Answer:
A. 216
Step-by-step explanation:
This is because the volume of a cube is worked out by doing . being the edge. Therefore, you just have to do (6 × 6 × 6), which is 216.
Select the term that best describes the statement.
If a polygon has six sides, then it is a hexagon.
A. conjunction
B. disjunction
C. negation
D. conditional
Answer:
D. Conditional
Step-by-step explanation:
The statement is a conditional statement.
what are the vertex focus and directrix of the parabola with the given equation
y=1/28(x-4)^2-5
The answer is:
vertex: (4,-5); focus: (4,2); directrix: y=-12
The vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.
To determine the vertex, focus, and directrix of a parabola given by the equation y = {1{28}(x - 4)² - 5, we must first identify the standard form of a parabolic equation, which is y = a(x - h)² + k where (h, k) is the vertex of the parabola. In this case, we can see that the vertex (h, k) is (4, -5).
The focus of a parabola is a fixed point from which the distance to any point on the parabola is equal to the distance from that point to the directrix.
The directrix is a fixed straight line. The distance between the vertex and the focus, denoted as 4p, can be determined from the coefficient a in the standard form, where a = {1}/{4p} or p = {1}/{4a}. Thus, p = {1}/{4({1}/{28})} = 7. The focus is then at (h, k + p) = (4, -5 + 7) = (4, 2).
The directrix has the equation y = k - p, so it will be y = -5 - 7 = -12. The parabola opens upwards because the value of a is positive.
In summary, the vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.
Which shows the conversion of 0.427 kg to pounds?
There are 2.2 pounds in 1 kilogram.
A.
0.427 kg × 2.2 lb/kg = 9.39 lb
B.
0.427 kg × 2.2 lb/kg = 0.939 lb
C.
0.427 kg + 2.2 lb/kg = 2.627 lb
D.
0.427 kg ÷ 2.2 lb/kg = 0.194 lb
To convert 0.427 kg to pounds, multiply 0.427 by 2.2, resulting in approximately 0.939 pounds. Thus, the correct answer is Option B.
To convert 0.427 kg to pounds, we use the given conversion factor: 1 kilogram (kg) = 2.2 pounds (lb). Here is the step-by-step explanation:
Write down the value to be converted: 0.427 kg.
Multiply by the conversion factor: 0.427 kg × 2.2 lb/kg.
Perform the multiplication: 0.427 × 2.2 = 0.9394 lb.
So, 0.427 kg is approximately 0.939 lb. Therefore, the correct answer is Option B.
Apply the rules for order of operations to simplify 2+3-4+(5X4)
Determine the zeros of x^2 + 4x - 16 = -2x .
What comes next in the following sequence? 13, 1113, 3113, 132113
1337
1332113
1113122113
3313121221
11311242321
the answer is :
1332113
The cost of producing pots is the initial investment, $175, plus $3.50 in materials per pot. Therefore, the function C(p) = 175 + 3.5p defines the cost, C, of producing a number of pots, p. To the nearest cent, how much will it cost to produce 125 pots? (Enter only the number without the dollar sign, such as 25.03 for twenty-five dollars and 3 cents.)
How many pots can be produced if the budget is limited to $450?
What is 0.0012 as a fraction
Carlos went out to a restaurant for dinner. he tipped 25% of his bill, which brought the sum of the dinner bill plus the tip to $45. how much was the original bill?
To solve the inequality 9x > -4, the inequality sign must be reversed.
true or false?
There are 84 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 5/7 of the remaining houses were sold. How many houses are left to be sold?
The number of houses left to be sold is 9, calculated from the initial total and the proportions sold each month.
The number of houses left to be sold is 9.
Initially, 1/3 of the 84 new houses were sold, which is 84 × (1/3) = 28 houses sold.
There were 84 - 28 = 56 houses remaining.
From these remaining houses, 5/7 were sold this month, which equates to 56 × (5/7) = 40 houses sold. Thus, 56 - 40 = 16 houses are left to be sold.
The product of two numbers is 48, and one of the numbers is 12. find the other number.
Ralph is 3 times as old as Sara. In 6 years, Ralph will be only twice as old as Sara will be then. Find Ralph's age now. Ralph's age is _____. A)6 B)12 C)18 D)24
Answer:
C)18
Step-by-step explanation:
Let Sara present age = x years.
According to question Ralph present age =3x
Sara age after 6 years =x+6.
Ralph age after 6 years =3x+6.
After 6 years Ralph will be only twice as old as Sara will be then.
3x+6=2(x+6)
Solving for x:
3x+6=2x+12
3x-2x=12-6
x=6.
Ralph present age = 3x=3(6)= 18 years.
Option C.
For what intervals is f(x)=xe^-x concave down?
The function f(x) = xe⁻ˣ is concave down for intervals where the second derivative f''(x) is negative, which occurs when x > 0.
To determine the intervals where the function f(x) = xe⁻ˣ is concave down, we need to find the second derivative of the function and identify where it is negative. The first derivative of the function f'(x) = e⁻ˣ - xe⁻ˣ is obtained using the product rule. Then, we take the second derivative: f''(x) = -e⁻ˣ - e⁻ˣ + xe⁻ˣ = -2e⁻ˣ + xe⁻ˣ.
To find where the function is concave down, we need to find the intervals where f''(x) < 0. By analyzing the second derivative, we can see that the term -2e⁻ˣ is always negative, while the term xe⁻ˣ can be either positive or negative depending on the value of x.
For x > 0, the term xe⁻ˣ is positive, making f''(x) more negative, therefore, the function is concave down for x > 0.
Graph the function. Identify the vertex and axis of symmetry.
f(x)=-2x^2+2x-1
Answer:
Part A) The vertex is the point [tex](0.5,-0.5)[/tex]
Part B) The axis of symmetry is [tex]x=0.5[/tex]
Part C) The graph in the attached figure
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
and the axis of symmetry is equal to the x-coordinate of the vertex
so
[tex]x=h[/tex] -----> equation of the axis of symmetry
In this problem we have
[tex]f(x)=-2x^{2}+2x-1[/tex]
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)+1=-2x^{2}+2x[/tex]
Factor the leading coefficient
[tex]f(x)+1=-2(x^{2}-x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)+1-(1/2)=-2(x^{2}-x+(1/4))[/tex]
[tex]f(x)+(1/2)=-2(x^{2}-x+(1/4))[/tex]
Rewrite as perfect squares
[tex]f(x)+(1/2)=-2(x-(1/2))^{2}[/tex]
[tex]f(x)=-2(x-(1/2))^{2}-(1/2)[/tex] -----> equation in vertex form
The vertex of the parabola is the point [tex](0.5,-0.5)[/tex]
Is a vertical parabola open downward
The axis of symmetry is equal to
[tex]x=0.5[/tex]
see the attached figure to better understand the problem
Is the following definition of supplementary reversible? If yes, write it as a true biconditional .
Linear pairs of angles are supplementary.
A. The statement is not reversible
B. Yes, if angles form a linear pair, they are supplementary
C. Yes, angles form a linear pair if ( and only if ) they are supplementary
D. Yes, angles are supplementary if they form a linear pair
The following table represents Tracie's earnings:
1 hour $25
2 hours $50
3 hours $75
How much does she make per hour?
$25
$50
$75
$150
Wesley ran of a mile on saturday and of a mile on sunday how many miles did wesley run in all
For the following system.
kx + y + z = 1
x + ky + z = 1
x+ y + kz = 1
Determine for what values of k the system has:
a) No solutions
b) One solution
c) A lot of solutions ...?
81 is 37.5% of what number
Is 701. 5 = to 701. 50.
Final answer:
701.5 is equal to 701.50 because in decimals, trailing zeroes after the decimal point do not change the value of the number; they only indicate precision.
Explanation:
The question is about whether 701.5 is equal to 701.50. In mathematics, when comparing numbers with different numbers of decimal places, it's important to understand the significance of trailing zeroes in the decimal part.
A zero after the decimal point but at the end of a number (trailing zero) does not change the value of the number.
Therefore, 701.5 is exactly equal to 701.50
This is because the trailing zero in 701.50 does not add any value but merely serves as a placeholder, indicating precision to the hundredth place without changing the number's value.
Form a polynomial, f(x), with real coefficients having the given degree and zeros.
Degree: 4; zeros: 4i and 5i Form a polynomial, f(x), with real coefficients having the given degree and zeros.
Degree: 4; zeros: 4i and 5i
Final answer:
To form a polynomial with real coefficients, given non-real zeros 4i and 5i, include their conjugates -4i and -5i. Multiply the corresponding factors to get f(x) = (x^2 + 16)(x^2 + 25), which simplifies to f(x) = x^4 + 41x^2 + 400.
Explanation:
To form a polynomial, f(x), with real coefficients having a specified degree and given zeros, you must use the fact that non-real roots of polynomials with real coefficients come in conjugate pairs. Since 4i and 5i are given as zeros of the polynomial, their conjugates, -4i and -5i, must also be zeros of the polynomial.
The factors of the polynomial that correspond to these zeros are (x - 4i), (x + 4i), (x - 5i), and (x + 5i). To find the polynomial, these factors are multiplied together.
Multiplying the factors that come in conjugate pairs first:
Next, multiply these two results to obtain the polynomial:
(x^2 + 16)(x^2 + 25) = x^4 + 25x^2 + 16x^2 + 400 = x^4 + 41x^2 + 400
Therefore, the polynomial with degree 4 and zeros 4i and 5i is f(x) = x^4 + 41x^2 + 400.
To form the polynomial f(x) with real coefficients and given the zeros 4i and 5i, we use the conjugate pairs and multiply the resulting factors to get x⁴ + 41x² + 400.
To form a polynomial f(x) with real coefficients given the degree and zeros, we start by noting that complex roots always come in conjugate pairs when dealing with polynomials that have real coefficients. Hence, for the zeros 4i and 5i, the polynomial must also include the conjugate roots -4i and -5i.
Using these roots, we can form the factors:Thus, the polynomial f(x) is x⁴ + 41x² + 400.
Factor completely 5x2 – 5x – 100
A)5(x + 4)(x – 5)
B)5(x – 2)(x + 10)
C)(5x + 20)(x – 5)
D)(5x – 10)(x + 10) ...?
Final answer:
The quadratic equation 5x² - 5x - 100 is factored completely by first taking out the greatest common factor of 5, and then finding two binomials that multiply to give the remaining quadratic. The correct factorization is 5(x - 5)(x + 4), which is option A.
Explanation:
To factor the quadratic equation 5x² − 5x − 100 completely, we need to find two binomials that, when multiplied together, will give us the original equation. First, we will factor out the greatest common factor (GCF), which is 5. This leaves us with:
5(x² − x − 20)
Now, we need to factor the quadratic expression inside the parentheses. The factors of −20 (the constant term) that add up to −1 (the coefficient of the middle term) are −5 and 4. Thus:
5(x − 5)(x + 4)
We can confirm that none of the other choices provide the correct factors:
Choice B does not give us the original middle term when expanded.Choice C is incorrect because it does not result in the original constant term when expanded.Choice D also doesn't give us the desired constant term.Therefore, the correct answer is 5(x − 5)(x + 4), which corresponds to option A.
If triangle RST is congruent to triangle WXY and the area of triangle WXY is 20 square inches, then the area of triangle RST is 20 in.²
True
False
Answer:
statement is true
Step-by-step explanation:
Given : If triangle RST is congruent to triangle WXY and area of triangle WXY is 20 square inches, then the area of triangle RST is 20 in.
To find : Statement is true or false .
Explanation :
Yes,if two triangles are congruent then you can place one above the other perfectly and both cover the same region.
So,we can say that both have the same area.
But the conversion is not true .
Therefore, statement is true .
What is 972 divided by 37?
A cookie recipe calls for two eggs and yields 4 dozen cookies. how many eggs would be necessary to make 10 dozen cookies?
Assume the availability of a function is_prime. Assume a variable n has been associated with positive integer. Write the statements needed to compute the sum of the first n prime numbers. The sum should be associated with the variable total.
Note: is_prime takes an integer as a parameter and returns True if and only if that integer is prime.
To find the sum of the first n prime numbers, use a while loop to add each prime number to a total. Use a function is prime to check if each integer is prime. Continue the loop until you've added n primes.
Explanation:To compute the sum of the first n prime numbers, you would first initialize the total and the count of primes to 0. Then, for each integer starting from 2, you would check if it is prime using the is prime function. If it is prime, you would add it to the total and increment the count of primes. This loop would continue until the count of primes reaches n.
Here is how the code might look in Python:
total = 0This code uses a while loop to continue adding prime numbers to the total until it has added the first n primes. The total of the prime numbers is updated inside an if statement that checks whether the current integer i is prime.
Learn more about Computing Sum of Primes here:https://brainly.com/question/31305838
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Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points. Suppose you take the SAT and several weeks later you receive a letter telling you that your results on the math portion of the test were in the 95th percentile.
Recalling that SAT scores are always expressed as multiples of 10, how many points did you get on the test? ...?
Answer:
Step-by-step explanation:
Given that Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points.
If X is the score in SAT, then X is N(500,100)
From std normal table we find 95th percentile as 1.645
i.e. your Z score = 1.645
Convert this to X score by [tex]X =1.645]\sigma + Mean\\= 1.645(100)+500\\=664.5[/tex]
Since expressed as multiples of 10, this equals 660
So points you got = 660
Okay, I really need help on this one. See attachment.
What is the description of one-hundredth of 36?
Answer:
0.36
Step-by-step explanation:
One - hundredth =[tex]\frac{1}{100}[/tex]
one hundredth means we have to divide 1 by hundred.
When we divide one by hundred we get 0.01
To find one-hundredth of 36, than we have to multiply 36 by 0.01
After multiplying we get
36×0.01=0.36
OR
36×[tex]\frac{1}{100}[/tex]=0.36
Hence, the correct answer is 0.36
One-hundredth of 36 is 0.36.
To find one-hundredth of 36, we simply need to divide 36 by 100. Dividing by 100 means shifting the decimal point two places to the left. Therefore, one-hundredth of 36 is 0.36.
For example, if we have the number 36, we can represent this as 36/1 to show that we have 36 whole parts. When we want one-hundredth of these 36 parts, we are seeking 1 part out of every 100 parts. So, we would write this as (36/1)/ (100/1) which simplifies to 36/100. After simplification, we get 0.36 as the final answer.
This concept is similar to understanding that 1 cm is 1/100th of a meter. By using division or understanding fractions and decimal places, we can easily find one-hundredth of any given number.