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9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent amounts invested at 6% and 9%, respectively.

  y = 3x +58 . . . . . . . the amount invested at 9%

  0.06x +0.09y = 1097.19 . . . . . . total interest earned

__

Substituting for y, we have ...

  0.06x +0.09(3x +58) = 1097.19

  0.33x + 5.22 = 1097.19 . . . . . . . . . simplify

  0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22

  x = 3309 . . . . . . . . . . . . . . . . divide by 0.33

  y = 3(3309) +58 = 9985

$3309 is invested at 6%; $9985 is invested at 9%.

Answer:

Step-by-step explanation:

5/7

Sum of a geometric series is a/(1-r) = 1/(1-(-2/5)) = 5/7

9514 1404 393

Answer:

  216 in³

Step-by-step explanation:

The ratio of volumes is the 3/2 power of the ratio of areas.

  small volume = ((small area)/(large area))^(3/2) × (large volume)

  = (212/1325)^(3/2) × 3375 in³ = (4/25)^(3/2) × 3375 in³ = (8/125)×3375 in³

  small volume = 216 in³

Answer:

6

Step-by-step explanation:

236/10 = 23 remainder 6, so 6 crayons is the answer

Answer:

6/5 n = a

Step-by-step explanation:

n = 5/6a

Multiply each side by 6/5

6/5 n = 6/5 * 5/6a

6/5 n = a

(8+3)(3+5)=88

88+(39+491)= 618.

88+(9+491)= 588

88+(24+152)= 264.

sorry could not find the last ansswer..

Answer:

60cm

Step-by-step explanation:

12x-10x=120

2x=120

x=60

Answer:

60 cm

Step-by-step explanation:

We know that 12x - 10x = 120.

We simplify that to 2x = 120.

That way, x = 60.

The length of the line is 60 cm.

Answer:

222

Step-by-step explanation:

add 7 no. to each of like 201+7 = 208, 208+7=215 ,215+7=222

(4)^2-3(4)=4Answer:

Step-by-step explanation:

Answer:

B. ⁴/3π(6)³

Step-by-step explanation:

Formula for volume of a sphere = ⁴/3πr³

Where,

radius (r) = 6 units

Plug in the given value into the volume formula

Volume of the sphere = ⁴/3 × π × (6)³

Volume of the sphere = ⁴/3π(6)³

The expression that represents the volume of the given sphere is therefore ⁴/3π(6)³ cubic units.

The expression for the volume of the sphere is:

V = (4/3)*3.14*(6)^3

For a sphere of radius R. the volume is given by:

V = (4/3)*pi*R^3

Where pi = 3.14

Here we know that the radius is 6 units, so we can write the volume as:

V = (4/3)*3.14*(6)^3

As you can see, the second option (counting from the top) is the correct one.

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Answer:

85

Step-by-step explanation:

I hope my answer help you

Answer:

3/2=1.5 sec

Step-by-step explanation:

Equate d=0 and solve the expression, t=-1 and 3/2 but t can't be negative.

The air bubble will reach the surface in 1.5 seconds.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression is d = 3.2(t+1)(2t - 3) where d is the height of the aquarium and t is the time taken by the bubbles to come to the surface.

When the bubble will come to the surface height D becomes zero.

d = 3.2(t+1)(2t - 3)

3.2(t+1)(2t - 3) = 0

t + 1 = 0  and  2t - 3 = 0

t = -1  and t = 3 / 2 = 1.5

Therefore, the air bubble will reach the surface in 1.5 seconds.

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Answer:

A sample of 3851 is required.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of .

That is z with a pvalue of , so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Variance is 5.76 kWh

This means that [tex]\sigma = \sqrt{5.76} = 2.4[/tex]

They would like the estimate to have a maximum error of 0.09 kWh. How large of a sample is required to estimate the mean usage of electricity?

This is n for which M = 0.09. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.09 = 2.327\frac{2.4}{\sqrt{n}}[/tex]

[tex]0.09\sqrt{n} = 2.327*2.4[/tex]

[tex]\sqrt{n} = \frac{2.327*2.4}{0.09}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327*2.4}{0.09})^2[/tex]

[tex]n = 3850.6[/tex]

Rounding up:

A sample of 3851 is required.

Answer:

11/10 is 1 1/10

Step-by-step explanation:

Answer:

63% of all undergraduates receive at least one grant or scholarship.

Step-by-step explanation:

Scholarships and grants, which covered 31% of cost, and parent income and savings, which covered 30%, are the top two sources of funding. The share of cost paid from other resources are 14% from student borrowing, 13% from student income and savings, 10% from parent borrowing, and 2% from friends and family.

Answer:

Step-by-step explanation:

A. Directrix: y = 4-6 = -2

:::::

B. Axis of symmetry: x = 6

Axis of symmetry intersects directrix at (6,-2)

:::::

C . Vertex is halfway between focus and directrix, at (6,1)

:::::

D. The focus lies above the directrix, so the parabola opens upwards.

:::::

E. Focal length p = 1/(4×0.5)

:::::

F. p = 0.5

::::

G. y = 0.5(x-6)² + 1

Answer:

the one above is correct

Step-by-step explanation:

h.We start with a circle and a line that goes through the center of the circle (C) and one vertex of the triangle (E).

Using the point on the line opposite the vertex as a center (D), we draw an arc with the same radius the circle has.

The two points of intersection with the circle are the other two vertices of the inscribed triangle (F, G).

Answer:

the green area stands for the safe operation space

Step-by-step explanation:

u say b×h meaning say 80degrees ×9cm which is 720..

Answer:

x < -5

Step-by-step explanation:

- 2x - 7 > x+ 8

Add 2x to each side

- 2x+2x - 7 > x+2x+ 8

-7 > 3x+8

Subtract 8 from each side

-7-8 > 3x+8-8

-15 > 3x

Divide by 3

-15/3 > 3x/3

-5 >x

x < -5

Answer: $40 / $80

Step-by-step explanation: 40$ if it's $8 for BOTH per hour, or if it's $8 for ONE per hour it's $80

Answer:

C

Step-by-step explanation:

(2+i)-(4-6i)(-3+3i)

=(2+i)-(-12+12i+18i-18i^2)

=(2+i)-[-12+30i-18(-1)]

=(2+i)-(-12+30i+18)

=(2+i)-(30i+6)

=2+i-30i-6

=-4-29i

Answer:

Step-by-step explanation:

We know:

All triangles have internal angles that add up to 180°.

And

All right triangles have acute angles that up to 90°.

Therefore

x + 30° + 90° = 180°

x + 120° = 180°     |subtract 120° from both sides

x + 120° - 120° = 180° - 120°

x + 30° = 90°     |subtract 30° from both sides

x + 30° - 30° = 90° - 30°

The size of angle x will be 60°

It is a plane figure with three straight sides and three angles.

The steps are as follow:

z = 90°

y = 30°

x = ?

∴ x + y + z = 180°

∴ x + 30 + 90 = 180

∴ x + 120 = 180

∴ x = 60°

So the size of angle x will be 60°

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9514 1404 393

Answer:

Step-by-step explanation:

In the transformed function f(x-h), the value of h is the right shift of the parent function.

For h positive, shift is to the right.

For h negative, shift is to the left.

Changing the value of h shifts the graph horizontally. Positive values of h shift the graph to the right. Negative values shift left.

Note: there is a minus sign in front while the value of h is positive, i.e. |x - 5| is shifted 5 units to the right, and |x - (-5)| = |x + 5| is shifted 5 units to the left.

Answer:

D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.

Answer:

[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]

For gradient, differentiate f(x):

[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]

Substitute for x as π:

[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]

Gradient of tangent = -8

[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]

Equation of tangent:

[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]

Answer:

60

Step-by-step explanation:

x² = 144×25

= 3600

x =√3600 =60

Answer:

110592 in³

Step-by-step explanation:

Since baggage should take the shape of a box; with the sum of it's dimension not exceeding 144 ;

Dimensions of a box : length, width, height

If ; l + w + h = 144

Greatest volume is obtained when the dimension is equal : such that l = w = h

Hence, each dimension becomes ; 144 / 3 = 48 in

Volume of box = length * width * height

Volume = 48 * 48 * 48

Volume = 48³ = 110592