Rationalise the denominator and simplify
A) 2sqrt3/sqrt12

B) 5sqrt7/sqrt35

Given Information:

Monthly payment = MP = $1500/4 = $375

Monthly interest rate = r = 25/12 = 2.083%

Required Information:

Present Value = ?

Answer:

[tex]PV = \$10,110[/tex]

Explanation:

n = 10*4

n = 40 monthly payments

The present value is found by

[tex]$ PV = MP \times \frac{ (1 - \frac{1}{(1+r)^n} )}{r} $[/tex]

Where r is monthly interest rate.

MP is the monthly payment.

[tex]$ PV = 375 \times \frac{ (1 - \frac{1}{(1+0.02083)^{40}} )}{0.02083} $[/tex]

[tex]PV = 375 \times (26.96)[/tex]

[tex]PV = \$10,110[/tex]

Therefore, $10,110 is the present value of 10 quarterly payments of $1500 each at 25% interest rate compounded each month.

Answer:

2 ¹/12

Step-by-step explanation:

convert 1 4/12 to an improper fraction

(1×12+4)=16/12

16/12+9/12=25/12

convert 25/12 to a mixed fraction

=2 ¹/12

Answer:  A) The log parent function has negative values in the range.

Step-by-step explanation:

The domain of y = ln (x)  is D: x > 0

The domain of y = [tex]\sqrtx[/tex][tex]\sqrt x[/tex]  is  D: x ≥ 0

The range of y = ln (x)  is: R: -∞ < y < ∞

So the only valid option is A because the range of a log function contains negative y-values when 0 < x < 1.

Answer:

[tex]\frac{4}{3}[/tex]

Step-by-step explanation:

The area of a regular octahedron is given by:

area = [tex]2\sqrt{3}\ *edge^2[/tex]. Let a is the length of the edge (diagonal).

area = [tex]2\sqrt{3}\ *a^2[/tex]

Given that the diagonal of the octahedron is equal to height (h) of the tetrahedron i.e.

a = h, where h is the height of the tetrahedron and a is the diagonal of the octahedron. Let the edge of the tetrrahedron be e. To find the edge of the tetrahedron, we use:

[tex]h=\sqrt{\frac{2}{3} } e\\but\ h=a\\a=\sqrt{\frac{2}{3} } e\\e=\sqrt{\frac{3}{2} }a[/tex]

The area of a tetrahedron is given by:

area = [tex]\sqrt{3}\ *edge^2[/tex] = [tex]\sqrt{3} *(\sqrt{\frac{3}{2} }a)^2=\frac{3}{2}\sqrt{3} *a^2[/tex]

The ratio of area of regular octahedron to area tetrahedron regular is given as:

Ratio = [tex]\frac{2\sqrt{3}\ *a^2}{\frac{3}{2} \sqrt{3}*a^2} =\frac{4}{3}[/tex]

Answer:

B

Step-by-step explanation:

Here, we have a grain silo having 2 shapes fused together to make it.

A cylinder and then a hemisphere ( half sphere)

Now, we want to calculate the volume of grain that could completely fill the silo.

Mathematically, to do that, we will need to add the volume of the cylinder to the volume of the hemisphere.

Mathematically,

Volume of cylinder is;

pi * r^2 * h

From the question, r = 6 ft and h = 168 with pi = 22/7

Substituting these values, we have

Volume of cylinder= pi * 6^2 * 168 = 6,048 pi

The volume of the sphere will be;

4/3* pi * r^3= 4/3 * pi * 6^3 = 288 pi

So the total volume of the silo will be;

288 pi + 6,048 pi = 6336 pi

So to have the final result, let’s multiply by value of pi

6336 * 22/7 = 19,193 ft^3

The closest answer here probably due to previous approximations is 19,008 ft^3

Answer:

Other equation: y = 1/3x + 5

Solution: (3, 6)

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Identify tables

1st table is the unknown equation

2nd table is the known equation (found using y-intercept 7)

Step 2: Find missing equation

m = (6 - 5)/(3 - 0)

m = 1/3

y = 1/3x + b

5 = 1/3(0) + b

5 = b

y = 1/3x + 5

Step 3: Find solution set using substitution

1/3x + 5 = -1/3x + 7

2/3x + 5 = 7

2/3x = 2

x = 3

y = 1/3(3) + 5

y = 1 + 5

y = 6

Answer:

5x² and 7x² are like terms because they contain x².

