A race car is traveling at a constant speed of 150 miles per hour how many feet does it travel in 5 seconds

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the men and women who own cats respectively. The population proportion of men and women who own cats would be p1 and p2 respectively.

p1 - p2 = difference in the proportion of men and women who own cats.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 ≠ p2

p1 - p2 ≠ 0

it is a two tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples

For men

n1 = 80

p1 = 55/100 = 0.55

x1 = p1n1 = 0.55 × 80 = 44

For women,

n2 = 100

p2 = 30/100 = 0.3

x2 = p2n2 = 0.3 × 100 = 30

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (44 + 30)/(80 + 100) = 0.41

1 - pc = 1 - 0.41 = 0.59

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.55 - 0.3)/√(0.41)(0.59)(1/80 + 1/100) = 3.39

Test statistic = 3.39

Answer:

(B ) .  34.2cm^2

Step-by-step explanation:

[tex]A = \frac{\alpha }{360} \times \pi r^2\\\alpha=20 \\r = 14\\\\A =\frac{20}{360} \times 22/7\times 14^2\\A = 1/18 \times4312/7\\A =34.2 cm^2[/tex]

Answer:

m∠3  = 115 degrees

Step-by-step explanation:

angle 6 and angle 8 are on a straight line

we know that sum of angles on straight line is 180

therefore

m∠8 = x+5

m∠6 +  m∠8 = 180

2x - 5 + x+5 = 180

=> 3x = 180

=> x = 180/3 = 60

Thus,

m∠6 = 2x-5 = 2*60 -  5 = 115

we know that for two parallel lines cut by a transversal

alternate opposite angles are equal

m∠6  and m∠3 are alternate opposite angles

thus

m∠6  = m∠3  = 115 (answer)

Answer:

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Standard error sm = 1.634

Test statistic t = 1.102

P-value = 0.28

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that women who exercise daily have a significantly different duration of labor than all women.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=16\\\\H_a:\mu\neq 16[/tex]

The significance level is 0.05.

The sample has a size n=29.

The sample mean is M=17.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{8.8}{\sqrt{29}}=1.634[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.8-16}{1.634}=\dfrac{1.8}{1.634}=1.102[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=29-1=28[/tex]

This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.102)=0.28[/tex]

As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Answer:

hope it helps uh......

Answer:

5(2a -5 + b)

Step-by-step explanation:

(10a - 25 + 5b) = 5( 2a - 5 + b)

5(b +  2a  - 5) = 5(2a - 5 + b)

Answer:

5(2a -5 + b)

Step-by-step explanation:

Answer:

3x / 2 + 9 = 5

3x / 2 = -4

3x = -8

x = -8/3

(2 + v) / 3 = 9

2 + v = 27

v = 25

32 / (d - 2) = 10

32 = 10 * (d - 2)

3.2 = d - 2

d = 5.2

2p - 4 = 3p / 2

2 * (2p - 4) = 3p

4p - 8 = 3p

p - 8 = 0

p = 8

3b / 2 = 12

3b = 24

b = 8

Answer:

C

Step-by-step explanation:

Tan = opposite / adjacent

= 1 / √3

= √3 / 3

Answer:

C.

Step-by-step explanation:

Tangent= opposite over adjacent.

Tangent = 1/√3

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2,  76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

                             P.Q.  =  [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2} __n_-_1[/tex]

where, s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }[/tex] = 5.063

            [tex]\sigma[/tex] = population standard deviation

            n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

So, 90% confidence interval for the population standard deviation, [tex]\sigma[/tex] is ;

P(11.59 < [tex]\chi^{2}__2_1[/tex] < 32.67) = 0.90  {As the critical value of chi at 21 degrees  

                                                  of freedom are 11.59 & 32.67}  

P(11.59 < [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] < 32.67) = 0.90

P( [tex]\frac{ 11.59}{(n-1) \times s^{2}}[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{ 32.67}{(n-1) \times s^{2}}[/tex] ) = 0.90

P( [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ) = 0.90

90% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] , [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ]

                                     = [ [tex]\frac{21 \times 5.063^{2} }{32.67 }[/tex] , [tex]\frac{21 \times 5.063^{2} }{11.59 }[/tex] ]

                                     = [16.48 , 46.45]

90% confidence interval for [tex]\sigma[/tex] = [[tex]\sqrt{16.48}[/tex] , [tex]\sqrt{46.45}[/tex] ]

                                                 = [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Answer:

V ≈ 1436.03 cm³

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}[/tex]πr³. r represents the radius, which is 7 cm since the diameter is 14 cm, so plug 7 into the equation as r. Also remember that the question states to use 3.14 for pi/π.

