Katherine has a points card for a movie theater.
She receives 75 rewards points just for signing up.
She earns 13.5 points for each visit to the movie theater.
She needs at least 120 points for a free movie ticket.
Which inequality can be used to determine s, the minimum number of visits
Katherine needs to earn her first free movie ticket?

Answer:

n(A) = {6,9}

n(B) = {3,9}

n(A intersection B) = {9}

nA union B) = {1,3,6,9}

hope to this helps

Answer:

$850.79

Step-by-step explanation:

Assuming "$ 796-99" meant $796.99

796.99 increase 6.75% =

796.99 × (1 + 6.75%) = 796.99 × (1 + 0.0675) = 850.786825

Answer:

Each can of soda costs about 33 cents.

Step-by-step explanation:

This is just a simple division problem, and you can find the answer by dividing the cost of the sodas by the total number of sodas, so 4/12. If you complete that problem, the answer is 0.33 repeating, and since it asks you to round to the nearest hundredth, the answer is just 0.33. It is in dollar amounts, so the answer is 33 cents.

The quadrilateral with no pair of parallel sides is trapezium

Given data ,

A = a quadrilateral with no pair of parallel sides

This type of quadrilateral is called a trapezium. In some countries, a trapezium is defined as having exactly one pair of parallel sides, while in other countries, a trapezium is defined as having at least one pair of parallel sides.

In any case, a quadrilateral with no pair of parallel sides is not considered a trapezium. Instead, it is known as a general quadrilateral.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

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Answer:

x-5

x-2

Step-by-step explanation:

Questions 1:

√(x²-10x+25)

x²-10x+25= (x-5)²

√(x-5)²= x-5

question 2:

x²-4x+4= (x-2)²

√(x-2)²= x-2

Answer:

Step-by-step explanation:

cdfbdfbf

Answer:

"then a student earns a b"

Step-by-step explanation:

Verifying that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c = 2  such that f'(c) = 0.

Given:

Consider the function f(x) = x2 - 4x + 8 on the interval 0, 4. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0.

f(x)=x^2−4x+8, [0,4]

when, x = 0

f(x) = x^2 -4x +8

f(0) = y = 0 - 0 + 8 = 8

when, x=4

f(5) = y = 16 - 16+8 =

thus, we have 2 points (0, 8) ; (4, 8)

slope,m = {8-(8)} / {4-0} = 0

hence, we have to calculate all the points,x where 0<x<8 and slope=0

f '(x) = 2x - 4 = 0

or, f '(c) = 2c - 4 = 0

c = 4/2 =2 ( 0<x<4)

hence, the there is only one solution c=2 which satisfies Rolle's theorem.

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Given the points ( 8 , 5 ) and ( 4 , 4 )

The general slop-intercept form of the equation of the line is:

y = mx + c

where m is the slope and c is y-intercept

The slope will be calculated as following:

So, the equation of the line will be:

Using the one of the given points to find the value of c

Let , we will use the point ( 4 , 4 )

so, when x = 4 , y = 4

So, the slope - intercept equation of the line is:

Answer:

17.32 minutes

Step-by-step explanation:

The standard deviation for a uniform distribution is:

\(\sigma =\frac{b-a}{\sqrt12}\)

If a = 20 minutes and b = 80 minutes, the standard deviation is:

\(\sigma =\frac{80-20}{\sqrt12} \\\sigma=17.32\ minutes\)

The standard deviation of the distribution of consumer usage time of computers in the public library is 17.32 minutes.

Answer: All of these expressions have the same value because the answer will always be 20.

Each dividend is 20 times the divisor.

Each dividend is 10 times the dividend below it.

Each divisor is 10 times the divisor below it.

The quotient of each pair of numbers is therefore the same.

Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and  0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.

a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.

b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)

Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,

P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228

P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392

P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269

P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093

P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016

P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011

d) The mean and standard deviation of the distribution is given by:

mean = n*p = 5*0.256 = 1.28

standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995

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The multiplier for this economy is 1.

To calculate the multiplier for this economy, we need to determine the relationship between changes in income (ΔY) and the resulting change in aggregate demand. The multiplier represents the ratio of the change in aggregate demand to the initial change in autonomous spending.

In this case, the autonomous spending components are consumption (C), investment (I), government spending (G), and exports (X), while imports (M) and taxes (tY) are considered to be induced components.

The aggregate demand (AD) can be calculated as follows:

AD = C + I + G + X - M

= (250 + 0.75Y) + 200 + 350 + 100 - (50 + 0.25Y)

= 950 + 0.5Y

The tax component (tY) can be calculated as:

tY = 0.2Y

The equilibrium condition in an economy is when aggregate demand (AD) equals income (Y):

AD = Y

Substituting the expressions for AD and Y, we get:

950 + 0.5Y = Y

Simplifying the equation:

0.5Y = 950

Y = 950 / 0.5

Y = 1900

Now, to calculate the multiplier (k), we need to determine the change in aggregate demand (∆AD) resulting from a change in autonomous spending (∆AS):

k = ∆AD / ∆AS

Let's assume a change in investment spending (∆I) by an amount of ∆I = 100. This change in investment spending (∆I) is an autonomous component.

