Which expression is equal to 97/33??

Hey there!

3/36 = x/72

FIRST: CROSS MULTIPLY the equation

3 * 72 = x * 36

3 * 72 = 36 * x

216 = 36x

36x = 216

SECOND: DIVIDE 36 to BOTH SIDES

36x/36 = 216/36

CANCEL out: 36/36 because it give you 1

KEEP: 216/36 because it help solve for the x-value

NEW EQUATION: x = 216/36

THIRD: SIMPLIFY IT!

x = 6

Therefore, your answer is: x = 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The Least Common Multiple ( LCM ) of 20 and 48 is 240

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the first number be A

Now , the value of A = 20

Let the second number be B

Now , the value of B = 48

The least common multiple LCM of A and B is calculated by

Prime factorization of 20 = 2 x 2 x 5

Prime factorization of 48 = 2 x 2 x 2 x 2 x 3

Now , LCM = 2 × 2 × 2 × 2 × 3 × 5

The LCM of 20 and 48 = 240

Hence , the LCM is 240

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The graph of the pH function can be created by plotting the output of

input values of the hydronium ions, x, in the range 0 < x ≤ 1.

Correct responses:

First part:

Please find attached the graph of the pH function

From the attached graph of the pH function, we have;

Second part

First part

The pH function is; f(x) = -log₁₀x

Please find attached the graph of the pH function created with MS Excel

Where;

x = Amount of hydronium ions

f(x) = pH level

When the pH is 0, we have;

-log₁₀x = 0

Which gives;

x = 10⁰ = 1

When the pH value is 1, we have;

-log₁₀x = 1

log₁₀x = -1

x = 10⁻¹ = 0.1

Second Part

The given transformations are;

f(x) + 1, and f(x + 1)

At the y-intercept, x = 0

From the transformation, f(x) + 1, we have;

At x = 0, the transformation = -log₁₀(0) + 1

log₁₀(0) = Does not exist (DNE)

Therefore;

f(x) + 1 = -log₁₀(0) + 1 = DNE

The transformation, f(x + 1), at x = 0, gives;

f(0 + 1) = -log₁₀(0 + 1) = -log₁₀(1) = 0

Therefore;

The function f(x + 1) = -log₁₀(x + 1) is defined at x = 0, and therefore, has a y-intercept

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Answer:

The circumference of a circle is calculated using the formula: C = πd, where C represents the circumference and d represents the diameter of the circle.

In this case, the diameter of the circle is given as 24 inches.

Using the formula, we can substitute the values:

C = πd

C = 3.14 * 24

C ≈ 75.36 inches

Therefore, the circumference of a circle with a diameter of 24 inches (and using π = 3.14) is approximately 75.36 inches.

Step-by-step explanation:

Answer:

you need to make 600 cookies to make back $12,000

Answer:

True

Step-by-step explanation:

-77 is less than -76. Since the symbol refers to less than or equal to, this statement will be true.

The Function is increasing (-∞, 0), decreasing (2, ∞), and constant [0, 2].

The intervals on which the function is increasing, decreasing, or constant, we need to analyze the behavior of the function in each interval.

1. Interval t < 0:

In this interval, the function is given by f(t) = t + 2. Since the coefficient of t is positive (1), the function is increasing. Therefore, the interval t < 0 is an interval of increasing values.

2. Interval 0 ≤ t ≤ 2:

In this interval, the function is constant and given by f(t) = 2. The value of the function remains constant at 2 for all values of t in this interval.

3. Interval t > 2:

In this interval, the function is given by f(t) = -t + 4. Since the coefficient of t is negative (-1), the function is decreasing. Therefore, the interval t > 2 is an interval of decreasing values.

To summarize:

Increasing interval: t < 0

Decreasing interval: t > 2

Constant interval: 0 ≤ t ≤ 2

Using interval notation, we can express the intervals as follows:

Increasing interval: (-∞, 0)

Decreasing interval: (2, ∞)

Constant interval: [0, 2]

In interval notation, (a, b) denotes an open interval, which means it includes all values between a and b, but excludes the endpoints. [c, d] denotes a closed interval, which includes both endpoints c and d.

Therefore, the function is increasing on the interval (-∞, 0), decreasing on the interval (2, ∞), and constant on the interval [0, 2].

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The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Answer:

1 28

2 14

4 7

Step-by-step explanation:

7 4

14 7

28 1

...........

Answer:

Part A)

784 feet in the air (after five seconds).

Part B)

After 12 seconds.

Step-by-step explanation:

The height h (in feet) of a rocket t seconds after being fired is modeled by the function:

\(h(t)=-16t^2+160t+384\)

Part A)

We want to find the rocket's maximum height.

Since our function is a quadratic, the maximum height will occur at its vertex. The vertex of a quadratic is given by:

\(\displaystyle \Big(-\frac{b}{2a}\, f\Big(-\frac{b}{2a}\Big)\Big)\)

In this case, a = -16, b = 160, and c = 384.

So, the vertex occurs at:

\(\displaystyle t=-\frac{160}{2(-16)}=\frac{160}{32}=5\text{ seconds}\)

The maximum height is reached after five seconds.

Then the maximum height is:

\(h(t)_\text{max}=h(5)=-16(5)^2+160(5)+384=784\text{ feet}\)

Part B)

When the rocket reaches the ground, its height h above the ground will be 0. Hence:

\(h(t)_\text{ground}=0=-16t^2+160t+384\)

Solve for t. We can first divide both sides by -16:

\(t^2-10t-24=0\)

Factor:

\((t-12)(t+2)=0\)

Zero Product Property:

\(t-12=0\text{ or } t+2=0\)

Solve for each case:

\(t=12\text{ or } t=-2\)

Time cannot be negative. Hence, our only solution is:

\(t=12\text{ seconds}\)

The rocket reaches the ground 12 seconds after it is fired.

Answer:

your answer is -1

Step-by-step explanation:

D = distributive property

S = switch

C = combine

I = inverse operations

F = finalize

\(4(3x - 5) -2x = -30\\12x -20 -2x = -30\\12x -2x = -30 + 20\\10x = -10\\x = \frac{-10}{10}\\ x = -1\)

Answer:

471,000

Step-by-step explanation:

Using the rate of the exponential growth to calculate the exponential function, the number of subscribers after 10 years is 3446

An exponential function is a function in which the variable appears in an exponent. It is of the form f(x) = aˣ, where a is a constant and x is the independent variable. The graph of an exponential function is a curve that increases or decreases at an increasing rate.

To solve this problem, we have to find the rate and then calculate the number subscribers after 10 years.

In a given exponential function;

A = P(1 + x)ⁿ

Since this is an exponential growth, we can calculate the rate as;

1 year = 250 subscriber

2 years = 3 * 250

rate = (250 / 750) * 100

rate = 30%

We can substitute the values into the formula and solve

A = 250(1 + 0.3)¹⁰

A = 3446.46

They are expected to have 3446 subscribers after 10 years

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Answer: D

Step-by-step explanation:

Hope it helps

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Answer:

the answer is e

Step-by-step explanation:

96 (high score) - 67 (low score) = 29 (range)

Answer:

15x+98=105

      -98    -98

15x=7

/15    /15

x=7/15

Step-by-step explanation:

x=7/15

Answer:

We can start by finding how many pages Jordayn reads per hour:

Pages per hour = 72 ÷ (1 1/2) = 72 ÷ 3/2 = 48

So, Jordayn reads 48 pages per hour.

To find out how long it would take her to read a 168-page book, we can use the following formula:

Time = Pages ÷ Pages per hour

Time = 168 ÷ 48

Time = 3.5

Therefore, it would take Jordayn 3.5 hours to read a 168-page book, assuming her reading speed remains constant

Answer:

? = 900

Step-by-step explanation:

lets change ? to x

(100 + x) / 100 = 10

we will substitute /100

(100 + x) /100 · 100 = 10 · 100

100 + x = 1000

we substitute +100

100 + x -100 = 1000 - 100

x = 900

hope this helps =D happy learning!!

The sequence (3n-2/n)n=1 converges to 1.

To show that (3n-2/n)n=1 converges, we need to find the limit as n approaches infinity.

Using algebraic manipulation, we have the following steps

lim (3n-2/n)n = lim (3-2/n)^n

lim (3n-2/n)n = (3-2/∞)^∞

lim (3n-2/n)n = 1^∞

lim (3n-2/n)n = 1

The basic definition of convergence states that a sequence converges if the limit of the sequence as n approaches infinity is equal to a finite number

Since the limit of (3n-2/n)n as n approaches infinity is 1, we can conclude that the sequence converges to 1.

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The p- value for the given significant figure and test statistic z score is equal to 0.2251.

As given in the question,

Probability of a test on the basis of true negative for certain cancer is given significantly more than 0.72.

As significant value is more than 0.72 need to perform right tailed test.

Sample data test statistic z -score is equal to

z = 1.213

Using table p- value is equal to 0.22513

Accurate up to 4 decimal places

p - value = 0.2251

As significant value is more than 0.72 .

Result is statistically significant.

Reject the null hypothesis and accept the alternative hypothesis.

Therefore, the p - value foe the given test statistic z score is equal to 0.2251.

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Answer: -4.16

Step-by-step explanation:

100/25=4

-4 4/25=

-4 4*4/(25*4)=

-4 16/100= -4.16

Answer:

Is it 11.6%?

Step-by-step explanation:

I divided 290/250

The rate is 9/4 players per spot

The given parameters are:

Players = 27

Spots = 12

The rate is calculated as:

Rate = Players/Spot

So, we have:

Rate = 27 players /12 spots

Divide by 3/3

Rate = 9 players /4 spots

Rewrite as:

Rate = 9/4 players per spot

Hence, the rate is 9/4 players per spot

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Answer:

D

Step-by-step explanation:

The solution of the inequality  -3x + 6 > 12 is x<-2, this solution is represented in D graph.

A number system is defined as a system of writing to express numbers.

The given inequality is -3x + 6 > 12

A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

We need to plot the solution of the inequality.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

-3x + 6 > 12

Subtract 6 from both sides

-3x>6

Divide both sides by 3

-x>2

x<-2

Hence, the solution of the inequality  -3x + 6 > 12 is x<-2, this solution is represented in D graph.

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Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)