what is the missing value in the table below? ​

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

for such more question on temperature

https://brainly.com/question/14820864

#SPJ8

Answer:

(a)9

(b)I. 0.28125

II. 0.46875

III. 0.25

Step-by-step explanation:

There are a total of 32 students, therefore the number of elements in the Universal set, n(U)=32

\(1$8 play the violin, n(V)=18\\16 play the piano, n(P)=16\\ 7 play neither, n(P \cup V)' =7\)

(a)The Venn diagram is attached below.

\(n(U)=n(V)+n(P)-n(V \cap P)+ n(P \cup V)'\\32=18+16+7-n(V \cap P)\\32=41-n(V \cap P)\\n(V \cap P)=41-32\\n(V \cap P)=9\\\)

Therefore, 9 students play both the violin and  piano.

(b)

I. Probability that the student  plays the violin but not the piano

Number of Students who play violin only =18-x=18-9=9

\(P(V \cap P') = \dfrac{n(V \cap P')}{n(U)}\\= \dfrac{9}{32}\\=0.28125\)

ii.Probability that the student does not play the violin

Number of Students who does not play violin only =17-x+7=17-9+7=15

P(does not play violin only)

\(= \dfrac{15}{32}\\=0.46875\)

iii.Probability that the student plays the piano but not the violin

Number of Students who play piano only =17-x=17-9=8

\(P(V' \cap P) = \dfrac{n(V' \cap P)}{n(U)}\\= \dfrac{8}{32}\\\\=0.25\)

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

To know more about continuous here

https://brainly.com/question/30089268

#SPJ1

Answer:

Hmmmm, very tricky question but I'll figure it out and type it in the comments

The velocity of the particle, in meters per second is 0.78 m/s

The position function is given as:

x(t) = e-(t - 3)2

Rewrite properly as

x(t) = e^-(t - 3)^2

Next, we differentiate the above function to determine the velocity function.

Using a graphing calculator, we have:

x'(t) = -2(t - 3) * e^-(t - 3)^2

At t = 2.5 s, we have:

x'(2.5) = -2(2.5 - 3) * e^-(2.5 - 3)^2

Evaluate

x'(2.5) = 0.78

Hence, the velocity of the particle, in meters per second is 0.78 m/s

Read more about velocity at

https://brainly.com/question/6504879

#SPJ1

Answer:

\(3x^{3} +10x^{2} +17x+12\)

Step-by-step explanation:

Answer:

3x³ + 10x² + 17x + 12

Step-by-step explanation:

Step 1: Write expression

(3x + 4)(x² + 2x + 3)

Step 2: Distribute 3x

3x³ + 6x² + 9x

Step 3: Distribute 4

4x² + 8x + 12

Step 4: Combine

3x³ + 6x² + 9x + 4x² + 8x + 12

Step 5: Combine like terms

3x³ + 10x² + 17x + 12

Answer:

Sale price of video game with tax = $20.3775

Yes, they both have enough money to purchase the video game.

Step-by-step explanation:

Given that:

Original price of video game = $28.50

Discount on original price = 35%

Sales tax = 10%

Money available with Pat and Henri = $21 each

First of all, let us find out the price as per Pat's method.

Step 1:

Taking 35% of $28.50

\(\Rightarrow \dfrac{35}{100}\times \$28.50 = \$9.975\)

Step 2:

Subtract from $28.50 to find the sale price:

$28.50 - $9.975 = $18.525

Step 3:

Take 10% of sale price:

\(\$18.525\times \dfrac{10}{100} = \$1.8525\)

Step 4:

Add to sale price to get the final amount to be paid:

$18.525 + $1.8525 = $20.3775

Now, let us use Henri's method:

Step 1:

Find 65% of original price:

\(\dfrac{65}{100}\times $28.50 = \$18.525\)

Step 2:

Find 110%:

\(\dfrac{110}{100}\times \$18.525 = \bold{\$20.3775}\)

Sale price of video game with tax = $20.3775

Yes, they both have enough money to purchase the video game.

