The original statement, 'If a number is a natural number, then it is also a whole number' is true because every natural number falls into the set of whole numbers. However, its converse is not true, as whole numbers include 0, which is not a natural number, making the inverse and the bi-conditional false. The contrapositive of the statement is true, maintaining logical consistency.
Explanation:If a number is a natural number, then it is indeed also a whole number. The relationship between natural numbers and whole numbers is an inclusive one, where all natural numbers (1, 2, 3, ...) are also whole numbers (0, 1, 2, 3, ...). The original statement can be expressed in logical form as: If P, then Q, where P is 'a number is a natural number,' and Q is 'it is also a whole number.'
Here is how the other forms of the statement look:
The inverse negates both the hypothesis and the conclusion: If not P, then not Q. So, 'If a number is not a natural number, then it is not a whole number.'
The converse switches the hypothesis and the conclusion: If Q, then P. For our statement, 'If a number is a whole number, then it is also a natural number.'
The contrapositive negates and switches the hypothesis and conclusion: If not Q, then not P. Therefore, 'If a number is not a whole number, then it is not a natural number.'
The bi-conditional states that P if and only if Q: A number is a natural number if and only if it is a whole number.'
The truth value of the original statement is true since all natural numbers are whole numbers. However, the converse is not true because whole numbers also include 0, which is not a natural number. Consequently, the inverse and the bi-conditional are false. The contrapositive is true because if it is not a whole number, then it can't be a natural number (considering that whole numbers include all natural numbers).
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What is the length of segment NS?
1 unit
2 units
4 units
6 units
Answer:
Option C. 4 units
Step-by-step explanation:
As we know median of a triangle intersect each other at a point in the ratio of 2.01.
Therefore, in Δ QNL,
[tex]\frac{NS}{SR}[/tex] = [tex]\frac{2}{1}[/tex]
[tex]\frac{(7x-3)}{(5x-3)}[/tex] = [tex]\frac{2}{1}[/tex]
By cross multiplication
(7x - 3) = 2(5x -3)
7x - 3 = 10x - 6
6 - 3 = 10x - 7x
3 = 3x
x = 1
Now length of NS
= (7x - 3)
= (7 × 1 - 3)
= (7 - 3)
= 4 units
Option C. 4 units is the answer.
Temperatures in the Gobi desert reach -40 F in the winter and 90 F in the summer. Find the range of the temperatures
add the 2 numbers together
40 + 90 = 130 degree range
Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
Answer:
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
Step-by-step explanation:
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} is not a function because 1 have two different images.
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} is not a function because -2 have two different images.
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} is not a function because -3 have two different images.
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} is a function because all x values has one only image value.
The perimeter of a rectangular pig pen is 310 ft. The length is 15 ft greater than the width. Find the width
Ellie bought 0.7kg of jelly beans from her local food festival for £1.89. She knows that to work out the price of a whole kilogram she simply needs to divide the price she paid by the quantity she bought. Work out the price of 1kg jelly beans
Answer:
x = 2.7
Step-by-step explanation:
To find x
1) 1.89 ÷ 0.7 = 2.7
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Given that x is a whole number, Niram conjectured that x3>x2 .
What value is a counterexample to Niram's conjecture?
(a) −2
(b) 1/10
(c) 1
(d) 5
Answer:
The answer is 1.
Step-by-step explanation:
Took the test.
In a study, a group of ten-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they gained. which factor is the dependent variable?
In the stated experiment, the weight gain of the ten-year-old boys is the dependent variable. It is expected to change based on the consumption of doughnuts, which is the independent variable.
Explanation:
In the study described, where a group of ten-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they gained, the dependent variable is the weight gain of the boys. The dependent variable is the outcome that is measured in an experiment or study. It is the factor that is expected to change as a result of changes to the independent variable, which in this case is the eating of doughnuts.
The dependent variable depends on the independent variable. For example, if the independent variable is the number of doughnuts eaten, the dependent variable (body weight) would likely change in response to the number of doughnuts consumed.
To illustrate this further, if we were to create a graph with the number of doughnuts eaten (independent variable) on the x-axis and the weight gained (dependent variable) on the y-axis, we could see if there is an exponential relationship or a different kind of correlation between these two variables. By understanding the dependent and independent variables, we can better interpret the results of studies and experiments.
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A computer and printer cost a total of $908. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Subtract. Your answer should be a polynomial in standard form. (-9g^4+3g^2h+1) -(6g^4-3g^2h+h)
Michael is riding his bicycle. He rides at a speed of 8 kilometers per hour for 12.8 kilometers. For how many hours does he ride?
