In the expression $c \cdot a^b - d$, the values of $a$, $b$, $c$, and $d$ are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum possible value of the result?

Answer:

3 students

Step-by-step explanation:

Now for RSM Olympiad are 8 math kangaroo are 7 studs that did both are 4

Total number of studs that participated are

(8-4) + 4 + (7-4)

4+4+3=11

those who didn't participate are

11-14-13

Using translation the graph of y = (x - 2)² - 5 is the graph of y = x² shifted 2 units to the right and 5 units down.

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

To translate the graph of y = x² to y = (x - 2)² - 5, apply the following transformations -

Shift the graph to the right by 2 units.

This means that we replace x with x - 2, which moves the graph 2 units to the right.

Shift the graph down by 5 units.

This means that we subtract 5 from the entire function, which moves the graph 5 units down.

So the transformed function is -

y = (x - 2)² - 5

To see how this transformation changes the graph, compare the original function y = x² to the transformed function y = (x - 2)² - 5.

The vertex of the parabola has moved from the origin (0,0) to the point (2,-5).

Therefore, the graph is shifted using translation.

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Answer:

Step-by-step explanation:

radius of a circle is half of the diameter

Diameter :D , Raduis : R

D = 2R

R = 1.4 angstrom

1 angstrom = 0.00000001 cm = 10^-7 cm

R = 1.4 * 10^-7 cm

D = 2.8 * 10^-7 cm

The Diameter is 2.8x10^-7 cm

The data set: 21, 22, 22, 24, 25, 26, 28, 28 have two values of mode, which are, 22 and 28.

What is meant by the mode of a data set?

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. Yet, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode. When the highest frequency was noted for more than one value in a data collection, there are many modes. The mode cannot be utilised in either of these examples to identify the distribution centre. Categorical variables can be summarised using the mode.

a)2, 2, 2, 5, 6, 7, 9, 10

Here most repeated value is only 2.

So the mode is 2.

b) 5, 6, 8,10, 11, 11, 15, 18

Here most repeated value is only 11.

So the mode is 11.

c)12, 12, 13, 13, 14, 14, 15, 15

Here the values 12,13,14 and 15 are repeated twice.

So this has 4 values as mode.

d) 21, 22, 22, 24, 25, 26, 28, 28

Here 22 and 28 are repeated twice.

So this data set has 2 values for the mode.

Therefore the data set: 21, 22, 22, 24, 25, 26, 28, 28 have two value of mode, which are, 22 and 28.

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Answer:

D

Step-by-step explanation:

here is a pic for proof

Answer:

Step-by-step explanation: sometimes it is hard to do in school because I'M and 15th-grade class and i got to take my time

Answer:

The first thing you want to d is find out how many centimeters are in 1 foot, because if a flat bar cost 2 pesos per centimeter, and they want 1 foot, then you will multiply how many centimeters in 1 foot, by how much each centimeter cost: 2 pesos:

There are exactly 30.48 centimeters in 1 foot, so you will multiply that by 2:

2 * 30.48 = 60.96

It will cost 60.96, or rounded up to 61 pesos for a 1 foot flat bar.

Step-by-step explanation:

Hope it helps! =D

Formula for the difference of cubes are,

⇒ x³ - y³ = (x - y) (x² + xy + y²)

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

To find the difference of cubes of two numbers.

Now, Let two numbers are x and y.

Hence, Formula for the difference of cubes of numbers x and y are,

⇒ x³ - y³ = (x - y) (x² + xy + y²)

Thus, Formula for the difference of cubes are,

⇒ x³ - y³ = (x - y) (x² + xy + y²)

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The total distance from Bethany’s house to her parents’ house would be = 524.8 miles

The first distance covered by Bethany towards the parents house = 127.56 miles.

The distance remaining for her to arrive to ab destination = 397.24 miles

The total distance covered

= 127.56 miles + 397.24 miles

= 524.8 miles.

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The total distance, in miles, from Bethany's house to her parents' house is 524.8 miles.

The total distance is determined using the mathematical operation of addition.

Addition is one of the four mathematical operations, including subtraction, division, and multiplication.

The distance already covered after driving from her house = 127.56 miles

The distance remaining = 397.24 miles

The total distance from Bethany's house to her parents' = 524.8 miles (127.56 + 397.24)

Thus, the total distance is 524.8 miles.

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The equation of the circle has the following format:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In which:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

From the figure, you must identify the coordinates of the center, and then replace the given point [tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex] into the equation to solve for the radius r.

The problem is incomplete, hence the procedure to obtain the equation of the circle was presented.

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Answer:

Step-by-step explanation:

Let's start by finding the six even numbers. We know that the median is 9, so the middle two numbers in the set must be 9. Since all of the numbers are even, these two numbers must be 8 and 10.

So we have four numbers remaining, and we know that they are even. We also know that the range is 8, which means that the largest number in the set minus the smallest number in the set is 8. Since the largest number is 10, the smallest number must be 2.

So far, we have the following numbers in the set:

2, 8, 9, 9, 10

Now we need to find one more even number to make a set of six. We are given that the mode is 6, which means that one of the numbers in the set must be 6. However, we cannot add 6 to the set because it is odd. Therefore, the other number in the set that is closest to 6 must appear twice in the set, making it the mode. The number closest to 6 is 8, so we can add one more 8 to the set.

The final set of six even numbers that satisfy the given conditions is:

2, 8, 8, 9, 9, 10

Answer:

280 yards * 3 feet/yard = 840 fee

Step-by-step explanation:

since the fencing is sold by the foot, we need to convert the given 280 yards to feet in order to determine how much fencing the farmer should buy.

To convert yards to feet, we multiply the number of yards by 3, since there are 3 feet in 1 yard.

280 yards * 3 feet/yard = 840 feet

Therefore, the farmer needs to buy 840 feet of fencing for his new grazing field.

Answer:

The answer is D.

Step-by-step explanation:

Answer: 7/13

Step-by-step explanation:

2(x-5)(x-3)/3(x-5)(x-2)

take (x-5) away from both

2x-3/3x-2

2(5)-3/3(5)-2

=7/13

Answer:

6

Step-by-step explanation:

to be very honest I'm not very good at mathematics but Im here to learn

The last number in Row 8 is 56.

The number in Row 12 and column 3 is 80.

The row and column that will contain the number 400 is Row 58 Column 1

The figure shown in the image represents the multiplication table 7.

Each column contains 7 numbers.

Beginning with the first Row and column, 7 numbers are added until the next row. At the end of each row is a multiple of 7.

The last number in Row 8 will be the product of 7 and 8 = 56

The number in Row 12 and Column 3 will be:

7 * 11 + 3 = 80

The row and column that will contain the number 400 will be:

400/7 = 77 remainder 1

Hence, it will be Row 58 Column 1.

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The possible rational roots of the polynomial are ±1, ±2, ±4, ±5, ±10, ±20.

The correct option is D.

Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.

And the standard form of the cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.

Given:

A cubic polynomial,

x³ + 5x² -8x - 20 = 0.

The possible rational roots are;

p/q = -20/1

= -20

The factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20.

Therefore, the possible roots are ±1, ±2, ±4, ±5, ±10, ±20.

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Answer:

2x + h - 5

Step-by-step explanation:

To find f(x + h) we simply plug (x + h) into the function f(x), anywhere we see an x.

[tex]f(x) = x^{2} -5x+9\\f(x+h) = (x+h)^{2}-5(x+h)+9[/tex]

Now we can plug them into the fraction:

[tex]\frac{((x+h)^{2}-5(x+h)+9)-(x^{2} -5x+9)}{h}[/tex]

Expanding all of the terms, we get:

[tex]\frac{(x^{2} +2hx + h^{2} -5x-5h+9)-(x^{2} -5x+9)}{h}[/tex]

Distributing the negative we get:

[tex]\frac{x^{2} +2hx + h^{2} -5x-5h+9-x^{2} +5x-9}{h}[/tex]

Now we see that [tex]x^{2} -x^{2} ,-5x+5x,[/tex] and [tex]9-9[/tex] all cancel, leaving us with:

[tex]\frac{2hx + h^{2}-5h}{h}[/tex] (Notice the only terms left are those with h in them)

As every term contains an h, we can remove an h from every term, giving us:

2x + h - 5

7 cars and 4 buses were used on the trip

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of cars used.

Let y be the number of buses used.

