The two statements that are logically true as per the given data is q=>p and p ∧ q .
p = raining
q = Robert is laughing
q=>p this is because the entire proposition is logically true when the conclusion of the condition is true.
and
p ∧ q means that it is raining and Robert is laughing which is again logically true.
If two logical statements have the same truth value in all circumstances, they are said to be comparable. This fact can occasionally be used to demonstrate a mathematical result by switching out one expression for an equivalent one while maintaining the original compound proposition's truth value.
Propositional types based on Truth values
tautologycontradictioncontingency.To learn more about proportional equivalence
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domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this
The reasonable domain is { 1,2,3,4,5 }
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.
Here, the situation is not given.
So, the reasonable domain is { 1,2,3,4,5 }
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On a coordinate plane, how are the location of the point (1 , -5) and (1 , 5) related?
Reflection across the y-axis on a coordinate plane.
What is the short definition of a coordinate plane?
Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is a single horizontal number line. The y-axis is a vertical number line, which is the other number line. A place known as the origin is where the two axes collide. The coordinate plane allows us to graph points, lines, and more.
What is reflaction of coordinate plane?
Transformation is the process of making each point in a shape appear at the same distance on the other side of a specified line.
The term "line of reflection" refers to introspection with relation to that line. A line is crossed to flip the image.
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statisticians have been able to show that the normal bell curve property also occurs when the sample size is 30 observations or fewer. true false
statisticians have been able to show that the normal bell curve property also occurs when the sample size is 30 observations or fewer: False.
Where in a normal curve can most observations be found?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.
The normal distribution is a continuous probability distribution with symmetry around its mean, a central peak around which the majority of observations cluster, and a tapering off of probabilities in both directions for values that are farther from the mean.
When a result is significant, it simply implies that you may be certain that it is true, not that you merely got fortunate (or unlucky) in the sample selection.
Thus, the statement given in the question is false.
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in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
HELP ME
The number of bacteria after 4 hours is 800
How to determine the number of bacteria after 4 hours?The complete question is added at the end of this solution
Given that,
Initial population = 50Reproduction = splitting every hourThis means that the rate of production is by doubling
So, we have the following parameters
a = 50
r = 2
An exponential function is represented as
A(n) = arⁿ
Substitute the known values in the above equation, so, we have the following representation
A(n) = 50(2)ⁿ
We have to find,
Find the number of bacteria after 4 hours.
This means that n = 4
So, we have
A(4) = 50(2)⁴
Evaluate
A(4) = 800
Hence, the population is 800
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Complete question
in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
Find the number of bacteria after 4 hours.
solve
pleaseeeeeeeeeeee
The equation can be written as - 8x + 12 = 8x + 12 which means it has infinite solutions. So, there are infinite values of [x] for which parameters are equal.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a square and a triangle as shown.
For equal perimeter -
4(2x + 3) = (2x - 2) + 2(3x + 7)
8x + 12 = 2x - 2 + 6x + 14
8x + 12 = 8x + 12
The equation can be written as -
8x + 12 = 8x + 12
which means it has infinite solutions.
So, there are infinite values of [x] for which parameters are equal.
Therefore, the equation can be written as - 8x + 12 = 8x + 12 which means it has infinite solutions. So, there are infinite values of [x] for which parameters are equal.
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Conider the algebraic expreion
32pq2−4p2q12pq−7
Find term that are not contant. A) 32p2q,−4p2q,12pq, 7
b) 32, -4, 12, 7
c) 32pq2,4pq2,12pq
d) 32pq2, −4p2q, 12pq
The correct part is (d) i.e. 32pq2, -4p2q and 12pq are not constants in the given algebraic expression.
What is a constant?
A constant is a value or number that is consistently the same, regardless of how it is expressed.
The algebraic expression given is 32pq2−4p2q + 12pq−7.
A constant is that term which does not any variable portion or which is fixed.
Here, all terms have variables in the form of p and q but The last term does not have any variable.
So, The terms which have variables are the terms which are not constant.
Hence, 32pq2, -4p2q and 12pq are not constant in the given expression.
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If 80% of 120 students passed the test, and (1)/(4) of these students received an A on the test, how many students received an A?
A 20 students
B 22 students
C 24 students
D 26 students
24 students received an A on the test.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
If 80% of 120 students passed the test, the number of students who passed is 120 * 80% = 96 students.
