The Escobar family and the Johnson family each used their sprinklers last month. The water output rate forthe Escobar family's sprinkler was 20 gallons per hour. The water output rate for the Johnson family's sprinkler was40 gallons per hour. The families used their sprinklers for a combined total of 32 hours, resulting in a total wateroutput of 960 gallons. How many hours was each family’s sprinkler used?

Answer:

7/9

Step-by-step explanation:

P(blue or odd) = P(blue) + P(odd) − P(blue and odd)

P(blue or odd) = 4/9 + 5/9 − 2/9

P(blue or odd) = 7/9

Alternatively:

P(blue or odd) = 1 − P(not blue and not odd)

P(blue or odd) = 1 − 2/9

P(blue or odd) = 7/9

Answer:

The range of T is a subspace of W.

Step-by-step explanation:

we have T:V→W

This is a linear transformation from V to W

we are required to prove that the range of T is a subspace of W

0 is a vector in range , u and v are two vectors in range T

T = T(V) = {T(v)║v∈V}

{w∈W≡v∈V such that T(w) = V}

T(0) = T(0ⁿ)

0 is  Zero in V

0ⁿ  is zero vector in W

T(V) is not an empty subset of W

w₁, w₂   ∈ T(v)

(v₁, v₂ ∈V)

from here we have that

T(v₁) = w₁

T(v₂) = w₂

t(v₁) + t(v₂) = w₁+w₂

v₁,v₂∈V

v₁+v₂∈V

with a scalar ∝

T(∝v) = ∝T(v)

such that

T(∝v) ∈T(v)

so we have that T(v) is a subspace of W. The range of T is a subspace of W.

Answer:

~0.3158

Step-by-step explanation:

Number of even numbers in the range of 1 - 38 is 38/2 = 19

=> P(E) = 19/38 = 1/2

Having: 38 = 3 x 12 + 2, then the number of numbers that is a multiple of 3 in the range of 1 - 38 is 12

=> P(M) = 12/38 = 6/19

Having: 38 = 6 x 6 + 2, then the number of numbers that is a multiple of 6 (or multiple of 2 and 3) is 6

=> P(E and M) = 6/38 = 3/19

Applying the conditional probability formula:

P(M|E) = P(E and M)/P(E) = (3/19)/(1/2) = 6/19 = ~0.3158

Answer:

2/3

Step-by-step explanation:

The equation for direct variation is: y = kx, where k is a constant.

Here, we see that y varies directly with x when y = 6 and x = 72, so let's plug these values into the formula to find k:

y = kx

6 = k * 72

k = 6/72 = 1/12

So, k = 1/12. Now our formula is y = (1/12)x. Plug in 8 for x to find y:

y = (1/12)x

y = (1/12) * 8 = 8/12 = 2/3

Thus, y = 2/3.

~ an aesthetics lover

Answer:

Step-by-step explanation: I hope i'm right

[tex]y \alpha x\\y=kx....(1)\\6=72k\\\frac{6}{72} =\frac{72k}{72} \\\\1/12 =k\\y = 1/12x=relationship-between;x-and;y\\x =8 , y =?\\y = \frac{8}{12} \\Cross-Multiply\\12y =8\\12y/12 = 8/12\\\\y = 2/3[/tex]

Answer:

C

Step-by-step explanation:

The critical value we are asked to state in this question is the value of the z statistic

Mathematically;

z-score = (x- mean)/SD/√n

From the question

x = 11.58

mean = 12

SD = 1.93

n = 80

Substituting this value, we have

z= (11.58-12)/1.93/√80 = -1.946

Answer:

Nx = λx

Nx = 0, with x≠0

if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions

Step-by-step explanation:

given that

let N be a square matrix in order of n

note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N

let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ

Nx = λx (x≠0)

N²x =  λNx = λ²x

∴[tex]N^{k}x[/tex] =  (λ^k)x

[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector

where x = 0, (λ^k) = 0

λ = 0

therefore, Nx = λx

Nx = 0, with x≠0

note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution

Answer:

false

Step-by-step explanation:

When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter

Answer:

60°C

Step-by-step explanation:

This is a great example of a problem that looks really complicated, but can be broken down and easily understood!

