Log(x - 3) + log(x + 4) – log x = log 5

The scale factor from a small triangle ABC to a large triangle XYZ is 5. How many times larger will the perimeter of triangle XY

Ierofanga [76]

Answer:

Answer below :)

Step-by-step explanation:

Hi there!

Question 4 - the answer will be 5. Since the scale factor is 5, we would (hypothetically) multiply the area by 5 to get the new area of XYZ, so area XYZ is 5 times the area of ABC.

Question 5 - A.

First we multiply 45 by 12 to find the amount in inches. This is 540. Now, we divide that by 6 to get 90. This is our scale factor in inches, but the answers only show the scale in feet, so we have to convert. Divide 90 by 12 to get 7.5.

I hope this helps!

4 0

3 years ago

Composition of functions Find g (f(x)) for the following problems

beks73 [17]

1.

$f(x)=-3x\qquad g(x)=5x-6\\\\g(f(x))=5(-3x)-6=\boxed{-15x-6}$

2.

$f(x)=x-6\qquad g(x)=x^2+6x-2\\\\g(f(x))=(x-6)^2+6(x-6)-2=x^2-12x+36+6x-36-2=\\\\=\boxed{x^2-6x-2}$

3.

$f(x)=4x+3\qquad g(x)=2x^2-x+1\\\\g(f(x))=2(4x+3)^2-(4x+3)+1=2(16x^2+24x+9)-4x-3+1=\\\\=32x^2+48x+18-4x-3+1=\boxed{32x^2+44x+16}$

4.

$f(x)=2x^2\qquad g(x)=8x^2+3x\\\\g(f(x))=8(2x^2)^2+3(2x^2)=8\cdot4x^4+6x^2=\boxed{32x^4+6x^2}$

7 0

3 years ago

The USDA conducted tests for salmonella in produce grown in California. In an independent sample of 252 cultures obtained from w

Marat540 [252]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 252$

The number that tested positive is $k_1 = 18$

The second sample size is $n_2 = 476$

The number that tested positive is $k_2 = 20$

The level of significance is $\alpha = 0.01$

Generally the first sample proportion is mathematically represented as

$\^ p _1 = \frac{k_1 }{ n_1 }$

=> $\^ p _1 = \frac{18 }{ 252 }$

=> $\^ p _1 = 0.071$

Generally the second sample proportion is mathematically represented as

$\^ p _2 = \frac{k_2 }{ n_2 }$

=> $\^ p _2 = \frac{20 }{ 476}$

=> $\^ p _2 = 0.042$

The null hypothesis is $H_o : p_1 - p_2 = 0$

The alternative hypothesis is $H_a : p_1 - p_2 \ne 0$

Generally the test statistics is mathematically represented

$z = \frac{ \^ p_1 - \^ p_2 - ( p_ 1 - p_2 )}{ \sqrt{\frac{\^ p_1 (1-\^ p_1)}{ n_1 } + \frac{\^ p_2 (1-\^ p_2)}{ n_2 } } }$

=> $z = \frac{ 0.071 - 0.042 - 0 }{ \sqrt{\frac{0.071 (1-0.071)}{ 252 } + \frac{0.042 (1-\^ 0.042)}{ 476 } } }$

=> $z = 1.56$

From the z table the area under the normal curve to the right corresponding to 1.56 is

$P(Z > 1.56 ) =0.05938$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > 1.56 )$

=> $p-value = 2 * 0.05938$

=> $p-value = 0.1188$

From the value obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There no sufficient evidence to show that the proportion of salmonella in the region’s water differs from the proportion of salmonella in the region’s wildlife

5 0

3 years ago

Jeff wants to buy tickets for a football game for his friends. The stadium is selling tickets for $7 each. The stadium requires

aniked [119]

Your answer is D){28, 42, 56, 70, 84}

To answer this question you just have to make sure the amount he pays is a multiple of 7.If you know you times table then this should be easy

Times table of 7:

7,14,21,28,35,42,49,55,63,70,77,84.

Now you just need to find an answer choice who has these numbers.Lets check it out!

A) 11 isn't a multiple of 7

B) 56 isn't a multiple of 7

C) None of these are multiples of 7 except 7 so this is also incorrect

D) This is correct because they are all multiples of 7

Hope this makes sense.

7 0

3 years ago

A pyramid has a base area of 44cm and a height of 12.6 cm what is the volume of the pyramid ?

aliya0001 [1]

Answer:

184.8 cubic cm

Step-by-step explanation:

The formula for the volume of a pyramid is

V = (1/3)(B)(h) where B is the area of the base, and h is the height

We are given B = 44 cm² andh = 12.6cm

Plug them into the formula and simplify...(I'm assuming you are allowed to use a calculator for these problems)

V = (1/3)(44cm²)(12.6cm)

<h2> V = 184.8 cm³ or 184.8 cubic cm</h2><h2 />

7 0

4 years ago