Which expression is equivalent to -
60x20, 24
30x10 12?​

Answer:

Step-by-step explanation:

[tex]y=2^x\\\\\text{Put}\ x=5\ \text{to the equation of the function:}\\\\y=2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]

The output, or the result when we input x=5 into the function y=2^x, is 32. This is found by substituting the given input into the function.

The function you've provided is y=2 to the power of x . It is an exponential function. The output for a function is simply the result you get when you substitute a given input into the function. In this case, the function is defined as y = 2^x. To find the output when x=5, replace x in the function with 5. So y = 2^5 = 32. Therefore, the output for an input of x=5 in your function is 32.

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Answer:

66 km ÷ 24 km/h = 2 3/4 hours =

2 hours, 45 minutes

Answer:

f of x equals 7 times one eighth to the x power

Step-by-step explanation:

Given phrase,

function f of x equals 7 times one half to the 3 times x power,

[tex]\implies f(x) = 7(\frac{1}{2})^{3x}[/tex]

By the power to power property of exponent,

That is,

[tex](a^m)^n=a^{m.n}[/tex]

[tex]f(x) = 7((\frac{1}{2})^3)^x[/tex]

[tex]f(x) = 7(\frac{1}{8})^x[/tex]

= f of x equals 7 times one eighth to the x power

The function g(x) = f(-x) represents a reflection of the graph of f(x) across the y-axis. This transformation swaps the values of the function for positive and negative x values, creating a mirror image.  So since the max of f was when x = 2, the max of g will be when x = -2.

Understanding the Transformation of Function g(x) = f(-x)

function g(x) = f(-x).

This indicates a transformation where the function f(x) is reflected across the y-axis.

To put it simply, the graph of y = f(-x) is the mirror image of the graph of y = f(x) across the y-axis.

f g(x) = f(-x), the graph of g looks like a mirror image of f, where the y-axis is the mirror.  

For example, g(1) will be what f's value at -1 was (-1).  g(2) = f(-2) = -3.  g(3) = f(-3) = -1.  etc.  

So since the max of f was when x = 2, the max of g will be when x = -2.

Here’s an example to illustrate:

Suppose f(x) = x².

The graph of y = f(x) is a parabola facing upwards.

For y = f(-x), or y = (-x)²,

the graph will still be a parabola facing upwards.

Since g(x) = f(-x), the absolute values are not changed but the sign change in x reflects each point across the y-axis.

This reflection happens because negating the independent variable x means we swap the values of the function at positive and negative x values.

Question:

If the function g is defined so that g(x)=f(-x), then for what value of x does g attain its maximum value?

Check the picture below.

Answer:

The total area of Ohio is about 30 times the total area of Rhode Island

Step-by-step explanation:

Let

x -----> the total area of Ohio in square miles

y -----> the total area of Rhode Island in square miles

we know that

[tex]x=4.5*10^{4}\ mi^{2}[/tex]  

[tex]y=1.5*10^{3}\ mi^{2}[/tex] (searched in Google)

To find out approximately how many times the total area of Ohio is compared to the area of Rhode Island, divide the area of Ohio by the area of Rhode Island

[tex]\frac{x}{y}[/tex]

substitute the values

[tex]\frac{4.5*10^{4}}{1.5*10^{3}}=(\frac{4.5}{1.5})( 10^{4-3}) =3*10^{1}=30[/tex]

therefore

The total area of Ohio is about 30 times the total area of Rhode Island

Ohio is approximately 37.5 times larger than Rhode Island.

To find out how many times larger Ohio is compared to Rhode Island, we need to know the area of both states and then divide the area of Ohio by the area of Rhode Island.

The total area of Ohio is given as[tex]\( 4.5 \times 10^4 \)[/tex]square miles.

The area of Rhode Island is approximately[tex]\( 1.2 \times 10^3 \)[/tex] square miles.

Now, we divide the area of Ohio by the area of Rhode Island to find the factor by which Ohio is larger:

[tex]\[ \frac{\text{Area of Ohio}}{\text{Area of Rhode Island}} = \frac{4.5 \times 10^4}{1.2 \times 10^3} \][/tex]

[tex]\[ = \frac{4.5}{1.2} \times \frac{10^4}{10^3} \][/tex]

[tex]\[ = 3.75 \times 10 \][/tex]

[tex]\[ = 37.5 \][/tex]

Answer:

A.2.251 cm , 2.349 cm, 2.295 cm

B. 0.023 meters.

Step-by-step explanation:

a. The possible actual measurements are 2.251 cm, 2.349 cm and 2.295 cm.

b. Rounded measurement in meters is 0.023 meters

a. To determine which measurements could be the actual measurement of the rainfall, we need to consider how rounding works.

When rounding to the nearest tenth of a centimeter, any measurement with a hundredth digit of 5 or greater rounds up, and any measurement with a hundredth digit less than 5 rounds down.

Given that the rounded measurement is 2.3 cm, let's evaluate the measurements:

2.251 cm: Rounds down to 2.3 cm

2.349 cm: Rounds up to 2.3 cm

2.352 cm: Rounds up to 2.4 cm

2.295 cm: Rounds down to 2.3 cm

So, the possible actual measurements are 2.251 cm, 2.349 cm and 2.295 cm.

b. To convert the rounded measurement to meters, we need to divide it by 100, since there are 100 centimeters in a meter.

Rounded measurement: 2.3 cm

Conversion to meters: 2.3 cm / 100 = 0.023 meters

Equation: Rounded Measurement (in meters) = Rounded Measurement (in centimeters) / 100

Rounded Measurement (in meters) = 2.3 cm / 100

= 0.023 meters

Learn more about Rounding figures click;

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Final answer:

To find the side length of the original square, we formed a quadratic equation based on the given information and solved it to get a side length of 5 meters.

Explanation:

The question asks us to find the length of a side of the original square when the sides are increased by 3 meters and the new area becomes 64 square meters. First, let's denote the side length of the original square as x. If each side of the square is increased by 3 meters, then the new side length is x + 3 meters. The area of the new square is given to be 64 m², which can be represented as the square of the new side length, so the equation becomes:

(x + 3)²= 64

This simplifies to:

x² + 6x + 9 = 64

Subtracting 64 from both sides:

x² + 6x - 55 = 0

This is a quadratic equation that we can solve by factoring or using the quadratic formula. In this case, the equation factors to:

(x + 11)(x - 5) = 0

This gives us two possible solutions for x: -11 or 5. Since a side length cannot be negative, we disregard the -11 and conclude that the side length of the original square is 5 meters.

Answer: c

Step-by-step explanation: because the first number has to be greater then 1 less then 10

Option C (0.21 X 10^7) is not in scientific notation.

The number that is NOT in scientific notation is 0.21 X 10^7 (option C).

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Answer:

(1, - 8 )

Step-by-step explanation:

We have P(- 2, 3 ) → P'(- 6, - 4 )

The image coordinates are 4 less than the original x- coordinate and 7 less than the original y- coordinate, thus the translation rule is

T : (x, y ) → (x - 4, y - 7 ), thus

(5, - 1 ) → (5 - 4, - 1 - 7 ) → (1, - 8 )

Answer: 15

Step-by-step explanation:

3x5 is 15

To find the total number of squares in 5 rows, multiply the number of squares in each row, which is 3, by the number of rows, which is 5.

To find the total number of squares in 5 rows, we need to multiply the number of squares in each row by the number of rows. Since there are 3 squares in each row, we can multiply 3 by 5 to get the answer.

Step 1: Multiply the number of squares in each row, which is 3, by the number of rows, which is 5: 3 x 5 = 15.

Step 2: Therefore, there are 15 squares in 5 rows.

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The answer is 810

10% of a number is 81.

All you need to do is multiply 81 by 10 (810) to see that 10% of 810 is 81.

Best of luck

Answer:

810

Step-by-step explanation:

Multiply 81 by 100 (8,100).

The decimal for 10% is 0.10.

Then multiply 8,100 by 0.10.

Answer:

x = [tex]\frac{1}{12}[/tex] y²

Step-by-step explanation:

Any point (x, y ) on the parabola is equidistant from the focus and the directrix

Using the distance formula, then

[tex]\sqrt{(x-3)^2+(y-0)^2}[/tex] = | x + 3 |

Squaring both sides

(x - 3)² + y² = (x + 3)² ← expanding both sides

x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides

- 12x + y² = 0 ( subtract y² from both sides )

- 12x = - y² ( divide both sides by - 12 )

x = [tex]\frac{1}{12}[/tex] y²

Answer:

y²-12x = 0

Step-by-step explanation:

The formula for calculating the equation of a parabola is y² = 4ax

and x = a

To find the equation of the parabola with focus (3, 0) and directrix x = –3,

The point given (x,y) = (3,0) and x = -3

From the data given, it can be seen that a = -3 by simply comparing x = a with x = -3

Similarly, x = 3 from the given point.