Answer:

p=0

Step-by-step explanation:

When you isolate both variables, one side becomes 0.

Answer:

p = 0

Step-by-step explanation:

16p=208p

Subtract 208p from both sides.

16p−208p=0

Combine 16p and −208p to get −192p.

−192p=0

Product of two numbers is equal to 0 if at least one of them is 0. Since −192 is not equal to 0, p must be equal to 0.

p=0

About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

Learn more about normal distribution on:

https://brainly.com/question/4079902

#SPJ1

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

Learn more on age word problems here;

https://brainly.com/question/17043336

#SPJ1

Using the cosine ratio, the distance between Dimitri and Sarah is calculated as approximately 12.4 m.

The cosine ratio is a trigonometric ratio that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is calculated by dividing the length of the adjacent side by the length of the hypotenuse.

Using the cosine ratio, we have:

Reference angle (∅) = 72 degrees

Hypotenuse length = 40 m

Adjacent length = distance between Dimitri and Sarah = x

Plug in the values:

cos 72 = x/40

x = cos 72 * 40

x ≈ 12.4 [to one decimal place]

Learn more about Cosine Ratio on:

https://brainly.com/question/15793827

#SPJ1

The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.

Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.

Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.

Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).

Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

Answer:

-216

Step-by-step explanation:

use the rule bodmas

bracket,othersign, division, multiplication, addition, subtraction

The given expression is

First, we factor out the third power of z, and factor 2.

Now, we simplify to get the final expression

The divisions made were

Answer:

last choice

Step-by-step explanation:

be the best option because the x+8 cross each other out which leaves you with x+3 x-3 over x²+4 unless you cross the x out but no option on there haves that

Answer:

1) Yes

2) No, this polynomial has complex roots

3) No, this polynomial has irrational roots

Step-by-step explanation:

a. Rational roots theorem provide a complete list of all roots of

f (x) = 4x² - 25

b. Rational roots theorem does not provide a complete list of all roots of

g (x) = 4x² + 25

c. Rational roots theorem does not provide a complete list of all roots of

h (x) = 3x² - 25

What is Function?

A relation between a set of inputs having one output each is called a function.

Functions are given as;

f (x) = 4x² - 25

g (x) = 4x² + 25

h (x) = 3x² - 25

Now,

a. f (x) = 4x² - 25

To find the roots we can set up 0,

f (x) = 4x² - 25 = 0

4x² - 25 = 0

4x² = 25

Divide by 4,

x² = 25/4

Take square root both side,

x = √25/4

x = ±5/2

Thus, The function has rational roots.

So, Rational roots theorem provide a complete list of all roots.

b) g (x) = 4x² + 25

To find the roots we can set up 0,

4x² + 25 = 0

4x² = - 25

Divide by 4,

x² = - 25/4

Taking square root,

x = √-25/4

x = ±5i/2

Thus, The function has complex roots.

So, Rational roots theorem does not provide a complete list of all roots.

c) h (x) = 3x² - 25

To find the roots we can set up 0,

3x² - 25 = 0

3x² = 25

Divide by 3,

x² = 25/3

x² = 8.333

Take square root both sides,

x = √8.333

x = ±2.89

Thus, The function has irrational roots.

So, Rational roots theorem does not provide a complete list of all roots.

Therefore,

a. Rational roots theorem provide a complete list of all roots of

f (x) = 4x² - 25

b. Rational roots theorem does not provide a complete list of all roots of

g (x) = 4x² + 25

c. Rational roots theorem does not provide a complete list of all roots of

h (x) = 3x² - 25

Learn more about the rational root theorem visit:

https://brainly.com/question/25216212

#SPJ5

The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.

Given the equation in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is no solution.

Learn more about equations here: https://brainly.com/question/9236233

#SPJ1

Answer:

L=19

Step-by-step explanation:

Since the formula to find the area of a rectangle is \(A= w(l)\) we must start by plugging the given data into this equation

\(13x+2=9(x+6)\)

Then solve!

\(13x+2=9(x+6)\\13x+2=9x+54\\4x+2=54\\4x=52\\x=13\)

Since we now know that x equals, we are able to find the length by plugging 13 into the given function for the length.

\(l=13+6=19\)

Make sure to check your work!

\(13(13)+2=9(13+6)\\169+2=9(19)\\171=171\)

The other information required while using the intermediate value theorem to show the existence of zero for the polynomial function plotted is

f(x₁) < 0 and f(x₂) > 0

The intermediate value theorem says that if "f" is a continuous function across a closed interval [a, b] with values f(a) and f(b) at its endpoints, then the function takes any value at a point inside the interval that is between the values of f(a) and f(b).

The root of a polynomial is the value of y when x is zero. hence to show that there is a zero between the points x₁ and x₂ there is a need to show there was a change of sign in the output value

Using the graph

At the point of change of sign is the required zero

Learn more about intermediate value theorem at:

https://brainly.com/question/21793689

#SPJ1

Answer:

x=3/2 Espero que esto te ayude

Answer:

x=3/2

hope this helps mate

The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .

In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.

Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.

Of all the given options: the only equations which imply that b(9)=4  are :

i) b(x)=72/x - 4 and  (iv) b(x)=4

Of this two options only the first option is non-linear.

Hence the required option is  b(x)=72/x - 4 .

To learn more about nonlinear function visit:

https://brainly.com/question/5758609

Disclaimer:

The missing options are:

i)   b(x) = 72/x - 4

ii) b(x) = √x + 7

iii)b(x)  = 2x+1

iv) b(x) = 4

#SPJ1

Answer:

20:50

20/50=40%

Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.

Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.

The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.

The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.

Minimum efficient scale is the level of output where economies of scale have been fully exploited.

A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.

To read more about economics, visit https://brainly.com/question/14787713

#SPJ4

The volume of the solid generated about the x-axis by revolving region r is equal to V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\) .

As given in the question,

Volume of the solid which is generated by revolving a plane region 'r' about vertical line which does not pass through the given plane:

'r' be the radius of the circle.

Area of the cross section is the circle area = πr²

As it is given it is about the x-axis then radius 'r' is the function of x

f(x) = r

Let 'V' be the volume.

Volume of the solid generated by revolving the region 'r' about the x‐axis on the interval [ a, b] is given by :

V = \(\int\limits^a_b \pi {[f(x)]^{2} } \, dx\)

As f(x) = y

⇒V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\)

Therefore, the integral used to represent the volume of the given solid generated by revolving about the x-axis is equal to V  = \(\int\limits^a_b \pi {[y]^{2} } \, dx\)

Learn more about volume here

brainly.com/question/13338592

#SPJ4

Answer:

321.50 dollars.

Step-by-step explanation:

Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.

This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results   , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.

Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.

Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.

Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.

Answer:

see the attachment photo!

Answer:

the first one is 16=-4+12

from here you can solve

Step-by-step explanation:

Answer:

the answer is 20

Step-by-step explanation:

y= –x+z

1. 16= –4+z

16+4=z

20=z

z=20

2. 15= –5+z

15+5=z

20=z

z=20

z=20 is true

According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.

Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:

n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

To learn more about permutation
https://brainly.com/question/28443757
#SPJ1

Answer:

6.5%, 1/2, 0.65, 2/3

Step-by-step explanation:

6.5%=6.5%, 1/2=x/100=50%, 0.65=.65/1.00=x/100=65%, 2/3=x/100=66.66%

The increasing order of the given set of numbers is 0.065>0.5>0.65>0.6667.

Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.

Given that, 0.65, 6.5%, 2/3, 1/2

Here, 0.65, 6.5/100 =0.065, 0.6667, 0.5

By comparing decimals, we get

0.065>0.5>0.65>0.6667

Therefore, the increasing order is 0.065>0.5>0.65>0.6667.

To learn more about the comparison of decimals visit:

https://brainly.com/question/18270620.

#SPJ5

The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

Learn more on residual values of a set of data here: https://brainly.com/question/31687998

#SPJ1