How many three-digit positive integers have three different digits and at least one prime digit?

Answer:

Step-by-step explanation:

[tex]\frac{1}{2} x=a=\frac{2}{3} y\\\frac{1}{2}x=a\\x=2a \\\frac{2}{3} y=a\\y=\frac{3}{2} a\\x+y=2a+\frac{3}{2} a=\frac{4a+3a}{2} =\frac{7}{2} a=na\\n=\frac{7}{2}[/tex]

The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Given the equation:

1 / (x - 1) + 2/x = x / (x - 1)

Multiplying through the equation by x(x - 1):

x + 2(x - 1) = x(x)

x² - 3x + 2 = 0

x² - 2x - x + 2 = 0

(x - 2)(x - 1) = 0

x = 2; and x = 1

The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

10 + 4i

Step-by-step explanation:

2 sqrt (25) + sqrt (-16) =

2 * 5     + 4i

10 + 4i

Answer:

[tex]10 + 4i[/tex]

Step-by-step explanation:

Original Equation:

[tex]2\sqrt{25} + \sqrt{-16}[/tex]

Simplify sqrt(25)

[tex]2*5+\sqrt{-16}[/tex]

Simplify multiplication

[tex]10+\sqrt{-16}[/tex]

Split the radical -16 into two, using the identity: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex]

[tex]10 + \sqrt{-1}*\sqrt{16}[/tex]

Simplify the sqrt(16) and sqrt(-1) using definition of an imaginary number

[tex]10 + 4i[/tex]

the area of the minor segment is 0. 29 cm^2

From the information given, we have the following parameters;

It is important to note the formula for area of a sector is given as;

Area = πr² + θ/360° - 1/ 2 r² sin θ

The value for π = 3.142

θ = 30°

Now, let's substitute the values

Area = 3. 142 × 5² × 30/ 360 - 1/ 2 × 5² × sin 30

Find the difference

Area = 3. 142 × 25 × 1/ 12 - 1/ 2 × 25 × 1/2

Multiply through

Area = 6. 54 - 6. 25

Area = 0. 29 cm^2

The area of the minor segment is given as 0. 29 cm^2

Thus, the area of the minor segment is 0. 29 cm^2

Learn more about circles here:

https://brainly.com/question/15673093

#SPJ1

Answer:  11

Step-by-step explanation:

XY + YZ = XZ

  XY + 3 = 14

         XY = 11

The function of the S&P Capital IQ Excel plug-in allows users to extract company data directly from CapIQ’s database and calculate the desired financial metrics using the CapIQ formulas is; Formula Builder

S&P Capital IQ Excel plug is a tool that helps to provide access to financial data, news and analytics for real estate investment trusts (REITs) including other industry data on bank & thrifts, financial services, insurance, real estate and other markets.

Now, when the Excel Plug-in has been installed, a new toolbar will be

available in Excel. This toolbar is called formula builder and it is useful for the following use in  S&P Capital;

Read more about Financial Tool at; https://brainly.com/question/14364696

#SPJ1

Step-by-step explanation:

since the sumation of f(x) of a probability is 1

thw probability to win is o.5 and to lose is o.5 so expected value is xf(x

your expected value will b 0.5 multiply by 5 thats is 2.5 thats your expected gain

The solution to the equation as given in the task content is; x = -3.47.

It follows from the task content that the equation given is; (43/7÷ x+32/9) ÷25/6=4/3

(43/7÷ x+32/9) = 25/6 × 4/3

(43/7÷ x+32/9) = 100/18

x +32/9 = 43/7 ÷ 100/18

x + 32/9 = 774/700

x = 774/700 - 32/9

x = -3.47.

