Which expression is equivalent to the following complex fraction?
-25
245 5
+
y
3 2
у

Answer:

1st option

Step-by-step explanation:

Evaluate f(- 5) then substitute the value obtained into g(x)

f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then

g(3) = - 4(3) + 6 = - 12 + 6 = - 6

Answer:

m<GEF = 66°

Step-by-step explanation:

(72+60)/2

= 132/2

= 66

Answered by GAUTHMATH

9514 1404 393

Answer:

  (x, y) = (3, 12)

Step-by-step explanation:

The first step in any problem solving is to look at the problem. Here, we see that the first equation can be reduced to standard form by dividing it by 2. This would give both terms a coefficient of 1.

We see that the second equation already has a variable with a coefficient of 1.

When solving a system by substitution, it can save some effort if you start by finding a variable with a coefficient of 1 or -1. Since we see that in the second equation, we choose to solve the second equation for y:

  y = 4x . . . . . . . add 4x to both sides of the second equation

Now, we have an expression for y that we can substitute into the first equation.

  2x +2(4x) = 30 . . . . substitute for y

  10x = 30 . . . . . . . . simplify

  x = 3 . . . . . . . . . . divde by 10

  y = 4(3) = 12 . . . . . find y using y=4x

The solution is (x, y) = (3, 12).

__

Additional comment

I doesn't matter what variable gets substituted. The purpose of the exercise is to reduce the number of variables in the equation. Here, we start with an equation that has 2 variables. Substituting for one of them gives an equation with only one variable, a lot easier to solve.

You don't have to find an expression for the "bare" variable. We could solve the second equation for 2x, for example: 2x = y/2, then substitute for 2x in the first equation: y/2 +2y = 30   ⇒   y = (2/5)(30) = 12. Or, we could solve the first equation for 2x and substitute into the second: 2x=30-2y, y-2(2x) = 0 ⇒ y-2(30-2y) = 0 ⇒ y = 60/5 = 12.

The substitution property of equality says you can make any substitution of equal values anywhere. "butter = margarine" means you can substitute butter for margarine, or vice versa, wherever you may wish.

Answer: Choice A)  y - 10 = 2(x - 3)

============================================================

Explanation:

We can rule out choices C and D because this diagonal line has a positive slope (as it moves uphill when moving to the right).

So m = 2 must be the slope.

---------

Recall that

y - y1 = m(x - x1)

represents the point slope form of a linear equation.

The point shown on this graph is (3,10) meaning that x1 = 3 and y1 = 10 pair up together.

So,

y - y1 = m(x - x1)

y - 10 = 2(x - 3)

which points to choice A as the final answer

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(

12

,

67.45

)

Equation Form:

x

=

12

,

y

=

67.45

Graph is attached below ;

Answer:

Unit rate = 12 computers per day

Step-by-step explanation:

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

That is ; the gradient ;

Slope = change in y / change in x

Slope = (y2 - y1) / (x2 - x1)

y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3

Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12

Slope = 12

Unit rate = 12 computers per day

Answer:

- 27.88

Step-by-step explanation:

Probability of earthquake = 0.0012

P(earthquake). = 0.0012

P(no earthquake) = 1 - p(earthquake) = 1 - 0.0012 = 0.9988

X ____ 60,000 ______ - 100

P(X) ___ 0.0012 _____ 0.9988

The expected value of the policy :

E(X) = Σx*p(x)

E(X) = (0.0012 * 60000) + (0.9988 * - 100)

E(X) = 72 - 99.88

E(X) = - 27.88

Answer:

9

Step-by-step explanation:

First multiple of 8 in that range is 8(2)=16.

The last multiple of 8 in that range is 8(10)=80.

So we just need to find how many numbers there are between 2 and 10. inclusive.

10-2+1=9

It's also not that long to write out and count.

1-2

2-3

3-4

4-5

5-6

6-7

7-8

8-9

9-10

9 numbers there are

Multiply those 9 numbers by i you will have all multiples of 8 btw 15 and 85.

8(2)=16

8(3)=24

8(4)=32

8(5)=40

8(6)=48

8(7)=56

8(8)=64

8(9)=72

8(10)=80

Answer:

8. -2a+14

9. w=3/2

Step-by-step explanation:

8.

The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.

For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as

-2 * a + (-2) * (-7) = final answer

= -2 * a + 14

We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out

9.

Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in

(-2/3)w = 4-5 = -1

Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get

w = (-3/2)

To check this, we can plug (-3/2) for w in our original equation, so

(-2/3) * (-3/2) + 5 = 4

-1 + 5 = 4

4 = 4

This works!

Answer:

10.97%

Step-by-step explanation:

There are 52 cards.

13 of them, are hearts.

Then

52 - 13 = 39 cards are not hearts.

4 cards are drawn, we want to find the percent chance that the fourth card is a heart card, but no before.

So the first card can't be a heart card.

because the deck is well-shuffled, all the cards have the same probability of being drawn.

Then the probability of not getting a heart card, is equal to the quotient between the number of non-heart cards (39) and the total number of cards (52), then the probability is:

p₁ = 39/52

The second card also can't be a heart card, the probability is calculated in the same way than above, but now there are 38 non-heart cards and a total of 51 cards (because one card was already drawn) then the probability here is:

p₂ = 38/51

For the third card the reasoning is similar to the two above cases, here the probability is:

p₃ = 37/50

The fourth card should be a hearts card, the probability is computed in the same way than above, as the quotient between the number of heart cards in the deck (13) and the total number of cards in the deck (now there are 49 cards)

then the probability is:

p₄ = 13/49

The joint probability (the probability of these 4 events happening together) is equal to the product between the individual probabilities:

P = p₁*p₂*p₃*p₄

P = (39/52)*(38/51)*(37/50)*(13/49) = 0.1097

The percent chance is the above number times 100%

Percent =  0.1097*100% = 10.97%

Answer:

Answer : 1/8.

Step-by-step explanation:

Hey there!

Please see the attached picture for your answer.

Hope it helps!

Answer:

0.868 = 86.8% probability that the student passes.

Step-by-step explanation:

Probability of the student passing:

94% of 91%(when the student studies for the test).

14% of 100 - 91 = 9%(when the student does not study for the test). So

[tex]p = 0.94*0.91 + 0.14*0.09 = 0.868[/tex]

0.868 = 86.8% probability that the student passes.

Answer:

(x-1)^2 + (y+4)^2 = 4

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-1)^2 + (y- -4)^2 = 2^2

(x-1)^2 + (y+4)^2 = 4

Answer:

€36 = 30.62 pounds sterling

9514 1404 393

Answer:

  x = 1.35 (12.22)

Step-by-step explanation:

The selling price x is ...

  x = cost + markup

  x = cost + 0.35 × cost = cost(1 +0.35)

  x = 1.35(12.22)

Answer:

21

Step-by-step explanation:

All three sides are equal

2x-7 = x+y-9 = y+5

Using the last two

x+y-9 = y+5

Subtract y from each side

x+y-9-y = y+5-y

x-9 = 5

Add 9 to each side

x -9+9 = 5+9

x=14

We know the side length is

2x-7

2(14) -7

28-7

21

The side length is 21

Answer:

The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

Step-by-step explanation:

According to the given information, vector stands in the 4th Quadrant ([tex]x > 0[/tex], [tex]y < 0[/tex]) and direction of the vector ([tex]\theta[/tex]) in sexagesimal degrees, is determined by following definition:

[tex]\theta = 360^{\circ} - \tan^{-1} \left(\frac{|y|}{|x|} \right)\pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]

Please notice that angle represents a function with a periodicity of 360°.

If we know that [tex]x = 4[/tex] and [tex]y = -3[/tex], then the direction of the vector is:

[tex]\theta = 360^{\circ}-\tan^{-1}\left(\frac{|-3|}{|4|} \right)\pm 360\cdot i[/tex]

[tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex]

The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].

The pillars and the pyramids in the stadium gate means that we have to calculate the area of the items that make up the gate one after the other. At the end of the calculation, the calculated areas are then added up.

The total cost of painting is Rs.21344

First, we calculate the area of 1 side of 1 pillar using:

[tex]A = Height * Base[/tex]

Where

[tex]Height = 10ft[/tex] --- Height of the pillar

[tex]Base = 3ft[/tex] --- Base of the pillar

So:

[tex]A = 10ft * 3ft[/tex]

[tex]A = 30ft^2[/tex]

The area of the 4 sides of the pillar is:

[tex]A_2 = 4 * A[/tex] --- i.e. 4 multiplied by the area of 1 side

[tex]A_2 = 4 * 30ft^2[/tex]

[tex]A_2 = 120ft^2[/tex]

The area of the 2 pillars is:

[tex]Area_1 = 2 * A_2[/tex] --- i.e. 2 multiplied by the area of 1

[tex]Area_1 = 2 * 120ft^2[/tex]

[tex]Area_1 = 240ft^2[/tex]

Because one part of the pyramid won't be visible, we calculate the area of the pyramid using:

[tex]Area = lw + l\sqrt{(w/2)^2 + h^2} + w\sqrt{(l/2)^2 + h^2}[/tex]

Where:

[tex]h = 2[/tex] -- the height

[tex]l = w = 3[/tex] --- the base of the pillar is the length & width of the pyramid.

So, we have:

[tex]Area = 3\sqrt{(2/2)^2 + 2^2} + 3\sqrt{(2/2)^2 + 2^2}[/tex]

[tex]Area = 3\sqrt{1 + 4} + 3\sqrt{1 + 4}[/tex]

[tex]Area = 3\sqrt{5} + 3\sqrt{5}[/tex]

[tex]Area = 6\sqrt{5}[/tex]

For the two pyramids, the area is:

[tex]Area_2 = 2 * 6\sqrt 5[/tex] -- 2 multiplied by area of 1

[tex]Area_2 = 12\sqrt 5[/tex]

[tex]Area_2 = 26.8[/tex]

So, the total area to be painted is:

[tex]Total = Area_1 + Area_2[/tex] --- the sum of the area of the pillars and the pyramids

[tex]Total = 240+26.8[/tex]

[tex]Total = 266.8ft^2[/tex]

The unit cost of paint is:

Rate = Rs80 per sq.ft

The total cost of painting is:

[tex]Cost = 80 * 266.8[/tex]

[tex]Cost = Rs.21344[/tex]

Hence, the total cost of painting is Rs.21344.

Read more at:

https://brainly.com/question/14320476

Answer:

133.3

Step-by-step explanation:

Volume of pyramid: 1/3 Base Area×height

Volume=

[tex] \frac{25 \times 16}{3} [/tex]

133.333 Sq. feet

Brainliest please~

Part (a)

The standard error (SE) formula is

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

where n is the sample size. We're given SE = 2 and sigma = 34, so,

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\2 = \frac{34}{\sqrt{n}}\\\\2\sqrt{n} = 34\\\\\sqrt{n} = \frac{34}{2}\\\\\sqrt{n} = 17\\\\n = 17^2\\\\n = 289\\\\[/tex]

So we need a sample size of n = 289 to have an SE value of 2.

========================================================

Part (b)

We'll use SE = 1 this time

[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\1 = \frac{34}{\sqrt{n}}\\\\1*\sqrt{n} = 34\\\\\sqrt{n} = 34\\\\n = 34^2\\\\n = 1156\\\\[/tex]

Because we require greater precision (i.e. a smaller SE value), the sample size must be larger to account for this. In other words, as SE goes down, then n must go up, and vice versa.

Answer:

A)   ± 54 cm^3 ( maximum possible error in volume )

B) i) 58.625 cm^3  ii) 49.625 cm^3

Step-by-step explanation:

A) using differential

edge of cube = 6 cm ,  maximum possible error = 0.5 cm

∴ side of cube ( x )= ± 0.5 cm

V = volume of cube

dv /dx = d(x)^3 / dx

∴ dv  = 3x^2 dx ---- ( 1 )

input values into 1

dv = 3(6)^2 * ( ± 0.5 )

    = ± 54 cm^3 ( maximum possible error in volume )

B) Using calculator

actual error in measuring volume when

i) radius = 6.5 cm instead of  6 cm

V1= ( 6.5)^3 = 274.625 ,  V = ( 6)^3 = 216

actual error = 274.625 - 216 = 58.625 cm^3

ii) radius = 5.5cm instead of 6cm

actual error = 49.625 cm^3

Answer:

(a) sin 60° = √ 3/ 2 OR 0.8660

(b) tan 34° = 0.6745

(c) cos 124°​ = − 0.5591

Answer:

The annual interest rate would have to be of 0.1%.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Jerod hopes to earn $1200 in interest in 4.9 years time from $24,000 that he has available to invest.

This means that:

[tex]A(4.9) = 1200 + 24000 = 25200[/tex]

[tex]t = 4.9[/tex]

[tex]P = 24000[/tex]

Compounded monthly:

This means that [tex]n = 12[/tex]

What would the annual rate of interest have to be?

We have to solve for r, so:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]25200 = 24000(1 + \frac{r}{12})^{12*4.9}[/tex]

[tex](1 + \frac{r}{12})^{12*4.9} = \frac{25200}{24000}[/tex]

[tex](1 + \frac{r}{12})^{58.8} = 1.05[/tex]

[tex]\sqrt[58.8]{(1 + \frac{r}{12})^{58.8}} = \sqrt[58.8]{1.05}[/tex]

[tex]1 + \frac{r}{12} = (1.05)^{\frac{1}{58.8}}[/tex]

[tex]1 + \frac{r}{12} = 1.00083[/tex]

[tex]\frac{r}{12} = 0.00083[/tex]

[tex]r = 12*0.00083[/tex]

[tex]r = 0.001 [/tex]

The annual interest rate would have to be of 0.1%.

Answer: hello your question is poorly written attached below is the complete question

answer:

1 ) =  I (

2) = F

3) = Z

4) = D

Step-by-step explanation:

attached below is the required solution.

1 ) =  I ( The sequence diverges to infinity )

2) = F ( The sequence has a finite non-zero limit )

3) = Z ( The sequence converges to zero )

4) = D ( The sequence diverges )

Answer:

A)x>-3

Step-by-step explanation:

as the circle is not coloured this means that -3 is not included so the ones that have

[tex] \geqslant \\ \leqslant [/tex]

are not answers and these means smaller or equal to/greater or equal to.

As the line is going to the right this means that x is greater than -3 so we use > for greater.

so in the end we get that the answer is x > -3

Answer:

A B C D

A×B×C×D

3×3×3×6

162

Step-by-step explanation:

A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.

h=-16t^2+16t+32