3x and 8x are like terms because they contain x.

10 and 11 are like terms because they are constants.

Step-by-step explanation:

Let's recall that the definition of like terms is that they are terms that contain the same variables raised to the same power and only like terms can be combined.

Upon saying that, we have:

5x² and 7x² are like terms because they contain x²

3x and 8x are like terms because they contain x

10 and 11 are like terms because they are constants.

Answer:

3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].

Step-by-step explanation:

x^2 = 6x - 4

x^2 - 6x + 4 = 0

Now, we can use the quadratic formula to solve.

[tex]\frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex], where a = 1, b = -6, and c = 4.

[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4 * 1 * 4} }{2 * 1}[/tex]

= [tex]\frac{6\pm\sqrt{36 - 4 * 4} }{2}[/tex]

= [tex]\frac{6\pm\sqrt{36 - 16} }{2}[/tex]

= [tex]\frac{6\pm\sqrt{20} }{2}[/tex]

= [tex]\frac{6\pm2\sqrt{5} }{2}[/tex]

= 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex]

x = 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].

Hope this helps!

Step-by-step explanation:

in each equation once substitute the value of x as 0 and again y as zero by this way you will get two values of X and y .

then again find the slope for each equation by the formula

slope= -coefficient of x / coefficient of y

for example,

X+y is greater or equals to 5

or, X+y= 5

or, X=5-y

or, when y is equals to zero

X= 5

and when X is equals to zero

y= 5

then plot the above point in the graph with respect to its slope and the shaded part is the solution

Answer:

(-4, 6), (0, 2), (4, -2)

Step-by-step explanation:

You just need to guess and check.

(-4,6) → -4 + 6 = 2 ✔

(0,2) → 0+2 = 2 ✔

(4,2) → 4 + 2 = 6

(4, -2) → 4 - 2 = 2 ✔

(-4,-6) → -4 - 6 = -10

The correct answer is the second list (-4, 6), (0, 2), (4, -2)

Answer:

the answer would be x is less than 6.

Step-by-step explanation:

the reason why it would not be x is less than or equal to 6 is that the circle is not filled in.

Answer:

B

Step-by-step explanation:

x≤6

We can see from the graph that it starts from 6 and goes to 5, 4, 3, 2.

Hope this helps ;) ❤❤❤

Answer:

5 is the answer..

Step-by-step explanation:

simply by calculating

Answer:

1. The size of shift from function f to function g is -12

2. The plot of the points of a function that is shifted only half as much as g from the parent function f is in the attached file in blue color.

Step-by-step explanation:

Parent function: f(x)=2^x

x=0→f(0)=2^0→f(0)=1

x=1→f(1)=2^1→f(1)=2

x=2→f(2)=2^2→f(2)=4

x=3→f(3)=2^3→f(3)=8

x=4→f(4)=2^4→f(4)=16

Size of the shift from function f to function g: s

s=g(0)-f(0)=-11-1→s=-12

s=g(1)-f(1)=-10-2→s=-12

s=g(2)-f(2)=-8-4→s=-12

s=g(3)-f(3)=-4-8→s=-12

s=g(4)-f(4)=4-16→s=-12

Points of a function h that is shifted only half as much as g from the parent function, f. Use the same x- values as used in the table for function:

s2=s/2→s2=(-12)/2→s2=-6

x   h(x)

0   1+(-6)=1-6=-5  

1    2+(-6)=2-6=-4

2   4+(-6)=4-6=-2

3    8+(-6)=8-6=2

4    16+(-6)=16-6=10

Answer:

A. The graph of g(x) is vertically compressed by a factor of 3.

Step-by-step explanation:

When there is a fraction, that means that there is a veritcal dilation.

Hope this helps! Good luck!

Answer:

£32.4

Step-by-step explanation:

£100 = 216 Swiss francs

x        =  70 francs

70 x 100=7000/216=32.4

Answer:

46 minutes.

Step-by-step explanation:

2 km in 13 minutes would equal to 6 minutes and 30 seconds per km.

minutes: 6 x 7 = 42

seconds: 30 x 7 = 210

seconds pt 2: 210/60 = 3 minutes 30 seconds

adding altogether: 42 minutes + 3 minutes 30 seconds + 45 minutes 30 seconds, rounded would equal to 46 minutes

Answer:

25 - 3x^5

Step-by-step explanation:

-2x^4+16+2x^4+9-3x^5

Combine like terms

-2x^4+2x^4+9+16-3x^5

0                 + 25 -3x^5

Answer:

3x^5-25

Step-by-step explanation:

you but the terms with the same power together and don't forget to add the signs that are in front of each terms when combining.

Answer:

  (-8,10)

Step-by-step explanation:

hope i helped!

u can substitute if u want to recheck

can i get brainliest pls?

-Zylynn

Answer:

Step-by-step explanation:

To use the regression function on your calculator, first hit STAT then choose 1:Edit by pressing ENTER. Then a table pops up. If it's not clear, arrow up to L1, hit CLEAR then ENTER and the table empties. Do the same with L2. Arrow left and right as needed to get from one column to the other. Then in L1 enter the x values one at a time, hitting ENTER after each. When all the x values are in, arrow over to L2 and enter the y values in the same way.

Next, hit STAT again, then right arrow over to CALC. Choose 6:CubicReg by either arrowing down to it or by pressing 6. If you have a TI 83+, the equation comes right up for you; if you have a TI 84+ or 84+CE, you have to arrow down to CALCULATE and hit ENTER to get your equation. The equation is

[tex]-2x^3+2x^2-4x+3[/tex] with a coefficient correlation (r-squared) value of 1 which means this is a perfect equation for this data and all the points you entered into the table fall perfectly on this curve.

Answer:

3x-4

Step-by-step explanation:

Have a good day!!

Answer:

3x-4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Berto’s train was 34 miles past the egg farm .

Eduardo’s train had 12 miles to go before it reached the egg farm.

Distance between two trains = 34 + 12 = 46 miles

This distance has to be reduced to zero for their crossing each other .

Rate at which this distance is reduced  = their relative velocity

= 110 - 85

= 25 miles / h       [ They are moving in the same direction ]

So, time taken for them to meet each other

= 46 / relative velocity

= 46 / 25

= 1.84 hours .

Answer:

The answer is D or 1.84 hours.

Step-by-step explanation:

I got 100% on this quiz.

Answer:

The function has two real roots and crosses the x-axis in two places.

The solutions of the given function are

x = (-0.4495, 4.4495)

Step-by-step explanation:

The given quadratic equation is

[tex]G(x) = -x^2 + 4x + 2[/tex]

A quadratic equation has always 2 solutions (roots) but the nature of solutions might be different depending upon the equation.

Recall that the general form of a quadratic equation is given by

[tex]a^2 + bx + c[/tex]

Comparing the general form with the given quadratic equation, we get

[tex]a = -1 \\\\b = 4\\\\c = 2[/tex]

The nature of the solutions can be found using

If [tex]b^2- 4ac = 0[/tex] then we get two real and equal solutions

If [tex]b^2- 4ac > 0[/tex] then we get two real and different solutions

If [tex]b^2- 4ac < 0[/tex] then we get two imaginary solutions

For the given case,

[tex]b^2- 4ac \\\\(4)^2- 4(-1)(2) \\\\16 - (-8) \\\\16 + 8 \\\\24 \\\\[/tex]

Since 24 > 0

we got two real and different solutions which means that the function crosses the x-axis at two different places.

Therefore, the correct option is the last one.

The function has two real roots and crosses the x-axis in two places.

The solutions (roots) of the equation may be found by using the quadratic formula

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

[tex]x=\frac{-(4)\pm\sqrt{(4)^2-4(-1)(2)}}{2(-1)} \\\\x=\frac{-4\pm\sqrt{(16 - (-8)}}{-2} \\\\x=\frac{-4\pm\sqrt{(24}}{-2} \\\\x=\frac{-4\pm 4.899}{-2} \\\\x=\frac{-4 + 4.899}{-2} \: and \: x=\frac{-4 - 4.899}{-2}\\\\x= -0.4495 \: and \: x = 4.4495 \\\\[/tex]

Therefore, the solutions of the given function are

x = (-0.4495, 4.4495)

A graph of the given function is also attached where you can see that the function crosses the x-axis at these two points.

Answer: <CED is the right angle, which measures 90 degrees. Since the measure of a straight angle is 180 degrees. <CEA must also be 90 degrees by the Definition of Right Angle. A bisector cuts the angle measure in half. m<AEB is 45 degrees.

Answer:

probability that a player wins after playing the game once = 5/9

Step-by-step explanation:

To solve this, we will find the probability of the opposite event which in this case, it's probability of not winning and subtract it from 1.

Since, we are told that there are 2 fair six sided die thrown at the same time and that he receives a five or a one on either die ;

Probability of not winning, P(not win) = 4/6.

Thus;

P(winning) = 1 - ((4/6) × (4/6))

P(winning) = 1 - 4/9 = 5/9

Answer:

B

Step-by-step explanation:

Answer:

3. time = 6.4999  approximately 6.5 years

4. $2235.35

5.  $ 3950

Step-by-step explanation:

4. amount of interest =  final amount - principle= 7535.35 - 5300 = 2235.35

5. principle = final amount - interest earned = 4435.25 - 485.25 = 3950

Answer:

Step-by-step explanation:

Solution,

Use the BODMAS Rule:

B = Bracket

O = Of

D = Division

M= Multiplication

A = Addition

S = Subtraction

Now,

Let's solve,

[tex]2 + 8 \div 2 \times 3[/tex]

First we have to divide 8 by 2

[tex] = 2 + 4 \times 3[/tex]

Calculate the product

[tex] = 2 + 12[/tex]

Calculate the sum

[tex] = 14[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

14

Step-by-step explanation:

2 + 8 ÷ 2 x 3 =

There is an addition, a division, and a multiplication. According to the correct order of operations, we do first the multiplications and divisions in the order they appear from left to right.

= 2 + 4 x 3

= 2 + 12

Now we do the addition.

= 14

Answer:

.0000416

Step-by-step explanation:

Since 10 is squared by a negative number, the number (4.16) will be smaller. To find the answer, move the decimal 5 places to the left

Answer:

0.0000416.

Step-by-step explanation:

When 10 is raised to a negative power, that means that the decimal point will be moved to the left a certain number of units.

In this case, it is 10^-5, so the decimal point will move to the left by 5 units.

4.16 * 10^-5 = 000004.16 * 10^-5 = 0.0000416.

Hope this helps!

Answer:

The surface area of the pyramid is 80.9 cm²

Step-by-step explanation:

The side length, s of the cube is given as 5 cm

Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm

The height, h of the largest pyramid = The height of the cube = 5 cm.

The surface area of a pyramid =  Area of base, A + 1/2 × Perimeter of base, P × Slant height, S

The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5

The perimeter of the base = 4×5 = 20 cm

The area of the base = 5×5 = 25 cm²

The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².

The surface area of a pyramid =  80.9 cm².

Answer: 2.

Step-by-step explanation:

Number of samples = 121

Average speed (sample mean) = 65mph

Population standard deviation = 22 mph

The standard error of the mean is:

Standard error of the mean(S.Em)

Standard error of the mean is the proportion of the population standard deviation and the square root of the sample size.

S.Em = standard deviation / √same size

S.Em = 22 / √121

S.Em = 22 / 11

S.Em = 2