by-step explanation:
The negation of a is written as ~a.
Note the following properties that are going to be applied in the problems here :
~(P → Q) = P → ~Q
De Morgan's Laws
~(P ∨ Q) = ~P ∧ ~Q
~(P ∧ Q) = ~P ∨ ~Q
~∃xP = ∀xP
~∀xP = ∃xP
So back to the original problem.
a) ∀x∃y∀zT(x, y, z)
We have the negation as
~[∀x∃y∀zT(x, y, z)]
= ∃x~∃y∀zT(x, y, z)
= ∃x∀y∀~zT(x, y, z)
= ∃x∀y∃z~T(x, y, z)
b) ∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)
Negation is:
~[∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)]
= ~∀x∃yP(x, y) ∧ ~∀x∃yQ(x, y)
= ∃x~∃yP(x, y) ∧ ∃x~∃yQ(x, y)
= ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)
c) ∀x∃y(P(x, y) ∧ ∃zR(x, y, z))
Negation is:
~[∀x∃y(P(x, y) ∧ ∃zR(x, y, z))]
= ~∀x∃y(P(x, y) ∧ ∃zR(x, y, z))
= ∃x~∃y(P(x, y) ∧ ∃zR(x, y, z))
= ∃x∀y~(P(x, y) ∧ ∃zR(x, y, z))
= ∃x∀y(~P(x, y) ∨ ~∃zR(x, y, z))
= ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))
d) ∀x∃y(P(x, y) → Q(x, y))
Negation is:
~[∀x∃y(P(x, y) → Q(x, y))]
= ~∀x∃y(P(x, y) → Q(x, y))
= ∃x~∃y(P(x, y) → Q(x, y))
= ∃x∀y~(P(x, y) → Q(x, y))
= ∃x∀y(P(x, y) → ~Q(x, y))
Square EFGH stretches vertically by a factor of 2.5 to create rectangle E′F′G′H′. The square stretches with respect to the x-axis. If point H is located at (-2, 0), what are the coordinates of H′ ? A. (-5, 0) B. (-2, 0) C. (0.5, 0) D. (-2, 2.5)
Answer:
The coordinates of point H' are (-2 , 0) ⇒ answer B
Step-by-step explanation:
* Lets revise the vertical stretch
- A vertical stretching is the stretching of the graph away from the
x-axis
- If k > 1, then the graph of y = k • f(x) is the graph of f(x) vertically
stretched by multiplying each of its y-coordinates by k
* Lets solve the problem
- Square EFGH stretches vertically by a factor of 2.5 to create
rectangle E′F′G′H′
∴ k = 2.5
- The square stretches with respect to the x-axis
∴ The square stretches vertically
∴ The y-coordinates of each vertex of the square EFGH are
multiplied by 2.5 to get the vertices of the rectangle E'F'G'H'
∵ Point H located at (-2 , 0)
∵ The image of point (x , y) after stretched vertically by k is (x , ky)
∴ Point H' located at (-2 , 0 × 2.5) ⇒ (-2 , 0)
∴ The coordinates of point H' are (-2 , 0)
∴ Point H' located at (-2 , 0)
Answer:
B. (-2, 0)
Step-by-step explanation:
Which statement about the figure below is true?
B
they have limited (3) common points where the planes meet.
A wall has been built with two pieces of sheetrock, a smaller one and a larger one. The length of the smaller one is stored in the variable small. Similarly, the length of the larger one is stored in the variable large. Write a single expression whose value is the length of this wall.
Answer:
The answer is: small+large.
Step-by-step explanation:
If the variable of the smaller sheetrock is stored in small:
var small.
And the variable of the larger sheetrock is stored in large:
var large.
The length of the wall will be the sum of the two pieces of sheetrock:
small+largeFor example:
var small = 5;
var large = 10;
small+large = 5 + 10 = 15 is the length of the wall.
Final answer:
To calculate the total length of a wall made with two sheets of sheetrock, use the expression 'small + large'. The correct unit for measuring large objects like walls is often feet, and including units is essential for clarity in measurements.
Explanation:
The question asks for an expression to calculate the total length of a wall built with two pieces of sheetrock with lengths stored in the variables small and large. Since the total length of the wall will be the sum of the lengths of the two pieces of sheetrock, the expression you would write is small + large. This will give you the length of the entire wall when you substitute in the numerical values for the lengths represented by the two variables.
