The given figure is a solid object formed by a cylinder and a hemisphere. If the total length of that solid object is 64 cm and length of the cylinder is 50 cm, find the total surface area of the solid object.​

The graph of the function has no asymptotes.

The function is given as:

c(t) = 5t - t² + 1

When t = 1, 2, 5, 10;

We have:

c(1) = 5(1) - 1² + 1 = 5

c(2) = 5(2) - 2² + 1 = 7

c(5) = 5(5) - 5² + 1 = 1

c(10) = 5(10) - 10² + 1 = -49

So, the table of values is

t        c(t)

1         5

2        7

5        1

10      -49

See attachment for the graph of the function

The domain

From the question, we understand that t represents time.

So, the domain is 0 ≤ t ≤ 5.2

The range

From the graph, the maximum of the graph is 7.25

So, the range is 0 ≤ f(t) ≤ 7.25

Asymptotes

From the graph, we can see that the graph has no asymptotes.

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The vertex of the function is a minimum and the coordinate of the vertex of the function is (0.2, -2.4)

The function is given as:

f(x) = 5x^2 + 2x - 3

Expand the function

f(x) = 5x^2 + 5x - 3x - 3

Factorize the function

f(x) = (5x - 3)(x + 1)

Set the function to 0

(5x - 3)(x + 1) = 0

Solve for x

x = 3/5 and x =-1

Hence, the x-intercept is 3/5 and -1

The vertex of the function is a minimum.

This is so because the leading coefficient of the function is positive

Here, we have:

f(x) = 5x^2 + 2x - 3

Differentiate and set to 0

10x + 2 = 0

Solve for x

x = -0.2

Substitute x = -0.2 in f(x) = 5x^2 + 2x - 3

f(0.2) = 5(0.2)^2 + 2(0.2) - 3

Evaluate

f(0.2) = -2.4

Hence, the vertex of the function is (0.2, -2.4)

To do this, we simply plot the x-intercept and the vertex.

And then connect the points

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Answer: 38 teachers.

Step-by-step explanation:

Let the share ratio be x.

So, quantity of teachers = 2x, quantity of male students = 17x,

quantity of female students = 18x.

17x+18x=665

35x=665

Divide the left and right sides of the equation by 35:

х=19.

2x=2*19

2x=38.

The two numbers are 68 and 55.

Given that the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343.

We need to find the numbers,

Let's call the two numbers x and y. According to the given information, we have the following two equations:

x + y = 123 (The sum of the two numbers is 123)

x + 5y = 343 (When the larger number is added to 5 times the smaller, the sum is 343)

Now, we can solve these two equations simultaneously to find the values of x and y.

Let's rearrange equation 1 to express x in terms of y:

x = 123 - y

Substitute this value of x into equation 2:

(123 - y) + 5y = 343

Now, solve for y:

123 + 4y = 343

4y = 343 - 123

4y = 220

y = 220 / 4

y = 55

Now that we have the value of y, we can find the value of x using equation 1:

x = 123 - y

x = 123 - 55

x = 68

So, the two numbers are 68 and 55.

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Using binomial distribution, the probability of

a. 5 will still be with the company after 1 year is 28%.

b. at most 6 will still be with the company after 1 year is 89%.

The probability of a new employee in a fast-food chain still being with the company at the end of the year is given to be 0.6, which can be taken as the success of the experiment, p.

We are finding probability for people, thus, our sample size, n = 8.

Thus, we can show the given experiment a binomial distribution, with n = 8, and p = 0.6.

(i) We are asked for the probability that 5 will still be with the company.

Thus, we take x = 5.

P(X = 5) = (8C5)(0.6⁵)((1 - 0.6)⁸⁻⁵),

or, P(X = 5) = (56)(0.07776)(0.064),

or, P(X = 5) = 0.27869184 ≈ 0.28 or 28%.

(ii) We are asked for the probability that at most 6 will still be with the company.

Thus, our x = 6, and we need to take all values below it also.

P(X ≤ 6)

= 1 - P(X > 6)

= 1 - P(X = 7) - P(X = 8)

= 1 - (8C7)(0.6)⁷((1 - 0.6)⁸⁻⁷) - (8C8)(0.6)⁸((1 - 0.6)⁸⁻⁸)

= 1 - 8*0.0279936*0.4 - 1*0.01679616*1

= 1 - 0.08957952 - 0.01679616

= 0.89362432 ≈ 0.89 or 89%.

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The provided question is incomplete. The complete question is:

If the probability of new employee in a fast-food chain still being with the company at the end of 1 year is 0.6, what is the probability that out of 8 newly hired people,

a. 5 will still be with the company after 1 year?

b. at most 6 will still be with the company after 1 year?

The area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter is equal to 1.21 cm².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

In order to calculate the area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter, we would determine the area of ​​each triangle as follows:

For triangle 1, we have:

Area = 1/2 × b × h

Area = 1/2 × 1 × 1

Area = 0.5 cm².

For triangle 2, we have:

Area = 1/2 × b × h

Area = 1/2 × √2 × 1

Area = 0.71 cm².

Total area = Area of triangle 1 + Area of triangle 2

Total area = 0.5 + 0.7

Total area = 1.21 cm².

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Complete Question:

Magda used a 1 cm square grid to draw the shaded figure, using right triangles. 1 cm 3 cm √2 cm 1 cm 1 cm what is the area of ​​the figure Magda shaded?​

Considering the definition of scale, you obtain:

A map is the conventional graphical representation of a portion of the earth or another celestial body that shows the size and position of elements of the landscape according to the selected scale and projection. That is, a map is a representation of a place, at a size smaller than the actual size.

The scale of a cartographic representation, or map scale (m), is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. In general, it is also defined as the ratio of the lengths of a linear element in the plane and its representation on the terrestrial reference surface.

That is, the scale of the map is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.

A map has a scale of 1:5000000000. This indicates that 1 unit on the map is equivalent to 5,000,000,000 in reality.

You know that the road on the map is 10 cm or 0.0001 km long (knowing that 1 km= 100,000 cm).

Then you can apply the following rule of three: if by definition of scale 1 km on the map is equivalent to 5,000,000,000 km in reality, 0.0001 km on the map is equivalent to how much distance in reality?

[tex]real length of the road=\frac{0.0001 kmx 5,000,000,000 km }{1 km}[/tex]

real length of the road= 500,000 km

Finally, the real length of the road is 500,000 km.

You know that the area of a farm of the map is 6 cm square, 0.0006 m sr 0.00000006 hectares (knowing that 1 cm square= 0.0001 m square and 10,000 m square= 1 hectare).

Then you can apply the following rule of three: if by definition of scale 1 hectare on the map is equivalent to 5,000,000,000 hectares in reality, 0.00000006 hectares on the map is equivalent to how much area in reality?

[tex]real area of the farm=\frac{0.00000006 hectaresx 5,000,000,000 hectares }{1 hectare}[/tex]

real area of the farm= 300 hectares

Finally, the real area of the farm is 300 hectares.

In summary, you get:

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Answer:

615.7536

Step-by-step explanation:

Remember the equation for finding the area of a circle is:

A=π[tex]r^2[/tex]

Just substitute in your radius for r and solve:

A=3.1416*[tex]14^2[/tex]

A=3.1416*196

A=615.7536

Answer:

E

Step-by-step explanation:

We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.

I chose the second way to work out.

Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:

[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]

The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]

The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.

Thus, we have

[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]

Answer:

B

Step-by-step explanation:

If x and y vary inversely, then as x increases, y decreases. That eliminates answers A, C, and D.

Answer: B

a. The area of [tex]R[/tex] is given by the integral

[tex]\displaystyle \int_1^2 (x + 6) - 7\sin\left(\dfrac{\pi x}2\right) \, dx + \int_2^{22/7} (x+6) - 7(x-2)^2 \, dx \approx 9.36[/tex]

b. Use the shell method. Revolving [tex]R[/tex] about the [tex]x[/tex]-axis generates shells with height [tex]h=x+6-7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le 2[/tex], and [tex]h=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With radius [tex]r=x[/tex], each shell of thickness [tex]\Delta x[/tex] contributes a volume of [tex]2\pi r h \Delta x[/tex], so that as the number of shells gets larger and their thickness gets smaller, the total sum of their volumes converges to the definite integral

[tex]\displaystyle 2\pi \int_1^2 x \left((x + 6) - 7\sin\left(\dfrac{\pi x}2\right)\right) \, dx + 2\pi \int_2^{22/7} x\left((x+6) - 7(x-2)^2\right) \, dx \approx 129.56[/tex]

c. Use the washer method. Revolving [tex]R[/tex] about the [tex]y[/tex]-axis generates washers with outer radius [tex]r_{\rm out} = x+6[/tex], and inner radius [tex]r_{\rm in}=7\sin\left(\frac{\pi x}2\right)[/tex] if [tex]1\le x\le2[/tex] or [tex]r_{\rm in} = 7(x-2)^2[/tex] if [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each washer has volume [tex]\pi (r_{\rm out}^2 - r_{\rm in}^2) \Delta x[/tex]. As more and thinner washers get involved, the total volume converges to

[tex]\displaystyle \pi \int_1^2 (x+6)^2 - \left(7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \pi \int_2^{22/7} (x+6)^2 - \left(7(x-2)^2\right)^2 \, dx \approx 304.16[/tex]

d. The side length of each square cross section is [tex]s=x+6 - 7\sin\left(\frac{\pi x}2\right)[/tex] when [tex]1\le x\le2[/tex], and [tex]s=x+6-7(x-2)^2[/tex] when [tex]2\le x\le\frac{22}7[/tex]. With thickness [tex]\Delta x[/tex], each cross section contributes a volume of [tex]s^2 \Delta x[/tex]. More and thinner sections lead to a total volume of

[tex]\displaystyle \int_1^2 \left(x+6-7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \int_2^{22/7} \left(x+6-7(x-2)^2\right) ^2\, dx \approx 56.70[/tex]

a. 1/ 15

b. 76/ 15

c. 1/12

a. 2/5 divided by 6

= 2/ 5 ÷ 6

= 2/ 5 ÷ 6/ 1

Take the inverse of the dividing fraction, we have

= 2/ 5 × 1/ 6

Multiply through

= 2/30

= 1/ 15

b.  3 and 1/3 times 5 and 2/5

= 3 + 1/ 3 × 5 + 2/ 5

From the knowledge of BODMAS, we multiply first

= 3 + 5/3 + 2/ 5

Find the LCM

= 45 + 25 + 6/ 15

= 76/15

c. 1/4 + 1/3 -1/2

Let's find the LCM

= 3 + 4 - 6 / 12

Add first

=  7 - 6/ 12

= 1/ 12

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The parts of algebraic expressions related to polynomials are variables and coefficients.

The parts of algebraic expressions are;

Polynomials are algebraic expressions composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, and multiplication

Polynomials consists of variables and coefficients. The variables in polynomials are also called indeterminates. The coefficients also multiply this variables.

Thus, the parts of algebraic expressions related to polynomials are variables and coefficients.

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Answer: 7 1/2 cups

Step-by-step explanation:

We first need to make both fractions have an equal denominator. Cross Multiply 3/4 and 1/10. You will end up with 30/40 and 4/40.

Next we divided 30 by 4, and we will end up with 7 1/2. 7 times 4 is 28, and half of 4 is 1/2, or in this case 2/10. John can fill 7 and 1/2 cups of orange juice.

The geometric sequence when the first term is 1/5 and the common ratio is 5 is; f(n) = f(n-1) . 5.

The geometric sequence described in the task content is one whose first term is; f(1) = 1/5.

Additionally, it follows from convention that the recursive function for a geometric sequence is; a product of a previous term and the common ratio.

Hence, we have; f(n) = f(n-1) . 5.

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Answer:

F

Step-by-step explanation:

There are 6 digits in the repeating pattern.

279 / 6 = 46.5 remainder 3.

we care about the remainder as this is how many digits in. it is the 3rd digit in so is 3.

value of n could be 252 degree. Option 4

It is important to note that a decagon is a ten-sided polygon.

Since, a decagon has 10 sides

And we know that the angle made in one complete rotation is 360 degree.

Now find angle made in each rotation by the decagon is 360,

= 360/ 10

= 36 degrees

Now, we have to find possible values of n, and 'n' must be a multiple of 36

Apply hit and trial from given options.

We observe that from given options, only 252 degree is multiple of 36.

Therefore, value of n could be 252 degree. Option 4

The complete question is ;

A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be:

1. 10 degrees

2. 150 degrees

3. 225 degrees

4. 252 degrees

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Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743[/tex]

The probability is the p-value of Z when X = 16 subtracted by the p-value of Z when X = 15, hence:

X = 16:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16 - 15}{0.4743}[/tex]

Z = 2.11

Z = 2.11 has a p-value of 0.9826.

X = 15:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15 - 15}{0.4743}[/tex]

Z = 0

Z = 0 has a p-value of 0.5.

0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

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Answer: Y = 4x + 2

(It would be either the third or fourth choice since they are the same, one of them must be mistaken)

Step-by-step explanation:

Given information

(x₁, y₁) = (1, 6)

(x₂, y₂) = (0, 2)

Find the slope through the formula

[tex]Slope~=~\frac{y_2~-~y_1}{x_2~-~x_1}[/tex]

[tex]\Large Slope~=~\frac{2~-~6}{0~-~1}[/tex]

[tex]\Large Slope~=~\frac{-4}{-1}[/tex]

[tex]\Large Slope~=~4[/tex]

Substitute values into the linear form

Equation: y = mx + b

Point (0, 2)

y = mx + b

(2) = (4) (0) + b

2 = 0 + b

b = 2 - 0

b = 2

Therefore, the equation is [tex]\Large\boxed{y=4x+2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

y = 4x+2

Step-by-step explanation:

The first step is to find the slope

m = ( y2-y1)/(x2-x1)

m = ( 2-6)/(0-1)

    = -4/-1

   = 4

The slope intercept form of the equation is

y = mx+b  where m is the slope and b is the y intercept

y = 4x+b

The y intercept is where x is equal to 0

The y intercept is 2

y = 4x+2

The pair of triangles in option A, C and D are congruent triangles.

