Expand (x-y)3 using Pascal triangle

Answer: 20,493

Step-by-step explanation:

%45 off of $37,260 is the same as (45 x 45) / 100 which equals to: 16,767

Then do: 37,260 - 16,767 = 20,493

And there you have it! Hope this helps!!

About 9.1% of people have a systolic blood pressure above 130.about 34.1% of people have a systolic blood pressure between 120 and 130.

A number can be expressed in fractions of 100 using a percentage. When expressing it, the notation %, which stands for "per hundred," is frequently used. 50%, for instance, equals 50/100, or the percentage 1/2.

a. To find the percentage of people with a systolic blood pressure above 130, we need to find the area under the normal curve to the right of 130. Using a standard normal distribution table or a calculator, we can find that this area is approximately 9.1%. Therefore, about 9.1% of people have a systolic blood pressure above 130.

b. To find the percentage of people with a systolic blood pressure between 120 and 130, we need to find the area under the normal curve between 120 and 130. Using a standard normal distribution table or a calculator, we can find that this area is approximately 34.1%. Therefore, about 34.1% of people have a systolic blood pressure between 120 and 130.

c. To find the range of systolic blood pressures for the middle 60% of the population, we need to find the two values of systolic blood pressure that separate the centre 60% of the normal curve's area under the curve. Using a standard normal distribution table or a calculator, we can find that these values are approximately 111.4 and 128.6. Therefore, the range of systolic blood pressures for the middle 60% of the population is approximately 111.4 to 128.6.

d. To find the systolic blood pressure that qualifies a person for additional monitoring if they are in the top 15% of the population, we need to find the value of systolic blood pressure that separates the top 15% of the area under the normal curve from the rest. Using a standard normal distribution table or a calculator, we can find that this value is approximately 131.4. Therefore, a systolic blood pressure of 131.4 or higher would qualify a person for additional monitoring.

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a. approximately 10.56% of people have a systolic blood pressure above 130.

b. approximately 39.44% of people have a systolic blood pressure between 120 and 130.

c.  a systolic blood pressure of 128.32 or higher would qualify a person for additional monitoring if they are in the top 15% of the population.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

a. To find the percentage of people with a systolic blood pressure above 130, we need to calculate the area under the standard normal curve to the right of the z-score corresponding to a systolic blood pressure of 130.

z = (130 - 120) / 8 = 1.25

Using a standard normal distribution table or calculator, we find that the area to the right of z = 1.25 is 0.1056 or 10.56%. Therefore, approximately 10.56% of people have a systolic blood pressure above 130.

b. To find the percentage of people with a systolic blood pressure between 120 and 130, we need to calculate the area under the standard normal curve between the z-scores corresponding to systolic blood pressures of 120 and 130.

z1 = (120 - 120) / 8 = 0

z2 = (130 - 120) / 8 = 1.25

Using a standard normal distribution table or calculator, we find that the area between z = 0 and z = 1.25 is 0.3944 or 39.44%. Therefore, approximately 39.44% of people have a systolic blood pressure between 120 and 130.

c. To find the range of systolic blood pressures for the middle 60% of the population, we need to find the z-scores corresponding to the 20th and 80th percentiles of the standard normal distribution, which are -0.84 and 0.84, respectively.

The corresponding systolic blood pressures are:

lower limit: z1 * 8 + 120 = 113.68

upper limit: z2 * 8 + 120 = 130

Therefore, the range of systolic blood pressures for the middle 60% of the population is approximately 113.68 to 130.

d. To find the systolic blood pressure that qualifies a person for additional monitoring if they are in the top 15% of the population, we need to find the z-score corresponding to the 85th percentile of the standard normal distribution.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 85th percentile is 1.04.

The corresponding systolic blood pressure is:

systolic blood pressure = z * 8 + 120 = 128.32

Therefore, a systolic blood pressure of 128.32 or higher would qualify a person for additional monitoring if they are in the top 15% of the population.

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Answer: -3x+y

Step-by-step explanation:

This is a subtraction problem and "from" means it's the 1st number so

(2x+7y) - (5x + 6y)       be careful to distribute negative

2x +7y - 5x -6y

-3x+y

To find the simplest expression when (5x + 6y) is subtracted from (2x + 7y), we subtract the coefficients of like terms. This gives us -3x + y as the final result.

