A passbook savings account has a rate of 5%. Find the effective annual yield if the interest is compounded quarterly.

Answer:

x = - 1/6 + √-119/6, and, - 1/6 - √-119/6

Step-by-step explanation:

Using the quadratic formula which is: - b ± √b² - 4ac / 2a

a = 3, b = 1, c = 10

- 1 ± √1² -4 * 3 * 10 / 2 * 3

- 1 ± √1 - 120 / 6

-1 ± √-119 / 6

= -1/6 + √119/6,               or                  - 1/6 - √-119/6

Answer:

4

Step-by-step explanation:

1) to find hcf, first look at what both 12 and 16 are divisible by

12 and 16 are divisible by 2

so

12/2=6

16/2=8

now we have 6,8

6 and 8 are divisible by 2 as well

6/2=3

8/2=4

3,4 is what we are left with

since we had to divide these numbers by 2 both times, multiply them.

2*2=4

4 is the hcf

Answer:

The area is 36

Step-by-step explanation:

hope it helps :3

multiple the length x width

6x6=36

Answer:

Im not sure but I thinks its the first one

f(x)=8(4)

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

This sequence is by adding 4 you get the next number

Addition is the function

Answer: 77/50

Step-by-step explanation:

Decimal: 1.54

Fraction: 77/50

Percentage: 154%

Answer:

6    

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Put the numbers in order from smallest to largest

10, 12,13, 15, 17, 18,  21,

The range is the largest number minus the smallest number

21-10

11

Answer:

I think it's D, sorry if i'm wrong but let me know if I'm right!

Step-by-step explanation:

Steps to solve:

-4(r + 3) = -42

~Distribute

(-4 * r) + (-4 * 3) = -42

~Simplify

-4r - 12 = -42

~Add 12 to both sides

-4r - 12 + 12 = -42 + 12

~Simplify

-4r = -30

~Divide -4 to both sides

-4r/-4 = -30/-4

~Simplify

r = 7.5

Best of Luck!

Answer:

7.5

Step-by-step explanation:

(-4) (7.5 + 3)= -42

Step-by-step explanation:

Putting values of x and y

2 = 4 + 2

2 = 6

= 6-2

= 4

Answer:

The ratio of the height of the cone to the height of the cylinder is 3 to 1

The ratio of the height of the cone to the radius of the sphere is 4 to 1

Step-by-step explanation:

First we need to know the volume of a cylinder, a cone and a sphere:

V_cylinder = pi*r^2*h

V_cone = (1/3)*pi*r^2*h

V_sphere = (4/3)*pi*r^3

If they have the same volume:

The ratio of the height of the cone to the height of the cylinder is:

V_cone / V_cylinder = 1

(1/3)*pi*r^2*h1 / pi*r^2*h2 = 1

(1/3) * h1 = h2

h1 / h2 = 3

So the ratio is 3 to 1

The ratio of the height of the cone to the radius of the sphere is:

V_cone / V_sphere = 1

(1/3)*pi*r^2*h / (4/3)*pi*r^3 = 1

h / 4r = 1

h / r = 4

So the ratio is 4 to 1

Answer:

2 • (2x - 3) • (3x - 2)

Step-by-step explanation:

Answer:

4x + 6(3x -2)

First distribute

4x + 18x - 12

Combine like terms

22x - 12

Step-by-step explanation:

Answer:

212

Step-by-step explanation:

volume of new figure = sum of the two individual figures

volume of one cuboid=l*b*h

volume of first cuboid=92

volume of second  cuboid=120

sum of two figures=212

hope this helps

plzz mark me brainliest

Answer:

212 is the answer

Step-by-step explanation:

First to find the area of the first figure, you must use the formula for volume: length times width times height.

so: 23(2)(2) is equal to 92.

then for the second figure: 8(5)(3) is equal to 120.

now you add the two answers.

92+120=212

Answer:

cos2θ = -0.7041

Cos θ = -0.3847

Step-by-step explanation:

Firstly, we should understand that since θ is in quadrant 2, the value of our cosine will be negative. Only the sine is positive in quadrant 2.

Now the sine of an angle refers to the ratio of the opposite to the adjacent. And since there are three sides to a triangle, we need to find the third side which is the adjacent so that we will be able to evaluate the cosine of the angle.

What to use here is the Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the adjacent and the opposite.

Since Sine = opposite/hypotenuse, this means that the opposite is 12 and the hypnotist 13

Thus the adjacent let’s say d can be calculated as follows

13^2 = 12^2 + d^2

169 = 144 + d^2

d^2 = 169-144

d^2 = 25

d = √25 = ±5

Since we are on the second quadrant, the value of our adjacent is -5 since the x-coordinate on the second quadrant is negative.(negative x - axis)

The value of cos θ = Adjacent/hypotenuse = -5/13

Cos θ = -5/13

Cos θ = -0.3846

Using trigonometric formulas;

Cos 2θ = cos (θ + θ) = cos θ cos θ - sin θ sin

θ = cos^2 θ - sin^2 θ

Cos 2θ = (-5/13)^2 - (12/13)^2

Cos 2θ = 25/169 - 144/169

Cos 2θ = (25-144)/169 = -119/169

Cos 2θ = -0.7041

There are four quadrants in a coordinate geometry.

The cosine values are [tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex] and [tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]

The given parameter is:

[tex]\mathbf{sin(\theta) = \frac{12}{13}}[/tex]

Using trigonometry ratio, we have:

[tex]\mathbf{sin^2(\theta) + cos^2(\theta)= 1}[/tex]

Substitute [tex]\mathbf{sin(\theta) = \frac{12}{13}}[/tex]

[tex]\mathbf{(\frac{12}{13})^2 + cos^2(\theta)= 1}[/tex]

Expand

[tex]\mathbf{\frac{144}{169} + cos^2(\theta)= 1}[/tex]

Collect like terms

[tex]\mathbf{ cos^2(\theta)= 1-\frac{144}{169}}[/tex]

Evaluate fraction

[tex]\mathbf{ cos^2(\theta)= \frac{25}{169}}[/tex]

Take square roots of both sides

[tex]\mathbf{ cos(\theta)= \pm \frac{5}{13}}[/tex]

The angle is in the second quadrant.

So, we have:

[tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex]

Also, we have:

[tex]\mathbf{ cos(2\theta) = cos^2(\theta) - sin^2(\theta)}[/tex]

So, the equation becomes

[tex]\mathbf{ cos(2\theta) = \frac{25}{169} - \frac{144}{169}}[/tex]

Take LCM

[tex]\mathbf{ cos(2\theta) = \frac{25-144}{169}}[/tex]

[tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]

Hence, the values are:

[tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex] and [tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]

Read more about quadrants at:

https://brainly.com/question/7196054

Answer:

[tex] y - \frac{7}{2}= \frac{1}{2} (x-4)[/tex]

[tex] y-\frac{7}{2}= \frac{1}{2}x - 2[/tex]

[tex] y = \frac{1}{2}x -2 + \frac{7}{2}[/tex]

[tex] y = \frac{1}{2}x + \frac{3}{2}[/tex]

[tex] y = mx +b[/tex]

Is given by:

Ο 3/2

Step-by-step explanation:

For this case we have the following function given:

[tex] y - \frac{7}{2}= \frac{1}{2} (x-4)[/tex]

If we distribute the 1/2 in the right we got:

[tex] y-\frac{7}{2}= \frac{1}{2}x - 2[/tex]

Now we can add on both sides 7/2 and we got:

[tex] y = \frac{1}{2}x -2 + \frac{7}{2}[/tex]

And simplifying we got:

[tex] y = \frac{1}{2}x + \frac{3}{2}[/tex]

And the answer for this case using the general formula:

[tex] y = mx +b[/tex]

Is given by:

Ο 3/2

Answer:

[tex]5400cm^{3}[/tex] more water could be added to the container before the container overflows

Step-by-step explanation:

The volume of the rectangular container is got by multiplying its given dimensions: Length X breadth X height

This will be  30 X 20 X 24 = [tex]14400 cm^{3}[/tex]

To find the volume of water inside the rectangular container, we will use the new height for our computation of volumes, keeping the length and breadth of the cylinder the same.

This will be [tex]30 \times 20 \times 15 =9000 cm^{3}[/tex]

The volume of water needed to be added until the container overflows will be got by subtracting the volume of water present in the container from the total volume of the container

[tex]14400 - 9000 =5400cm^{3}[/tex]

Note 1 [tex]cm^{3}= 1 ml[/tex]

Answer:

I think its 46...

Step-by-step explanation:

Answer:

the answer is 40

Step-by-step explanation:

15+8+17=40

Answer:

612

Step-by-step explanation:

The lateral surface area does not include the bases.

The bases are the triangles

We will add up the areas of the three rectangles

We have the two rectangles on the sides which are 17 by 13 and the rectangle on the bottom which is 17 by 10

17* 13 + 17*13 + 17*10 =612

Answer:12

Step-by-step explanation:

Given

A quarter and a spinner is played simultaneously so

A quarter can show two outcomes i.e. head and tail

While spinner can show 6 outcomes from 1 to 6

So there can be [tex]2\times 6=12[/tex] possible outcomes

(H,1),(H,2) ,(H,3) ,(H,4) ,(H,5) ,(H,6) ,(T,1) ,(T,2) ,(T,3) ,(T,4) ,(T,5) ,(T,6)

Answer:

The reason why both have the same value is because you are only moving the decimal place. The difference between 51.2 and 5.12 is that you divided 10 from 51.2 to get 5.12. Same goes for 6.4 and 0.64.

51.2 / 6.4 = 8

5.12 / 0.64 = 8

Final answer:

The quotient of 51.2 divided by 6.4 is the same as 5.12 divided by 0.64 because both numerators and denominators are related by a factor of 10. This maintains the value of the quotient unchanged when both are multiplied or divided by the same power of 10.

Explanation:

When dividing two numbers, you can often simplify the expression by dividing both numbers by a common factor. In this case, both 51.2 and 6.4 have a common factor of 0.64. Dividing both numbers by 0.64, we get:

51.2 ÷ 0.64 = 80

6.4 ÷ 0.64 = 10

So, as you can see, the result is the same: 80 divided by 10 is equal to 8. This is why dividing 51.2 by 6.4 has the same value as dividing 5.12 by 0.64.

Answer:

Actual dimension of the field = 42 ft × 21 ft

Equation : [tex]y=\frac{7}{2}x[/tex]

Step-by-step explanation:

Scale for the drawing of a rectangular playing field is,

2 inches = 7 feet

Or 1 inch = 3.5 feet

If length of the playing field on drawing = 12 in

Then actual length of the field = 12×3.5 = 42 feet

And width on the drawing = 6 inches

Therefore, actual width of the field = 6×3.5 = 21 feet

If 'x' is the dimension of a scale drawing and 'y' be the corresponding dimension of the actual field,

[tex]\frac{x}{y}=\frac{2}{7}[/tex]

[tex]y=\frac{7}{2}x[/tex]

Answer:

3. Look at the least amount of time practicing. That is 1/4 hours. Then look at the most time practicing, an hour and a half. Subtract 1  1/2 by 1/4.

4. Look at the dots in the plot. The one in the middle is the highest because it appears the most. The most common time is 3/4 of an hour.

5. To see the total time, add all of the numbers up, including the repeated ones.

The amplitude of the cosine function "y = cos(x)" is 1. Therefore, the correct answer is "d. 1", as it represents the maximum absolute value of the function.

The function "y = cos(x)" represents a cosine function, and its amplitude is the maximum absolute value of the function. The amplitude of the cosine function "cos(x)" is 1. This is because the cosine function oscillates between -1 and 1, and the amplitude is the absolute value of this maximum value.