Pair of triangles are given.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

A) In the given figure, two angles and one side of the one triangle is equal to two angles and one side of the other triangle

By AAS congruence, two triangles are congruent.

B) In the given figure, one angle and one side is equal

So, two triangles are not congruent

C) Here, two sides and one included angle of the one triangle is equal to two sides and one included angle of the other triangle

D) Here, two angles and one included side of the one triangle is equal to two angles and one included side of the other triangle.

Therefore, the pair of triangles in option A, C and D are congruent triangles.

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If the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.

Given that the value of n is 9 and the value of p is 0.3.

We are required to find the probability when the value of x is equal to 3.

Probability is the calculation of chance of happening an event among all the events possible.It lies between 0 and 1.

Probability=Number of items/total items.

Binomial probability is basically the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes.

[tex](a+b)^{n}[/tex]=[tex]nC_{0}a^{0} b^{n-0} +nC_{1}a^{1} b^{n-1} +................nC_{n}a^{n} b^{0}[/tex]

We have to find the value when n=9, p is 0.3 and r=3.

=[tex]9C_{3} (0.3)^{3} (1-0.3)^{6}[/tex]

=9!/3!6!*0.027*0.16807

=84*0.00453789

=0.381182

Hence if the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.

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Answer:

it's C. 2.26s

but you wrote 2.16s nearly

The soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds,  option D.

To determine how long the soccer ball was in the air, we can use the vertical motion of the ball. When a projectile is launched at an angle, its vertical motion can be analyzed separately from its horizontal motion.

In this case, the initial velocity of the soccer ball can be divided into vertical and horizontal components. The initial velocity in the vertical direction can be calculated using the sine of the launch angle:

Vertical component (Vy) = initial speed (v) * sin(angle)

Vy = 16 m/s * sin(45°)

Vy = 11.31 m/s

Now, we can use the vertical motion equation to find the time the ball spends in the air:

Vertical displacement (y) = Vy * time - (1/2) * gravity * time^2

Since the ball reaches the same vertical position when it lands as when it was launched, the vertical displacement is 0. Therefore, we can set the equation equal to zero:

0 = (11.31 m/s) * time - (1/2) * 9.8 m/s^2 * time^2

Simplifying the equation:

4.9 * time^2 = 11.31 * time

Dividing both sides by time:

4.9 * time = 11.31

time = 11.31 / 4.9

time ≈ 2.31 seconds

Therefore, the soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, which corresponds to option D.

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The volume of the cylinder and the cone is equal

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where

r is the radius

h is the height

For the cylinder

r = 8/2 = 4 in

h = 5

Substitute

V = π(4)²*5
V = 80π cubic inches

For the cone

r = 4 in

h = 15in

Substitute

V = 1/3πr^2h

V = 1/3(π)(4)^2 * 15

V = 80π cubic inches

Hence the volume of the cylinder and the cone is equal

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Step-by-step explanation:

1500*.02*1=30

50*12*1=60

g(x)=50(12x) good

The solutions to the given quadratic equation are as follows:

x = 1.10, x = 10.9.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

For this problem, the equation in item D is:

-x² + 12x - 12 = 0

x² - 12x + 12 = 0

Hence the coefficients are:

a = 1, b = -12, c = 12.

Then the solutions to the equation are found as follows:

The solutions are:

x = 1.10, x = 10.9.

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The value of x according to the secant-secant theorem is 4

Secant-secant theorem states if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant.

Using the equation below;

6(x+6) = 5(5+x+3))

Expand the expression
6x+36 = 5(x+8)

6x + 36 = 5x + 40

Subtract 5x from both sides

6x-5x +36 = 40

Subtract 36 from both sides

6x - 5x = 40 - 36

x = 4

Hence the value of x according to the secant-secant theorem is 4

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Answer:

The value of x according to the secant-secant theorem is 4

Step-by-step explanation:

[tex]58.41 < f(x) < 150[/tex] inequality represents the range of the exponential function that models this situation

The exponential decay function is as follows:

[tex]y = a(1-r)^t[/tex]

Here,

y = final value

a = initial value

r = decay rate

t = time taken

Given that:

a = 150 mg

r = 9% = 0.09

Then the next hour the amount of caffeine in the body will be:

[tex]y = a (1-r)^t\\y = 150 \times (1-0.09)^2[/tex] = 136.5

Similarly, after 10 hours the amount of caffeine in the body will be:

[tex]y = 150 \times (1- 0.09)^{10} = 58.41[/tex]

Then the inequality representing the range of the exponential function that models this situation is:

58.41 < f(x) < 150

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f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B

Inverse variation can be defined as the relationships between variables represented in the form of y = k/x

where;

From the options given, we can see that;

f(x) = -1/ 3x

f(x) = -z/xy

Both take the form of inverse variations

Thus, f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B

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