Evaluate the given expression for x = 4 and y= 3. 7x2 + 6xy + 6y?

The answer is: _____​

Answer:

Step-by-step explanation:

f(x) = -1 is actually the same as y = -1.  Find y = -1 on the y axis and then draw a horizontal line through this point.  The resulting graph is that called for here.

Answer:

3.75 miles per hour

Step-by-step explanation:

(5/8)/(1/6)=3.75 mph, or you could do 5/8 x 6, since 1/6 x 6 equals one hour

Answer:

3 3/4 miles per hour

Step-by-step explanation:

Take the miles and divide by the hours

5/8 ÷ 1/6

Copy dot flip

5/8 * 6/1

Rewriting

5/1 * 6/8

5/1 * 3/4

15/4

3 3/4

"no terms independent of x" basically means there is no constant term, or the coefficient of x ⁰ is zero.

Recall the binomial theorem:

[tex]\displaystyle (a+b)^n=\sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]

So we have

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 \binom 6k \left(\frac2x\right)^{6-k}(-3x)^k[/tex]

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}[/tex]

[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}+a\sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-4}[/tex]

The first sum contributes a x ⁰ term for 2k - 6 = 0, or k = 3, while the second sum contributes a x ⁰ term for 2k - 4 = 0, or k = 2. The coefficient of the sum of these terms must be zero:

[tex]2^{6-3}(-3)^3\dbinom 63 + a\times2^{6-2}(-3)^2\dbinom 62 = 0[/tex]

which reduces to

2160a - 4320 = 0

2160a = 4320

a = 2

Answer:

(0.123 ; 0.277)

Step-by-step explanation:

Given :

Sample size, n = 180

x = 36

Proportion, p = x / n = 36/180 = 0.2

Confidence interval for sample proportion :

Confidence interval :

p ± Zcritical * √p(1 - p) / n

Zcritical at 99% = 2.576

0.2 ± 2.576 * √0.2(1 - 0.2) / 180

0.2 ± 2.576 * 0.0298142

0.2 ± 0.0768013792

(0.123 ; 0.277)

Answer:

0.84

Step-by-step explanation:

4x2+13a+10=7

13a=7-10-8

13a=-11

a=-11:13

a=0.84

Answer:

[tex] 1,017.36 \: {cm}^{2} [/tex]

Step-by-step explanation:

Surface area of a sphere

[tex] = 4\pi {r}^{2} \\ = 4 \times 3.14 {(6)}^{2} \\ = 12.56 \times 81 \\ = 1,017.36 \: {cm}^{2} [/tex]

Answer:

1017.36 cm²

Step-by-step explanation:

Given :-

We know ,

Answer:

I think 55%

Step-by-step explanation:

Answer:

Step-by-step explanation:

price on monday go to: 100% + 20% = 120% = 1,2 x first price

price on tuesday go to: 125% of 120% = 1,25 x 1,2 = 1,5 x first price

Increases = 50%

on Wednesday, sammy must decrease 50% (of price after second increases) to return to original price

For example for understanding:

If original price is $100

firs increase: new price: $100 + $20 = $120

second increase: new new price: $120 + $30 = $150

final price - original price = $150 - $100 = $50

And  icreases/original = $50/$100 =0,5 = 50%

For return to orignial price, sammy must have to reduce 50% the price of avocados in wednesday

Answer:

Harry collected 180 stamps

Harry's sister collected 60 stamps

Step-by-step explanation:

Let X be the number of stamps that Harry's sister colleted.

The number of stamps Harry colleted is 3 time as many as his sister's

⇒ 3*X + X = 240

⇒ X = 60

⇒ 240 - 60= 180

Answer:

180 for harry and 60 for his sister

Step-by-step explanation:

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

Answer:

D. 9n = 27

Step-by-step explanation:

If we need one adult for every 9 students, we can represent that as 9n:

if n is the number of adults.

Because we have 27 students, the equation 9n = 27 works.

A better way of formatting the equation is:

n = 27/9

Because it directly shows what the number of adults is, but with some reformatting, it is clearly the same equation.

Answer:

100$or 20.4 that is the answer

Answer:

Graph the same exact curve, but move every y value up 6.

Step-by-step explanation:

A transformation to the y-values is outside of the argument of the function. i.e., outside of the parentheses.

Step-by-step explanation:

pandemic times: Potential ... - CAF

have shown evidence that the effect of corruption on real GDP per capita is more pronounced in countries with low levels of8

Answer:

She could wear 7 different outfits

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Starting from right to left...

9 is in the ones place

8 is in the tenths place

4 is in the hundreds place

7 is in the thousands place.

I hope this helps!

Answer: [tex]6.12\ \text{years}[/tex]

Step-by-step explanation:

Given

Rate of interest is [tex]r=3\%[/tex] compounded quarterly

So, annually it is [tex]r=12\%[/tex]

Suppose [tex]P[/tex] is the Principal and A is the amount after certain time period.

Amount in Compound interest is given by

[tex]\Rightarrow A=P[1+r\%]^t[/tex]

for given conditions

[tex]\Rightarrow 2P=P[1+0.12]^t\\\Rightarrow 2=(1.12)^t\\\\\Rightarrow t=\dfrac{\ln (2)}{\ln (1.12)}\\\\\Rightarrow t=6.116\approx 6.12\ \text{years}[/tex]

It take [tex]6.12\ \text{years}[/tex] to double the invested amount.

Answer: width = 4 and length = 10

Step-by-step explanation:

Width = w and length = w + 6

2(w) + 2 (w + 6) = 28

2w + 2w + 12 = 28

4w = 28 - 12

W = 16/4

W = 4 (width)

Length = w + 6

4 + 6 = 10

Answer:

(8.608, 9.392)

Step-by-step explanation:

We have the following information

Population standard deviation = 1.8

Sample mean = 9 hours

Sample n = 81

C I = 95%

So level of significance

Alpha = 1-0.95

= 0.05

Z critical at 0.05/2

Z(0.025) = 1.96

The 95% c.i =

9+-(1.96)(1.8/√81)

9+-(1.96)(0.2)

(9-0.392)(9+0.392)

(8.608, 9.392)

This is the confidence interval at 95%.

I hope you find my solution useful. Good luck!!!

Answer:

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation is 9.5 for a population.

This means that [tex]\sigma = 9.5[/tex]

Sample of 60:

This means that [tex]n = 60[/tex]

What is the standard deviation of the distribution of sample means for samples of size 60?

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264[/tex]

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Answer: No, The goal when testing a hypothesis is to to guess a large significant level to possibly have the answer correct based upon evidence. False. It needs to be a large significant level

Step-by-step explanation:

Answer:

65.03 meters

Step-by-step explanation:

The line of best fit, for the distance of the winning throw, in x years after 1980 is:

[tex]y = 0.34x + 44.63[/tex]

Using the line of best fit, estimate what the distance of the gold medal winning discus throw was in 1980.

1980 - 1920 = 60, so this is y(60).

[tex]y(60) = 0.34(60) + 44.63 = 65.03[/tex]

So the answer is 65.03 meters.

Answer:

$150

Step-by-step explanation:

discount=60%

let the price=x

(100-60)% of x=$60

40% of x=60

x=60×(100/40)=150

Answer:

m = -6

Step-by-step explanation:

The slope of a line is calculated as the change in y divided by the change in x.

Teachers use the phrase "rise over run". In this case the rise is negative as the line moves from a higher y value to a lower y value as x increases.

(y-final - y-initial)/(x-final - x-initial)

You are given two points on the line and just plug them in.

(1-7)/(7-6) = -6/1 = -6

Answer:

y = 9x-10

Step-by-step explanation:

Slope-Intercept form is y = mx + b where m is the slope and b is the y intercept.

plug in what we are given

8 = 9(2) + b

solve for the y intercept (b)

8=18+b

8-18 = b

-10 = b

plug the slope (m) and y intercept (b) into our formula

y = 9x - 10

[tex]\boxed{ \sf{Answer}} [/tex]

[tex]\sf \: g(x) = {x}^{2} - 4 \\ \\ \sf \: x = 5 \\ \\ \sf \: g(5) = {5}^{2} - 4 \\ \sf \: g(5) = 25 - 4 \\ \sf \: g(5) =\underline 2\underline1[/tex]

Answer ↦21 [Option C]

[tex]\tt \: g(x) = {x}^{2} - 4[/tex]

Substitute the value of x as 5 (given) in the above equation. The equation changes too..

[tex]\tt \: g(5) = {5}^{2} - 4[/tex]

Now you can easily solve the equation.

[tex]\tt \: g(5) = {5}^{2} - 4 \\\tt g(5) =( 5 \times 5) - 4 \\ \tt \: g(5) = 25 - 4 \\ \tt \: g(5) = 21[/tex]

Answer - [tex]\boxed{\sf{21}}[/tex]

Answer:

(1)

[tex]E(x) = 0.72[/tex]

[tex]Var(x) = 1.1616[/tex]

[tex]\sigma = 1.078[/tex]

(2)

[tex]E(x) = 12[/tex]

[tex]Var(x) = 1.3[/tex]

[tex]\sigma = 1.14[/tex]

Step-by-step explanation:

Solving (1):

[tex]\begin{array}{ccccccc}{Days} & {0} & {1} & {2} & {3} & {4}& {5} \ \\ {Probability} & {0.60} & {0.20} & {0.12} & {0.04} & {0.04} & {0.00} \ \end{array}[/tex]

(a): Mean

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 0 * 0.60 + 1 * 0.20 + 2 * 0.12 + 3 * 0.04 + 4 * 0.04 + 5 * 0.00[/tex]

[tex]E(x) = 0.72[/tex]

Solving (b): The variance

This is calculated as:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Where:

[tex]E(x) = 0.72[/tex]

and [tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 0^2 * 0.60 + 1^2 * 0.20 + 2^2 * 0.12 + 3^2 * 0.04 + 4^2 * 0.04 + 5^2 * 0.00[/tex]

[tex]E(x^2) = 1.68[/tex]

So, we have:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = 1.68 - 0.72^2[/tex]

[tex]Var(x) = 1.1616[/tex]

Solving (c): The standard deviation.

This is calculated as:

[tex]\sigma = \sqrt{Var(x)}[/tex]

[tex]\sigma = \sqrt{1.1616}[/tex]

[tex]\sigma = 1.078[/tex]

Solving (2):

[tex]\begin{array}{ccccccc}{x} & {10} & {11} & {12} & {13} & {14}& { } \ \\ {P(x)} & {0.1} & {0.25} & {0.3} & {0.25} & {0.1} & { } \ \end{array}[/tex]

(a): Mean

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 10 * 0.10 + 11 * 0.25 + 12 * 0.3 + 13 * 0.25 + 14 * 0.1[/tex]

[tex]E(x) = 12[/tex]

Solving (b): The variance

This is calculated as:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Where:

[tex]E(x) = 12[/tex]

and [tex]E(x^2) = \sum x^2 * P(x)[/tex]

So, we have:

[tex]E(x^2) = 10^2 * 0.10 + 11^2 * 0.25 + 12^2 * 0.3 + 13^2 * 0.25 + 14^2 * 0.1[/tex]

[tex]E(x^2) = 145.3[/tex]

So, we have:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = 145.3 - 12^2[/tex]

[tex]Var(x) = 1.3[/tex]

Solving (c): The standard deviation.

This is calculated as:

[tex]\sigma = \sqrt{Var(x)}[/tex]

[tex]\sigma = \sqrt{1.3}[/tex]

[tex]\sigma = 1.14[/tex]

Answer:

yefeihuerijohiftv3ugrhoerfujfy

Step-by-step explanation:

Answer:

Ans: -21.87 ≅ -22°C

Step-by-step explanation:

T(x)=-22+44e^-0.03x

Initial temperature (x = 0):

T(0) = = -22 + 44e-0.03(0) = -22 + 44(1) = 22°C

After 18 minutes (x = 18):

T(18) = -22 + 44e-0.03(18) = -21.87°C ≅ -22°C