A pencil cup is a cylinder made of plastic with one base missing. The cup is 5 inches tall and has a radius of 1.75 inches. Approximately how many square inches of plastic were used to make the cup? 54.98 in.2 74.22 in.2 48.11 in.2 64.60 in.2

The length of the segment SR for the given pentagons is 9 units.

A polygon having 5 sides and 5 angles is called a pentagon. The words "pentagon" (which implies five angles) are formed up of two other terms, namely Penta and Gonia. End to end, the sides of a pentagon come together to form a shape. Hence, there are 5 sides in a pentagon.

The pentagon is a polygon with five sides and five angles, just like other polygons including triangles, quadrilaterals, squares, and rectangles. There are several sorts of pentagon forms, including regular and irregular pentagons as well as convex and concave pentagons, depending on the sides, angles, and vertices.

We know that, for similar figures the length of the ratios of their corresponding segments are equal.

Thus,

NM/TS = ML/SR

4/7.2 = 5/x

Using cross multiplication we have:

4x = 5(7.2)

4x = 36

x = 9

Hence, the value of the segment SR for the given pentagons is 9 units.

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Answer:

1

Step-by-step explanation:

listing the factors of both numbers

factors of 10 are 1, 2, ,5, 10

factors of 3 are 1, 3

the only common factor to both is 1

the greatest common factor is 1

Answer:

{-3, -4}

Step-by-step explanation:

hope it will help you☺

Answer:

\( 65 \leqslant x \leqslant 100 \\ = 65\%\)

Answer:

The Greatest Common Factor (GCF) for 65 and 100, notation CGF(65,100), is 5.

Step-by-step explanation:

Explanation:

The factors of 65 are 1,5,13,65;

The factors of 100 are 1,2,4,5,10,20,25,50,100.

So, as we can see, the Greatest Common Factor or Divisor is 5, because it is the greatest number that divides evenly into all of them.

T/F Solution that can be analytically obtained but is not an actual answer to the equation often due to restrictions in the type of function such as a negative in the log

This statement is true.

Because, Sometimes, when solving an equation using analytical methods, we may arrive at a solution that is mathematically correct but is not a valid answer due to the restrictions in the type of function used.

For example, if a negative value appears in the logarithmic function, the solution may not be valid because the logarithmic function is only defined for positive values.

In such cases, we need to go back and recheck our work and take into account the restrictions of the function to arrive at a valid solution.

Sometimes when solving an equation analytically, the resulting solution may not be a valid answer due to restrictions in the domain of the function.

For example, if we solve an equation involving a logarithmic function, we may end up with a negative value inside the logarithm, which is not defined for real numbers. In such cases, the solution obtained analytically is not a valid answer to the equation.

Another example is when solving for the roots of a quadratic equation using the quadratic formula, we may obtain complex solutions even though we are only interested in real solutions.

Thus, it is important to always check the solutions obtained to ensure that they satisfy any domain or range restrictions of the functions involved in the equation.

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The probability that the random variable will assume a value greater than 290 is 0.1778.

Given that :

a = 50, b = 375 and m = 250.

The maximum is 375 and the minimum is 50.

Here the mode is 250.

The value of x = 290 is greater than the mode.

x greater than 290 means 290 < x < 375.

This is triangular distribution.

P(x > 300) = P(290 < x < 375)

                 =  \(2\int\limits^{375}_{290} {\frac{(375-x)}{(375-50)(375-250)} } \, dx\)

Now take the constant outside the integral.

P(x > 300) = \(\frac{2}{40625} \int\limits^{375}_{290} {(375-x)} \, dx\)

Integrating, we get (375x - x²/2).

Substitute the upper and lower limits.

P(x > 300) = 2/40625 {[(375)(375)-(375²/2)] - (375)(290)-(290²/2)]}

                 = 0.177846

Hence the probability is 0.1778.

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Answer:

2/5, a and b

Step-by-step explanation:

Answer:

Each dog got 4 cookies.

Answer:

D

Step-by-step explanation:

subsitute each of the x and y values for each of the equations and if they both equal each other It is correct.

Answer:

x = 2, y= -1

Step-by-step explanation:

12x - y = 25

9x + y = 17

add both equations to eliminate y

21x = 42

divide by 21

x = 42/21

x = 2

sub x in equation i to find y

12(2) - y = 25

24 - y = 25

-y = 1

therefore y = -1, x = 2

(-4 , 2 ) so x1 = -4 and y1 = 2. The slope is still 1/2 so m = 1/2. y = 1/2 x +4 final answer

The value of the expression is 4.

The code :

int a[4] = {1, 2, 3, 4};

int *p = a;

what is *(p + 3)?

The variable a is an array of integers, and the variable p is a pointer to the first element of the array.

The expression *(p + 3) is the value of the element of the array that is 3 elements after the element that p points to.

Since p points to the first element of the array, the expression *(p + 3) is the value of the fourth element of the array, which is 4.

Therefore, the value of the expression is 4.

Here is a breakdown of the code:

int a[4] = {1, 2, 3, 4}: This line declares an array of integers called a and initializes it with the values 1, 2, 3, and 4.

int *p = a; This line declares a pointer to an integer called p and initializes it with the address of the first element of the array a.

what is *(p + 3)?: This line asks what the value of the expression *(p + 3) is.

The expression *(p + 3) is the value of the element of the array that is 3 elements after the element that p points to.

Since p points to the first element of the array, the expression *(p + 3) is the value of the fourth element of the array, which is 4.

Therefore, the value of the expression is 4.

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Correct Question :

Int a[4]={1,2,3,4}, int *p=a. What is the value of *(p+3)?

Answer:

The probability that the laughter after one of the comedians jokes lasts for more than 7 seconds is approximately 0.474

Step-by-step explanation:

The nature of the distribution of the given data = Evenly distributed data

The range of the laughter times = Between 4 seconds and 9.7 seconds

The probability density function, f(x), is given as follows;

\(f(x) = \dfrac{1}{b - a}\)

The mean of the uniform distribution, μ, is given as follows;

\(\mu = \dfrac{a + b}{2}\)

The standard deviation, σ, is given as follows;

\(\sigma = \sqrt{\dfrac{\left (b - a\right)^2}{12} }\)

Where;

a = 4, and b = 9.7, we have;

μ = (4 + 9.7)/2 = 6.85

σ = √((9.7 - 4)²/12) ≈ 1.64545

The probability density function, f(x) = 1/(b - a) for a ≤ x ≤ b

∴ f(x) = 1/(9.7 - 4)

For P(x > 7), we have;

P(x > 7) = 1 - P(x < 7) = 1 - (7 - 4) × 1/(9.7 - 4) ≈ 0.474

The probability that the laughter after one of the comedians jokes lasts for more than 7 seconds P(x >7) ≈ 0.474.

Answer:

y = -4x + 9

Step-by-step explanation:

y = mx + b

First, we will find 'm', aka slope,

(\(y_{2}\) - \(y_{1}\) ) / (\(x_{2}\) - \(x_{1}\)) = m

(-7 -7)/ (4 - (-3)) = m

-14/ 7 = m

∴ m = -2

Then we can substitute m = -2 and point 1 in to find 'b', aka y-intercept,

7 = -2 (-3) + b

7 = 6 + b

7 - 6 = b

∴ b = 1

Hence the equation is,

y = -2x + 1

Answer:

whats your question im confused

Step-by-step explanation:

Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.

Given:

Octahedron has 8 faces

Let F be the faces of octahedron

Let V be the vertices of octahedron

we know that:

V + F = 14

Given F = 8 substitute

V + 8 = 14

V = 14 - 8

V = 6

Therefore Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.

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The shadow price for the labor time constraint will remain at -6, regardless of whether the right-hand-side decreases to 400 or not. So the answer is: It will remain at -6.

The labor time constraint has a shadow price of -6, which means that for every unit decrease in the right-hand-side (R.H. Side) of this constraint, the optimal objective function value will decrease by $6.

If the right-hand side for this constraint decreases to 400, the allowable decrease in the right-hand side is 300 (i.e., 700 - 400).

The allowable increase on the right-hand side is also 300. Since the constraint has been solved to optimality, any change in the right-hand side within the allowable range will not change the optimal solution.

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Answer:

z=97 x=21

Step-by-step explanation:

so straight angles always equal 180°

And assuming that your lines are parallel, the angle under angle z should be 83° just like the angle above angle z

There for to solve for x, first subtract 83 from 180 because that's what that angle is equal to.

Now that you have the equation 4x+13 and you know that it's equal to 97 you can solve it just like a normal inequality.

4x+13=97

4x=84

x=21

Answer:

262,576.28

Step-by-step explanation:

35,000(1+.065)^32

To calculate the annual payment required to pay off a five-year, $25,000 loan at an interest rate of 3.50 percent EAR, we can use the formula for calculating the equal annual payment for an amortizing loan.

The formula is: A = (P * r) / (1 - (1 + r)^(-n))

Where: A is the annual payment,

P is the loan principal ($25,000 in this case),

r is the annual interest rate in decimal form (0.035),

n is the number of years (5 in this case).

