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algol13
3 years ago
12

3. If x +4, 2x+5, and 4x +3 represent the first three terms of an arithmetic sequence, then find the

Mathematics
1 answer:
solong [7]3 years ago
8 0

first term = initial number

second term = initial number + common difference

third term = initial number + 2(common difference)

So...

2x+5-(x+4) = common difference

4x+3-(2x+5) = also common difference

2x+5-(x+4) = x+1

4x+3-(2x+5) = 2x-2

Because x+1=2x-2 we can solve for x.

x=3

So the sequence goes... 7,11,15...

19 is the fourth term

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15=5+4(2d-3). How to you write this out? And what is the answer for d?
Monica [59]
15 = 5 + 8d - 12
15 = 8d - 7
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3 years ago
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Let X denote the number of flaws along a 100-m reel of magnetic tape (an integer-valued variable). Suppose Zdenote the number of
Lemur [1.5K]

Answer:

a) P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)

P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)

And we can find this probability like this:

P(-1.1 \leq Z \leq 1.1)= P(Z\leq 1.1) -P(Z\leq -1.1) = 0.864-0.136= 0.728

b) P(X \leq 30)= P(X

And using the z score we got:

P(X

c) P(X

And if we use the continuity correction we got:

P(X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Continuity correction means that we need to add and subtract 0.5 before standardizing the value specified.

Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(25,5)  

Where \mu=25 and \sigma=5

Part a

For this case we want to find this probability:

P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)

And if we use the z score given by:

z =\frac{x-\mu}{\sigma}

We got this:

P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)

And we can find this probability like this:

P(-1.1 \leq Z \leq 1.1)= P(Z\leq 1.1) -P(Z\leq -1.1) = 0.864-0.136= 0.728

Part b

For this case we want this probability:

P(X \leq 30)

And if we use the continuity correction we got:

P(X \leq 30)= P(X

And using the z score we got:

P(X

Part c

For this case we want this probability:

P(X

And if we use the continuity correction we got:

P(X

3 0
3 years ago
If LK is congruenat to MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28, find LJ
Juliette [100K]

Answer:

Step-by-step explanation:

Xqual-5

4 0
3 years ago
A chef buys 9cucumbers,18 peppers, and 21 tomatoes at the farmer's market. How much does she spend?
stepladder [879]
HAY THERE!

ACCORDING TO QUESTION:-
Cucumbers = 6 for $2
Peppers = 12 for $9
Tomatoes = 6 fir $4
____________
SO NOW
____________
\huge{SOLUTION:- }
____________
For 9 cucumbers = as 6 cucumbers is for $2 then 9 will be of $3........1️⃣

For 18 peppers = as 12 peppers are for$9 so 18 will be of $12.........2️⃣

For 21 tomatoes =as 6 tomatoes are for $4 then 21 tomatoes are $14 .......3️⃣

Now add 1️⃣ +2️⃣ + 3️⃣

here $3 +$12 + $14= $29

HOPE IT HELPED YOU.
6 0
4 years ago
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