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3 years ago

Which is a correct first step for solving this equation? 4x=7+3(2x−5)

Mathematics

2 answers:

Gemiola [76]3 years ago

7 0

Answer:

Step-by-step explanation:

The easiest first step is to remove the brackets. Other things could be done, but they are done just because you can.

4x = 7 + 3*2x - 5*3 Just to show you more, I'll keep going.

4x = 7 + 6x - 15 Combine the minus 15 and 7

4x = 6x + 7 - 15

4x = 6x - 8 Now add 8 to both sides. It's a toss up of what to do

4x + 8 = 6x - 8 + 8

4x + 8 = 6x Subtract 5x from both sides

4x - 4x + 8 = 6x - 4x

8 = 2x Divide by 2

x = 4

The steps usually follow this order.

Dvinal [7]3 years ago

6 0

Answer:

x=4

Step-by-step explanation:

you have to do the ( ) first then you combine like terms and then you add them up and boom you got the answer

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In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

Marina86 [1]

Answer:

(a) 0.94

(b) 0.20

Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let $p_1$ be the probability that a bearing meets the specification.

So, $p_1=0.9$

Sample size, $n_1=500$ , is large.

Let X represent the number of acceptable bearing.

Convert this to a normal distribution,

Mean: $\mu_1=n_1p_1=500\times0.9=450$

Variance: $\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45$

$\Rightarrow \sigma_1 =\sqrt{45}=6.71$

(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.

So, $X\geq 440.$

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56$ .

So, the probability that a given shipment is acceptable is

$P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062$

Hence, the probability that a given shipment is acceptable is 0.94.

(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.

Denote the probability od acceptance of a shipment by $p_2$ .

$p_2=0.94$

The total number of shipment, i.e sample size, $n_2= 300$

Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, $\mu_2$ , and variance, $\sigma_2^2$ .

Mean: $\mu_2=n_2p_2=300\times0.94=282$

Variance: $\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92$

$\Rightarrow \sigma_2=\sqrt(16.92}=4.11$ .

In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85$ .

So, the probability that a given shipment is acceptable is

$P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977$

Hence, the probability that a given shipment is acceptable is 0.20.

(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).

The area right to the z-score=0.99

and the area left to the z-score is 1-0.99=0.001.

For this value, the value of z-score is -3.09 (from the z-score table)

Let, $\alpha$ be the required probability of acceptance of one shipment.

So,

$-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}$

On solving

$\alpha= 0.977896$

Again, the probability of acceptance of one shipment, $\alpha$ , depends on the probability of meeting the thickness specification of one bearing.

For this case,

The area right to the z-score=0.97790

and the area left to the z-score is 1-0.97790=0.0221.

The value of z-score is -2.01 (from the z-score table)

Let $p$ be the probability that one bearing meets the specification. So

$-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}$

On solving

$p=0.9053$

Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.

8 0

3 years ago

Help me someone:((!!!!!

LiRa [457]

Answer:

Hope this helps!

Step-by-step explanation:

2L + 3S = 83

4L + 8S = 197

Multiplies the top equation by -2.

-4L + -6S = -166

4l + 8S = 197

Adding them together...

2S = 31

S = 31/2 = 15.5

Plugging into the first equation:

2L + 3S = 83

2L + 3(15.5) = 83

2L + 46.5 = 83

2L = 83 - 46.5

2L = 36.5

L = 36.5/2 = 18.25

check:

2L + 3S = 2(18.25) + 3(15.5) = 36.5 + 46.5 = 83

4L + 8S = 4(18.25) + 8(15.5) = 73 + 124 = 197

The Large box weighs 18.25

The small box weighs 15.5

6 0

3 years ago

Marci, Bobby, and Max began their homework at the same time. Marci finished her homework in 60 minutes. Bobby finished his homew

NeX [460]

Answer: Marci: 60 minutes

Bobby: 30 minutes

Max: 90 minutes

Step-by-step explanation:

50% of 60 is 30.

100% of 60 is 60, plus 50% is 60+30, which gets you 90.

5 0

3 years ago

Read 2 more answers

M is a degree 3 polynomial with m ( 0 ) = 53.12 and zeros − 4 and 4 i . Find an equation for m with only real coefficients (i.E.

Nitella [24]

Answer:

Therefore the required polynomial is

M(x)=0.83(x³+4x²+16x+64)

Step-by-step explanation:

Given that M is a polynomial of degree 3.

So, it has three zeros.

Let the polynomial be

M(x) =a(x-p)(x-q)(x-r)

The two zeros of the polynomial are -4 and 4i.

Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.

Then,

M(x)= a{x-(-4)}(x-4i){x-(-4i)}

=a(x+4)(x-4i)(x+4i)

=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]

=a(x+4)(x²-16i²)

=a(x+4)(x²+16) [∵i² = -1]

=a(x³+4x²+16x+64)

Again given that M(0)= 53.12 . Putting x=0 in the polynomial

53.12 =a(0+4.0+16.0+64)

$\Rightarrow a = \frac{53.12}{64}$

=0.83

Therefore the required polynomial is

M(x)=0.83(x³+4x²+16x+64)

5 0

3 years ago

I will give the BRAINIEST!!! Please help!!

kap26 [50]

Answer: B. y-1=2(x-3)

Step-by-step explanation:

First subtract both sides by 2x so it becomes -y=-2x-1

Second divide both sides by -1 so it becomes y=2x+1

After that to get it in the form they want it subtract 1 from both sides so that it becomes y-1=2x

7 0

4 years ago