Express the first quantity as a percentage of second quantity $45, $120.

Answer: x=6.8

Step-by-step explanation:

I figured it out ;)

Answer:

x=6.889

Step-by-step explanation:

9x=62

x=62/9

x=6.889

Answer:

B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

X is many things but B is correct.

Answer:

x= 5.45 or -5.45

The side length of the cube is approximately 12.84 inches.

What is cube?

A cube is a nathree-dimensiol geometric shape that has six square faces of equal size, 12 edges of equal length, and eight vertices where the edges meet. The cube is a regular polyhedron, which means that all of its faces are congruent (identical) squares and all of its angles are right angles (90 degrees). The cube is often used in mathematics and geometry to illustrate concepts such as volume, surface area, and spatial relationships. It is also a common shape in architecture and design, where it can be used to create buildings, furniture, and other objects.

To solve for the side length of a cube with a volume of 1833 in³, we can use the equation V = s³, where V is the volume and s is the measure of one side of the cube.

To solve for s, we can rearrange the equation to isolate s:

s = V^(1/3)

Substituting the given value for V, we get:

s = 1833^(1/3)

Using a calculator or estimation, we can find that the cube root of 1833 is approximately 12.84. Therefore, the side length of the cube is approximately 12.84 inches.

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Answer:

Price after discount: $33.75

You saved: $11.25

Step-by-step explanation:

When parking downhill next to a curb, you should turn your front wheels into the curb.

This means you should steer the wheels towards the curb or to the right if you are in a country where vehicles drive on the right side of the road.

By turning the wheels into the curb, it provides an extra measure of safety in case the vehicle rolls downhill. If the brakes fail, the curb will act as a barrier, preventing the car from rolling into traffic.

Turning the wheels away from the curb leaves the vehicle vulnerable to rolling freely downhill and potentially causing an accident.

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The equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.

In the given equation we have to find the equation of circle with center and radius.

The given center is (-3, -5).

Radius = 4

The standard equation of a circle with center and radius.

(x−a)^2+(y−b)^2=r^2

where a and b represent a point of center and r represent a radius.

So a=-3, b=-5 and r=4.

Putting the value in the standard equation.

(x−(-3))^2+(y−(-5))^2=(4)^2

Simplifying

(x+3)^2+(y+5)^2=16

Hence, the equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.

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Two hikers walked 42 km on the Trans Canada Trail in 5 hours. Their average speed for the trip was 8.4 km/h.

The average speed of the two hikers can be calculated as follows

Average speed = Total distance ÷ Total time

The total distance covered by the hikers is 42 km, and the total time taken is 5.0 hours. Therefore, the average speed of the two hikers is

Average speed = 42 km ÷ 5.0 h

Average speed = 8.4 km/h

Therefore, the average speed of the two hikers on the Trans Canada Trail is 8.4 kilometers per hour.

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If we want to provide a 99% confidence interval for the mean of a population, the confidence coefficient will be 0.99. This means that there is a 99% probability that the true population mean falls within the calculated interval.

The confidence coefficient for a confidence interval represents the level of confidence we have in our estimate.

In the case of a 99% confidence interval, the confidence coefficient is 0.99. This means that we are 99% confident that the true population mean falls within the calculated interval. The confidence coefficient is derived from the desired level of confidence, which is typically expressed as a percentage.

A higher confidence level corresponds to a larger confidence coefficient. In practical terms, a 99% confidence interval indicates that if we were to repeat the sampling process multiple times and construct 99% confidence intervals, approximately 99% of those intervals would contain the true population mean.

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Answer:

m = 3, c = 0

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x , or y = 3x + 0 ← is in slope- intercept form

with m = 3 and c = 0

Answer:

\(-4 \leq x < -2.2\)

Step-by-step explanation:

-5x - 3 > 8
-5x > 11
x < -11/5
We know that -4 ≤ x ≤ 3 and x < -11/5 (-2.2)
-4 <= x < -2.2

Step-by-step explanation:

3x+2y=9

3x+2(x-3)=9

3x+2x-6=9

x=9+6

x=15

Answer:

7 m = 0.0037797 n mile

7 meters are 0.0037797 nauticals mile.

7 m = 275.59055 inch

7 meters are 275.59055 inches.

7 m = 0.0043496 mile

7 meters are 0.0043496 miles.