If (1)/(4) of these students received an A on the test, the number of students who received an A is (1)/(4) * 96 = 24 students.
Therefore, 24 students received an A on the test.
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(x2 – 2x – 37) ÷ (x2 – 3x – 40)
Answer:
If you divide:
[tex]1+\frac{x+3}{x^2-3x-40}[/tex]
If you simplify:
[tex]\frac{x^2-2x-37}{(x-8)(x+5)}[/tex]
Step-by-step explanation:
nasa is conducting an experiment to find out the fraction of people who black out at g forces greater than 6. in an earlier study, the population proportion was estimated to be 0.43. how large a sample would be required in order to estimate the fraction of people who black out at 6 or more gs at the 99% confidence level with an error of at most 0.03? round your answer up to the next integer.
The sample size of 502 should be the required size to perform the experiment.
The confidence interval (1 - alpha )% for population percentage p is as follows,
CI =p +- z √pq/n
The following formula is used to determine the margin of error,
MOE = z * √pq/n
The information provided is, with a margin of error of 0.03 and = 0.32.
The z-value for an 85% degree of confidence is,
For the z-value, use a z-table.
The sample size n is then determined by,
MOE = z * √pq/n
= 1.44 √ 0.32( 1 - 0.32 ) ²/ 0.03
= ( 22.392 )²
= 502
Therefore, a sample of size 502 would be needed to assess the percentage of subjects that experience blackouts at 6 or more Gs.
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Please help, I don't quite understand.
Answer:
[tex]y=-\frac{3}{4}x-2[/tex]
Step-by-step explanation:
Substitute into point-slope form and rearrange to slope-intercept form.
[tex]y+8=-\frac{3}{4}(x-8) \\ \\ y+8=-\frac{3}{4}x+6 \\ \\ y=-\frac{3}{4}x-2[/tex]
A teacher grades 27 tests in 3 hours.
find the constance of variation
Answer: 9
Step-by-step explanation:
27 divided by 3 is 9 so 9 is the constant variation
What is the major difference between the alternate hypothesis and the null hypothesis?.
The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.
Hypothesis;-
A put forward explanation for a phenomenon is called a hypothesis (plural: hypotheses).
A hypothesis cannot be called a scientific hypothesis unless it can be tested using the scientific process. Observations from the past that cannot be fully explained by the body of knowledge at this time often serve as the foundation for scientific ideas.
A scientific hypothesis is distinct from a scientific theory, despite the fact that the phrases "hypothesis" and "theory" are sometimes used interchangeably.
A working hypothesis is a theory that has been accepted provisionally and is put forth for further investigation[1], beginning with an educated guess or way of thinking.
As a result, the alternative hypothesis of a test indicates the effect or relationship that your research predicts, whereas the null hypothesis of a test always predicts that there will be no effect or no association between variables.
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3x + 5y = 5
-2x-8y = 6
How can you eliminate the x-terms in this system?
3x + 5y = 5
Multiply by ? on both sides.
-2x8y=-6
Multiply by ?
on both sides.
Answer:
3x + 5y = 5
Multiply by 2 on both sides.
-2x - 8y = -6
Multiply by 3 on both sides.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} \;\;\:3x + 5y = 5\\-2x-8y = 6\end{cases}[/tex]
To eliminate the x-terms in the given system of equations:
Multiply 3x + 5y = 5 by 2 on both sides.Multiply -2x - 8y = 6 by 3 on both sides>3x + 5y = 5 → Multiply by 2 on both sides:
[tex]\implies 2(3x+5y)=2(5)[/tex]
[tex]\implies 6x+10y=10[/tex]
-2x - 8y = 6 → Multiply by 3 on both sides:
[tex]\implies 3(-2x - 8y) = 3(6)[/tex]
[tex]\implies -6x - 24y = 18[/tex]
Add them together to eliminate x:
[tex]\begin{array}{crcccc}&6x&+&10y&=&10\\+&(-6x&-&24y&=&18\\\cline{2-6} &&-&14y&=&28\end{array}[/tex]
You deposit $3000 in an account earning 8% interest compounded monthly. How much will you have in the account in 5 years?
Answer: $5580
The formula for compound interest is:
A = P(1 + r/n)^nt
where A is the final amount, P is the initial principal (the amount you deposited in the account), r is the annual interest rate (8% in this case), n is the number of times the interest is compounded per year (12 times per year if the interest is compounded monthly), and t is the number of years the money is invested (5 years in this case).