When measuring large objects like walls, the appropriate unit of measure is often feet, as inches would be too small and miles or kilometers would be excessively large. It's important to always include units in your measurements to avoid confusion and to ensure that the measurements are useful for practical applications, such as buying fabric or building materials.
PLEASE HELP Use the rules of exponents to simplify the expressions. Place a final answer in fraction form. (-1/2)to the power of 3 *(-1/2) to the power of 2
Answer:
-1/32.
Step-by-step explanation:
(-1/2)^3 * (-1/2)^2
= -1/8 * 1/4
= -1/32.
What is the slope for 3x + 2y = 8
Answer:
[tex] -1 \frac{1}{2} = m[/tex]
Step-by-step explanation:
3x + 2y = 8
-3x - 3x
___________
2y = -3x + 8
___ _______
2 2
y = -1½x + 4
↑
rate of change [slope]
I am joyous to assist you anytime.
OMG HELP A GIRL OUT !!HELP ME PLEASE I NEED A 70%
1. Translate and solve: What number is 408% of 568? Round to the nearest hundredth.
2.In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the total percent decrease.
3.A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each bill does it contain?
4.Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost $3.45 per pound, and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him $6.96 per pound?
Answer:
#1. 408% of 568
We get two equations from this
408% = x
568 = 100%
568/x=100%/408%
Solve and you'll get
408% of 568
=2317.44
2. New - Original = % change
712500 - 950000 = -237500
3. 10 at $1, 7 at $5
4. 2.2 lb. of raisins, 7.8 lb. of nuts
As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
What is equation?
" Equation is defined as the relation between the variables using sign of equality."
What is percentage?" Percentage is defined as the hundredth part of the given number."
According to the question,
1. 'x' represents the number
As per given condition,
x = 408% of 568
⇒ [tex]x= \frac{408}{100} (568)[/tex]
⇒ [tex]x = 2317.44[/tex]
Therefore, the number which is 408% of 568 is equals to 2317.44.
2. Total population of Detroit = 950,000
Population after 10 years = 712,500
Decrease in population = 950,000 - 712,500
= 237,500
Total percentage decrease in population = [tex]\frac{237500}{950,000}(100)[/tex]
= 25%
Therefore, total decrease in percentage of the population of Detroit is equals to 25%.
3. 'x' represents the bill of $1
'y' represents the bill of $5
As per the condition given equation we have,
$1x + $5y = $45 ______(1)
x = y + 3 ______(2)
Substitute the value of equation (2) in (1) we get,
[tex]1(y + 3) + 5y = 45\\\\\implies 6y = 45-3\\\\\implies y \frac{42}{6} \\\\\implies y = 7[/tex]
Substitute the value y in (2) we get,
[tex]x= 7 + 3\\\\\implies x =10[/tex]
Therefore , cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. 'x' represents the pounds of raisins
'10- x ' represents the pounds of nuts
Cost of trail mix from raisins and nuts per pound = $6.96
Therefore,
Cost of 10 pounds of trail mix of raisins and nuts = $(6.96 ×10)
= $69.6
Cost per pound of raisins = $3.45
Cost per pound of nuts = $7.95
Equation formed as per given condition we get,
[tex]3.45x + 7.95(10-x) = 69.6\\\\\implies 3.45x + 79.5 -7.95x = 69.6\\\\\implies -4.5x = 69.6 - 79.5\\\\\implies-4.5x= -9.9\\\\\implies x =\frac{9.9}{4.5}\\ \\\implies x = 2.2 pounds[/tex]
Pounds of raisins = 2.2pounds
Pounds of nuts = 10 - 2.2
= 7.8 pounds
Therefore, pounds of raisins is equals to 2.2 and pounds of nuts is equals to 7.8 for the trail mix.
Hence, As per the given conditions we have
1. Number which is 408% of 568 is equals to 2317.44 ( nearest hundredth).
2. Total decrease in percentage of the population of Detroit is equals to 25%.
3.Cash box contain bill of $1 is equals to 10 and bill of $5 is equals to 7.