7 m = 7000000 μm

7 meters are 7000000 micrometers.

7 m = 275590.5511814 mil

7 meters are 275590.5511814 mils.

7 m = 7000 mm

7 meters are 7000 milimeters.

7 m = 700 cm

7 meters are 700 centimeters.

7 m = 70 dm

7 meters are 70 decimeters.

7 m = 0.07 hm

7 meters are 0.07 hectometers.

7 m = 0.007 km

7 meters are 0.007 kilometers.

7 m = 22.96588 ft

7 meters are 22.96588 feet.

7 m = 7.65529 yd

7 meters are 7.65529 yards.

Answer:

21years old

Step-by-step explanation:

Let Sam's age be x

Let Ashton present age be y

If Sam is 34 years younger than Ashton then;

x = y - 34 .... 1

If by 4 years ago, Ashton's age was 3 times Sam's age then;

Sam = x - 4

Ashton = y - 4

y-4 = 3(x-4)

y-4 = 3x - 12 ....2

Substitute 1 into 2;

y-4 = 3(y-34)-12

y-4 = 3y-102-12

y-4 = 3y - 114

y-3y = -114 + 4

-2y = -110

y = 110/2

y = 55

Since x = y- 34

x = 55-34

x = 21

Hence Sam will be 21years old now

Answer:

13

Step-by-step explanation:

\(DE=.5*BC=.5*26=13\)

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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Step-by-step explanation:

Hi, there!!!!

The main purpose of developing si unit is to have standard unit of measurements and to bring uniformity in whole world in terms of measurements.

I hope it helps you...

Step-by-step explanation:

A function is continuous at x is

Limit as x approaches c= f(c).

Step 1: Find f(4).

4 is defined for 2x-1 so plug in. 4 for x.

\(2(4) - 1 = 7\)

Note that what we just calculated was not only f(4) but also the left sided limit of f(x).

Step 2: Make sure the left sided and right sided limit are equal to 7.

\(a + 5x = 7\)

Plug in 4 for x

\(a + 5(4) = 7\)

\(a = - 13\)

Answer:

17.5

Step-by-step explanation:

You have to find n right?

9+4n-79 = 0

-> 4n = 70

-> n = 17.5

Answer:

2/3 or -5 is correct for all future users.

Step-by-step explanation:

The roots of the quadratic equations or the values of x are -5 and 2/3.

A quadratic equation is an algebraic equation of degree two. An algebraic equation of degree n has exactly n number of roots.

Given a quadratic equation 3x² + 13x = 10 which can be written as,

3x² + 13x - 10 = 0.

Now two numbers that add to 13 and multiplied to -30 are 15 and - 2.

3x² + 15x - 2x - 10 = 0.

3x(x + 5) - 2(x + 5) = 0.

(x+5)(3x-2) = 0.

x + 5 = 0 OR 3x -2 = 0.

x = -5 OR x = 2/3.

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The equation written in slope-intercept form withn a slope of -5 and a y-intercept of 5 is y = -5x + 5

intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

equation of straight line in slope intercept form is given as

y = mx + c

where m = slope and c = y-intercept

from the question, it means m = -5 and c = 5

substituting we have,

y = -5x + 5

In conclusion, the equation in slope-intercept form is y = -5x + 5

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a) The probability that there will be an accident on Highway 48 today is 0.36%.

b) The probability that the weather today was wet given that there was an accident on Highway 48 is approximately 55.56%.

a) To find the probability that there will be an accident on Highway 48 today, we need to consider both the probability of an accident when it's dry and when it's wet, and the probability of each type of weather. We can use the formula: P(A) = P(A|B) × P(B) + P(A|B') × P(B'), where A represents an accident, B represents wet weather, and B' represents dry weather.
P(A) = P(Accident|Wet) × P(Wet) + P(Accident|Dry) * P(Dry)
P(A) = (0.01) × (0.2) + (0.002) × (0.8)
P(A) = 0.002 + 0.0016
P(A) = 0.0036
b) To find the probability that the weather was wet given that there was an accident on Highway 48, we can use Bayes' theorem: P(B|A) = (P(A|B) × P(B)) / P(A)
P(Wet|Accident) = (P(Accident|Wet) × P(Wet)) / P(Accident)
P(Wet|Accident) = (0.01 × 0.2) / 0.0036
P(Wet|Accident) = 0.002 / 0.0036
P(Wet|Accident) = 0.5556

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To write Euler's number in Symbolab, you can simply use the notation "e". For example, if you want to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.

Euler's number, denoted as "e", is a mathematical constant that is approximately equal to 2.71828. To write Euler's number in Symbolab, you can simply use the letter "e" in lowercase. For example, to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.

Alternatively, if you want to use the built-in function for Euler's number in Symbolab, you can use the "exp(x)" notation, where x is the exponent. For example, to evaluate e raised to the power of 2, you can enter "exp(2)" in Symbolab. Symbolab supports various mathematical functions and constants, including trigonometric functions, logarithmic functions, and mathematical constants, which can be used to solve various mathematical problems.

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h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Answer:

To find the largest possible rank of a matrix A, we can use the Rank-Nullity Theorem, which states that for any matrix A, the sum of the rank and the dimension of the kernel (nullity) is equal to the number of columns of A.

Given that A is a 6 x 4 matrix, the largest possible rank of A would be min(6, 4) = 4. This is because the rank of a matrix cannot exceed the number of columns in the matrix.

Now, to find the smallest possible dimension of the kernel (ker(A)), we subtract the rank of A from the number of columns:

Smallest dimension of ker(A) = Number of columns - Rank = 4 - 4 = 0

Therefore, the smallest possible dimension of ker(A) is 0, indicating that the kernel is trivial or consists only of the zero vector.

To provide an example of a matrix A that achieves these bounds, we can consider the following 6 x 4 matrix:

A = [[1, 0, 0, 0],

[0, 1, 0, 0],

[0, 0, 1, 0],

[0, 0, 0, 1],

[0, 0, 0, 0],

[0, 0, 0, 0]]

In this example, the matrix A has full column rank (4) since all columns are linearly independent. The dimension of the kernel is 0, as there are no non-zero vectors that, when multiplied by A, would yield the zero vector.

Thus, the matrix A = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]] achieves the bounds we found, with a rank of 4 and a kernel dimension of 0.

Step-by-step explanation:

the matrix A given above serves as an example that achieves the largest possible rank of 4 and the smallest possible dimension of the kernel of 2 for a 6x4 matrix.

The largest possible rank of a 6x4 matrix A is 4, and the smallest possible dimension of the kernel (null space) of A is 2. An example of such a matrix A that achieves these bounds is:

A = [1 0 0 0;

0 1 0 0;

0 0 1 0;

0 0 0 1;

0 0 0 0;

0 0 0 0]

In the given matrix A, the first four rows form an identity matrix of size 4x4, ensuring that the rank of A is 4. The last two rows are all zeros, representing the kernel (null space) of A. Since the two rows are linearly independent, the dimension of the kernel is 2.

To verify that this matrix achieves the bounds, we can perform row reduction on matrix A. The row reduction process will not change the rank or the dimension of the kernel, and it will confirm that the first four rows are linearly independent and the last two rows are linearly dependent, leading to a rank of 4 and a kernel dimension of 2.

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True. The central limit theorem states that if the sample size n is large enough (usually considered to be at least 30), then the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution.

The sampling distribution of the mean can be approximated by the normal distribution if the sample size (n) is at least 30. This statement is based on the Central Limit Theorem, which states that the sampling distribution of the mean of a random sample drawn from any population will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. A sample size of 30 is often considered the threshold for approximating a normal distribution in such cases.

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From the given sample space the probability of P(at least 2 tails) is 68.75%.

Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the occurrence. Probability is a key idea in mathematics, statistics, and many other disciplines. It is used to describe uncertain events. Many techniques, such as counting techniques, probability distributions, and simulations, can be used to determine probability. Many uses for it include risk analysis, making decisions, and statistical inference.

From the given sample space the outcomes with at least 2 tails are:

{TTTT, TTT H, TT HT, T H TT, H TTT, H HTT, HT HT, HTTH, THHT, THTH, THH H}

Now,

P(at least 2 tails) = 11/16 = 0.6875 ≈ 68.75%

Hence, from the given sample space the probability of P(at least 2 tails) is 68.75%.

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Answer:

No because 35/3 is 11.67 :))

Step-by-step explanation:

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