Write the expression in exponential form

Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it use

evablogger [386]

Answer:

(1) Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$

Alternate Hypothesis, $H_1$ : $\mu_1\neq \mu_2$

(2) Test statistics = -1.48

(3) At the 0.05 significance level, Fair field conclude that the population means are same.

Step-by-step explanation:

Let $\mu_1$ = mean annual family income for 12 people making inquiries at the first development

$\mu_2$ = mean annual family income for 24 people making inquiries at the second development

$s_1$ = standard deviation of annual family income for 12 people making inquiries at the first development

$s_2$ = standard deviation of annual family income for 24 people making inquiries at the second development

$n_1$ = sample of people of first development i.e. 12

$n_2$ = sample of people of second development i.e. 24

(1) Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$ {population means are same}

Alternate Hypothesis, $H_1$ : $\mu_1\neq \mu_2$ {population means are different}

DECISION RULE ;

If the test statistics is less than the critical value of t from table at 5% significance level, then we will accept null hypothesis, $H_0$ .
If the test statistics is more than the critical value of t from table at 5% significance level, then we will reject null hypothesis, $H_0$ .

(2) The test statistics is given by;

$\frac{(X_1bar -X_2bar) - (\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t_n__1+n_2-2$

where, $X_1bar$ = Sample mean income of people at first development

= $153,000

$X_2bar$ = Sample mean income of people at second development = $171,000

$s_1$ = $42,000 and $s_2$ = $30,000

$s_p= \sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2}}$ = $\sqrt{\frac{(12-1)42000^{2}+(24-1)30000^{2} }{12+24-2}}$ = 34344.30

Test statistics = $\frac{(153000 -171000) - 0}{34344.30\sqrt{\frac{1}{12}+\frac{1}{24} } }$ ~ $t_3_4$

= -1.48

(3) At 5% level of significance, t table gives critical value of 2.032 at 34 degree of freedom.Since our test statistics is less than the critical value of t so considering our decision rule, we will accept null hypothesis.

And conclude that population means are same.

4 0

4 years ago

I need help someone help pls

nexus9112 [7]

So for the left side put

0,30,60,150,240,330,1470

sorry but I only no the left side I hope that helps(:(:(:(:

3 0

4 years ago

A golf ball is hit with a club from the ground on a flat surface. The height of the ball, h(t), in feet, t seconds after it was

Arlecino [84]

Answer:

The correct numbers are;

1) 0

2) 25

3) 1.25

4) 2.5

When the ball is hit at 0 seconds, it has a height of 0 feet. The ball's height increases until it reaches its maximum height of 25 feet after 1.25 seconds. The ball's height then decreases until it reaches the ground 2.5 seconds after it was hit

Step-by-step explanation:

The given equation for the height of the ball, h(t), in feet, is given as follows

h(t) = 40·t - 16·t²

Therefore;

1) When the ball is hit at 0 seconds, it has a height of h(0) = 40×0 - 16×0² = 0 feet

2) The time to reach maximum height by the ball is found by taking the derivative (slope) of the function for the height of the ball and noting that at maximum height, the derivative (slope) = 0

Therefore;

h'(t) = 40 - 2 × 16·t = 0

40 - 32·t = 0

t = 40/32 = 5/4 seconds = 1.25 seconds

3) The maximum height is then found from the value of the function at t = 5/4 seconds as follows;

h(5/4) = 40×5/4 - 16×(5/4)² = 50 - 25 = 25 feet

4) The time in which the ball reaches the ground where h(t) = 0 is given from the formula for the height of the gulf ball as follows;

h(t) = 0 = 40·t - 16·t²

40·t - 16·t² = 0

(40 - 16·t)·t = 0

Therefore;

t = 0 seconds or t = 40/16 = 2.5 seconds

(40 - 16·t) = 0/t = 0

t = 40/16 = 2.5 seconds

Therefore, the filling the blanks with the correct numbers gives;

When the ball is hit at 0 seconds, it has a height of 0 feet. The ball's height increases until it reaches its maximum height of 25 feet after 1.25 seconds. The ball's height then decreases until it reaches the ground 2.5 seconds after it was hit

4 0

3 years ago

Can someone help me with this math homework please!

lapo4ka [179]

Answer:

The answers are options A and C.

They are (-2,0) and (0,0).

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

If p(x) = x 2 + 7x + 3 is divided by x + 4, the remainder is

igor_vitrenko [27]

tep 1 : 3 Simplify — x Equation at the end of step 1 : 3 px - ((9x + —) + 4) = 0 x Step 2 :Rewriting the whole as an Equivalent Fraction :

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using x as the denominator :

9x 9x • x 9x = —— = —————— 1 x

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

9x • x + 3 9x2 + 3 —————————— = ——————— x x Equation at the end of step 2 : (9x2 + 3) px - (————————— + 4) = 0 x Step 3 :Rewriting the whole as an Equivalent Fraction :

3.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x as the denominator :

4 4 • x 4 = — = ————— 1 x Step 4 :Pulling out like terms :

4.1 Pull out like factors :

 9x2 + 3 = 3 • (3x2 + 1)

Polynomial Roots Calculator :

4.2 Find roots (zeroes) of : F(x) = 3x2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 3 and the Trailing Constant is 1.

The factor(s) are:

of the Leading Coefficient : 1,3
of the Trailing Constant : 1

Let us test ....

P Q P/Q F(P/Q) Divisor -1 1 -1.00 4.00 -1 3 -0.33 1.33 1 1 1.00 4.00 1 3 0.33 1.33

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3 Adding up the two equivalent fractions

3 • (3x2+1) + 4 • x 9x2 + 4x + 3 ——————————————————— = ———————————— x x Equation at the end of step 4 : (9x2 + 4x + 3) px - —————————————— = 0 x Step 5 :Rewriting the whole as an Equivalent Fraction :

5.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x as the denominator :

px px • x px = —— = —————— 1 x Trying to factor by splitting the middle term

5.2 Factoring 9x2 + 4x + 3

The first term is, 9x2 its coefficient is 9 .
The middle term is, +4x its coefficient is 4 .
The last term, "the constant", is +3 

Step-1 : Multiply the coefficient of the first term by the constant 9 • 3 = 27

Step-2 : Find two factors of 27 whose sum equals the coefficient of the middle term, which is 4 .

-27 + -1 = -28 -9 + -3 = -12 -3 + -9 = -12 -1 + -27 = -28 1 + 27 = 28 3 + 9 = 12 9 + 3 = 12 27 + 1 = 28

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

5.3 Adding up the two equivalent fractions

px • x - ((9x2+4x+3)) px2 - 9x2 - 4x - 3 ————————————————————— = —————————————————— x x Equation at the end of step 5 : px2 - 9x2 - 4x - 3 —————————————————— = 0 x Step 6 :When a fraction equals zero : 6.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

px2-9x2-4x-3 ———————————— • x = 0 • x x

Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
 px2-9x2-4x-3 = 0

Solving a Single Variable Equation :

6.2 Solve px2-9x2-4x-3 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

6 0

4 years ago