In mathematical terms, the amplitude (A) of a cosine function "A cos(x)" is equal to the absolute value of the coefficient of the cosine term. In this case, "A = |1| = 1".

Therefore, among the given options:

a. 2

b. π

c. 2π

d. 1

The correct answer is "d. 1" as it accurately reflects the amplitude of the cosine function "y = cos(x)".

The question probable may be:

The graph given above shows the following function y= cos(x)

What is the amplitude of the function?

a. 2

b. pi

c. 2pi

d. 1

Answer:

25 cubic feet of concrete

Step-by-step explanation:

Given the information:

=>The volume of concrete darryl need for the highest stair is:

The volume of the staircase - the volume of the lowest stair -  the volume of middle stair

= 34 -  3 - 6

= 25 cubic feet of concrete

Hope it will find you well.

Answer:

Step-by-step explanation:

Answer:

Point Form:

( − 2 , 3 )

Equation Form:

x  =  − 2 ,  y  =  3

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Answer:

x = -2, y = 3

Step-by-step explanation:

x + 3y = 7

2x + 4y = 8

Make the x term the same for both equations by multiplying the first equation by 2.

Now you have two equations with the same x terms.

2x + 6y = 14

2x + 4y = 8

Take the larger equation from the smaller to remove the x terms from the equations.

2x + 6y = 14

                   -

2x + 4y = 8

2y = 6

y = 3

Put the known y term back into the equations to find the y term

3(3) + x = 7

9 + x = 7, x = -2

12 + 2x = 8

2x = -4, x = -2

Answer:

The value of x is 42°.

Step-by-step explanation:

Given AB and BC are perpendicular lines which means that AB is 90° to BC. So in order to find the value of x, you have to substract 24° and 24° from 90° :

[tex]24° + x + 24° = 90°[/tex]

[tex]x = 90° - 24° - 24°[/tex]

[tex]x = 42°[/tex]

The total surface area of the composite figure will be 134 square units.

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]

That ∑ sign shows "sum"

We are given that;

The dimensions of figure

Now,

The area of the shared face is already calculated as 20 square units. So, to find the total surface area, we subtract this from the sum of the surface areas:

TSA=(60+94)−20

TSA=154−20

TSA=134

Therefore, the area of the figure will be 134 square units.

Learn more about area of a composite figure here:

https://brainly.com/question/10254615

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Answer: The face that is shared with the rectangular prism is

✔ 2(5)

.

The area of each base of the rectangular prism is

✔ 10

square units.

The lateral area (excluding the shared face) for the rectangular prism is

✔ 18

square units.

The total surface area of the composite figure will be

✔ 66

square units.

Step-by-step explanation:

Answer:

x = -31

Step-by-step explanation:

x-19=2x+12

Subtract x from each side

x-x-19=2x-x+12

-19 = x+12

Subtract 12 from each side

-19-12=x+12-12

-31 =x

Answer:

The length of the equal side is 27 meters each and that of the unequal side is 36 meters

Step-by-step explanation:

An isosceles triangle is a triangle with two sides being equal (also two equal base angles).

Let us assume the length of the two equal sides to be x meters each, and the length of the unequal side to be y meter. Since the perimeter of the triangle is 90 m, it can be expressed as:

x + x + y = 90

2x + y = 90

But the length of the equal side is  three fourth of the unequal side, i.e x = 3/4y

Therefore:

2(3/4y) + y = 90

3/2y + y = 90

2.5y = 90

y = 90/2.5

y = 36 meters

Also x = 3/4 * 36 = 27 meters

The length of the equal side is 27 meters each and that of the unequal side is 36 meters

Answer:

[tex] 2.226 \times {10}^{8} [/tex]

Step-by-step explanation:

[tex](5.3 \times {10}^{4} )(4.2 \times {10}^{3} ) \\ = 5.3 \times 4.2 \times {10}^{4 + 3} \\ = 22.26 \times {10}^{7} \\ = 2.226 \times {10}^{8} [/tex]

Answer:C

Step-by-step explanation: