(a) All the values in the last column of the truth table are T, the statement [p ^ (p V q)] → q is a tautology.
(b) All the values in the last column of the truth table are T, the statement [(p → q) ^ (q + r)] → (p + r) is a tautology.
(c) All the values in the last column of the truth table are T, the statement [p ^ (p → q)] → q is a tautology.
Here is the truth table for each of the conditional statements
a) [p ^ (p V q)] → q
p p V q p ^ (p V q) q [p ^ (p V q)] → q
T T T T T
T T T F F
T F F T T
F T F T T
F F F T T
F F F F T
Since all the values in the last column of the truth table are T, the statement [p ^ (p V q)] → q is a tautology.
b) [(p → q) ^ (q + r)] → (p + r)
p q r p → q q + r (p → q) ^ (q + r) p + r [(p → q) ^ (q + r)] → (p + r)
T T T T T T T T
T T F T T T T T
T F T F T F T T
T F F F F F T T
F T T T T T T T
F T F T T T F T
F F T T T T F T
F F F T F F F T
Since all the values in the last column of the truth table are T, the statement [(p → q) ^ (q + r)] → (p + r) is a tautology.
c) [p ^ (p → q)] → q
p p → q p ^ (p → q) q [p ^ (p → q)] → q
T T T T T
T F F T T
F T F T T
F T F T T
Since all the values in the last column of the truth table are T, the statement [p ^ (p → q)] → q is a tautology
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Hudson bought snacks for his team's practice. He bought a bag of apples for $1.59
and a 10-pack of juice bottles. The total cost before tax was $7-39.
Write and solve an
equation which can be used to determine r, how much each bottle of juice cost.
Answer:
Step-by-step explanation:
Let r be the cost of each juice bottle.
The total cost of the juice bottles is 10 * r = 10r.
The total cost of the apples and the juice is $1.59 + 10r = $7.39.
We can set up an equation using the above information:
$1.59 + 10r = $7.39
10r = $7.39 - $1.59 = $5.80
r = $5.80 / 10 = $0.58
Therefore, each juice bottle costs $0.58.
Please help me with this question.
Based on the information provided, the area of this triangle is 44.17 square centimeters.
How to calculate the area of a triangle?The area of a triangle (surface occupied by the triangle) can be calculated using the three lengths of the sides of the triangle or using two sides and one angle as it is shown below:
Multiply the two sides given: 5.6 cm x 18.6 cm = 104.16 square centimeters.Multiply this value by sin (y) 104.16 x 58 sin = 44.17 cmBased on this, the area of the triangle given is 44.17 square centimeters.
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5.___________________means if an event happens by chance
What number has 1 ten thousand, the same number of thousands as ten thousands, 8 more hundreds than thousands, 7 fewer tens than hundreds, and 1 more than tens?
Answer: 11,923
Step-by-step explanation:
If bookshelf A is 3 feet long and bookshelf B is 4 feet long, what is the length of bookshelf C?If bookshelf A is 3 feet long and bookshelf B is 4 feet long, what is the length of bookshelf C?
A. 5 feet is the length of bookshelf C.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
this is a Pythagorean theorem problem, and it involves right triangles.
If this is the case, then we can use the formula: a² + b² = c².
In this case, it gives us the values of a and b,
so we have 3² + 4² = c².
This is equal to 9 + 16 = c², and further simplified, 25 = c².
So we can then find the square root of 25,
written as √25, which would equal 5,
as 5² = 5 * 5,
and 5 * 5 = 25.
So therefore your answer would be A. 5 feet.
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Use the distributive property to rewrite the expression 5(n+9)
Need help on Hw is this correct? If not please help.
Answer:
D
Step-by-step explanation:
(f(g(x))' = g'(x)×f'(g(x))
so,
4×e^(-7x) = g'(x)×f'(g(x)
we know that
(e^x)' = e^x
and the integral vice versa (+ C of course).
4×(e^(-7x))' = 4×(-7x)'×e^(-7x) = 4×-7×e^(-7x)
so, in order for
(f(g(x))' = 4×e^(-7x)
we need to have an additional -1/7 factor in f(g(x)) (which is the integral of (f(g(x))'):
-1/7 × 4 × e^(-7x) = -4/7×e^(-7x)
so, D is the correct answer
Given a power function, h (x) = 3x0.5, determine which statement(s) accurately
describes the behavior of h(x).
The domain for h(x) is [0, ∞).
h(x) has a zero at x=0.
h(x) is increasing on (-∞, ∞).
h(x) has no relative maximum.
Submit Answer
attempt 3 out of 3/problem 1 out of max 1
The power function, h(x) = [tex]$$3x^{0.5[/tex] then the domain for h(x) is [0, ∞).
