What is the range of the function? f(x) = -2^x + 1

The average number of feet per day they need to ascend is 'Feet climbed per day ≥ 1,761.5'.

The mountain climbing team must calculate the average number of feet to climb each day in order to reach the summit of Mount Everest, which is at an altitude of 29,029 feet. Starting from an altitude of 18,460 feet, the team needs to climb the remaining distance to the summit within 6 days. To find the average feet per day they need to ascend, we use an inequality.

First, we determine the total feet that the team must climb:

Total feet to climb = Summit altitude - Current altitude
                        = 29,029 feet - 18,460 feet
                        = 10,569 feet

Now we divide the total feet by the number of days to find the average feet per day:

Average feet per day = Total feet to climb / Number of days
                      = 10,569 feet / 6 days

Since the team must climb at least this average number of feet daily, the inequality will be:

Feet climbed per day ≥ 10,569 feet / 6 days

By solving the inequality, we find that the team must climb at least 1,761.5 feet per day.

Therefore, the inequality to represent the average number of feet the team must climb per day to reach the summit within 6 days is:

Feet climbed per day ≥ 1,761.5

Answer:

67

Step-by-step explanation:

First number between 100 to 500 which is divisible by 6 is 102

Multiples of 6 between 100 to 500 :

102,102+6,102+6+6,....

This Forms an AP

a= first term = 102

d = common difference = 6

Last number between 100 to 500 which is divisible by 6 is 498

So, [tex]a_n=498[/tex]

Formula of nth term = [tex]a_n=a+(n-1)d[/tex]

[tex]498=102+(n-1)6[/tex]

[tex]498-102=(n-1)6[/tex]

[tex]396=(n-1)6[/tex]

[tex]\frac{396}{6}=n-1[/tex]

[tex]66=n-1[/tex]

[tex]66+1=n[/tex]

[tex]67=n[/tex]

Hence there are 67 multiples of 6 between 100 to 500.

Answer:

C.  3x2 − 3x − 60

Step-by-step explanation:

3(x + 4) (x - 5) = (3x+12) (x-5)

(3x+12) (x-5) = 3x2+12x-15x-60

3x2+12x-15x-60 = 3x2 − 3x − 60

C. 3x^2-3x-60 Hope it helps

ANSWER

[tex]a_n= \frac{1}{2}( {2}^{n - 1} )[/tex]

EXPLANATION

The corresponding ordered pairs from the graph are:

(2,1) (3,2) (4,4) (5,8)

The y-values are:

1,2,4,8

The first term term is the term before 1,this has to be.

[tex]a_1= \frac{1}{2} [/tex]

The common ratio is

[tex]r = \frac{2}{1} = 2[/tex]

The nth term is given by

[tex]a_n=a_1 {(r}^{n - 1} )[/tex]

Let's substitute the values to get,

[tex]a_n= \frac{1}{2} \times {(2}^{n - 1} )[/tex]

This simplifies to,

[tex]a_n= \frac{1}{2} {(2}^{n - 1} )[/tex]

The graph represents a geometric sequence with a common ratio of 2, best defined by the function an = 2(2)^n – 1.

This graph represents a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'common ratio'. In this case, the common ratio is 2, because each y-coordinate is twice the y-coordinate of the point before it (2, 1), (3, 2), (4, 4), (5, 8). Therefore, the sequence is best represented by the option A an = 2(2)^n – 1.

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For this case we must find three consecutive whole numbers whose sum is equal to 363. These numbers should be close to 120. So, these numbers are:

120,121 and 122. If we add them together we have:

[tex]120 + 121 + 122 = 363[/tex]

Answer:

120,121 and 122

[tex]120 + 121 + 122 = 363[/tex]

Answer:

x=21

Step-by-step explanation:

Set the two similar sides in a fraction to be compared and set them equal to another set of similar sides whose values are already known. Solve from there. See work for more.

Answer:

Step-by-step explanation:

-1 is included in the inequality. 2 is not included.

-1 ≤ x < 2

So this reads as x is greater than or equal to - 1 and x is less than 2.

Answer: -1 less equals x < 2

Answer:

d)96π

Step-by-step explanation:

Given:

Cyliner with radius,a= 4

Height b=8

Surface area of cylinder, A=2πrh+2πr^2

=2π(rh+r^2)

=2π(4(8) + 4^2)

= 2π(32+16)

 =2π(48)

 =96π !

Answer: Option D.

