Answer:
p (13 - 4 p)
Step-by-step explanation:
Simplify the following:
2 p (p + 2) - 3 p (2 p - 3)
Hint: | Pull a common factor out of 2 p (p + 2) - 3 p (2 p - 3).
Factor p out of 2 p (p + 2) - 3 p (2 p - 3), resulting in p (2 (p + 2) - 3 (2 p - 3)):
p (2 (p + 2) - 3 (2 p - 3))
Hint: | Distribute 2 over p + 2.
2 (p + 2) = 2 p + 4:
p (2 p + 4 - 3 (2 p - 3))
Hint: | Distribute -3 over 2 p - 3.
-3 (2 p - 3) = 9 - 6 p:
p (2 p + 9 - 6 p + 4)
Hint: | Group like terms in 2 p - 6 p + 4 + 9.
Grouping like terms, 2 p - 6 p + 4 + 9 = (4 + 9) + (2 p - 6 p):
p (4 + 9) + (2 p - 6 p)
Hint: | Combine like terms in 2 p - 6 p.
2 p - 6 p = -4 p:
p (-4 p + (4 + 9))
Hint: | Evaluate 4 + 9.
4 + 9 = 13:
Answer: p (13 - 4 p)
3. What are the coordinates of the
centroid of a triangle with vertices at
Q (1,0), R (-10,-6), and S (0, -6)?
Answer:
coordinates for the centroid is at (-3, -4)
Step-by-step explanation:
The centroid of a triangle is simply defined as the center point which is equidistant from the three vertices.
Let's denote the centroid as O. Thus, the coordinates of O will be: (O_x, O_y).
Now, the formula to calculate the centroid of a triangle with coordinates (O_x, O_y) is given by;
For x - coordinate;
O_x = (A_x + B_x + C_x)/3
For y - coordinate;
O_y = (A_y + B_y + C_y)/3
From the question,
A_x = 1
B_x = -10
C_x = 0
A_y = 0
B_y = -6
C_y = -6
Thus;
O_x = (1 - 10 + 0)/3
O_x = -9/3
O_x = -3
Also,
O_y = (0 - 6 - 6)/3
O_y = - 12/3
O_y = - 4
Thus, coordinates for the centroid is at (-3, -4)
What is n less than 7?
n less than 7, is represented as this:
n>7
Step-by-step explanation:
You just need to think about what the question is, if it's less than, you use the > symbol to prove one variable is smaller than the other.
i hope this helps!
Answer:
[tex]\Huge \boxed{-n+7}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
n is the variable.
n less than 7 as an expression would be:
[tex]\Longrightarrow \ \ 7-n[/tex]
Rearranging terms:
[tex]\Longrightarrow \ \ -n+7[/tex]
[tex]\rule[225]{225}{2}[/tex]
Assume the triangle has given measurements. solve for the remaining sides and angles.
Answer:
Step-by-step explanation:
You can calculate the length of side a using the Cosine Rule:
a^2 = 32.6^2 + 41.4^2 - 2.32.6.42.4 cos pi/6
a^2 = 456.01
a = √456.01
a = 21.35
By the Sine Rule:
32.6 / sin B = 21.35 / sin pi/6
sin B = (32.6 * sin pi/6) / 21.35
sin B = 0.76347
B = 0.869 radians.
C = pi - pi/6 - 0.869 = 1.749 radians.
Please help!!!!!!!!!!!
QR = QU - RU
QR = 24 -19 = 5
QR = RS = ST = 5
QR + RS + ST = 5 + 5 + 5 = 15
TU = 24-15 = 9
SU = 5 + 9 = 14
Calculus Ch. 1.2 Classwork Problems Evaluating limits Graphically
Answer:
16) 2
17) -5
18) doesn't exist
19) doesn't exist
20) doesn't exist
21) 3
22) 4
23) 6
Step-by-step explanation:
16) as you move towards -9, the function adopts the value 2
17) as one moves towards x = -6 , from both sides (right and left) the function goes to the value -5
18) As one moves towards x = -4 (from the right and from the left, the functions seems to diverge towards + ∞. So normally the convention for limits stipulates: Undefined or Doesn't exist
19) f(-4) doesn't exist (for same reasons as above (there is a singularity here)
20) As one moves towards 2 from the right, the function gets towards the value 3, while approaching from the left the function goes towards the value 5. So formally we say that the limit doesn't exist (from the left and from the right limits don't agree)
21) f(2) is the well defined value of 3
22) approaching x= 4 from the right and from the left both lead towards the value 4.
23) f(4) is 6
Looking at the image, What is the value of x?
Answer: 98
Step-by-step explanation: 53+45 = 98 subtract that from 180 you get 82 which is the other corner. the other side of the line adds up to 180 with the 82
Answer:
Step-by-step explanation:
inside the triangle
a + 53 + 45 = 180
a + 98 = 180
a = 82
x + 82 = 180
x = 98
I have 6.8 grams of fat in my cereal and 8 grams of fat in my milk ...how much fat do I have ...answer
Answer:
You have 14.8 grams of fat in total.
Step-by-step explanation:
6.8 + 8 = 14.8
Find the distance between the pair of points and then round your answer to the nearest tenth.
(-4,5) and (4.0)
d=(22 – 21) + (92 – 41)?
Answer:
[tex] d = 9.4 units [/tex] (nearest tenth)
Step-by-step explanation:
Given the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], distance between (-4, 5) and (4, 0) is calculated as follows:
Let [tex] (-4, 5) = (x_1, y_1) [/tex]
[tex] (4, 0) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(4 - (-4))^2 + (0 - 5)^2} [/tex]
[tex] d = \sqrt{(8)^2 + (- 5)^2} [/tex]
[tex] d = \sqrt{64 + 25} [/tex]
[tex] d = \sqrt{89} [/tex]
[tex] d = 9.4 units [/tex] (nearest tenth)
Given the sample mean = 21.15, sample standard deviation = 4.7152, and N = 40 for the low income group,Test the claim that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm. Test at the 0.1 significance level.Identify the correct alternative hypothesis:p=21.21p=21.21μ>21.21μ>21.21μ=21.21μ=21.21μ<21.21μ<21.21p<21.21p<21.21p>21.21p>21.21
Answer:
Null hypothesis:
[tex]\mathtt{H_o : \mu = 21.21}[/tex]
Alternative hypothesis
[tex]\mathtt{H_1 : \mu \geq 21.21}[/tex]
t = -0.080
Decision Rule: To reject the null hypothesis if t > 1.340 at t
Since t = -0.080, this implies that t < 1.340 that means the t statistics value did not fall into the rejection region. Hence, we fail to reject the null hypothesis at the level of significance 0.10
Conclusion: We conclude that there is insufficient evidence to support the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.
Step-by-step explanation:
Given that:
the sample mean [tex]\overline x[/tex] = 21.15
the standard deviation [tex]\sigma[/tex] = 4.7512
sample size N = 40
The objective is to test the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.
At the level of significance of 0.1
The null hypothesis and the alternative hypothesis for this study can be computed as follows:
Null hypothesis:
[tex]\mathtt{H_o : \mu = 21.21}[/tex]
Alternative hypothesis
[tex]\mathtt{H_1 : \mu \geq 21.21}[/tex]
This test signifies a one-tailed test since the alternative is greater than or equal to 21.21
The t-test statistics can be computed by using the formula:
[tex]t= \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{21.15- 21.21 }{\dfrac{4.7152}{\sqrt{40}}}[/tex]
[tex]t = \dfrac{-0.06 }{\dfrac{4.7152}{6.3246}}[/tex]
t = -0.080
degree of freedom = n - 1
degree of freedom = 40 - 1
degree of freedom = 39
From the t statistical tables,
at the level of significance ∝ = 0.1 and degree of freedom df = 39, the critical value of [tex]\mathtt{{T_{39,0.10} = 1.304}}[/tex]
Decision Rule: To reject the null hypothesis if t > 1.340 at t
Since t = -0.080, this implies that t < 1.340 that means the t statistics value did not fall into the rejection region. Hence, we fail to reject the null hypothesis at the level of significance 0.10
Conclusion: We conclude that there is insufficient evidence to support the claim that the mean nickel diameter drawn by children in the low-income group is greater than 21.21 mm.
The density of a certain material is such that it weighs 10 ounces per gallon of volume. Express this density in pounds per pint. Round your answer to the nearest hundredth.
Answer:
0.08 pounds per pint.
Step-by-step explanation:
Given: The density of a certain material is such that it weighs 10 ounces per gallon.
We are to express this density in pounds per pint.
1 gallon ⇒ 10 ounces
1 pound = 16 ounces
How many pounds? = 10 ounces.
Cross-multiplying gives;
[tex]\frac{10 * 1}{16} = 0.625[/tex] pounds
1 gallon = 8 pints
The density in pounds per pint is;
0.625 pounds ÷ 8 pints = 0.078125 pounds per pint = 0.08 pounds per pint (answer rounded up to the nearest hundredth).
ANALYZING RELATIONSHIPS Data from North
American countries show a positive correlation
between the number of personal computers per capita
and the average life expectancy in the country.
a. Docs a positive correlation make sense in this
situation? Explain
b. Is it reasonable to
conclude that
giving residents
of a country
personal computers
will lengthen their
lives? Explain
Answer:
Can u add more context pls then I'll answer
Step-by-step explanation:
Let f (x) = x4 + x3 + x2 + x + 1 ∈ Z2[x]. Prove that f(x) is irreducible over Z2[x] or not?
Answer and Step-by-step explanation:
Let f(x) = x4 + x3 + x2 +x + 1 Є Z2[x]. Prove that f(x) is irreducible over Z2[x] or not?
Proof:-
Let f(x) = x4 + x3 + x2+ x+1 Є Z2[X].
Then f (0) = 1 = f(1), so f(x) has no roots, By Factor theorem, which states that polynomial f(x) has a factor(x-a) if and only if f(a)=0. Hence, f(x) has no linear factor. If f(x) is reducible, it must have factors of degree 2 and degree 3. But f(x) has no degree 2 factors.
We know that only irreducible quadratic in Z2[X] is x2 + x +1. When we divide f(x) by x2 + x +1 we get a remainder of 1, so x2 + x +1 is not a factor of f(x) therefore f(x) is irreducible.
what does b≠0 mean??
Answer:
b≠0 means b is not equal to zero.
Hope I helped!
Best regards!
Answer:
The special symbol ≠ It is used to show that one value is not equal to another. a ≠ b says that a is not equal to b. Example: 4 ≠ 9 shows that 4 is not equal to 9.
Step-by-step explanation:
How many bricks each 0.16m2 are required for paving a courtyard of 5.5m long and 4.8m wide?
You are allowed to multiply as many 2's and/or as many 5's as
you want. What can be the last digit of your result?
If 5 's multiplied many times then always unit digit will be 5.
If power of 2 is divide by 4 then , if remainder is zero then unit digit will be 6 and if remainder is 1 then unit digit will be 2 , if remainder is 2 then unit digit will be 4 and if remainder is 3 then unit digit will be 8.
First here we analyse when many of 2's is multiplied.
[tex]2^{1} =2\\2^{2} =4\\2^{3}=8\\2^{4} =16\\2^{5} =32\\2^{6}=64[/tex]
Here , we observed that after [tex]2^{4} =16[/tex] , unit digit will be repeat.
So, If power of 2 is divide by 4 then , if remainder is zero then unit digit will be 6 and if remainder is 1 then unit digit will be 2 , if remainder is 2 then unit digit will be 4 and if remainder is 3 then unit digit will be 8.
Now, analyse when many of 5's multiplied.
[tex]5^{1}=5 \\5^{2}=25\\5^{3}=125[/tex]
So, When 5 's multiplied many times then always unit digit will be 5.
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(6 + 7) + 8 = 6 + (7 + 8)
which property of addition shows
Answer: Associative Property of Addition
Step-by-step explanation: The problem (6 + 7) + 8 = 6 + (7 + 8)
demonstrates the associative property of addition.
Notice that the addends, or the number we're adding,
are the same on both sides of the equals sign, 6 + 7 + 8.
The associative property of addition tells us that when we're adding more
than two numbers, the grouping of addends does not change the sum.
For example here, (6 + 7) gives us 13, and 14 + 8 gives us 21.
On the right side, (7 + 8) gives us 15, and 6 + 15 gives us 21.
So the sum is the same, regardless of which way we group the addends.
The absolute value of some number x is 17, and the number y is 23. How much is
sum x + y? How many different results do you get?
Answer:
we get only one solution that is 23 + 17 = 40
Hope it helps
Would like an answer for this question. Which represents 7(45) using the distributive property to simplify? SELECT THE TWO THAT APPLY. 1# 7 (40 - 5) 2# 7 (4) + 7 (5) 3# 7 (40 +5) 4# 7 (40) + 7(5)
Answer:
7(45)=7(40)+7(5)
Step-by-step explanation:
We need to represent 7(45) using the distributive property to simplify.
We can write 45 as 40+5
So it becomes,
7(45) = 7(40+5)
Distributive property is : a(b+c)=ab+ac
a=7, b = 40 and c = 5
7(40+5)=7(40)+7(5)
So, the correct option is (4).
Many people enjoy taking cruises for their vacations. Each cruise ship has different options and features. Which of the following is an example of a continuous quantitative variable that might be reported about each cruise ship?
A - Type of engine used.
B - Number of guest rooms.
C - Average speed in the ocean.
D - Number of restaurants on the ship.
Answer: Option ( C ) Average speed in the ocean
Step-by-step explanation: This is because continuous quantitative variable is a variable whose value is obtained by measuring. The average speed is measured.
The example of a continuous quantitative variable that might be reported about each cruise ship is the average speed in the ocean so option (C) will be correct.
What is the reasoning?
The procedure of utilizing logical reasoning to analyze a condition to determine the best problem-solving approach for a particular issue, then using this approach to create and explain a resolution.
In another word, reasoning is a tricky but interesting problem in mathematics that required relations of variables to solve.
The quantitative variable is a variable whose value is measurable for example weight of any object.
In the given question the average speed in the ocean is only a variable and can be measured for each ship.
Hence"The example of a continuous quantitative variable that might be reported about each cruise ship is the average speed in the ocean".
For more about reasoning,
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Solve for x
4( 3x - 5) = -2(-x + 8) - 6x
Answer:
Step-by-step explanation:
12x - 20 = 2x -16 - 6x
12x - 20 = -4x - 16
16x - 20 = -4x
20x = 20
x = 1
Which expression is a factor of 21x2 + 13x – 20?
A. 3x – 4
B. 7x - 5
C. 7x + 4
D. 3x + 5
Answer:c
Step-by-step explanation:
7x - 5 is the factor of 21x²+13x-2.Option B is correct.
What is the equation?An equation is a statement indicating the equality of two expressions that contain variables and/or numbers. In essence, equations are questions, and the pursuit of methodically resolving these questions has been the impetus for the development of mathematics.
It is given that, the expression is 21x²+13x-2.
We have to find the factor of the expression.
Algebraic expression factorization is the process of identifying two or more expressions whose product equals the given expression. Algebraic expression factorization is hence the multiplication procedure in reverse.
[tex]=21x^2+13x-20 \\\\ =\left(21x^2-15x\right)+\left(28x-20\right) \\\\ =3x\left(7x-5\right)+4\left(7x-5\right) \\\\ =\left(7x-5\right)\left(3x+4\right)[/tex]
The factors of the expression are (7x-5) and (3x-4).
Thu option B is correct.
Learn more about the equation here,
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How do you find the area?
Answer:
• First attachment's graph is correct
• Second attachment, the area is approximately 8.6
Step-by-step explanation:
Remember that the area between two curves is defined as the following:
[tex]\mathrm{The\:area\:between\:curves\:is\:the\:area\:between\:curve\:f(x)\:and\:curve\:g(x)\:on\:interval\:[a,b]} :\\A=\int _a^b|f\left(x\right)-g\left(x\right)|dx[/tex]
We are given the curves y = 7cos(2x), and y = 7 - 7cos(2x) on interval [0, π/2]. Therefore, applying the area formula, we have the solve the following integral:
[tex]\int _0^{\frac{\pi }{2}}\left|7\cos \left(2x\right)-\left(7-7\cos \left(2x\right)\right)\right|dx[/tex]
From now on take a look at the attachment. It shows how to solve the integral, and it's exact value. The area is not 9.727 as you entered, it is approximately 8.6. Your graph however was accurate, but there can be no work shown for that as it's much easier to use a graphing calculator.
College precalc! Please help! I've been struggling.
Answer:
B) f(x) = x if x ≤ -2
2 if x > -2
Step-by-step explanation:
B) f(x) = x if x ≤ -2 (The x and y coordinate have the same value)
2 if x > -2
Find the solution for the following: Three backpackers cooked rice for dinner. The first one gave 400g of rice and the second 200g of rice. The third one did not have any rice so he gave $6 to the other two. How should they divide the $6 in a fair way ( assume they equally shared the dinner) ?
Answer:
First backpacker should receive $4 and the second one $2
Step-by-step explanation:
notice that the total amount of rice for the three is 600 g.
Then, the first one that gave 400 g contributed 400 out of 600, that is 400/600 = 2/3
The second one contributed 200 out of 600, that is 200/600 = 1/3
then the first one should receive 2/3 of the $6 = (2/3) x 6 = $4
and the second one should receive 1/3 of the %6 = (1/3) x 6 = $2
Solve for d. d−(−12)=100
Answer:
A - 6
Step-by-step explanation:
The lines are parallel.
Theorem: If two parallel lines are cut by a transversal, then same side interior angles are supplementary.
The angles measuring 16x + 4 and 80 are supplementary, so thjeir measures add to 180.
16x + 4 + 80 = 180
16x + 84 = 180
16x = 96
x = 6
Let X be a random variable with CDF given byFX(t) =0 for t < 1,1 /2 for ?1 t < 11/ 2 t for 1 t < 21 for t 2Calculate E[X]
Answer:
[tex]\mathbf{E(X) = \dfrac{3}{4}}[/tex]
Step-by-step explanation:
From the given data, the cumulative distribution function of a random variable can be represented as:
[tex]F_X(t) =\left\{ \begin{array}{c}0........... t <-1 \\ \dfrac{1}{2} ... -1 \leq t < 1\\ \dfrac{1}{2} ....... 1 \leq t < 2 \\ 1 .............. t \geq 2\\\end{array}\right.[/tex]
The objective is to estimate E(X), to do that, let's first evaluate the probability density function by differentiating the cumulative distribution function from above.
[tex]f_X(x) =\left \{ {{\dfrac{1}{2} .......1 \leq x \leq 2 } \atop {0..... otherwise }} \right.[/tex]
∴
[tex]f_X(t) =\left\{ \begin{array}{c} \dfrac{d}{dx}(0)=0........... <-1 \\ \dfrac{d}{dx}(\dfrac{1}{2} ) =0... -1 \leq t < 1\\ \dfrac{d}{dx}(\dfrac{1}{2}x) = \dfrac{1}{2}....... 1 \leq x < 2 \\ \dfrac{d}{dx}(1) = 0 .............. x \geq 2\\\end{array}\right.[/tex]
The expected value of x i
.e E(X) can now be estimated by taking the integral:
[tex]E(X) = \int ^{\infty}_{\infty} x f(x) \ dx[/tex]
[tex]E(X) = \int ^{1}_{- \infty} x 0 dx + \int^2_1 \ x \dfrac{1}{2}\ dx + \int ^{\infty}_2 \ x0dx[/tex]
[tex]E(X) = \int ^{2}_{1} x \dfrac{1}{2} dx[/tex]
[tex]E(X) = \dfrac{1}{2}[\dfrac{x^2}{2}]^2_1[/tex]
[tex]E(X) = \dfrac{1}{2}[\dfrac{4}{2}-\dfrac{1}{2}][/tex]
[tex]E(X) = \dfrac{1}{2} \times [\dfrac{3}{2}][/tex]
[tex]\mathbf{E(X) = \dfrac{3}{4}}[/tex]
Last year a banquet hall charged $65 per person to attend a function. The function C(p) = 65p represents the total cost, C, to rent the hall based on the number of people, p, that would attend the event. If the hall can hold a total of 50 people, what is the domain and range for this function?
Answer:
Domain = [0, 50]
Range = [0, 3250]
Step-by-step explanation:
A function shows the relationship between two variables (independent variable and dependent variable). The independent variable is a variable not dependent on any variable, it is the input of the function while the dependent variable is a variable dependent on other variable, it is the output of the function.
The domain of a function is the set of all input variables (independent variable) and the range of a function is the set of all output variables (dependent variables).
In the function C(p) = 65p, p is the independent variable and C(p) is the dependent variable.
Since the hall can hold a total of 50 people, the domain of the function = [0, 50]
C(0) = 65(0) = 0, C(50) = 65(50) = 3250
Hence, the range of the function = [0, 3250]
Consider xưy" – 14xy' + 56y = 0. Find all values of r such that y=x" satisfies the differential equation for x > 0. Enter as a comma separated list: r= 7,8 help (numbers) Enter two linearly independent solutions of the form above: y1 = x7 help (formulas) y2 = 48 help (formulas) Now find a solution satisfying the initial values y(1) = 4, y'(1) = 3: y= 29x? – 25,28 help (formulas)
I bet the ODE is supposed to read
[tex]x^2y''-14xy'+56y=0[/tex]
Then if [tex]y=x^r[/tex], we have [tex]y'=rx^{r-1}[/tex] and [tex]y''=r(r-1)x^{r-2}[/tex], and substituting these into the ODE gives
[tex]r(r-1)x^r-14rx^r+56x^r=0\implies r(r-1)-14r+56=r^2-15r+56=0[/tex]
Solving for r, we find
[tex]r^2-15r+56=(r-8)(r-7)=0\implies \boxed{r=8\text{ or }r=7}[/tex]
so that [tex]y_1=x^8[/tex] and [tex]y_2=x^7[/tex] are two fundamental solutions to the ODE. Thus the general solution is
[tex]\boxed{y(x)=C_1x^8+C_2x^7}[/tex]
Given that [tex]y(1)=4[/tex] and [tex]y'(1)=3[/tex], we get
[tex]\begin{cases}4=C_1+C_2\\3=8C_1+7C_2\end{cases}\implies C_1=-25\text{ and }C_2=29[/tex]
So the particular solution is
[tex]\boxed{y(x)=29x^7-25x^8}[/tex]
Please help :) what is the area of the triangle
Answer:
30 units ^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
The base is on the left b = 10
The height is perpendicular to the base = 6
A = 1/2 * 10 * 6
= 30 units ^2
I need help please no one helps me
Answer:
the first blank is 9 and the second is 8. when you switch the numbers in the equation the answer will still be the same. hope this was helpful!
Answer:72 is 8 times as many as 9 and 9 times as many as 8
Step-by-step explanation: