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2 years ago

Can you help me in my math work

Mathematics

1 answer:

Ket [755]2 years ago

7 0

The LCM of 18 and 24 using the prime-factorization method is 72.

The LCM of 27, 81, and 54, using the division method is 162.

In the first question, we are asked to find the LCM of the given numbers using the prime factorization method.

(i) 18, 24.

Prime factorization gives:

18 = 2*3², and 24 = 2³*3.

The LCM is the product of the highest power of each prime factor.

Thus, LCM = 2³*3² = 8*9 = 72.

Thus, the LCM of 18 and 24 using the prime-factorization method is 72.

Doing similarly for other sub-parts, The LCM of:

(ii) 16, 40 is 80.

(iii) 30, 36 is 180.

(iv) 28, 44 is 308.

(v) 20, 32 is 160.

(vi) 20, 135 is 540.

(vii) 45, 75 is 225.

(viii) 36, 84 is 252.

(ix) 12, 18, 24 is 72.

(x) 25, 35, 45 is 1575.

(xi) 9, 15, 21 is 315.

(xii) 25, 50, 75 is 150.

In the second question, we are asked to find the LCM of the given numbers, using the division method.

(i) 27, 81, 54.

The division method gives:

$\underline{2|27,81,54}\\\underline{3|27,81,27}\\\underline{3|9,27,9}\\\underline {3|3,9,3}\\\underline{3|1,3,1}\\{1|1,1,1}$

The LCM is the product of all the numbers used for division.

LCM = 2*3*3*3*3*1 = 162.

Thus, the LCM of 27, 81, and 54, using the division method is 162.

Doing similarly for other sub-parts, The LCM of:

(ii) 18, 45, 63 is 630.

(iii) 35, 55, 100 is 7700.

(iv) 210, 140, 315 is 1260.

(v) 112, 120, 150 is 8400.

(vi) 144, 180, 300 is 3600.

Learn more about LCM at

brainly.com/question/420337

#SPJ1

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The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.18 F and a standard deviat

S_A_V [24]

Answer:

99.7%

Step-by-step explanation:

Empirical rule formula states that:

• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

From the question, we have mean of 98.18 F and a standard deviation of 0.65 F

The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 F is

μ - 3σ

= 98.18 - 3(0.65)

= 98.18 - 1.95

= 96.23 F

μ + 3σ.

98.18 + 3(0.65)

= 98.18 + 1.95

= 100.13 F

Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 F which is within 3 standard deviations of the mean is 99.7%

6 0

4 years ago

Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed w

jok3333 [9.3K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The sales level that is the cut-off between quarters that are considers as "failure" and those that are not is evaluated as

$y = 6.3 \ million \ dollars$

Step-by-step explanation:

From the question we are told that the

Mean is $\mu = 8 \ million \ dollars$

Standard deviation is $\sigma = 1.3 \ million \ dollars$

Let Y be the random variable that denotes the sales made quarterly among health care information system

The normal distribution for this data is mathematically represented as

$Y$ ~ N $(\mu = 8 , \sigma^2 = 1.69)$

From the question we are told that a quarter is consider a failure by the company if the sales level that quarter in the bottom 10% of the of all quarterly sales

The the Probability of obtaining quarterly sales level that is equal to 10% of all quarterly sale (It is not below 10%) is mathematically represented as

$P[Y < y ] = 0.10$

This can be represented as a normal distribution in this manner

$P [ \frac{Y- \mu}{\sigma } < \frac{y -\mu}{\sigma} ] = 0.10$

Where $\frac{Y - \mu }{\sigma } = Z$ ~ $N(0 , 1)$

{This mean that this equal to the normal distribution between 0, 1 which is the generally range of every probability }

Therefor we have

$P[Z < \frac{y- 8}{1.3} ]$

The cumulative distribution function for a normal distribution of y is mathematically represented as

$\phi [\frac{y- 8}{1.3} ] = 0.10$

This is because a cumulative distribution function of a random value Y or a distribution of Y evaluated at y is the probability that Y will take will take a value that is less or equal to y

$\frac{y- 8}{1.3} = \phi ^{-1}(0.10)$

Calculating the inverse of the cumulative distribution function value of 0.10 which is negative the the critical value(Critical values determine what probability a particular variable will have when a sampling distribution is normal or close to normal.) of 0.01

$\phi ^{-1}(0.10) =- [1 - \frac{0.10}{2}]$

$= - 1.28155$

$\frac{y - 8}{1.3} = - 1.2816$

$=> y = 8 - (1.2816)(1.3)$

$y = 6.3 \ million \ dollars$

5 0

3 years ago

The price of the box of 10 markers is $7. The price of the box of 24 markers is $14. All prices without tax, and the price of th

stepladder [879]

Answer:

see below

Step-by-step explanation:

10 markers =7 dollars

Divide each side by 10

10/10 = 7 /10

1 marker = 7/10

y =7/10 x where y is the cost and x is the number of markers

24 markers =14 dollars

Divide each side by 24

24/24 = 14 /24

1 marker = 7/12

y = 7/12 x where y is the cost and x is the number of markers

6 0

3 years ago

Solve each system of equations using the elimination method 3x+8y=2 4x-2y=-10

LenaWriter [7]

x = -2

y = 1

let's multiply second equation by 4 to get a common coefficient of y variable.

16x-8y=-40

add the equations

3×+8y=2

16x-8y=-40

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

3x+16x = -38

19x = -38

x = -2

substitute x

3×-2 + 8y = 2

-6 + 8y = 2

8y = 2+6

y = 1

check the answer

-6+8 = 2

-8-2= -20

8 0

3 years ago

Convert 800 grams into ounces. Round your answer to the nearest tenth.

topjm [15]

800 grams into ounces is 28.2, rounded to the nearest tenth.

6 0

3 years ago