Substituting the value of x = -3 in the formula for equation of a parabola gives;

y² = 4(-3)x

y²= -12x

y²-12x = 0

Answer:

AB=15 BC=60

Step by step:

AB+BC=AC

AC=75

Plug in AC to the equation: AB+BC=75

BC=4(ab)

Plug in BC into the equation: AB+4(AB)=75

Simplify: 5AB=75

Divide each side by 5: AB=15

BC=4(15)=60

Answer:  AB = 60, BC = 15

Step-by-step explanation:

AB is 4 times bigger than BC ⇒    AB = 4BC

Use the Segment Addition Property: AB + BC = AC

and substitution (replace AB with 4BC) and (AC with 75) to solve for BC

4BC + BC = 75

        5BC = 75

          BC = 15

AB = 4BC

    = 4(15)

    = 60

Answer: 0.6666666

Step-by-step explanation:

Answer:

0.6 repeatedly. as a fraction is 2/3

The measure of an angle being equal to itself is an example of the Reflexive Property, which states that any quantity is equal to itself.

The statement "The measure of an angle is equal to itself" is true because of the Reflexive Property. This property states that any quantity is equal to itself, which is a fundamental idea in mathematics and logic. In the context of geometry and angles, it means that an angle is always equal to its measure. So, if θ represents the measure of an angle, then we could say θ = θ, which demonstrates the Reflexive Property.

The other properties listed—the Property of Equality, Symmetric, and Transitive—are also important in the realms of algebra and geometry but do not directly apply to the fact that an entity is equal to itself. Instead, these properties involve the relationship between different entities or the equality between them derived from other equalities.

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Answer:

21: 7*3

22: 11*2

23: prime

24: 2^3 * 3

25: 5^2

26: 13*2

27: 3^3

28: 2^2*7

29: prime

30: 3*2*5

Answer:

True

Step-by-step explanation:

The n th term rule for an arithmetic sequence is

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

here d = 9 - 7 = 2 and a = 7, thus

[tex]a_{n}[/tex] = 7 + 2(n - 1)

Answer: Hello there!

initially Maria has 6 red marbles, 6 blue marbles, and 4 green marbles.

You know that in the first pick, Maria gets a green marble ( this means that now there are 3 green marbles left)

Now we want to know the probability that she gets a red marble on the second pick.

Now there are 6 + 6 + 3 = 15 marbles in the bag, and 6 of them are red ones. Then the probability of getting one red is the number of red ones divided by the total amount ( which is the ratio of red marbles to total marbles)

this is 6/15.

now you can see that there is no 6/15 in the options, so we need to see which one is equivalent.

if we took the option C, 2/5, and multiply both denominator and numerator by 3, we get (3*2)/(3*5) = 6/15, then 2/5 and 6/15 are equivalents.

Then the correct answer is C.

The probability that she gets a red marble on her second pick is 2/5.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that she gets a red marble on her second pick = [number of red marbles / (total number of marbles - 1)]

6 / 15 = 2/5

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Writing in scientific notation is writing in power form.

Writing in power form is usually in the form:

X.y × 10ⁿ

We now write 3 920 000 000 000 in this form.

3.92 × 10¹²

Answer :

3.92 × 10¹²

This is the scientific notation.

Hope I helped :)

3,920,000,000,000 in scientific notation is 3.92×10^12.

To express a large number in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, we start with the number 3.92 and move the decimal point to the right 10 places.

Therefore, 3,920,000,000,000 in scientific notation is written as 3.92×1012.

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The IQR is a measure of data distribution and used in outlier detection. The IQR is calculated by subtracting Q1 from Q3. After calculating the IQR, the lower and upper cut-offs can be calculated and data points below or above these cut-offs are considered as outliers.

The interquartile range (IQR) is a measure of statistical dispersion, and it can be useful in identifying 'outliers' in data. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) in a data set.

For the provided data set, to find the IQR, it should be sorted in ascending order and then Q1 and Q3 should be calculated. In your case, the sorted data set is: 12.8, 13.0, 13.5, 15.0, 15.0, 15.1, 15.2, 15.5, 15.6, 16.4, 16.6, 17.7, 18.3, 19.1, 19.3, 19.6, 20.5, 21.0, 26.2, 27.8, 33.5.

After finding Q1 and Q3, subtract Q1 from Q3 to get IQR (a.). Then, find the lower and upper cut-offs by subtracting 1.5 times of IQR from Q1 (b.) and adding 1.5 times of IQR to Q3 (c.), respectively. Any data points below the lower cut-off or above the upper cut-off are considered as outliers (d.).

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Answer:

6,75

Step-by-step explanation:

It's necessary the addition of all numbers, divided between the number of the numbers.  It means: 8 +7 +5 +7 +4 +7 +6 +7 +8 +8 +8 +6 = 81, then we'll divide 81 between 12 (because there are 12 numbers), and the result is 6,75

Mean = ∑numbers/n numbers

Answer:

5 inches

Step-by-step explanation:

The formula for a cube's volume is its side length cubed. So to get the side length when given the volume, you can take the cube root of the volume. [tex]\sqrt[3]{125}  = 5[/tex] inches.

Answer:

1

Step-by-step explanation:

Starting from the y-intercept of [0, 1], you do rise\run by either moving one block south over one block west or one block north over one block east. Either way, you will still get a rate of change [slope] of 1.

I am joyous to assist you anytime.

Answer:

The Correct answer:

CORRECT (SELECTED)

14x+23=14x-23

Step-by-step explanation:

We are given four equations and are asked to identify which has no solutions. By isolating the variable 'x' in each equation, we can see that the only equation without a solution is Choice C: 14x+23=14x-23 because it results in an incorrect statement.

The subject of this question is about identifying which equations have no solutions. To find the solution of an equation, you need to isolate the variable, here, it is 'x'. Let's evaluate the provided choices:

Thus, only equation Choice C: 14x+23=14x-23 has no solutions.

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Answer:

1.25 gallons per second

Step-by-step explanation:

To figure this out divide 50 by 40

I don't know how to explain this further, hope this is good enough.

- Que

Answer:

It use 1.25 gallons of water per  second

Step-by-step explanation:

Amount of water used for car wash in 40 seconds = 50 gallons

Amount of water used for car wash in 1 seconds = [tex]\frac{50}{40}[/tex]

Amount of water used for car wash in 1 seconds = [tex]1.25[/tex]

So, Amount of water used in 1 second is 1.25 gallons

So, Unit rate = 1.25 gallons per second

Hence it use 1.25 gallons of water per  second

Final answer:

To find the number of new games rented, set up an equation using the given information. Assume all 6 games rented were new games, and solve for the number of new games.

Explanation:

To find the number of new games rented, we can set up an equation using the information given.

Let x represent the number of new games rented and y represent the number of older games rented.

We know that the total cost of renting 6 games is $22. Therefore, we can write the equation:

4x + 2y = 22

To find the number of new games rented, we want to solve for x. We can do this by substituting a value for y and solving for x.

Let's assume all 6 games rented were new games, so y = 0.

Substituting this value into the equation gives:

4x + 2(0) = 22

Simplifying, we get:

4x = 22

Dividing both sides by 4, we find that x = 5.5.

Since we can't rent a fractional number of games, the student rented 5 new games.

Answer:

40.7m^2

Step-by-step explanation:

Base×Height= 5.2m×3=15.6m2

Area of semicircle= Pie r^2= Pie×4^2=16×pie

pie×16÷2=8×pie

8×3.14=25.12m2

15.6m2+25.12m2=40.72m2

rounded to nearest tenth=40.7m2

Answer: [tex]40.7\ m^2[/tex]

Step-by-step explanation:

Given : A parallelogram has base 5.2 meters and height 3 meters, and a semicircle with a radius of 4 meters.

Area of parallelogram is given by :-

[tex]A_p=b\times h[/tex] , where b is base and h is height of parallelogram.

[tex]=5.2\times3=15.6\ m^2[/tex]   (1)

Area of semicircle :-

[tex]A_s=\dfrac{\pi r^2}{2}[/tex], where r is radius.

[tex]=\dfrac{3.14\times4^2}{2}=25.12[/tex]     (2)

Now from (1) and (2),. the area of the combined figure will be :-

[tex]A=A_p+A_s\\\\=15.6+25.12=40.72\approx40.7\ m^2[/tex]