[tex]\\ \sf\longmapsto \dfrac{AK}{DK}=\dfrac{CK}{BK}[/tex]
[tex]\\ \sf\longmapsto \dfrac{14}{12}=\dfrac{4x+1}{3x+3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{7}{6}=\dfrac{4x+1}{3x+3}[/tex]
[tex]\\ \sf\longmapsto 7(3x+3)=6(4x+1)[/tex]
[tex]\\ \sf\longmapsto 21x+21=24x+6[/tex]
[tex]\\ \sf\longmapsto 24x-21x=21-6[/tex]
[tex]\\ \sf\longmapsto 3x=15[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{15}{3}[/tex]
[tex]\\ \sf\longmapsto x=5[/tex]
Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save?
Step-by-step explanation:
100% = $70.99
there is a discount of 25%.
that means 75% (100 - 25) of the original price remains.
the equation to get any x% amount of a 100% total is simply
x% amount = 100% total amount × x/100
25% = 70.99 × 25/100 = $17.75
What is the vertex of the graph of y = 2(x + 5)2 - 2?
Answer:
The vertex is (-5, -2)
Step-by-step explanation:
y = 2(x + 5)^2 - 2
The vertex form of a parabola is
y =a(x-h)^2 +k where (h,k) is the vertex
y = 2(x - -5)^2 - 2
The vertex is (-5, -2)
I’m so confused. Need the help
1.621 kN
Step-by-step explanation:
Let the centerline of the canal be the x-axis. Because the forces exerted by the horses are symmetric to the centerline, only the x-components of these forces contribute to the resultant force on the barge, i.e., the y-components cancel out. Each x-component is equal to [tex]F_x = 839\cos 15[/tex] = 810.4 N. Therefore, the resultant force on the barge is twice this:
[tex]F_{net} = 2(839\:\text{N})\cos 15 = 1620.8\:\text{N}[/tex]
[tex]= 1.621\:\text{kN}[/tex]
Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?
Answer:
The team can assign field positions to 9 of the 19 players in 181,440 different ways.
Step-by-step explanation:
Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:
3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X
21 x 30 x 12 x 24 = X
630 x 12 x 24 = X
181,440 = X
Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.
Line p and q are parallel lines. The slope of line q is -3. Determine the slope of line p
Answer:
-3
Step-by-step explanation:
since the lines are parallel, they have the same slope because they never intersect
Will give brainliest answer
Answer:
Step-by-step explanation:
What are the x-intercepts of this quadratic function?
g(x) = -2(x - 4)(x + 1)
Answer:
4 and -1
Step-by-step explanation:
A quadratic function is given to us and we need to find the x Intercepts of the given function . The function is ,
[tex]\bf \implies g(x) = -2( x -4)(x+1)[/tex]
Step 1 : Equate the function with 0,
[tex]\bf \implies -2( x -4)(x+1) = 0 [/tex]
Step 2: Equating with 0 :-
Now equate each factors seperately with 0 , to get the x Intercepts.
Step 3: Finding the intercepts :-
[tex]\bf \implies x - 4 = 0 \\\\\implies\boxed{\bf\blue{ x = 4 }} [/tex]
Again ,
[tex]\bf \implies x + 1 = 0 \\\\\implies\boxed{ \blue{\bf x = -1}} [/tex]
Hence the x intercepts are 4 and -1 .
Answer:D (4,0) and (-1,0)
Step-by-step explanation:
there are 10 crates of eggs stacked in the corner. each crate of eggs holds 20 eggs. If there is only 1 broken egg in the entire stack of crates, what percent of the crates have broken eggs in them?
Answer: 5%
Step-by-step explanation: If there is one broken egg in each crate (1/20), you would change that to5%
And if there are ten crates, then you see how many eggs there a re total.
(10 × 20 = 200)
If there are 200 eggs and for every 20 eggs there is on broken one, then there will be 10 broken eggs total. or 10/200
convert the fraction to a decimal ( 10 ÷ 200 = .05)
then convert the decimal to a percent. .05 is equal to 5%
PLEAZE RATE BRAINLIEST!!!
A researcher is studying the effect of 10 different variables on a critical measure of business performance. In selecting the best set of independent variables to predict the dependent variable, the stepwise regression technique is used. How are variables selected for inclusion in the model?
A. Smallest regression coefficient.
B. Largest p-value.
C. Smallest p-value.
D. Highest increase in the multiple R2.
Answer:
D. Highest increase in the multiple R2.
Step-by-step explanation:
Included variables in a multiple regression model are those variables which have the most effect on the model ; variables which have no effect on the performance of the model ar discarded. Model performance are based on the variables affect the multiple R² value of the model. The R² value is the coefficient of determination which gives the proportion of change in predicted value based on the regression line. Higher R² value means the variable has greater effect in the model performance. Therefore, variables which have the highest increase on the multiple R² value , are included.
help with num 9 please. thanks
Answer:
See Below.
Step-by-step explanation:
We want to show that the function:
[tex]f(x) = e^x - e^{-x}[/tex]
Increases for all values of x.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
[tex]\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right][/tex]
Differentiate:
[tex]\displaystyle f'(x) = e^x - (-e^{-x})[/tex]
Simplify:
[tex]f'(x) = e^x+e^{-x}[/tex]
Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of x.
Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.
Answer:
The answer is "[tex]\frac{5\pi}{6}[/tex]"
Step-by-step explanation:
Please find the graph file.
[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]
Hi can someone reply me I am not sure how to factorise (2x+3)(4x-1)-(3+2x)(x-5)
I hope this is a real answer
Plz help me find sides M and N round to the nearest tenth
Answer:
44
Step-by-step explanation:
gradpoint
What is the length of ef in the right triangle below 25 7
Answer:
Can we see the picture?
Step-by-step explanation:
A line has a slope of -5 and
passes through the point
(0, -7). What is its equation in
slope-intercept form?
Write your answer using integers,
proper fractions, and improper
fractions in simplest form.
(752+158)-625
Compute in most convenient way
Answer:
285
Step-by-step explanation:
First, you would add 752 and 158. The sum is 910. Then, you subtract 625 and get 285.
I’ll mark u plz help
Answer:
A. 3/2
Step-by-step explanation:
I like to think of it as shift left or right by the numerator and shift up or down by the denominator. So I go over three and up two from (-3, -1) to reach (0, 1)
Answer:
3divided by 2 I think...
Consider the sequence {an}={3n+13n−3n3n+1}. Graph this sequence and use your graph to help you answer the following questions.
Part 1: You can simplify [tex]a_n[/tex] to
[tex]\dfrac{3n+1}{3n}-\dfrac{3n}{3n+1} = \dfrac1{3n}+\dfrac1{3n+1}[/tex]
Presumably, the sequence starts at n = 1. It's easy to see that the sequence is strictly decreasing, since larger values of n make either fraction smaller.
(a) So, the sequence is bounded above by its first value,
[tex]|a_n| \le a_1 = \dfrac13+\dfrac14 = \boxed{\dfrac7{12}}[/tex]
(b) And because both fractions in [tex]a_n[/tex] converge to 0, while remaining positive for any natural number n, the sequence is bounded below by 0,
[tex]|a_n| \ge \boxed{0}[/tex]
(c) Finally, [tex]a_n[/tex] is bounded above and below, so it is a bounded sequence.
Part 2: Yes, [tex]a_n[/tex] is monotonic and strictly decreasing.
Part 3:
(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.
(b) Since [tex]a_n[/tex] is decreasing and bounded below by 0, its limit as n goes to infinity is 0.
Part 4:
(a) We have
[tex]\displaystyle \lim_{n\to\infty} \frac{10n^2+1}{n^2+n} = \lim_{n\to\infty}10+\frac1{n^2}}{1+\frac1n} = 10[/tex]
and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.
(b) Taking the limit gives
[tex]\displaystyle\lim_{n\to\infty}\frac{10n^3+1}{n^2+n} = \lim_{n\to\infty}\frac{10+\frac1{n^3}}{\frac1n+\frac1{n^2}} = \infty[/tex]
so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.
For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".
(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge
(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.
(e) does : this is true and is known as the monotone convergence theorem.
(6 + 8) (3 - 2) = help plz
Answer:
Step-by-step explanation:
(6+8i)(3-2i)
use FOIL
18 - 12i + 24i - (16[tex]i^{2}[/tex])
18 + 12i - (-16)
18 + 12i + 16
34 + 12i
The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error
Answer:
(a) Hence the maximum error in the calculated area of the disk is 32.67[tex]cm^{2}[/tex].
(b) Hence the relative error is 1.54%.
Step-by-step explanation:
Here the given are,
The Radius of the circle r = 26cm.
The maximum error in measurement dr = 0.2 cm.
Answer:
(a) [tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) [tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
Step-by-step explanation:
radius, r = 26 cm
error = 0.2 cm
(a) The area of the disc is given by
[tex]A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66[/tex]
Now
A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2
So, the area with error is given by
[tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) The relative error is
[tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
A student writes
2
pages of a report in
2
an hour. What is her unit
rate in pages per hour?
Answer:
1 page of a report per hour
Step-by-step explanation:
2/2= 1 page per hour
Lets find unit rate
[tex]\\ \sf\longmapsto \dfrac{2\dfrac{1}{2}}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{2}\div 2[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]
[tex]\\ \sf\longmapsto 1.2pages/hour[/tex]
Do 8 plz find OS thanks
Answer:
OS = 10
Step-by-step explanation:
We can use a ratio to solve
QP PR
----- = ------
QO OS
14 7
----- = -------
14+6 OS
14 7
----- = -------
20 OS
Using cross products
14 * OS = 7*20
14 OS = 140
Divide by 14
OS = 140/14
OS = 10
3/4 divided by 1/2
multiple choices
2/3
1 1/4
1 1/2
3
please hurry and choose between those
Answer:
Step-by-step explanation:
#16 What is the value of x?
Answer:
x = 25 , x = 136
Step-by-step explanation:
(15)
The opposite angles of a cyclic quadrilateral are supplementary , sum to 180°
3x + 105 = 180 ( subtract 105 from both sides )
3x = 75 ( divide both sides by 3 )
x = 25
(16)
The chord- chord angle is half the sum of the arcs intercepted by the angle and its vertical angle, then
x = [tex]\frac{1}{2}[/tex] (VW + UX) = [tex]\frac{1}{2}[/tex](115 + 157) = [tex]\frac{1}{2}[/tex] × 272 = 136
In the figure, L1 || L2. 2x=174º. Find Za+Zb.
9514 1404 393
Answer:
12°
Step-by-step explanation:
We assume you mean ...
∠x = 174°
Angle a is supplementary to angle x, so is ...
∠a = 180° -174° = 6°
Angle b is a vertical angle with respect to angle 'a', so is the same measure.
∠a +∠b = 6° +6° = 12°
please answer all the questions and get 15 pts
Answer:
Here you go
Ans is in pictures.
A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
!!!!!!!!PLEASE HELP NOW !!!!!!!!!!!!!!!!!!
What is the following product?
45 47 47.45
4(977)
O AN
74
7
Answer:
7
Step-by-step explanation:
You can convert the fourth square roots to [tex]7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}} * 7^{\frac{1}{4}}}[/tex]. Using the product of powers rule, we can add the four terms' exponents, resulting in [tex]7^1[/tex], which is 7.
2) Consider the quadratic sequence 72, 100, 120, 132
2.1.1) Determine Tn the nth term of the quadratic.
Answer:
Tn = -4n²+40n+36
Step-by-step explanation:
A general quadratic sequence, Tn = an²+bn+c, where n is the term of the sequence.
So, when n = 1, Tn = 72, which means T1 = a+b+c=72.
when n = 2, Tn = 100, which means T2= 4a+2b+c = 100
when n = 3, Tn = 132, which means T3 = 9a+3b+c = 132.
Now, use a calcaulatot to solve the 3 variable simultaneous equation. According to my calculator, a = -4, b = 40, c = 36.
Hence, you a, b, and c in the Tn equation given above.
Therefore, Tn = -4n²+40n+36
The jury pool for the upcoming murder trial of a celebrity actor contains the names of 100,000 individuals in the population who may be called for jury duty. The proportion of the available jurors on the population list who are Hispanic is .40. A jury of size 12 is selected at random from the population list of available jurors. Let X = the number of Hispanics selected to be jurors for this jury.
a. What is the expected number of hispanic jurors being on the jury?
b. What is the expected value (or theoretical mean) of a great earthquake off the coast of Oregon in two years?
c. Use the poisson distribution to appropriate the probability that there will be at least one major earthquake in the next two years.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Have a Spanish Jury possibility[tex]= 0.40[/tex]
Jury member No. to be chosen[tex]= n= 12[/tex]
Hispanic Juror Expected [tex]= np = 12\times 0.40 = 4.8[/tex]
The jury group will be constituted by Hispanic Jurors [tex]4.8[/tex]
OR
The binomial distribution defines the behavior of a count variable X, provided:
There are a set number of data points n.
Set [tex]n=12[/tex]
Each perception is independent. This will not affect others if your first juror is selected
One of two results is that each observation ("success" or "failure"). English or not
Each result has the same chance of "success" p. for every [tex]p=0.40[/tex]
Well by the binomial distribution. Mean[tex]=E(x)=np=4.8[/tex]