Answer:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Step-by-step explanation:
To find:
Simplified product of:
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]
Solution:
First of all, let us have a look at some of the formula:
1. [tex](a+b) (c+d) = ac+bc+ad+bd[/tex]
2. [tex]a^b\times a^c =a^{b+c }[/tex]
3. [tex]\sqrt{a^{2b}} = \sqrt{a^b.a^b}=a^b[/tex]
4. [tex]\sqrt a \times \sqrt b = \sqrt{a\times b}[/tex]
Now, let us apply the above formula to solve the given expression.
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\\Rightarrow(\sqrt{10x^4})(2\sqrt{15x^4})+(\sqrt{10x^4})(\sqrt{3x^3})-(x\sqrt{5x^2})(2\sqrt{15x^4})-(x\sqrt{5x^2})(\sqrt{3x^3})\\\\\Rightarrow2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\\Rightarrow\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
The answer is:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Answer:
Its D
Step-by-step explanation:
The expression $16x^2-106x-105$ can be written as $(8x + a)(2x + b),$ where $a$ and $b$ are integers. What is $a + 2b$?
Answer:
-23
Step-by-step explanation:
16x² - 106x - 105
factoring X
14 x -120 = -1680
14 - 120 = -106
16x² + 14x - 120x - 105
(16x² + 14x) -(120x - 105)
factor out 2 and -15 to get the same expression (8x + 7)
2x(8x + 7) - 15(8x + 7)
(8x + 7)(2x - 15)
a = 7
b = -15
a + 2b
7 + (-15 x 2)
7 + (-30)
= -23
A line passes through A(3,7) and B(-4,9). Find the value of a if C(a, 1) is on the line.
Answer: a=24
Step-by-step explanation:
Lets find the line's formula (equation of the line).
As known the general formula of any straight line (linear function) is
y=kx+b
Lets find the coefficient k= (Yb-Ya)/(Xb-Xa)=(9-7)/(-4-3)=-2/7
(Xb;Yb)- are the coordinates of point B
(Xa;Ya) are the coordinates of point A
Now lets find the coefficient b. For this purpose we gonna use the coordinates of any point A or B.
We will use A
7=-2/7*3+b
7=-6/7+b
b=7 6/7
So the line' s equation is y= -2/7*x+7 6/7
Now we gonna find the value of a usingcoordinates of point C.
Yc=1, Xc=a
1=-2/7*a+7 6/7
2/7*a= 7 6/7-1
2/7*a=6 6/7
(2/7)*a=48/7
a=48/7: (2/7)
a=24
Answer:
a=24
Step-by-step explanation:
PLEASE HELP!!! (1/5) - 50 POINTS-
Answer:
consistent independent
Step-by-step explanation:
This is a graph of consistent independent equations
The lines cross and there is one solution
Inconsistent equations never cross and there is no solutions
Consistent dependent equations are equations of the same line
Answer:
Linear
Step-by-step explanation:
This is a graph of linear system of equation.
The two lines represent different equations connected with each other.
They intersect at a common point showing the solution to the system of equation.
The mean area of 7 halls is 55m².If the mean of 6 of them be 58m², find the area of the seventh all.
Answer:
Area of 7th hall = 37 m^2
Step-by-step explanation:
Total area of 7 halls = 7*55 = 385
Total area of 6 halls = 6*58 = 348
Area of 7th hall = 385-348 = 37 m^2
Answer:
The area of the seventh hall = 37m²
Step-by-step explanation:
for 6 halls
Mean area of 6 halls = 58m²
[tex]Mean\ area = \frac{sum\ of\ areas}{Number\ of\ halls} \\58\ =\ \frac{sum\ of\ areas}{6} \\sum\ of\ areas\ of\ 6\ halls\ = 58\ \times\ 6 = 348\\sum\ of\ areas\ of\ 6\ halls\ = 348[/tex]
Let the area of the 7th hall be x
The sum of the areas of 7 halls = 348 + x - - - - - - (1)
[tex]Mean = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\55 = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\sum\ of\ the\ areas\ of\ 7\ halls\ = 55\ \times\ 7\ = 385\\sum\ of\ the\ areas\ of\ 7\ halls\ =\ 385 - - - - (2)[/tex]
notice that equation (1) = equation (2)
348 + x = 385
x = 385 - 348 = 37m²
Therefore, the area of the seventh hall = 37m²
Brandon is paid 150% of his regular hourly rate for overtime hours. He is paid \$45.00 an hour for overtime hoursWhat is his regular hourly rate?