The expression represents the difference when (5x + 6y) is subtracted from (2x + 7y) can be found using the properties of addition and subtraction for algebraic expressions. We will combine like terms to simplify.

So, Subtract (5x + 6y) from (2x + 7y), it's like saying (2x + 7y) - (5x + 6y) this will give us:

-3x + y is the final expression in the simplest form.

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The ratio of the number of sweets that Amber has to the number of sweets that Callum has is 16:9.

A quantitative comparison of two or more quantities that shows their relative sizes is called a ratio.

In terms of how many times one is greater or less than the other, it describes the relationship between the two quantities.

Let's assume that Amber and Bethan bought x number of sweets, then Callum and David also bought x number of sweets.

According to the problem, Amber and Bethan share the sweets in the ratio 2:1. Therefore, Amber has (2/3)(x) sweets and Bethan has (1/3)(x) sweets.

Also, Callum and David share the sweets in the ratio 3:5. Therefore, Callum has (3/8)(x) sweets and David has (5/8)(x) sweets.

Now, we can find the ratio of the number of sweets that Amber has to the number of sweets that Callum has as follows:

Amber/Callum = [(2/3)(x)]/[(3/8)(x)] = (16/9)

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Answer:

To determine the type of function that best models the data in the table, we can observe the differences or ratios between successive values of y.

Using differences:

The first differences between successive values of y are:

1.5 - 0 = 1.5

6 - 1.5 = 4.5

13.5 - 6 = 7.5

24 - 13.5 = 10.5

The second differences between successive values of y are:

4.5 - 1.5 = 3

7.5 - 4.5 = 3

10.5 - 7.5 = 3

Since the second differences are constant, the function that best models the data is a quadratic function.

Using ratios:

The ratios between successive values of y are:

1.5/0 = undefined

6/1.5 = 4

13.5/6 = 2.25

24/13.5 ≈ 1.78

Since the ratios are not constant, the function that best models the data is not an exponential function.

Therefore, the type of function that best models the data in the table is a quadratic function. We can try to find a quadratic function of the form y = ax^2 + bx + c that passes through the given points. Using the first three points, we get the system of equations:

a(0)^2 + b(0) + c = 0

a(1)^2 + b(1) + c = 1.5

a(2)^2 + b(2) + c = 6

Solving this system of equations, we get:

a = 3/2

b = 0

c = 0

Therefore, the quadratic function that best models the data is y = (3/2)x^2.

Because automatic automobile frequency is different from the dealership, there will be an association.

A list of objects is contained in a frequency table together with the frequency of each item.

The quantity of times that an event or value occurs is its frequency.

A frequency table, then, is a table that contains some facts and their frequency.

Considering the dealership's frequency schedule for both manual and automatic.

We can see that whereas manual transmission dealerships all use the same frequencies, automatic transmission dealerships use distinct frequencies. Since there is a relationship between the two, there will be an association.

Because automatic automobile frequency is different from dealership frequency, there will therefore be a link.

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The complete question is:

Three car dealerships were surveyed about the percentage of vehicles on their lot with automatic or manual transmission. The results are displayed below.

Answer:

Please refer to the attachment

Step-by-step explanation:

Substitute x-values in g(x).

Eg. g(x) at x=0 is g(0)

=> -5(0) -5

= (-5)

Answer:

Step-by-step explanation

A=bh for a parallelogram.  The diagram is flipped(turn your paper)

b=9

h=6.7

A=(9)(6.7)=60.3 in²

Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways

n(A ∪ B ∪ C) = 16

n(A u B u C) = 2.

To find the number of elements in the set ( A cup B cup C), we need to find the union of the sets A, B, and C. This can be done by combining all the elements in A, B, and C, and then removing any duplicates.

So, (A ∪ B ∪ C) = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 20}

Therefore, n(A ∪ B ∪ C) = 16.

To find the number of elements in the set ( A ∩ B ∩ C), we need to find the intersection of the sets A, B, and C. This can be done by finding the elements that are common to all three sets.

So, (A ∩ B ∩ C) = {8, 20}

Therefore, n(A u B u C) = 2.

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[tex]f''(x)=-2+24x-12x^2\hspace{5em}f'(0)=16\hspace{5em}f(0)=2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \displaystyle \int~(-2+24x-12x^2)dx\implies -2x+12x^2 - 4x^3 + C=f'(x) \\\\\\ \stackrel{\textit{since we know that}}{f'(0)=16}\hspace{5em}-2(0)+12(0)^2-4(0)^3+C=16 \\\\\\ C=16\hspace{5em}\stackrel{\textit{so then we know that}}{-2x+12x^2 - 4x^3 + 16=f'(x)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\displaystyle \int~(-2x+12x^2 - 4x^3 + 16)dx\implies -x^2+4x^3-x^4+16x+C=f(x) \\\\\\ \stackrel{\textit{since we know that}}{f(0)=2}\hspace{5em}-(0)^2+4(0)^3+16(0)+C=2 \\\\\\ C=2\hspace{5em}\boxed{-x^2+4x^3-x^4+16x+2=f(x)}[/tex]

x = -1 is a root of the polynomial only if C = 3.

We want to have x = -1 as a root of the polynomial, then we just need to solve:

f(-1) = 0

this is:

2(-1)³ - 4(-1)² - 3(-1) + C  =0

-2 - 4 + 3 + C = 0

-3 + C = 0

C = 3

Tha must be the value of C.

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20.49 trillion is 412.25% larger than 4.00 trillion.

To calculate the percentage increase of a value from an initial value to a final value, you can use the following formula:

increase in percentage = ((final value - initial value) / initial value) x 100%

Percentage increase is useful in a variety of contexts, including: Finance, Sales, Economics, Science, Education. Percentage increase is a useful tool for measuring growth or change over time and comparing different values.

To find the percentage increase, we first need to calculate the difference between the two numbers:

20.49 trillion - 4.00 trillion = 16.49 trillion

Next, we can divide the difference by the original amount (4.00 trillion) and multiply by 100 to get the percentage increase:

(16.49 trillion / 4.00 trillion) * 100 = 412.25%

Therefore, 20.49 trillion is 412.25% larger than 4.00 trillion.

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The solution to the word problems are:

1) ∠JML = 63°

2) The center of the circle is (4, -4) and Radius = 4

3) The required measurement of the table cloth should be:

48 in x 36 in

4) The correct option of the similar triangles is:

UY/UV = UZ/ZW

1) The angle subtended by an arc at the Centre is twice the angle subtended at the circumference . More simply, the angle at the centre is double the angle at the circumference. Thus:

∠JML = 126/2 = 63°

2) The general formula for equation of a circle is expressed as:

(x - h)² + (y - k)² = r²

where:

(h, k) is the coordinate of the center of the circle

r is the radius

We are given the circle equation as:

(x + 4)² + (y - 4)² = 16

This can be rewritten as:

(x + 4)² + (y - 4)² = 4²

Thus:

Coordinates of center = (4, -4)

Radius = 4

3) The required measurement of the table cloth should be:

48 in x 36 in

4) Since both triangles are similar, then it means ratio of corresponding sides will be equal and as such:

UY/UV = UZ/ZW

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Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.

Exponents, usually referred to as powers and indices, are a type of mathematical operation that requires increasing a base number to a specific exponent. You can multiply the minimum amount by itself a given number of times using the exponent. For instance, the number 2 raised toward the power of 3 (printed as 23) is equivalent to 2 x 2 x 2, which is 8. Exponents are frequently employed in scientific notation, algebra, and other areas of mathematics to express extremely big or extremely small integers.

given

The distributive property of multiplication is used to multiply out the expression when expanding (x+2y) in ascending powers of x.

[tex](x + 2y) = x + 2yx^0[/tex]

By remembering that every number raised to the power of zero equals 1, we may simplify the second term. We thus have:

(x + 2y) = x + 2y(1) (1)

When we multiply the expression, we get:

(x + 2y) = x + 2y

Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.

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Answer:

half-life ≈ 2.74

Step-by-step explanation:

One formula we can use for half life is,

N(t) = No * (1/2)^(t / t_1/2), where

We already know that N(t) = 28, No = 128, the base is 1/2, and t is 6.  Thus, we must solve for t_1/2 using the following equation:

28 = 128 * (1/2) ^ (6 / t_1/2)

(28 = 128 * (1/2) ^ (6 / t_1/2) / 128

0.21875 = (1/2) ^ (6 / t_1/2)

ln (0.21875) = ln (1/2 ^ (6 / t_1/2))

ln (0.21875) = 6 / t_1/2 * ln (1/2)

(ln ( 0.21875) = 6 / t_1/2 * ln (1/2)) / ln (1/2)

ln (0.21875) / ln (1/2) = 6 / t_1/2

[tex]\frac{ln(0.21875)}{ln(1/2)}=\frac{6}{t_{1/2} }\\ \\ t_{1/2}*ln(0.21875)=6*ln(1/2)[/tex]

(t_1/2 * ln (0.21875) = 6 * ln (1/2)) / ln (0.21875)

t_1/2 = (6 * ln (1/2) / ln (0.21875)

t_1/2 = 2.736420983 hours

t_1/2 = 2.74 hours

The only real difference between the longer number and the rounded number is that the longer answer gives a more exact answer when you plug it in, but the rounded answer seems to make more sense to write:

Result when plugging in exact answer for t_1/2:

N (2.736420983) = 128 (1/2) ^ (6 / 2.736420983) = 28

Result when plugging in rounded answer for t_1/2:

N (2.74) = 128 (1/2) ^ (6 / 2.74) = 28.05564116

Answer:

Step-by-step explanation:

Therefore, the height of the tower is approximately 121.4 meters.

To answer this question, we need to compare the ratios of miles traveled to gallons of gas used for car A and car B when they both use 1 gallon of gas.

For car A, we can see from the graph that 50 miles are traveled for every 2 gallons of gas used, or in other words, 25 miles are traveled for every 1 gallon of gas used. Therefore, car A can travel 25 times the distance for 1 gallon of gas.

For car B, we can see from the table that 40 miles are traveled for every 2 gallons of gas used, or in other words, 20 miles are traveled for every 1 gallon of gas used. Therefore, car B can travel 20 times the distance for 1 gallon of gas.

To compare the two ratios, we can divide the ratio of miles traveled to gallons of gas used for car A by the ratio for car B:

25/20 = 1.25

Therefore, car A can travel 1.25 times the distance car B can travel when both cars use 1 gallon of gas.

[tex]\displaystyle \int_{0}^{\frac{\pi }{3}}~\sin(x)dx\implies \left.\cfrac{}{} -\cos(x)\right]_{0}^{\frac{\pi }{3}}\implies\left( -\cfrac{1}{2}\right) ~~ - ~~(-1)\implies \cfrac{1}{2}[/tex]

For the frequency distribution table;

1. The total number of observation is 24.

2. The width of each class is 11

3. The midpoint of the second class is 26

4. The model class is 65-75

5. The class limits of the next class is 76-86

For the frequency distribution table,

1. Total observation is the sum of the frequency:

2 + 3 + 5 + 6 + 0 + 8 = 24

2. The width is the first limit lower class - first limit of upper class.

21-10 = 11 or 32-21 = 11

3. The midpoint of class 2 is 21 + 31 = 52/2 = 26

4.   The class with the highest frequency is the model class      

5. Next class lower limit = 75 + 1 = 76

   Next class upper limit = 75 + 11 = 86

Use the frequency distribution to complete parts (a) through (e).

                                                                               Class            Frequency

a) Determine the total number of observations. 10-20               2

b) Determine the width of each class.                 21-31                 3

c) Determine the midpoint of the second class. 32-42               5

d) Determine the modal class (or classes).          43-53               6

e) Determine the class limits of the next class    54-64                0

if an additional class were to be added.             65-75               8

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Answer:

Step-by-step explanation:

8 points

Answer:1

Step-by-step explanation:

Taking into account the zeros of a quadratic function, the time of the rocket when it is in the air is equal to 1.5 seconds.

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

The zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

A rocket launched with height function h(t)= -16t²+ 24t

where

Time for which rocket is in the air given by h(t) = 0, so:

0= -16t²+ 24t

where:

Solving:

[tex]x1=\frac{-24+\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]

[tex]x1=\frac{-24+\sqrt{24^{2}} }{2x(-16)}[/tex]

[tex]x1=\frac{-24+24 }{2x(-16)}[/tex]

[tex]x1=\frac{0 }{-32}[/tex]

x₁= 0

and

[tex]x2=\frac{-24-\sqrt{24^{2} -4x(-16)x0} }{2x(-16)}[/tex]

[tex]x2=\frac{-24-\sqrt{24^{2} } }{2x(-16)}[/tex]

[tex]x2=\frac{-24-24}{2x(-16)}[/tex]

[tex]x2=\frac{-48}{-32}[/tex]

x₂= 1.5

Therefore, the time of the rocket in the air is 1.5 seconds.

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The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.

1. Let's calculate the probability of selecting a blue disk

We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is = 3/8

2. Let's calculate the probability of selecting the blue disk labeled with number 2 =

We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is = 1 /3

3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:

Probability of selecting a 2 given that a blue disk is selected =

3/8 x  1/3 = 3/24 = 1/8

Thus,it is correct to state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.

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Full Question:

See attached image.

Answer:

Let's call the average speed on the winding road "x". Then, the average speed on the level road is "x + 20".

We know that the bus traveled on the winding road for 2 hours, so the distance traveled on the winding road is:

distance = rate × time = x × 2 = 2x

We also know that the bus traveled on the level road for 3 hours at an average speed of "x + 20", so the distance traveled on the level road is:

distance = rate × time = (x + 20) × 3 = 3x + 60

The total distance traveled is 290 miles, so we can write:

2x + 3x + 60 = 290

Combining like terms and solving for x, we get:

5x + 60 = 290

5x = 230

x = 46

Therefore, the average speed on the winding road is 46 mph, and the average speed on the level road is:

x + 20 = 46 + 20 = 66 mph.

The theoretical probability of each section is 1/8, since there are 8 equal-sized sections on the spinner. To find the theoretical frequency, we multiply the theoretical probability by the total number of spins:

Theoretical frequency = (1/8) x 450 = 56.25

We can then calculate the experimental probability for each section by dividing the frequency by the total number of spins:

Experimental probability = Frequency/Total number of spins

Using this formula, we can calculate the experimental probabilities for each section:

Part 1: Experimental probability = 58/450 ≈ 0.129

Part 2: Experimental probability = 52/450 ≈ 0.116

Part 3: Experimental probability = 39/450 ≈ 0.087

Part 4: Experimental probability = 77/450 ≈ 0.171

Part 5: Experimental probability = 50/450 ≈ 0.111

Part 6: Experimental probability = 43/450 ≈ 0.096

Part 7: Experimental probability = 60/450 ≈ 0.133

Part 8: Experimental probability = 71/450 ≈ 0.158

To find the number with the greatest difference between the theoretical and experimental probability, we can calculate the difference between the two probabilities for each section:

Part 1: |0.125 - 0.129| = 0.004

Part 2: |0.125 - 0.116| = 0.009

Part 3: |0.125 - 0.087| = 0.038

Part 4: |0.125 - 0.171| = 0.046

Part 5: |0.125 - 0.111| = 0.014

Part 6: |0.125 - 0.096| = 0.029

Part 7: |0.125 - 0.133| = 0.008

Part 8: |0.125 - 0.158| = 0.033

As we can see, the greatest difference between the theoretical and experimental probability is for Part 4 with a difference of 0.046. This indicates that the experimental frequency for Part 4 is significantly different from the theoretical frequency, which may suggest that the spinner is biased towards that section.

Answer:

$27.00

Step-by-step explanation:

6 × $4.50 = $27.00

Answer:27

Step-by-step explanation:

4.50 x 6 = 27

The equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

A linear equation has the formula y = mx + b, where x and y are variables, m is the angle of the line's slope, and b denotes the y-intercept (the location where the line crosses the y-axis). On a graph, this equation represents a straight line.

The y-intercept of a linear equation, which is determined by the value of b, is first plotted on a graph. The slope is then used to determine further points along the line. How much y changes for each unit of x is indicated by the slope. For instance, if the slope is 2, then y grows by 2 for every unit increase in x.

Given that, a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.

Let us suppose number of minutes = x.

Then,

Cost = 0.75 + 0.15(x - 3)

hence, the equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

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The complete question is:

Answer:

Step-by-step explanation:

The point (2, 7) belongs to the solution region of the system of inequalities.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The system of inequalities given is:

y > 1.5x + 4

y > -x + 6

One point that belongs to the solution region of this system of inequalities is (2, 7).

To check if this point satisfies the system of inequalities, we can substitute the values of x and y into each inequality:

For the first inequality, y > 1.5x + 4, we have:

7 > 1.5(2) + 4

7 > 7

This is true, so the point (2, 7) satisfies the first inequality.

For the second inequality, y > -x + 6, we have:

7 > -(2) + 6

7 > 4

This is also true, so point (2, 7) satisfies the second inequality.

Therefore, points (2, 7) belong to the solution region of the system of inequalities.

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