On what interval is the function h(x) = |x − 2| + 5 increasing? A. (2, ∞) B. (5, ∞) C. (-∞, 2) D. (-∞, 5)

Answer:

Hopefully this graph helps you!

Answer:

8 hours

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer: 50 and 59

I divided 2950 by 25 because I knew it would somehow factor into that since it ends in 50. Then, I got 25 and 118. From there, I just divided 118 by 2 since I knew that it would end in a 9 and I multiplied 25 by 2. Not sure if this is really helpful, but you also try using a GCF calculator and look up all the factors of that number next time!

Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.

Mary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.

Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.

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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.

Answer:

a) 27. b) 27.3333 c) 40.75

In the formula

putting in the given values of R_1, R_2, and R_3 gives

We add the fractions on the right-hand- side to get:

Taking the reciprocal both sides gives

Which is our answer!

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

sin(t) = \(3\sqrt10\\\)

cos(t) = \(1\sqrt 10\)

tan(t) = 3/1

What does Sin mean?

In mathematics, sin is an abbreviation for the trigonometric function sine. It is used to calculate the ratio between the length of the opposite side and the hypotenuse of a right triangle. The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The function is written as sin(x), where x is an angle in radians.

The sine of an angle is related to the cosine of the angle by the Pythagorean identity, which states that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse. In other words, sin2(x) + cos2(x) = 1.

The sine of an angle can also be used to calculate the area of a triangle with two sides of known length. The area of a triangle is equal to half of the product of the lengths of two sides and the sine of the angle between them. This is known as the Sine Law.

The sine function is also used in calculus to calculate the derivatives of trigonometric functions. The derivative of the sine function is equal to the cosine of the angle, written as cos(x).

The terminal point p(x,y) with determining the given number t,

sin(t) = y/p

     = 3/sqrt 10 (Given)

cos(t) = x/p

     = 1/sqrt 10 (Given)

tan(t) = y/x

     = 3/1 (Divide both numerator and denominator by sqrt 10)

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Answer:  Slope intercept form:  y = mx + b

A. y = 4/7 x + 27/7

Screenshot attached.

Step-by-step explanation:  Slope is m. In this example, it is 4/7.  The y-intercept is b. in this example it is 2 in the question and 27/7 in the answer choice.

First clue why A is the answer: the slope must be the same if the lines are parallel

The ratio of the given 240 kg to 6 kg will be 40:1.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

the ratio 240 kg to 6 kg.

It will be simple 240/6 :: 40 :1

Hence the ratio of the given data will be 40:1

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Answer:

step 2

Step-by-step explanation:

9 = -3(e - 2)

9 = -3e + 6

9-6 = -3e

3 = -3e

divide both sides by -3

-1 = e

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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Answer:

\( \frac{1}{2} \: as \: a \: decimal = \\ 0.5\)

Step-by-step explanation:

thats the answer

The decimal form, the mixed fraction can be written as 112.5.

To find out mixed fraction in the form of decimal.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

The mixed fraction is a fraction whose nominator is greater than its denominator or improper fraction is a fraction in which the denominator is always less than the numerator.

 112 1/2

= (2 x 112 + 1)/2

= (224 + 1)/2

= 225/2

To divide the 225 by 2 ,we get

=112.5

So,  the decimal form, the mixed fraction can be written as 112.5

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Answer:

b+10

Step-by-step explanation:

You combine all the variable terms with the letter b (in this case, there's just b) and combine all the numbers that are by themselves without a letter attached (these are called constants)

Answers:

If x is a probability value, then \(0 \le x \le 1\)

A probability of 0 means "impossible" while a probability of 1 means "100% certain".

Answer:

0.03125 = 3.125% probability that the person flipped 5 heads

Step-by-step explanation:

For each coin, there are only two possible outcomes. Either it was heads, or it was tails. The result of a coin toss is independent of other coin tosses. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Five coins:

This means that n = 5.

Fair coin:

Equally as likely to be heads or tails, so p = 0.5.

What is the probability that the person flipped 5 heads?

This is P(X = 5).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125\)

0.03125 = 3.125% probability that the person flipped 5 heads

Answer:

Formula  for arc length  =

arc length  =  r  θ         where θ is in radians

So  we  have

2pi  =  5 θ             solve for θ  and we have that

θ  =  [ 2 pi ]  / 5

The area  of the sector   =

(1/2) r^2 θ   =   (1/2)(5^2) (2pi) / 5   =   5 pi  in^2  ≈ 15.7  in ^2

The rectangular  shape  has more area  = (5 * 4)   = 20 in ^2

Step-by-step explanation:

I don't think this will help but hope it does

Answer:

$121,683.79

Step-by-step explanation:

A= P(1+ r)^t

A= Amount, P = Principal, r = Rate (decimal form), t= time

A = 47000(1+0.0825)^12

A = 47000(1.0825)^12

A = 47000(2.589016751)

A = 121683.7873

Rounded Answer = $121,683.79

(If there is meant to be no cents then $121,684). Good luck :)

Answer: \(\boxed{y=\frac{4}{5}x-2}\)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.

Substituting into point-slope form,

\(y-6=\frac{4}{5}(x-10)\\\\y-6=\frac{4}{5}x-8\\\\\boxed{y=\frac{4}{5}x-2}\)

Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

m = (0-(-1))/(2-0)

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

Answer:

the last one

Step-by-step explanation:

Answer:

slope -1/3 and y-intercept is -1

Step-by-step explanation:

Slope of line is 1/2.

What is slope?

In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.

Main body:

to find the slope from a graph , we need to fix two co-ordinates at slope for axis

let point at x be = (40,40)

let point y = (80,60)

Formula for slope ,

m = y₂-y₁/x₂-x₁

m = 60-40/80-40

m = 20/40

m = 1/2

hence , slope of line is 1/2.

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From the given list, we can choose the numbers 80 and 65 as potential values for the variable representing the height (in inches) of a bookcase.

Let's go through each number and reason why it could represent the height of a bookcase:

-80: It is highly unlikely for a bookcase to have a negative height as it implies being below ground or submerged. Negative heights do not make sense in this context, so we can eliminate -80 as a viable option.

10208: This number seems unreasonably high for the height of a bookcase. Most bookcases are not taller than a few feet or a couple of meters. A height of 10208 inches would be more than 850 feet, which is much larger than any standard bookcase. Therefore, we can eliminate 10208 as a realistic option.

80: This is a plausible height for a bookcase. Many bookcases range in height from a few feet to around six or seven feet, and 80 inches falls within this typical range.

65: Similarly, a height of 65 inches is also plausible for a bookcase. Smaller bookcases or shelves designed for specific purposes, such as children's bookcases or shorter units, often have heights around this range.

Based on these considerations, we can conclude that the numbers 80 and 65 are reasonable options for representing the height of a bookcase.

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Answer:

x = 4√3

Step-by-step explanation:

x² = 4(8 + 4) => tangent secant theorem

Solve for x

x² = 4(12)

x² = 48

Take the square root of both sides

√x² = √48

x = √(16 × 3)

x = 4√3

Answer:

To find the cost of filling Binaya's water tank, we need to calculate the volume of the tank first. The tank is in the shape of a cylinder surmounted by a hemisphere, so we can find the volume by calculating the volumes of the cylinder and hemisphere separately and adding them together.

The formula for the volume of a cylinder is V_cyl = πr^2h, where r is the radius and h is the height.

Given that the internal radius of the tank is 90 cm and the total height is 3.8 m, we convert the height to cm to match the radius unit and get 380 cm in height.

So, the volume of the cylinder part of the tank will be V_cyl = π(90)^2(380) = 9147600 cm^3.

The formula for the volume of a hemisphere is V_hem = (2/3)πr^3, where r is the radius of the hemisphere. By halving the internal radius of the cylinder, we get the radius of the hemisphere as 45 cm.

So, the volume of the hemisphere part of the tank will be V_hem = (2/3)π(45)^3 = 95325π cm^3.

The total volume of the tank will be the sum of the volumes of the cylinder and hemisphere:

V_total = V_cyl + V_hem = 9147600 + 95325π = 9457589.25 cm^3.

To convert this volume to litres, we divide by 1000:

V_total_l = 9457.59 l.

The cost of filling the tank with water at the rate of 20 paisa per litre will be:

Cost = 9457.59 x 0.20 = 1891.52 paisa = 18.92 rupees (rounded to two decimal places).

Therefore, it will cost Binaya 18.92 rupees to fill his water tank with water at the given rate.

Answer:

16

Step-by-step explanation:

Since the perimeter of the rectangle is 80, we can set up the perimeter formula:

80=2L+2W=2(3x+3)+2(2x+2)=6x+6+4x+4=10x+10

10x=70

x=7

AB=2x+2=2(7)+2=14+2=16

Answer:

AB= 16

Step-by-step explanation:

2x+2+3x+3=40

Add like terms: 2x+3x= 5x and 2+3=5

New equation: 5x+5=40

Solve: 40-5= 35

Now we know that x is equal to 7.

2(7)+2= 16

Side DC equals 16.

Side AB has the same length as side DC since it's a rectangle.

Side AB equals 16.

Let's check: 16+16=32 (side DC and side AB)

24 must be the length of the other sides.

So, when you add all the sides together...

16+16+24+24= 80

You get 80, the perimeter!

I hope this helped!

Answer:

If each fish tank must have at least one pebble, the many different ways that Mark can put the pebbles in the tanks is:

60.

Step-by-step explanation:

Permutations nPr Calculator

P(n,r)=  n!

(n−r)!  = ?

n (objects) = 5

r (sample) =  3

Answer:

P(n,r)=P(5,3)

=  5! /(5−3)!

= 60

The result shows that Mark can put the 5 pebbles in the 3 fish tanks in 60 different ways, if each fish tank must have at least one pebble.  Using the permutation calculator, the number of ways is calculated to be 60 ways.

The minimum sample size required to construct a 95% confidence interval for the population mean is 16.

To determine the minimum sample size required to construct a 95% confidence interval for the population mean circumference of tennis balls within 0.05 inch, we need to use the formula for the margin of error:

Margin of error = Z* (σ/√n)

Where Z* is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Since we want a 95% confidence interval, Z* = 1.96 (from a standard normal distribution table).

We are given that σ = 0.10 inch and we want the margin of error to be 0.05 inch. Plugging in the values, we get:

0.05 = 1.96 * (0.10 / √n)

Solving for n, we get:

n = [(1.96 * 0.10) / 0.05]² = 15.36

We can't have a fractional sample size, so we round up to the nearest whole number. Therefore, the minimum sample size required is 16.

This means that the manufacturer needs to randomly select and measure the circumferences of at least 16 tennis balls to estimate the population mean circumference with 95% confidence and a margin of error of 0.05 inch.

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The amount that should be deposited monthly is $286.66.

The monthly deposit is the periodic payment into an investment account that earns interest at a compound rate.

The monthly deposit can be determined using an online finance calculator.

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 6%

PV (Present Value) = $0

FV (Future Value) = $20,000

Results:

Monthly Deposit = $286.66

Sum of all periodic deposits = $17,199.36

Total Interest = $2,800.64

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