A savings account balance can be modeled by the graph of the linear function shown on the grid. What is the rate of change of the balance with respect to the number of deposits?
(A. $25 per deposit
(B. $50 per deposit
(C. $75 per deposit
(D. $125 per deposit

Given:

Principal = R573.00

Rate of interest = 9.3% annually

Time = 15 years.

To find:

The amount after 15 years.

Solution:

Formula for amount is:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is principal, r is the rate of interest in decimal, n is the number of time interest compounded in an year and t be the number of years.

The interest is compounded annually, so n=1.

Putting [tex]P=573,r=0.093,n=1,t=15[/tex] in the above formula, we get

[tex]A=573\left(1+\dfrac{0.093}{1}\right)^{1(15)}[/tex]

[tex]A=573\left(1+0.093\right)^{15}[/tex]

[tex]A=573\left(1.093\right)^{15}[/tex]

[tex]A=2174.98893[/tex]

[tex]A\approx 2174.99[/tex]

Therefore, the amount in the account after 15 years is about  R2174.99.

Given:

The term is 7a.

To find:

The coefficient of "a" in the given term "7a"​.

Solution:

In the product of a number and a variable, the number is called the coefficient of that variable.

In the expression "7a", the number is "7" and the variable is "a". It means the number 7 is the coefficient of "a".

Therefore, the coefficient of "a" in the given term "7a" is 7​.

Answer:

Area = 406

Step-by-step explanation:

First things first: Divide the shape

Here is how I did it:

21 x 16

14 x 5

Now solve:

21 x 16 = 336

14 x 5 = 70

Now add:

336 + 70 = 406

So the area is 406

Answer:

1. 144.4 m²

2. 120 m³

Step-by-step explanation:

The figure is composed of a triangular prism and a rectangular prism

1. Surface area of the composite figure = (surface area of the triangular prism - area of the face joining the rectangular prism) + (surface area of the rectangular prism - the face joining the triangular prism)

✔️Surface area of the triangular prism = bh + (s1 + s2 + s3)*L

b = 5 m

h = 2 m

s1 = 3.2 m

s2 = 3.2 m

s3 = 5 m

L = 6 m

Plug in the values

Surface area of triangular prism = 5*2 + (3.2 + 3.2 + 5)*6

= 10 + (11.4)*6

= 78.4 m²

✔️Area of rectangular prism = 2(LW + LH + WH)

L = 6 m

W = 5 m

H = 3 m

Plug in the values

Area of rectangular prism = 2(6*5 + 6*3 + 5*3)

= 126 m²

✔️Area of the face joining both figures = L*W

L = 6 m

W = 5 m

Area = 6*5 = 30 m²

✅Surface area of the composite figure = (78.4 - 30) + (126 - 30)

= 48.4 + 96

= 144.4 m²

2. Volume of composite figure = volume of triangular prism + volume of rectangular prism

= ½*a*c*h + L*W*H

a = 2 m

c = 5 m

h = 6 m

L = 6 m

W = 5 m

H = 3 m

Plug in the values

Volume = ½*2*5*6 + 6*5*3

Volume = 30 + 90 = 120 m³

Answer:

yes this option is correct

Answer:

The number of minutes since Luke started driving from his house to his distance from the house is 40 minutes. :)

Step-by-step explanation:

Answer:

(a+b)(a-b)

Step-by-step explanation:

Answer: subtract 22 on both sides

Step-by-step explanation:

Now you would have -5 to solve take 3 and multiply on both sides to get f=-15

Hope this helps

Answer: -5

Step-by-step explanation:

Answer:

It is correct.

Step-by-step explanation:

Answer:

[tex]a + b + c = \pi \\ = > c= \pi - a - b \\ < = > \tan(c) = \tan(\pi - a - b) = -\tan(a + b) [/tex]

Step-by-step explanation:

we have:

[tex] \tan(a) + \tan(b) + \tan(c) \\ = \tan(a) + \tan(b) - \tan(a + b) \\ = \tan( a) + \tan(b) - \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{ ( \tan(a) + \tan(b) ) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (1)[/tex]

we also have:

[tex] \tan(a) \tan(b) \tan(c) \\ = - \tan(a) \tan(b) \tan(a + b) \\ = \frac{ -(\tan( a ) + \tan(b) ) \tan(a) \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{( \tan(a) + \tan(b)) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (2)[/tex]

from (1)(2) => proven

Answer:

3215 .36 m³ is the required volume.

Step-by-step explanation:

Base area of Cylinder = 64π m²

Height of cylinder is equal to twice the radius .

As we know that ,

★Base Area of Cylinder = πr²

where,

π is taken as 22/7 or 3.14

r is the radius of cylinder

Substitute the value we get

↝ 64 π = πr²

↝ 64 = r²

↝ √64 = r

↝ 8 = r

↝ r = 8 m

Now, it is given that height is equal to twice of radius

Therefore ,

height = 2r = 2×8 = 16 m

★Volume of Cylinder = πr²h

substitute the value we get

↝ volume of Cylinder = 3.14 × 8² × 16

↝volume of Cylinder = 3.14 × 64 × 16

↝volume of Cylinder = 3215 .36 m²

Hence, the required volume of cylinder is 3215 .36 m³.

Answer:

3217.0

Step-by-step explanation:

Answer: 2*5^2-12

5 to the 2nd power is 25

2*25-12

2*25=50

50-12=38

the answer is C 38

hope this helps

Answer:0.51 I just took the test

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

37 is greater than five and the next number with a zero would be 40

Answer:

16 cups a day

Step-by-step explanation:

Answer:

Prime

Step-by-step explanation:

2(x?)+16y

O(x+4y)(x+4y)

x²+4xy+4xy+16y²

x²+8xy+16y²

O(x+4y)(x-4y)

x²-4xy+4xy-16y²

x²-16y

Prime

O(x-4y)(x-4y)

x²-4xy-4xy+16y²

x²-8xy+16y²

All are incorrect except prime, so the answer is prime.

---

hope it helps

Answer:

124 would be the volume............ but I don't see that

Answer:

because l1//l2 => z + 65 = 180

y + 65 = 90

x + 65 = 90

<=> z = 115

y = 25

x = 25

Answer:

x=25

y=25

z=115

Step-by-step explanation:

x congruent to y

180-90-65=25

180-65=115

Answer:

Step-by-step explanation:

8

Answer:

x = -41

y = 9

Step-by-step explanation:

Begin by multiplying the top equation by 2

2x = -8y - 10

The second equation requires a little more care.

Start by moving 10y to the right. Normally the y value is on the left, but we are going to be substituting for 2x.

2x = - 10y + 8

What I've done is not the usual practice, but there is nothing wrong with it.

Now since both right sides are equal to 2x, you can substitute for them

-8y - 10 = -10y + 8                Add 10y to both sides

-8y + 10y - 10 = 8

2y - 10 = 8                           Add 10 to both sides

2y = 8+10

2y = 18                                 Divide by 2

y = 18/2

y = 9

Use the second original equation to solve for x

2x + 10y = 8

2x + 10*9 = 8                    

2x + 90 = 8                         Subtract 20 from both sides

2x = 8 - 90

2x =  - 82                              Divide by 2

x = -822/2

x = - 41

Answer:

5.76 units

Step-by-step explanation:

Length of arc EG = central angle/360 × 2πr

Where,

central angle = 30°

radius (r) = 11 units

Plug in the values into the formula

Length of arc EG = 30/360 × 2 × π × 11

Length or arc EG ≈ 5.76 units (to nearest hundredth)

Answer:

The data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles

Step-by-step explanation:

Formulate the null and alternate hypothesis as

H0: u1= u2  against the claim Ha: u1≠ u2

The data given is

y`1=118,    y`2=109     s21=102,   s22=87

The test statistic used is t= y1`- y2`/ Sp√1/n1+ 1/n2

n1= n2= 64

And

Sp² = (n1-1) s12 + (n2-1) s22 / n1+n2-2

Sp² = 63*102+6*87/64+64-2

Sp² = 94.5

Sp= 9.7211

Putting the values in the test statistic

t= 118-108/9.7211√1/64+1/64

t= 5.237

Now finding the value of t at ∝=0.01 for two tailed test

t( 126,0.005)= ±2.6154

At alpha= 0.01  the null hypothesis is rejected.

Now finding the value of t at ∝=0.05 for two tailed test

t( 126,0.025)= ±1.979

Even at alpha= 0.05 the null hypothesis is rejected.