Plugging in the values from the problem, we get:
A = $3000(1 + 0.08/12)^(12*5)
= $3000(1.0067)^60
= $3000*1.86
= $5580
So, after 5 years, you will have $5580 in the account if you deposit $3000 and earn 8% interest compounded monthly.
The value of amount after 5 years is,
⇒ A = $4,380
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
You deposit $3000 in an account earning 8% interest compounded monthly.
Hence, The value of amount after 5 years is,
⇒ A = 3000 [ 1 + 0.08]⁵
⇒ A = 3000 × 1.08⁵
⇒ A = 3000 × 1.46
⇒ A = $4,380
Thus, The value of amount after 5 years is,
⇒ A = $4,380
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When given these two equations:
y = 2x + 4
y = 3x - 6,
How would I set up these systems of equations so that I could find the solution?
O Manipulate my variables to have the same coefficient, but different signs
O Make the two equations equal to each other and solve
O add the equations together
O subtract the equations together
There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer:
subtract the equations
Step-by-step explanation:
the second answer option is nonsense.
if the equations really have exactly one solution, then it is impossible to make them equal.
if 2 equations can be made equal, that means they have infinitely many solutions.
the other answers have all some merit.
but the last one (subtract the equations) is the best one.
it means
y = 2x + 4
- y = 3x - 6
------------------
0 = -x + 10
after adding x to both sides we get
x = 10
with that we use any of the 2 basic equations to get y :
y = 2x + 4 = 2×10 + 4 = 24
this worked right away, because the y terms have the same coefficients (1). so, by subtracting one equation from the other we eliminate y as variable and can solve for x.
if that was not the case like in
2y = 4x + 8
y = 3x - 6
we would have to do some transformation or manipulation to bring the system into a form like here in the beginning.
and the first and the third answer option would apply.
Which statement about the graph of y=12·(1/2)x is true?
The graph has an asymptote at y = 0.
Option (A) is correct.
What is the asymptote of the graph?
An asymptote is a straight line that constantly approaches a given curve but does not meet at an infinite distance. In other words, an Asymptote is a line that a curve approaches as it moves toward infinity.
The given function is:
[tex]y = 12.(\frac{1}{2})^x[/tex]
Now let's draw the graph for this given function,
By observing the graph we can conclude that the graph has an asymptote at y = 0 cause it is not meeting to the x-axis when it is approaching infinity.
Hence, the graph has an asymptote at y = 0.
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HELP ASAP 100 POINTZZZZZZ
ollow the instructions below.
(a) Rewrite the percentage in the sentence below as a decimal. Decimal:
In a recent poll, 5% of the people surveyed were in favor of the new law.
(b) Rewrite the decimal in the sentence below as a percentage. Percent:%
The model was 0.274 of the size that the original was.
Decimal of 5% = 0.05, 0.274 to Percent:% 27.4%
What is percentage?A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The sign "%" is frequently put after the number to indicate percentages.
What is decimal?A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole amounts.
a).
so we have to write this in decimal that is remove percentage
To remove % we have , divide it by 100
suppose x% to remove % we divide it by 100, x% = x/100
5% = 5/100 =0.05 which is in decimal
b). The model was 0.274 of the size that the original was. we need to add percentage so to add percentage multiple it by 100
making x to percentage
x*100 = x%
so 0.274 to % will be
0.274 *100
27.4%
Decimal of 5% = 0.05, 0.274 to Percent:% 27.4%
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A customer pays an initial fee and a daily fee to rent a snowmobile. The total payment for 3 days is 92 dollars. The total payment for 5 days is 120 dollars. What is the daily fee?.
A snowmobile can be rented for $14 per day with a $50 initial fix cost.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Let the initial fee be x and daily fee be y,
92=x+3y
120=x+5y
x+5y=120
x+3y=92
Subtract both,
2y=28
y=$14
x+5y=120
x+70=120
x=$50
The daily fee to rent a snowmobile is $14 per day with a initial fix fee of $50.
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An item is regularly priced at $83. It is on sale for 35% off the regular price.
Answer: $53.95
Step-by-step explanation:
Original Price: $83
Discount: 35%
35%=0.35
$83 x 35%, or 83 x 0.35
=29.05
$83-29.05
=$53.95
the width of a confidence interval for a population mean depends on group of answer choices the sample proportion. the population size. the level of confidence chosen. the sample mean.
The width of a confidence interval for a population mean depends on group of answer choices the sample proportion is population size and sample mean .
Given :
What is population size ?
population is the entire set of items from which you draw data for a statistical study. It can be a group of individuals, a set of items, etc.
What is sample mean ?
The sample mean from a group of observations is an estimate of the population mean .
so the width of a confidence interval is dependent on population size and sample mean .
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Which number represents a square root of 3 cos
3 [cos()+isin()]?
2
O √[cos()+sin()]
8
O
√3 cos (1) + i sin()]
5
O √3 [cos (STT)+isin (STT)]
6
O
3π
√3 [cos (3T) + sin(3)]
i
2
Square root of 3 cos
Consider the given data.
[tex]$$\begin{aligned}& \sin \theta+\sin ^2 \theta=1 \\& \sin \theta=1-\sin ^2 \theta \\& \sin \theta=\cos ^2 \theta\end{aligned}$$[/tex]
We have,
[tex]$$\begin{aligned}& =\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta+2 \cos ^4 \theta+2 \cos ^2 \theta-2 \\& =\cos ^{12} \theta+3 \cos ^{10} \theta+3 \cos ^8 \theta+\cos ^6 \theta+2\left(\cos ^4 \theta+\cos ^2 \theta-1\right) \\& =\left(\cos ^4 \theta+\cos ^2 \theta\right)^3+2\left(\cos ^4 \theta+\cos ^2 \theta-1\right)\end{aligned}[/tex]
[tex]$$Since, $\sin \theta=\cos ^2 \theta$Therefore,$$\begin{aligned}& =\left(\sin ^2 \theta+\sin \theta\right)^3+2\left(\sin ^2 \theta+\sin \theta-1\right) \\& =1^3+2(1-1) \\& =1+0\end{aligned}[/tex]
[tex]=1[/tex]
Hence, the required value is 1.
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a triangle has two sides of length 18 and 3. what is the largest possible whole-number length for the third side?
Answer:
20
Step-by-step explanation:
Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.
And 18+3... 21, that is smaller than 21.
If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.
80% of what number is 16
a. PART
b.TOTAL
c.PERCENT
d. WRITE AND SOLE THE PROPORTION
Answer:
:)
Step-by-step exp
16/.8 = 20
Answer:
20
Step-by-step explanation:
ask urself what 80/100 is to 16 call the number x find xF(x) is defined by the equation f(x) = 5x² - 9x-12. What effect will multiplying
f(x) by 0.5 have on the graph?
A. The graph will be compressed vertically.
B. The graph will be stretched horizontally.
C. The graph will be stretched vertically.
D. The graph will be compressed horizontally.
F(x) is defined by the equation f(x) = 5x² - 9x-12, the effect will multiplying
f(x) by 0.5 have on the graph ,then the graph will be compressed vertically.
What is a compressed graph?A transformation in which all distances on the coordinate plane are shortened by multiplying either all x-coordinates (horizontal compression) or all y-coordinates (vertical compression) of a graph by a common factor less than 1.
Given that;
f(x) = 5x² - 9x-12
Effect will multiplying f(x) by 0.5 , After the transformation
g(x) = (0.5) f(x)
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.After transformation the graph will be composed vertically.
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You in-line skate from an elevation of 720 feet to an elevation of 750 feet in 30 minutes. Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour. Compare your rates of change in elevation.
Please help im stuck on this problem
Your friend's rate of change in elevation is 0.5 feet per minute more than your rate.
What is the formula for the rate of change in elevation?To find the height of the building (QR), we can use the angle of elevation formula tan θ=QR/PR.If you're looking for an exact number, use an altimeter, computer, or smartphone to calculate your current position above sea level. If you're trying to find a difference in elevation between 2 points of land, use tie a length of string between two posts and use a level to determine the difference.Let the area of the triangle be xy/2 and dA/dt becomes dA/dt= (xy' +yx')/2. To find y' use the Pythagorean theorem x2 +y2 =z2 where z is constant. So xx' +yy' =0 and y'=-xx'/y and substituting this into dA/dt gives dA/dt =(-x2x'/y +x'y)/2 = x'(y2 -x2)/2y.An angle of elevation is an angle with one horizontal arm, and one arm above horizontal. Usually an angle of elevation is less than or equal to 90°.Rate of change in elevation = elevation of distance/time
The elevation of 720 feet to an elevation of 750 feet in 30 minutes.