4. Raisins is equals to 2.2 pounds and nuts is equals to 7.8 pounds for the trail mix.
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Someone please help me
Answer:
14. 61.2 mi N, 49.8 mi W
15. 7.3 ft
Step-by-step explanation:
14. The components in the different directions are found using the sine and cosine functions. (Draw yourself a diagram to help see this.)
north distance = (78.9 mi)cos(39°10') ≈ 61.2 mi
west distance = (78.9 mi)sin(39°10') ≈ 49.8 mi
__
15. Let d represent the distance from the observation point to the door. Then ...
8.8 ft = d·tan(56°)
x = d·tan(51°)
Dividing the second of these equations by the first cancels d and gives ...
x/(8.8 ft) = tan(51°)/tan(56°)
Multiplying by 8.8 ft, we can find x:
x = (8.8 ft)(tan(51°)/tan(56°)) ≈ 7.3 ft
30 POINTS AND BRAINLIEST PLZ HELP
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
A. 2
B. 3
C. 4
D. 5
Answer:
B. 3
Step-by-step explanation:
"k" represents the number of units of upward translation between f and g. Since g is translated 3 units upward from f, we must have k=3.
The scale on a map of Virginia shows that 1 inch represents 15 miles. The actual distance from Richmond, VA, to Washington, D.C., is 110 miles. On the map, how many inches are between the two cities? Enter your answer as a mixed number with the fraction in simplest form.
The distance on the map is __ in.
Answer:
The answer to your question is: 7 1/3 inches
Step-by-step explanation:
Data
1 inch --------- 15 miles
Distance from Richmond to Washington = 110 miles
Use a rule of three to solve it
1 inch ----------------- 15 miles
x -------------------- 110 miles
x = 110x 1 /15
x = 110 / 15 simplify dividing by 5
x = 22/3
Convert it to a mix number
22/3 = 7 1/3 inches
Final answer:
On the map, 7.6 inches are between the two cities
Explanation:
To find out how many inches are between two cities on a map given the scale and the actual distance. The scale here is that 1 inch represents 15 miles. Therefore, for an actual distance of 110 miles, we simply divide the actual distance by the scale factor to obtain the distance on the map.
By setting up the proportion:
1 inch / 15 miles = x inches / 110 miles, we cross-multiply and solve for x,
which is the number of inches on the map. The calculation would be:
(1 inch / 15 miles) * 110 miles = 110 inches / 15 = 7 3/5 inches or 7.6 inches.
A stand-up comedian uses algebra in some jokes, including one about a telephone recording that announces "You have just reached a pure imaginary number. Please multiply by i and dial again." Explain the joke.
Answer:
i * i = -1
Step-by-step explanation:
W hen you multiply an imaginary number or i number by another imaginary pure number, the answer is going to be a negative number, due that i *i= -1. The joke is funny because if you do what the recording is saying there you won't have a pure imaginary number and if you dial again, the same would happen again and again.
Answer:
When we work with imaginary numbers, we have that
i = √(-1)
then, we have that i*i = √(-1)*√(-1) = -1
An imaginary number is a number of form A + B*i, where A and B are real numbers.
Now, a purely imaginary number is a number of the form B*i, where B is a real number.
Then, if we multiply this number by i, we have that:
B*i*i = B*(-1) = -B
now we have a real number.
The joke is that now you can "reach" a real number.
A teacher divides the students into three groups for project each group has the same number of students in the total of number students prime or composite
Answer:
The total number of students is composite
Step-by-step explanation:
* Lets explain how to solve the problem
- A teacher divides the students into three groups for project
- Each group has the same number of students
- We need to know the total number of students is prime number or
composite number
∵ The least number of any group is 2 students
∵ There are three groups
∵ The number of students in each group equal
∴ The least number of the students is 6
∵ Any number of students must be multiple of 3 because it will
divide by 3
∵ Any prime number has only two factors 1 and itself
∵ Any multiple of 3 (except 3) has more than two factors
∵ The class can not be 3 students because when divided to 3
groups each group will have 1 students and the least number of
students in a group is 2
∴ The number of the students in the class must be composite
Final answer:
The question deals with evenly dividing students into three groups for a group assignment, indicating that the total number of students is composite, as it is divisible by three.
Explanation:
The question involves dividing a number of students into groups for a group assignment. A key concept here is understanding whether the total number of students is a prime or composite number.
If the students were evenly divided into three groups, this implies that the total number must be divisible by three, making it a composite number.
Examples of group work dynamics include cases where students divide work equally but one ends up doing the most of it, evenly distributing tasks, or each taking on different aspects of a complex problem.
A test consists of 10 true/false questions. To pass the test a student must answer at least 88 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places.