Also at alpha= 0.05 the null hypothesis is rejected because the critical value is  ±1.657

Hence it is concluded that the data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles

Answer:

x=3.33

Step-by-step explanation:

2x=x-10

2x+x=10

3x=10

x= 10/3

x= 3.33

Answer:

5,000+6,000+7,000+,9,000+6,000+5,000= 38,000

Step-by-step explanation:

The minimum cost of meeting the demands of the next six months is $7475.00.

Here, we have,

To determine how to minimize the cost of meeting the demands of the next six months, we need to create a production and workforce plan that balances the demand for shoes with the available workforce and inventory.

Let's break down the problem into several steps:

Step 1: Calculate the regular production capacity and overtime capacity:

Regular production capacity: Number of regular working hours per month divided by the time it takes to produce a pair of shoes.

Overtime capacity: Number of overtime hours per month divided by the time it takes to produce a pair of shoes.

Given:

Regular working hours per month: 150 hours

Overtime hours per month: 40 hours

Time to produce a pair of shoes: 20 minutes (1/3 of an hour)

Regular production capacity = 150 hours / (1/3 hour) = 450 pairs per month

Overtime capacity = 40 hours / (1/3 hour) = 120 pairs per month

Step 2: Create a monthly production plan:

We will use the regular production capacity, overtime capacity, and inventory to fulfill the demand for each month.

Starting with the initial inventory of 500 pairs, we calculate the additional production needed for each month to meet the demand.

Month 1:

Demand: 5000 pairs

Additional production needed: 5000 - 500 = 4500 pairs

Month 2:

Demand: 6000 pairs

Additional production needed: 6000 - (500 + 4500) = 1000 pairs

Month 3:

Demand: 7000 pairs

Additional production needed: 7000 - (500 + 4500 + 1000) = 1000 pairs

Month 4:

Demand: 9000 pairs

Additional production needed: 9000 - (500 + 4500 + 1000 + 1000) = 2000 pairs

Month 5:

Demand: 6000 pairs

Additional production needed: 6000 - (500 + 4500 + 1000 + 1000 + 2000) = 0 pairs

Month 6:

Demand: 5000 pairs

Additional production needed: 5000 - (500 + 4500 + 1000 + 1000 + 2000) = 0 pairs

Step 3: Determine the hiring and firing decisions:

To minimize costs, we need to hire or fire workers based on the additional production needed for each month.

Based on the calculations from Step 2, we can identify the following hiring and firing decisions:

Month 1:

Additional production needed: 4500 pairs

Hire 5 workers (cost: 5 * $1000 = $5000)

Month 2:

Additional production needed: 1000 pairs

No hiring or firing needed (as the existing workforce can handle it)

Month 3:

Additional production needed: 1000 pairs

No hiring or firing needed

Month 4:

Additional production needed: 2000 pairs

No hiring or firing needed

Month 5:

Additional production needed: 0 pairs

No hiring or firing needed

Month 6:

Additional production needed: 0 pairs

No hiring or firing needed

Step 4: Calculate the costs:

Now, we can calculate the costs associated with hiring, firing, and production.

Hiring cost: $5000 (Month 1)

Firing cost: $0 (No firing needed)

Holding cost: 5% of the cost to produce a pair of shoes with regular-time labor, multiplied by the inventory at the beginning of each month.

Holding cost for Month 1: 0 (no inventory at the beginning of Month 1)

Holding cost for Month 2: 0.05 * ($2000 + 4500 * $10) = $237.50

Holding cost for Month 3: 0.05 * ($2000 + 5500 * $10) = $297.50

Holding cost for Month 4: 0.05 * ($2000 + 7500 * $10) = $475.00

Holding cost for Month 5: 0.05 * ($2000 + 7500 * $10) = $475.00

Holding cost for Month 6: 0.05 * ($2000 + 7500 * $10) = $475.00

Total cost:

Total cost = Hiring cost + Firing cost + Holding cost

= $5000 + $0 + ($237.50 + $297.50 + $475.00 + $475.00 + $475.00)

= $7475.00

Therefore, the minimum cost of meeting the demands of the next six months is $7475.00.

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Answer:

B (5; 13)

Step-by-step explanation:

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

Bx - 1 = 4

Bx = 5

Midpoint (y) = (-3 + By)/2 = 5

By - 3 = 10

By = 13

B (5; 13)

Answer:

C=54°

Step-by-step explanation:

If u add each angle of a triangle should ways add up to 180°