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s2008m [1.1K]
3 years ago
15

A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ŷ = 50,000 − 8x The a

bove equation implies that an increase of _____. a. $8 in price is associated with an increase of $8,000 in sales b. $1 in price is associated with a decrease of $8,000 in sales c. $1 in price is associated with a decrease of $42,000 in sales d. $1 in price is associated with a decrease of $8 in sales
Mathematics
1 answer:
andrew-mc [135]3 years ago
8 0

Answer:

b. $1 in price is associated with a decrease of $8,000 in sales

Step-by-step explanation:

Linear function:

A linear function has the following format:

y = mx + b

In which m is the slope, which represents by how much y changes when x changes by 1.

ŷ = 50,000 − 8x

This means that m = -8, in thousands of dollars, so when the price x increases by 1, the sales will be decrease by $8,000, and thus, the correct answer is given by option b.

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Linda's penny bank is 2/3 full. After she removes 80 pennies, it is 1/2 full. How many pennies can Linda's bank hold?
Ksju [112]
Let x = the total number of pennies her piggy bank can hold.
Then 2/3x = the number of pennies she started with
Then 2/3x - 80 = the number of pennies she has left after taking out 80 pennies.
Then 1/2x = the number of pennies she has left after taking out 80 pennies.
Build the equation.

2/3x - 80 = 1/2x

Subtract 1/2x from each side of the equation.

(2/3x - 80) - 1/2x = 1/2x - 1/2x

1/6x - 80 = 0

Add 80 to both sides of the equation.

(1/6x - 80) + 80 = 0 + 80

1/6x = 80

Divide both sides by 1/6.

(1/6x) / 1/6 = 80 / 1/6

x = 480

So, Linda's piggy bank can hold 480 pennies!

8 0
3 years ago
CAN SOMEONE PLEASE HELP ME ASAP! (SHOW YOUR WORK)
Sergio039 [100]

Answer:

Step-by-step explanation:

-5/3 + -5/4

-50/12 + -15/12 = -65/12 = -5 5/12

4 0
2 years ago
Read 2 more answers
N is an integer<br> write down all the possible values of n<br><br> -2≤n&lt;5
melisa1 [442]

Answer:

-2, -1, 0, 1, 2, 3, 4

Step-by-step explanation:

The number has to be smaller than 5 but greater than or equal to - 2

8 0
3 years ago
Read 2 more answers
What is the relative maximum and minimum of the function?
nevsk [136]
Take the derivitive
f'(x)=3x^2+12x
find where it equals zero
it equal zero at x=0 and x=-4
find the y values
f(0)=-36
f(-4)=-4
the critical points are (0,-36) and (-4,-4)

make sign chart
evalutat f'(x) at x=-5 and x=-1 and x=1, and see their signs
f'(-5)=(+)
f'(-1)=(-)
f'(1)=(+)
see below attachment

max is where sign changes from (+) to (-)
min is where sign changes from (-) to (+)

so
max at (-4,-4)
min at (0,-36)
none of the options are correct, do you have te right problem?

8 0
3 years ago
1) The two triangles are congruent. Find the missing side lengths and the missing angle measures.
gregori [183]

<u>Answers:</u>


Two <u>triangles are congruent</u> if they have the <u>same sides</u> and the <u>same size</u>.

In other words: they have the same shape and size, regardless of their position or orientation.



If we want to verify if two triangles are congruent, they must fulfill some conditions:


a) Two triangles are congruent if their three sides are respectively equal



b) Two triangles are congruent if two of their sides and the angle between them are respectively of equal length.



c) Two triangles are congruent if they have a congruent side and the angles with vertex at the ends of that side are also congruent.  


d) Two triangles are congruent if they have two sides respectively congruent and the angles opposite the greater of the sides are also congruent



<h2>According to these criteria, it is not necessary to verify the congruence of the three sides and three angles of each triangle </h2>

Now, knowing these criteria, let’s answer the questions:



1) Here both triangles are<u> congruent</u> and are <u>Right Triangles</u> (have a right angle or a 90\º angle), as well.



This means angle u=90\º and according to the <u>criterion b</u> listed above, the angle t=35\º and angle v=55\º.



This can be proven by the rule that states the sum of the three interior angles of a triangle is 180\º.



Then, according <u>criterion a</u>, w=10.4m and s=6m.



<u>This can be proven by the use of </u><u>two trigonometric functions,</u>  sine and cosine:


<h2>sin(35\º)=\frac{6m}{w}    (1) </h2>

w=\frac{6m}{sin(35\º)}=10.4m    




Where  6m is the <u>Opposite side</u> to the 35\º angle and w is the <u>hypotenuse</u>.




<h2>cos(55\º)=\frac{s}{10.4m}    (2) </h2>

s=cos(55\º)(10.4m)=5.9m≅6m   




Where  s is the <u>Adjacent side</u> to the 55\º angle and 10.4m is the <u>hypotenuse</u>.



<h2>Therefore, the answer is B: </h2>

s=6m, t=35\º, u=90\º, v=55\º, w=10.4m



2) According to the second figure shown, both triangles are congruent and fulfill the four criteria described above.

Therefore, the answer is:


<h2>CBA≅MPN</h2>

3) “Knowing that line segment AB is the same length as line segment CD is enough to prove that triangles ABD and BCD are congruent”



This statement is <u>True</u>, because <u>both triangles share the line segment BD</u>.

<h2>This means <u>they have two equal sides</u>, and according to <u>criterion b</u> they are congruent  </h2>




6 0
3 years ago
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