Answer:
The probability that the student is going to pass the test is 0.0545
Step-by-step explanation:
The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:
[tex]P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}[/tex]
Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2
Then, if the student pass the test with at least 8 questions correct, the probability P of that is:
P = P(8) + P(9) + P(10)
[tex]P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})[/tex]
P = 0.0439 + 0.0097 + 0.0009
P = 0.0545
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! THIS IS THE LAST DAY TO COMPLETE THIS ASSIGNMENT AND I DESPERATELY NEED TO FINISH THIS ASSIGNMENT WITH AN 100%.
Answer: d. 75% of the screen is occupied by the image
Step-by-step explanation:
First we have to find a relation between image area and screen area.
Image area is the product of image dimensions.
Screen area is the product of screen dimensions.
We have to divide the major image dimension between the major screen dimension
Major image dim/Major screen dim = 20/5 = 4
Now we have to multiply this relation by the minor screen dimension
Minor screen dim x 4 = 4 x 4 = 16
Then we have found 5/4 = 20/16
Now we can calculate what percent of the screen area is occupied by the image area.
Major image dim x minor image dim/Major screen dim x minor screen dim
Since major image dim = major screen dim, we have:
Minor image dim/Minor screen dim = 12/16 = 0.75 = 75% of the screen
Answer: d. 75% of the screen is occupied by the image
[tex]\textit{\textbf{Spymore}}[/tex]
Have to bake a lot of brownies to sell! You have plenty of flour, cocoa, milk, and oil, but you only have 6 1/2 sticks of butter. You need to know how many batches of brownies you can bake, based on your limited amount of butter. You can cook partial batches in order to use up every bit of butter, which will also help you to bake the most brownies possible. Each batch needs 3/4 of a stick of butter.
Answer: 8 + 2/3 batches of brownies you can bake.
Step-by-step explanation:
6 1/2 butter = 6 + 1/2 = (2·6 + 1)/2 = 13/2 sticks of butter, we have this
Since we have 13/2 sticks of butter and each batch of brownies needs 3/4 of a stick of butter, we have to divide the amount of butter we have between the amount of butter we use to bake a batch of brownies.
13/2 butter ÷ 3/4 butter/batch = 13·4/2·3 batches = 52/6 batches = 8 + 2/3 batches
Answer: 8 + 2/3 batches of brownies you can bake.
[tex]\textit{\textbf{Spymore}}[/tex]
By dividing the total amount of butter (13/2 sticks) by the amount required per batch (3/4 stick), we find that it's possible to make 8 full batches of brownies with 6 1/2 sticks of butter, with some butter left over.
To determine how many batches of brownies you can bake with 6 1/2 sticks of butter, you have to divide the total amount of butter you have by the amount required for one batch. Since each batch requires 3/4 stick of butter, you calculate as follows:
Total sticks of butter: 6 1/2
Required per batch: 3/4
Now convert 6 1/2 to an improper fraction: 6 1/2 = 13/2.
Next, calculate the number of batches by dividing the total butter by the butter per batch:
Number of batches = (13/2) / (3/4) = (13/2) * (4/3) = 52/6
When you simplify 52/6, you get 8 with a remainder, meaning you can make 8 full batches of brownies, and you will have some butter left over.
Order the function from the least steep slope to the steepest slope.
The functions ordered from the least steep slope to the steepest slope are: logarithmic (log(x)), linear (x), quadratic (x²), exponential (eˣ), and cubic (x³).
Explanation:To compare the steepness of the slopes for different types of functions, we consider the growth or decay rates of each function. The order is determined by the behavior of the functions as x increases.
1. Logarithmic function (log(x)): It grows slowly and approaches infinity as x increases, making it the least steep slope.
2. Linear function (x): It has a constant slope, making it steeper than logarithmic but less steep than quadratic, exponential, and cubic functions.
3. Quadratic function (x²): It increases faster than linear but slower than exponential and cubic functions.
4. Exponential function (eˣ): It grows at an increasing rate, making it steeper than quadratic but less steep than cubic.
5. Cubic function (x³): It has the steepest slope as x increases, making it the most rapidly increasing function.
This order is based on the general behavior of each function type and their rates of growth or decay. Understanding the characteristics of these functions helps in comparing and ordering them in terms of steepness.
