now find new Z
Z = 18X
Z = 18(12)
Z = 216
PLEASE HELP!!!!!!!
f(x)=x^2−3x+9
g(x)=3x^3+2x^2−4x−9
Find (f−g)(x)
Select one:
a. −3x^3−x^2+x+18
b. 3x^3+3x^2−7x
c. 3x^3+x^2−x−18
d. 3x^3−x^2−x
A sum of money amounting to $4.25 consists of dimes and quarters if there are 26 coins in all how many are quarters
d= dimes
q = quarters
d+q=26 coins
rewrite as d=26-q
0.25q +0.10d=4.25
0.25q+0.10(26-q)=4.25
0.25q+2.6-0.10q=4.25
0.15q=1.65
q=11
d=26-11=15
11*0.25 = 2.75, 15*0.10=1.50, 2.75+1.50=4.25
there are 11 quarters
Find the value of n in the equation 6.2n – 3.7n = 85 + 45. A. 16 B. 52 C. 13.13 D. 325
Which of the following equations represents a line that is parallel to the line below?
A.
y=1/3x-2
B.
y =-1/3x-2
C.
y=3x-2
y=-3x-2
If n is a positive integer and the product all the integeres from 1 to n inclusive is a multiple of 990 what is the least possible value of n
Solve x3 = 64 over 27.
±8 over 3
8 over 3
±4 over 3
The solution of the given equation is ±8/3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is x³= 64/27
x=±∛(64/27)
x=±∛(8³/3³)
x=±8/3
Therefore, the solution of the given equation is ±8/3.
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What is the number 212three in base-two form?
The correct answer is: B. 10111
To convert the number [tex]\(212_{\text{three}}\)[/tex] to base-two (binary) form, we need to first convert it to base-ten and then convert the base-ten number to base-two.
[tex]\(212_{\text{three}}\)[/tex] in base-ten:
[tex]\[ 212_{\text{three}} = 2 \cdot 3^2 + 1 \cdot 3^1 + 2 \cdot 3^0 = 18 + 3 + 2 = 23_{10} \][/tex]
Now, we convert [tex]\(23_{10}\)[/tex] to base-two:
[tex]\[ 23_{10} = 16 + 4 + 2 + 1 = 2^4 + 2^2 + 2^1 + 2^0 = 10111_{2} \][/tex]
Final answer:
The number 212 in base three (212three) converts to 17 in decimal, which is represented as 10001 in binary notation (base-two).
Explanation:
The number 212 in base three (2123) needs to be converted into base-two form (binary). Converting from base three to base two requires understanding each digit's place value in base three and then converting that to binary. Starting from the rightmost digit to the left, we have:
The units place (30), with a value of 2The threes place (31), also with a value of 2The nines place (32), with a value of 1So, we have:
2123 = (1 × 32) + (2 × 31) + (2 × 30)
2123 = (1 × 9) + (2 × 3) + (2 × 1)
2123 = 9 + 6 + 2 = 17 in decimal.
Now we need to find the binary representation of 17:
17 divided by 2 is 8 with remainder 1 (20)8 divided by 2 is 4 with remainder 0 (21)4 divided by 2 is 2 with remainder 0 (22)2 divided by 2 is 1 with remainder 0 (23)1 divided by 2 is 0 with remainder 1 (24)So, the binary equivalent is 1(24)0(23)0(22)0(21)1(20), which is 100012.
Prove that if one solution for a quadratic equation of the form x 2 + bx + c = 0 is rational (where b and c are rational), then the other solution is also rational. (use the fact that if the solutions of the equation are r and s, then x 2 + bx + c = (x − r)(x − s).)
Final answer:
If one root of a quadratic equation with rational coefficients is rational, the other root must be rational too because the sum and product of the roots are related to the coefficients, which are also rational.
Explanation:
To prove that if one solution for a quadratic equation of the form x^2 + bx + c = 0 is rational, then the other solution is also rational, we can use the quadratic formula and properties of rational numbers. If the quadratic equation has rational coefficients and one rational solution, then the sum and product of the roots must also be rational. This is because a quadratic equation with roots r and s can be factored as (x - r)(x - s) = 0, which expands to x^2 - (r + s)x + rs = 0. Matching coefficients, we see that - (r + s) = b and rs = c. Since b and c are rational, r + s and rs must be rational as well.
Given that we have one rational root, let's say r, the sum of the roots r + s is rational, so s must also be rational because the difference of two rational numbers is rational. Hence, if one root of a quadratic equation with rational coefficients is rational, the other root must be rational as well.
PLEASE HELP ON THESE ILL GIVE 20 POINTS AND A BRAINLIEST IF YOUR CORRECT!!
Variation is a term that is used to describe __________.
A.
how repetitive a data set is
B.
how large or small a data set is
C.
how spread out or scattered a data set is
D.
how different a data set is from other data sets
The length of a rectangular lawn is measured to twice its width. the perimeter of the lawn is given as 30 m. find the length and width of the lawn.
Adam has $450. he spends $210 on food. later he divides all the money into four parts out of which three parts were distributed and one part he keeps for himself. then he found $50 on the road. write the final expression and find the money he has left?
Is #7 correct? Please explain.
Last year, there were n pies baked for the bake sale. This year, there were 156 pies baked. Using n, write an expression for the total number of pies baked in the two years
cot^2x-csc^2x=-1 for all values of x true or falsse
The original equation cot^2x - csc^2x = -1 is true for all values of x.
How to determine if cot^2x-csc^2x=-1 for all values of xThe equation cot^2x - csc^2x = -1 is true for certain values of x, but not for all values of x.
To see why, let's break down the equation using trigonometric identities:
cot^2x - csc^2x = -1
Using the reciprocal identities, we can rewrite cot^2x and csc^2x in terms of sine and cosine:
(cos^2x / sin^2x) - (1 / sin^2x) = -1
Now, let's simplify:
(cos^2x - 1) / sin^2x = -1
Using the Pythagorean identity cos^2x + sin^2x = 1, we can substitute cos^2x with (1 - sin^2x):
(1 - sin^2x - 1) / sin^2x = -1
-sin^2x / sin^2x = -1
Now, we can cancel out the sin^2x terms:
-1 = -1
This equation holds true for all values of x. Therefore, the original equation cot^2x - csc^2x = -1 is true for all values of x.
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How do I simplify this problem?
3. Elizabeth opened a library with 19,000 books in the year 1998. The number of books increases at a rate of 6.49% each year. Use a graph to predict the number of books in 2020.
A) ≈ 71,160
B) ≈ 75,779
C) ≈ 80,697
D) ≈ 66,824
Answer: ≈ 75,779
Step-by-step explanation:
The sum of four consecutive even integer numbers is 84. find the four numbers.
84/4=21
now take the 2 even numbers below 21 and the 2 even numbers above 21
18 +20 + 22 +24 = 84
the numbers are 18, 20, 22 & 24
The law of cosines is a^2+b^2-2abcos(C). Find the value of 2abcos(C).
A. 37
B. -40
C. 40
D. 20
43% of adults say cashews are their favorite kind of nut. you randomly select 12 adults and ask each to name his or her favorite nut. find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. if convenient, use technology to find the probabilities.
This question involves the concept of binomial probability in statistics. The scenarios involve calculating the probability of a certain number of successes (cashew preference) among a set number of trials (12 adults). It's recommended to use a calculator or software tool to perform the calculations.
Explanation:The subject of the query is known as binomial probability which is part of statistics in mathematics. Here, we need to find the probability of 'success' (in this case, the preference of cashews) exactly a set number of times when conducting a set number of trials (12 adults).
(a) Exactly 3: In this scenario, you want exactly 3 out of 12 adults to prefer cashews. Using binomial probability formula, it would be [tex]12C3\times (0.43)^3 \times (0.57)^9.[/tex](b) At least 4: Here, you want 4 or more adults to prefer cashews. You can either calculate separate probabilities for exactly 4, 5, 6, and so on up to 12, and then add them together. Or, you can use the complement rule: 1 - (P(0) + P(1) + P(2) + P(3)).(c) At most 2: In this case, you want 2 or fewer adults to prefer cashews. Similar to (b), you take the probability of 0, 1, and 2 'successes' and add them together.
It's also important to note, the results in these examples would be more accurate if you use a calculator or software like Excel to handle the computations.
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The probability of exactly 3 cashews in a random sample of 12 adults is approximately 19.4%.
The probability of at least 4 cashews is approximately 15.0%.
The probability of at most 2 cashews is approximately 72.0%.
These probabilities were calculated using the binomial probability formula and considering the complementary event for cases with "at least" or "at most" conditions. Technology like calculators or statistical software can be helpful in performing these calculations efficiently.
Determining the Probability of Nut Preference in a Random Sample
In this scenario, we're analyzing the probability of specific outcomes when randomly selecting 12 adults and inquiring about their favorite nut, knowing that 43% prefer cashews. Here's a breakdown of the requested probabilities:
(a) Exactly Three Cashew Preferences:
Imagine having 12 slots to fill with "cashew" or "other." We need 3 "cashew" slots and 9 "other" slots. Using the binomial probability formula, the probability of this specific arrangement is:
P(3 cashews in 12 trials) = (12 choose 3) * (0.43)^3 * (0.57)^9 ≈ 0.194
(b) At Least Four Cashew Preferences:
This includes scenarios with 4, 5, 6, 7, 8, 9, 10, 11, or all 12 adults preferring cashews. We can calculate the probability for each case and sum them up, but a simpler approach is to find the probability of the opposite event (fewer than 4 cashews) and subtract it from 1:
P(at least 4 cashews) = 1 - P(fewer than 4 cashews)
P(at least 4 cashews) ≈ 1 - (0.194 + 0.237 + 0.184 + 0.115 + 0.063 + 0.034 + 0.015 + 0.006 + 0.002) ≈ 0.150
(c) At Most Two Cashew Preferences:
This includes scenarios with 0, 1, or 2 adults preferring cashews. Similar to (b), we can calculate the probability for each case and sum them up:
P(at most 2 cashews) = P(0 cashews) + P(1 cashew) + P(2 cashews)
P(at most 2 cashews) ≈ 0.237 + 0.299 + 0.184 ≈ 0.720
Find two positive numbers such that their product is 192 and their sum is a minimum pre-calc
The two numbers with a product equal to 192 such that their sum is minimized are:
A = √192 and B = √192
How to find the two numbers?
Let's define A and B as our two numbers, we know that their product must be equal to 192, then we have:
A*B = 192.
Now, the sum of these two numbers is:
A + B.
And we want to minimize this, to do it, we need to use the first equation to rewrite one variable in terms of the other. For example, if we isolate A, we get:
A = 192/B
Replacing this in the sum, we get:
192/B + B
To minimize this, we need to find the values of B that make 0 the differentiation of the above expression.
The differentiation is:
-192/B^2 + 1
Then we need to solve:
-192/B^2 + 1 = 0
192/B^2 = 1
192 = B^2
√192 = B
To get the value of A, we use:
A = 192/B = 192/√192 = √192
Then we can conclude that the two positive numbers such that their product is 192, and their sum is minimized, is:
A = √192 and B = √192.
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A cube is packed with decorative pebbles. If the cube has a side length of 6 inches, and each pebble weighs on average 0.5 lb per cubic inch, what is the total weight of the pebbles in the cube?
What are the phase shift and period for the function y = 3cos[4(θ + 60°)] − 2?
Phase shift = right 60°, period = 90°
Phase shift = right 60°, period = −90°
Phase shift = left 60°, period = 90°
Phase shift = left 60°, period = −90°
The tip of an 11-inch wiper blade wipes a path that is 31 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
2.8 radians is the answer.
A trapezoid has two right angles and bases that measure 16m and 8m. The right triangle formed by an altitude has a hypotenuse of 4 square root 5m. Sketch the trapezoid. What are its perimeter and area?
Final answer:
The trapezoid forms a right-angled triangle with one additional rectangle. Its area is found to be 48m^2, and its approximate perimeter is 36.944m, by adding the lengths of all its sides together.
Explanation:
To find the perimeter and area of a trapezoid with two right angles and bases of 16m and 8m, we must first visualize the trapezoid. This trapezoid appears like a right-angled triangle with an additional rectangle attached to its hypotenuse.
We are given the hypotenuse of the altitude's right triangle is 4√5m, thanks to Pythagoras' theorem, we can find the two legs (which are the altitude h and the difference in bases). Let's call the altitude h and the difference in bases 'd'. Now, we know that the length of the longer leg of the right triangle is 16m - 8m = 8m.
Using the Pythagorean theorem where hypotenuse2 = altitude2 + difference in bases2, we have (4√5)2 = h2 + 82. Solving for 'h', we have h = √(80 - 64) = √16 = 4m. The area of a trapezoid is given by the formula A = (1/2) × (sum of the bases) × (height), which in this case is A = (1/2) × (16m + 8m) × 4m = 48m2.
For the perimeter, it can be calculated by adding the lengths of all sides. So, perimeter = 16m + 8m + 4m + 4√5m = 28m + 4√5m. To find the approximate value of 4√5m, we can calculate 4 × 2.236 (since √5 = 2.236), which gives us approximately 8.944m. Adding this to 28m gives us a perimeter of approximately 36.944m.
What is the probability that when a fair coin is flipped 25 times, there will be exactly five heads
The following two-way table shows the number of students of a school who have a video game and/or have a laptop:
Have Video Game Do Not Have Video Game Total
Have Laptop
15
50
65
Do Not Have Laptop
50
15
65
Total
65
65
130
Based on the table, how many students have both a laptop and a video game?
15
50
65
130
Based on the table given, the number of students who have both a laptop and a video game is 15 students.
Which students have both laptops and video games?In order to solve this question, look at the part of the table where the row on students who have laptops intersects with the column on those who have video games.
That part of the table has 15 in the cell. This means that 15 students have both video games and laptops.
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Bicycle city makes custom bicycles. They charge $160 plus $80 for each day that it takes to build the bicycle. If you have $480 to spend on your new bicycle, how many days can it take Bicycle City to build the bike?
The midpoint of a segment is (4,3) and one endpoint is (10,8) Find the coordinates of the other endpoint.
Answer:
[tex](-2,-2)[/tex].
Step-by-step explanation:
Let us assume that coordinates of other endpoint are [tex](x_1,y_1)[/tex]
We have been given that the midpoint of a segment is (4,3) and one endpoint is (10,8). We are asked to find the coordinates of the other endpoint.
We will use midpoint formula to solve our given problem.
[tex]x\text{-coordinate of midpoint}=\frac{x_1+x_2}{2}[/tex]
[tex]y\text{-coordinate of midpoint}=\frac{y_1+y_2}{2}[/tex]
Upon using our given information, we will get:
[tex]4=\frac{x_1+10}{2}[/tex]
[tex]4\cdot 2=\frac{x_1+10}{2}\cdot 2[/tex]
[tex]8=x_1+10[/tex]
[tex]8-10=x_1+10-10[/tex]
[tex]x_1=-2[/tex]
Similarly, we will find y-coordinate.
[tex]3=\frac{y_1+8}{2}[/tex]
[tex]3\cdot 2=\frac{y_1+8}{2}\cdot 2[/tex]
[tex]6=y_1+8[/tex]
[tex]6-8=y_1+8-8[/tex]
[tex]y_1=-2[/tex]
Therefore, the coordinates of other endpoint would be [tex](-2,-2)[/tex].
Find the arc length of a central angle of pi/4 in a circle whose radius is 8 inches
If the polynomial x5 − 105 can be split as the product of the polynomials
x − 10 and a, what is a?
the value of a is
[tex]\( a = \frac{9845}{x - 10} \)[/tex].
To find a, we can use polynomial long division or synthetic division to divide [tex]\( x^5 - 105 \)[/tex] by [tex]\( x - 10 \)[/tex]. The remainder should be zero if [tex]\( x - 10 \)[/tex] is a factor of [tex]\( x^5 - 105 \)[/tex].
Let's perform polynomial long division:
____________________________
x - 10 | x^5 + 0x^4 + 0x^3 + 0x^2 + 0x - 105
- (x^5 - 10x^4)
____________________________
10x^4 + 0x^3 + 0x^2 + 0x - 105
- (10x^4 - 100x^3)
____________________________
100x^3 + 0x^2 + 0x - 105
- (100x^3 - 1000x^2)
___________________________
1000x^2 + 0x - 105
- (1000x^2 - 10000x)
___________________________
995x - 105
- (995x - 9950)
___________________________
9845
```
Since the remainder is a constant term, it's clear that [tex]\( x - 10 \)[/tex] is a factor of [tex]\( x^5 - 105 \)[/tex]. So, [tex]\( a = \frac{9845}{x - 10} \)[/tex].
Therefore, [tex]\( a = \frac{9845}{x - 10} \)[/tex].