An element with a mass of 230 grams decays by 14.5% per minute. To the nearest
tenth of a minute, how long will it be until there are 60 grams of the element
remaining?

The given conditions to find the values of all six trigonometric functions is cos (x) =-5/9, sin (x) = 2 root(14)/9, tan(x)= - 2 root(14)/5 and cot(x)= - 5 (2 root 14), csc(x)= 9 /2root (14).

What is trigonometric functions ?

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the angles and sides of a triangle.

[tex]$\sec (x)=-\frac{9}{5} < 0$[/tex]and [tex]$\tan (x) < 0$[/tex]

so, x is in the second quadrant.

So, [tex]$\cot (x), \cos (x)$[/tex]are negative and [tex]$\sin (x), \csc (x)$[/tex] are positive.

Hence,

[tex]$$\begin{aligned}\cos (x) & =\frac{1}{\sec (x)}=-\frac{5}{9} \\\sin (x) & =\sqrt{1-\cos ^2(x)}=\sqrt{1-\frac{25}{81}}=\frac{2 \sqrt{14}}{9} \\\tan (x) & =\frac{\sin (x)}{\cos (x)} \\& =-\frac{2 \sqrt{14}}{5} \\\cot (x) & =\frac{1}{\tan (x)}=-\frac{5}{2 \sqrt{14}} \\\csc (x) & =\frac{1}{\sin (x)}=\frac{9}{2 \sqrt{14}}\end{aligned}$$[/tex]

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Step-by-step explanation:

Riders must be at least 48 inches. "At least" means greater than or equal to. Therefore, the inequality is:

h ≥ 48

To graph this, we draw a solid dot at the 48 mark (because it can equal 48) and an arrow to the right (because it can be greater than 48).

The total weight of the carton after packing the apples is 29.825 kg.

Empty carton: 8.350 kg

Apples: 21.475 kg

Since we are placing the apples inside the empty carton, now the carton will also contain the weight of the apples, additional to its own weight.

8.350 kg + 21.475 kg= 29.825 kg.

The total weight of the carton after packing the apples is 29.825 kg.

Answer:  1.8  divided by 0.6 is 3

The equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number 1.8 is divided by the number 0.6. The mathematical model for the division can be written as:-

E = 1.8 / 0.6

Hence, the equation of the model for 1.8 is divided by 0.6 will be E = 1.8 / 0.6.

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The antenna's height is determined to be 10 m using right triangle relations.

Following are the relationships in a right triangle:

The sine of an angle is equal to the length of the hypotenuse divided by the length of the side opposite the angle.

The cosine of an angle is equal to the neighboring side's length divided by the hypotenuse's length.

The tangent of an angle is calculated by dividing the length of the angle's adjacent side by its opposite side.

So, n this case, the side opposite to the 17o angle is the vertical height from her eyes to the top of the antenna, and the next side is the horizontal distance of 29 m, then:

tan 17° = h/29

h = 29 tan 17°

h = 8.87

Including eye height:

h = 8.87 + 1.51 = 10.38 m.

The antenna is 10 meters tall, rounded to the nearest meter.

Therefore, the antenna's height is determined to be 10 m using right triangle relations.

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Answer:

Data set 1: 20

Data set 2: 25

Step-by-step explanation:

Range is where you take the lowest value and subtract it from the highest value. So with data set 1, the highest number is 40 and the lowest is 20.cSo 40-20=20. Answer 20. Then with data set number 2, the highest number is 60 and the lowest is 35. So 60-35=25. Answer 25.

I hope this helps!!!

Answer:

hola

Step-by-step explanation:

Answer: You say Hola

Step-by-step explanation:

Which sounds like (Ohw·laa)  = This means Hi or Hello

After solving, the maximum height of the ball is 90.25 feet.

In the given question,

A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.

The quadratic function

h(t) = -16t^2+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown.

We have to find the maximum height of the ball.

Height is given that;

h(t) = -16t^2+52t + 48

Now comparing the given equation by the standard equation ax^2+bx+c=0

Here b = 52, a = -16

For maximum height put t= -b/2a

t = -52/2(-16)

t = 52/32

t = 1.625

Maximum height

h(1.625) = -16(1.625)^2+52(1.625) + 48

h(1.625) = -42.25+ 84.5 + 48

h(1.625) = 90.25 feet

The maximum height of the ball is 90.25 feet.

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Answer:

44

Step-by-step explanation:

BxH/2=Area

8x11=88

88/2=44

area=44

There are 160 ways to fill the four committee positions.

What is Combination?

Faculty members can be selected in A = 2 ways

Male student can be selected in B= 4 ways

Female student can be selected in C = 4 ways

One parent can be selected in D = 5 ways.

Total number of ways to select committee of four = A*B*C*D

= 2* 4 * 4 * 5

= 160 Ways

Hence, there are 160 ways to fill the four committee positions.

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The sum of 3/4 and 4/5 is 31/20 and To divide the common denominators by the individual denominators without using fractions or decimals, we need common denominators or the LCM of the two denominators.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, are two fractions 3/4 and 4.5 and their sum is,

= 3/4 + 4/5.

= (15 + 16)/20.

= 31/20.

So, the answer of the student is wrong.

We need common denominators or LCM of the two denominators so that we can divide the common denominators by the individual denominators without having fractions or decimals.

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Answer:

Step-by-step explanation: h(t)=-16t2+85

Let h(t)=0 to find when the object will hit the ground

0=-16t2+85

Solve for t=?

We need to get t term on its own

Take 85 from both sides

0-85=-16t2+85-85

-85=-16t2

To get t term on its own

Divide both sides by -16

-85/-16=-16t2/-16

5.3=t2

We have to solve for t squared that means we must take the square root of both sides

the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds

The ingredients for 4 brownies would be: 1/2 cup butter, 15/4 ounces unsweetened chocolate, 9/8 cup sugar, 3 teaspoons vanilla, 3 eggs, and 3/4 cup flour.

A percentage is a component of a total amount, and the measures are related by the rule of three.

Keep in mind that in a particular ratio, such as: a/b=c/d a*d=b*c

Create the following ratio for each ingredient:1/8 cup butter, 5/8 ounces of unsweetened chocolate, 1/4 cup sugar, 1/8 teaspoon vanilla, 1/2 egg, and 3/16 cup flour.

Explanation:

Given that the original recipe calls for 16 brownies;

Butter:

(1/8)/16=b/12

(2/3)(12)=16b

8=16b

b=1/2

Chocolate:

5/16=c/12

60=16c

c=60/16

c=15/4

Sugar: (3/2)/16=s/12

(3/2)(12)=16s

18=16s

s=18/16

s=9/8

Vanilla: 2/16=v/12

24=16v

v=3/2

Eggs: 2/16=e/12

e=3/2

Flour:1/16=f/12

f=3/4

As a result, the following would be the components for four brownies,

3/4 cups flour, 1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, and 3/2 eggs.

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Answer:

If one of the answers is 5 hours and 50 minutes, that. If its 7 hours and 30 minutes, that. In between is 6 hours and 40 minutes.

Step-by-step explanation:

Volume = 201 cm

Here is an equation to help you find the volume of a cone:

V=πr²[tex]\frac{h}{3}[/tex]=π·4²·[tex]\frac{12}{3}[/tex] ≈ 201.06193cm³

This equation is what I used to solve your question. The answer is 201.06193, but is says round to the nearest whole number, so the answer is actually 201 cm.

In the equation:

V means Volume

π means Pi (3.14)

r² means radius squared

[tex]\frac{h}{3}[/tex] means height divided by 3

4² means 4 · 4

[tex]\frac{12}3}[/tex] means 12 ÷ 3

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The volume of water that runs off the Shoppes at Fremont parking lot after a 5 cm rainfall event is [tex]1000m^{3}[/tex].

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Basically, the volume of a liquid is measured in liters, where 1 liter is equal to 1000 cubic centimeters.

1 liter = 1000 cubic centimeters = 0.001 cubic meters

Hence,

1 cubic meters = 1000 liters

Given,

[200m x 100m = [tex]20000m^{2}[/tex]]

[5cm x 1m/ 100cm = 0.05m]

20,000m2 x 0.05m = [tex]1000m^{3}[/tex]

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Answer:

Step-by-step explanation:

Answer:

89 m

Step-by-step explanation:

p/2 = 376/2 = 188 m

l + a = 188

a = 188 - l

a = 188 - 99

a = 89 m

The required graph is as follows.

The graph of an equation in x and y is the value of y for the

corresponding value of x.

Given,

y = -x - 2

or x + y = -2

The line cuts x axis when y = 0 and cuts y axis when x = 0.

Therefore, the line cuts x axis at x = -2

                  the line cuts y axis at y = -2

Hence, required graph is:

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The difference between 246 and 31 tripled is

The problem is solved using subtraction

the term difference is similar to subtraction in mathematics

Then tripling is raise to power 3 or exponents of 3, hence after subtraction then exponents is applied to the end result of subtraction to give the answer

The subtraction

= 246 - 31

= 215

The exponents

= 215³

= 215 * 215 * 215

= 9938375

'

On the second thought, we have a different answer in this case

= 246 - 31³

= 346 - 31 * 31 * 31

= -29545

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Answer:

Alex will have a total of $990 in 5 years.

Step-by-step explanation:

Using the formula [tex]i=prt[/tex] we get [tex]i=900[/tex] × [tex]0.2[/tex] × [tex]5[/tex] which equals 90

[tex]900 + 90 = 990[/tex]

Yes, a triangle can be drawn with side lengths of 7.3 meters, 4.6 meters, and 11 meters this is in the case whereby the lengths of any two sides combined is longer than the length of the 3rd side.

Triangle inequality, in Euclidean geometry, theorem  can be described as the theorem that states that the  sum of any two sides of a triangle is greater than or equal to the third side.

This can be represented using the  symbols, {a + b ≥ c.}  and this can be explained that the the shortest distance between two points is a straight line.

Then cherck this illustration to confirm that we are right:

7.3 + 4.6 > 11

7.3 + 11 > 4.6

4.6 + 11 > 7.3

Hence from this we can see that triangle can be drawn

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Answer:

Step-by-step explanation:

To find the arc length of the polar curve r = 8cosθ between 0 and π/4, we can use the formula for arc length:

L = ∫a^b √(r^2 + (dr/dθ)^2) dθ

Substituting in the values for r and dθ, we get:

L = ∫0^(π/4) √(8^2cos^2θ + (-8sinθ)^2) dθ

= ∫0^(π/4) √(64cos^2θ + 64sin^2θ) dθ

= ∫0^(π/4) √(64) dθ

= ∫0^(π/4) 8 dθ

= 8(π/4 - 0)

= 8π/4

= 2π

Therefore, the arc length of the polar curve r = 8cosθ between 0 and π/4 is 2π.

Answer:

This is because the function is an exception - it is a special type of function called a Separatrix Separation Function.

Step-by-step explanation:

The Separatrix Separation Function theorem helps us prove through complex conjugates the reason why there is no hole at x =2.

When the card is a jack, there is a 0.25 probability that you will receive a spade.

The ratio of good outcomes to all possible outcomes of an event is known as the probability.

The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application. Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

P(Spade) = 13/52 = 1/4 P(Jack) = 4/52

= 1/13 P(Spade and Jack)

= (1/4)(1/13) = 1/52 P(Spade/Jack)

= P(Spade and Jack)/P(Jack)

= (1/52)/(1/13) = (1/52)(13/1)

= 13/52 = 1/4 = 0.25

Hence, When the card is a jack, there is a 0.25 probability that you will receive a spade.

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Complete question-

A single card is drawn from a standard 52- card deck. Find the conditional probability that the card is a spade, given that it is a jack.?

Answer:

If you connect the 2 dots it will give a X image.Both lines will cross each other forming the X

The number of apples x will be 10 and the number of bananas y will be 4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether.

The number of apples and bananas will be calculated as,

0.75x +0.30y = 6

x + y = 14 or x = 14 - y

0.75(14-y) = 0.30y = 6

10.5-0.75y + 0.30y = 6

y = 10

x = 14  - y

x = 14 - 10 = 4

Therefore, the number of apples x will be 10 and the number of bananas y will be 4.

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