Your rate of change in elevation = 750 - 720 / 30
Your rate of change in elevation = 30 / 30
Your rate of change in elevation = 1 foot per minute
Your friend in-line skates from an elevation of 600 feet to an elevation of 690 feet in one hour.
Your friend's rate of change in elevation = 690 - 600 / 60
Your friend's rate of change in elevation = 90 / 60
Your friend's rate of change in elevation = 1.5 feet per minute
The difference in rate of change in elevation = 1.5 - 1 = 0.5 feet per minute
Thus, your friend's rate of change in elevation is 0.5 feet per minute more than your rate.
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Bryan says that every equation that has one variable has a solution to it. Disprove Bryan’s assertion with two counterexamples.
Bryan's assertion is not true. Here are two counter examples to disprove it:
1) x = 0
This equation has only one variable, x, but it has no solution because there is no value of x that will make the equation true.
2) x^2 + 1 = 0
This equation also has only one variable, x, but it has no solution because there is no value of x that will make the equation true.
These examples show that it is possible for an equation with one variable to have no solution.
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This one is confusing please someone help:
1. give another name for plane p
2. name a line that intersects the plane
3. name two rays
4. name 3 points in plane p
1.You can find another name for plane P by using any three points in the
plane that are not on the same line. Hence, the another name for plane P is the plane GAC .
2. The line intersects the plane is EF
3. The two rays in the plane are CB , DB
4. A,B,C are three points in the plane p.
What is meant by plane?Spanned by two linearly independent vectors, a plane is a doubly ruled surface in two dimensions. Hyperplanes are the result of extending the plane to higher dimensions. The dihedral angle is the angle at which two planes intersect.
Using any three points on the plane that are not on the same line, you can come up with another name for plane P. Therefore, another name for plane P is GAC. The plane is intersected by the line at EF. CB and DB are the two rays in the plane. There are three points in the plane p, A, B, and C.
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On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0. 62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0. 71. A random sample of 40 workers was selected from Company B and another random sample of 40 workers was selected from Company C. The proportion of workers from Company B who purchased coffee was
The correct unit of measure for the mean of the sampling distribution of (pˆB - pˆC) is Workers , the correct option is (d) .
In the question ,
it is given that ,
the proportion of workers who purchase coffee from company B is = 0.62
the proportion of workers who purchase coffee from company C is = 0.71
the random sample taken from company B is = 40 workers
the random sample taken from company C is = 40 workers
we know that , a proportion is written as two equivalent fractions.
So , Each ratio compares the same units, percentage of workers purchasing the coffee in the restaurant,
hence, the unit of measure for the mean of sampling distribution is workers .
Therefore , the unit for the measurement for the mean is (d) Workers .
The given question is incomplete , the complete question is
On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0.62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0.71. A random sample of40 workers was selected from Company B and another random sample of 40 workers was selected from Company C. The proportion of workers from Company B who purchased coffee was pˆB=0.70 and the proportion of workers from Company C who purchased coffee was pˆC=0.75.
What is the correct unit of measure for the mean of the sampling distribution of pˆB - pˆC ?
(a) Days
(b) Dollars
(c) Companies
(d) Workers .
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A website displayed the following formula for the volume of a cone.
V = 1/3 nrh
James had never seen this formula before, but he knew there must be a typographical error in this formula. How could he tell
there was an error?
A. The calculated volume would be in linear units instead of cubic units.
B. The calculated volume would be in square units instead of cubic units.
C. The calculated volume would be in cubic units instead of square units.
D. The calculated volume would be in square units instead of linear units
James will declare the error by saying that the calculated volume would be in cubic units instead of square units.
What formula is correct for volume of cone?A cone has circular base and smooth curved surfaces that ends at the top.
volume of cone formula is denoted by V = 1/3×(πr²h) cubic unit
r is the radius of base of cone
h is the height of cone
π =3.142
hence, James needs to say that the unit of volume of cone should be written in cubic
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While working a summer job, Evelyn earned $198.10 in 7 hours. Find the rate of change.
Answer:
$221
Step-by-step explanation: