Choose the best definition for the term:

Answer:

1/2

Step-by-step explanation:

Prim number are 1, 2, 3, 4, 7, and 11. That is six numbers out of twelves, 6/12, is 50%.

If  cagney can frost a cupcake every 2020 seconds and lacey can frost a cupcake every 3030 seconds. working together, they can frost 2.72 cupcakes.

cagney can frost a cupcake every 2020 seconds

In 1 second she can frost 1 /2020 cupcake

lacey can frost a cupcake every 3030 seconds

In 1 second she can frost 1/3030 cupcake

Both working together

In 1 second they can do 1/2020 + 1/3030 cupcake

= (3030 + 2020)/3030x2020

= 5050/6120600

1 minute =  60 seconds

55 minutes = 60 x 55 = 3300 seconds

In 55 minutes they can frost 3300 x (5050/6120600)

In 55 minutes they can together frost 2.72 cupcakes

Therefore, if  cagney can frost a cupcake every 2020 seconds and lacey can frost a cupcake every 3030 seconds. working together, they can frost 2.72 cupcakes.

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Answer: y = -3/2x + 3

Step-by-step explanation:

The slope is -3/2 (down 3, right 2)

The slope goes before x in graph functions so it’s -3/2x

The line goes through 3 on the y-axis (vertical line), so that’s where + 3 comes in.

y = -3/2x + 3

The sequence that shows a pattern where each term is 1.5 times the previous term is option D

Series of numbers can be in a sequence either in arithmetic or in geometric. In the above question, it is geometric because the sequence shows a pattern where each term is 1.5 times the previous term.

Let us test each option one by one.

Option A

1.5 x -4 = -6

But the next number in the series is 6

Option B

1.5 x 10 = 15

1.5 x 15 = 22.5

But the next number in the series is 25

Option C

1.5 x 98 = 147

But the next number in the series is 99.5

Option D

1.5 x -200 = -300

1.5 x -300 = -450

1.5 x -450 = -675

Therefore, the sequence that shows a pattern where each term is 1.5 times the previous term is option D

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Answer: D (-200,-300,-450,-675,...)

Step-by-step explanation:

Recognizing the pattern in a sequence is used to write the function that represents it.

Answer:

80 cm²

Step-by-step explanation:

Given 2 similar figures with sides in the ratio a : b , then

ratio of areas = a² : b²

Here ratio of sides = 7 : 14 = 1 : 2

ratio of areas = 1² : 2² = 1 : 4

Thus area of B is 4 times area of A

area of B = 4 × 20 = 80 cm²

Answer:

its called a calculator division and multiplication

Step-by-step explanation:

Answer: No

Step-by-step explanation: Two positives divided never make a negative

Answer:

No, 80/10 turned into a whole number is 8, not -8.

Step-by-step explanation:

To get a whole (1), you need to have 10/10. Since we have 10/10 8 times (80/10) this means we get a whole number of 8, not -8. Therefore, its false. 80/10 is NOT equal to -8

The equation of the circle is x² + y² − 8x - 6y + 9 = 0.

(x - h)2+ (y - k)2 = r2 is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius. A circle touches the x-axis at (3,0) if it is tangent to the x-axis at that location.

From the graph,

It is clear that radius = 2 units and center = (4,3)

The standard equation of the circle is -

(x − a)² + (y − b)² = (r)²

where (a,b) represents the coordinates of the circle and r = radius

Now putting the values in the above equation,

(x − 4)² + (y − 3)² = (4)²

(x − 4)² + (y - 3)² = 16

If required for further work you can expand this to give:

x² - 8x + 16 + y²-6y+9-16= 0

x² + y² − 8x - 6y + 9 = 0

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Answer: 8 (2y-1)

Step-by-step explanation: first start by writing like this below:

16y-8

Then factorise the numbers(cut the numbers)

2×2×2×2×y - 2×2×2

Now take all which is common like:

2×2×2=8

Then,take the remained numbers and add it into the brackets.

8 (2y - 1) Here, why we should put 1,because there's nothing left.

If you want to check the answer, factorise this expression and see:

8 (2y-1)

16y-8.

Hope it helps you!!

To solve for x at an angle, you must first understand what type of angle you are working with. If the angle is a right angle, you can use the Pythagorean theorem to solve for x. If the angle is an obtuse angle, you can use the law of cosines to solve for x. If the angle is an acute angle, you can use the law of sines to solve for x.

To solve for x at a right angle using the Pythagorean theorem, you must have the lengths of the two neighboring sides of the triangle. The sum of the squares of the two sides is equal to the square of the hypotenuse, according to the Pythagorean theorem. By rearranging the components and solving for x, this equation may be used to find x.

To use the law of cosines to solve for x at an obtuse angle, you must know the lengths of all three sides of the triangle. According to the law of cosines, the square of one side's length equals the sum of the squares of the other 2 sides minus twice the product of the other 2 sides multiplied by the cosine of the obtuse angle. You can use this equation to solve for x by rearranging the terms and solving for x.

To apply the law of sines to solve for x in an acute angle, you should first know the lengths of the triangle's two sides as well as the acute angle's measurement. According to the law of sines, the ratio of one side's length to the sine of the opposite angle equals the ratio of the other side's length to the sine of the acute angle. By rearranging the terms and solving for x, you may use this equation to solve for x.

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Answer:

61

Step-by-step explanation:

marque esta respuesta como la más inteligente

Answer:

Step-by-step explanation:

Sure! I'll perform the mathematical operations using the given numbers and apply the rules of precision. Please find the results below:

(9.11) + (6.232)

The sum of 9.11 and 6.232 is 15.342.

(7.4023) x (19)

The product of 7.4023 and 19 is 140.844.

(9.162) - (2.39)

The difference between 9.162 and 2.39 is 6.772.

(0.00482) x (213)

The product of 0.00482 and 213 is 1.02786.

(8.73) / (5.198)

The division of 8.73 by 5.198 is 1.67920734.

(7644) / (0.13)

The division of 7644 by 0.13 is 58,800.

Please note that the results are rounded to the appropriate number of decimal places based on the precision rules.

a. Mean = 18.5

b. Median = 16

c. The measure of center would reduce if we eliminate the greatest value, 42.

The mean and the median are both measures of center.

The mean of a data = average of all the data points in the data set.

The median, on the other hand, is the center value of the data distribution or the average of the two center values.

Given the data, 12, 14, 22, 14, 18, 23, 42, 13, 9, 19, 22, 14

a. Mean = (12 + 14 + 22 + 14 + 18 + 23 + 42 + 13 + 9 + 19 + 22 + 14)/12

Mean = 222/12

Mean = 18.5

b. Median = (14 + 18)/2 = 16

c. Eliminating 42, we would have:

Mean = (12 + 14 + 22 + 14 + 18 + 23 + 13 + 9 + 19 + 22 + 14)/11 = 180/11 = 16.3636

Median = 14

This means, the measure of center would reduce if we eliminate the greatest value, 42.

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The mean and the standard deviation of the sampling distribution of x are given as follows:

The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:

The parameters for this problem are given as follows:

Hence the standard deviation for the sampling distribution of x is given as follows:

s = 60/sqrt(10) = 19 seconds.

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The slope is 1/2 and the y-intercept is 3/4 in the equation  - [ (1/2)x - y ] = 3/4.

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We know that the equation for slope(m) and y - intercept(c) of a line is given by :

y = mx + c

Here given the equation - [ (1/2)x - y ] = 3/4, lets simplify

⇒ - [ (1/2)x - y ] = 3/4

⇒ -(1/2)x + y  = 3/4

⇒ y =  (1/2)x + 3/4

Hence, the slope is 1/2 and the y-intercept is 3/4 in the equation  - [ (1/2)x - y ] = 3/4

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The ratio of protonated/deprotonated acetic acid at the given pH is:

Therefore, the ratio of protonated/deprotonated acetic acid at the given pH is:

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Answer:

1. see the attached image

2. y < (6/2)x + 5/2, see the attached image for a graph

Step-by-step explanation:

1. see the attached image

2. 6x > 2y - 5

Add 5 to both sides:

6x + 5 > 2y

Divide by 2:

(6/2)x + 5/2 > y

Rearrange so that y is on the left:

y < (6/2)x + 5/2

Finally, shade below the line since the sign is less than.

See the attached image for the graph.

Answer:

Step-by-step explanation:

density is mass divided by volume

15 divided by 9 is

1.6666666666

so its 1.666 repeating g/cm^3

After evaluating the algebraic expression we can infer that both students were correct.

An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .

If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).

Again the expression 2a +3 is a sum with only two terms.

Hence both students were correct.

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After evaluating the algebraic expression we can infer that both students were correct.

An algebraic expression in mathematics is one that was produced utilizing integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

On the other hand, transcendental numbers, such and e, are not algebraic because they are not generated from integer constants and algebraic operations. While the definition of e necessitates an infinite number of algebraic operations, the creation of is frequently done as a geometric expression .

If an expression can be converted into a rational fraction using the characteristics of the arithmetic operations, it is said to be rational expression (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).

Again the expression 2a +3 is a sum with only two terms.

Hence both students were correct.

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Answer:

-77

Step-by-step explanation:

-3 x 4 x 7 = -84

-84 + 7 = -77

Answer:

57

Step-by-step explanation:

edg 2021

The general solution for y₁, y₂, and y₃ is given by:

y₁ = c₁e^x + (-2c₂ - 2c₃)e^(-2x) - 2c₃e^(-2x)

y₂ = 2c₁e^x + (-c₂ + 0c₃)e^(-2x) + 0c₃e^(-2x)

y₃ = -c₁e^x + (c₂ + c₃)e^(-2x) + c₃e^(-2x)

It seems that the given equations represent a system of linear ordinary differential equations. To find the general solution, we can solve the system of equations using matrix notation.

Let's represent the given equations in matrix form:

dy/dx = AY

where Y is the column vector [y₁, y₂, y₃]ᵀ and A is the coefficient matrix:

A = [2  5  4]

       [-1  4  2]

       [2 -6 -3]

To find the general solution, we need to find the eigenvalues and eigenvectors of matrix A. The eigenvalues can be found by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix.

By calculating the determinant of (A - λI) and solving the resulting equation, we can find the eigenvalues:

λ₁ = 1

λ₂ = -2

λ₃ = -2

Next, we find the eigenvectors corresponding to each eigenvalue. We substitute each eigenvalue back into the equation (A - λI)X = 0, where X is the column vector [x₁, x₂, x₃]ᵀ, and solve for X.

For λ₁ = 1, we have the eigenvector:

X₁ = [1, 2, -1]ᵀ

For λ₂ = -2, we have the eigenvector:

X₂ = [-2, -1, 1]ᵀ

For λ₃ = -2, we have the eigenvector:

X₃ = [-2, 0, 1]ᵀ

Now, we can write the general solution as a linear combination of the eigenvectors multiplied by exponential terms:

Y = c₁X₁e^(λ₁x) + c₂X₂e^(λ₂x) + c₃X₃e^(λ₃x)

where c₁, c₂, and c₃ are constants determined by the initial conditions.

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5/12 is the answer but 1/3 x 5/4 is the reduced version of your question and the alternate form of the answer is 0.416

Answer:

4.32%

Step-by-step explanation:

you divide 7.35 ÷ 100 = 0.0735, then multiply 0.0735 × 58.80 = 4.32%

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer: 30 gallons

Step-by-step explanation:

First translate 2 hours into 120 minutes.  Then multiply 120 * 4 = 480.  Then divide 480/16 = 30

Answer:

John

Step-by-step explanation:

6/20=0.3

1/4=0.25

Juaquine is solving problems at a faster rate as compared to John.

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

As per the question, we can compare their rates of problem-solving by calculating the number of problems they can solve per minute.

For John, this is 6 problems / 20 minutes = 0.3 problems per minute.

For Juaquine, this is 6 problems / (4 minutes/problem) = 1.5 problems per minute.

Since Juaquine can solve 1.5 problems per minute compared to John's 0.3 problems per minute, Juaquine is solving problems at a faster rate.

Hence, Juaquine works faster as compared to John.

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Given:

The given volume formulas to calculate the volume of a rectangular

pyramid.

To find:

The correct volume formula.

Solution:

The volume of a rectangular pyramid is:

\(V=\dfrac{1}{3}Bh\)

Where, B is the base area of the rectangular pyramid and h is the vertical height of the rectangular pyramid.

Therefore, the correct volume of a rectangular pyramid is \(V=\dfrac{1}{3}Bh\).

Note: In the given problem, the options are not in correct form.

The unique solution (1,4), none of the given options correspond to the system with the unique solution (1,4).

The system that has the unique solution (1,4) is option (H) x + y = 5 and y = -x + 3.

To determine the system with a unique solution, we need to check if the given solution values satisfy both equations of the system.

For option (H), substituting x = 1 and y = 4 into the equations:

x + y

= 1 + 4

= 5 (satisfied)

y

= -1 + 3

= 2 (not satisfied)

Since the second equation is not satisfied, so  option (H) does not have the unique solution (1,4).

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