What is the value of the following expression?
2 + [(15 + 3) × 2]

The volume of cone as per given figure is 314cm³.

The following mathematical operation must be carried out in order to determine a cone's volume: V = Π(h/3)r². The surface area of the circular portion of a cone is simply πr2. The lateral face wrapping around this base is calculated as πrl, or if you aren't given the slant height, you can use the formula πr√(r2+h2).

To calculate the volume of a cone, we apply the following formula:

, where V = volume

h = height

r = radius

π = pi

(h = height of cone, r= radius of cone)

Given:

Height of cone = 12 cm

Radius of cone = 5 cm

Volume of cone, V =  3.14 * (12/3 )* 5* 5

= 3.14 * 20 * 5

= 3.14 * 100

= 314 cm³

Therefore, The volume of cone as per given figure is 314cm³.

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The slope of the line tangent to the curve y³-xy²+x³=5 at the point (1,2) is option (B) 1/8.

To find the slope of the line tangent to the curve at the point (1,2), we first need to find the derivative of the curve with respect to x, and then evaluate it at x=1, y=2.

Taking the derivative of both sides of the equation y³-xy²+x³=5 with respect to x using the product rule, we get

3y²(dy/dx) - y² - 2xy(dy/dx) + 3x² = 0

Simplifying this expression and solving for dy/dx, we get:

dy/dx = (y² - 3x²)/(3y² - 2xy)

Substituting x=1 and y=2, we get:

dy/dx = (2² - 3(1)²)/(3(2)² - 2(1)(2))

dy/dx = (4 - 3)/(12 - 4)

dy/dx = 1/8

Therefore, the correct option is (B) 1/8

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Answer:

The answer for the Area is 8

Step-by-step explanation:

Area of semi circle =1/2pir²

r=d/2=8/2=4

A=1/2×4²

A=1/2×4×4

A=2×4

A=8

Answer:

32 or 100.53

Step-by-step explanation:

*assuming 8 is radius and not diameter*

A = [tex]r^{2}[/tex]

r = 8

[tex]8^{2} = 64[/tex]

A = 64 or ≈201.062

divide by 2 for half of the circle

32 or 100.53

The given figure is a hexagonal pyramid and it has 7 faces, 7 vertices, and 12 edges. The correct option is c)

A hexagonal pyramid is a three-dimensional geometric figure that has a hexagonal base and triangular faces that meet at a common vertex. It is also known as a hexagonal pyramid or a hexagonal pyramid.

According to the given information:

The given shape is a Hexagonal pyramid

Here are the characteristics of a hexagonal pyramid:

Faces: 7 (1 hexagonal base and 6 triangular faces)

Vertices: 7 (1 common vertex where all the triangular faces meet and 6 vertices on the hexagonal base)

Edges: 12 (6 edges on the hexagonal base and 6 edges connecting the base to the common vertex)

So, a hexagonal pyramid has 7 faces, 7 vertices, and 12 edges.

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The equation that shows the relationship is w = 38m.

If Mrs. Lopez types at a constant rate, then the number of words she types is directly proportional to the amount of time she types. We can express this relationship using the formula:

w = km

where w is the number of words typed, m is the number of minutes spent typing, and k is the constant of proportionality.

We are given that k = 38, so we can substitute this value into the formula to get:

w = 38m

Therefore, the equation that shows the relationship between the number of words Mrs. Lopez types and the number of minutes she types is w = 38m.

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We can see here that the amplitude of the function is: A. 3.

The amplitude of a function is the measure of its maximum deviation from its central value. In simpler terms, it is the height of a wave or the distance from the center line to the peak or trough of a function.

For example, in a sine wave, the amplitude is the distance from the center line (or zero) to the highest point of the wave. In mathematical terms, if f(x) is a periodic function with period T, then the amplitude A of f(x) is given by:

A = (f(x)_max - f(x)_min)/2

where f(x)_max and f(x)_min are the maximum and minimum values of f(x) over one period.

Max = 4

Min = -2

A = [4 - (-2)]/2 = 6/2 = 3

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Answer:

82 and 95

Step-by-step explanation:

Most repeated

Answer:

y + 21 = - 4(x - 7)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, - 21 ) and (x₂, y₂ ) = (- 4, 23 )

m = [tex]\frac{23-(-21)}{-4-7}[/tex] = [tex]\frac{23+21}{-11}[/tex] = [tex]\frac{44}{-11}[/tex] = - 4

using (a, b ) = (7, - 21 ) , then

y - (- 21) = - 4(x - 7) , that is

y + 21 = - 4(x - 7)

In the given triangle, using the law of Cosines, the value of angle θ is 103°

From the question, we are to calculate the value of angle θ in the diagram.

From the given diagram,

We have a triangle ABC with given side lengths

From the given information,

a = 42 cm

b = 78 cm

c = 57 cm

From the law of Cosines, we have that

cos B = (a² + c² - b²)/2ac

Thus,

cos θ = (a² + c² - b²)/2ac

Substitute the parameters

cos θ = (42² + 57² - 78²)/2(42)(57)

cos θ = (1764 + 3249 - 6084) / (4788)

cos θ = -1071/4788

θ = cos⁻¹(-1071/4788)

θ = 102.9255

θ ≈ 103°

Hence, the value of θ is 103°

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The 95% confidence interval for the population proportion of student loan borrowers with loans totaling more than $20,000 is approximately (0.3235, 0.3765).

To construct a 95% confidence interval for the population proportion of student loan borrowers with loans totaling more than $20,000, we need to calculate the sample proportion, standard error, and critical value.

1. Sample proportion (p) = Number of students with loans over $20,000 / Total sample size
p = 448 / 1280 ≈ 0.35

2. Standard error (SE) = √(p * (1 - p) / n)
SE ≈ √(0.35 * (1 - 0.35) / 1280) ≈ 0.0135

3. For a 95% confidence interval, we use a critical value (z) of 1.96.
Margin of error (ME) = z * SE
ME ≈ 1.96 * 0.0135 ≈ 0.0265

4. Calculate the confidence interval:
Lower limit = p - ME ≈ 0.35 - 0.0265 ≈ 0.3235
Upper limit = p + ME ≈ 0.35 + 0.0265 ≈ 0.3765

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The area of the given circle is 616 sq.cm.

The volume of rectangular prism is 416 mm³

A circle is a particular type of ellipse when the eccentricity is zero and both foci are present. The locus of points drawn equally apart from the centre is also referred to as a circle. The radius of a circle is the separation between its centre and its periphery. The circle's diameter, which is equal to twice its radius, is the line that splits the circle into two equal pieces.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m², cm², etc.

Area of Circle = πr² or πd²/4, square units

where π = 22/7 or 3.14

according to question,

Area = pi times the radius squared

A = pi * r²

A = 22/7 * 14²

A = 22/7 * 196

A = 4,312 / 7

A = 616 sq. cm.

V = l*w*h

To determine the volume, multiply all three dimensions together.

For Connexus users Rectangular prisms and volume quiz part 2:

l * w * h = 8 * 5 * 10.4 = 416

the volume of rectangular prism is 416 mm³

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The percentage of Container B that is full after the pumping is complete is 77.2%.

To find the percentage of Container B that is full after the water from Container A is pumped into it, we first need to find the volume of both containers.

The volume V of a cylinder can be calculated using the formula:

V = πr²h

Volume of Container A (V A) = π x (10^2) x 20 = 2000π cubic feet

Volume of Container B (V B) = π x (12^2) x 18 = 2592π cubic feet

Percentage = (V A / V B) x 100

Percentage = (2000π / 2592π) x 100

Percentage = (2000 / 2592) x 100 = 77.1604938

To the nearest tenth, the percent of Container B that is full after the pumping is complete is approximately 77.2%.