First, we want to know the temperature the instant it is removed from the heat source. In that case, the time that has elapsed after it has been removed is 0, so we're looking for:

[tex]T(0)=55e^{-0.1(0))}+15=55e^{0}+15[/tex]

Now, any number raised to to the power of zero is 1, so this becomes:

[tex]T(0)=55(1)+15=60[/tex]

For more information on why any number raised to the zero power is 1, I highly recommend researching if it interests you. One of the most intuitive ways is to think of the pattern of exponents:

[tex]3^{3}=3*3*3=27[/tex]

[tex]3^{2}=3*3=9[/tex]

[tex]3^{1}=3[/tex]

You might notice that with each decrease in power, it can be read as dividing the expression by three, so following that pattern gives:

[tex]3^{0}=\frac{3}{3}=1[/tex]

And if we follow the division pattern, we do end up going into negative exponents correctly:

[tex]3^{-1}=\frac{1}{3^{1}}[/tex]

[tex]3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}[/tex]

[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{27}[/tex]

Answer:

The Hudson Record Store

1. As a fraction, discount rate = $3/$18 = 0.167

2. As a percentage, discount rate = 16.67%

3. Selling price during 2nd week = $13.50

4. The rate of the new selling price to the old is $13.50/$18 = 75%

Step-by-step explanation:

Selling price of CDs = $18

1st Week, sold CDs at $15

Discount = $3 ($18 - $15)

As a fraction, discount rate = $3/$18 = 0.167

As a percentage, discount rate = 16.67%

2nd Week, sold CDs at $13.50 ($18 - (25% of $18))

Discount = $4.50 ($18 - $13.50)

Price during the second week of the sale = $13.50

The rate of discount = $4.50/$18 = 25%

Answer:

{58.02007 , 61.97993]

Step-by-step explanation:

Data are given in the question

Sample of cars = n = 121

Average speed = sample mean = 60

Standard deviation = sd = 11

And we assume

95% confidence t-score = 1.97993

Therefore

Confidence interval is

[tex]= [60 - \frac{1.97993 \times 11}{\sqrt{121} }] , [60 + \frac{1.97993 \times 11}{\sqrt{121} }][/tex]

=  {58.02007 , 61.97993]

Basically we applied the above formula to determine the confidence interval

Answer: 6 cm, V=48π or V=150.8 cm³

It appears the question is asking for the radius, but below I have shown how to find the volume.

Step-by-step explanation:

The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.

The formula to find the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. Now that we have the radius from above, we can use that to plug into the equation along with the given height.

[tex]V=\pi (6^2)\frac{4}{3}[/tex]                    [expand the exponent]

[tex]V=36\pi \frac{4}{3}[/tex]                       [combine like terms]

[tex]V=48\pi[/tex] or [tex]V=150.8 cm^3[/tex]            

Answer:

The new price is 8.80

Step-by-step explanation:

First find the increase

8 * 10%

8 * .10

.80

Add this to the original price

8 + .80

8.80

The new price is 8.80

Answer:

the answer is $8.80 :))

Answer: (-2,-7)

Step-by-step explanation:

A function f(x-c) , where c>0 , represents the horizontal shift of original function to the right c units.

The function f(x-c) is going to add c to the x value, while keeping the y value the same.

Similarly,

The function f(x-5) is going to add 5 to the x value, while keeping the y value the same.

So, the corresponding point to (-7,-7) on f(x-5) = (-7+5,-7)

= (-2,-7)

hence, the corresponding point to (-7,-7) on f(x-5)  =  (-2,-7)

Answer:

x = - 4, y = 7

Step-by-step explanation:

Given the 2 equations

- 7x - 2y = 14 → (1)

6x + 6y = 18 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate the y- term

- 21x - 6y = 42 → (3)

Add (2) and (3) term by term to eliminate y

- 15x = 60 ( divide both sides by 15 )

x = - 4

Substitute x = - 4 into either of the 2 equations and evaluate for y

Substituting into (2)

6(- 4) + 6y = 18

- 24 + 6y = 18 ( add 24 to both sides )

6y = 42 ( divide both sides by 6 )

y = 7

Answer:

The sample size is [tex]n = 2401[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of error is  [tex]E = 0.02[/tex]

Given that the confidence level is  95% then the level of significance can be mathematically evaluated as  

            [tex]\alpha = 100 - 95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we would obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the values is  

     [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]

The reason we are obtaining critical value of   [tex]\frac{\alpha }{2}[/tex]  instead of     [tex]\alpha[/tex] is  because  

[tex]\alpha[/tex]  represents the area under the normal curve where the confidence level interval (   [tex]1-\alpha[/tex]  ) did not cover which include both the left and right tail while

 [tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the  sample  size

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)      

   Generally the sample size is mathematically evaluated as

          [tex]n = [ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p)[/tex]

Where [tex]\r p[/tex] is the proportion of sample taken which we will assume to be [tex]\r p = 0.5[/tex]            

        substituting values  

                 [tex]n = [\frac{ 1.96}{0.02} ]^2 *( 0.5 (1- 0.5)[/tex]

                [tex]n = 2401[/tex]

Answer:

a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

b) The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Step-by-step explanation:

Step(i):-

Sample size 'n' =75

Mean of the sample x⁻ = 17.8

standard deviation of the sample (S) = 5.9

Mean of the Population = 15

Null hypothesis:H₀:μ = 15 years

Alternative Hypothesis :H₁:μ≠15 years

Step(ii):-

Test statistic

                         [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

                        [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]

                    t = 4.111

Degrees of freedom

ν = n-1 = 75-1=74

t₀.₀₂₅ = 1.9925

The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

P-value:-

The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Answer:

Answer:

The  probability is  [tex]P(J|B) = 0.36[/tex]

Step-by-step explanation:

B =business

J=jumbo

Or =ordinary

From the question we are told that  

     The proportion of the passenger on business in the ordinary jet  is [tex]P(B| Or) = 0.25[/tex]

     The proportion of the passenger on business in the jumbo jet  is  [tex]P(B|J) = 0.30[/tex]

     The  proportion of the passenger on jumbo jets is  [tex]P(j) = 0.40[/tex]

      The   proportion of the passenger on ordinary jets is evaluated as

         [tex]1 - P(J) = 1- 0.40 = 0.60[/tex]

According to  Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as

        [tex]P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}[/tex]

substituting values

         [tex]P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}[/tex]

         [tex]P(J|B) = 0.36[/tex]

Step-by-step explanation:

Answer:

The required probability = 0.144

Step-by-step explanation:

Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%

Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.

That would be;

P(making money) * P(making money) * P(losing money)

Kindly recollect;

P(making money) = 60% = 60/100 = 0.6

P(losing money) = 40% = 40/100 = 0.4

The probability we want to calculate is thus;

0.6 * 0.6 * 0.4 = 0.144

Answer: t = 10

Step-by-step explanation:m

 Given that; n₁ = 10, n₂ = 10

ж₁ = 50, ж₂ = 30

Sˣ₁ = 20, Sˣ₂ = 20

Now using TEST STATISTICS

t = (ж₁ - ж₂) / √ ( Sˣ₁/n₁ + Sˣ₂/n₂ )

so we substitute our figures

t = ( 50 - 30 ) / √ ( 20/10 + 20/10 )

t = 20 / √4

t = 10

Hey there! I'm happy to help!

We see that light travels 186,000 miles per second. How many miles is this per minute. Well, there are 60 seconds a minute, so we multiply by 60!

186,000×60=11160000

And there are 60 minutes in an hour, so we multiply by sixty again!

