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andrew-mc [135]
3 years ago
11

in spencers garden the number of rose bushes is 7 less than 1.5 times the number of carnation bushes. If the number of carnation

bushesis c,then the expressions represents the number of rose bushes is ?
Mathematics
1 answer:
Step2247 [10]3 years ago
7 0
<span>1.5 times the number of carnation bushes. 
If the number of carnation bushes is c.
R = 1.5c - 7
Hope this helps:-)</span>
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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
Please help right away
Ilya [14]

Answer:

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Step-by-step explanation:

either 340 or 1152 vehicles

7 0
3 years ago
5. Find the mZABC if<br> ZABD = 35°, ZDBC = 55º.
Reika [66]

Answer:

m\angle ABC=90^o

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

m\angle ABC=m\angle ABD+m\angle DBC ----> by angle addition postulate

substitute the given values

m\angle ABC=35^o+55^o=90^o

5 0
3 years ago
Find an antiderivative F(x) with F′(x) = f(x) = 6 + 24x^3 + 18x^5 and F(1)=0.
7nadin3 [17]

Answer:

The antiderivative is F(X) = 6x + 6x^4 + 3x^6 - 15.

Step-by-step explanation:

Antiderivative F(x)

This is the integral of F^{\prime}(x)

So

F′(x) = f(x) = 6 + 24x^3 + 18x^5

Then:

F(x) = \int (6 + 24x^3 + 18x^5) dx

F(x) = 6x + \frac{24x^4}{4} + \frac{18x^6}{6} + K

F(x) = 6x + 6x^4 + 3x^6 + K

F(1)=0

F(X) = 0 when x = 1. We use this to find K.

F(x) = 6x + 6x^4 + 3x^6 + K

0 = 6 + 6 + 3 + K

K = -15

Thus

The antiderivative is F(X) = 6x + 6x^4 + 3x^6 - 15.

7 0
3 years ago
Prove the following statements: (a) For every integer x, if x is even, then for every integer y, xy is even. (b) For every integ
Murrr4er [49]

Answer and Step-by-step explanation:

(a) Given that x and y is even, we want to prove that xy is also even.

For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.

(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:

Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.

(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.

3 0
3 years ago
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