Answer: here’s the correct answer
19. While serving, the shuttlecock must land within JLMN, the service box. Find the probability that a shuttlecock will land in the service box, relative to the court. (JUSTIFY)
Answer:
HI! I'M TAKING THE TEST FOR IT! SO I HOPE THIS IS RIGHT! IF NOT, FORGIVE ME! SO THE ANSWER IS 25.094
Step-by-step explanation:
I attached the step by step, so look at it for me!
Correct answers only please! If you don't know the answer, then please don't guess or say what you think it is.
A student was conducting a study to determine how many mini chocolate chip cookies would fit in a plastic sealed container. He used random packing to find the following.
Using the collected data above what would be a reasonable rough estimate of a ratio of how many cubic inches per cookie?
A. 2.2 in^3/cookie
B. 0.45 in^3/cookie
C. 17.82 in^3/cookie
D. 23.76 in^3/cookie
Answer:
Option A is correct.
Step-by-step explanation:
From the dimensions first find the volume of the container and then find the estimate ratio of each cookie on diving the volume by number of cookies.
[tex]i.e. \\ 11 \times 6 \times 3 = 198 \\ = > \: \frac{198}{90} = 2.2 \\ \\ also \: from \: the \: second \: relation \\ 6 \times 6 \times 2 = 72 \\ = > \frac{72}{33} = 2.18 \: ( = approx \: 2.2)[/tex]
MAX POINTS AND BRAINLIEST
Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(275)?
Houses sell on the market for an average of $275,000 and stay on the market an average of 275 days before being sold.
Houses sell for an average of $275,000.
f(275) indicates houses stay on the market an average of 275 days before being sold.
f(275) represents the average number of days houses stay on the market before being sold for $275,000.
The problem states:
f(p) is the average number of days a house stays on the market before being sold for price p in $1,000s
So we know:
p is the price in $1000s and
f(p) is the number of days before its sold for p
This means f(275) would be the number of days before its sold for 275,000 (since p is in $1000s).
The answer is:
f(275) represents the average number of days houses stay on the market before being sold for $275,000.
The statement "f(275) represents the average number of days houses stay on the market before being sold for $275,000" best describes the meaning of f(275).
Given,
Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s.
In the given function f(p), the variable p represents the price of a house in thousands of dollars ($1,000s), and f(p) represents the average number of days a house stays on the market before being sold for that price.
Therefore, when you evaluate f(275), it tells you the average number of days houses stay on the market before being sold for $275,000.
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Sviatoslav solved the quadratic equation x^2-x-1=0 by completing the square. In the process, he came up with the equivalent equation (x+a)^2 = b, where a and b are constants. What is b?
Answer:
[tex]x=\frac{1+\sqrt5}{2}[/tex] and [tex]x=\frac{1-\sqrt5}{2}[/tex]
and b=[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
We are given that a quadratic equation
[tex]x^2-x-1=0[/tex]
We have to solve the equation by completing square and find the value of b.
[tex](x)^2-2\times x\times \frac{1}{2}+(\frac{1}{2})^2-(\frac{1}{2})^2-1=0[/tex]
[tex](x-\frac{1}{2})^2-\frac{1}{4}-1=0[/tex]
[tex](x-\frac{1}{2})^2-\frac{1-4}{4}=0[/tex]
[tex](x-\frac{1}{2})-\frac{5}{4}=0[/tex]
[tex](x-\frac{1}{2})^2-(\frac{\sqrt5}{2})^2=0[/tex]
[tex](x-\frac{1}{2})^2=(\frac{\sqrt5}{2})^2[/tex]
[tex]x-\frac{1}{2}=\frac{\sqrt5}{2}[/tex] and [tex]x-\frac{1}{2}=-\frac{\sqrt5}{2}[/tex]
[tex]x=\frac{\sqrt5}{2}+\frac{1}{2}=\frac{1+\sqrt5}{2}[/tex]
And [tex]x=\frac{1}{2}-\frac{\sqrt5}{2}=\frac{1-\sqrt5}{2}[/tex]
Therefore,[tex]x=\frac{1+\sqrt5}{2}[/tex] and [tex]x=\frac{1-\sqrt5}{2}[/tex]
and b=[tex]\frac{5}{4}[/tex]
Final answer:
To complete the square for the equation x²-x-1=0, we add (1/2)² = 1/4 to both sides, resulting in the equivalent equation (x-1/2)² = 5/4, where b is 5/4 or 1.25.
Explanation:
To solve the quadratic equation x²-x-1=0 by completing the square, we need to transform the equation into the form (x+a)² = b. First, we would rearrange the equation to isolate the terms with x: x² - x = 1. The next step is completing the square by adding (1/2 ×-1)² = (1/2)² = 1/4 to both sides of the equation, resulting in x² - x + 1/4 = 1 + 1/4. Therefore, the complete square form is (x-1/2)²= 5/4 and the constant b is 5/4 or 1.25.
Can someone help me with this?
Answer:
see below
Step-by-step explanation:
3. The answers in the image below are in "interval notation". In set notation, they might be ...
increasing: {x∈ℝ: -2 < x < 0 ∪ 2 < x}
decreasing: {x∈ℝ: 0 < x < 2}
positive: {x∈ℝ: -4 ≤ x < 1.5 ∪ 3 < x}
negative: {x∈ℝ: 1.5 < x < 3}
domain: {x∈ℝ: x ≥ -4}
range: {x∈ℝ: x ≥ -3}
y-intercept: y ∈ {2}
x-intercepts: x ∈ {1.5, 3}
relative minimum: (x, y) ∈ {(2, -3)}
relative maximum: (x, y) ∈ {(0, 2)}
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4. Answers are in the image below.
The function is increasing where its slope is positive, decreasing where its slope is negative. Where the slope changes sign, there may be a point where the slope is 0 or undefined. The function is neither increasing nor decreasing there, so those points are not part of the intervals for increasing or decreasing.
The function is positive when it is above the x-axis, negative when it is below the x-axis. The function is neither positive nor negative where it is on the x-axis or where it is undefined.
The domain is the horizontal extent of the function. Any points where the function is undefined are excluded.
The range is the vertical extent of the function, all of the y-values where the function output is defined. Here, m(2) is not defined, so y=-7 is not an output at that point. However, y=7 is an output for m(-14 2/3). Likewise, m(9) does not have an output of 0, but m(3) does, so 0 is part of the range.
X- and y-intercepts are where the graph intersects the x- or y-axis, respectively. M(x) is undefined at (9, 0), so there is no x-intercept there.
A relative minimum is any point where the y-values increase on either side of the point. For m(x), the function is undefined at its relative minima, so it cannot be said to have any.
A relative maximum is any point where the y-value decreases on either side of the point. M(x) has one at the vertex of the parabolic segment.
Suppose your state lottery has an expected value of
−34%.
If you spend $40 per month on lottery tickets, how much money would you be expected to lose in an average year?
We can expect to lose $
.
Final answer:
With an expected value of −34% for the state lottery and monthly spending of $40 on tickets, a person can expect to lose $13.60 monthly or $163.20 annually.
Explanation:
If the expected value of playing the state lottery is −34%, and a person spends $40 per month on lottery tickets, we can calculate the expected annual loss as follows:
Firstly, an expected value of −34% means that on average, for every dollar spent, you would expect to lose 34 cents. So for $40 spent in one month, the expected loss would be 34% of $40, which equals $13.60.
Next, we can find the expected loss for a year by multiplying the monthly loss by the number of months in a year:
Monthly expected loss: 0.34 × $40 = $13.60Annual expected loss: $13.60 × 12 months = $163.20Therefore, on average, you can expect to lose $163.20 per year if you continue spending $40 on lottery tickets every month.
PLEASE HELP!!!
The area of a triangle is given by the
formula A = 1/2bh Solve this for h.
Answer:
h = [tex]\frac{2A}{b}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] bh
Multiply both sides by 2 to clear the fraction
2A = bh ( isolate h by dividing both sides by b )
h = [tex]\frac{2A}{b}[/tex]
Answer: h = 2a/b
Step-by-step explanation:
A ball is dropped from a height of 600 feet. The height of the ball, H, after t seconds can be modeled by the function rule, ()=−4.92+600. What would be the independent quantity?
Answer:
the independent quantity is "t" (time in seconds)
Step-by-step explanation:
The problem statement tells you the function rule gives you H (the dependent quantity) as a function of t seconds. "t seconds" is the independent quantity.
Please please help me out with this
Answer:
y = [tex]\frac{3}{4}[/tex] x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ( = (0, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line
m = [tex]\frac{5-2}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]
Note the line crosses the y- axis at (0, 2) ⇒ c = 2
y = [tex]\frac{3}{4}[/tex] x + 2 ← equation of line
the following shows the result of a random survey about favorite seasons. you decide to display the information as a pie chart. what percentage would represent each season? round to the nearest tenth. show or explain your work.