11160000×60=669600000

Now, we need to write this in scientific notation. To do this, we move the decimal back enough places to have a one digit number, and we multiply that one digit number by 10 to the power of how many places you moved the decimal back.

In the number 669600000 we can move the decimal point back 8 times which gives us 6.696 (we don't need the zeroes after a decimal) multiplied by 10 to the 8th power because we moved the decimal back eight places.

This can be written as 6.696×10^8, which is closest to the answer option 6.7×10^8 miles.

Have a wonderful day! :D

Answer:

D

Step-by-step explanation:

D because they are congruent try measuring it.

Answer:

[tex]\boxed{\mathrm{D}}[/tex]

Step-by-step explanation:

The triangles are congruent.

The angles that are corresponding on both triangles must be congruent.

Angle Q in triangle PQR must be congruent to angle T in triangle STU.

Answer:

Step-by-step explanation:

In computer programming relational operators are used to check conditions, that is if one conditions matches another and returns true if the condition is met or satisfied.

Answer:

1/2

Step-by-step explanation:

i think sin 5 pi/6

[tex]sin \frac{5 \pi}{6} =sin (\frac{\pi}{2} +\frac{\pi}{3} )=cos \frac{\pi}{3} =\frac{1}{2} \\or\\sin\frac{5 \pi}{6} =sin (\pi-\frac{\pi}{6} )=sin \frac{\pi}{6} =\frac{1}{2}[/tex]

The exact Value of sin 5x/6 is 1/2.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin 5x/6

We can Split it as

sin (5π / 6) = sin (π/2 + π/3)

                  = cos π/3

                  = 1/2

Also, sin (5π / 6) = sin (π - π/6)

                  = sin π/6

                  = 1/2

Hence, the exact value is 1/2.

Learn more about Trigonometry here:

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We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.

4(5+3) = 2(22-6)

4(8) = 2(16)

32 = 32

Once you finish distributing each side, you can check to see if it is equal on both sides.

In our case it is since they both equal 32 after distributing the terms.

Answer:

Your answer is B

Step-by-step explanation:

rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'

Answer:

[tex]y(x)=100+0.1x[/tex]

Step-by-step explanation:

Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.

We know that there is an initial fee of $100, so we know that if we climb x=0 meters, we have a fee of y(0)=100.

[tex]y(0)=100[/tex]

As there is a constant fee (lets called it m) for each vertical meter climbed, we have a linear relationship as:

[tex]y(x)-y(0)=m(x-0)\\\\\\y(x)-100=mx\\\\\\y(x)=100+mx[/tex]

We know that for x=3000, we have a fee of $400, so if we replace this in the linear equation, we have:

[tex]y(3000)=100+m(3000)=400\\\\\\100+3000m=400\\\\3000m=400-100=300\\\\m=300/3000=0.1[/tex]

Then, we have the equation for the total fee in function of the vertical distance:

[tex]y(x)=100+0.1x[/tex]

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

(C) The area of the cylinder's base is [tex]\dfrac{1}{4} \pi x^2[/tex] square units.

(E)The height of the cylinder is 4x units.

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius = x/2

Area of the Base

[tex]=\pi (x/2)^2\\=\dfrac{ \pi x^2}{4} $ square units[/tex]

Next, we know that:

The volume of a cylinder = Base Area X Height

[tex]\pi x^3=\dfrac{ \pi x^2}{4} \times Height\\Height =\pi x^3 \div \dfrac{ \pi x^2}{4}\\=\pi x^3 \times \dfrac{ 4}{\pi x^2}\\\\Height=4x$ units[/tex]

Therefore, the correct options are: C and E.

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Answer:

Don

Step-by-step explanation:

1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

David says he has 2/3 of a line length left, while Wear says he has 11/16 of a length left.

Convert the fraction numbers 2/3 and 11/16 into the decimal number. Then we have

2/3 = 0.6667

11/16 = 0.6875

The decimal number 0.6875 is greater than 0.6667. Then the fraction number 11/16 is greater than the fraction number 2/3.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

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Answer:

2

Step-by-step explanation: