MATHEMATICS COLLEGE

17.Find the value of k that will make 4x² – 12x + k a perfect square trinomial.
k =
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Answers

Answer 1

Answer:

Solution:

Using formula (a-b)^2 = a^2-2ab+b^2

$4x^(2) - 12x + k \n = > (2x) ^(2) - 2(2x)(3) + {3}^(2) \n \n = > {(2x)}^(2) - 2(2x)(3) + 9$

Answer:

k = 9

Answer 2

Answer:

Answer:

Using formula (a-b)^2 = a^2-2ab+b^2

4x 2 −12x+k

=>(2x) 2 −2(2x)(3)+3 2

=>(2x) 2 −2(2x)(3)+9

=> k = 9

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0.8 divided by 405.2

Answers

Answer: 0.00197433

Step-by-step explanation:

Keith has a bag of Skittles. He is trying to get Jashawn to figer out how many Skittles are in his bag. There are 16 red. 25% of the bag is orange. 1/8 of the skittles are yellow. Tge rest of the skittles are green.If 2/5 of the bag is red,how many skittles are in the bag? How many skittles are orange? How many of the skittles are green?

Answers

Answer:

Total number of skittles in bag are 40

There are 10 orange skittles.

There are are 9 green skittles.

Step-by-step explanation:

Suppose there are "x" number of skittles in the bag.

Given that 2/5 of x = 16

Solving above equations gives , x = 40

That means total numbers of skittles are 40.

2/5 of 40 = 16 red skittles.

25 % of 40 = 10 orange skittles

1/8 of 40 = 5 yellow skittles

40-16-10-5 = 9 green skittles.

Brand X batteries have a mean life span of 102 hours, with a standard deviation of 6.8 hours. Brand Y batteries have a mean life span of 100 hours, with a standard deviation of 1.4 hours. Complete each of the sentences.

Answers

Answer:

Step-by-step explanation:

Hello!

X₁: Life span of a battery of Brand X

X₁~N(μ₁;σ₁²)

μ₁= 102hours

σ₁= 6.8hours

X₂: Life span of a battery of Brand Y

X₂~N(μ₂;σ²)

μ₂= 100hours

σ₂= 1.4hours

To complete the first two sentences, you have to use the empirical rule:

μ±δ= 68% of the distribution

μ±2δ= 95% of the distribution

μ±3δ= 99% of the distribution

1. About 68% of brand x’s batteries have a lifespan between 95.2 and 108.8 hours.

μ₁±σ₁= 102 ± 6.8= 95.2; 108.8

2. About 68% of brand y’s batteries have a lifespan between 98.6 and 101.4 hours.

μ₂±σ₂= 100 ± 1.4= 98.6; 101.4

3. The life span of brand Y ’s battery is more likely to be consistently close to the mean.

The standard deviations show you the dispersion of the distribution. A low standard deviation indicates that the values are close to the mean. A high standard deviation indicates that the values are further away the values are from the mean.

The standard deviation for the X batteries is σ₁= 6.8hours and the Y batteries are σ₂= 1.4hours since the standard deviation for the Y batteries is less than the standard deviation for the X batteries, you'd expect that the life span of the Y batteries will be closer to the mean than the life span of the X batteries.

I hope it helps!

Quadrilateral STRW is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary.

Answers

Minor point: the quadrilateral is STWR, not STRW. Vertices are named in order.

The measure of angle T is half the measure of arc WRS. The measure of angle R is half the measure of arc STW. The sum of the measures of the two arcs is the measure of a circle, 360°, so you have

... T + R = (WRS)/2 + (STW)/2

... ... = (WRS + STW)/2

... ... = 360°/2 = 180°

Since the sum of T and R is 180°, they are supplementary.

Please Help Me For the figure below m<ABC = 70°. Which theorem or postulate can be used to determine m<DBC? What is m<DBC? (pic of the drawing below)

Answers

Answer:

38°

Step-by-step explanation:

<ABD and <DBC are two interior angles that make up <ABC.

Based on the Angle Addition Theorem, the following equation can be used to find m<DBC:

$(3x + 5) + (6x - 16) = 70$

Find x

$3x + 5 + 6x - 16 = 70$

$9x - 11 = 70$

$9x = 70 + 11$

$9x = 81$

$x = (81)/(9)$

$x = 9$

We are given that, m<DBC = (6x - 16)°

Plug in the value of x to find the measure

m<DBC = 6(9) - 16 = 54 - 16 = 38°

In a poll conducted by the Gallup organization in April 2013, 48% of a random sample of 1022 adults in the U.S. responded that they felt that economic growth is more important than protecting the environment. We can use this information to calculate a 95% confidence interval for the proportion of all U.S. adults in April 2013 who felt that economic growth is more important than protecting the environment. Make sure to include all steps.

Answers

Answer:

The 95% confidence interval is $0.449 < p < 0.48 + 0.511$

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 0.48$

The sample size is $n = 1022$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $(\alpha )/(2)$ from the z-table , the value is

$Z_{(\alpha )/(2) } =Z_{(0.05 )/(2) }= 1.96$

The reason we are obtaining critical value of $(\alpha )/(2)$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while $(\alpha )/(2)$ is just the area of one tail which what we required to calculate the margin of error