What is this expression in simplified form?
(6/2)(-35)

Using the right cone formula we know that the surface area is 1281.77638m³ respectively.

An axis that is perpendicular to the base plane defines a right circular cone. By rotating a right triangle around one of its legs, we may create a right cone.

The right circular cone in the illustration has an axis that is perpendicular to the base and a circular base with a radius r.

So, the formula for the surface area of the right cone is as follows:

πr(r+√h²+r²)

We have the values: r = 13m and h = 13m

Now, insert values as follows:

= πr(r+√h²+r²)

= π13(r+√13²+13²)

= 1281.77638

Therefore, using the right cone formula we know that the surface area is 1281.77638m³ respectively.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

The equation represents the image of the line y = 3x +1 is y' = 3(x - 3) +1.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

The transformation that translates function y = f(x) by h units right and k units up is

y' = f(x -h) +k

We have y= 3x+ 1

So, After translating 3 units to x axis the function will become

y' = 3(x - 3) +1

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Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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Given in the situation:

a.) The scale of a map of Florida is 2 cm = 3 miles.

b.) The distance between Apopka and Miami is 249 miles.

For this type of problem, we will be applying ratio and proportion.

The ratio of the map scale = 2 cm : 3 miles

Using this ratio, let's determine how far apart are Apopka and Miami on the map. Let x be the scale equivalent of the distance on the map.

We get,

Therefore, Apopka and Miami are scaled as 166 cm apart on the map.

Answer:

Step-by-step explanation:

term            | Phrase

inequality   | 63<8k

Expression | bc+1-(8d-4)

Equation     | w^4=81

Answer:

Inequality 63 < 9k

Expression bc + 1 - (8d - 4)

Equation w⁴ = 81

Step-by-step explanation:

w⁴ = 81

⁴√w⁴ = ⁴√81

w = 3

3 × 3 × 3 × 3 = 81

9 × 3 × 3 = 81

9 × 9 = 81

bc + 1 - (8d - 4)

bc + 1 - 8d + 4

bc + 5 - 8d

Answer: The energy balance equation states that the amount of energy (calories) consumed must be equal to the amount of energy used or expended in order for body weight to remain stable. If the amount of energy consumed is greater than the amount of energy used, the excess energy will be stored as body fat, leading to weight gain. If the amount of energy used is greater than the amount of energy consumed, the body will use stored body fat for energy, leading to weight loss.

The energy balance equation can be expressed as: Energy Intake (calories consumed) = Energy Expenditure (calories burned through physical activity and metabolism).

Individuals have control over two parts of the energy balance equation: energy intake (what and how much they eat) and energy expenditure (physical activity level).

To tip the energy balance equation in favor of weight loss, individuals can either decrease their energy intake (eat fewer calories) or increase their energy expenditure (burn more calories through physical activity). To tip the energy balance equation in favor of weight gain, individuals can either increase their energy intake (eat more calories) or decrease their energy expenditure (burn fewer calories through physical activity).

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

So all you have to do is -2+5 = 3

since -2 is below zero, it takes 2 to get to zero and now we have to add the 3 to get the answer of 3.

There are total 15 students per teacher and 8 students per tutor. For 100 students, total 13 tutors are required.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the given data provided in the question,

4 teachers  = 60 students

For 1 teacher = 60/4 = 15 students

Similarly,

6 tutors = 48 students

For 1 tutor = 48/6 = 8 students.

For total 100 students, total number of tutors = 100/8

= 12.5 or 13 tutors are required.

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Answer:

14

Step-by-step explanation:

used a calculator to check the answer

1/4π radians is approximately equal to 45 degrees.

To convert a value from radians to degrees, multiply the value by 180/π. For example, to convert π/4 radians to degrees, multiply π/4 by 180/π to get 45 degrees. This conversion is useful for converting angles between the two units of measurement.

Degrees = Radians × 180/π.

Therefore, to convert 1/4π radians to degrees, we have:

Degrees = (1/4π) × (180/π) ≈ 45°

Hence, 1/4π radians is approximately equal to 45 degrees.

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The value of n that satisfies the given polynomial expression is 10

From the question, we are to determine determine the corresponding value of n in the simplified expression.

The given expression is

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

First, we will simplify this expression

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

(12x⁵ + 6x³ + x) - (2nx³ + x + 52nx² + 26)

(12x⁵ + 6x³ + x - 2nx³ - x - 52nx² - 26)

Simplify further

(12x⁵ + 6x³ - 2nx³ - 52nx² - 26)

(12x⁵ + (6 - 2n)x³ - 52nx² - 26)

By comparison with (12x⁵ - 14x³ - 520x² - 26)

(6 - 2n)x³ = - 14x³

and

- 52nx² = - 520x²

Solve (6 - 2n)x³ = - 14x³ for n

(6 - 2n)x³ = - 14x³

6 - 2n = - 14

6 + 14 = 2n

20 = 2n

n = 20/2

n = 10

Similarly,

Solve - 52nx² = - 520x² for n

52n = 520

n = 520/52

n = 10

Hence, the value of n is 10

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The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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Answer:

10.0 but if you want it in fraction it is 0.100

Step-by-step explanation:

Step 1:

\(1.0 \times 10.0\)

Step 2:

\( = \dfrac{10}{10} \times \dfrac{100}{10} \)

To make them in fraction we have to remove decimals

Step 3:

\( = \dfrac{1000}{100} \)

Step 4:

\( = \dfrac{10}{1}✓\)

Answer:

\(area = \frac{1}{2} \times 21 \times 17 \\ area = 178.5 {mm}^{2} \)

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".

When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.

In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.

a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.

b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.

c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.

d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.

Therefore, "time(length)" is the most suitable and appropriate name for the function.

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

Evan ordered cranberry juice

Daria ordered orange juice

Fernando ordered lemonade

Step-by-step explanation:

hope this helped :)

Answer:

Evan had cranberry juice fernando had lemonade and daria had orange juice

Step-by-step explanation:

It says even had cranberry juice so you don't need to worry about cranberry juice, and daria said she didn't have lemonade so she must of had orange juice, and fernendo must of had lemonade

The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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Answer:

Direct variation; k=5/2

Step-by-step explanation:

Edge quiz, got it right

Answer:

z(-1) = -9, z(2) = 18

Step-by-step explanation:

z(-1) = 2(-1)^2 + 7(-1) -4

      = 2(1) - 7 -4

      = 2 - 11

      = -9

z(2) = 2(2)^2 + 7(2) - 4

      = 2(4) + 14 - 4

      = 8 + 10

      = 18

( a ) The null hypothesis, represented by \(H_{0}\), should be equivalent to 0.6 pounds per square inch, considering it normally is predicted to be equivalent to the population parameter, which, in this case, is 0.6 psi ( pounds per square inch. ) The alternative hypothesis on the other hand contradicts the null hypothesis, and as the manager feels the pressure has been reduced, the alternative hypothesis points that the pressure is less than 0.6 psi -

\(H_0: stigma = 0.7,\\H_a: stigma < 0.7\)

stigma is represented by the sign ( σ )

( b ) Now if you were to reject the null hypothesis when true, that would lead to a type I error. That would mean that to reject the fact that σ = 0.7, and accept that σ < 0.7, even though σ = 0.7 is true, would make a type I error.

_______

( c ) A type II error is quite the opposite. Accepting the null hypothesis while rejecting the alternative hypothesis would make a type II error.

From the information given and using error concepts, it is found that:

a)

The null hypothesis is \(H_0: \sigma = 0.6\)

The alternative hypothesis is \(H_1: \sigma < 0.6\)

b) It would mean a conclusion that the standard deviation is of less than 0.6 psi when in fact it is not.

c) It would mean a conclusion that the standard deviation not significantly less than 0.6 psi when in fact it is.

At the null hypothesis, we test if the standard deviation is of 0.6 psi, that is:

\(H_0: \sigma = 0.6\)

At the alternative hypothesis, we test if variability has been reduced, that is, if the standard deviation is of less than 0.6 psi, hence:

\(H_1: \sigma < 0.6\)

Item b:

A Type I error happens when a true null hypothesis is rejected, hence, it would mean a conclusion that the standard deviation is of less than 0.6 psi when in fact it is not.

Item c:

A Type II error happens when a false null hypothesis is not rejected, hence, it would mean a conclusion that the standard deviation not significantly less than 0.6 psi when in fact it is.

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From the model, we notice that for three hours Jonathan earns $105. This means that he earns $35 (105 divided by 3) per hour.

Now, we have in total 10 hours in the model, hence he will earn a total of $350 (35 times 10).

Answer:

a is 4 because 4 x 16=20 i hope this help

a + 16 = 20

a = ?

a = 20 + 16

a = 36

a = 36 ✔️

The annual interest rate for the given compound interset is 6%

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.  

Given that, Rs.2250 is deposited for 2 years in an account, it amounts to Rs.2560 compounded annually.

A = P(1+r)ⁿ

2560 = 2250(1+r)²

2560 / 2250 = (1+r)²

1.13 = (1+r)²

Taking roots,

1+r = √1.13

r = 0.06

r = 6%

Hence, the annual interest rate for the given compound interset is 6%

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Answer:

Step-by-step explanation:

The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.

Step 1: Evaluate the expression inside the parentheses.

7.4 - 3.6 = 3.8

After evaluating the expression inside the parentheses, the expression becomes:

12 ÷ 3.8 + 8 - 2

Step 2: Perform the division.

12 ÷ 3.8 = 3.158

After performing the division, the expression becomes:

3.158 + 8 - 2

Step 3: Perform the addition and subtraction from left to right.

3.158 + 8 = 11.158

11.158 - 2 = 9.158

Therefore, the value of the given expression is approximately 9.158.

The first step is:

Work/explanation:

The expression is:

12 ÷ (7.4 − 3.6) + 8 − 2

Let's recall the order of operations first:

So we evaluate

\(\sf{12\div(7.4-3.6)+8-2}\)

\(\sf{12\div3.8+8-2}\)

Next, division:

\(\sf{3.158+8-2}\)

Next, addition & subtraction:

\(\sf{9.158}\)