CH 7 Forces: pages 294 & 296
Calculate net forces. Draw an arrow to show direction. SC.6.P.13.3
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combined Forces
Net Force
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30 N
70 N
30 N
40 N
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60 N
60 N
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18 N 12 N
30N

Answer:

The value of the test statistic is t = 2.19.

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Sample of 1300 voters:

This means that [tex]n = 1300[/tex]

Found that 45% of the residents favored construction.

This means that [tex]X = 0.45[/tex]

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.

This means that [tex]\mu = 0.42[/tex], and by the Central Limit Theorem:

[tex]\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137[/tex]

So, the test statistic is:

[tex]t = \frac{X - \mu}{s}[/tex]

[tex]t = \frac{0.45 - 0.42}{0.0137}[/tex]

[tex]t = 2.19[/tex]

The value of the test statistic is t = 2.19.

Answer:

Step-by-step explanation:

Taking the determinant of the matrices we will have;

= 4x(5y) - 2x(3y)

= 20xy - 6xy

= 14xy

Given x = -2 and y = 3

Determinant = 14(-2)(3)

Determinant = -28*3

Determinant = -84

Answer:

The new jar is smaller.

Step-by-step explanation:

Like what the statements says, the normal size of coffee is reduced by 1/5 and it become as the new jar which is smaller than the original.

Given:

Purchasing price = 6.1 lakh

Amount spent of repair = 30000

Selling price = 8 lakh

To find:

The gain percentage.

Solution:

We have,

Purchasing price = 6.1 lakh

Amount spent of repair = 30000 = 0.3 lakh

So, total cost price is

[tex]C.P.=6.1+0.3[/tex]

[tex]C.P.=6.4[/tex]

The total cost price is 6.4.

Selling price(S.P.) = 8 lakh

Now,

[tex]Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100[/tex]

[tex]Gain\%=\dfrac{8.0-6.4}{6.4}\times 100[/tex]

[tex]Gain\%=\dfrac{1.6}{6.4}\times 100[/tex]

[tex]Gain\%=\dfrac{1}{4}\times 100[/tex]

[tex]Gain\%=25\%[/tex]

Therefore, the gain percent is 25%.

Question:

[tex]5x-3y=14[/tex]

[tex]3x-5y=2[/tex]

Find x and y

Answer:

[tex]x = 4[/tex]

[tex]y =2[/tex]

Step-by-step explanation:

Given

[tex]5x-3y=14[/tex]  -- (1)

[tex]3x-5y=2[/tex] -- (2)

Required

Find x and y

We'll solve this using elimination method.

Multiply (1) by 3 and (2) by 5 to eliminate x

([tex]5x-3y=14[/tex]) * 3

([tex]3x-5y=2[/tex]) * 5

-------------------------------

[tex]15x - 9y = 42[/tex]

[tex]15x - 25y =10[/tex]

Subtract

[tex]15x - 9y = 42[/tex]

- ([tex]15x - 25y =10[/tex])

-----------------------

[tex]15x - 15x - 9y + 25y = 42 - 10[/tex]

[tex]- 9y + 25y = 42 - 10[/tex]

[tex]16y = 32[/tex]

Make y the subject

[tex]y = \frac{32}{16}[/tex]

[tex]y =2[/tex]

Substitute 2 for y in [tex]5x-3y=14[/tex]

[tex]5x - 3 * 2 = 14[/tex]

[tex]5x - 6 = 14[/tex]

Collect Like Terms

[tex]5x = 14+6[/tex]

[tex]5x = 20[/tex]

Make x the subject

[tex]x = \frac{20}{5}[/tex]

[tex]x = 4[/tex]

Answer:

probability that a rivet is defective is 0.00868

Step-by-step explanation:

given data

rivets = 20

all seam need reworking P = 16% = 0.16

solution

we consider here probability of a defective rivet = p

and 0.16 = P [Seam needs reworking) = P (at least one rivet in the seam is defective)

so that for non-defective = 1 - P [all the rivets are non-defective]

and that will be here as = 1 - P [rivet 1 is non-defective, rivet 2 is non-defective, rivet 3 is non-defective,...............,rivet 20 is non-defective]

= [tex]1 - (p})^{20}[/tex]     ....................1

so

1-0.16 = [tex]1 - (p})^{20}[/tex]

0.84 = [tex]1 - (p})^{20}[/tex]

[tex]0.84^{\frac{1}{20}}[/tex] = 1 - p

solve it we get

p = 0.00868

so, probability that a rivet is defective is 0.00868

Answer:

y=20x+10

Step-by-step explanation:

You start with $10, so this will be added on, and is not affected by the number of months.

You add $20 each month, so the 20 is dependant on x.

ANSWER: y=20x+10

Answer:

C- t=411

Step-by-step explanation:

there is this really cool site/app called

math

way

it helps for everything, just use it

Anwser: First triangle area =0.5*8*10=40 in2. Secound triangle area =0.5*8*6=24 in2 Sum is 1st area + 2nd area, which is 64 in2.

Answer:

$12.49

Step-by-step explanation:

cost of two purses = $57.97 - cost of dress = $57.97 - $32.99 = $24.98

cost of one purse = $24.98 ÷ 2 = $12.49

Answer:

Attached please find answer

Step-by-step explanation:

= (x² + x - 42) / (x - 6)

= [x² + (7x - 6x) - 42] / (x - 6)

= [x² + 7x - 6x - 42] / (x - 6)

= [(x² + 7x) - (6x + 42)] / (x - 6)

= [x(x + 7) - 6(x + 7)] / (x - 6)

= [(x + 7)(x - 6)] / (x - 6)

= x + 7 → when x approches 6

= 6 + 7

= 13

Other method:

Lim   (x² + x - 42) / (x - 6)

x→ 6

When x → 6, there is an indeterminate expression because: 6 - 6 = 0

Do you know the l'Hôpital's rule, when x → a:

Lim [ f(x) / g(x) ] = Lim [ f'(x) / g'(x) ]

f(x) = x² + x - 42

f'(x) = 2x + 1

g(x) = x - 6

g'(x) = 1

= f'(x) / g'(x)

= (2x + 1)/1

= 2x + 1 → when x approches 6

= 12 + 1

= 13

Step-by-step explanation:

Difference of Squares: a² - b² = (a + b)(a - b)

(x² - 16) / (x - 4)

= [(x + 4)(x - 4)] / (x - 4)

= x + 4, where x =/= 4.

Answer:

1.    (x+4)

2.     4

Step-by-step explanation:

got right on edge

Answer:

5/12

Step-by-step explanation:

Probability of getting either heads or tails of a coin : 1/2

Probability of getting 1,2,3,4, or 6 on a dice: 5/6

Multiply those two probabilities : 1/2 * 5/6 = 5/12

You have a 5 out of 12 chances of getting heads on a coin AND any number but a 5 on a dice.

Hope this helps!

Hey there!

[tex]\text{The word \underline{of} means \underline{multiply} in \underline{mathematical terms}}[/tex]

[tex]\bold{Equation: 20\% \times 155}\\\bold{20\% = \dfrac{20}{100}=\dfrac{20\div20}{100\div20}=\dfrac{1}{5}}\\\bold{\dfrac{1}{5}\times 155=?}\\\bold{155\times1=155}\\\\\bold{\dfrac{155}{5}=31}\\\boxed{\boxed{\bold{Answer: 31}}}\huge\checkmark[/tex]

Good luck on your assignment and enjoy your day!

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

no, its not

Step-by-step explanation:

you can find the decimals by dividing the numerator and the denominator

4/10 = 0.4

2/3 = 0.6666666......

so the values are obviously different

Answer:

y=2/3x+1

Step-by-step explanation:

m= (slope)

b= (y-intercept

Answer:

-8x + 3

Step-by-step explanation:

Answer:

0.45 and 0.5

Step-by-step explanation:

plato/edmentum

The 90% confidence interval for the true proportion of club members who use compost is given as (0.4, 0.507)

This refers to the probability of a parameter falling across a set of values around the mean.

To find the 90% confidence interval,

Probability=  45%= 0.45

Level of significance= 90%

1-0.90

= 0.10

[tex]z\alpha /2 = z(0.1/2) = 0.05[/tex]

The value of 0.05

P0.05= 1.645

P ± 1.645 x [tex]\sqrt{P0-p/n}[/tex]

0.45 ± 1.645 * [tex]\sqrt{0.48 (1-0.45)/200}[/tex]

0.45 ± 1.645 * 0.035178

0.45 ± 0.0578

0.45 - 0.0578, 0.45 + 0.0578

(0.4, 0.507)

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Answer:

I hope I helped sorry l didn't understand question number 19

Amon the following situation 2 cases follow the general rule for basis of inherited property

Given , Statements of inheritance.

1. Louis died on August 12. 2019 leaving his house to his sister, Etty.

2. On August 15, 2018, Leroy give his brother Ralph appreciated stock. Leroy's brother died on February 16, 2019, Ralph's only heir was Leroy.

3.Mick died on June 30, 2019. He named his brother Emmett as the beneficiary of his 401(k) plan.

This is also a case of inheritance but not the case of inheritence of property. Retirement Savings account is not considered as property.

4.Janet died January 1, 2019. At that time, she had a IRA with balance of $32640. She named her daughter, Emily, as the beneficiary of her IRA.

Know more about inheritance of property,

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Answer:

Step-by-step explanation:

The first term here is -50 and the common ratio is 0.70.  Note that the second term is 0.70(50) = 35.

The formula a(n) = a(0)*r^(n -1) becomes  a(n) = -50*0.70^(n -1), and so

the 5th term is a(5) = -50*0.70^4 = -12.005

Answer:

I think it's the second one(200(1.034)t = 250)

Step-by-step explanation:

if not correct me. or try the third one.

Answer:

i believe 1-3-5

Step-by-step explanation:

Answer: the 2nd and 6th

Step-by-step explanation:

i did the test thing

Answer:

You need to have an average speed of at least 35 miles per hour for the rest of the trip to get to the church on time

Step-by-step explanation:

We use the following relation to solve the question:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance, and t is the time.

First 15 minutes:

Time of 15 minutes = 0.25 hour, so [tex]t = 0.25[/tex]

Velocity of 5 miles per hour. So the distance is of:

[tex]d = vt = 5*0.25 = 1.25[/tex]

Final 15 minutes:

The will need to drive 10 - 1.25 = 8.75 miles in 15 minutes = 0.25 hours. So, the average speed will need to be of at least:

[tex]v = \frac{d}{t} = \frac{8.75}{0.25} = 35[/tex]

You need to have an average speed of at least 35 miles per hour for the rest of the trip to get to the church on time

Answer:

Please check the explanation.

Step-by-step explanation:

Given

First we need to determine the percentage decrease such as:

Percentage decrease = 2.6% of 28

                                     = 2.6/100 × 28

                                     = 0.026 × 28

                                     = 0.73

New value can be determined using the formula

New vaue = 28 - percentage decrease

                 = 28 - 0.73

                 = 27.27

The probability that a student is a female given that they have an A is 0.2

The given parameters are:

Female = 11

A= 10

Female and A = 2

The probability is calculated using:

P(Female given A) = P(female and A)/P(A)

This gives

P(Female given A) = 2/10

Simplify

P(Female given A) = 0.2

Hence, the probability that a student is a female given that they have an A is 0.2

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