What do you know to be true about the values of a and b?
60"
75"
O A. a b
O B. a = b
O c. a> b
O D. Can't be determined

Answer: 0.1587

Step-by-step explanation:

Given : The weight load on an airplane pallet is normally distributed with a mean of 250 pounds and a standard deviation of 40 pounds.

i.e. [tex]\mu = 250[/tex] pounds

[tex]\sigma=40[/tex] pounds

Let x be the weight load on an airplane pallet.

Then, the probability that a randomly selected pallet will support more than 290 pounds will be :-

[tex]P(X>290)=P(\dfrac{X-\mu}{\sigma}>\dfrac{290-250}{40})\\\\=P(Z>1)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<1)\\\\=1-0.8413\ \ \ \ [\text{by z-table}]\\\\=0.1587[/tex]

Hence, the required probability is 0.1587 .

Answer:

a. c = 2030,

b. n = 1.42,

c. x = 2.875,

d. k = 140

Step-by-step explanation:

a ) 8120 = 4c,

c = 8120 / 4 = 2030

b ) 0.5n = 0.71,

n = 0.71 / 0.5 = 1.42

c ) 8x = 23,

x = 23 / 8 = 2.875

d ) 7 : 6 = k : 120

Here we want to convert this ratio into fraction form,

7 / 6 = k / 120

And now we can cross - multiply to determine the value of k,

6k = 7(120) = 840,

k = 840 / 6 = 140

We can check the value of k, by plugging it back into our ratio, and see if it reduces to 7 : 6,

140 : 120,

14 : 12,

7 : 6

Answer/Step-by-step explanation:

1. (7j³ - 2) + (5j³ - j - 3)

Open the parentheses

7j³ - 2 + 5j³ - j - 3

Collect like terms. Like terms are terms that have the same degree.

7j³ + 5j³ - j - 2 - 3 (7j³ and 5j³, have the same degree, 2 and 3 are if the same degree)

12j³ - j - 5 (this already in descending order)

2. (8a⁵ - 4) + (3a⁵ + a - 2)

Open parentheses

8a⁵ - 4 + 3a⁵ + a - 2

Collect like terms

8a⁵ + 3a⁵ + a - 4 - 2

12a⁵ + a - 6 (in ascending order from largest to smallest degree)

3. (6m² + 1) + (3a⁵ + a - 2)

6m² + 1 + 3a⁵ + a - 2

Collect like terms

6m² + 3a⁵ + a + 1 - 2

6m² + 3a⁵ + a - 1

Rearrange from largest to smallest degree

3a⁵ + 6m² + a - 1

4. (3m⁵ + 1) + (9m⁵ + 3m - 2)

3m⁵ + 1 + 9m⁵ + 3m - 2

Collect like terms

3m⁵ + 9m⁵ + 3m + 1 - 2

12m⁵ + 3m - 1

5. (- 5x² - x + 4) + (- 3x² - 5x + 2)

Open parentheses

-5x² - x + 4 - 3x² - 5x + 2

Collect like terms

-5x² - 3x² - x - 5x + 4 + 2

-8x² - 6x + 6

Answer: Hi!

Your answer is 5/9.

Step-by-step explanation:

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 8 by 3, and get 24.

Then we multiply 1 by 9, and get 9.

Next we give both terms new denominators -- 9 × 3 = 27.

So now our fractions look like this:

24/27 - 9/27

Since our denominators match, we can subtract the numerators.

24 − 9 = 15

So the answer is:

15/27

(After you simplify it, it will be 5/9.)

Hope this helps!

The value of the expression "8/9 minus 1/3" is 5/9.

To subtract fractions, we need a common denominator. In this case, the least common multiple (LCM) of 9 and 3 is 9.

