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4 years ago

9

Your baseball team has 16 players. Use the Distributive Property to write and simplify an expression for the total cost of buyin

g the items shown for all the players.

2 answers:

liq [111]4 years ago

8 0

Answer:

<h2>D. $16(12+4+x)$ </h2>

Step-by-step explanation:

The correct answer is $16(12+4+x)$ , because this express the total cost of all players.

We know that there are 16 players, and each of them have to spend $12 for a Jersey, $4 for a pair of socks and $x for a hat. So, to express this mathematically, we have to sum this three costs sixteen times. However, if we consider the operation of multiplications and the distributive property, we can summarize the procedure.

Then, the expression would be:

$16(12+4+x)$

Because, we have to multiply the total player (16) to the total cost (12+4+x).

Viktor [21]4 years ago

5 0

Answer:

I think the answer is TC = 16 * cost of buying of 1 item

Step-by-step explanation:

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Let $A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$. There exists a point $X$ and a constant $k$ such that for any point $P$,

goldfiish [28.3K]

Answer:

k=32

Step-by-step explanation:

Given the points:

$A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$.$

The first step is to find the <u>Centroid</u> of the triangle.

Centroid, X

$=\left(\dfrac{x_1+x_2+x_3}{3} ,\dfrac{y_1+y_2+y_3}{3} \right)\\=\left(\dfrac{4+6+(-1)}{3} ,\dfrac{-1+2+2}{3} \right)\\=\left(\dfrac{9}{3} ,\dfrac{3}{3} \right)=(3,1)$

Next, let P be a point (x,y)

Using the <u>distance formula, </u> $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ <u />

<u /> $PA^2=(x-4)^2+(y-(-1))^2\\PB^2=(x-6)^2+(y-2)^2\\PC^2=(x-(-1))^2+(y-2)^2\\PX^2=(x-3)^2+(y-1)^2\\$ <u />

On Substitution into: $PA^2 + PB^2 + PC^2 = 3PX^2 + k$

$(x-4)^2+(y-(-1))^2+(x-6)^2+(y-2)^2+(x-(-1))^2+(y-2)^2=3[(x-3)^2+(y-1)^2]+k$

Let us simplify the LHS first

$\\LHS: x^2-8x+16+y^2+2y+1+x^2-12x+36+y^2\\-4y+4+x^2+2x+1+y^2-4y+4\\=3x^2-18x+3y^2-6y+62$

Also, the Right Hand Side

$RHS:3[(x-3)^2+(y-1)^2]+k\\=3[x^2-6x+9+y^2-2y+1]+k\\=3x^2-18x+27+3y^2-6y+3+k\\=3x^2+3y^2-18x-6y+30+k$

Therefore:

$3x^2-18x+3y^2-6y+62=3x^2+3y^2-18x-6y+30+k\\k=3x^2-18x+3y^2-6y+62-3x^2-3y^2+18x+6y-30\\k=3x^2-3x^2+3y^2-3y^2-18x+18x+62-30\\k=32$

7 0

3 years ago

Quadrilateral ABCD has diagonals that are congruent and perpendicular to each other. What classification can be given to ABCD? (

Anuta_ua [19.1K]

The answer to ur question will be a square since all diagonals are congruent and bisect each other at right angles
Note:'this is not applicable for the other quadrilaterals from the given options'
Hope this helps u..!!!
Good luck!

8 0

3 years ago

Suppose that the speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles p

denis23 [38]

Answer:

A) $X \sim N(68 , 25)$

B) the probability that is traveling more than 70 mph is 0.3446

C) the probability that it is traveling between 65 and 75 mph is 0.6449

D) 90% of all cars travel at least 56.85 mph fast on the freeway

Step-by-step explanation:

The speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles per hour.

Mean = $\mu = 68 mph$

Standard deviation = $\sigma = 5 mph$

A) X ~ N( _____, _______ )

In general $X \sim N( \mu , \sigma^2)$

$\mu = 68 mph$

$\sigma = 5 mph$

$\sigma^2 = 5^2 = 25$

So, $X \sim N(68 , 25)$

B) If one car is randomly chosen, find the probability that is traveling more than 70 mph.i.e.P(X>70)

So, $Z = \frac{x-\mu}{\sigma}\\Z=\frac{70-68}{5}$

Z=0.4

Using Z table

P(Z>70)=1-P(Z<70)=1-0.6554=0.3446

Hence the probability that is traveling more than 70 mph is 0.3446

C) If one of the cars is randomly chosen, find the probability that it is traveling between 65 and 75 mph.

P(65<X<75)

$Z = \frac{x-\mu}{\sigma}$

AT x = 65

$Z=\frac{65-68}{5}$

Z=-0.6

AT x = 75

$Z=\frac{75-68}{5}$

Z=1.4

Using Z table

P(65<X<75)=P(-0.6<Z<1.4)=P(Z<1.4)-P(Z<-0.6)=0.9192-0.2743=0.6449

Hence the probability that it is traveling between 65 and 75 mph is 0.6449

D)90% of all cars travel at least how fast on the freeway?

Since we are supposed to find at least how fast on the freeway

So,P(X>x)=0.9

1-P(X<x)=0.9

1-0.9=P(X<x)

0.1=P(X<x)

Z value at 10% =-2.23

So, $Z=\frac{x-\mu}{\sigma}\\-2.23=\frac{x-68}{5}\\-2.23 \times 5 =x-68\\(-2.23 \times 5)+68=x$

56.85 = x

Hence 90% of all cars travel at least 56.85 mph fast on the freeway

8 0

3 years ago

Can you pls help me find the slope when the coordinates are (2,3) and (4,1)

mezya [45]

The slope is -1.

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment

3 0

3 years ago

Read 2 more answers

Determine equation of a line passing through a point (5,-3) with and undefined slope

avanturin [10]

Slope is calculate using the following equation:
slope = (y2-y1) / (x2-x1)
since the slope is undefined, therefore, the denominator is equal to zero, which means that x2 = x1.

Based on this, the only curves with undefined slopes are the curves with equation: x = constant

Therefore, <span>equation of a line passing through a point (5,-3) with and undefined slope is x = 5</span>

5 0

3 years ago