Substituting the given values into the formula, we have:

A = (25,000 * 0.035) / (1 - (1 + 0.035)^(-5))

Simplifying the equation, we can calculate the annual payment:

A = 6,208.61

Therefore, the annual payment required to pay off the five-year, $25,000 loan at an interest rate of 3.50 percent EAR is $6,208.61.

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The value of the given expression 105 times 3 is equal to 315.

Calculation of the expression 105 times 3 is equal to :

  1

1 0 5

×    3

3 1 5

Therefore, the calculated value of the expression 105 times 3 is equal to 315.

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Answer:

The least common multiple 150 is a product of common & odd prime factors between the integers which is divisible by each one an integer of this same group.

Answer:

150

Step-by-step explanation:

25*6=150

10*15=150

30*5=150

Answer:

\(y = -\frac{1}{2} x + 3\)

Step-by-step explanation:

Perpendicular lines have a negative reciprocal gradient to the original line. This means you have to make the gradient negative and flip the original fraction.

The original gradient is 2 (which can be written 2/1), so the reciprocal is 1/2 and made negative it is -1/2.

Put this into the equation using form y = mx +c to get y = -1/2x + c.

To work out c, substitute the values of x and y given in the point:

5 = -1/2(-4) + c

5 = 2 + c

c = 3

Therefore, the equation for the perpendicular is:

\(y = -\frac{1}{2} x + 3\)

The size of the city at the beginning of 2003 is 16,261. The population of the city will reach 14,166,171 in the year 2062.

(a) To find the size of the city at the beginning of 2003, we need to calculate the population after 26 years of growth. Since the city has been growing at a rate of 8% per year, we can use the formula for compound interest to calculate the population:

Population = Initial Population * (1 + Growth Rate)^Number of Years

Substituting the given values into the formula, we get:

Population = 6,506 * (1 + 0.08)^26 = 16,261

Therefore, the size of the city at the beginning of 2003 is 16,261.

(b) To determine the year when the population of the city will reach 14,166,171, we need to find the number of years it takes for the population to grow from 6,506 to 14,166,171 at a growth rate of 8% per year. Again, we can use the compound interest formula and solve for the number of years:

14,166,171 = 6,506 * (1 + 0.08)^Number of Years

Dividing both sides of the equation by 6,506 and taking the logarithm, we can solve for the number of years:

log(14,166,171 / 6,506) / log(1 + 0.08) ≈ 50.56

Therefore, the population of the city will reach 14,166,171 in approximately 50.56 years. Since the population growth is counted from the beginning of 1977, we need to add this to find the year:

1977 + 50.56 ≈ 2062

Thus, the population of the city will reach 14,166,171 in the year 2062.

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Answer:

12 ft

Step-by-step explanation:

Hi there!

1) Find the length of the other leg in the right triangle

There are two ways we can go about this. The first way is to use trigonomic ratios:

We're given one of the legs and we're trying to solve for the other, so we can use the tangent ratio:

\(tan\theta=\frac{opp}{adj}\)

Let x be equal to the length of the other leg. Plug in the known values:

\(tan45=\frac{x}{7}\\7*tan45=x\\x=7\)

The other way to find this is to observe the angles. Because we're given that two of the angles are 45 and 90 degrees, we know that the third angle is 45 degrees. This makes this an isosceles triangle, meaning the other leg is 7 ft long.

2) Determine the height of the hoop

Add 7 ft and 5 ft (the person's height):

7+5=12 ft

I hope this helps!

Answer:

x = 2

Step-by-step explanation:

Hope this helps, have a good day

The reasonable estimate of the  probability that it is sunny tomorrow is option D: 25%

The concept of probability is determining the chance or likelihood of a certain event occurring. When we lack certainty regarding the result of a happening, we can discuss the chances of particular consequences, which denote their level of probability. The value of probability is one that ranges form  0-1

From the graph,

Total numbers of days of weather = days of weather that is  sunny + days of weather that is rainy + days of weather that is snowy

= 3 + 5 + 2 + 2 = 12

So, the probability of days of weather to be sunny + 3.12 = 1/4

= 0.25

Hence there is a 25 % chance that the weather will be sunny.

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The following bar graph summarizes the weather conditions in Crayonton for each day this month so far. Based on this data, what is a reasonable estimate of the probability that it is sunny tomorrow? Choose the best answer.

a 14

b 17

c 21

d 25

Answer:

A single number that estimates the value of an unknown parameter is called a point estimate.

Step-by-step explanation:

Don't see the point (haha) of elaborating

Answer:

7 and 5

Step-by-step explanation:

Answer:

I think it means to take the measurements  of the bigger trash bin and turn it into the scale of 0.75