1. Determine the lowest common multiple of 4, 9 and 12
A. 30
B. 36
C. 48
D. 54

2. Simplify 80g : 16kg
A. 4 : 5
B. 3 : 4
C. 2 : 7
D. 1 : 20

3. How many square-shaped tiles with sides of y cm that are required to cover 15y × 4y floor?
A. 60
B. 64
C. 72
D. 86

4. Puan Anis bought 8kg of beef which cost RMx per kilogram. She paid with 2 pieces of RM50 note and received a balance of RM4. Find the value of x
A. 12
B. 14
C. 16
D. 18

5. Find the circumference of a circle with radius of 21 cm
A. 66
B. 44
C. 63
D. 132

6. Anita has RMb. She spent RM(2a + 1) per day for a week. Given the balance of her money is RM45, find a formula for b
A. 2a + 46
B. 14a - 38
C. 14a + 45
D. 14a + 52

7. Given 9x²/y² - 3x = 5w, express y in terms of w and x
A. y = x/5w+x
B. y = 3x/5w+3x
C. y = 3x²/5w+3x
D. y = 3x/5w+x

I NEED ANSWERS FOR THESE QUESTIONS TQ :)​​

Answer:

10 shelves

Step-by-step explanation:

out of the other choices, 10 is most suitable to divide with 80

Answer:

6 x (3+9) add 3 and 9 = 12

6×12 = 72

Answer:

72

Step-by-step explanation:

3+9=12

12*6= 72

do everything in parenthesis first so to solve this you would do 3+9 which equals 12 then multiply 12 with 6 which gives you the answer 72 hope this helps have a good rest of your night :) ❤

Answer:

  a) 489.77 ft from friend

  b) 470.80 ft from cliff

Step-by-step explanation:

Given a man on a 135 ft cliff sees his friend at an angle of depression of 16°, you want to know the distance of the man from his friend, and the distance of the friend from the cliff.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

The 135 ft height of the cliff is modeled as the side of a right triangle that is opposite the angle of elevation from the friend to the top of the cliff. (See attachment 2.) That angle is the same as the angle of depression from the top of the cliff to the friend.

The hypotenuse of the triangle is the distance between the man and his friend. The side of the triangle adjacent to the friend is the distance to the cliff.

Using the above relations, we have ...

  sin(16°) = (cliff height)/(distance to friend)

  tan(16°) = (cliff height)/(distance to cliff)

Solving for the variables of interest gives ...

  distance to friend = (cliff height)/sin(16°) = (135 ft)/sin(16°) ≈ 489.77 ft

  distance to cliff = (cliff height)/tan(16°) = (135 ft)/tan(16°) ≈ 470.80 ft

The ma is 489.77 ft from his friend; the friend is 470.80 ft from the cliff.

__

Additional comment

The distances are given to more decimal places than necessary so you can round the answer as may be required.

<95141404393>

Given: RS and TS are tangents to the circle V at R and T, respectively, and intersect at the exterior point S.Prove: m∠RST= 1/2(m(QTR)-m(TR))

Let us consider a circle V with two tangents RS and TS at points R and T respectively as shown below. In order to prove the given statement, we need to draw a line through T parallel to RS and intersects QR at P.As TS is tangent to the circle V at point T, the angle RST is a right angle.

In ΔQTR, angles TQR and QTR add up to 180°.We know that the exterior angle is equal to the sum of the opposite angles Therefore, we can say that angle QTR is equal to the sum of angles TQP and TPQ. From the above diagram, we have:∠RST = 90° (As TS is a tangent and RS is parallel to TQ)∠TQP = ∠STR∠TPQ = ∠SRT∠QTR = ∠QTP + ∠TPQThus, ∠QTR = ∠TQP + ∠TPQ Using the above results in the given expression, we get:m∠RST= 1/2(m(QTR)-m(TR))m∠RST= 1/2(m(TQP + TPQ) - m(TR))m ∠RST= 1/2(m(TQP) + m(TPQ) - m(TR))m∠RST= 1/2(m(TQR) - m(TR))Hence, proved that m∠RST = 1/2(m(QTR) - m(TR))

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Surrender charges safeguard against such losses. Surrender costs on some annuities and insurance products can apply for as short as 30 days or as long as 15 years. If you cash in your investment in year one, the surrender cost for annuities and life insurance is typically 10%.

The surrender period is the amount of time that an investor must wait before withdrawing cash from an annuity without penalty. Surrender periods can last many years, and withdrawing funds before the conclusion of the surrender term may result in a surrender charge, which is basically a delayed sales cost.

The longer the surrender time, in general, but not always, the better the annuity's other terms.

The surrender period is the period during which an investor may withdraw funds from an annuity without incurring a surrender charge.

The surrender term can last many years, and annuitants may face large fines if they remove their invested assets before the time has finished.

Other financial instruments include a surrender period as well B-share mutual funds and entire life insurance plans are two examples.

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5.3

It is a rational number because 5.3 can be made into a fraction or ratio .

hope it helps!

In Costello et al. (2003), the independent variable that was not manipulated by the research team was the gender of the participants.

The study examined the effects of different levels of alcohol consumption on cognitive performance and mood states in young adults. Participants were assigned to different alcohol consumption groups based on their self-reported drinking habits. However, the gender of the participants was not manipulated, and the study included both male and female participants. This means that any differences in the results based on gender cannot be attributed to the research team's manipulation of the independent variable, but rather to other factors that may have affected the results.

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a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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The cost of the holiday after the discount has been applied is £1440.

Discount is a reduction in the regular price of a product or service. It is often given when a customer buys multiple items or spends a certain amount of money. Discounts are a common way for businesses to increase sales by incentivizing customers to buy more. Discounts can be a percentage of the regular price, a fixed amount, or a free gift with purchase. Discounts can be applied to items already on sale or can be applied to the full price of an item.

The customers will receive a 20% discount on the cost of the holiday, which is 20% of £1800, which is £360.
Therefore, the cost of the holiday after the discount has been applied is £1800 - £360 = £1440.

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Minimum  number is 33+4*6= 57

Give us two positive numbers, x and y.

196 is the result: x*y = 19

The minimum is the product of the first plus four times the second: x + 4y.

The first equation results in y = 196/x. Put that into the second equation as a replacement:

x + 4y = x + 4(196/x) = x + 784/x

Taking the first derivative now, we can solve for x by setting it to zero.

d(x + 784/x)/dx = 1 - 784/\(x^{2}\)

0 = 1 - 784/\(x^{2}\)

0 = \(x^{2}\)- 784 [\(x^{2}\) multiplied on both sides]

784 = \(x^{2}\)

\(\sqrt{784}\) = \(\sqrt{x^{2} }\)

Y = 196/x = 7 since we want a positive integer, hence x = 28

The factors of 196 are 196*1, 99*2, 66*3, 6*33,22*19, and 11*18 as a check.

196 + 4*1 = 200

99 + 4*2 = 107

66 + 4*3 = 78

33+4*6= 57

22 + 4*19 = 98

11 + 4*18=82

In fact, 33+4*6= 57 is minimum.

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Answer:

12

Step-by-step explanation:

Type Into Calculator:

SAT-EDIT-TYPE IN X VALUES AND Y VALUES (FROM ORDERED PAIR)-STAT-CALC-4-ENTER

Answer:

1/10

Step-by-step explanation:

The probability an event will happen is the number of desired outcomes divided by the total number of possible outcomes.

The desired outcome is pulling out a 4. The number of desired outcomes is 1 since only 1 card contains the number 4.

The total number of possible outcomes is 10 since there are 10 different cards with numbers.

p(4) = 1/10

Answer: 1/10

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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the area of the circle with a radius of 3 is approximately 28.27 square units., we use the formula A = πr^2, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Plugging in the given value of the radius, we get:

A = π(3)^2

A = π9

A ≈ 28.27

Therefore, the area of the circle with a radius of 3 is approximately 28.27 square units.

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The test statistic has a value of -633.6915 if a sample mean of 10 bottles was chosen, and the average number of ounces was 12.005.

As stated. Sample mean is 10.

12.005 people on average.

0.01 is the standard deviation.

The test statistic's value is -633.6915 when calculated using the formula:

T = mean - average population / s/root n

= 10-12.005 / 0.01/3.16

= -2.005 /0.0031

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The amount of total cost at q* is 1.

To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):

TC(q) = 10 - 6q + q^2

To find the minimum point, we differentiate TC(q) with respect to q:

d(TC(q))/dq = -6 + 2q

Setting the derivative equal to zero and solving for q:

-6 + 2q = 0

2q = 6

q = 3

So the production level q* that minimizes the total cost is 3.

To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):

TC(q*) = 10 - 6(3) + (3)^2

TC(q*) = 10 - 18 + 9

TC(q*) = 1

Therefore, the amount of total cost at q* is 1.

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Answer:

1719-1051.50 +667.50

667.50/44.50 =15

Step-by-step explanation:

The first equation is to find out how much money they have after buying the bus. The second equation is to find out how many people can come on the trip. So the amount of people that can come on the trip is 15 persons

Answer:

No.

Step-by-step explanation:

f(x) = 3x^4-4x^2-3

If a function is odd then  f(-x) = -f(x) for all values of x.

Here f(-x) = 3(-x)^4 - 4(-x)^2 - 3

= 3x^4 - 4x^2 - 3

So f(-x) = f(x) which makes it even.

By solving a system of equations we will see that the quadratic equation is:

y = 3*x^2 - 10*x - 4

We know that a general quadratic function can be written as:

y = a*x^2 + b*x + c

Here we know that the equation passes through (0, -4), replacing these values:

-4 = a*0^2 + b*0 + c

-4 = c

Then the quadratic equation is:

y = a*x^2 + b*x - 4

Now we can use the other two points (-3, -7) and (2, -12), replacing these values we will get a system of equations:

-7 = a*(-3)^2 + b*(-3) - 4

-12 = a*(2)^2 + b*(2) - 4

We can simplify these equations to get:

-3 = 9a + 3b

-8 = 4a + 2b

We can isolate b on the second equation to get:

2b + 4a = -8

2b = -8 - 4a

b = (-8 - 4a)/2

b = -4 - 2a

Now we can replace that in the other equation to get:

-3 = 9a + 3*(-4 - 2a)

-3 = 9a -12 - 6a

-3 + 12 = 3a

9 = 3a

9/3 = a

3 = a

And the value of b is:

b = -4 - 2a

b = -4 - 2*3

b = -4 - 6 = -10

Then the quadratic equation is:

y = 3*x^2 - 10*x - 4

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Step-by-step explanation:

Hey there!

Your answer is Option A.

Check all:

A. y = 6x-2

Comparing the equation with y = mx+b, we get;

m= 6

and b= -2

B. y= 6x+2

Comparing the equation with y= mx+b, we get;

m = 6

b= 2

C. y = 2x+6

Comparing the equation with y= mx+b, we get;

m= 2

b = 6

D. y= -2x-6

Comparing the equation with y= mx+b, we get;

m= -2

b= -6

Therefore, Option A is correct answer.

Hope it helps...

Answer:

\(1)then \: we \: can \: seperate2x \\ 2)then \: we \: can \: get \: x \: alone \\ 3)we \: add \: and \: divide \: in \: both \: side \\ \: of \: this \: equation \: equally \: \\ 4)we \: get \: wrong \: answer \\ thank \: you\)

Answer:

1) 10

2) 16

Step-by-step explanation:

1) 2x+15=37-2

2x+15=35

2x=35-15

2x=20

2 2

x=10

2)10x-8=9x+8

10x-9x=8+8

x=16

Hope this helps ❤

If the atmospheric pressure of 5 is measured in millibars, it would correspond to a pressure of 0.5 kPa or a pressure of approximately 1.47 inHg. However, this value should be considered as a rough estimate and would still be subject to the variability of atmospheric conditions.

It is not possible to accurately determine the altitude at which atmospheric pressure reaches 5 without additional information about the context and conditions of the atmosphere being considered. The atmospheric pressure at a given altitude can vary widely depending on factors such as temperature, humidity, and atmospheric composition.

However, in general, atmospheric pressure decreases with increasing altitude. At sea level, the standard atmospheric pressure is about 101.3 kilopascals (kPa). At an altitude of approximately 5.6 kilometers, the atmospheric pressure drops to around 50 kPa. However, this value can vary greatly depending on the conditions of the atmosphere being considered.

It is worth noting that atmospheric pressure is typically measured in units of kilopascals (kPa), millibars (mb), or inches of mercury (inHg). The conversion between these units is as follows:

1 kPa = 10 mb = 0.2953 inHg

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Your question seems incomplete. I could not find the exact question details online so I answered in general.

The required number of ways is:

C(4,1)×C(4,3)×C(4,1)³ + C(4,2)×C(4,2)²×C(4,1)²+C(4,1)×C(4,2)×C(4,1)³×C(36,1) +  C(4,1)⁴×C(36,2)

What is the combination?

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.

