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1 year ago

Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?

Mathematics

2 answers:

jek_recluse [69]1 year ago

8 0

Answer:

Step-by-step explanation:

ipn [44]1 year ago

5 0

Answer:

We have to determine the graph of the given inequality as:

$x^2+2x+1>0$

on solving this equation we get:

$(x+1)^2>0$

Since we know that:

$(x+1)^2=x^2+1^2+2\times x\times 1\\\\(x+1)^2=x^2+1+2x$

Now we know that when $x=-1$ the value of:

$(x+1)^2=0$

Also for the value other than -1 the function being a quadratic function will always give a non-zero positive value.

Hence, range of the function in intervals could be written as:

(-∞,-1)∪(-1,∞).

Hence, the graph of the function will be the whole of the number line with a open circle on -1.

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Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

Step-by-step explanation:

The random variable X and Y are defined as follows:

X = amount of ice cream in the box

Y = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

X + 3Y.

Compute the expected value of (X + 3Y) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (X + 3Y) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (X + 3Y) is:

$SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25$

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

X - Y.

Compute the expected value of (X - Y) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (X - Y) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (X - Y) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

7 0

1 year ago

Andrew invested $20,000 in mutual funds and received a sum of $35,000 at the end of the investment period. Calculate the ROI.

mario62 [17]

Answer: $15,000

As $35,000-$20,000=$15,000.

That's basically the profit he had made, or the return on his investment (ROI).

As he already had $20,000, he had "only" made $15,000.

5 0

2 years ago

Simplify the expression to a form in which 2 is raised to a single integer power. fraction numerator open parentheses 2 to the p

anzhelika [568]

Answer:

2^27

Step-by-step explanation:

Given the following expression:

[(2^10)^3 x (2^-10)] ÷ 2^-7

This can be easily simplified. Let us simplify the numerator first. To do that, we have

(2^10)^3 making use of the power rule of indices that says:

(A^a)^b = A^ab where a and b are powers, we have:

2^(10x3) = 2^30

Therefore the numerator becomes:

2^30 x 2^-10. Also making use of the multiplication rule that says:

A^a x A^b = A^(a + b), we have

2^30 x 2^-10 = 2^(30 – 10) = 2^20.

Now we have:

(2^20) ÷ (2^-7)

To simplify this, we need the division rule of indices which says:

A^a ÷ A^b = A^(a – b)

Therefore we have:

(2^20) ÷ (2^-7) = 2^[20 – (–7)] = 2^(20+7) = 2^27

5 0

1 year ago

Geometry 7.2 puzzle time where did columbus land when he found america

kobusy [5.1K]

Answer:

Plymouth Rock

Step-by-step explanation:

he landed in plymouth

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2 years ago

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If terri were stretching 4 days per week, how many days per week would she need to stretch to increase her frequency variable? 1

Olin [163]

Answer:

3 days is the right answer!!!!! good luck

Step-by-step explanation:

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1 year ago

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