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2 years ago

A quality control engineer is testing the battery life of a new smartphone. The company is advertising that the

Mathematics

1 answer:

DIA [1.3K]2 years ago

4 0

The question requires stating the Null and Alternative hypothesis for the scenario described :

Answer:

H0 : μ = 24

H1 : μ < 24

Step-by-step explanation:

The claim or hypothesis to be tested in a statistical problem or analysis is the alternative hypothesis. This is usually the opposite of the Null hypothesis which is the usually the initial truth until there is significant evidence provided using statistical test to prove otherwise.

The null hypothesis, H0 in the scenario above is :

H0 : μ = 24 ( average battery life is 24 hours)

The alternative hypothesis is the claim, that is. The mean battery life not up to 24 hours ;

H1 : μ < 24

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Help please If f(x) = -3x - 5 and g(x) = 4x-2, find (1-9)(x).

Mandarinka [93]

9514 1404 393

Answer:

-7x -3

Step-by-step explanation:

(f -g)(x) = f(x) -g(x) = (-3x -5) -(4x -2)

(f -g)(x) = -3x -5 -4x +2 = (-3-4)x +(-5+2)

(f -g)(x) = -7x -3

4 0

3 years ago

If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?

Leni [432]

Answer:

1.6 units

Step-by-step explanation:

Coordinates of A : (-1,1)

Coordinates of B : (3,2)

Coordinates of C :( -1,-1)

Now to find the length of the sides of the triangle we will use distance formula :

$d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

To find length of AB

A = $(x_1,y_1)=(-1,1)$

B= $(x_2,y_2)=(3,2)$

Now substitute the values in the formula:

$d =\sqrt{(3-(-1))^2+(2-1)^2}$

$d =\sqrt{(4)^2+(1)^2}$

$d =\sqrt{16+1}$

$d =\sqrt{17}$

$d =4.12$

Now to find length of BC

B= $(x_1,y_1)=(3,2)$

C = $(x_2,y_2)=(-1,-1)$

Now substitute the values in the formula:

$d =\sqrt{(-1-3)^2+(-1-2)^2}$

$d =\sqrt{(-4)^2+(-3)^2}$

$d =\sqrt{16+9}$

$d =\sqrt{25}$

$d =5$

Now to find length of AC

A = $(x_1,y_1)=(-1,1)$

C = $(x_2,y_2)=(-1,-1)$

Now substitute the values in the formula:

$d =\sqrt{(-1-(-1))^2+(-1-1)^2}$

$d =\sqrt{(0)^2+(-2)^2}$

$d =\sqrt{4}$

$d =2$

Thus the sides of triangle are of length 4.12, 5 and 2

Now to find area of triangle we will use heron's formula :

To calculate the area of given triangle we will use the heron's formula :

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

Where $s = \frac{a+b+c}{2}$

a,b,c are the side lengths of triangle

a = 4.12

b=5

c=2

Substitute the values

Now substitute the values :

$s = \frac{4.12+5+2}{2}$

$s =5.56$

$Area = \sqrt{5.56(5.56-4.12)(5.56-5)(5.56-2)}$

$Area = 3.99$

Now to find the height of altitude corresponding to side BC

So, formula of area of triangle $=\frac{1}{2} \times Base \times Height$

Since Area = 3.99 square units

So, $3.99 =\frac{1}{2} \times BC \times Height$

So, $3.99 =\frac{1}{2} \times 5\times Height$

$3.99 =2.5 \times Height$

$\frac{3.99}{2.5}=Height$

$1.596=Height$

Thus the altitude corresponding to the BC is of length 1.596 unit ≈ 1.6 units

Thus Option D is correct.

7 0

2 years ago

Read 2 more answers

A manufacturing company has two retail outlets. It is known that 30% of all potential customers buy

aleksandrvk [35]

Answer:

(a) A y P(A) = 0.4 (b) $\bar{B}$ y $P(\bar{B})$ =0.5 (c) $\bar{A}$ ∪ $\bar{B}$ y P( $\bar{A}$ ∪ $\bar{B}$ ) = 0.9 (d) $\bar{A}$ ∩ $\bar{B}$ y P( $\bar{A}$ ∩ $\bar{B}$ )=0.2

Step-by-step explanation:

A was defined as the event that a potential customer, randomly chosen, buys from outlet 1 in the original problem statement. We know that B denotes the event that a randomly chosen customer buys from outlet 2. So

P( $A\cap \bar{B}$ ) = 0.3, P( $B\cap \bar{A}$ ) = 0.4 and P( $A\cap B$ ) = 0.1

(a) P(A) = P( $A\cap (B\cup\bar{B})$ ) = P( $A\cap B$ ) + P( $A\cap \bar{B}$ ) = 0.1 + 0.3 = 0.4

(b) P(B) = P( $B\cap (A\cup\bar{A})$ ) = P( $B\cap A$ ) + P( $B\cap \bar{A}$ ) = 0.1 + 0.4 = 0.5

P( $\bar{B}$ ) = 1-P(B) = 1-0.5 = 0.5

(c) The customer does not buy from outlet 1 is the complement of A, i.e., $\bar{A}$ , and the customer does not buy from outlet 2 is the complement of B, i.e., $\bar{B}$ , so, the customer does not buy from outlet 1 or does not buy from outlet 2 is $\bar{A}$ ∪ $\bar{B}$ and P( $\bar{A}$ ∪ $\bar{B}$ ) = P( $(A\cap B)^{c}$ ) by De Morgan's laws

P( $(A\cap B)^{c}$ ) = 1-P(A∩B)=1-0.1=0.9

(d) The customer does not buy from outlet 1 is the complement of A, and the customer does not buy from outlet 2 is the complement of B, so we have that the statement in (d) is equivalent to $\bar{A}$ ∩ $\bar{B}$ and P( $\bar{A}$ ∩ $\bar{B}$ ) = P( $(AUB)^{c}$ ) by De Morgan's laws, and

P( $(AUB)^{c}$ ) = 1-P(A∪B)=1-[P(A)+P(B)-P(A∩B)]=1-[0.4+0.5-0.1]=1-0.8=0.2

8 0

3 years ago

Please help me....<br> (45 points!!!)

maksim [4K]

I think the equation you would use is y=26x+0.003.

8 0

3 years ago

Question lastttttttt..............

leonid [27]

Answer:

Answer is c

Step-by-step explanation:

Solve for x

To solve for x, set the left hand side equal to 0 and solve for x with the quad equation

5 0

3 years ago