Here, we have

First case: 3 cards either king, Queen, Jack, or Ace and rest three cards are one from each of the three denominations king, Queen, Jack, or Ace

A number of ways of selecting 1 denomination out of four kings, Queens, Jack, or Ace are C(4,1).

Then selecting 2 cards from this denomination is C(4,3).

The number of ways of selecting 1 card from each of rest three denominations is C(4,1)³

So, in this case, the number of ways of selecting at least one Ace, at least one King, at least one Queen, and at least one Jack is:  C(4,1)C(4,3)C(4,1)³

Second case: 2 cards each of two selected denominations king, Queen, Jack, or Ace and rest two cards are one from each of the two remaining denominations king, Queen, Jack, or Ace

A number of ways of selecting 2 denominations out of four kings, Queen, Jack, or Ace are C(4,2).

Then selecting 2 cards from these two denominations is C(4,2).

The number of ways of selecting 1 card from each of rest two denominations is C(4,1)^2

So, in this case, the number of ways of selecting at least one Ace, at least one King, at least one Queen, and at least one Jack is:  C(4,2)C(4,2)²C(4,1)²

Third case: 2 cards each of one selected denominations king, Queen, Jack, or Ace and rest three cards are one from each of the three remaining denominations king, Queen, Jack, or Ace

A number of ways of selecting 1 denomination out of four kings, Queens, Jack, or Ace are C(4,1).

Then selecting 2 cards from this selected denominations is C(4,2)

The number of ways of selecting 1 card from each of rest three denominations is C(4,1)^3

The number of ways of selecting 1 card from rest 36 cards is C(36,1)

So, in this case, the number of ways of selecting at least one Ace, at least one King, at least one Queen, and at least one Jack is:  C(4,1)×C(4,2)×C(4,1)³×C(36,1)

Fourth case:

A number of ways of selecting one card from each given denomination and the rest 2 the remaining 36 cards are:

C(4,1)⁴xC(36,2)

Hence, the required number of ways is:

C(4,1)×C(4,3)×C(4,1)³ + C(4,2)×C(4,2)²×C(4,1)²+C(4,1)×C(4,2)×C(4,1)³×C(36,1) +  C(4,1)⁴×C(36,2)

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The value of y0 for which the solution of the initial value problem y' − y = 1 + 3 sin t, y(0) = y0 is:

y(0) = 3√2 - 1 = 3.24

Now, According t o the question:

A linear equation or polynomial, with one or more terms, consisting of the derivatives of the dependent variable with respect to one or more independent variables is known as a linear differential equation.

The general solution y of this equation is y = y0 + y1

where y0  = A\(e^t\) is the solution for the equation y' - y = 0 (homogeneous equation), an

  y1 = (3/2)(sint + cost) - 1 = 3√2 sin(t + (π/4)) - 1 -

particular solution of the inhomogeneous equation. Thus, we have

  y(t) =A\(e^t\) + 3√2 sin (t + (π/4))  - 1

To have the function y(t) finite for t → ∞ ,

We have to put  A = 0. Then, it follows

y(0) = 3√2 - 1 = 3.24

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The correct set of hypotheses for testing the effect of the bonus plan is:

To test the effect of the new bonus plan on increasing sales at the automobile dealership, the manager can use the following set of hypotheses:

Null Hypothesis: The mean sales rate per salesperson remains the same or less than five automobiles per month (H0: μ ≤ 5)

Alternative Hypothesis: The mean sales rate per salesperson increases with the implementation of the bonus plan (HA: μ > 5)

These hypotheses will help determine if the bonus plan has a significant impact on increasing sales.

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Answer: As x increases, the slope of the graph increases.

We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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Thus, the total cost of the first 64 units is approximately $2730.67.

To find the total cost of the first 64 units, we need to integrate the marginal cost function over the range of production from x=0 to x=64.

The marginal cost function is given by C'(x) = 8√x.

Integrating this function with respect to x, we get:
C(x) = ∫(8√x dx) = 8 * (2/3)x^(3/2) + C

To find the total cost for the first 64 units, we need to evaluate C(x) at x=64 and x=0 and subtract the results:
C(64) - C(0) = (8 * (2/3) * 64^(3/2) + C) - (8 * (2/3) * 0^(3/2) + C)

Simplifying the equation, we get:
C(64) - C(0) = 8 * (2/3) * 64^(3/2)

Now, compute the value:
C(64) - C(0) = 8 * (2/3) * 512 = (16/3) * 512 ≈ 2730.67

So, the total cost of the first 64 units is approximately $2730.67.

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