Read more on equation solution;

https://brainly.com/question/25678139

#SPJ1

Answer:

4:24 or also 1:6

Step-by-step explanation:

From the information given, F(x) = 9.3319419 or approximately 9. This is  problem relating to math functions

Recall that we are given x to be = 16.1

Hence,

[tex]f\left(x\right)=\ 2x^{\frac{1}{4}}\ +\ 3x^{\frac{1}{2}}[/tex] =

2 (16.1) ⁰°²⁵ + 3 (16.1)⁰°⁵

= 32.2⁰°²⁵ + 48.3⁰°⁵

= 2.3821218 +6.9498201

f(x) = 9.3319419

f(x) approximately 9

Learn more about functions:
https://brainly.com/question/17043948
#SPJ1

Using a line of best fit, the predicted tsunami speed for the following depths is given by:

a. 1151 km/h.

b. 572 km/h.

c. 130 km/h.

d. 122 km/h.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (depth, velocity) are given by:

(7000, 943), (4000, 713), (2000, 504), (200, 159), (50, 79), (10,36)

Inserting these points in the calculator, the velocity in function of the depth is:

v(d) = 0.12879d + 121.03448

Hence, the velocities are given as follows:

a. v(8000) = 0.12879 x 8000 + 121.03448 = 1151 km/h.

b. v(3500) = 0.12879 x 3500 + 121.03448 = 572 km/h.

c. v(70) = 0.12879 x 70 + 121.03448 = 130 km/h.

d. v(5) = 0.12879 x 5 + 121.03448 = 122 km/h.

More can be learned about a line of best fit at https://brainly.com/question/13203683

#SPJ1

The factors of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex]  are x=1, -2, 4/3, -2/5.

Given equation is [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex],

By performing L-division method, we get

[tex]y = (x-1)(15x^{3} +16x^{2} -36x-16)[/tex]

Then again doing the same L-division method to the cubic equation [tex]15x^{3} +16x^{2} -36x-16[/tex], we get

[tex]15x^{3} +16x^{2} -36x-16 = (x+2)(15x^{2} -14x-8)[/tex]

Therefore, [tex]y = (x-1)(x+2)(15x^{2}-14x-8)[/tex]

Then finally the roots of the quadratic equation [tex]15x^{2}-14x-8[/tex] are (x-(4/3)) and (x+(2/5))

Hence, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x = (x-1)(x+2)(x-\frac{4}{3} )(x+\frac{2}{5} )[/tex]

Therefore, the roots of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.

Learn more about factors of equation on

https://brainly.com/question/19814847

#SPJ1

Answer:

$580

Step-by-step explanation:

{371x(100-34)/100}+371=580

The original price (rounded to the nearest dollar) is $497.

In this problem, we need to identify what's the original price of the new mattress.

Since we know that the sale price is $371 and is 34% lesser than the original price, we need to add 371 and 34%.

Grab a calculator and add 371 and 34%

we get:

371 + 34% = 497.14

Now round it to the nearest whole number, we get: 497

This is how the answer gets 497.

Hope this helps :)

Answer:

A and D

Step-by-step explanation:

Let's find the slope of the functions in all tables.

A. -1/2

B. -1/2

C. -1/2

D. 1

E. -1/2

Option D. is out since it has a different slope.

The answer has to be two tables out of A, B, C, and E.

Start with Table A.

As x goes from 8 to 6, y goes up by 1.

We can create points for x = 0 and x = 2

x = 2, y = 9

x = 8, y = 6

This is exactly table D.

Answer: Tables A and D

Answer:

c)  3 units

d)  g(x) - f(x) = x² + 2x

e)  (-∞, -2] ∪ [0, ∞)

Step-by-step explanation:

To calculate the length of FC, first find the coordinates of point C.

The y-value of point C is zero since this is where the function f(x) intercepts the x-axis.  Therefore, set f(x) to zero and solve for x:

[tex]\implies 1-x^2=0[/tex]

[tex]\implies x^2=1[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]

[tex]\implies x= \pm 1[/tex]

As point C has a positive x-value,  C = (1, 0).

To find point F, substitute the x-value of point C into g(x):

[tex]\implies g(1)=2(1)+1=3[/tex]

⇒ F = (1, 3).