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First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:

[tex]\text{C}=2\pi \text{r}[/tex]

If we substitute 175 ft for [tex]\text{r}[/tex] and use 3.14 to approximate [tex]\pi[/tex] we get a circumference of:

[tex]\text{C}=2\times3.14\times175 \ \text{ft}[/tex]

[tex]\text{C}=6.28\times175 \ \text{ft}[/tex]

[tex]\text{C}=1099 \ \text{ft}[/tex]

We can now convert the circumference in feet to inches:

[tex]1099 \ \text{ft}\times \dfrac{12 \ \text{in}}{1 \ \text{ft}} \implies[/tex]

[tex]1099\times12 \ \text{in}\implies[/tex]

[tex]=13188[/tex]

To find how many flowers we need we can divide the circumference in inches by the 3 inches between flowers giving:

[tex]13188 \ \text{in}\times\dfrac{1 \ \text{flower}}{3 \ \text{in}}\implies[/tex]

[tex]13188 \ \text{in}\times\dfrac{1 \ \text{flower}}{3 }\implies[/tex]

[tex]\dfrac{13188 \ \text{flower}}{3 }\implies[/tex]

[tex]=4396 \ \text{flower}[/tex]

You would require 4,396 flowers

The expression representing the width of the garden is given as follows:

6w + 2.

An equivalent expression is given as follows:

2(3w + 1).

The width of the rectangle is represented as follows:

w.

Six times the width of the rectangle is represented as follows:

6w.

Two feet plus six times the width of the rectangle is represented as follows:

6w + 2.

6 = 2 x 3, hence the simplified expression can be given as follows:

2(3w + 1).

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Answer:

it is 12 percent

Step-by-step explanation:

your welcome

Programming languages, including Python, you can use the print() function to output the value of a variable to the screen.

To output the value of the variable x, you would write:

print(x)

The current value of the variable x in the console or terminal window.

If you want to include additional text in the output, you can concatenate it with the variable using the string concatenation operator "+" in Python like this:

print("The value of x is: " + str(x))

"The value of x is: " is a string of text that will be displayed before the value of x.

The str() function is used to convert the value of x to a string, so that it can be concatenated with the other text.

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The arithmetic sequence is 49 x 4 = 196,  94 x 6 = 564.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

1. 76 x 8 = 608

2. 84 x 9 = 756

3. 68 x 4 = 272

4. 32 x 6 = 192

PART 2

5. 59 x 7 = 413

6. 74 x 8 = 592

7. 68 x 8 = 544

8. 95 x 9 = 855

9. 84 x 5 = 420

10. 22 x 4 = 88

11. 48 x 5 = 240

12. 84 x 8 = 672

13. 76 x 9 = 684

14. 89 x 9 = 801

15. 63 x 5 = 315

16. 32 x 9 = 288

17. 63 x 8 = 504

18. 79 x 9 = 711

19. 78 x 5 = 390

20. 49 x 4 = 196

21. 94 x 6 = 564

Therefore, The arithmetic sequence is 49 x 4 = 196,  94 x 6 = 564

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The probability that a randomly selected adult has an IQ score between 89 and 121 is 0.5328

To find the probability that a randomly selected adult has an IQ score between 89 and 121, we need to calculate the area under the normal curve between these two scores.

First, we need to standardize the scores by converting them into z-scores using the formula

z = (x - μ) / σ

where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For x = 89

z = (89 - 105) / 20 = -0.8

For x = 121

z = (121 - 105) / 20 = 0.8

Now, we need to find the area under the normal curve between z = -0.8 and z = 0.8. We can do this by using a standard normal distribution table or a calculator.

The area under the curve between z = -0.8 and z = 0.8 is 0.5328.

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The given question is incomplete, the complete question is:

Assume that adults have iq scores that are normally distributed with a mean of 105 and a standard deviation of 20. Find the probability that a randomly selected adult has an iq between 89 and 121.

A scatter plot is a graphical representation of a set of data points that displays the relationship between two variables.

How to solve the question?

The plot uses a Cartesian coordinate system, with one variable plotted on the x-axis and the other on the y-axis. Each data point is represented by a dot, with its location on the plot determined by its values for the two variables. The pattern of the dots on the plot gives insight into the relationship between the two variables.

