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3 years ago

A father is 28 years older than his daughter. In six years' time, he will be three times her age. Find their present ages.

Mathematics

2 answers:

konstantin123 [22]3 years ago

8 0

Answer:

<h2>Daughter's age = 6</h2><h2>Father's age = 34</h2>

Step-by-step explanation:

Let the age of daughter be x

Then the age of father will be x + 28

<u>In 6 years time:-</u>

The age of father = x + 28 + 2 = 30 + x

The age of daughter = x + 6

According to the question,

Father will be three times the age of his daughter.

30 + x = 3(x + 6)

30 + x = 3x + 18

x - 3x = 18 - 30

-2x = - 12

x = - 12/-2

x = 6

So therfore,

Daughter's present age = 6 years

Father's present age = 34 years

Hope this helps :)

frozen [14]3 years ago

8 0

A father is 28 years older than his daughter. In six years' time, he will be three times her age. Find their present ages.

Please include your working out!!

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5) Two machines M1, M2 are used to manufacture resistors with a design

Basile [38]

Answer:

Since M1 has the higher probability of being in the desired range, we choose M1.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

Two machines M1, M2 are used to manufacture resistors with a design specification of 1000 ohm with 10% tolerance.

So we need the machines to be within 1000 - 0.1*1000 = 900 ohms and 1000 + 0.1*1000 = 1100 ohms.

For each machine, we need to find the probabilty of the machine being in this range. We choose the one with the higher probability.

M1:

Resistors of M1 are found to follow normal distribution with mean 1050 ohm and standard deviation of 100 ohm. This means that $\mu = 1050, \sigma = 100$

The probability is the pvalue of Z when X = 1100 subtracted by the pvalue of Z when X = 900. So

X = 1100

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1100 - 1050}{100}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915.

X = 900

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{900 - 1050}{100}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.6915 - 0.0668 = 0.6247.

M1 has a 62.47% probability of being in the desired range.

M2:

M2 are found to follow normal distribution with mean 1000 ohm and standard deviation of 120 ohm. This means that $\mu = 1000, \sigma = 120$

X = 1100

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1100 - 1000}{120}$

$Z = 0.83$

$Z = 0.83$ has a pvalue of 0.7967.

X = 900

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{900 - 1000}{120}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033

0.7967 - 0.2033 = 0.5934

M2 has a 59.34% probability of being in the desired range.

Since M1 has the higher probability of being in the desired range, we choose M1.

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3 years ago

The original price of a pair of jeans is $32 the sales price 15% off the original price what is the amount off the original pric

ivolga24 [154]

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3 years ago

Question 6 (2 points)

irinina [24]

to inverse a equation make all y's x and andy x's y

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x=4y-8

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3 years ago

A trust fund worth $25,000 is invested in two different portfolios, this year, one portfolio is expected to earn 5.25% interest

OLEGan [10]

Answer:

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

$I=P(rt)$

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

Let

x ------> the amount of money that should be invested at the rate of 5.25%

25,000-x -----> the amount money that should be invested at the rate of 4%

in this problem we have

$t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150$

substitute in the formula above

$I=P_1(r_1t)+P_2(r_2t)$

$1,150=x(0.0525*1)+(25,000-x)(0.04*1)$

Solve for x

$1,150=0.0525x+1,000-0.04x$

$0.0525x-0.04x=1,150-1,000$

$0.0125x=150$

$x=\$12,000$

$|$25,000-x=\$13,000$

therefore

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

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Read 2 more answers

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Dennis_Churaev [7]

point slope form is y=mx+ b

m is slope which is given as 1/2

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