At an intersection, the red light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Approximately what percent of red lights last between 2.5 and 3.5 minutes? (2 points)

Answer:

b = 50°

c = 130°

Step-by-step explanation:

Two angles A and B are complementary if:

A + B = 90°

And two angles are supplementary if:

A + B = 180°

Then, we know that:

a = 40°

b is a complement of a (this means that a and b are complementary angles)

c is a supplement of b (this means that b and c are supplementary angles).

From the first statement, we have that:

b + a = 90°

Replacing the value of a we get

b + 40° = 90°

b = 90° - 40° = 50°

b = 50°

And now we can use that b and c are supplementary, then:

b + c = 180°

replacing the value of b we get:

50° + c  = 180°

c = 180° - 50° = 130°

c = 130°

Then the values we wanted are:

b = 50°

c = 130°

Answer:

its a

Step-by-step explanation:

trust did test

Answer:

[tex]ac - bd[/tex]

Step-by-step explanation:

[tex]ac - bd [/tex]

Answer:

the sum is 3m-12

Step-by-step explanation:

The nunbers are:

[tex]m-2\\m-4\\m-6\\the~sum~is:\\sum=(m-2)+(m-4)+(m-6)\\sum=m-2+m-4+m-6=m+m+m-2-4-6\\sum=3m-12[/tex]

The sum of three odd consecutive integers is 3m - 12

"These are the integers which are not divisible by 2."

For given question,

We need to find the sum of three consecutive odd integers.

Let x, x + 2, x + 4 be three consecutive odd integers.

We have been given the last one is m - 2

This means x + 4 = m - 2

So, the second odd integer would be,

x + 2 = m - 4

and the first odd integer would be,

x = m - 6

, we find the sum of the three odd consecutive integers.

⇒  (m - 6) + (m - 4) + (m - 2)

= m + m + m - 6 - 4 - 2

= 3m - (6 + 4 + 2)

= 3m - 12

Therefore, the sum of three odd consecutive integers is 3m - 12

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Answer:

[tex]\frac{-2x+11}{(x-4)(x+1)}[/tex]

Step-by-step explanation:

I don't think we can factor this so we'll have to multiply to make the denominators the same

[tex]\frac{3(x+1)}{(x^2-3x-4)(x+1)}-\frac{2(x^2-3x-4)}{(x+1)(x^2-3x-4)}\\\\\frac{3x+3-(2x^2-6x-8)}{(x^2-3x-4)(x+1)}=\frac{-2x^2+9x+11}{(x^2-3x-4)(x+1)}\\-2x^2+9x+11=(x+1)(-2x+11)\\\\x^2-3x-4=(x+1)(x-4)\\\frac{(x+1)(-2x+11)}{(x+1)(x-4)(x+1)}=\frac{-2x+11}{(x-4)(x+1)}[/tex]

Answer:

a.) m⁴n²

Step-by-step explanation:

( -m)⁴ × n ²

A negative base raised to an even powers equals a positive.

m ⁴ × n²

multiply the terms

m⁴n²

Answer:

a.) m⁴n²

Step-by-step explanation:

yea

Answer:

hey hi mate

Ur answer is

Step-by-step explanation:

u have to think

hope u like it

plz mark it as brainliest

tiene 40 años de edad

bond 40

jude 20

joh 30

40+20+30 = 90

Answer:

y = 5/4 x - 23/4

Step-by-step explanation:

4x + 5y = 31

5y = - 4x +31

y = -4/5 x + 31/5

⊥ slope = 5/4

-7 = 5/4 (-1) + B

-28 = -5 + 4b

-23 = 4B

b = -23/4

Answer:

to find the missing number is all u have to do is understand the problem and silve the problem!

Step-by-step explanation:

paki brainly po

Answer:

x ≥ 3.5

y ≥ 2

2x + 1.5y ≤ 20

Step-by-step explanation:

Given :

Total Amount to spend ≤ $20

Let:

Amount of flour purchased = x

Amount of sugar purchased = y

Cost :

Flour = $2 per pound

Sugar = $1.5 per pound

Pounds of :

flour to be purchased ≥ 3.5

Sugar to be purchased ≥ 2

Hence, the system of inequalities :

x ≥ 3.5

y ≥ 2

Total Cost of x + total cost of y must be less than or equal to total amount

2x + 1.5y ≤ 20

Answer: x ≥ 3.5

y ≥ 2

2x + 1.5y ≤ 20

Step-by-step explanation: To write a system of inequalities, it is important to determine the restrictions. One restriction is that Sarah wants to buy at least 3.5 pounds of flour. "At least" means that 3.5 is the smallest amount she would buy and 3.5 can be included. This is expressed as x ≥ 3.5. She also wants at least 2 pounds of sugar, so similar to the flour, this can be written as y ≥ 2. Finally, the cost can be expressed as 2x + 1.5y. This is a restriction because Sarah can spend up to $20, so 2x + 1.5y is less than or equal to $20, or 2x + 1.5y ≤ 20.