Scatter plots are useful for visualizing the strength and direction of a relationship between two variables. A positive relationship between the variables means that as one variable increases, the other variable also increases. In contrast, a negative relationship means that as one variable increases, the other variable decreases. A scatter plot can also help to identify any outliers or unusual data points.

Scatter plots can be used to analyze many types of data, including scientific data, financial data, and social data. They can be used to identify trends, correlations, and patterns that might not be immediately apparent from a simple numerical analysis of the data. Scatter plots are a valuable tool for data analysis and visualization, and are widely used in scientific research, data analysis, and data-driven decision making.

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We can simplify the expression by distributing the 2 and combining like terms:

-3.75 + 2(-4x + 6.1) - 3.25x

= -3.75 - 8x + 12.2 - 3.25x (distributing the 2)

= -11.75 - 11.25x (combining like terms)

Therefore, any expression that simplifies to -11.75 - 11.25x is equivalent.

Possible equivalent expressions are:

-3(-3.92x + 3.917)

-11.75 - 11.25(x+1)

-11.75 - 9x - 2.25x

-1.5(-15 + 9x)

11.25x - (11.75 + 2(-3.75))

Note that there are many other possible expressions that are equivalent to -3.75+ 2(-4x +6.1) - 3.25x, but the key is that they all simplify to the same value of -11.75 - 11.25x.

The nth term of the sequence as:  an =  {  4 (n - 1) if n is odd

1 if n is even and n ≠ 4   8/2n when n = 4

An arithmetic progression is a list of numbers where each term is obtained by adding a specific number to the previous term, except for the first term. The following formulas help  solve arithmetic progression problems: AP common difference: d = an - an-1. AP nth term: an = a (n -1)d

Sum of n terms of  AP: Sn = n/2 (2a (n - 1)d)

The given sequence is 4, 5/3, 6/5, 1, 8/9.

 To find the expression for the nth term, we must observe the pattern of the sequence. We  see that the numerators of the series fractions increase by 1 for each term, while the denominators increase by 2 for each term except  the fourth term, which is 1.  Therefore, we can write the nth term of the sequence as:

an =  {  4 (n - 1) if n is odd

1 if n is even and n ≠ 4

8/2n when n = 4

where n is a positive integer representing the position of the term in the sequence.

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The match of the given defines are any measure representing the center of a set of data arranged in a decreasing or increasing order of magnitude is Measure of central tendency, Commonly referred to as the average of all values is Mean, Middle value in the set of data arranged in increasing or decreasing order is Median, Contains two modes is Bimodal, Most frequently occurring score is Mode.

The identified match from the box to the given defines are the mean is the sum of all values divided by the total number of values. The median is the middle value when data is arranged in order.

The mode is the value that appears most frequently in a set of data. Bimodal refers to a distribution that has two modes. Finally, measure of central tendency refers to any method used to represent the center of a set of data.

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--The given question is incomplete, the complete question is given

" identify the following defines. and choose from below box:

mean, mode, median, measure of central tendency, bimodal

1. ) Any measure representing the center of a set of data arranged in a decreasing or increasing order of magnitude.

2. ) Commonly referred to as the average of all values.

3. ) Middle value in the set of data arranged in increasing or decreasing order.

4. ) Contains two modes.

5. ) Most frequently occurring score.

pls answer my grade dropped to 75 last grading pls answer correctly​"--

Since the number of men must be a whole number, we can round it up to 267. Therefore, there were initially 267 men in the fort before the reinforcement arrived.

Let's solve this problem step-by-step:

1. Initially, the fort is provisioned for 42 days.
2. After 10 days, a reinforcement of 200 men arrives.
3. With the additional men, the remaining food will now last for 24 days.

Let x represent the initial number of men in the fort.

Since the fort was provisioned for 42 days initially, we can write an equation for the total amount of food:

Total food = x men * 42 days

After 10 days, 200 men arrive and the remaining food lasts for 24 days:

Remaining food = (x + 200) men * 24 days

Since the total food and remaining food are equal, we can set the two equations equal to each other:

x * 42 days = (x + 200) * 24 days

Now, let's solve for x:

42x = 24x + 4800

Subtract 24x from both sides:

18x = 4800

Divide both sides by 18:

x = 266.67

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.

Answer:

Sydney’s age is 45 & Devaughn's age is 33

Step-by-step explanation:

D= Devaughn

S= Sydney

D+S= 78

S-12=D

(S-12)+S=78

2S=90

S=45

D=33

Answer:

2. Yes, there are potential problems with Kiran's study. The first group consists of the first 25 people who turned in the signed form. This means that the first group may not be representative of the entire population of 50 people. For example, if the first 25 people who turned in the signed form are all from a particular demographic group, then the results of the study may not be generalizable to the entire population.

3. It is important to randomly assign people to groups in an experimental study because it helps ensure that the groups are similar in all respects except for the studied variable. This helps reduce the impact of confounding variables and increases the study's internal validity. Random assignment also helps to ensure that any differences between the groups are due to chance rather than systematic differences between the groups.

Step-by-step explanation:

Answer:

2. Yes, Kiran's study does have possible flaws, indeed. The first 25 people who submitted the signed form are in the first group. This indicates that the first group might not be typical of the total 50-person population. The study's findings might not apply to the entire population, for instance, if the first 25 persons to submit a signed form are all from the same demographic group.

3. In this experimental study, it's crucial to divide participants into groups at random since it helps to ensure that the groups are comparable in all regards outside the studied variable. This raises the study's internal validity and lessens the effect of confounding variables. Also, random assignment makes sure that any discrepancies between the groups are the result of chance, rather than deliberate divisions.

Answer: 350

Step-by-step explanation:

First, 32% divided by 100 becomes a decimal.

     32% / 100 = 0.32

Next, let x be equal to a number.

Then, "of" indicates multiplication and "is" indicates equals.

     0.32x = 112

Lastly, we will divide both sides of the equation by 0.32.

     x = 350

This problem can be represented by turning 32% into a decimal and rewriting it like this: .32x = 112, where x is the unknown number. Dividing both sides of the equation by .32 gives you x = 350, so 32% of 350 is 112

This method is unlikely to give an accurate estimate of the percentage since it chooses only 5 customers from a small sample size, which may not be representative of the entire population of customers.

In statistical terms, the sample size of 5 is considered very small and may not be large enough to capture the variability in customers' preferences. A larger sample size would increase the precision and accuracy of the estimate of the percentage of customers who would buy a new flavor.

A small sample size may lead to unreliable estimates and may not be representative of the population, highlighting the importance of using appropriate sample sizes in statistical analysis.

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The value of x in the regular polygon is 15.4.

The value of x is calculated as follows;

The sum of the interior angles of a polygon with n sides is given by the formula;

(n-2) x 180

Since the regular polygon in question can be decomposed into 46 triangles, it has 46 x 3 = 138 sides.

The value of each interior angle is calculated as;

= (n - 2) x 180 / n

= (138 - 2) x 180 / 138

= 169.6⁰

9.5x + 26.2 = 169.6

9.5x = 143.4

x = 15.1

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For the given expressions f(x) and g(x), the simplified expression is f(-5) = 90 and g(2) = -11.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to produce a value. Expressions can be simple, like 2 + 3, or complex, like (5x² + 3) / (x - 1). Expressions can also include functions, trigonometric functions, logarithms, and more. The value of an expression depends on the values of the variables involved and the operations performed.

To find f(-5), we simply substitute -5 for x in the expression for f(x) and simplify:

f(-5) = 3(-5)² - 3(-5) = 3(25) + 15 = 90

Therefore, f(-5) = 90.

To find g(2), we substitute 2 for x in the expression for g(x) and simplify:

g(2) = -4(2) - 3 = -8 - 3 = -11

Therefore, g(2) = -11.

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