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2 years ago

6

Teo makes a necklace of x wooden beads at $0.50 each and 6 glass beads at $1.25 each. The average cost of the beads in the neckl

ace is $0.75. Write an equation to model the situation.

1 answer:

Ainat [17]2 years ago

4 0

Answer:

0.50x + 7.50 = 0.75(x+6)

Hope this helps :)

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PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

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Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

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What is the quotient of StartStartFraction 90 (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 En

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Answer:

The answer is C

Step-by-step explanation:

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2 years ago

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∆ABC has vertices at A(12, 8), B(4, 8), and C(4, 14). ∆XYZ has vertices at X(6, 6), Y(4, 12), and Z(10, 14). ∆MNO has vertices a

koban [17]

To get the length of each side,
use the distance formula with equation:
Distance = ((x2-x1)^2+(y2-y1)^2)^0.5
Solving
<span>AB = 8 units   BC = 6 units AC = 10 units
</span><span>MN =8units    NO = 6 units MO = 10 units
</span><span>XY = 6.32 units   YZ = 6.32 units XZ = 8.94 units
</span>JK = 4.47 units    KL = 4.47 units JL = 6 units

1 The right answer is the letter b) triangle ABC and Triangle MNO are Congruent <span>triangles
ABC and MNO are triangles that have the same lengths of its three sides.

</span>2 The answer is the letter c) rotation
There is a rotation of 90º about ABC and MNO the origin is B=N
B=N
C----------O
A----------M

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A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table

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Answer: is D

Visit Dentist Yearly Don’t Visit Dentist Yearly

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Above 40 0.57 0.43

Work: 8+22=30 17+13=30 turn into a fraction then simplify to get answer;

22/30 simp= 73.0 (0.73)

13/30 simp= 43.0 (0.43)

8/30 simp= 26.667 (0.27)

17/30 simp= 56.667 (0.57)

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2 years ago

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From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electri

Leviafan [203]

Answer:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=201.77$ represent the sample mean

$s=2.41$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =200$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :

Null hypothesis: $\mu = 200$

Alternative hypothesis: $\mu = 200$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic is given by:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

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2 years ago