We can convert both fractions to have a denominator of 9:

(8/9) - (1/3)

Multiplying the numerator and denominator of the first fraction by 3, we get:

(8/9) - (1/3)

This gives us:

8/9 - 1/3

Since both fractions now have a common denominator of 27, we can subtract the numerators:

(8 - 3x 1) / 9

= (8-3)/9

= 5/9.

Therefore, 8/9 minus 1/3 is equal to 5/9.

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Answer:

2×3=6

or 6×5=30

Step-by-step explanation:

Theres a lot!

Answer:

I am pretty sure it is J

Step-by-step explanation:

128 divided by 16 equals 8

Answer:

F

8 ounce per serving

Step-by-step explanation:

128 ounce jug of iced tea.

label says = serves 16 people

therefore, the number of ounces per serving = 128 ounce / 16 serving

= 8 ounce per serving

so the answer is option F

Answer:

D

Step-by-step explanation:

Triple means 3 times something. "Times" means multiplication and the "something" is h so the answer is 3 * h = 3h.

Answer:

H0:p= 0.80                 H1: p< 0.80  one tailed test

Step-by-step explanation:

We state the null and alternative hypotheses as that the results are 80 % against the claim that the results are less than 80%.

H0:p= 0.80                 H1: p< 0.80  one tailed test

p2= 0.8 , p1= 74/97= 0.763

q1= 1-0.763= 0.237    q2= 0.2

The level of significance is 0.05 .

The Z∝= ±1.645 for ∝= 0.05

The test statistic used here is

Z= p1-p2/ √pq/n

Putting the values:

Z= 0.763 -0.8 / √ 0.8*0.2/97

z= -0.037/ 0.0406

z= -0.9113

The Z∝ = ±1.645 for ∝= 0.05 for one tailed test.

As the calculated value  does not fall in the critical region  we fail to reject the null hypothesis. There is not sufficient evidence to support  the claim that such polygraph results are correct less than 80% of the time.

Using the normal probability table.

P (Z <  -0.9113)= 1- P(z= 0.9311) = 1- 0.8238= 0.1762

If P- value is smaller than the significance level reject H0.

0.1762> 0.005  Fail to reject H0.

Answer:

shifted horizontally to the right 4 units, then stretched vertically by a factor of "3" , and finally shifted vertically up 6 units.

Step-by-step explanation:

Given the function

[tex]f(x)=\frac{3}{x-4} +6[/tex]

we can say that its parent function

[tex]f(x)=\frac{1}{x}[/tex]

was:

shifted horizontally to the right 4 units (given by the 4 units subtracted from the variable x)

stretched vertically by a factor of "3"

and finally shifted vertically up 6 units.

Answer:

18

Step-by-step explanation:

25=7+r     25-7=18     7-7=0

r=18 Do you understand? I really hoped I helped. I was in your position when i was learning that.

Answer:

x = -5

Step-by-step explanation:

Step 1: Write out equation

15x - 24 - 4x = -79

Step 2: Combine like terms

11x - 24 = -79

Step 3: Add 24 to both sides

11x = -55

Step 4: Divide both sides by 11

x = -5

Step 5: Check step

Plug in -5 into the original equation

15(-5) - 24 - 4(-5) = -79

-75 - 24 + 20 = -79

-99 + 20 = -79

-79 = -79

Answer:

x = -5

Step-by-step explanation:

15x - 24 - 4x = -79

11x - 24 = -79

11x = -55

x = -5

Check:

15 * -5 - 24 - 4 * -5

= -75 - 24 + 20

= -79

Answer: 20, -7, and -3

Step-by-step explanation:

`1.) 15 plus 8 is 23

23 minus 3 equals 20

2.) -25 plus 5 equals -20

-20 plus 13 is -7

3.) i can see the last one to show work

Answer:

Mean = $123.8

Range= $72

Variance= $607.344

Standard deviation=$ 24.64

Step by step explanation:

The list of the data of electricity bill on ascending order

$88,$90,$90,$95,$110,$115,$120,$126,$144,$150

Mean = (summation of($88,$90,$90,$95,$110,$115,$120,$126,$144,$150))/10

Mean = 1238/10

Mean = $123.8

Range= highest value- Lowest VA

Range= 150-88

Range= $72

Variance=( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)/10

Variance= (1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)/10

Variance= 6073.44/10

Variance=$ 607.344

Standard deviation= √variance

Standard deviation= √ 607.344

Standard deviation=$ 24.64

The mean monthly electric bill is $123.8

The Range is $72

The variance is $607.344

The standard deviation is $ 24.64

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

Σx = 88+90+90+95+110+115+120+126+144+150

Σx = 1238

Here n = 10

⇒ Mean = Σx/n

⇒ Mean = 1238/10

⇒ Mean = $123.8

Hence, the mean monthly electric bill is $123.8

⇒ Range = Largest value - Least value

⇒ Range = 150-88

⇒ Range= $72

Hence, the Range is $72

⇒ Σ(x -mean)² = ( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)

⇒ Σ(x -mean)² =(1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)

⇒ Σ(x -mean)² = 6073.44

Here n = 10

⇒ Variance = Σ(x -mean)²/10

⇒ Variance = 6073.44/10

⇒ Variance = $607.344

⇒ Standard deviation = √variance

⇒ Standard deviation = √607.344

⇒ Standard deviation = $24.64

Hence, the standard deviation is $24.64.

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Answer:

The value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].

Step-by-step explanation:

In this problem, we need to evaluate [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex]. Here, c and d are variable with exponents.

Taking both c together

[tex]=(10c^6{\cdot} 2c^{-5})\\\\=20(c^6{\cdot} c^{-5})\\\\=20c^{6-5}\\\\=20[/tex]

Taking both d together

[tex]=(d^{-5}{\cdot}d^4)\\\\=d^{-5+4}\\\\=d^{-1}[/tex]

So,

[tex](10c^6d^{-5})(2c^{-5} d^4)=20d^{-1}[/tex]

Hence, the value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].

Answer: 10 : 9

Step-by-step explanation:

GIVEN

20 girls tried out

18 boys tried out

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

The final ratio should be girl to boy

 girl to boy

=20 : 18

=10 : 9 ⇔ divide 2 on both sides (simplify the ratio)

Hope this helps!! :)

Please let me know if you have any question

Answer:

Hey there!

The correct answer would be a line from the point (0, 0) to the point (4, 2).

Let me know if this helps :)

Hi

(-9+V) /8 = 3

-9/8 +V/8 = 24/8

 -9+V = 24

  V = 24+9

  V = 33

let's check :   -9+33 = 24    and 24/8 = 3

Answer:

butterflies (b)=50

butterflies in 6 months =20/100×50=10+b =60

butterflies in 12 months =2(6months)

butterflies in 12 months= 120

The population of butterflies after 1 year is 72 butterflies

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the present population of butterflies be A = 50 butterflies

The percentage increase after 6 months = 20 %

The population of butterflies after 6 months = present population of butterflies + percentage increase after 6 months

The population of butterflies after 6 months = 50 + ( 20/100 ) x 50

                                                                         = 50 + ( 0.2 x 50 )

                                                                         = 50 + 10

                                                                         = 60 butterflies

The population after 6 more months =  population of butterflies after 6 months + percentage increase after 6 months

The population after 6 more months =  60 + ( 20/100 ) x 60

                                                              = 60 + 0.2 x 60

                                                              = 60 + 12

                                                              = 72 butterflies

Hence , The population of butterflies after 1 year is 72 butterflies

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Answer:

Step-by-step explanation:

  1+tan2A(tanA)=sec2A  

Right hand side  

sec2A=1cos2A=1cos2A−sin2A  

=cos2A+sin2Acos2A−sin2A  

=1+tan2A1−tan2A  

=1−tan2A+2tan2A1−tan2A  

=1−tan2A1−tan2A+2tan2A1−tan2A  

=1+2tanA1−tan2A×tanA  

=1+tan2A×tanA  

=Left hand side  

I HOPE THIS WILL HELP YOU

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IF MY ANSWER IS HELP FUL

Answer: B) 0.28

Step-by-step explanation:

Given that:

Lean/Healthy Overweight/ ObeseSelf Esteem Low 18 32 High 32 18

                Overweight/Obese      Lean/Healthy               Total

Low          32                                   18                                 50

High         18                                    32                                50

Total         50                                   50                               100

the phi correlation coefficient is defined by Ф = √x²/n

where n = 100 ( total number of response )

x² = [(32×32 - 18×18)² × 100] / [50 × 50 × 50 × 50]

Ф = √ [(700)² x 100) / (50)⁴ × 100

Ф = 700 / 50²

Ф = 0.28

Therefore option B) is the correct answer

Answer:

a) 0.4647

b) 24.6 secs

Step-by-step explanation:

Let T be interval between two successive barges

t(t) = λe^λt where t > 0

The mean of the exponential

E(T) = 1/λ

E(T) = 8

1/λ = 8

λ = 1/8

∴ t(t) = 1/8×e^-t/8   [ t > 0]

Now the probability we need

p[T<5] = ₀∫⁵ t(t) dt

=₀∫⁵ 1/8×e^-t/8 dt

= 1/8 ₀∫⁵ e^-t/8 dt

= 1/8 [ (e^-t/8) / -1/8 ]₀⁵

= - [ e^-t/8]₀⁵

= - [ e^-5/8 - 1 ]

= 1 - e^-5/8 = 0.4647

Therefore the probability that the time interval between two successive barges is less than 5 minutes is 0.4647

b)

Now we find t such that;

p[T>t] = 0.95

so

t_∫¹⁰ t(x) dx = 0.95

t_∫¹⁰ 1/8×e^-x/8 = 0.95

1/8 t_∫¹⁰ e^-x/8 dx = 0.95

1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t  = 0.95

- [ e^-x/8]¹⁰_t = 0.96

- [ 0 - e^-t/8 ] = 0.95

e^-t/8 = 0.95

take log of both sides

log (e^-t/8) = log (0.95)

-t/8 = In(0.95)

-t/8 = -0.0513

t = 8 × 0.0513

t = 0.4104 (min)

so we convert to seconds

t = 0.4104 × 60

t = 24.6 secs

Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is 24.6 secs

a.) we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.

b.) the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.

Given to us:

exponential distribution with mean = E(T) = 8,

The mean of the exponential

E(T) = 1/λ

 1/λ = 8

λ = 1/8

∴ [tex]t(t) =\frac{1}{8} \times e^\frac{-t}{8} }\ ;\ [ t > 0][/tex]

(a) The probability that the time interval between two successive barges is less than 5 minutes.

Now the probability we need

[tex]\begin{aligned} \ [T<5] &= \int\limits^5_0 {t(t)} \, dt\\&= \int\limits^5_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\\\&= [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^5\\&= - [ e^{-t/8}]_0^5\\&= - [ e^{-5/8} - 1 ]\\&= 1 - e^{-5/8}\\&= 0.4647\end{aligned}[/tex]

So, we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.

b)  Now we find t such that;

[tex]\begin{aligned} \ &p[T>t]=0.95\\ & \int\limits^{10}_0 {t(t)} \, dt=0.95\\& \int\limits^{10}_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt=0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt = 0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt=0.95 \\\\& [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^{10}=0.95\\\\& - [ 0 - e^{-t/8} ] = 0.95&\ \ e^{-t/8} = 0.95\\\end{aligned}[/tex]

taking logs,

t = 24.6 secs

Hence,the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.

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Answer: 5

Step-by-step explanation:

First of all, keep in mind that absolute value of any real number (positive and negative) is always positive because it stands for the distance from zero, and distance will never be negative.

         i.e. |x|=x, |-x|=x

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

 |-9|-|-4|

=9-4

=5

Hope this helps!! :)

Answer:

[tex]\huge \boxed{5}[/tex]

Step-by-step explanation:

[tex]|-9|-|-4|[/tex]

Apply rule : [tex]|-a|=a[/tex]

[tex]9-4[/tex]

Subtract.

[tex]=5[/tex]

Answer:

it is an example of an expression

Step-by-step explanation:

it is an example of an expression because it is asking a question without an equal sign. so its not a question, but an expression

Answer:  (1) 26   (2) 1, 3, 25

Step-by-step explanation:

Let a, b, and c represent the three discs.

a + b + c + 12 + 9 = 50

a + b + c = 29

1) Since a, b, and c are all different numbers then the one possibility is:

a = 1, b = 2, --> c = 26

2) There are many different possibilities for creating a sum of three numbers whose total is 29.

One example is provided above in #1.

Here are few other examples:

1, 3, 25               2, 3, 24            3, 4, 19               4, 5, 20

1, 4, 24               2, 4, 23            3, 5, 18               4, 6, 19

1, 5, 23               2, 5, 22            3, 6, 17               4, 7, 18

Using a system of equations, it is found that:

[tex]x + y + z = 29[/tex]

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

[tex]x + y + z + t + w = 50[/tex]

[tex]x + y + z + 9 + 12 = 50[/tex]

[tex]x + y + z + 21 = 50[/tex]

[tex]x + y + z = 29[/tex]

[tex]x + y + z = 29[/tex]

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Answer:

he interval itself is either correct in its estimate [i.e. the true parameter value is in ... year, and then interviews all students in that class, the sampling method is a ... If the target population is all U.S. adults, then a telephone directory would not

Step-by-step explanation:

Answer:

A e/f

Step-by-step explanation:

[tex]\frac{-e}{-f} = \frac{e}{f}[/tex]

Two negatives always equal one positive

Recall:

Negative + Negative = Positive

Negative + Positive = Negative

Positive + Positive = Positive

Answer:

Well, we know that there exists a function f(x) such that f(x-1) is a direct transformation of its parent function. First we want to set x=x-1. Conceptually, it might be easier just to annotate one of the x’s as a completely different variable, because we know that x doesn’t equal x-1. So let’s rewrite as x=y-1 and solve for y.

We now have y=x+1 where y(x) is actually our parent function and y(x)=f(x+1). So take our equation f(x-1) and substitute each x with (x+1). So f(x)=2(x+1) + 3

f(x)= 2x + 5. We can check this by finding f(x-1) because it should equal 2x+3.

f(x-1)= 2(x-1) + 5

f(x-1)= 2x + 3.

Hoped I helped

Answer:

Yes we reject the null hypothesis

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 9[/tex]

   The  population mean is  [tex]\mu = 40[/tex]

    The  sample  mean is  [tex]\= x = 33[/tex]

    The  standard deviation is [tex]\sigma = 9[/tex]

    The  level of significance is  [tex]\alpha = 0.05[/tex]

For a two-tailed test

The  null hypothesis is  [tex]H_o : \mu = 40[/tex]

The alternative hypothesis is  [tex]H_a : \mu \ne 40[/tex]

Generally the test statistics is mathematically represented as

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

=>     [tex]t = \frac{ 33 - 40 }{ \frac{9}{\sqrt{9} } }[/tex]

=>     [tex]t = -2.33[/tex]

The  p-value for the two-tailed test  is mathematically represented as

     [tex]p-value = 2 P(z > |-2.33|)[/tex]

From the z-table  

            [tex]P(z > |-2.33|) = 0.01[/tex]

       [tex]p-value = 2 * 0.01[/tex]

       [tex]p-value = 0.02[/tex]

Given that [tex]p-value < \alpha[/tex] Then we reject the null hypothesis