Answer:
Regular hourly rate for Brandon is $30
Step-by-step explanation:
Let the payment for regular hours be $x
given that
Brandon is paid 150% of his regular hourly rate for overtime hours
payment for overtime hours = 150% of payment for regular hours
payment for overtime hours = 150/100 * x = 3x/2
Given that He is paid \$45.00 an hour for overtime hours
thus,
3x/2 = 45
=> x = 45*2/3 = 30
Thus, regular hourly rate for Brandon is $30
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown
Answer:
The minimum sample size is [tex]n = 2123[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.028[/tex]
Given that the confidence level is 99% then the level of significance is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1 \%[/tex]
[tex]\alpha =0.01[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]
Now let assume that the sample proportion is [tex]\r p = 0.5[/tex]
hence [tex]\r q = 1 - \r p[/tex]
=> [tex]\r q = 0.50[/tex]
Generally the sample size is mathematically represented as
[tex]n =[ \frac{Z_{\frac{ \alpha }{2} }}{ E} ]^2 * \r p * \r q[/tex]
[tex]n =[ \frac{2.58}{ 0.028} ]^2 * 0.5 * 0.5[/tex]
[tex]n = 2123[/tex]
In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?
Answer:
There are 80 10th graders in the school
Step-by-step explanation:
Let the number of 10th graders be x
There are 25% fewer 11th graders
That mean x - 25% of x
x -0.25x = 0.75x
There are 20% more 11th graders than 12th graders
So if number of 12th graders = y, then
0.75x = y + 20/100 * y = y + 0.2y = 1.2y
Since ;
0.75x = 1.2y
then y = 0.75x/1.2 = 0.625x
So let’s add all to give 190
x + 0.75x + 0.625x = 190
2.375x = 190
x = 190/2.375
x = 80
A washer and dryer cost a total of $980. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answer:
Washer $735
Dryer $245
Step-by-step explanation:
If x is the cost of the washer, and y is the cost of the dryer, then:
x + y = 980
x = 3y
Solve with substitution.
3y + y = 980
4y = 980
y = 245
x = 735
What expression is equal to6 e + 3 (e-1)
Answer:
9e -3
Step-by-step explanation:
Perform the indicated multiplication:
6 e + 3 (e-1) = 6e + 3e - 3
This, in turn, simplifies to
9e -3, or 3(3e - 1).
Answer:
ANSWER: 9e-3
Step-by-step explanation:
6e+3(e−1)
As we need to simplify the above expression:
First we open the brackets :
3(e-1)=3e-33(e−1)=3e−3
Now, add it to 6e.
So, it becomes,
$$\begin{lgathered}6e+3e-3\\\\=9e-3\end{lgathered}$$
Hence, equivalent expression would be 9e-3.
Find the domain of the Bessel function of order 0 defined by [infinity]J0(x) = Σ (−1)^nx^2n/ 2^2n(n!)^2 n = 0
Answer:
Following are the given series for all x:
Step-by-step explanation:
Given equation:
[tex]\bold{J_0(x)=\sum_{n=0}^{\infty}\frac{((-1)^{n}(x^{2n}))}{(2^{2n})(n!)^2}}\\[/tex]
Let the value a so, the value of [tex]a_n[/tex] and the value of [tex]a_(n+1)[/tex]is:
[tex]\to a_n=\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}[/tex]
[tex]\to a_{(n+1)}=\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}[/tex]
To calculates its series we divide the above value:
[tex]\left | \frac{a_(n+1)}{a_n}\right |= \frac{\frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2}}{\frac{(-1)^2n x^{2n}}{2^{2n}(n!)^2}}\\\\[/tex]
[tex]= \left | \frac{(-1)^{n+1} x^{2(n+1)}}{2^{2(n+1)}((n+1))!^2} \cdot \frac {2^{2n}(n!)^2}{(-1)^2n x^{2n}} \right |[/tex]
[tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)!^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |[/tex]
[tex]= \left | \frac{ x^{2n+2}}{2^{2n+2}(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\= \left | \frac{x^{2n}\cdot x^2}{2^{2n} \cdot 2^2(n+1)^2 (n!)^2} \cdot \frac {2^{2n}(n!)^2}{x^{2n}} \right |\\\\[/tex]
[tex]= \frac{x^2}{2^2(n+1)^2}\longrightarrow 0 <1[/tex] for all x
The final value of the converges series for all x.
