Answer:
f(10)=342
Step-by-step explanation:
f(10)= 3(10)^2+6(10)-18
complete your exponet first and multiply 6(10)
f(10)=3(100)+60-18
multiply the 3(100)
f(10)=300+60-18
add and subtract all the numbers together
f(10)=342
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in
20.4 days
22.5 days
25.6 days
30.1 days
what is the GCF of 20 and 6x^2
Answer:
2
Step-by-step explanation:
A plot of land has vertices as follows, where each coordinate is a measurement in feet. find the perimeter of the plot of land (1,7),(7,7),(7,1),(1,1) A.24ft B.32ft C.16ft D.36ft
Answer:
D. 36ft
Step-by-step explanation:
Answer:
the real answer is 24 :)
Step-by-step explanation:
8a+5b+3abc when a = 1, b= 2 and c= 3
Answer:
8*1+5*2+3*1*2*3
8+10+18
36 is the answer
Five computer program modules are ranked as M1, M2, M3, M4, and M5 according to the ascending order of effort required to debug them, among which M1 requires the least amount of effort and M5 requires the most amount of effort. A software engineer must randomly select three program modules from the five modules. He (or she) does not know the amount of effort each module costs when selecting.
A) What is the sample space?
B) Let A be the event that one selected module requires the least amount of effort. List the outcomes in A, and calculate the probability of A.
C) Let B be the event that the one selected module requires the most effort. List the outcomes in B, and calculate the probability of B.
D) List the outcomes in the compound event AnB, and calculate the probability of it.
E) List the outcomes in the compound event AUB, and calculate the probability of it.
F) List the outcomes in the compound event AnB, and calculate the probability of it.
G) List the outcomes in the compound event AUB, and calculate the probability of it.
H) Are events A and B mutually exclusive? Explain why?
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Technician selects three out of 5 systems
In C(5,3)=10ways, this can be achieved
In part a:
Space sample chooses 3 of a 5 systems
\((M_1, \ M_2,\ M_3),\)\((M_1,M_2,M_4) \ (M_1,M_2,M_5) \ (M_1,M_3,M_4) \ (M_1,M_3,M_5),\)\((M_1,M_4,M_5) \ (M_2,M_3,M_4)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5)}\)
In point b:
A =MODULE WHICH INCLUDE M1 minimal amount of effort
Outcomes probable =
\((M_1,M_2,M_3),\ (M_1,M_2,M_4) \ (M_1,M_2,M_5)\ (M_1,M_3,M_4)\\\\(M_1,M_3,M_5),\ (M_1,M_4,M)5)\ =\ 6\)
\(\to p(A)=\frac{6}{10}\\\\\)
\(=0.6\)
In point c:
B = highest effort that is \(M_5\)
Potential result=
\((M_1,M_2,M_5) \ (M_1,M_3,M_5) \ (M_2,M_3,M_5)\(M_2,M_4,M_5) \\ (M_2,M_4,M_5), \ (M_3,M_4,M_5) \ =\ 6 \\\\\)
\(\to B= \frac{6}{10} \\\\\)
\(=0.6\)
\(\to P(B)=10\)
In point d:
\(\to \ A \ intersection \ B=(M_1,M_2,M_5), \ (M_1,M_3,M_5) \ ,(M_1,M_4,M_5)\)
\(\to A (A \ intersection \ B) = \frac{3}{10} \\\\\ \ \ \ \ \\)
\(=0.3\)
In point e:
\(\to (A \cup B) = (M_1,M_2,M_3),\ (M_1,M_2,M_4)\ (M_1,M_2,M_5)(M_1,M_3,M_4)\ (M_1,M_3,M_5), \\ (M_1,M_4,M_5)\ (M_2,M_3,M_5) \ (M_2,M_4,M_5),(M_3,M_4,M_5) \ = \ 9\)\(\to P(A \cap B)=\frac{9}{10}\)
\(= 0.9\)
In point f:
\(\to (A\cap B) = \frac{3}{10}\)
\(= 0.3\)
In point g:
\(\to (A \cup B) = \frac{7}{10}\)
\(=0.7\)
In point h:
\(\to p(A \cap B) = 0.3 \neq 0\)
Ms. Suen found a trapezoid shaped aquarium for her pet beta fish. The trapezoid has a height of 12 in and bases of 8 in and 5 in. The length of the aquarium is 18 in. If Ms. Suen wanted to fill the tank with water how much water does she need to completely fill the aquarium?
Answer:
poop
Step-by-step explanation:
yes
Determine whether each expression is equivalent to
81^0.5t^2+t
Answer:
All are equivalent.
Step-by-step explanation:
Find g(x), where g(x) is the translation 5 units right of f(x)= – 7(x–5)2+3.
g(x) is the translation 5 units right of f(x)= – 7(x–5)²+3.
A function called f(x) accepts an input of "x" and outputs "y". You can write it out as y = f. (x).‘x’ is a variable that represents an input to a function.
To translate a function, we need to replace x with (x-a) in the function f(x) where ‘a’ is the amount of translation.
To translate a function 5 units right, we need to replace x with (x-5) in the function f(x).
So, g(x) = f(x-5) = -7(x-5-5)²+ 3 = -7(x-10)²+ 3.
Therefore, g(x) is the translation 5 units right of f(x)= – 7(x–5)²+3.
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lect the correct answer.
Under which condition is the sample proportion, , a point estimate of the population proportion?
A.
The sample proportion is never a point estimate of the population proportion.
B.
The sample represents a proportion of the population.
C.
The sample proportion is unbiased.
D.
The sample size, n, is small enough.
Reset Next
The correct answer is B. The sample represents a proportion of the population.
What is the sample population ?
A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.
The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.
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A line segment has end points V (-4,-4) and W (11, 2). What is the x-coordinate of the point that is 2/5 of the way from V to W on this line segment
the x-coordinate of the point that is 2/5 of the way from V to W on this line segment is approximately 8.08.
What is coordinate?A coordinate is a number or set of numbers that specifies the position of a point in a space. Coordinates are used to describe the position of objects in various mathematical systems, including two-dimensional and three-dimensional Euclidean spaces, as well as non-Euclidean spaces like spherical or hyperbolic geometries.
by the question.
The x-coordinate of the point that is 2/5 of the way from V to W can be found by first determining the x-coordinate of the point that is 2/5 of the way from V to W and then using the formula for finding the x-coordinate of a point on a line given its y-coordinate.
To find the point that is 2/5 of the way from V to W, we need to first find the distance between V and W. Using the distance formula:
d =\(\sqrt{11-(-4)^{2} }\) + (2 - \((-4)^{2}\)) = \(\sqrt{225+36}\)= \(\sqrt{261}\)
Then, the distance between V and the point we're looking for is (2/5) * \(\sqrt{261}\), and the distance between the point we're looking for and W is (3/5) * \(\sqrt{261}\).
To find the x-coordinate of the point we're looking for, we can use the formula:
x = (distance from V to point we're looking for)/ (total distance) * x
coordinate of W + (distance from point we're looking for to W)/(total distance) * x-coordinate of V.
Substituting the values, we found:
x = (2/5 *\(\sqrt{261}\))/\(\sqrt{261}\)) * 11 + (3/5 * \(\sqrt{261}\))/\(\sqrt{261}\)) * (-4) = 8.08
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SOMEONE PLEASE HELP ME OUTCalculate the minimum and maximum possible areas. Round your answers to the nearest whole square unit. A rectangular garden plot measures 12 feet by 28.6 feet. The minimum possible area is about ft. The maximum possible area is about ft ?
For this problem we have the following info given: We have a rectangular garden and the measures are 12 ft of width and 28.6ft of lenght . We also know that the definition for the area of a rectangular figure is given by:
\(A=wl\)Where w represent the width and l the length. and we want to estimate the maximun and minimum area for this case so we need to use a delta of error in order to have two measures for the area:
\(A=(w+\Delta w)(l+\Delta w)\)And let's assume an error of 0.2 ft so then the maximum area would be:
\(A_{\text{max}}=(12+0.2)ft(28.6+0.2)ft=351.36ft^2\)And the minimum area would be:
\(A_{mi}=(12-0.2)ft(28.6-0.2)ft=335.12ft^2\)And for this case the minimum area would be 335.12 ft2 and the maximum 351.36ft2. It's important to remember that the answer depends on the delta value used for this case we use 0.2ft but if we use for example 0.5ft the answer would change.
Thank you for the help!
Answer:
c 57
Step-by-step explanation:
It takes 1/2 can of paint to paint a table. A man has 2 cans of paint, how many tables can he paint
Answer:
it takes 4 tables for the man to paint
Solve the equation for all real solutions.
X^2 + 11z +9 = 5z
Someone help plz ):
Answer:
\(z = -3\)
Step-by-step explanation:
Given
\(z^2 +11z+9 = 5z\) --- the correct equation
Required
Solve
Equate to 0
\(z^2 +11z-5z+9 = 0\)
\(z^2 +6z+9 = 0\)
Expand
\(z^2 +3z+3z+9 = 0\)
Factorize
\(z(z +3)+3(z+3) = 0\)
Factor out z + 3
\((z +3)(z+3) = 0\)
Split
\(z + 3 =0\) --- twice
\(z = -3\)
Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. R = 6 sin theta and r = 6 cos theta the intersection point(s) is/are_______
(Type an ordered pair. Type exact answer for each coordinate, using phi as needed. Type the coordinate for theta in radians between 0 and phi. Use a comma to separate answers as needed)
The intersection points are (6, 6) and (-6, -6).
What is Intersection points?
The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.
The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.
6 sin(Ф) = 6 cos(Ф)
Dividing both sides by 6 and rearranging terms, we get:
tan(Ф) = 1
This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].
Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.
Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).
Therefore, the intersection points are (6, 6) and (-6, -6).
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Question in the pic, please explain your answer
The statement translated to an algebra equation will give the value of the unknown number w = 11/5
What is algebra?Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.
Let us represent the unknown number with the letter w so that the statement can be written as the equation:
5w - 8 = 3
add 8 to both sides
5w - 8 + 8 = 3 + 8
5w = 11
divide through by 5
5w/5 = 11/5
w = 11/5
Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5
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Data is collected from the US Geologic Survey about the flow rate of the Poudre river. After some study, and unit conversions, a scientist makes a first model of the historical flow rate data as F(t) = 1.5 + 1.2 cos(2 t) in billions of cubic feet per year, while t is measured in fractions of a year since May 1, 2000. Use the Fundamental Theorem of Calculus to find the net amount of water from t = 0) to t = using this flow rate F"(t).First, F(t) = +C The model predicts the net amount of water discharged from the Poudre is F112 -Filo 0.75 What does the model predict the net discharge will be from t = 0 to t = 12 Net discharge = 1.5 Billions of ft 3
The model predicts that the net discharge will be -0.8 + 1.2 cos(24) billions of cubic feet from t = 0 to t = 12.
The net amount of water discharged from the Poudre river from t = 0 to t = 12 can be found using the Fundamental Theorem of Calculus, which states that the net change in a function over an interval is equal to the function evaluated at the endpoints of the interval minus the function evaluated at the beginning of the interval.
In this case, the net discharge from t = 0 to t = 12 can be calculated as follows:
Net discharge = F(12) - F(0)
= (1.5 + 1.2 cos(212)) - (1.5 + 1.2 cos(20))
= 1.5 + 1.2 cos(24) - 1.5 - 1.2
= -0.8 + 1.2 cos(24)
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Consider the following measurements of the heat-producing capacity of the coal produced by two mines (in millions of calories per ton): Mine 1: 8260 8130 8350 8070 8340 Mine 2: 7950 7890 7900 8140 7920 7840 Can it be concluded that the two population variances are equal?
F0.05 (4,5)=5.19>f according to the F-distribution table. Following that, P(F>1.442)>P(F>f0.05 (94.5))=0.05. This leads us to conclude that the sample has a higher than 5% chance of producing such data under the premise that σx=σy.
We cannot conclude that the variances of the two populations are not equal based on the standards of a 95% confidence interval.
Step 1 : the mines' 1 and 2 standard deviations should be calculated. \(n_{x}\) =5&\(n_{y}\)=6.
To determine the sample means, use the formulas
x bar = 8260 + 8130 + 8350 + 8070 + 8340/ \(n_{x}\)
x bar = 41150/ 5
x bar = 8230 and y bar = 7950 + 7890 + 7900 + 8140 + 7920 + 7840/ \(n_{y}\)
y bar = 47640/6
y bar = 7940.
step 2: Now, \(s_{x}\)provides the standard deviations.
\(s_{x}^{2}\) =1/4i=1∑^5i=1(xi−x)^2
=1/ 4 ⋅63000
=15750
for \(s^{2}_{y}\)
\(s^{2}_{y}\)^2=1/5∑i=1^6(yi−y)^2
=1/5⋅54600
=10920
If we assume that the variances of the two populations are equal—
that is, σx=σy and
\(s_{x}^{2}\) and\(s^{2}_{y}\) are the variances of independent random samples with sizes of \(n_{x}\)=5 and\(n_{y}\) =6 drawn from normal populations—then we can say that the random variable exists.
The formula F is
=\(s_{x}^{2}\)/ \(s^{2}_{y}\)has an F distribution with
v1=nx- 1
=5- 1
=4 and
v2=ny-1
=6- 1
=5
The observed samples' f-value is f=\(s_{x}^{2}\) / \(s^{2}_{y}\)
=15750/10920
=1.442.
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Max used 12 1⁄2 pounds of deli meat in one week at his sandwich shop. If he uses 1⁄4 of a pound of meat for each sandwich, how many sandwiches did he make with the deli meat?
Answer:
\(12 \frac{1}{2} \div \frac{1}{4} = x \\ 12.5 \div 0.25 = x \\ x = 50\)
Max made 50 sandwiches
. In a 30°-60°-90° triangle, the length of the hypotenuse is 12 inches. What is the length, in inches, of the side opposite the 60° angle?
Use the long division method to find the result when 12x^3+25x^2+4x-112x
3
+25x
2
+4x−1 is divided by 3x+13x+1.
Answer:
(4x + 3) • (x + 2) • (3x - 2)
Thats finding the root polynomials hope it helps a bit
What is a cubic polynomial function with zeros -20, -15, and -6?
What is a quartic polynomial function with zeros -20, -16, -11, and -9?
What are the zeros of x^3 + 16x^2 + 60x? What are their multiplicities?
Answer:(x + 1)(x - 1)(x + 5)(x - 3) is the fully factored form of the polynomial.
The zeros are (-1, 0), (1, 0), (-5, 0), and (3, 0).
x^4 + 2x^3 - 16x^2 - 2x + 15
We can use the rational roots theorem to find some of the possible roots, and after finding just one root, we can simplify this polynomial.
List factors of 15:
1, 3, 5, 15.
List factors of 1:
1.
Our possible rational factors are:
+/- 1, +/- 3, +/- 5, +/- 15.
To find factors, we can use the remainder theorem.
Replace all x values with 1.
1^4 + 2(1)^3 - 16(1)^2 - 2(1) + 15 = 0
Because the answer is zero, it means that 1 is a root.
We can divide this polynomial by x - 1 to find a simplified form.
After dividing, our quotient is: x^3 + 3x^2 - 13x - 15
We can continue finding factors by using the rational roots theorem. Once we have only three terms, we can try to factor using the AC method.
Our next possible root is -1.
(-1)^3 + 3(-1)^2 - 13(-1) - 15 = 0
We know that -1 is also a root, and so we can divide the polynomial by x + 1.
After diving we're left with x^2 + 2x - 15.
Now, we can try to factor using the AC method.
List factors of -15.
1 * -15
-1 * 15
3 * -5
-3 * 5 (these digits satisfy the criteria.)
Split the middle term.
x^2 - 3x + 5x - 15
Factor binomials.
x(x - 3) + 5(x - 3)
Rearrange binomials.
(x + 5)(x - 3)
Add in the two factors we already factored out.
(x - 1)(x + 1)(x + 5)(x - 3)
Step-by-step explanation:
ook at the following sum.
1 + 1⁄2 + 1⁄4 + 1⁄8 + 1⁄16 + 1⁄32 + 1⁄64. . .
Notice that the denominator of each fraction in the sum is twice the denominator that comes before it.
If you continue adding on fractions according to this pattern, when will you reach a sum of 2?
Answer: We will never reach a sum of 2
We get closer and closer to 2, but never actually reach this exact value.
==============================================================
Explanation:
The sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
is geometric with these properties
a = 1 = first termr = 1/2 = common ratioWe multiply each term by 1/2 to get the next one.
Examples:
(1/8)*(1/2) = 1/16(1/32)*(1/2) = 1/64----------------
Notice how -1 < r < 1 is true, i.e. -1 < 1/2 < 1 is true.
Because of this fact, we can determine the sum of infinitely many terms.
That infinite sum is
S = a/(1-r)
This is our upper bound of what we can reach for S.
Calculating it gives:
S = a/(1-r)
S = 1/(1-0.5)
S = 2
Therefore, the sum of the infinitely many terms of this geometric sequence is 2.
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... = 2
We never quite reach 2 exactly due to the fact we cannot reach infinity on the number line. Infinity is not a number, but rather a concept.
Therefore, we never reach a sum of 2. We simply get closer and closer.
-------------
Using computer software, I was able to generate this:
1 + 1/2 = 1.51 + 1/2 + 1/4 = 1.751 + 1/2 + 1/4 + 1/8 = 1.8751 + 1/2 + 1/4 + 1/8 + 1/16 = 1.93751 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 1.968751 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 = 1.984375The decimal values are exact without any rounding done to them. As you can see, the results of 1.5, 1.75, 1.875, etc are slowly approaching 2 but never get to that exact value itself. Visually you can think of an asymptote.
Find the inequality represented by the graph.
What is 888 x - 666?
What is 888 x - 666? = -591408
\(Hello\) \(There!\)
Ummmmm... I could be wrong?
I think it is...
-591408
Hopefully, this helps you!!
\(AnimeVines\)
Lmk asap please cuz I need it by tonight
Answer: 20
Step-by-step explanation:
2x^2 + 4y=
2(2)^2 + 4(3)=
2(4)+12=
8+12=20
What is 7/25 written as a decimal? 0.18 0.28 0.725 3.57
Answer:
0.28
Step-by-step eplanation:
Answer:
0.28
Step-by-step explanation:
Use a calculator
Freda bought 700 grams of almonds and 500 grams of cashews. How many kilograms of nuts did Freda buy in all?
Answer:
1.2kl
Step-by-step explanation:
1000grams=1kilogram
700+500=1200
so 1.2kilograms
What is the intermediate step in the form
(x+a)^2=b as a result of completing the square for the following question
The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)
To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:
1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).
2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).
3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:
\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).
4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).
This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)
This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.
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I will mark you brainiest!
One of the sides of a pentagon has length 12. Which of the following points, when paired with (2, 3), will make a side equal to this length?
A) (14, 15)
B) (2, -9)
C) (-2, -3)
D). (-9, 2)
The correct option for the given sum is option B. The point (2,-9) paired with (2, 3), will make a side equal to this length.
Let the other point of the pentagon will be M(n, o).
The given point be A (a, b)
Also given one of the sides of a pentagon has length 12.
Now, we need to find the distance between the two points,
Distance between two points: |AM| = √\((a-n)^2+(b-o)^2\)
Now,
\(12 = \sqrt{(2-n)^2+(3-o)^2}\)
\((12)^2\) = \((2-n)^2+(3-o)^2\)
\((2-n)^2+(3-o)^2\) = 144 ----------------------------- eq (1)
Now, check every point for the values to match with equation (1)
Option A: \((2-14)^2+(3-15)^2\) = 288. So the option is false.
Option B:
\((2-2)^2+(3-(-9))^2\) =114
0+114 =114
Therefore option B is correct. The other point is (2,-9).
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