We know that there were a total of 11 vehicles used, so we can write an equation based on that:

x + y = 11

We also know that the total number of students who went on the trip is 155.

We can use this information to set up another equation:

5x + 30y = 155

This equation represents the fact that the total number of students in cars (5x) plus the total number of students in buses (30y) equals the total number of students (155).

Now we have two equations with two unknowns. We can solve for x and y using a method like substitution or elimination.

Let's use substitution. Solve the first equation for x in terms of y:

x + y = 11

x = 11 - y

Substitute this expression for x into the second equation:

5x + 30y = 155

5(11 - y) + 30y = 155

Simplify and solve for y:

55 - 5y + 30y = 155

25y = 100

y = 4

Now that we know y, we can use the first equation to find x:

x + y = 11

x + 4 = 11

x = 7

Therefore, there were 7 cars and 4 buses used on the trip.

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let's say the segment with A(-5 , -8) and B(10 , 7) gets partitioned by point C

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-5,-8)\qquad B(10,7)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(-5,-8)=3(10,7)[/tex]

[tex](\stackrel{x}{-10}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{30}~~,~~ \stackrel{y}{21}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +30}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +21}}{3+2} \right)} \\\\\\ C=\left( \cfrac{ 20 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies C=(4~~,~~1)[/tex]

Answer:

( 4, 1 )

Step-by-step explanation:

When two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.

Relationships generally regarded to as symmetrical when they continuously maintain a similar ratio. For instance, the number of trees in a vineyard and the number of apples in a yield of apples depend upon that average number of apples delivered by each tree. A linear relationship among two quantities or variables is described to as being proportional in mathematics. If the initial quantity doubles, the other amount does do so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two quantities be proportional, it means that if one grows, the other climbs as well, and their connection is constant at all values. The size and circumference of a sphere are used as an example.

given

To compare a proportion of replies or values in a sample of data to a (hypothesized) proportion in the population .

from which our sample data are obtained, one can use the single proportion (or one-sample) binomial test.

We rarely have access to statistics for a whole population, so this is significant.

when two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.

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Answer:

55°

Step-by-step explanation:

supplementary angle sum to 180° , then supplement of G is

supplement = 180° - 125° = 55°

The value of x is 11. 18

The value of y is 8. 67

Using the Pythagorean theorem, we have that;

x² = y² + z²

Substitute the values, we get;

x² = 10² + 5²

find the squares

x² = 100 + 125

Add the values

x² = 125

Find the square root

x = 11. 18

Using the Pythagorean theorem, we have;

y² = 9² - (√6)²

Find the squares

y² = 81 - 6

substract the values

y² = 75

Make 'y' the subject

y = 8. 67

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Answer:

Step-by-step explanation:

a. The average rate of change in DVD sales during this period can be calculated as:

average rate of change = (change in DVDs sold) / (change in years)

We are given that in 2011, 6.1 billion DVDs were sold, and in 2021, 1.2 billion DVDs were sold. The change in DVDs sold is:

change in DVDs sold = 1.2 billion - 6.1 billion = -4.9 billion

The change in years is:

change in years = 2021 - 2011 = 10

So the average rate of change in DVD sales during this period is:

average rate of change = (-4.9 billion) / 10 = -0.49 billion DVDs per year

Therefore, DVD sales declined by an average of 0.49 billion per year during this period.

b. Using the numbers in 2011 as an initial value, we can write a linear model that models the number of DVD sales worldwide as:

DVD sales = -0.49(t - 2011) + 6.1

where t is the year and DVD sales are measured in billions.

c. If the rate stays the same, we can predict the number of DVD sales in the year 2023 by substituting t = 2023 into the linear model and solving for DVD sales:

DVD sales = -0.49(2023 - 2011) + 6.1 ≈ 0.5 billion DVDs

Therefore, if the rate of decline in DVD sales stays the same, we can predict that there will be about 0.5 billion DVDs sold worldwide in 2023.

Answer: Let's assume that each time the ball rebounds, it bounces back up to exactly 2/3 of its previous height. We can use this information to create a table and plot the expected rebound heights for the first ten bounces.

Bounce Number                                  Rebound Height (feet)

0                                                               30.0

1                                                                20.0

2                                                               13.3

3                                                               8.9

4                                                               5.9

5                                                               3.9

6                                                               2.6

7                                                               1.7

8                                                               1.1

9                                                               0.7

10                                                              0.5

To plot this data, we can use a scatter plot with the bounce number on the x-axis and the rebound height on the y-axis. The points should be connected by a line to show the trend.

Tennis ball bounce heights

Note that the rebound heights decrease quickly and approach zero, but they never actually reach zero due to the rounding in our calculations.

Step-by-step explanation:

Answer:

First add, then subtract
10

Step-by-step explanation:

First subtract, then determine the result:

27 + 33 = 60

60 - 50 = 10

Macy has 10 stickers left.

The operations needed to solve the problem are:

First add, then subtract.

The equivalent function for .5=2⁻¹ is: 2x = 1 or log2(0.5) = -1 These are alternative ways of expressing the same relationship between 0.5 and 2⁻¹.

Understanding the Exponential Function

In mathematics, the exponential function is a function that is defined as f(x) = a^x, where 'a' is a constant called the base of the exponential function, and 'x' is the exponent. The exponential function is an important function in mathematics and is used in many different fields, such as finance, physics, and engineering.

To understand the relationship between an exponential function and a power of a number, we can consider the example of 0.5 = 2⁻¹ This means that 2 raised to the power of -1 is equal to 0.5.

To prove this, we can use the definition of the exponential function as f(x) = a^x. In this case, a = 2 and x = -1. So, we have:

f(-1) = 2⁻¹

We can simplify this expression using the property of negative exponents that states that a^-n = 1/a^n. Therefore:

f(-1) = 1/2¹

Simplifying further, we get:

f(-1) = 1/2

So, we see that 2 raised to the power of -1 is indeed equal to 0.5.

In conclusion, understanding the exponential function is important in mathematics and many other fields. The example of 0.5 = 2⁻¹ helps to illustrate the relationship between an exponential function and a power of a number, and how we can use the properties of exponents to simplify expressions involving exponential functions.

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Answer:

the probability is that the teacher will most likely pick between 2-4 boys and the rest would be girlso so the probability of it being all girls unless he choosing all girls on pourpose it would be a slim chance. if you need a percentage it would probably be like a 1.25% chance

Step-by-step explanation:

Answer:

x = 145

Step-by-step explanation:

We are given a polygon that has 7 sides. We can use the formula [tex]S=(n-2) * 180[/tex] which allows us to write an algebraic expression to solve for x where n = number of sides.

[tex]S=(7-2) * 180[/tex]

Evaluate

[tex]S=5*180[/tex]

[tex]S=900[/tex]

Now that we have our number, lets write an algebraic expression that will help us find the value of x.

[tex]x+116+129+120+130+135+125=900[/tex]

Add like terms

[tex]x+755=900[/tex]

Subtract 755 on both sides

[tex]x=145[/tex]

We can check our work by adding all the angle measures together

[tex]145+116+129+120+130+135+125=900[/tex]

Thus we know 145 is the correct answer.

a.  The probability that they are actually lying is 0.3214. b. The polygraph test must be 98.7% in order that this probability is at least 80%.

It is simpler to construct and see every possible scenario using the tree diagram. Its two main sites are the ends and the branches of the tree. The probability is written on each branch, and the ends hold the final findings. Use tree diagrams to identify when to multiply and when to add.

The probability of lie = 0.5

The probability of truth = 1 - 0.5 = 0.95

The liars that pass polygraph = 0.10

The liars that fail the polygraph is = 0.90

The truth that pass on polygraph = 0.90

The truth that fails on polygraph = 0.10

a. The probability that they are actually lying is:

P (Lying| fair) = P (fair| Lying) P (lying) / P (fair)

= (0.90)(0.05)/ (0.70)(0.05) + (0.10)(0.95)

= 0.3214

b. P (Lying| fair) > 0. 80

= (x)(0.05)/ (x)(0.05) + (1-x)(0.95) > 0.80

x > 0.987

Hence, the polygraph test must be 98.7% in order that this probability is at least 80%.

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Answer:

The equation is false

Step-by-step explanation:

(x+5)^2 = x^2+25

FOIL the left hand side.

(x+5)(x+5)

x^2 +5x+5x+25

x^2 +10x+25

This does not equal x^2+25.