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2 years ago

13 If B is the midpoint of AC, and AC = 8x – 20, find BC. 3x-1 А в

Mathematics

1 answer:

Papessa [141]2 years ago

7 0

Answer:

BC = 26

Step-by-step explanation:

Given that:

B is the midpoint of AC

Then AC = AB + BC

AC = 8x - 20 and AB = 3x - 1

Then,

8x - 20 = (3x - 1) + BC

8x - 20 - (3x - 1) = BC

8x - 20 - 3x + 1 = BC

5x - 19 = BC

But AB = BC

5x - 19 = 3x - 1

5x - 3x = - 1 + 19

2x = 18

x = 9

Hence,

Since BC = AB = 3x - 1

3(9) - 1

27 - 1

= 26

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: The You Move It Company (YMI) advertises that the cost to rent a moving truck for one day is $40 plus $1.99 for each mile the

mars1129 [50]

Part A: For 100 miles, the cost will be same for both companies.

Part B: Alex should use Drive and Move company as it will cost him less money.

Step-by-step explanation:

Given,

Starting amount of YMI= $40

Per mile charges = $1.99

Let,

x be the number of miles.

y be the total charges.

y = 1.99x+40 Eqn 1

Starting amount of DM = $60

Per mile charges = $1.79

y=1.79x+60 Eqn 2

Part A:

For same charges;

Eqn 1 = Eqn 2

$1.99x+40=1.79x+60\\1.99x-1.79x=60-40\\0.20x=20$

Dividing both sides by 0.20

$\frac{0.20x}{0.20}=\frac{20}{0.20}\\x=100$

For 100 miles, the cost will be same for both companies.

Part B:

Total miles = x = 150

Putting x=150 in Eqn 1

y=1.99(150)+40

y=298.5+40

y=$338.50

Putting x=150 in Eqn 2

y=1.79(150)+60

y=268.5+60

y=$328.50

Alex should use Drive and Move company as it will cost him less money.

4 0

2 years ago

Find a right triangle that has legs with your irrational Lengths and a hypotenuse with a rational Length

cluponka [151]

gg easy

the legs of a triangle are related as $a^2+b^2=c^2$ wehre a, b, and c are the legs and the hypotonuse of a triangle respectively

let's find some stuff

one easy way is to find a rational value for c find values of a and b

lets pick c=5

$a^2+b^2=5^2$

$a^2+b^2=25$

now split up 25 into 2 things that don't have rational square roots

if we say $a^2=19$ and $b^2=6$ then we get

$a=\sqrt{19}$ and $b=\sqrt{6}$ (which are both irrational)

4 0

2 years ago

Seams Personal advertises on its website that 95% of customer orders are received within four working days. They performed an au

Bezzdna [24]

Answer:

a. Yes(n=500>=5, n(1-p)=25>=5)

b. 0.15241

Step-by-step explanation:

a. A normal approximation to the binomial can be used $n\geq$ 5 and n(1-p)>=5:

#We calculate our p as follows:

$\hat p$ =x/n=470/500=0.94

n=500

n(1-p)=500(1-0.95)=25

Hence, we can use the normal approximation.

b. This is a normal approximation.

-Given that p=0.95(95%)

-We verify if our distribution can be approximated to a normal:

$np=0.95\times 500=475\\n(1-p)=500(1-0.95)=25\\\\np\geq 5,\ n(1-p)\geq 5$

Hence, we can use the normal approximation of the form:

$P_{bin}(k,n,p)->N(\mu,\sigma^2)\left \{ {{\mu=np=475} \atop {\sigma=\sqrt{np(1-p)}=4.8734}} \right. \\\\\\P_{bin}(k\leq 470)\approx P_{norm}(x\leq 470.5)=P_{norm}(z\leq \frac{470-475}{4.8734})\\\\P_{norm}(z\leq -1.0260)=0.15241$

Hence, the probability of the sample proportion is the same as the proportion of the sample found is 0.15241

3 0

2 years ago

A researcher wants to estimate the mean weekly family expenditure on clothing purchases and maintenance. First, she needs to det

Blizzard [7]

Answer: C. 461

Step-by-step explanation:

We know that the formula to find the sample size is given by :-

$n=(\dfrac{z^*\cdot \sigma}{E})^2$

, where $\sigma$ = Population standard deviation from prior study.

E = margin of error.

z* = Critical value.

As per given , we have

$\sigma=125$

E= 15

Significance level : $\alpha=0.01$

Critical value (Two tailed)= $z^*=z_{\alpha/2}=z_{0.005}=2.576$

Now , Required sample size = $n=(\dfrac{(2.576)\cdot 125}{15})^2$

$n=(21.4666666667)^2\\\\ n=460.817777779\approx461$ [Round to next integer]

Hence, the required sample size to be taken is 461.

Correct answer = C. 461

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2 years ago

Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2

Aleksandr [31]

Given that the x-axis represented the number of small tanks and the y-axis represented the number of large tanks.

Given that his small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner and there are a total of 72 oz of water conditioners available.

The line representing the various combinations of tanks he could put the water conditioner into is given by 2x + 6y = 72.

Since, the manager labeled only the intercepts.

The x-intercept is the value of x when y = 0 and is given by

2x + 6(0) = 72

x = 72 / 2 = 36

Thus, the x-intercept is (36, 0)


The y-intercept is the value of y when x = 0 and is given by

2(0) + 6y = 72

y = 72 / 6 = 12

Thus, the x-intercept is (0, 12)

Therefore, the points labeled by the manager are: (0, 12) and (36, 0)

4 0

2 years ago