Find the number of real number solutions for the equation. x2 – 4x + 4 = 0
The quadratic equation x^2 - 4x + 4 = 0 has one real number solution, x = 2, which is a repeated solution since the discriminant of the equation is zero.
To determine the number of real number solutions for the equation x2
- 4x + 4 = 0, we can use the discriminant method. The discriminant D of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac. For our equation, a = 1, b = -4, and c = 4.
Calculating the discriminant gives us D = (-4)2 - 4(1)(4) = 16 - 16 = 0. Since the discriminant is equal to zero, it indicates that there is exactly one real number solution, which means the quadratic has a perfect square trinomial, or the two real solutions are identical.
In this case, the solution to the equation can be found by factoring the quadratic as (x - 2)2 = 0, which implies that x = 2. Therefore, the equation x2 - 4x + 4 = 0 has one real solution, x = 2, which is repeated.
Name one particular solution to 5x-(x+2)>-5(1+x)+3
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3/x-1-5*x/x+2-(1/4)=0
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
5.2 Adding up the two equivalent fractions
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x as the denominator :
7.1 Pull out like factors :
3 - 6x = -3 • (2x - 1)
7.2 Adding up the two equivalent fractions
8.1 Find the Least Common Multiple
The left denominator is : x
The right denominator is : 4
Least Common Multiple:
4x
8.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 4
Right_M = L.C.M / R_Deno = x
8.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
8.4 Adding up the two equivalent fractions
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
Now, on the left hand side, the 4x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
12-17x = 0
9.2 Solve : -17x+12 = 0
Subtract 12 from both sides of the equation :
-17x = -12
Multiply both sides of the equation by (-1) : 17x = 12
Divide both sides of the equation by 17:
x = 12/17 = 0.706
The inequality 5x-(x+2)>-5(1+x)+3 simplifies to x>5/9 after combining like terms and isolating x. Therefore, any x greater than 5/9 is a solution, including x=1, which satisfies the inequality.
To find a particular solution to the inequality 5x-(x+2)>-5(1+x)+3, we first simplify both sides of the inequality:
5x - x - 2 > -5 - 5x + 3
This further simplifies to:
4x - 2 > -5x + 3
Next, we add 5x to both sides and add 2 to both sides to get:
9x > 5
Now, we divide both sides by 9 to isolate x:
x > 5/9
Therefore, any x greater than 5/9 is a particular solution to the original inequality. For example, x=1 is such a solution, as it satisfies the inequality:
5(1) - ((1)+2) > -5(1+(1)) + 3
That simplifies to:
5 - 3 > -5(2) + 3
2 > -10 + 3
2 > -7, which is true, thus confirming x=1 is a solution.
A plumber finished there jobs on Tuesday. The first two only cost the owner the $45 trip fee because they book very little to complete. For the third job, the plumber charged the trip fee plus 6 times his hourly rate. If the plumber received a total of $303 for the day, what is the hourly rate
Fred's frog jumped 7 times as far as al's frog. The two frogs jumped a total of 56 inches. How far did Fred's frog jump?
Bruce wants to make sure that each tiger at the zoo has 1,000 square feet of space. He wants to write an equation to represent the relationship between the number of tigers, t, and the number of square feet of space, f. Based on this information, answer these questions. Write an equation to represent the relationship between the number of tigers, t, and the total number of square feet of space, f, if each tiger has 1,000 square feet of space.
Answer:
The equation that represents the relationship between the number of tigers and the total number of square feet of space is f = 1,000t.
Step-by-step explanation:
The sum of the ages of ruth and her mother is 77 years. the difference in their ages is 27 years. how old is each?
At what point on the curve x = t 3, y = 3t, z = t 4 is the normal plane parallel to the plane 6x + 6y − 8z = 1?
The coordinates of the point are x=3 / 4, y = 3 / 4, and z = 3 for the plane.
What is a plane?A plane is a two-dimensional Euclidean surface that extends indefinitely in mathematics. A plane is the two-dimensional equivalent of a point, a line, and space.
Given that the points are x = 3t, y = 3t and z = 4t. The equation of the plane is 6x + 6y -8z = 1.
Substitute the value of x,y, and z in the equation and solve for the value of 't'.
6x + 6y -8z = 1.
6 x 3t + 6 x 3t - 8 x 4t = 1
18t + 18t - 32t = 1
4t = 1
t = 1 / 4
The coordinates will be calculated as,
x = 3t = 3 x 1 / 4= 3 / 4
y = 3t = 3 x 1 / 4= 3 / 4
z = 4t = 4 x 3 / 4 = 3
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Pedro has $50. He wants to go to Disney World after 12 weeks saving weekly . The trip will cost him $530 for the long weekend. How much does he need to save every week ?
In dividing an irregular shape into polygons it is permissible for the polygons to overlap
On a town map, each unit of the coordinate plane represents 1 mile. three branches of a bank are located at a(−3, 1), b(2, 4), and c(4, −2). a bank employee drives from branch a to branch b and then drives halfway to branch c before getting stuck in traffic. what is the minimum total distance the employee may have driven before getting stuck in traffic? round to the nearest tenth of a mile if necessary. answer
To compute for distance from a to b:
Distance A = 4 miles, base of triangle formed between a and b
Distance B = 3 miles, height of triangle formed between a and b
Distance AB = (A^2 + B^2)^0.5 hypotenuse of triangle formed between a and b, or square root of (A^2 + B^2)
Distance AB = ((4)^2 + (3)^2)^0.5
Distance AB = (16 + 9)^0.5
Distance AB = (25)^0.5
Distance AB = 5 miles
To compute for distance from b to where bank employee got stuck
BC = distance from b to c
BC = 4 miles
Total distance driven by bank employee
= AB + 0.5(BC)
= 5 + 0.5(4)
= 5 + 2
= 7 miles, total distance driven by the bank employee
Answer:
The minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.
Step-by-step explanation:
Given information: a(−3, 1), b(2, 4), and c(4, −2).
On a town map, each unit of the coordinate plane represents 1 mile.
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between bank a and bank b is
[tex]ab=\sqrt{(2-(-3))^2+(4-1)^2}[/tex]
[tex]ab=\sqrt{(5))^2+(3)^2}[/tex]
[tex]ab=\sqrt{25+9}[/tex]
[tex]ab=\sqrt{34}[/tex]
Distance between bank b and bank c is
[tex]bc=\sqrt{(4-2)^2+(-2-4)^2}[/tex]
[tex]bc=\sqrt{(2)^2+(-6)^2}[/tex]
[tex]bc=\sqrt{4+36}[/tex]
[tex]bc=\sqrt{40}[/tex]
[tex]bc=2\sqrt{10}[/tex]
A bank employee drives from branch a to branch b and then drives halfway to branch c before getting stuck in traffic. It means total distance employee may have driven before getting stuck in traffic is
[tex]Distance=ab+\frac{1}{2}bc[/tex]
[tex]Distance=\sqrt{34}+\frac{1}{2}(2\sqrt{10})[/tex]
[tex]Distance=\sqrt{34}+\sqrt{10}[/tex]
[tex]Distance=8.99323[/tex]
[tex]Distance\approx 9.0[/tex]
Therefore the minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.
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Students observed that their teacher's desk plant looked wilted on Monday morning compared to how it looked at the end of the day on Friday. Some students hypothesized that a warmer room temperature over the weekend caused the plant to wilt. Other students hypothesized that the lack of light caused the plant to wilt. Both hypotheses are valuable because they
A.) are reasonable and testable ---- (My answer)
B.) compare independent variables
C.) compare light and temperature
D.) are the only possible explanations.
Which of these facts is used to prove that triangle ptr is similar to triangle qts? (1 point)?
In a certain region the number of highway accidents increased by 20% over a four years. How many accidents were in the 2006 if there was 5120 in 2002? hint when the percent increases if you want the original 100% plus the additional 20%
A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?
a
(x − 4)2 + (y − 4)2 = 16
b
x2 + y2 = 16
c
(x + 4)2 + (y + 4)2 = 16
d
x2 + y2 = 4
e
(x − 4)2 + (y − 4)2 = 4
The equation of the circle is: is (x - 4)² + (y - 4)² = 16 Option A
How the equation of the circle was derivedTo find the equation of a circle tangent to the x-axis at (4, 0) and tangent to the y-axis at (0, 4)
Let's use the general form of the equation for a circle:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
The center of the circle is (4, 4) because it's tangent to both the x-axis and y-axis at 4.
The radius can be found by the distance from the center to the point (4, 0) (which is on the x-axis):
r = √((4 - 4)² + (0 - 4)²) = √(0 + 16) = √16 = 4
So the equation of the circle is:
(x - 4)² + (y - 4)² = 4²
(x - 4)² + (y - 4)²= 16
The correct option is: a) (x - 4)² + (y - 4)² = 16
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find the coordinates of G if f(1, 3.5) is the midpoint of Line GJ and J has coordinates (6, -2).
The banner over the finish line of a running race is 400. Centimeters long and 85 centimeters high. What is the area over the banner?
solve y=x^2+2 for x.
Why does a negative times a negative equal a positive proof?
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What is meant by the term financial planning?