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3 years ago

Solve the equation.

Mathematics

1 answer:

Nutka1998 [239]3 years ago

3 0

Answer:

Step-by-step explanation:

In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that:

N1⋅N2=a⋅c=1⋅−12=−12

AND

N1+N2=b=−1

After trying out a few numbers we get N1=3 and N2=−4

3⋅−4=−12, and 3+(−4)=−1

x2−x−12=x2−4x+3x−12

x(x−4)+3(x−4)=0

(x+3)(x−4)=0

Now we equate the factors to zero.

x+3=0,x=−3

x−4=0,x=4

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The answer of this question is 13/24

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3 years ago

Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard

Bumek [7]

Answer:

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

The question is

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

The volume of the open top box is

$V=LWH$

we have

$L=(10-2x)\ cm$

$W=(10-2x)\ cm$

$H=x)\ cm$

substitute

$V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Find the domain for x

we know that

$(10-2x) > 0\\10> 2x\\ 5 > x\\x < 5\ cm$

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

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3 years ago

(20 points) A 2-liter bottle of soda (67.6 ounces) costs $1.89. A case of twelve 12 ounce

horrorfan [7]

Answer:

Unit price of a 2-liter bottle of soda: $\$0.028\ per\ ounce$
Unit price of a case of twelve 12 ounce cans: $\$0.021\ per\ ounce$
The better bargain is the case of 12 ounce cans.

Step-by-step explanation:

Let be "x" the unit price (price/ounce) of the soda in the 2-liter bottle and "y" the unit price (price/ounce) of the soda in the case of twelve 12 ounces cans.

According to the data provided in the exercise, you know that:

1. The 2-liter bottle of soda is equal to 67.6 ounces.

2. That bottle costs $1.89

Then, the unit price is:

$x=\frac{1.89}{67.6}\\\\x\approx0.028$

3. There are 12 ounce cans in the case. Then the total ounces is:

$12\ oz*12=144\ oz$

4. It costs $2.99. So the unit price is:

$y=\frac{2.99}{144}\\\\y\approx0.021$

Since:

$y$

The better bargain is the case of 12 ounce cans.

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Answer:

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3 years ago

An article measured speeds of vehicles on several roads in the state of Kansas. On South Cedar Niles, 73 vehicles were observed,

kifflom [539]

Answer:

The sample supports the hypothesis that more than half of the vehicles in South Cedar Niles exceed the speed limit.

p-value = 0.00092

Step-by-step explanation:

To solve this problem, we run a hypothesis test about the population proportion.

Proportion in the null hypothesis $\pi_0 = 0.5$

Sample size (n) = 73

Sample proportion (p) = 49/73 = 0.6712

H0: $\pi_0 = 0.5$

Ha: $\pi_0 \geq 0.5$

Test statistic = $(p - pi)\sqrt{n} / \sqrt{\pi_0 (1-\pi_0)}$

Calculated statistic = $(0.6712 - 0.5)\sqrt{73} / \sqrt {0.5(1-0.5)} = 2.9255$

p-value = 0.00092

Since, p - value is less than or equal to 0.05, the null hypothesis must be rejected. The sample supports the hypothesis that more than half of the vehicles in South Cedar Niles exceed the speed limit.

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3 years ago