Answer:

He did not control for lurking variables and their impacts on the results of his experiment. Amount of sunlight and water received are two outside variables(or confounding variables) that may impact the growth of his plants and influence the results. He needs to apply the same amount of sunlight and water to each plant within a different planting soil in order to rule out the influence of those two variables and test the sole effect of the soil brand on the plant growth. Otherwise, it would be hard to determine whether his plant growth was because of the soil brand or the different amounts of sunlight and water received

Answer:

Invalid

Step-by-step explanation:

Xavier did not control variables or the impacts of the results. Confounding variable being sunlight and water received are two outside variables that can impact growth influence results. Within a different planting soil, Xavier will apply the same amount of sunlight & water to each plant to rule out the influence of those two variables. The test for sole effect on the plant with growth otherwise be determine. Is the plant growth because of the soil brand or the different amounts of sunlight and water received? This could and will impaired the results of this experiment, therefore, making it invalid.

Answer:

4 over 3

because is in side the bracket is part of inequalities

Answer:

1. number line or 3

2. D

3. E and K

4. B

5. A

Brainliest please~

Answer:

Bunny Hill Ski Resort:

y = 10x + 35

Diamond Ski Resort:

y = 5x + 40

Point where the cost is the same:

(1, 45)

Step-by-step explanation:

The question tells us that:

$35 and $40 are initial fees

$10 and $5 are hourly fees

This means that x and y will equal:

x = number of hours

y = total cost of ski rental after a number of hours

So we can form these 2 equations:

y = 10x + 35

y = 5x + 40

Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.

Because they both equal y, we can set the equations equal to each other:

10x + 35 = 5x + 40

And we use basic algebra to solve for x:

10x + 35 = 5x + 40

(subtract 5x from both sides)

5x + 35 = 40

(subtract 35 from both sides)

5x = 5

(divide both sides by 5)

x = 1

Remember, x equals the number of hours.

That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)

Hope it helps (●'◡'●)

Answer:

The z-score for the trainee is of 2.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean of the test scores is 72 with a standard deviation of 5.

This means that [tex]\mu = 72, \sigma = 5[/tex]

Find the z-score for a trainee, given a score of 82.

This is Z when X = 82. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{82 - 72}{5}[/tex]

[tex]Z = 2[/tex]

The z-score for the trainee is of 2.

Answer:

4yz^2

Step-by-step Explanation:

Answer: The answer is 295,222.

Step-by-step explanation: The area of a rectangle is base times height, which is 914 x 323. If you do the math correctly, you will get 295,222.

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

Length (l) = 914 units

Breadth (b) = 323 units

Area = ?

Area of a rectangle (a) = l × b ----> use this formula

[tex]a = l \times b \\ a = 914 \times 323 \\ a = 295222 \: \: sq.units[/tex]

=> The area of the rectangle is 295222 sq.units.

Answer:

[tex]791.7\:\mathrm{ft^3}[/tex]

Step-by-step explanation:

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]A_{cyl}=r^2h\pi[/tex].

By definition, all radii of a circle are exactly half of all diameters of the circle. Therefore, if the diameter of the circular base of the cylinder is 6 feet, the radius of it must be [tex]6\div 2=3\text{ feet}[/tex].

Now we can substitute [tex]r=3[/tex] and [tex]h=28[/tex] into our formula [tex]A_{cyl}=r^2h\pi[/tex]:

[tex]A=3^2\cdot 28\cdot \pi,\\A=9\cdot28\cdot \pi,\\A=791.681348705\approx \boxed{791.7\:\mathrm{ft^3}}[/tex]

Step-by-step explanation:

Here, two angles i.e, (x + 13)° and (4x + 2)° are forming a straight line, thus the sum of these two angles will be 180° because they are forming a linear pair.

[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°

[tex]\longrightarrow[/tex] x + 13 + 4x + 2 = 180°

[tex]\longrightarrow[/tex] 5x + 15 = 180°

[tex]\longrightarrow[/tex] 5x = 180° ― 15

[tex]\longrightarrow[/tex] 5x = 165°

[tex]\longrightarrow[/tex] x = 165° ÷ 5

[tex]\longrightarrow[/tex] x = 33°

Therefore, the value of x is 33°.

Quick Check!

[tex]\longrightarrow[/tex] x + 13

[tex]\longrightarrow[/tex] (33 + 13)°

[tex]\longrightarrow[/tex] 46°

And, another angle :

[tex]\longrightarrow[/tex] (4x + 2)°

[tex]\longrightarrow[/tex] {4(33) + 2}°

[tex]\longrightarrow[/tex] (132 + 2)°

[tex]\longrightarrow[/tex] 134°

★ Sum of the angles should be 180° :

[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°

[tex]\longrightarrow[/tex] 46° + 134° = 180°

[tex]\longrightarrow[/tex] 180° = 180°

L.H.S = R.H.S, hence verified!

The value of x is 33

"It is  a mathematical statement which consists of equal symbol between two algebraic expressions."

"Two angles are supplementary angles if the sum of the angles is 180° "

For given question,

angle (x + 13) and angle (4x + 2) form linear pair of angles.

So, these angles are supplementary angles.

⇒ (x + 13)° + (4x + 2)° = 180°

We solve above equation to find the value of x

⇒ x + 4x + 13 + 2 = 180

⇒ 5x + 15 = 180

⇒ 5x = 165

⇒ x = 33

Therefore, the value of x is 33

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Step-by-step explanation:

6m/6 =12/6

m=2

Answer:

m=2

Step-by-step explanation:

Divide 6 on both sides

6m / 6 = 12/6

m= 12/6 = 2

So, m=2

Verification:

LHS = 6m   m=2

6 * 2 = 12

RHS = 12

Both the LHS and RHS are same, so our answer is correct

Answer: D. 99.7%

Step-by-step explanation:

Scores that lies within the first deviation(1σ) =

(20 - 5) to (20 + 5) → 15 to 25

Scores that lies within the second deviation(2σ) =

(20 - 5 - 5) to (20 + 5 + 5) → 10 to 30

Scores that lies within the third deviation(3σ) =

(20 - 5 - 5 - 5) to (20 + 5 + 5 + 5) → 5 to 35

As shown by the distribution graph below, 99.73% of the scores lies within the third deviation(3σ).

Answer:

(1/8x)-(5/6)

Step-by-step explanation:

-3/4x-1/3+7/8x-1/2

-6/8x-2/6+7/8x-3/6

-6/8x+7/8x-2/6-3/6

1/8x-5/6

Answer:

3:2, 6;4 hope this helps

Answer:

C, D

Step-by-step explanation:

If you multiply both numbers of a ratio by the same number, you get an equivalent ratio.

A.  Divide both numbers by 10

40:30 = 4:3 No

B. 10:0 No

C. Multiply both numbers by 10

3:2 = 30:20 Yes

D. Multiply both numbers by 5

6:4 = 30:20 Yes

Answer:

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean life of 82 months with a standard deviation of 7 months.

This means that [tex]\mu = 82, \sigma = 7[/tex]

Sample of 71

This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]

What is the probability that the mean monitor life would be greater than 83.8 months?

1 subtracted by the p-value of Z when X = 83.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

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

[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]

[tex]Z = 2.17[/tex]

[tex]Z = 2.17[/tex] has a p-value of 0.985.

1 - 0.985 = 0.015

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Answer:

22

Step-by-step explanation:

3x-14= 4(x-9)

3×-14= 4x-36

4x-36-3x+14=0

×-22÷0

x=22

Answer:

1 There is no number that make it divisible by 6 with no decimals

2 1,4,7

Step-by-step explanation:

2 23718/6= 3953

 23748/6= 3958

 23778/6= 3963

Answer:

There exists a relationship between interpersonal violence and health.

Step-by-step explanation:

The relationship between interpersonal violence and health :

The null hypothesis will be ; the is no relationship between interpersonal violence and health while the alternative will negate the Null ;

If no relationship exists, correlation Coefficient = 0 and if a relationship exists, then correlation Coefficient is not = 0

H0 : ρ = 0

H1 : ρ ≠ 0

α = 0.05

Reported Pvalue = 0.016

Decison region :

Reject H0 ; If Pvalue < α

Therefore, Since Pvalue < α ; we reject H0 and conclude that there exists a relationship between interpersonal violence and health.

Answer:

3(m-4)=33

3m-12=33

3m=45

m=15

Check:

3(15-4)=33

3(11)=33

33=33

Hope This Helps!!!

Answer:

m = 15

Step-by-step explanation:

3 ( m - 4 ) = 33

Solve for m

3 ( m - 4 ) = 33

Divide both side by 3

[tex]\small \sf \frac{3(m-4)}{3} = \frac{33}{3} \\ [/tex]

m - 4 = 11

Add 4 to both side

m - 4 + 4 = 11 + 4

m = 15

Answer: [tex]R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}[/tex]

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts [tex]38^{\circ}[/tex] angle to each other

The resultant of the two forces is given by

[tex]\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]

Insert the values

[tex]\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb[/tex]

Resultant makes an angle of

[tex]\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}[/tex]

So, the resultant makes an angle of [tex]22.57^{\circ}[/tex] with 9 lb force

Angle made with 13 lb force is [tex]38^{\circ}-22.57^{\circ}=15.43^{\circ}[/tex]

Answer:

Step-by-step explanation:

Answer:

4.076

Step-by-step explanation:

tan27°= |AC|/8

8*tan27°= 4.076

Use the tangent to find the unknown side lengths.

This is the answer

Ac= 4.07

Ab=8.97