V = [tex]\frac{4}{3}[/tex] (3.14)(7)³

V ≈ 1436.03 cm³

Answer:

no solution

Step-by-step explanation:

4x+3y = 6

8x + 6y = 5

Multiply the first equation by -2

-2(4x+3y) = 6*-2

-8x -6y = -12

Add this to the second equation

-8x-6y = -12

8x + 6y = 5

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

0x + 0y = -7

0 = -7

Since this is never true there is no solution

Answer:

X = 8/3, y= -14/9

Step-by-step explanation:

using elimination method:

subtract equation 1 from equation 2

8x-4x + 6y-3y = 5-6

4x+3y= -1

4x= -1-3y

divide both sides by 4

x = -1-3y÷4

substitute x = -1-3y/4 in equation 2

8(-1-3y)/4 +6y = 5

-8-24y/4+ 6y =5

-8-24y+6y/4 =5

-8-18y/4 = 5

Cross multy

-8-18y × 1 = 4×5

-8-18y = 20

collect like terms

-18y = 20+8

-18y = 28

divide both sides by-18

y = 28/-8

y = -14/9

put y = -14/9 in equation 1

4x+3(-14/9) = 6

4x-42/9 = 6

42/9 = 14/3

so, 4x=6+14/3

LCM =3

4x = 18+14/3

4x= 32/3

cross multiply

4x×3 = 32

12x = 32

divide both sides by 12

12x/12= 32/12

x = 8/3

so, x = 8/3, y = -14/9

check:

first equation:

4(8/3) + 3(-14/9)

32/3 - 14/3( 3 cancels 9 rem 3)

LCM= 3

32 - 14/3

= 18/3

= 6

Answer:

(-0.5, 0)

Step-by-step explanation:

Coordinates of endpoints of segment are:

A= (-2, 1)

B= (1, - 1)

By mid-point formula:

The midpoint of [tex] \overline{AB} [/tex]

[tex] = \bigg(\frac{ - 2 + 1}{2}, \: \: \frac{1 + ( - 1)}{2} \bigg) \\ \\ = \bigg(\frac{ - 1}{2}, \: \: \frac{0}{2} \bigg)\\ \\ = \bigg(\frac{ - 1}{2}, \: \: 0 \bigg)\\ \\ = ( - 0.5, \: \: 0 )[/tex]

Answer:

the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Step-by-step explanation:

Given that:

Mean = 30000

Standard deviation = 9000

sample size = 100

The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:

[tex]P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)[/tex]

[tex]P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})[/tex]

From Z tables:

[tex]P(31000 < X <33000) = 0.9996 -0.8665[/tex]

[tex]P(31000 < X <33000) = 0.1331[/tex]

Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Answer:

2.89

Step-by-step explanation:

just do 1.7×1.7=2.89

Question:

A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by

s(t) = -16t² + v₀t + s₀

Determine the position and velocity functions for the coin.

Answer:

position function: s(t) = (-16t² + 64) ft

velocity function: v(t) = (-32t) ft/s

Step-by-step explanation:

Given position equation;

s(t) = -16t² + v₀t + s₀                ---------(i)

v₀ and s₀ are the initial values of the velocity and position of the coin respectively.

(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e

v₀ = 0.  

Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e

s₀ = 64ft

Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;

s(t) = -16t² + (0)t + 64    

s(t) = -16t² + 64

Therefore, the position function of the coin is;

s(t) = (-16t² + 64) ft

(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;

v(t) = [tex]\frac{ds(t)}{dt}[/tex]

v(t) = [tex]\frac{d(-16t^2 + 64)}{dt}[/tex]

v(t) = -32t + 0

v(t) = -32t

Therefore, the velocity function of the coin is;

v(t) = (-32t) ft/s

Answer:

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890 miles

Step-by-step explanation:

Step(i):-

Given mean of the Population = 100 miles per day

Given standard deviation of the Population = 23 miles per day

Let 'X' be the normal distribution

Let x₁ = 86

[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]

Let x₂= 86

[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]

Step(ii):-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)

                      = P(Z≤ 1.08) - P(Z≤ -0.61)

                      = 0.5 +A(1.08) - ( 0.5 - A(-0.61))    

                      = A(1.08) + A(0.61)             ( A(-Z)=  A(Z)

                      = 0.3599 + 0.2291

                     = 0.5890

Conclusion:-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890  miles per day

Answer:

2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.

Step-by-step explanation:

do some math

The correct answer is The line will be less steep because the rate will be slower

Explanation:

The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.

However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.

Answer:

2

Step-by-step explanation:

[tex]\sqrt{((\sqrt{2} - 0)^2 + (0 - (-\sqrt{2}))^2)[/tex]

Answer:  [tex]\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}[/tex]

Step-by-step explanation:

  a₁,  375,  a₃,   a₄,  81

First, let's find the ratio (r). There are three multiple from 375 to 81.

[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]

Next, let's find a₁

[tex]a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625[/tex]

Lastly, Use the Infinite Geometric Sum Formula to find the sum:

[tex]S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}[/tex]

Answer:

69.5309950592 cm²

Step-by-step explanation:

Area of Square:

Area = [tex]Length * Length[/tex]

Area = 18*18

Area = 324 square cm

Area of circle:

Diameter = 18 cm

Radius = 9 cm

Area = [tex]\pi r^2[/tex]

Area = (3.14)(9)²

Area = (3.14)(81)

Area = 254.469004941 square cm

Area of Shaded area:

=> Area of square - Area of circle

=> 324 - 254.469004941

=> 69.5309950592 cm²

Answer:

P [ x > 59000} = 0,6057

Step-by-step explanation:

We assume Normal Distribution

P [ x > 59000} = (x - μ₀ ) /σ/√n

P [ x > 59000} =  (59000 - 60000)/ 3800

P [ x > 59000} = - 1000/3800/√35

P [ x > 59000} = - 1000*5,916 /3800

P [ x > 59000} =  - 5916/3800

P [ x > 59000} = - 1,55

We look for p value for that z score n z-table and find

P [ x > 59000} = 0,6057

Answer:

144

Step-by-step explanation:

Find: Length of segment BC

CD+DB=BC

3x+8+4x+10=BC

7x+18=BC

BC also equals 8x (given on the screen shot)

7x+18= 8x

x=18

18 times 8 = 144

Check:

3( 18) + 8 + 4(18) + 10

54+8 + 72+10

64+ 80= 144  TRUE

Answer:

D. 3 and -4

Step-by-step explanation:

Given the expression, x² - x - 12, let's factorise to find the value of p and q using the table, for which we would have the expression simplified as (x + p)(x + q)

From the table, let's find the values of p and q that would give us -12 when multiplied together, and would also give us -1 when summed together.

Thus, from the table given, the row containing the values of p(3) and q(-4) gives us = -1 (p+q) . p = 3, q = -4 would be our values to use to factor x² - x - 12, as multiplying both will also give us "-12".

Thus, x² - x - 12 would be factorised or simplified as (x + 3)(x - 4)

Therefore, the answer is: D. 3 and -4

Answer:

D a p e x

Step-by-step explanation:

Answer:

-$3576

Step-by-step explanation:

Depreciation using double declining method=100%/useful life*2

Depreciation using double declining method=100%/10*2=20%

2017 depreciation=$60,000*20%=$12000

2018 depreciation=($60,000-$12000)*20%=$9600

2019 depreciation=($60,000-$12000-$9600 )*20%=$7680

2020 depreciation=($60,000-$12000-$9600-$7680 )*20%=$6144

carrying value in 2021=$60000-$12000-$9600 -$7680-$6144 =$24576

Loss on disposal of machine=$21,000-$24576  =-$3576

Answer:

x=9,3

Step-by-step explanation:

x²-12x=-27

x²-12x+(12/2)²=-27+(12/2)²

x²-12x+6²=-27+36

(x-6)²=9

x-6=[tex] \frac{ + }{ - } \sqrt{9} [/tex]

x-6=+3 and x-6=-3

x=9 and 3

Answer:

B. Multiply 6 by 3

Step-by-step explanation:

Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:

B. Multiply 6 by 3

Your step by step for getting the number Hannah started with:

First, multiply 6 with 3:

6 x 3 = 18

Next, subtract 4:

18 - 4 = 14

Next, divide by 2:

14/2 = 7

Hannah started with the number 7.

~

Answer: Hannah started with 7.

B. Multiply 6 by 3

Explanation:

Let the number be y

2 × y = 2y

(2y + 4)/3 = 6

2y + 4 = 6×3 = 18

2y + 4 = 18

2y = 18 - 4 = 14

y = 14/2 = 7

To solve the problem backward, the first step is to multiply 6 by 3.

Answer:

Subtract 2 and two-thirds from both sides of the equation

8 minus 2 and two-thirds = 5 and one-third

Substitute the value for r to check the solution.

Step-by-step explanation:

2 2/3  + r   = 8

Subtract 2 2/3 from each side

2 2/3  + r  - 2 2/3   = 8 - 2 2/3

r = 5 1/3

Check the solution

2 2/3 +5 1/3 =8

8 =8

Answer:

1, 3, 5

Step-by-step explanation:

edge

Answer:

z= 56°

hope u understood it...

Answer:

Z=56

Step-by-step explanation:

Because i said so

Answer:

1.88

Step-by-step explanation:

8-2√5=3.527864045

square root of 3.527864045=1.87826090972

the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88

Answer:

The square root of 8 - 2√5 is

[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]

Step-by-step explanation:

To find the square root

8-2√5 must be in the form √a - √b where a > b

√ 8 - 2√5 = √a - √b

Square both sides

8 - 2√5 = (√a - √b)²

That's

8 - 2√5 = (a + b) - 2√ab

Since the two surd expressions are equal we can equate them

That's

8 = a + b ........ 1

a = 8 - b ........ 2

2√5 = 2√ab

Simplify

Divide both sides by 2

√5 = √ab

square both sides

We have

5 = ab ....... 3

Substitute a = 8 - b into equation 3

5 = ( 8 - b)b

5 = 8b - b²

b² - 8b + 5 = 0

After solving

b = 4 + √ 11 or 4 - √ 1

Since b is less than a

b = 4 - √11

a = 4 + √11

So the square root of 8 - 2√5 is

[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]

Hope this helps you.