How many triangles can be constructed with sides measuring 6 cm, 2 cm, and 7 cm?

Sharon Bernstein rents an apartment for $1,110 a month. She has these annual expenses: electricity, $980; gas, $1,100; phone/cab

sweet-ann [11.9K]

Answer:

Annual expenses INCLUDING cost of annual rent: = $17,597

Annual expenses EXCLUDING cost of annual rent: = $4,277

Step-by-step explanation:

Annual expenses EXCLUDING cost of annual rent:

Electricity = $980

Gas = $1,100 Phone/cable/Internet = $2,100

Insurance = $45

Lost interest = $52

Total = $980 + $1,100 + $2,100 + $45 + $52

= $4,277

Annual expenses EXCLUDING cost of annual rent: = $4,277

Annual expenses INCLUDING cost of annual rent:

Rent = $1,110 per month

Annual rent = $1,110 per month × 12

= $13,320

Electricity = $980

Gas = $1,100 Phone/cable/Internet = $2,100

Insurance = $45

Lost interest = $52

Total = $13,320 + $980 + $1,100 + $2,100 + $45 + $52

= $17,597

Annual expenses INCLUDING cost of annual rent: = $17,597

5 0

3 years ago

A group of students are planning a mural at a wall the rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning

zvonat [6]

Answer: $46x^2+73x+15$

Step-by-step explanation:

The area of a rectangle can be calculated with the formula:

$A=lw$

l: the length of the rectangle.

w: the width of the rectangle.

The area of the remaning wall after the mural has been painted, will be the difference of the area of the wall and the area of the mural.

Knowing that the dimensions of the wall are $(6x+7)$ by $(8x+5)$ , its area is:

$A_w=(6x+7)(8x+5)\\\\A_w=48x^2+30x+56x+35\\\\A_w=48x^2+86x+35$

As they are planning that the dimensions of the mural be $(x+4)$ by $(2x+5)$ , its area is:

$A_m=(x+4)(2x+5)\\\\A_m=2x^2+5x+8x+20\\\\A_m=2x^2+13x+20$

Then the area of the remaining wall after the mural has been painted is:

$A_{(remaining)}=A_w-A_m\\\\A_{(remaining)}=48x^2+86x+35-(2x^2+13x+20)\\\\A_{(remaining)}=48x^2+86x+35-2x^2-13x-20\\\\A_{(remaining)}=46x^2+73x+15$

8 0

4 years ago

Andre says 10x + 6 and 5x + 11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?

Serga [27]

Answer:

No, They are not equivalent

Step-by-step explanation:

The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.

The variable in this question is x.

To prove this, we equate both expressions:

$10x + 6 = 5x + 11$

$10x - 5x = 11 - 6\\\\\\5x = 5\\\\\\x = 1$

This shows that they have the same value ONLY when x is 1.

This is why Andre says that they are equivalent, but they are not.

8 0

3 years ago

An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From pre

Shtirlitz [24]

Answer:

Null Hypothesis, $H_0$ : $\mu \leq$ 250 W

Alternate Hypothesis, $H_A$ : $\mu$ > 250 W

Step-by-step explanation:

We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Let $\mu$ = mean power consumption of microwave ovens.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 250 W

Alternate Hypothesis, $H_A$ : $\mu$ > 250 W

Here, null hypothesis states that the mean power consumption of microwave ovens is no more than 250 W.

On the other hand, alternate hypothesis sates that the mean power consumption of microwave ovens is more than 250 W.

The test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.

5 0

3 years ago

Jack wants to buy a pair of trousers for 60$ when he went to the store he found that the price was marked down by 20% how much d

Lemur [1.5K]

$48 (because you would do $60•0.20=$12 so then you would do $60-$12=$48)

3 0

3 years ago