sorry to keep asking questions
Answer:
y = [tex]\sqrt[3]{x-5}[/tex]
Step-by-step explanation:
To find the inverse of any function you basically switch x and y.
function = y = x^3 + 5
Now we switch x and y
x = y^3 +5
Solve for y,
x - 5 = y^3
switch sides,
y^3 = x-5
y = [tex]\sqrt[3]{x-5}[/tex]
Answer:
[tex]\Large \boxed{{f^{-1}(x)=\sqrt[3]{x-5}}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=x^3 +5[/tex]
The inverse of a function reverses the original function.
Replace f(x) with y.
[tex]y=x^3 +5[/tex]
Switch variables.
[tex]x=y^3 +5[/tex]
Solve for y to find the inverse.
Subtract 5 from both sides.
[tex]x-5=y^3[/tex]
Take the cube root of both sides.
[tex]\sqrt[3]{x-5} =y[/tex]
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 250,823. Its current population is 325,823. By about what percentage has the city grown over the past ten years? Round to the nearest percent.
Answer:
I just answered it
Step-by-step explanation:
Circle O has a circumference of 36π cm. Circle O with radius r is shown. What is the length of the radius, r? 6 cm 18 cm 36 cm 72 cm
Answer:
18 cm.
Step-by-step explanation:
The circumference of a circle is found by calculating 2 * pi * r.
In this case, the circumference is 36 pi cm.
2 * pi * r = 36 * pi
2 * r = 36
r = 36 / 2
r = 18 cm.
Hope this helps!
Answer:
18 centimeters
Step-by-step explanation:
The circumference of a circle can be found using the following formula.
[tex]c=2\pi r[/tex]
We know the circumference is 36π cm, therefore we can substitute 36π in for c.
[tex]36\pi= 2 \pi r[/tex]
We want to find r, the radius. Therefore, we must get r by itself. First, divide both sides of the equation by pi.
[tex]36\pi / \pi = 2 \pi r / \pi\\\\36= 2 \pi r / \pi\\\\36=2r[/tex]
Next, divide both sides of the equation by 2.
[tex]36=2r \\\\36/2=2r/2\\\\36/2=r\\\\18=r\\\\r=18 cm[/tex]
The radius of Circle O is 18 centimeters.
Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/2 and λˆ 2 = Y . Derive the efficiency of λˆ 1 relative to λˆ 2.
Answer:
The answer is "[tex]\bold{\frac{2}{n}}[/tex]".
Step-by-step explanation:
considering [tex]Y_1, Y_2,........, Y_n[/tex] signify a random Poisson distribution of the sample size of n which means is λ.
[tex]E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda[/tex]
Let assume that,
[tex]\hat \lambda_i = \frac{Y_1+Y_2}{2}[/tex]
multiply the above value by Var on both sides:
[tex]Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )[/tex]
[tex]=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\[/tex]
now consider [tex]\hat \lambda_2[/tex] = [tex]\bar Y[/tex]
[tex]Var (\hat \lambda_2 )= Var(\bar Y )[/tex]
[tex]=Var \{ \frac{\sum Y_i}{n}\}[/tex]
[tex]=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\[/tex]
For calculating the efficiency divides the [tex]\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2[/tex] value:
Formula:
[tex]\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}[/tex]
[tex]=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}[/tex]
Use the equation p=6k+12 to find the value of p when k=9.
Answer:
66
Step-by-step explanation:
when you plug in 9 for k. you do 6(9) which is 54. then add 12 to 54 and thats ur answer, 66.
area to the right of z=0.72
I don’t have a graphing calculator and I couldn’t find one online. I’m completely clueless on this one.
Answer:
Desmos could come in handy
Pablo rented a truck for one day. There was a base fee of $19.99, and there was an additional charge of 80 cents for each mile driven. Pablo had to pay
$221.59 when he returned the truck. For how many miles did he drive the truck?
Answer:
252 miles
Step-by-step explanation:
19.99 + .80x = 221.59
,80x = 201.60
x = 252
Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent
The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]
where T is the set
[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]
(a) I've attached an image of the integration region.
[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]
(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.
Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]
[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]
Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.
4.9x10^_8 In decimal notation
Answer:
490000000
Step-by-step explanation:
For every exponent of 10, move the decimal point one place to the right.
please help me to answer this question
Answer:
I can not see any questions
Nina skated for 2 hours and 14 min she stop at 8:24 pm when did Nina start skating
Answer:
6:10 pm
Step-by-step explanation:
she skate for 2 h and 14 min so,
8:24- 2:14
=6:10 pm
What would the 60 is x% of 12. Find the value of x.
Answer:
The value of x= 20
Step-by-step explanation:
I believe the question is ,"60% of x is us, find x"
So , if the percentage of x to 60 is 12.
60/100 * x = 12
0.6 *x = 12
Dividing both sides by 0.6
X= 12/0.6
X= (12/6) *(10)
X= 2*10
.x= 20
The value of x= 20
What is 1/3 of 675 is left
I really need help please answer!
Answer:
-2, b, a+c
Step-by-step explanation:
Answer:
-2, b, a+c
Step-by-step explanation:
By looking at where A and C are on the number line, we can tell that A is a negative number close to zero and C is a positive number a little greater than four. This means that if we add the two together, we'll get a positive number a little below four.
By looking at the number line, we can tell that the value of B is a positive number a little below the number three.
Now that we know that B is less than A+C, and we know where -2 is on the number line (two marks to the left of zero) we can decide the least to greatest values.
Since negatives are always less than positives, we know that -2 has the smallest value. Next, we know that B is lower on the number line than A+C. So, in order, from least to greatest, the answer is:
-2, B, A+B
Hope this helps!! <3 :))
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.8% of the people who have that disease. However, it erroneously gives a positive reaction in 3.3% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions.
a. What is the probability of Type I error?
b. What is the probability of Type II error?
Answer:
Probability of Type 1 error = 0.033
Probability of type II error = 0.952
Step-by-step explanation:
H0: Individual does not have disease
H1: individual has disease
Type 1 error occurs when we fail to accept a correct null hypothesis and accept an alternate Instead
Type ii error occurs when we accept a false null hypothesis instead of the alternate hypothesis
Probability of people with disease = 98.4%
Probability of people without disease = 3.3%
1.probability of type 1 error = 3.3/100
= 0.033
2. Probability of type ii error = (1-98.4%) = 1-0.948
= 0.052
the ration of men to women in a certain factory is 3 to 4. there are 204 men. how many workers are there?
Answer:
476 workers
Step-by-step explanation:
Men: women : total
3 4 3+4 = 7
We want 204 men
204/3 =68
Multiply each by 68
Men: women : total
3*68 4*68 7*68
204 272 476
Answer:
There are 476 workers
Step-by-step explanation:
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.
V6 18
311
123 45
6
7
8
+
x
Question: Perform the following computation with radicals. Simplify the answer. √6 • √8
Answer:
[tex] 4\sqrt{3} [/tex]
Step-by-step explanation:
Given, √6 • √8, to perform the computation, we would simply evaluate the radicals and try as much as possible to leave the answer in the simplest form in radicals.
Thus,
[tex] \sqrt{6}*\sqrt{8} = \sqrt{6*8} [/tex]
[tex] = \sqrt{48} [/tex]
[tex] = \sqrt{16*3} = \sqrt{16}*\sqrt{3}[/tex]
[tex] = 4\sqrt{3} [/tex]
Graph the following set of parametric equations on your calculator and select the matching graph.
Answer:
Graph 2
Step-by-step explanation:
As you can see the first equation is present with a negative slope, and none of the graphs have a line plotted with a negative slope, besides the second graph. That is your solution.
i will rate you brainliest
Answer:
Option (3)
Step-by-step explanation:
For a geometric progression,
[tex]a,ar,ar^{2},ar^3.........a(r)^{n-1},a(r)^n[/tex]
First term of the progression = a
Common ratio of each successive term to the previous term = r
Recursive formula for geometric progression will be,
[tex]a_1=a[/tex]
And [tex]a_{n}=a_{n-1}(r)[/tex]
Following this rule for the G.P. given in the question,
[tex]a_1=4[/tex]
[tex]a_n=-1.5a_{n-1}[/tex]
Therefore, from the recursive formula,
Common ration 'r' = -(1.5)
Option (3) will be the correct option.
Determina el valor absoluto de 13 – 11|
Responder:
2
Explicación paso a paso:
El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).
Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.
Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;
= | 13-11 |
= | 2 |
Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.
Por tanto, el valor absoluto de la expresión es 2
