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2 months ago

9

In the company Educational Solutions, the ratio of the employees using a laptop computer to those not using one was 1:3 in the y

ear 2005. In 2006, the number of employees using a laptop as well as those not using it doubled. What was the ratio of the employees using a laptop to those not using one in 2006?

1 answer:

babunello [11.8K]2 months ago

3 0

Answer:

Step-by-step explanation:

In 2005, the number of employees who utilized laptop computers compared to those who did not was at a ratio of 1:3. By 2006, this proportion changed because both users and non-users had their counts doubled. Consequently, the new ratio of employees using laptops to those not using them in 2006 became

2:6

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Which statement correctly names the congruent triangles and justifies the reason for congruence? ΔABC ≅ ΔFDE by HL ΔABC ≅ ΔFED b

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Answer: The triangles ΔABC and ΔFED are congruent by the SAS criterion

Step-by-step explanation:

Examining the provided diagram,

it is noted that Side AC is equal to Side DF at 3.2

and Side AB matches Side FE at 4 units

with Angle A equal to angle F at 72 degrees

As two sides and the angle between them are equal, triangle FED is congruent to triangle ABC by SAS (side-angle-side)

This allows for the following ratio

AB/FE = AC/DF

The HL specification refers to the hypotenuse leg. This does not apply, as these are not right triangles.

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1 month ago

A tobacco company claims that the amount of nicotine in its cigarettes is a randomvariable with mean 2.2 mg and standard deviati

PIT_PIT [12445]

Response:

0.0000

Unusual

To explain step-by-step:

A tobacco company asserts that the nicotine content in its cigarettes behaves as a random variable with a mean of 2.2 mg and a standard deviation of.3 mg.

This means the population parameters are

$\mu =2.2 \\s = 0.3$

The likelihood that the sample average would equal or exceed 3.1

$=P(X\geq 3.1)\\=P(Z\geq \frac{3.1-2.2}{\frac{0.3}{\sqrt{100} } } )\\=P(Z\geq 30)\\$

equals 0.0000

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2 months ago

You are hiking and trying to determine how far away the nearest cabin is, which happens to be due north from your current positi

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Answer:

The cabin is located 567 yards away.

Step-by-step solution:

The bearing angle of 21.2° corresponds to the interior angle near the cabin in the triangle.

Apply the tangent function:

Opposite side length: 220 yards

Adjacent side length: x (distance to cabin)

tan(21.2°) = opposite / adjacent

tan(21.2°) = 220 yards / x

Multiply both sides by x:

x × tan(21.2°) = 220 yards

Isolate x:

x = 220 yards / tan(21.2°)

x = 220 / 0.388

x = 567 yards

Hence, the cabin is 567 yards away.

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3 months ago

Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your o

Svet_ta [12734]

For $\fbox{\begin \\\math{x}=6\\\end{minispace}}$ the function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ both yield the same result.

Detailed breakdown:

The functions involved are

$f(x)=-x^{2}+4x+12$

$g(x)=-x+6$

Step 1:

Insert $x=1$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(1)$ .

$f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15$

Insert $x=1$ in $g(x)=-x+6$ to find the value of $g(1)$ .

$g(1)=-1+6\\g(1)=5$

Step 2:

Insert $x=2$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(2)$ .

$f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16$

Substitute $x=2$ into $g(x)=-x+6$ to find the value of $g(2)$ .

$g(2)=-2+6\\g(2)=4$

Step 3:

Replace $x=3$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(3)$ .

$f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15$

Also, replace $x=3$ in $g(x)=-x+6$ to find the value of $g(3)$ .

$g(3)=-3+6\\g(3)=3$

Step 4:

Insert $x=4$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(4)$ .

$f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12$

Also, replace $x=4$ in $g(x)=-x+6$ to obtain the value of $g(4)$ .

$g(4)=-4+6\\g(4)=2$

Step 5:

Insert $x=5$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(5)$ .

$f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7$

Replace $x=5$ in $g(x)=-x+6$ to find the value of $g(5)$ .

$g(5)=-5+6\\g(5)=1$

Step 6:

Insert $x=6$ into $f(x)=-x^{2} +4x+12$ to find the value of $f(6)$ .

$f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0$

Also, substitute $x=6$ in $g(x)=-x+6$ to obtain the value of $g(6)$ .

$g(6)=-6+6\\g(6)=0$

Step 7:

According to the provided condition $f(x)=g(x)$ .

(a). Insert $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ into the previously mentioned equation.

$-x^{2} +4x+12=-x+6$

(b). Multiply through by $-1$ on both sides.

$x^{2} -4x-12=x-6$

(c). Move the term $x-6$ to the left side of the equation.

$x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0$

(d). Divide the middle term so that its sum equals 5 and the product equals 6.

$x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1,6$

From the analysis above, it is noted that for $x=6$ both functions $f(x)$ and $g(x)$ yield the same outcome.

Using a direct approach:

$f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1$

The table representing function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ is included below.

For more information:

1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

2. Which is the graph of f(x) = (x – 1)(x + 4)?

6 0

1 month ago

Find the value of x in the isosceles triangle shown below.

Leona [12618]

Solution:

x=8

Detailed explanation:

This isosceles triangle consists of two right triangles with sides equal to 8, $\sqrt{80}$ , and y

Considering we possess two sides of a right triangle, determining the third side can be achieved using the Pythagorean Theorem

$(\sqrt{80} )^2=8^2+y^2\\\\80=64+y^2\\\\y^2=16\\\\y=4$

Because it is an isosceles triangle, these two right triangles are the same, thus x=2y

Hence, x=2(4)=8

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2 months ago

Read 2 more answers