What is the constant of proportionality, ?
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The null and alternative hypotheses are H0: µ ≥ 1000 and Ha: µ < 1000 respectively.

The evidence to reject the manufacturer's claim is in the rejection region for the test statistic which is z < -1.54.

The null hypothesis consist of the inequality sign “equal” sign (“=” or “≥” or “≤”).

Alternative hypothesis is the complement to the null hypothesis.

The claim: The mean life of a certain type of light bulb is at least 1000 hours”. At least in inequality is represented by “≥” sign, it is null hypothesis.

H0: µ ≥ 1000

Alternative hypothesis:

The alternative hypothesis is the complement, that is, the mean life of a certain type of light bulb is less than 1000 hours.

Ha: µ < 1000

As the alternative hypothesis contains “<” sign, the test is left-tailed.

Using α = 0.02, we have critical value from standard table of normal distribution:

z0 = -1.54

Therefore, the rejection region for the test statistic is z < -1.54.

Complete question:

A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime \bar x x ˉ x, with, \bar, on top of the bulbs in each package. 1. What is the null and alternative hypotheses? 2. At a = .02, do you have enough evidence to reject the manufacturer's claim?

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The value of 6204 ÷ 4 is 1551

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of it. For example if 30 mangoes are to be shared between 6 students. It shows that 5 mangoes will be given to each student. i.e 30/6= 5

the value of 6204/4 can be obtained by using long division:

4 in 6 gives 1 remainder 2

4 in 22 gives 5 remainder 2

4 in 20 gives 5 remainder 0

4 in 4 gives 1 remainder 0

Therefore the value of 6204/4 = 1551

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The arrangement of the fraction from least to greatest is 5/11, 2/3 and 7/8.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers

The fraction can be changed to percentage to make it easier.

7/8 = 7/8 × 100 = 87.5%

5/11 = 5/11 × 100 = 45.5%

2/3 = 2/3 × 100 = 66.7%

The arrangement is 5/11, 2/3 and 7/8.

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The total profit that the company would make on the trip can be found to be £7,320

The revenue that the company makes would be:

= Number of passengers x Amount that each passenger pays

= 400 x 23

= £9, 200

Each coach takes 50 passengers so the number of coaches needed are:

= 400 passengers / 50 passengers per coach

= 8 coaches

The total cost to the company for the trip is:
= (Number of coaches x Driver cost per coach) + (Number of coaches x Fuel per mile x Distance traveled for each coach)

= ( 8 x 95) + ( 8 x 70p x 200)

= 760 + 112, 000 p

= 760 + 112, 000/ 100 pence per pound

= £ 1,880

The total profit is:

= Revenue - total cost

= 9, 200 - 1, 880

= £7,320

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Answer:

[tex]f(x) = 2(x-9)^{2} + 3[/tex]

Step-by-step explanation:

In vertex form, (h, k) represents the vertex.

With the given vertex of (9, 3), h = 9 and k = 3. You can substitute those values into the equation.

In vertex form, a represents vertical stretch or compression.

In this case, since the parent function, x^2 is multiplied by 2, a = 2. You can substitute this into the equation.

You end up with [tex]f(x) = 2(x-9)^{2} + 3[/tex]

Answer:

  x = 10

Step-by-step explanation:

You want the value of x that satisfies x -(x-1)/3 -(2x-5)/5 +(x+8)/6 = 7.

The least common denominator is 5·6 = 30, so we can eliminate the fractions by multiplying by 30:

  30x -10(x -1) -6(2x -5) +5(x +8) = 7·30

  30x -10x +10 -12x +30 +5x +40 = 210 . . . . . eliminate parentheses

  13x +80 = 210 . . . . . . . . . collect terms

  13x = 130 . . . . . . . . . . subtract 80

  x = 10 . . . . . . . . . . divide by 13

__

Additional comment

Often an equation can be nicely solved by a graphing calculator. We like to write the equation in the form f(x) = 0, and look for the x-intercepts. Those are usually labeled by the calculator. Here that rewrite is accomplished by subtracting 7 from both sides.

The graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

Given, The function f(x) is graphed in the figure and we have to find the points on the graph representing the relative extreme values

As, we got the extreme values on the graph of a function when the graph makes a turn and the given function graph is turning at two points.

So, the graph has extreme values at two points i.e. b and d

So, the graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

Hence, the graph of the given function f(x) has two extreme values at the point 'b' and the point 'd'.

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Answer:

each water is $1.25 each coffee is $1.95

Step-by-step explanation:

we know that the difference between $10.85 and $16.70 is 3 cups of coffee

if we subtract $10.85 from $16.70 we get $5.85

$5.85 divided by 3 is $1.95

so each cup of coffee is $1.95

now we subtract the same $5.85 from the price of 4 waters and 3 coffees

$10.85 minus $5.85 equals $5.00

divide that by 4 to get the price of each water bottle and you get $1.25 per water

Answer:no picture

Step-by-step explanation:

The value of the variable x is,  x = 22.

What is variable in equation?

In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically. A linear equation with x as a variable and 9 and 4 as constants, for instance, is x+9=4.

Consider, the given equation

√(x - 6) + 2 = 6

Subtract 2 on both sides,

√(x - 6) + 2 - 2 = 6 - 2

          √(x - 6) = 4

Taking square on both sides,

[tex](\sqrt{x-6})^2=4^2\\ (x-6)=16[/tex]

     x - 6 = 16

Add 6 on both sides,

x - 6 + 6 = 16 + 6

           x = 22

Hence, the value of the variable x is x = 22.

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Answer: I am not sure if you're accustomed to using a z-score and table of probabilities or technology, so I will answer using both!

a) Since you're choosing one person from the population, you will use the mean and standard deviation from the population.  z= (210.9-197.5)/8.6 = 1.56 Using a table of normal probabilities,

P(x>210.9)= 1-P(z<1.56)= 1- 0.9406=0.0594

Using technology: normalcdf(210.9, 1E99, 197.5, 8.6)=0.0596

b) Since you're calculating the population for a sample to occur, you need to get a mean of the sampling distribution and standard deviation of the sampling distribution.

Meanpop=Meansampling dist.=197.5

St. Devsampling dist.= Stdpopulation/√n = 8.6/√15 = 2.22

Using technology, P(X>196.20)= normalcdf( 196.20, 1E99, 197.5, 2.22) = 0.7209

c) You only have to worry about the sample size in a sampling distribution if you either do not know the shape of the distribution of the population or if the distribution of the population is not normally distributed. Since this population is normally distributed (as stated in the given information), then your sample size does not have to be greater than 30.

Hope this helps! I can solve part b using a z-score if you need me to.

Step-by-step explanation:

The total volume of 3:12 is 90 gallons  

In math, the term Ratio is used to compare two or more numbers or quantities. It indicates how small or big a quantity is when compared to each other. In a ratio, the comparison between two values is done by using division.  

Here we have    

54 gallons is the volume of 2:7

=> As we know 2+7 = 9

Therefore, for 9 parts = 54 gallons of volume

=> 1 part = 54/9 = 6 gallons of volume

Here we need to find 3: 12

For 3 parts = 3 × 6 gallons of volume = 18 gallons

For 12 parts = 12 × 6 gallons of volume = 72 gallons

=> total volume = 18 gallons + 72 gallons = 90 gallons

Therefore,

The total volume of 3:12 is 90 gallons  

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According to the intercepts and points, the equation is of the parabola is y = (1/2)*(x + 2 + √2)*(x + 2 - √2)

Equation of the parabola:

The general form of a parabola with the x-intercepts (a, 0) and (b, 0) can be written as:

y = a*(x - a)*(x - b).

Given.

Here we have the x - intercepts (-2 - √2, 0) and (-2  + √2, 0) and the points (-1, 1).

Now, we have to find the equation of the parabola.

Here we know that the x-intercepts are (-2 - √2, 0) and (-2  + √2, 0)

When we apply the values on the general form of the equation of the parabola, then we get the equation as:

=> y = a*(x + 2 + √2)*(x + 2 - √2)

Here we also know that the y-intercept is (-1, 1), which means that when x = -1, we must have y = 1, replacing that we get:

=> 1 = a*(2 + √2)*( 2 - √2)

=> 1 = a*(4 - 2)

=> 1 =  2a

=>  a = 1/2

Therefore, the equation of the parabola is written as,

=> y = (1/2)*(x + 2 + √2)*(x + 2 - √2)

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The number of hours that it will take Alonso to drive 288 miles is 12 hours.

Since Alonso was driving down a road and after 4 hours he had traveled 96 miles, the speed will be:

Speed = Distance / Time

Speed = 96 / 4

Speed = 24 miles per hour.

Therefore, the time taken for 288 miles will be:

Time = Distance / Speed

Time = 288 / 24

Time = 12

The time taken is 12 hours.

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Answer:

35h+180≤400

Step-by-step explanation:

You multiply 35 by the amount of hours the clown can be at the party (h) and add $180 for the amount of food, which should equate to less than or equal to $400. Hope this helps! :D

Please please PLEASE mark BRAINLIEST!! <3

Answer:

35h+180≤400

I did this question, and I got it correct.

The time that it take the wevaer to complete 3 1/3 baskets is 5 days.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the weaver completes 2/3 of a basket each day. The time that it will take the wevaer to complete 3 1/3 baskets will be:

= Number of baskets / Number completed daily

= 3 1/3 ÷ 2/3

= 10/3 ÷ 2/3

= 10/3 × 3/2

= 5

It'll take 5 days.

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Answer:

?????

Step-by-step explanation:

The measure of angle 4 is 121 degrees.

We know that the sum of all angles of triangle is 180 degrees.

∠1 + ∠2 + ∠3 = 180°

81° + 40° + ∠3 = 180°

∠3 = 180° - 121°

∠3 = 59°

We can observe that, angle 3 and angle 4 are linear angles.

So, ∠4 + ∠3 = 180°

∠4 = 180° - ∠3

∠4 = 180° - 59°

∠4 = 121°

Therefore, the measure of angle 4 is 121 degrees.

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Answer:

y = -30

(0, -30)

Step-by-step explanation:

f(x) = 2(2x - 3) (5x + 5)

2 = 0, 2x - 3 = 0, 5x + 5 = 0

               +3    +3      -5     -5

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

             2x = 3 ,     5x = -5

            ÷2    ÷2      ÷5    ÷5

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

                x = (3/2),   x = -1

f(x) = 2(2(0) - 3) (5(0) + 5)

        2(0 - 3) (0 + 5)

         2(-3) (5)

             -6 × 5 = -30

f(x) = -30

y = -30

(0, -30)

f(x) = 2(2x - 3) (5x + 5)

        2(2(3/2) - 3) (5(3/2) + 5)

        2(3 - 3) (15/2 + 5)

         2(0) (25/2)

y = 0

((3/2), 0))

f(x) = 2(2x - 3) (5x + 5)

        2(2(-1) - 3) (5(-1) + 5)

         2(-2 - 3) (-5 + 5)

          2(-5) (0)

             -10(0)

y = 0

(-1, 0)

I hope this helps!

The true statement is 'Every irrational number can be represented with the help of decimals.'

The correct answer is an option (B)

We know that the rational numbers are of the form p/q (i.e., simple fraction) where p, q are integers with q ≠ 0

And an irrational numbers are real numbers that cannot be represented as simple fractions.

An irrational numbers can be written in decimals.

√3 = 1.7321

We know that every terminating decimal is a rational number (for example, 2.5 = 5/2) but every rational number may not be a terminating decimal (for example, 2/3 = 0.666...)

So, a statement 'Every irrational number can be represented as a fraction.' is false.

A statement 'Every irrational number can be represented with the help of decimals.' is True

A statement 'Every rational number can be represented as a terminating decimal.' is False.

and a statement 'Every rational number can be represented as an integer.' is False.

Therefore, the true statement is 'Every irrational number can be represented with the help of decimals.'

The correct answer is an option (B)

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At a z-score of 1.80, the percentage of the scores that are better than yours is equal to 3.59%.

In Mathematics, a z-score is sometimes referred to as a z-value or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Since a score of 85 on a test corresponds to a z-score of 1.80, the percentage of the scores that are better than yours is given by:

P(x > 85) = P(z > 1.80)

P(z > 1.80) = 0.0359

P(z > 1.80) = 3.59%.