The change in aggregate demand (∆AD) can be calculated as:

∆AD = ∆C + ∆I + ∆G + ∆X - ∆M

= 0 + 100 + 0 + 0 - 0

= 100

The change in autonomous spending (∆AS) is equal to the change in investment spending (∆I):

∆AS = ∆I = 100

Finally, we can calculate the multiplier:

k = ∆AD / ∆AS

= 100 / 100

= 1

Therefore, the multiplier for this economy is 1, indicating that a change in autonomous spending will lead to an equal change in aggregate demand and income.

Correct Question :

Consider an economy that is described by the following model:  

C=250+0.75Y

M=50+0.25Y

I=200

G=350

X=100

t=20%

Where:  

C= consumption spending

M= imports

Y= income

I= investment spending

G= government spending

X= exports

t= tax rate

​Calculate the multiplier for this economy.

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Answer:

5 liters

Step-by-step explanation:

Let x represent the number of liters of the 17% solution, and represent the percentages as decimal values:

0.1(2) + (0.17)(x) = 0.15(x + 2)

Simplify:

0.2 + 0.17x = 0.15x + 0.3

Solve for x:

0.17x = 0.15x + 0.1

0.02x = 0.1

x = 5

So, you would need 5 liters of a 17% solution to get a 15% solution

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The side of the square of each block = 2 feet

Given,

Shelly sews a square blanket that has an area of 144 square feet.

and,  it has 36 square blocks, each the same size.

To find the approximate length of each side of a block

Now, According to the question:

36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks

= 144/ 36

= 4

The area of each square = 4 square feet

We know that

Area of square = side ^2

Side ^2 = 4

side = \(\sqrt{4}\)

Side = 2

Hence, The side of the square of each block = 2 feet

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Barnes and Nobel pay $25.6 for this book and the profit Barnes and Noble make on this book sale is $6.4

Let the cost price of the book that Barnes and Nobel buy is x

Barnes and Nobel marks up the price that it pays the publisher for a book by 25%

the selling price of a book is $32. 00

x + 25 % of x is 32

x + (25/100)x = 32

x + 1/4 x = 32

5/4 x = 32

x = 32 (4/5)

x = 25.6

Profit = selling price - cost price

Profit = 32.00 - 25.6

= 6.4

Therefore,  Barnes and Nobel pay $25.6 for this book and the profit Barnes and Noble make on this book sale is $6.4

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(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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Answer:

x = 17

<2 = 121

Step-by-step explanation:

We know that angle 1 and angle 3 form a linear pair, which means they add to 180

7x+2 + 3x+8 = 180

Combine like terms

10x+ 10 = 180

Subtract 10 from each side

10x+10-10 = 180-10

10x = 170

Divide by 10

10x/10 =170/10

x = 17

Angle 1 and angle 2 are vertical angles and vertical angles are equal

<1 = <2 = 7x+2 = 7(17) +2 =119+2=121

Answer:

 6z ^ 4-4 is a factor

Step-by-step explanation:

Given data

6z ^ 4 - 4 + 9(y ^ 3 + 3)

open bracket

6z ^ 4 - 4 + 9y ^ 3 + 27

collect like terms

6z ^ 4+9y^3 - 4 +27

6z ^ 4+9y^3 - 23

From the above expression  6z ^ 4-4

Answer:

its a.

(y^3+3)

Step-by-step explanation:

common sense

The screw's area is 93.5 mm^2 since it is a regular hexagon with a side length of 6 mm. The correct answer is option D.

How do you locate the location of the screw?

The following equation may be used to calculate the area of a hexagon:

\(A = \frac{3.\sqrt3}{2} * a^2\)  , where a = side length

However, the figure is a composite figure made up of two triangles and one rectangle, and the side lengths are not equal;

The triangles' base length is 12

The triangles' height is 3

Each triangle's area is equal to 0.5 x 12 x 3 = 18.

The rectangle's width is 12.

The height of the rectangle equals 6.

72 is the area of the rectangle (12 x 6).

The screw area is 18 + 18 + 72, or 108.

Nevertheless, if we consider the screw to be a normal hexagon with a side length of 6, we have:

\(A = \frac{3.\sqrt3}{2} * 6\) mm^2 = 93.5 mm^2

Therefore, the correct answer is option D.

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The correct question would be as in the image

Answer:

A

Step-by-step explanation:

h determines how much d she will get and hence B and D are wrong

independent variable means the cause

dependent variable means the effect

9514 1404 393

Answer:

  a) (x < -3) ∪ (-1 < x)

  b) all real numbers

  c) x ≤ 1

  d) no solution

Step-by-step explanation:

An absolute value inequality of the form |f(x)| ? a resolves to two inequalities:

  ±f(x) ? a

where ? is some comparison symbol.

__

a) |x +2| > 1

resolves to the inequalities ...

  x + 2 > 1   ⇒   x > -1

and the other inequality this resolves to is ...

  -(x +2) > 1

  -x -2 > 1

  -x > 3

  x < -3

Then the solution is the union of the disjoint solution spaces:

  (x < -3) ∪ (-1 < x)

__

b) |2(x -1)| ≥ 0

  2(x -1) ≥ 0   ⇒   x ≥ 1

and the other inequality this resolves to is ...

  -2(x -1) ≥ 0

  x -1 ≤ 0 . . . . . divide by -2

  x ≤ 1

The union of these solutions is ...

  x ∈ all real numbers

__

c) 9x -4 ≤ 6 -x

  10x ≤ 10 . . . . . . add x+4 to both sides

  x ≤ 1 . . . . . . . . . divide by 10

__

d) No solution. (An absolute value cannot be negative.)

__

The attachment shows the solutions plotted against a number line.

_____

Additional comment

When the inequality is of the form ...

  |f(x)| < a

it can be written as the compound inequality ...

  -a < f(x) < a

If the comparison is > instead of <, using the same "expansion" results in an inconsistency:

  -a > f(x) > a . . . . . . never true for a > 0

If you ignore that technicality (which your teacher may not understand), you can do the solution in the same way you would for the other inequality symbol(s). Just remember the result should be the union of the two disjoint solution spaces.

Using (a) as an example:

  -1 > x+2 > 1 . . . . . to solve this, we subtract 2 everywhere

 -3 > x > -1   ⇒   the solution is (-3>x) ∪ (x>-1)

Answer:

1 and 23

Step-by-step explanation:

Answer:

1 and 23

Step-by-step explanation:

Since 23 is a prime number, therefore, it has only two factors. Factor pairs of the number 23 are the natural numbers but not a fraction or decimal number.

Step-by-step explanation:

19 m = 0.019 km

28 m = 0.028 km

686 m = 0.686 km

75 km 6 m = 75.006 km

8282 m = 8.282 km

hope this answer helps you dear...take care!

Answer:

19 m = 0.019 km

28 m = 0.028 km

686 m = 0.686 km

75 km 6 m = 75.006 km

8282 m = 8.282 km

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The probability that a sample of 120 female graduates will = 0.8905

what is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

= |y -µ| ≥ 0.60

z = y -µ /σ√n

= 0.60/4.10√120

= 0.60/0.3742770

=1.60

Pr ( y -µy) ≤ 0.60 = P |z|≤1.60

=P ( -1.60≤ Z≤ -1.60)

=P (Z ≤ 1.60) -P ( Z≤ -1.60)

= 0.9452 - 0.0547 using z table

= 0.8905

Female graduates

mean = 27.83

sd = 4.10

sample = 120

µx = 27.83

σx = σ/√n

= 4.10/√120

a) P (X bar > 27.83)

= P (X bar -µx)/ σx > 27.83-27.83/4.10/√120

= P ( z > -1.60)

= 0.9452

For men

Mean=µ=37.39

Sd=σ=4.60 ,n=50

Probability that sample mean within $1.00 of the population mean

u-1=37.39-1=36.39

u+1=37.39+1=38.39

P = (36.39 <X bar < 38.39)

= P \(\frac{36.39-37.39 }{4.60/\sqrt{60} } < \frac{X bar - µ}{σ/\sqrt{n} } < \frac{39.39-37.39}{4.60/\sqrt{60} }\)

= P ( -1.6839 < Z <1.6839

= P ( -1.68 < Z <1.68)

= P (Z < 1.68) - P(Z < -1.68)

= 0.9535- 0.0465

= 0.9070

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The probability of drawing a red marble from the jar is 5/11 and the probability of drawing a blue marble from the jar is 6/11.

There are 22 marbles in the jar in total, 10 of which are red and 12 of which are blue. To find the probability of drawing a red marble, we can use the formula for probability:

Probability = Number of favorable outcomes / Total number of outcomes

In this case, the number of favorable outcomes is 10 (the number of red marbles), and the total number of outcomes is 22 (the total number of marbles in the jar). Plugging these values into the formula, we get:

Probability of drawing a red marble = 10/22

This fraction can be reduced to 5/11 by dividing both the numerator and denominator by 2. So, the probability of drawing a red marble from the jar is 5/11.

To find the probability of drawing a blue marble, we can use the same formula:

Probability = Number of favorable outcomes / Total number of outcomes

In this case, the number of favorable outcomes is 12 (the number of blue marbles), and the total number of outcomes is 22 (the total number of marbles in the jar). Plugging these values into the formula, we get:

Probability of drawing a blue marble = 12/22

This fraction can also be reduced to 6/11 by dividing both the numerator and denominator by 2. So, the probability of drawing a blue marble from the jar is 6/11.

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