What is meant by power function?A power function is a single-term function that has a real number, a coefficient, and a variable raised to a specified real number as its product. Coefficients are numbers that multiply a variable by itself when it is increased to an exponent.
A variable base raised to a fixed power is a component of a power function. This function is raised to a variable power from a constant base. Not a power function, but an exponential function is what this is.
The power function in statistics is a function that connects the likelihood of rejecting a null hypothesis on the value of a parameter to its true value. An exponential function has its variable in its exponent, whereas a power function has its variable in its base. This is the key distinction.
Therefore, the correct answer is option a) The domain for h(x) is [0, ∞).
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SHOW WORK! PLEASE EXPLAIN! Thank you
Answer:
Below
Step-by-step explanation:
Calculate the unit price of $ per ounce of the 4 options to find the smallest
$2 / 4 = .50 per ounce
4.25 /8 = .53
6/12 = .50
6.75/18 = .375 per ounce <=====cheapest
[tex]7x/5x^2-x[/tex]
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem! (see explanation)
Step-by-step explanation:
Simplify:[tex]7x/5x^2-x\\= \frac{-5x^2+7x}{5x^2} \\=\frac{-5x^2+7}{5x}[/tex]
(Hope this helps!)
The city is building a rectangular parking lot. The city wants the width of the parking lot to be 8 yards. The area of the parking lot must be at most 80 square yards. (These are city regulations.) Write an Inequality that describes the possible lengths (in yards) of the parking lot.
Use l for the Length of the rectangular parking lot.
Answer:The area of the parking lot is length * width. If the width of the parking lot is 8 yards, the area of the parking lot can be represented by the inequality:
Area <= 80
length * 8 <= 80
To get the possible lengths of the parking lot we need to divide both sides by 8:
length <= 10
Therefore, the inequality that describes the possible lengths of the parking lot (in yards) is:
length <= 10 yards
The possible lengths of the parking lot is any value less than or equal to 10 yards.
Step-by-step explanation:
Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution? 3x + 4y = 38 5x - 5y = 30
The solution of given system of equations is (10, 4).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are 3x+4y=38 -----(I) and 5x-5y=30 -------(II)
x-y=6 -------(III)
x=6+y
Substitute x=6+y in equation (I), we get
3(6+y)+4y=38
18+1y+4y=38
5y=20
y=4
Substitute y=4 in equation (III), we get
x=10
So, the solution is (10, 4)
Therefore, the solution of given system of equations is (10, 4).
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PLEASE LIST A,B,C,D,E,F (image attached)
Answer:
[tex]a (5)[/tex]
[tex]b (0,5)[/tex]
[tex]c (-3,0,5)[/tex]
[tex]d (1/3, 5/8, 66/67, -1.27)[/tex]
[tex]e( \sqrt{2} \: \sqrt{7} \: )[/tex]
[tex]f( - 3 \: 5 \: \frac{1}{3} \: \frac{5}{8} 0 \: \sqrt{2 \:} \sqrt{7} - 1.27 \: \frac{66}{67} )[/tex]
Fill in the blank: when you build a sumif or countif formula, the first part of the formula in parentheses is the_______ A. Criteria B. Cndition C. Operator D. Range
The Range is the first component of the formula in parentheses.
What is Range
The range in statistics is the difference between the highest and lowest values for a specific data collection. For instance, if the given data set has the values 2, 5, 8, 10, and 3, the range will be 10 - 2 = 8.
It is possible to think of the range as the distance between the highest and lowest observation as a result. The consequence is known as the scope of observation. The breadth of statistics reflects the diversity of observations.
The first component of a sum or count calculation that is enclosed in the parenthesis is the Range.
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What is 32% expressed as a decimal?
Given the problem:
What is 32% expressed as a decimal?
To convert percentages to decimals, simply divide the percentage by 100. Or move the percentage sign two places to the left and change it to a decimal point.
So the answer is 0.32
Please help me with this question.
The area of the shaded region is given as follows:
70 cm².
How to obtain the area of the shaded region?The area of a triangle is given by half the multiplication of the base and of the height of the triangle.
For the triangle, the area is of 30 cm², while the height is of 6 cm, hence the base is obtained as follows:
0.5 x 6 x b = 30
3b = 30
b = 30/3
b = 10 cm.
Considering the side length of 10 cm², the area of the square is given as follows:
10² = 100cm².
The area of the shaded region is given by the subtraction of the area of the square by the area of the triangle, hence:
100 - 30 = 70 cm².
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Choose the ratio that is equivalent to this one 2/9
A bakery sells three varieties of muffins. On a recent morning, the bakery sold 41 blueberry muffins, 27 bananas nut muffins and 20 bread muffins. Estimate the total number of muffins sold.
suppose a pipe containing water with 0.2 kg of sugar per liter runs into a tank filled with 400 liters of water currently containing 10 kg of sugar. the flow from the pipe enters the tank at 10 liters per minute. the solution is kept thoroughly mixed and drains from the tank at the same rate. setup and solve an initial value differential equation.
An initial value differential equation is S(t) = 10 * e^(-0.005t).
Sugar Amount Differential EquationThe initial value differential equation for the amount of sugar in the tank can be modeled as:
dS/dt = (0.2 kg/L) * 10 L/min - (S/400 L) * 10 L/min
where S is the amount of sugar in the tank in kg and t is the time in minutes.We can solve this equation using separation of variables:dS/S = -0.005 dt
Integrating both sides:ln(S) = -0.005t + C
Using the initial condition that S = 10 kg at t = 0:ln(10) = C
So the solution is:S(t) = 10 * e^(-0.005t)
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75° 30’ convert into radian
When 75°30' converted into radian it will be 1.309 radians.
What do you mean by radian?A radian is a unit of measurement for angles in mathematics. It is defined as the angle formed at the center of a circle by an arc that is equal in length to the radius of the circle. In other words, a radian is the angle that subtends an arc equal in length to the radius of the circle.
The radian is used as a unit of measurement because it provides a convenient and natural way to describe angles in terms of their relationship to circles. It allows for the calculation of angles in terms of lengths, making it easier to solve problems involving circular motion and trigonometry. The conversion between degrees and radians is given by the formula: 1 radian = 180/π degrees, where π is the mathematical constant pi.
To convert degrees to radians, use the formula: radians = (degrees × π) / 180.
For 75° 30', the conversion to radians is:
radians = (75° 30' * π) / 180 = (75 + 30/60) * π / 180 = 1.309 radians.
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K
W
Use the accompanying radiation levels in
kg
phones. Find the percentile P25-
P25 =
for 50 different cell
W
(Type an integer or a decimal. Do not round.)
kg
0.25 0.29 0.35 0.52 0.62 0.62 0.63 0.65 0.73 0.82
0.87 0.90 0.91 0.92 0.94 0.94 0.96 0.99 1.05 1.09
1.09 1.10 1.12 1.15 1.15 1.16 1.16 1.17 1.18 1.19
1.19 1.21 1.28 1.28 1.29 1.32 1.32 1.34 1.34 1.36
1.36 1.38 1.39 1.41 1.43 1.43 1.44 1.44 1.51 1.56
na
01
The 25th percentile of radiation levels is given as follows:
P25 = 0.905 W/kg.
How to obtain the percentile rank?A measure is said to be in the xth percentile of the data-set if it the bottom separator of the bottom x% of measures of the data-set and the top (100 - x)% of measures, that is, it is greater than x% of the measures of the data-set.
In this problem, the data-set has 50 elements, hence the position of the element at the 25th percentile is given as follows:
0.25 x 50 = 50/4 = 12.5.
Meaning that the 25th percentile is the mean of the 12th and 13th elements, as follows:
P25 = (0.9 + 0.91)/2
P25 = 0.905 W/kg.
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Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on the due date until the card is paid off. How many months does it take to pay off the card, and what is the total amount paid including interest?
Each month, the interest for the current balance is calculated as:
$3,287.90 * 14.5% / 12 = $48.22
How Do Interest Rates Work?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
The new balance after each payment is:
$3,287.90 + $48.22 - $1,200.00 = $2,147.12
Repeat the calculation until the balance is zero:
Month 1:
Balance: $3,287.90
Interest: $48.22
New Balance: $2,147.12
Month 2:
Balance: $2,147.12
Interest: $31.14
New Balance: $1,178.26
...
Month 26:
Balance: $0.00
So, it takes 26 months to pay off the credit card, and the total amount paid including interest is $31,622.68.
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Is it ever possible to have a graph of a function that is symmetric about the y-axis AND the origin? Explain your thinking. (say yes or no and explain in more detail)
Yes, it is possible to have a graph of a function that is symmetric about both the y-axis and the origin. This means that if (x, y) is a point on the graph, then (-x, y) and (x, -y) are also points on the graph.
In other words, the function has both reflectional symmetry about the y-axis and rotational symmetry about the origin. An example of such a function is y = x², which is a parabolic function that opens upwards and is symmetric about both the y-axis and the origin.
What is the function about?A graph is symmetric about the y-axis if the graph is unchanged when reflected over the y-axis. This means that for any point (x,y) on the graph, the corresponding point (-x,-y) will also be on the graph. A graph is symmetric about the origin if the graph is unchanged when reflected over the origin.
Therefore, This means that for any point (x,y) on the graph, the corresponding point (-x,y) will also be on the graph. When a graph is symmetric about both the y-axis and the origin, it means that the graph is unchanged when reflected over either the y-axis or the origin.
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please answer fast, question from ixl.
Coach Yamada can make fewer than 10 full teams.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Each team can have 8 players.
and, not more than 80 players can the Coach take.
let x be the number of teams formed then the inequality is
8x < 80
Now, solving the inequality
x< 80/8
x < 10.
Hence, Fewer than 10 full teams can be made.
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In ΔOPQ, q = 75 cm, mm∠O=113° and mm∠P=18°. Find the length of o, to the nearest centimeter.
The length of o to the nearest centimeter is 91 cm.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
We have the law of sine of triangles, which is stated as,
a / sin A = b / sin B = c / sin C
where a, b and c are the sides opposite to the angles of the triangle A, B and C respectively.
Given, In ΔOPQ, m ∠O=113° and m ∠P=18°.
m ∠Q = 180° - (m ∠O + m ∠P)
= 180° - (113° + 18°)
= 49°
q / sin Q = o / sin O
o = (q / sin Q) (sin O)
= (75 / sin 49°) (sin 113°)
= (75 / 0.7547) (0.9205)
= 91.476 cm
≈ 91 cm
Hence the length of o is 91 cm.
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Answer: 91 is the answer on dlta
Find the first and second derivative of the following function in terms of the parameters
c1 and c2.
y=c1x + c2x5
y′=
y″=
Find a linear second-order differential equation
F(x, y, y′, y″) = 0
for which
y = c1x + c2x5
is a two-parameter family of solutions. Make sure that your equation is free of the arbitrary parameters c1 and c2. (Use yp for y′ and ypp for y″.)
On solving the provided question, we can say that the derivative will be y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
what is derivative?The derivative of a function with real variables in mathematics gauges how sensitively the function's value will change in response to changes in its arguments. Calculus's fundamental tools are derivatives. Differentiation (in mathematics, the rate of change of a function with respect to a variable) (in mathematics, the rate of change of a function with respect to a variable). Calculus and differential equation problem-solving depend heavily on derivatives. Finding the "slope" of a specific function is the definition of "derivative" or "taking a derivative" in calculus. Because it is often the slope of a straight line, the slope should be enclose in quotations. While applying to practically every function, derivatives are measures of rate of change.
Linear second-order differential equation F(x, y, y′, y″) = 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
differential equation
y = c₁x + c₂x⁴ ...(i)
Differentiating equation (i)
y¹ = c₁(1) + c₂ ( 4 x³ ) ...(ii)
Differentiating equation (ii)
y¹¹ = c₂ ( 12 x² )
12 x² y = (y¹12 x³ - 4 x⁴ y¹¹) + x⁴ y¹¹
x⁴ y¹¹ - 4 x⁴ y¹¹ + y¹12 x³ - 12 x² y= 0
y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0
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13. A rectangle is 3 feet wide and has an area of 438 square feet. What is the
perimeter of the rectangle?
Answer:
Below
Step-by-step explanation:
L x W = 438
L = 438/W
L = 438/3 = 146 ft
then perimeter = 3 + 3 + 146 + 146 = 298 ft
Answer:
It should be 146
need assistance with This Math question here I’ll give you brainliest
Answer:
A. (3 + 4)² - 9
Step-by-step explanation:
She must add 3 and 4 first but in order to do so she must put them in brackets thus correctly following the order of operations
Answer:
(3 + 4)² - 9
3 + 4 first so that goes in brackets
The result is squared so the ² goes outside the brackets
Finally, subtract 9 so that goes after
A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The gourmet coffee usually sells for
$6.00 per pound. The cheaper brand sells for $3.00 per pound. How much of each type should be mixed in order to
have 20 pounds of coffee that is worth $4.50 per pound?
The amount of each type that should be mixed in order to have 20 pounds of coffee mixture that is worth $4.50 per pound is: 10 pounds $6.00 Gourmet coffee, 10 pounds $3.00 Cheap brand.
How to find the mixtures of coffee?Gourmet coffee $6.00 ---- x pounds
Cheap brand $3.00 --- 20 - x pounds
Mixture $4.50 ---- 20
Total 20 pounds6 x + 3 ( 20 - x ) = 4.50 × 20
6 x + 3 ( 20 - x ) = 90
6 x + 60 - 3 x = 90
Collect like terms
6 x - 3 x = 90 -60
3 x = 30
x = 10
Cheap brand
20-x pounds
20-10
=10 pounds $3.00 Cheap brand
Therefore 10 pounds and 10 pounds should be mixed.
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Add.
4 2/8+ 9 4/8
Please help me. Thank u
:)
The solution of the addition of term is; 43/4
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given terms as;
4 2/8+ 9 4/8
We have to add the terms, so first convert into normal fraction.
4 2/8 = 10/8
9 4/8 = 76/8
Now add;
10/8 + 76/8
= 86/8
= 43/4
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Answer:
13 6/8
Step-by-step explanation:
