Answer:
[tex]\large\boxed{-15x^{2} + 31x - 14}[/tex]
Step-by-step explanation:
(5x - 7)(-3x + 2)
The values inside of the parenthesis cannot be simplified, so distribute and multiply.
Distribute
(5x - 7)(-3x) + (5x - 7)(2)
Multiply
-15x² + 21x + 10x - 14
Add 21x to 10x
-15x² + 31x - 14
[tex]\large\boxed{-15x^{2} + 31x - 14}[/tex]
Hope this helps :)
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
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.
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
It costs $204.00 to buy beef to make 180 burgers. What will the cost be to make 80 burgers?
Answer:
It would cost $90.66
Step-by-step explanation:
because 180 dived by 204 equals 1.13 then times that by 80 and there's your answer
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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How many bricks each 0.16m2 are required for paving a courtyard of 5.5m long and 4.8m wide?
Each plastic bottle holds 5.1 ounces of water. How much water can 6 plastic bottles hold? ounces
Answer:
30.6 ounces of water
Step-by-step explanation:
Since on bottle holds 5.1 ounces, in order to find the amount of water in 6, you must take 5.1 and multiply it by 6 which gives you your final answer of 30.6 ounces. Hope this helps!
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
Dependent and independent variables The following research studies consist of two or more groups of scores being compared. For each, decide whether the study is experimental or nonexperimental, and then identify the dependent, independent, or quasi-independent variables. Fourth-grade classrooms in several elementary schools are randomly assigned to different antibullying training programs at the beginning of the school year. The school district keeps track of the number of incidents of bullying in each classroom This study is an example of study The type of training program is the variable. The number of incidents of bullying is the variable. Researchers at a school of public health conducted a study to test the effect of organic produce on cancer mortality The 400 patients with prostate cancer who volunteered for the study were randomly assigned to a diet of either organic or length of time each patient survived I produce. The progression of their cancer was monitored, and researchers documented the This study is an example of:_______ study The survival time is the _______ variable. The type of diet is the _______ variable.
Answer:
- This study is an example of Experimental study
- The survival time is the dependent variable.
- The type of diet is the independent variable.
Step-by-step explanation:
I) This research study is an experimental study because it makes use of a scientific approach using 2 variables which in this case are organic diet and survival time.
II) Survival time is the dependent variable because it depends on the response of the patients to the organic diet.
III) Type of diet is the independent variable because it doesn't depend on any other factor or variable.
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]
(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.
What is the image point of
(9,−2) after a translation left 2 units and down 1 unit? I need help
Answer:
Hey there!
Left 2 units: (7,-2)
Down 1 unit: (7, -3)
Final answer: (7, -3)
Let me know if this helps :)
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
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]
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
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
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]
The graph of a function contains the points (3,5) , (4,6), (7,8) and (x,y) . Witch of the following could be (x,y)? (4,9) (7,9) (3,9) (2,9)
Answer:
(2,9)
Step-by-step explanation:
The only point that could be included is (2, 9), since any of the other three would preclude the relationship between x and y values from being a function. Notice that 3, 4, and 7 are already connected/associated with other values in the Range of the function.
Which is the standard form of the equation 8n + 4 = -2n + 9 ? *
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
Which one best models line l?
ans : A
reason : gradient = 0 and the line does not touch Y axis
i hope this helps :))
The equation of line l if the line is shifted 4 units to the right is x = 4, so option A is correct.
What is line?A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction. While Euclid's initial definition is now regarded as a line segment, such an extension in both directions is now thought of as a line.
Given:
The lines y and l are given in the graph,
The equation of the line y can be written as shown below,
y = x + c
x = c (as the y coordinate of the y-axis is zero)
The equation of the line shifted 4 units to the right can be represented as
y = mx + c
Here, the slope is 1 and the intercept is -4 so,
x = 4
Thus, the line l is x = 4.
To know more about the line:
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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)
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.
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:
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:
Three dozen cookies require 4 cup of flour. How many dozens of cookies can be made with 16 cups of flour
Answer:
4 dozen
Step-by-step explanation:
4 cups flour = 12 cookies [1 dozen=12]
1 cup of flour= 12/4 cookies
=3 cookies
now,
16 cups of flour= 3*16 cookies
=48 cookies
= 4 dozens [48/12=4 dozen]
therefore, 4 dozen cookies can be made with 16 cups of flour
Answer: 144
Step-by-step explanation:
It is 4:15 now.What time was it six hours ago?
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 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
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]