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2 years ago

If the values of the supplementary angles are 40 and 2x, what is the value of x? ANSWER QUICKLY PLS!

Mathematics

1 answer:

Zolol [24]2 years ago

8 0

Answer:

140°

Step-by-step explanation:

The value of supplement is 40 and X. We know that the sum of the sumplementary angles is 180. Therefore ,

=> x + 40° = 180°

=> x = 180° - 40°

=> x = 140°

<h3>Hence the value of x is 140° .</h3>

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The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes

mixer [17]

Answer:

0.02275

Step-by-step explanation:

We have been given that the time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. We are asked to find the probability of completing the exam in one hour or less.

We know that 1 hour equals 60 minutes. First of all, we will find the z-score corresponding to 60 minutes.

$z=\frac{x-\mu}{\sigma}$

z = z-score,

x = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

$z=\frac{60-80}{10}$

$z=\frac{-20}{10}$

$z=-2$

Now, we will use normal distribution table to find area under z-score of $-2$ as:

$P(z< -2)$

$P(z< -2)=0.02275$

Therefore, the probability of completing the exam in one hour or less is 0.02275.

7 0

2 years ago

The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

6 0

1 year ago

Read 2 more answers

Which statement is true about the function f(x) = 7

TEA [102]

Answer:

the function is EVEN because f(x)= f(-x)

Step-by-step explanation:

Key to find if a function f(x) is even or odd is to replace the x with -x

if the results comes out to be f(x) then it is even function

if the results comes out to be -f(x) then it is odd function

where as graphically even f(x) will be symmetric around the y-axis and odd f(x) will be symmetric around the origin.

In given case f(x)=7

if we replace x with -x in above equation then results is 7

f(-x)= 7

hence f(x)= f(-x) = 7

7 0

3 years ago

Question 2 please fas

Len [333]

Answer:

a = 3, b = 2

Step-by-step explanation:

It is given that both the polynomials are equal.

Therefore, h(x) = k(x)

${x}^{3} + (a + b) {x}^{2} - 4x + 2 \\ = {x}^{3} + 5 {x}^{2} - (2a - b)x + 2 \\ \\ equating \: like \: terms \: on \: both \: sides \\ (a + b) {x}^{2} = 5 {x}^{2} \\ \implies \: a + b = 5.....(1) \\ \\ - (2a - b)x = - 4x \\ 2a - b = 4....(2) \\ \\ adding \: equations \: (1) \: and \: (2) \\ \\ 3a = 9 \\ \implies \: a = \frac{9}{3} \\ \huge \red{ \boxed{\implies \: a = 3}} \\ \\ substituting \: a = 3 \: in \: equation \: (1) \\ 3 + b = 5 \\ \implies \: b = 5 - 3 \\ \huge \purple{ \boxed{ \implies b = 2}}$

5 0

2 years ago

Not sure need help

lord [1]

Answer:

Step-by-step explanation:

3-2i+8=23

5+2i+23

2i=18

i=-9

3 0

2 years ago

If the values of the supplementary angles are 40 and 2x, what is the value of x? ANSWER QUICKLY PLS!​

If the values of the supplementary angles are 40 and 2x, what is the value of x? ANSWER QUICKLY PLS!