Answer:
The answer is below
Step-by-step explanation:
Data
Winter = 234
Spring = 673
Summer = 843
Fall = 425
Total = 2175
Then
Winter 2175 ------------------------- 100%
234 ----------------------- x
x = 234(100)/2175 = 10.8 %
Spring 2175 ------------------------ 100%
673 ----------------------- x
x = 673(100)/2175 = 30.9 %
Summer 2175 ------------------------ 100%
843 ------------------------ x
x = 843(100) /2175 = 38.8 %
Fall 2175 ------------------------ 100%
425 ---------------------- x
x = 425(100)/2175 = 19.5%
Total = 10.8 + 30.9 + 38.8 + 19.5 = 100%
If you give siri 0 cookies and she has 0 cookies but then gives you back a cookie where did she get the cookie from? if You and her had 0 cookies ?
Answer:
Maybe she borrowed a cookie from somone? or maybe bought a cookie?
Which of these numbers are divisible by 9? 7,625 4,932 9,180 2,969 9,180 and 4,932 2,969, 9,180, and 7,625 9,180 and 7,625 2,969 and 4,932
Answer:
The answer to your question is below:
Step-by-step explanation:
A number is divisible by 9 if the sum of all the individual digits is evenly divisible by 9.
7,625 example 7 + 6 + 2 +5 = 20 it's not divisible by 9
4,932 4 + 9 + 3 + 2 = 19 it's not divisible by 9
9,180 18 it is divisible
2,969 26 it's not divisible by 9
9,180 18 it is divisible
4,932 18 it is divisible
2,969 26 it's not divisible by 9
Answer:
9180 is divisible by 9 .
Step-by-step explanation:
A number is divisible by 9 if the sum of all of it's digits is divisible by 9.
Here, for each of the given numbers, we will find sum of digits then check if the sum of digits is divisible by 9.
For 7,625 :
7 + 6 + 2 +5 = 20 ( not divisible by 9)
For 4,932 :
4 + 9 + 3 + 2 = 19 (not divisible by 9)
For 9,180 :
9+1+8 = 18 ( divisible by 9 )
For 2,969 :
2+9+6+9=26 (not divisible by 9)
if (fx)=5x, what is f^-1(x)
Answer:
x/5
Step-by-step explanation:
To get the inverse function you need to leave the x alone and then switch variables ( f(x) = y)
f(x) = 5x
y = 5x
y/5 = x
Now that x is alone you switch the x for y and the y for x and you get:
x/5 = y
And this new y is the inverse function of f(x) ( f^-1(x))
f^-1(x) = x/5
Jessica wants to buy a new team jacket that costs $35. If Jessica saves $5 a week for 4 weeks and $4 a week for 3 weeks, will she have enough money to buy the team jacket? Explain
No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Lets x represent the number of weeks it will take to save enough money. If she saves $11 each week, then in x weeks she will save 11x dollars.
Also, Add this to the 107 she has already saved, and at the end of 11 weeks she will have 11x + 107 dollars.
We want the amount saved to be equal to the price of the bike, so our equation;
11x + 107 = 173
Now we solve the equation.
Subtract 107 from both sides ;
11x = 66
Divide both sides by 11;
x = 6
No, Jessica he will not have enough to buy the jacket. She would have saved $32, not $35.
Learn more about equations here;
https://brainly.com/question/10413253
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The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. The amount collected can be modeled by the equation , where x represents the number of small vehicles and y represents the number of larger vehicles. If the number of larger vehicles washed was 50, how many small vehicles were washed in total?
a.55
b.60
c.130
d.150
Answer:
b. 60
Step-by-step explanation:
We have been given a formula [tex]5x+10y=800[/tex], where x represents the number of small vehicles and y represents the number of larger vehicles.
To find the number of small vehicles, we will substitute [tex]y=50[/tex] in the given equation as:
[tex]5x+10(50)=800[/tex]
[tex]5x+500=800[/tex]
[tex]5x+500-500=800-500[/tex]
[tex]5x=300[/tex]
[tex]\frac{5x}{5}=\frac{300}{5}[/tex]
[tex]x=60[/tex]
Therefore, 60 small vehicles were washed in total and option 'b' is the correct choice.