The statement "the product of two negative rational numbers is greater than either factor" is never true.
The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.
We have,
Part A:
The statement "the product of two negative rational numbers is greater than either factor" is never true.
This can be proved by considering a negative rational number, say -1/2, and multiplying it by a negative rational number that is greater in magnitude, say -2/3.
The product of these two negative rational numbers is 1/3, which is less than either factor.
Another example is -3/4 multiplied by -1/2 which results in 3/8, again less than either factor.
Part B:
The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.
For example, if we take 1/2 and 2/3, the product is 1/3 which is less than either factor.
Similarly, if we take 3/4 and 4/5, the product is 3/5 which is less than either factor.
Therefore, the statement is only sometimes true and not always true.
Thus,
The statement "the product of two negative rational numbers is greater than either factor" is never true.
The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.
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There are 9 players on a youth baseball team. To create the lineup, the coach chooses three players to play pitcher, catcher, and first base. How many ways can the coach choose these three positions?
Step-by-step explanation:
how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .
11
Select the correct answer.
The values in the table define the function fix). If g(x) is the inverse of f(x), what is the value of g(1)?
x f(x)
-1 -3
1
-1
4 1
6
4
7 6
OA 1
OB. 2
OC. 3
OD. 4
OE
5
Reset
Nerm
Answer:
D) 4
Step-by-step explanation:
Since g(x) is the inverse of f(x), g(f(x))=x. Therefore, we need to find the value of x such that f(x) = 1. Looking at the table, we can see that f(4) = 1, so g(1) = 4.
Therefore, the correct answer is (D) 4.
explain why the graph would look like the line y=x if you graph it
The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
How to explain the informationBoth the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.
A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.
Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.
In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
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x P(x)
0 0.3
1 0.25
2 0.2
3 0.25
Find the standard deviation of this probability distribution.
The circumference of a circle is 17.584 inches. What is the circle's area?
Step-by-step explanation:
Given the circ , you can find the diameter....then the radius
circ = pi * d
17.584 = pi * d
d = 5.597 in then radius = 1/2 d = 2.798
AREA = pi r^2 = pi * 2.798^2 = 24.6 in^2
The graph of a quadratic function with vertex (0, 3) is shown in the figure below.
The domain of the function is (-∞, ∞.)
The range of the function is {3, ∞}.
We have,
From the given quadratic function,
We see that,
The x-values are -∞ to ∞
The y-values are from 3 to ∞
Now,
The x-values are called the domain.
The y-values are called the range.
Thus,
The domain of the function is (-∞, ∞.)
The range of the function is {3, ∞}.
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help me pls right answer only. here is screenshot algebra, quick
x at the vertex would help Charlie to find out how long it takes his basketball to reach the highest point.
When a quadratic function is in vertex form, the vertex (h, k) represents the highest or lowest point of the parabola.
In this case, the time it takes for the basketball to reach the highest point can be found by finding the x-value of the vertex of the function that represents the height of the basketball over time.
Therefore, option (A) x at the vertex would help Charlie to find the time at which the basketball reaches the highest point.
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Which integers are opposites?
14 and –4
17 and –17
32 and –23
15 and –51
Answer:
A
Step-by-step explanation:
The opposite of an integer is the number on the opposite side of the number line with the same distance from zero. So, the integers that are opposites are 14 and -14, 17 and -17, 32 and -32, and 15 and -15. This is because these pairs have the same absolute value but different signs. For instance, the absolute value of 14 is 14, and the absolute value of -14 is also 14. Therefore, -14 is the opposite of 14. Similarly, -17 is the opposite of 17 and so on.
Answer:
a
Step-by-step explanation:
got it right on edge
On the 6th grade math test, twelve students had a score of 80 points. Eight students had a score of 88 points.
What was the class average?
The requried class average is 83.2 points.
To find the class average, we need to calculate the total number of points earned by all the students and divide by the total number of students.
The 12 students who scored 80 points earned a total of 12 × 80 = 960 points.
The 8 students who scored 88 points earned a total of 8 × 88 = 704 points.
The total number of points earned by all the students is 960 + 704 = 1664 points.
The total number of students is 12 + 8 = 20.
To find the class average, we divide the total number of points by the total number of students:
average = total points / total students
average = 1664 / 20
average = 83.2
Therefore, the class average is 83.2 points.
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marking as brainlist pls help
HELP PLEASE 8TH GRADE MATH
The measures of the angles are 33°, 105° and 42°
We can call the top angle P, the bottom left angle Q, and the bottom right angle R. We are also given that angle P is (x - 9) degrees, angle Q is (x + 63) degrees, and angle R is x degrees.
Now, we can use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation:
Angle P + Angle Q + Angle R = 180
To find Angle, we can use the fact that the sum of the angles in a straight line is 180 degrees. We can see that Angle and Angle A are on a straight line, so we have:
(x – 9) + ( x + 63) + x = 180
=> 3x + 54 = 180
=> 3x = 126
=> x = 42
We can now use this value to find the measures of the angles.
Angle P is (x -9) degrees, so Angle P = 42 - 9 = 33 degrees.
Angle Q is (x + 63) degrees, so Angle Q = 42 + 63 = 105 degrees.
Angle R is x degrees, so Angle R = 42 degrees.
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Zoe kicks a football. Its height in feet is given by h(t) = − 16t² + 56t where
t represents the time in seconds after kick. What is the football's greatest
height?
The maximum height of the ball can reach is 49 feet high.
Which is the greatest height?We know that the height is modeled by the quadratic equation:
h(t) = -16t² + 56t
Remember that for the general quadratic equation is written as:
y = ax² + bx +c
The vertex is at the value x of:
x = -b/2a
The maximum height is at the vertex, which in this case is at the value:
t = -56/(2*-16)
t = 1.75
Evaluating the height equation in that time, we get:
h = -16*(1.75)² + 56*1.75
h = 49
The maximum height that the ball can reach is 49ft
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Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars. Select the equation that matches this situation. Choose 1 answer: Choose 1 answer: (Choice A) 5 = 15 \times w5=15×w5, equals, 15, times, w A 5 = 15 \times w5=15×w5, equals, 15, times, w (Choice B) w = 15 +5w=15+5w, equals, 15, plus, 5 B w = 15 +5w=15+5w, equals, 15, plus, 5 (Choice C) w = 5 \times 15w=5×15w, equals, 5, times, 15 C w = 5 \times 15w=5×15
The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.
Which equation correctly matches the given situation?It follows from the task content that the equation which correctly represents the Given situation is to be determined.
Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;
Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.
Consequently, answer choice C; w = 5 × 15 is correct.
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Use the image to determine the type of transformation shown.
Graph of polygon VWXYZ with W at point 2 comma 4. A second polygon V prime W prime X prime Y prime Z prime with W prime at point negative 2 comma 4.
Reflection across the x-axis
Reflection across the y-axis
270° counterclockwise rotation
Horizontal translation
The image is reflected over the y-axis. Then the correct option is B.
Given that:
Point of the polygon VWXYZ, W(2, 4)
Point of the polygon V'W'X'Y'Z', W'(-2, 4)
The translation does not change the shape and size of the geometry. But changes the location.
The reflection does not change the shape and size of the geometry. But flipped the image.
The point W' can be obtained by reflecting the shape across the y-axis.
Thus, the correct option is B.
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The missing diagram is given below.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The volumes of smaller container and larger container are 10.6 in³ and 166.22 in³ respectively.
Given that are two containers in a conical shape and cylindrical shape,
Volume of conical shape = 1/3 × π × radius² × height
= 1/3 × 3.14 × 1.5² × 4.5
= 10.6 in³
Volume of cylindrical shape = π × radius² × height
= 3.14 × 2.75² × 7
= 166.22 in²
When we pour water from smaller container to larger container = 10.6 / 166.22 × 100 = 6.4 % of larger container will be filled.
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what is -33 divided by (-3)
Answer: 11
Step-by-step explanation:
-3 x 11 = -33
How many times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284
The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.
Here, we have,
given that,
the value represented by the digit 8 in the number 8,342
and, the value represented by the digit 8 in the number 284.
now, we have to find that how many times greater is the value.
so, we have to differentiate the value represented by the digit 8 in the number 8,342 with the value represented by the digit 8 in the number 284.
so, we get,
the value represented by the digit 8 in the number 8,342 is 8000
and, the value represented by the digit 8 in the number 284 is 80
so, difference between them is:
8000 - 80
=7980
Hence, The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.
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While much of organized crime involves dealing with illegal goods and practices, some of it, like pirated music or videos, occurs with products
consumers access through questionable websites or at street markets. What does this information reveal about consumers?
OA
OB.
O. C.
O D.
Consumers are willing to buy illegal goods if they are cheaper.
Consumers are not aware that organized crime is a problem.
Consumers don't realize that organized criminals replace legitimate goods.
Consumers don't realize that organized criminals take over legitimate businesses.
Determine whether or not it defines a function. Pease shows steps so I understand the answer.
The requried, justification for the given function has been shown below.
(a) Yes, R₁ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is 0 in this case.
(b) No, R₂ does not define a function. For some values of n, there may be multiple animals with n legs, so there is no unique output for each input.
(c) Yes, R₃ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is the remainder of n divided by 5.
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a fish tank 60 litres of water round to 1 significant figure
40 litres of water rounded to 1 significant figure is removed from the tank
work out the upper bound of the water left in the tank
The upper bound of the volume of water left in the fish tank is 20 liters.
In the given statement is :
A fish tank contains 60 liters of water, rounded to 1 significant figure. 40 liters of water, rounded to 1 significant figure, are removed from the tank.
Work out the upper bound of the volume of water left in the fish tank.
Now, According to the question:
Initial water in tank = 60 liters
Amount of water removed = 40 liters
Hence, To calculate the upper bound of the volume of water left in the fish tank;
= 60 - 40
= 20 liters
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Find the area of each triangle.
The area of the triangle is 2√2 square units.
This is a right triangle, and the base (the side opposite the right angle) has a length of 2√2.
We can use the Pythagorean theorem to find the length of the other two sides:
x² + x² = (2√2)²
2x² = 8
x² = 4
x = 2
So the two other sides have a length of 2.
Now we can use the formula for the area of a triangle:
Area = (1/2) × base × height
In this case, the base is 2√2 and the height is 2, so we have:
Area = (1/2)×2√2 ×2
Area = 2√2
Therefore, the area of the triangle is 2√2 square units.
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How many coupons can be generated
The number of coupon codes that can be generated is given as follows:
247,808 coupon codes.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The codes are composed as follows:
Two letters -> each with 22 options, as letters can be repeated.Three digits -> each with 8 options, as digits can also be repeated.Thus the total number of codes is obtained as follows:
N = 22² x 8³
N = 247,808 coupon codes.
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The table shows some values of x and y that satisfy the equation y = acosx" + b X 10 30 Find the value of y when x = 45 80 7 90 4 120 1 150 4-3√3 180
Examine the figure of two parallel lines cut by a transversal.
One interior angle has a measure of 75 degrees; the alternate interior angle has a measure of 4 x plus 7 degrees.
What is the value of x?
The value of x is 17.
Given that, two parallel lines cut by a transversal, forming one interior angle has a measure of 75 degrees; the alternate interior angle has a measure of 4x + 7 degrees.
Since, we know that, the alternate interior angles between parallel lines are equal so,
4x+7 = 75
4x = 68
x = 17
Hence the value of x is 17.
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A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
A Pew Research Center poll of 1060 teens aged 13 to 17 showed that 57% of them have made
new friends online. Use a 0.01 significance level to test the claim that half of all teens have
made new friends online.
Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.
For test the claim that half of all teens have made new friends online, we can use a hypothesis test.
Null hypothesis:
The proportion of teens who have made new friends online is equal to 0.5.
Alternative hypothesis:
The proportion of teens who have made new friends online is not equal to 0.5.
We will use a one-sample proportion test with a significance level of 0.01.
For calculate the test statistic, we can use the formula:
z = (p - P₀) / sqrt(P₀ * (1 - P₀) / n)
where p is the sample proportion, P₀ is the hypothesized proportion (0.5), and n is the sample size.
Using the given information, we have:
p = 0.57
P₀ = 0.5
n = 1060
Plugging these values into the formula, we get:
z = (0.57 - 0.5) / sqrt(0.5 x 0.5 / 1060)
z = 4.39
Hence, Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.
Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that more than half of all teens have made new friends online.
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Jordan has gone into the nut business. He wants to make a mixture of walnuts and cashews that cost $1.00 per pound. How many pounds of walnuts that cost $0.80 per pound must be mixed with 8 pounds of cashews that costs $1.25 per pound to make his mixture of nuts cost $1.00 per pound?
A. 16 lbs
b. 11 lbs
c. 20 lbs
d. 10 lbs
Answer:
The answer is (d) 10 lbs.
Step-by-step explanation:
Let's start by using the weighted average formula:
weighted average price = (price of first item x weight of first item + price of second item x weight of second item) / total weight
Let x be the number of pounds of walnuts needed.
The total weight of the mixture is x + 8 pounds.
The price of the walnuts is $0.80 per pound, and the price of the cashews is $1.25 per pound.
We want the mixture to cost $1.00 per pound.
Using the formula, we get:
1.00 = (0.80x + 1.25(8)) / (x + 8)
Simplifying, we get:
1.00(x + 8) = 0.80x + 10
1.00x + 8.00 = 0.80x + 10.00
0.20x = 2.00
x = 10
Therefore, Jordan needs to mix 10 pounds of walnuts with 8 pounds of cashews to make a mixture that costs $1.00 per pound.
The very top one I need help with it
As the class sizes range from 22 to 34 students, the answer must be 30,
Let the number of girls in the class "3x" and the number of boys "7x".
Then the total number of students in the class is:
Total students = 3x + 7x = 10x
We don't know the value of "x" yet, but we do know that the total number of students is between 22 and 34.
So we can set up an inequality:
22 ≤ 10x ≤ 34
Divide both sides of the inequality by 10:
2.2 ≤ x ≤ 3.4
Therefore, x can be either 3 or 4.
If x = 3, then the total number of students is:
Total students = 3x + 7x = 30
If x = 4, then the total number of students is:
Total students = 3x + 7x = 40
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If my network downloads 3 GB in 20 mins how long will 119GB take if 47GB is already done?
Answer:480 minutes
Step-by-step explanation:
119-47=72
72/3=24
24*20=480
Find each measure of these angles and arcs
The measure of arc and angle in the given circle are as follow,
Measure of arc CA = 144°
Measure of arc AD = 98°
Measure of ∠C = 90°
In the circle ,
Center of the circle = Q
m∠ABC = 72°
Measure of arc CD = 46°
Measure of arc CA
Measure of ∠ABC = 72°
In a circle angle at the center is double of angle at the circumference of the circle in the same arc.
Measure of ∠CQA = 2 ×∠ABC
= 2× 72°
= 144°
measure of arc CA = measure of ∠CQA
= 144°
Measure of arc AD ,
m ∠AQD + m ∠CQD = m ∠CQA
⇒m ∠AQD = 144° - 46°
⇒m ∠AQD = 98°
⇒ Measure of arc AD = 98°
Measure of angle C = ( 1/2) times of measure of BQD
= ( 1/2) × 180°
= 90°
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