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The altitude of the airplane=300 m

What is altitude?

The height at which something is relative to a planet's or a natural satellite's surface, like sea level or land

The Pythagorean Theorem is a well-known geometric principle that states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equal the total of the squares on the legs.

The given figure is a right triangle.

opposite side=x

hypotenuse=500 m

Adjacent side=400 m

According to Pythagoras' theorem,

hypotenuse²=opposite side²+Adjacent side²

500² = x²+400²

2500=x²+1600

x²=2500-1600=900

x=√900=±300

x=300, x=-300

consider positive value

So, the altitude of the airplane=300 m

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The required coordinates of vertex A' are (3, 4) in the trapezium ABCD.

Trapezium ABCD is given in the question which has :

The coordinates of vertex A is (2, 6)

Here the scale factor is 2

A = (2, 6)

The scale factor of a dilation is given as

k = 2

The center of dilation is given as

Center = (1, 8)

The rule of the dilation is calculated using as

B' = (k(x - a) + a, k(y - b) + b)

Where

(a, b) = (1, 8)

k = 2

(x, y) =  (2, 6)

So, we have

A' = (2 × (2 - 1) + 1, 2 × (6 - 8) + 8)

A' = (3, 4)

Hence, the required coordinates of vertex A' are (3, 4).

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The question seems to be incomplete the correct question has been attached

Answer:

67

Step-by-step explanation:

a+45=112

  -45.  -45

a=67

Hopes this helps please mark brainliest

Answer:

a = 67

Step-by-step explanation:

Given equation,

→ a + 45 = 112

Now the value of a will be,

→ a + 45 = 112

→ a = 112 - 45

→ [ a = 67 ]

Hence, the value of a is 67.

Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years,

What is an interest rate?

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Here, we have

A = P e^(rt) ......(1)

P = Amount Invested = $7000

Interest Rate = 9%

A = Accumulated Amount Double the amount invested = 2P = $14000

t = time in years

from equation (1) , we get

14000 = 7000×e^(0.09)t

2 =  e^(0.09)t

㏑2 = 0.09t

0.6931 = 0.09t

t = 0.6931/0.09

t = 7.7 years

Hence, Amount Invested Annual $7000, Interest Rate of 9%  Accumulated Amount is Double the amount invested in 7.7 years.

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Answer:

Step-by-step explanation:

so there are square root properties that they want you to recognize and respect :P  everyone wants a little respect,  even the square root sign :D

first we can move things under one root sign, like this...

[tex]\sqrt{10}[/tex] * [tex]\sqrt{6}[/tex] = [tex]\sqrt{10 * 6}[/tex]

now we can do that multiplication under the square root sign.

[tex]\sqrt{10 * 6}[/tex] = [tex]\sqrt{60}[/tex]

now we can think about this for a long long time and see that 60 can be split up in other ways besides  10 * 6

for instance 15 * 4  also is  60

so this is equal  [tex]\sqrt{15 * 4}[/tex] = [tex]\sqrt{10 * 6}[/tex] = [tex]\sqrt{60}[/tex]

now just take out the perfect square part

2 * [tex]\sqrt{15}[/tex]

this isn't one of the listed answers but it is a correct answer , for what is being asked.   The teacher got the question wrong :o

Answer:

120, 60, 180

Step-by-step explanation:

The polynomial expressions are arranged from least to greatest based on their degree as: I, III, II, IV.

The degree of a polynomial expression can be described as the highest exponential power that the terms of a polynomial has.

For example, if we have the polynomial expression that is given as 5x³ + 2x² + 4, the highest power is 3, therefore, the degree of the polynomial is 3.

Thus:

The degree of x + 2xyz is one.

The degree of 9x³y² is three.

The degree of 18x² + 5ab − 6y is two.

The degree of 4x^4 + 3x² − x − 4 is four.

Therefore, from least to greatest, we have: I, III, II, IV.

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Answer:

x = 20

Step-by-step explanation:

12x + 11 = 251

12x + 11 - 11 = 251 - 11

12x = 240

12x /12  = 240/12

x=20