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3 years ago

3 4 ( 1 6 x+16)= 3 7 (4 3 8 x−21)

Mathematics

2 answers:

babunello [35]3 years ago

7 0

Answer:

x = 1321/15662

x = 0.0843442728

Step-by-step explanation:

To solve for "x", we need to simplify the equation, then isolate "x".

To simplify, expand each bracket using the <u>distributive property</u>. (This means you can multiply the number outside the brackets with each number inside the brackets).

To isolate "x" to the left side, move all the other numbers to the right side. You move a number by canceling it out on one side by doing the <u>reverse operation to the whole equation</u>.

Simplify first:

34( 16 x + 16 ) = 37( 438x − 21 ) Distribute over each bracket

(34*16)x + (34)(16) = (37*438)x − (37)(21) Showing what to multiply

544x + 544 = 16206x − 777

Start isolating "x":

544x + 544 − 544 = 16206x − 777 − 544 Subtract 544 from both sides

544x = 16206x − 1321 On the left side: 544 cancelled out

544x − 16206x = 16206x − 16206x − 1321 Subtract 16206x on both sides

−15662x = −1321 On the right side, there is no more "x"

−15662x/−15662 = −1321/−15662 Divide both sides by −15662

x = −1321/−15662 "x" is isolated. Simplify the fraction.

x = 1321/15662 Answer as a fraction. This number can't be reduced.

x = 0.0843442728 Answer as an exact decimal.

klasskru [66]3 years ago

5 0

Answer:

x = 0.0843442728

Step-by-step explanation:

34(16x + 16) = 37( 438 x −21) distribute the 438 and the 37

(34*16x) + (34*16) = (37*438x) + (37*(−21))

544x + 544 = 16206x - 777) then isolate the x

-544x + 777

1321 = 15662 x then divide

1321 divided by 15662 = 0.0843442728

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A public rectangular-shaped pool is 15 m by 30 m. Public pools must be surrounded by a cement

n200080 [17]

Answer:

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Step-by-step explanation:

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3 years ago

USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counse

pychu [463]

Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

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".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=4, p=1-0.25=0.75)$

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

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

4 0

3 years ago

Evaluate the expression if a=2,b=-3,C=-1, and D=4<br><br><br> -2(b^2-5c)

Alenkasestr [34]

$\qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star$

Equivalent value = -28

$\textsf{ \underline{\underline{Steps to solve the problem} }:}$

$\qquad❖ \: \sf \: - 2( {b}^{2} - 5c)$

( put the values )

$\qquad❖ \: \sf \: - 2 \{( - 3) {}^{2} - 5( - 1) \}$

$\qquad❖ \: \sf \: - 2(9 - (- 5))$

$\qquad❖ \: \sf \: - 2(9 + 5)$

$\qquad❖ \: \sf \: - 2 \times 14$

$\qquad❖ \: \sf \: - 28$

$\qquad \large \sf {Conclusion} :$

-2(b² - 5c) = -28

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1 year ago

The angle 01 is located in Quadrant III, and cos(01) = -30/13

larisa [96]

Answer:

Step-by-step explanation:

Given cos(01) = -30/13 where angle 01 is located in quadrant III. In the third quadrant, both cos and sin are negative. only tan is positive.

To calculate sin(01), we will apply the trigonometry expression as shown below;

cos(01) = -30/13

According to SOH CAH TOA;

cos(01) = adjacent/hypotenuse = -30/13

sin(01) = opposite/ hypotenuse

To get the hypotenuse, we will use the pythagoras theorem

$hyp^{2}=opp^{2}+adj^{2} \\opp^{2}= hyp^{2}-adj^{2}\\opp^{2}= 13^{2} -(-30^{2} )\\opp^{2} = 169+900\\opp^{2}=1069\\opp = \sqrt{1069} \\opp = 32.70\\$

sin(01) = 32.70/13

Since sin is also negaitve in the third quadrant, the value of

sin(01) = -32.70/13

$01 = cos^{-1}- 30/13$

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2 years ago

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