[tex]A =96\pi\ cm^2[/tex]

Step-by-step explanation:

The area of the circular bases is:

[tex]A_c = 2\pi(a) ^ 2[/tex]

Where

[tex]a=4\ cm[/tex] is the radius of the circle

Then

[tex]A = 2\pi(4) ^ 2[/tex]

[tex]A = 32\pi\ cm^2[/tex]

The area of the rectangle is:

[tex]A_r=b * 2\pi r[/tex]

Where

[tex]b=8\ cm[/tex]

b is the width of the rectangle and [tex]2\pi r[/tex] is the length

Then the area of the rectangle is:

[tex]A_r=8 * 2\pi (4)[/tex]

[tex]A_r=64\pi\ cm^2[/tex]

Finally the total area is:

[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]

[tex]A =96\pi\ cm^2[/tex]

Answer:

Vaccinated: 465, 771, 1236

Not Vaccinated: 485, 600, 1085

Total: 950, 1371, 2321

Step-by-step explanation:

Next Question: 465/1236

It is given that:

This means that the total of all the entries i.e. total of each row and each column is equal to 2321

Also, the sum of the second row is equal to: 1085

This means that the sum of second column is: 1371

The table is attached to the answer.

Answer:

The answer is A.

Step-by-step explanation:

I got this answer by going through the regular division system.

Take the total price - rate . 0.12

38 - 8 = 30 / 0.12 = 250 <- The customer used 250 mins.

Hope I helped :)

Answer:

It ends at 7:30.

Final answer:

Tim's swimming practice starts at 7 o'clock and after adding the 30 minutes duration, it ends at 7:30.

Explanation:

The question pertains to adding time, specifically calculating the end time of an activity based on its duration. If Tim's swimming practice starts at 7 o'clock and ends 30 minutes later, the end time can be found by adding 30 minutes to the start time.

Here's how you calculate it:

Start with the initial time of the practice, which is 7:00.

Add the duration of the practice, which is 30 minutes.

Since there are 60 minutes in an hour, adding 30 minutes to 7:00 does not increase the hour value. Therefore, the practice ends at 7:30.

So, Tim's swimming practice ends at 7:30.

Answer:

A 36

Step-by-step explanation:

We can determine the scale factor

From triangle ABC BC =9

                     DEF  EF = 90

We multiply by 10

The scale factor is 10

AC ( 10) = DF

We know DF = 360

b  * 10 = 360

Divide each side by 10

10b/10 = 360/10

b = 36

Answer: 401.952380952

Step-by-step explanation:

Answer:

400000 + 10000 + 300 + 9

Step-by-step explanation:

Just simply take each place value and turn the rest after to zeros, but DO NOT include the zeros that are within the number. Zeros are unnecessary.

I am joyous to assist you anytime.

Answer: f(x) has a domain that contains the domain of g(x).

Step-by-step explanation:

The domain of f(x) is: x - 2 > 0

                             -->       x > 2

The domain of the graph g(x) is: x ≥ 3

All of the values of x ≥ 3 are included in x > 2.

Answer:

SAS Similarity Theorem

Step-by-step explanation:

we know that

SAS Similarity Theorem: States that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem

∠HJZ=∠RJW ----> by vertical angles

and

WJ/HJ=JR/JZ

substitute the values

8/4=6/3

2=2 ----> is true

so

Two sides of triangle HJZ are proportional with the two corresponding sides of triangle WJR and the included angle is congruent

therefore

Triangles are similar by SAS Similarity Theorem

Answer:

an = -1.3n -2.4

Step-by-step explanation:

The formula for an arithmetic sequence is

an = a1 +d (n-1)

where a1 is the first term and d is  the common difference

an = -3.7 - 1.3(n-1)

Distribute

an = -3.7 -1.3n +1.3

an = -2.4 - 1.3n

an = -1.3n -2.4

Answer:

x = 4

Step-by-step explanation:

The volume (V) of the triangular prism is calculated as

V = area of triangular face × length

Area of triangle = [tex]\frac{1}{2}[/tex] bh

b is the base and h the perpendicular height

here b = 9 and h = 12 ← sides at right angles

A = [tex]\frac{1}{2}[/tex] × 9 × 12 = 54 m²

The length of the prism = x and V = 216, hence

54x = 216 ( divide both sides by 54 )

x = 4

To find the missing lengths of the sides, you need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

To find the missing lengths of the sides, you need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). So, the equation is: a² + b² = c².

For example, if b is missing and c is 16, you can plug the values into the equation and solve for b: a² + b² = 16². Once you find the value of b, you can follow the same process for the other missing lengths.

Remember to square each side length before adding them. Then, find the square root of the sum to find the length of the hypotenuse.

Answer:

3;14;27;48

Step-by-step explanation:

Answer:

3, 12, 27, 48

Step-by-step explanation:

To find the first 4 terms substitute n = 1, 2, 3, 4 into the rule, that is

n = 1 → 3 × 1² = 3 × 1 = 3 ← first term

n = 2 → 3 × 2² = 3 × 4 = 12 ← second term

n = 3 → 3 × 3² = 3 × 9 = 27 ← third term

n = 4 → 3 × 4² = 3 × 16 = 48 ← fourth term

Answer:

The ratio of x:y is 1/2

Step-by-step explanation:

Let

x----> the number of Kg of brand A

y ---> the number of Kg of brand B

we know that

400x+280y=320(x+y)

400x+280y=320x+320y

400x-320x=320y-280y

80x=40y

x/y=40/80

x/y=1/2

Final answer:

The ratio of Brand A coffee to Brand B coffee (x to y) required to achieve a mixture cost of $320/kg is 1 : 2. This is derived using the weighted average cost formula and simplifying the resulting equation.

Explanation:

To find the ratio of x to y for the mix of Brand A and Brand B coffee beans, we can use a weighted average cost formula since the mixture's cost is given to be $320/kg. Let's assume we have x kilograms of Brand A coffee at $400/kg and y kilograms of Brand B coffee at $280/kg. The total cost for all the coffee is then $400x + $280y.

The combined weight of the coffee is x + y kilograms, and for the mixture to cost $320/kg, the total cost divided by the total weight must equal $320. Therefore, we can set up the following equation:

($400x + $280y) / (x + y) = $320

Multiplying both sides by (x + y) we get:

$400x + $280y = $320x + $320y

Now, we subtract $320y from both sides to isolate terms with x:

$400x - $320x = $320y - $280y

$80x = $40y

Dividing both sides by $40 gives us the simplified ratio:

x : y = 1 : 2

Thus, the ratio of Brand A coffee to Brand B coffee in the mixture to get a $320/kg cost is 1 : 2.

1) domain of the first is ( R ) because of its root(3) and its range is (R) because of its root again

2)and domain of the last , is [0,+infinity)

and for its range , you can draw it such as picture and will be [0,- infinity)

Answer:

1. [tex]Dom(f)=\mathbb{R} [/tex], [tex]Ran(f)=\mathbb{R} [/tex].

2. [tex]Dom(f)=\{x\in \mathbb{R} : x\geq 0 \} [/tex], [tex]Ran(f)=\{x\in \mathbb{R} : x \leq 0 \}  [/tex].

Step-by-step explanation:

1. Since the degree of the radical is an odd number, the radicand can be any real number, then [tex] x [/tex] can take any real value, so the domain of [tex] f [/tex] is the set of all real numbers, [tex] \mathbb{R} [/tex].

Now, if [tex] x\in \mathbb{R} [/tex] , then [tex] x-3 \in \mathbb{R}  [/tex], so  [tex] \sqrt[3]{x-3} \in \mathbb{R}  [/tex], and thus [tex] f(x)\in \mathbb{R} [/tex], which leads us to affirm that the range of  [tex] f [/tex]  is the set of all real numbers, [tex] \mathbb{R} [/tex].

2. Since the degree of the radical is an even number, the radicand can not be a negative number, then [tex] x [/tex] can take only nonnegaive values, so the domain of [tex] f [/tex] is the set of all nonnegative numbers, [tex] \{x\in \mathbb{R} : x\geq 0 \}  [/tex].

Now, if [tex] x\geq 0 [/tex] , then [tex]  \sqrt{x}\geq 0  [/tex] so  [tex]  -3\sqrt{x}\leq 0  [/tex], and thus [tex] f(x)\in \mathbb{R} [/tex], which leads us to affirm that the range of  [tex] f [/tex]  is the set of all nonpositive numbers, [tex] \{x\in \mathbb{R} : x \leq 0 \} [/tex].

ANSWER

36√3 square units.

EXPLANATION

The area of a parallelogram is obtained by multiplying the base by the height.

We use the sine ratio to obtain the height.

[tex] \sin(60 \degree) = \frac{h}{6} [/tex]

[tex]h = 6 \sin(60 \degree) [/tex]

[tex]h = 3 \sqrt{3} [/tex]

The area becomes:

[tex]12 \times 3 \sqrt{3} = 36 \sqrt{3} {units}^{2} [/tex]

Answer:

Step-by-step explanation: the answer is 21%

Answer:

21%

Step-by-stStep-by-stepep explanation:

Answer: The answer I got was 39

Step-by-step explanation:

False, the min and max of A are the same distance as the min and max of B from each other, therefore the standard deviation is the same.

6.5 x 4 = 26

The perimeter of the square is 26 ft.

Answer: 26 ft

Step-by-step explanation: you have add all sides.