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Pachacha [2.7K]
3 years ago
12

Evaluate the expression for the given value of variable(s)

Mathematics
1 answer:
Olenka [21]3 years ago
8 0
You would: 
(4 * 2 - 4) + (3 - 2^2) + (2 * 2^3)
(8 - 4) + (3 - 4) + (16)
4 + -1 + 16 = 19
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-3x-6y=11. 2x+y = 4 solving linear systems using multiplication and addition show your work
sladkih [1.3K]
<span>Example<span>Problem<span><span>Use elimination to solve the system.</span>   x –<span> y = </span>−6x <span>+ y = 8</span></span> </span><span> Add the equations.</span><span> <span><span>2x = 2</span>x = 1</span><span>Solve for x.</span></span><span> <span>x<span> + y = 8</span><span>1 + y = 8</span>y = 8 – 1y = 7</span><span>Substitute x = 1 into one of the original equations and solve for y.</span></span><span> <span>x<span> – y = −6</span>1 – 7 = −6−6 = −6 TRUE</span><span>x<span> + y = 8</span>1 + 7 = 88 = 8TRUE</span><span>Be sure to check your answer in both equations!</span></span><span>AnswerThe solution is (1, 7). </span></span>
3 0
3 years ago
Javier and his friends go out to eat. The restaurant they chose automatically adds a 15% gratuity to their food bill since they
siniylev [52]

well, we know that 213.90 includes the 15% gratuity, so if the meal price was say "x", namely that is the 100%, and we add 15% to that, then 100% + 15% = 115%, so 213.90 is really the 115%.

now, if 213.90 is the 115.%, what is "x"?  the 100%.


\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 213.90&115\\ x&100 \end{array}\implies \cfrac{213.9}{x}=\cfrac{115}{100}\implies 21390=115x \\\\\\ \cfrac{21390}{115}=x\implies 186=x


so since we know the meal without the tip is 186 bucks, the tip was then 213.90 - 186 = 27.90.

but they got extra potato wedges with butter and the waitress was wearing her best hat, they added $20 more, so the tip ended  up as 27.90 + 20 = 47.90.

now, if the cost of the meal was $186 and that is the 100%, what is 47.90 off of it in percentage?


\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 186&100\\ 47.90&x \end{array}\implies \cfrac{186}{47.90}=\cfrac{100}{x}\implies 186x=4790 \\\\\\ x=\cfrac{4790}{186}\implies x\approx \stackrel{\%}{25.75}

7 0
3 years ago
Read 2 more answers
The U.S. government has devoted considerable funding to missile defense research over the past 20 years. The latest development
Bad White [126]

Answer:

a) Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

X \sim Bin(n =20, p=0.8)

b) X \sim Bin(n =20, p=0.8)

c) P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456

d) P(X \geq 15) = P(X=15)+ .....+P(X=20)

P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456

P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218

P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205

P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137

P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058

P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012

P(X\geq 15)=0.804208

e) E(X) = np = 20*0.8 = 16

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

X \sim Bin(n =20, p=0.8)

Part b

X \sim Bin(n =20, p=0.8)

Part c

For this case we just need to replace into the mass function and we got:

P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456

Part d

For this case we want this probability: P(X\geq 15)

And we can solve this using the complement rule:

P(X \geq 15) = P(X=15)+ .....+P(X=20)

P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456

P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218

P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205

P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137

P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058

P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012

P(X\geq 15)=0.804208

Part e

The expected value is given by:

E(X) = np = 20*0.8 = 16

5 0
3 years ago
Angle C and angle D are supplementary. If the measure of angle D is 84 degrees, what is the measure
garik1379 [7]

Suplementary is angles add up to 180 degrees

C=180-D

C=180-84

C=96 degrees

Hope this helped :)

3 0
2 years ago
Read 2 more answers
3x2 + 5x - 7(x2 + 4)
goldenfox [79]

Answer:

-4x^2+5x-28

Step-by-step explanation:

Expand -7(x^2 +4) = 3x^2+5x-7x^2-28

Simplify 3x^2+5x-7x^2-28 = -4x^2+5x-28

5 0
3 years ago
Read 2 more answers
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