Length FC is the difference in the y-value of points C and F:

[tex]\begin{aligned} \implies \sf FC& = \sf y_F-y_C\\ & = \sf 3-0\\ & =\sf 3\:units \end{aligned}[/tex]

Given functions:

[tex]\begin{cases}f(x)=1-x^2\\ g(x)=2x+1 \end{cases}[/tex]

Therefore:

[tex]\begin{aligned}\implies g(x)-f(x) & = (2x+1) - (1-x^2)\\& = 2x+1-1+x^2\\& = x^2+2x\end{aligned}[/tex]

The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):

Point A is the y-intercept of both functions, therefore the x-value of point A is 0.

To find the x-value of point E, equate the two functions and solve for x:

[tex]\begin{aligned}g(x) & = f(x)\\\implies 2x+1 & = 1-x^2\\x^2+2x & = 0\\x(x+2) & = 0\\\implies x & = 0, -2\end{aligned}[/tex]

As the x-value of point E is negative ⇒ x = -2.

Therefore, the values of x for which g(x) ≥ f(x) are:

Answer:

a)

A = (0, 1)

B = (-1, 0)

C = (1, 0)

D = (-0.5, 0)

b) E = (-2, -3)

c) FC = 3 units

d) x² + 2x

e) x ≤ -2 and x ≥ 0

Explanation:

This question displays one equation of a linear function g(x) = 2x + 1 and a parabolic function f(x) = 1 - x².

a)

A point is where the linear function cuts the y axis.

y = 1 - (0)²

y = 1

A = (0, 1)

B and C point is where the parabolic function cuts the x axis.

1 - x² = 0

-x² = -1

x² = 1

x = ±√1

x = -1, 1

B = (-1, 0), C = (1, 0)

D point is where the linear function cuts x axis.

2x + 1 = 0

2x = -1

x = -1/2 or -0.5

D = (-0.5, 0)

b)

E point is where both equations intersect each other.

y = y

2x + 1 = 1 - x²

x² + 2x = 0

x(x + 2) = 0

x = 0, x = -2

y = 1, y = -3

E = (-2, -3)

c)

C : (1, 0)

To find F point

y = 2(1) + 1

y = 3

F : (1, 3)

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]\sf d = \sqrt{(1 - 1)^2 + (3 - 0)^2}[/tex]

[tex]\sf d = \sqrt{0 + 3^2}[/tex]

[tex]\sf d = 3[/tex]

FC length = 3 units

d)

g(x) - f(x)

(2x + 1) - (1 - x²)

2x + 1 - 1 + x²

x² + 2x

e)

g(x) ≥ f(x)

2x + 1 ≥ 1 - x²

x² + 2x ≥ 0

x(x + 2) ≥ 0

[tex]\boxed{If \ x \ \geq \ \pm \ a \ then \ -a \ \leq x \ \ and \ x \ \geq \ a }[/tex]

x ≤ -2 and x ≥ 0

Answer:

Step-by-step explanation:

Equivalent polar coordinates will have the same modulus and some multiple of 360° added to the argument, or the opposite modulus and some odd multiple of 180° added to the argument.

  a∠b° = a∠(b+360n)° = -a∠(b +180 +360n)°

Equivalents will be ...

  (2, (-60 +360n)°) = (2, 300°)

  (-2, (-60 +180 +360n)°) = (-2, -240°) = (-2, 120°)

Equivalents will be ...

  (-2, (240 +360n)°) = (-2, -120°)

  (2, (240 +180 +360n)°) = (2, -300°) = (2, 60°)

Answer:

The area of windowpane is answer.

Answer:

The area of the window pane

Step-by-step explanation:

The area of an object is the width x length of said object.

Ex: A  4 x 4 sized square has an area of 16 ( 4 x 4 = 4 by 4)

P.S. The area of Andrea´s windowpane is 648.

From the 2 selected employees, the probability that they will both be females is; C: 4/15

We are given;

Number of male employees = 7

Number of female employees = 8

Total number of employees = 8 + 7 = 15

Now, 2 random employees are chosen and so the number of ways of selecting this is; 15C2

Now, out of the 2 selected employees, the probability that they will be female = 8C2/15C2 = 28/105 = 4/15

Thus, we can conclude that from the 2 selected employees, the probability that they will both be females is; C: 4/15

Read more about Probability at; https://brainly.com/question/25688842

#SPJ1

a. Central angle: Angle BAC

b. A major arc is: Arc BEC

c. A minor arc is: Arc BC

d. Measure of arc BEC in circle A = 260°

e. Measure of arc BC = 100°

According to the central angle theorem the measure of central angle (i.e. angle BAC in circle A) is the same as the measure of the intercepted arc (i.e. arc BC in circle A).

Referring to the image given, a central angle (i.e. angle BAC) is formed by two radii of a circle (i.e. AB and AC in circle A), where the vertex of the angle (i.e. vertex A in circle A) is at the center of the circle.

An arc that is bigger than a semicircle (half a circle) or with a measure greater than 180 degrees is called a major arc of a circle.  

An arc that is smaller than a semicircle (half a circle) or with a measure less than 180 degrees is called a minor arc of a circle.  

a. Central angle in circle A is: ∠BAC

b. Major arc in circle A is: Arc BEC

c. Minor arc in circle A is: Arc BC.

d. Based on the central angle theorem, we have:

Measure of arc BEC in circle A = 360 - 100

Measure of arc BEC in circle A = 260°

e. m∠BAC = 100° [given]

Based on the central angle theorem, we have:

m(arc BC) = m∠BAC

Measure of arc BC = 100°

Learn more about major and minor arcs on:

https://brainly.com/question/16289520

#SPJ1

Expanding the desired form, we have

[tex]A \sin(\omega t + \phi) = A \bigg(\sin(\omega t) \cos(\phi) + \cos(\omega t) \sin(\phi)\bigg)[/tex]

and matching it up with the given expression, we see that

[tex]\begin{cases} A \sin(\omega t) \cos(\phi) = 2 \sin(4\pi t) \\ A \cos(\omega t) \sin(\phi) = 5 \cos(4\pi t) \end{cases}[/tex]

A natural choice for one of the symbols is [tex]\omega = 4\pi[/tex]. Then

[tex]\begin{cases} A \cos(\phi) = 2 \\ A \sin(\phi) = 5 \end{cases}[/tex]

Use the Pythagorean identity to eliminate [tex]\phi[/tex].

[tex](A\cos(\phi))^2 + (A\sin(\phi))^2 = A^2 \cos^2(\phi) + A^2 \sin^2(\phi) = A^2 (\cos^2(\phi) + \sin^2(\phi)) = A^2[/tex]

so that

[tex]A^2 = 2^2 + 5^2 = 29 \implies A = \pm\sqrt{29}[/tex]

Use the definition of tangent to eliminate [tex]A[/tex].

[tex]\tan(\phi) = \dfrac{\sin(\phi)}{\cos(\phi)} = \dfrac{A\sin(\phi)}{\cos(\phi)}[/tex]

so that

[tex]\tan(\phi) = \dfrac52 \implies \phi = \tan^{-1}\left(\dfrac52\right)[/tex]

We end up with

[tex]y(t) = 2 \sin(4\pi t) + 5 \cos(4\pi t) = \boxed{\pm\sqrt{29} \sin\left(4\pi t + \tan^{-1}\left(\dfrac52\right)\right)}[/tex]

where

• amplitude:

[tex]|A| = \boxed{\sqrt{29}}[/tex]

• angular frequency:

[tex]\boxed{4\pi}[/tex]

• phase shift:

[tex]4\pi t + \tan^{-1}\left(\dfrac 52\right) = 4\pi \left(t + \boxed{\frac1{4\pi} \tan^{-1}\left(\frac52\right)}\,\right)[/tex]

The integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2

We are given the functions as;

y = ¹/₂x - 2

y = ∛x

Now, from the graph the coordinate of the point where both curves intersect is at; (8, 2)

Thus, the x-coordinate here is x = 8

∛x - (¹/₂x - 2)

∛x - ¹/₂x + 2

Similarly, another point of intersection of both curves is at the coordinate (0, -2). Thus, the x-coordinate here is; x = 0

Thus, the integral which expresses the area of the region bounded by y = ¹/₂x - 2 and y = ∛x is; ∫⁸₀((x^(1/3)) - ¹/₂x + 2

Read more about Integration at; https://brainly.com/question/16415788

#SPJ1

Answer:

Step-by-step explanation:

why is it so hard omg

According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.

According to the statement

we have given that the mean of 7 hours per day watching TV, and a standard deviation of 1.8 hours.

And we have to find that the At least how many hours of daily TV watching are necessary for a person to be eligible for the interview.

So, For this purpose,

The confidence interval is is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level.

Let us Assume x is the amount of hours that 5% of the persons exceeds.

Then P(z<(x-7)/1.8) = 0.95

From a standard normal table, we know that:

(x-7)/1.8 = 1.6449

x-7 = 2.9607

x = 9.9607

So, According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.

Learn more about confidence interval here

https://brainly.com/question/17097944

#SPJ1

Answer:

What is the expected value when rolling a fair 12-sided die?

132=6.5

Recall the definition of the expected value:

E[X]=∑ni=1xp(x)

Here, we have 12 possible values the die can take on, and the probability of each one is the same: 1/12. So we can just pull the term p(x), the probability of each outcome, out of the summation:

E[X]=112∑12i=1x

A useful trick here is that the sum of the numbers 1..N=N(N+1)2. So:

E[X]=11212(13)2

E[X]=12(13)12(2)

E[X]=132

Step-by-step explanation:

hope it helps you :)

The best estimate for the correlation coefficient of the data is: C. 0.5.

Correlation can be defined as a quantitative measure that describes the relationship between variables. Correlation coefficient, r, is a number that ranges from -1 to 1.

The farther the correlation coefficient from 0, the stronger the relationship between two variables, and also, the more closer the data points are on a plotted graph. Also, a negative correlation value will show a trendline on a plot that slopes downward, while positive correlation value will show a trendline that slopes upwards.

In the graph given, the points are moderately closer to each other. Also, the trendline slopes upward, which suggest a positive correlation.

Since the points are moderately spaced from each other, the correlation coefficient would positive and be approximately 0.5.

Therefore, the best estimate for the correlation coefficient of the data is: C. 0.5.

Learn more about the correlation coefficient on:

https://brainly.com/question/4219149

#SPJ1

Answer:

0

Step-by-step explanation:

because 1-0=1*2^3=8

because2^3=8

The solution to the following equations is given below;

y - 6 = 12

y = 12 + 6

y = 18

-5 + k = 1

k = 1 + 5

k = 6

-2g = -14

g = -14/-2

g = 7

y - 4 = 12

y = 12 + 4

y = 16

12 + u = -12

u = -12 - 12

u = -24

f - 7 = 10

f = 10 + 7

f = 17

8t = 42

t = 42/8

t = 5.25

-9 + z = 18

z = 18 + 9

z = 27

7 + w = 14

w = 14 - 7

w = 7

13 - 5 = 12

8 ≠ 12

D - 2 = -10

D = -10 + 2

D = -8

Learn more about equation:

https://brainly.com/question/2972832

#SPJ1

Answer:

R = 47.49 kg

Step-by-step explanation:

To find answer, I will put things in terms of Raju's mass

J =  R + 10.48

J - 9.23  = F       or   R + 10.48   - 9.23   = F  

F                              +                 J                +   R = 154.2

(R + 10.48- 9.23)      +     (R+10.48 )            +   R  = 154.2    

3R = 142.47

R=47.49 kg

Answer:

B

Step-by-step explanation:

using the Sine Rule in Δ QRS

[tex]\frac{QR}{sinS}[/tex] = [tex]\frac{RS}{sinQ}[/tex] ( substitute values )

[tex]\frac{QR}{sin52}[/tex] = [tex]\frac{67}{sin80}[/tex] ( cross- multiply )

QR × sin80° = 67 × sin52° ( divide both sides by sin80° )

QR = [tex]\frac{67sin52}{sin80}[/tex]

Answer:

matrices can be added together if both have the same order

Addition is both commutative and associative

matrices can be multiplied together if the number of column in the right hand matrix equals the number of row in the left hand matrix