a. The cost of renting the gym and paying for supplies, which is $300. b. $10, c. y = 10x - 300 d. $200 e. 30 tickets f. the slope of the line is 1/6.
Describe Linear Equation?The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate. It represents the rate of change of the line. A positive slope indicates that the line is increasing, while a negative slope indicates that the line is decreasing. A slope of zero indicates that the line is horizontal.
The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is equal to zero.
Linear equations can be solved algebraically or graphically. In algebra, the goal is to isolate the variable and find its value. In graphing, the equation is plotted on a coordinate plane and the solution is the point where the line intersects with the x- or y-axis.
a. The constant in this situation is the cost of renting the gym and paying for supplies, which is $300.
b. The rate in this situation is the cost per ticket, which is $10.
c. Let x be the number of tickets sold and y be the total profit. The linear equation that represents this situation is:
y = 10x - 300
d. If Amanda sells 50 tickets, then the profit is:
y = 10(50) - 300 = $200
e. To break even, the profit must be 0. So we can set y = 0 and solve for x:
0 = 10x - 300
10x = 300
x = 30
Therefore, Amanda needs to sell 30 tickets to break even.
f. The graph of the linear equation is:
graph{y=10x-300 [-10, 50, -500, 500]}
To calculate the slope of a line that goes through points (10, 6) and (-2, 4), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
slope = (4 - 6) / (-2 - 10) = -2 / -12 = 1/6
Therefore, the slope of the line is 1/6.
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in the number 240.149, how does the value of the 4 in the hundredths place compare to the value of the 4 in the tens place?
The 4 in the hundredths place has a smaller value than the 4 in the tens place.
In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.
In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.
Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.
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any process that generates well-defined outcomes is . a. an event b. an experiment c. a sample point d. a probability
Every procedure that produces predictable results is considered an experiment, and the sample space (S) for an experiment is the collection of all possible results.
What does probability mean in its simplest form?The possibility or chance that a particular occurrence will occur is expressed numerically as a probability. Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range.
What is probability research, exactly?Probability theory, a branch of mathematics, is concerned with the study of random events. A random occurrence can take on any number of distinct shapes, but its conclusion cannot be predicted before it occurs. The way things came out is thought to have been influenced by chance.
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The figure below is made of 2 rectangular prism.
What is the volume of this figure?
Total volume of the shape is 124 cm³
What is a cuboid?A cuboid is a three-dimensional solid shape that has six rectangular faces or sides, where each face meets at a right angle with its adjacent faces.
The formula for the volume of a cuboid is:
Volume = Length x Width x Height
So, the Volume of first cuboid = 3 × 4 × 5 = 60 cm³
and the Volume of second cuboid = 2 × 4 × 8 = 64 cm³
Total volume of the shape = Volume of first cuboid + Volume of second cuboid
Total volume of the shape = 60 cm³ + 64 cm³
Total volume of the shape = 124 cm³
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a cylindrical tank with radius m is being filled with water at a rate of . how fast is the height of the water increasing?
The height of the water is increasing at the rate of 3 meters per minute.
We know that a cylindrical tank with radius r and height h has a volume of V = πr²h.
The rate at which the water is being filled in the tank is given as dV/dt = 2πr²( dh/dt).
On rearranging the above equation we get dh/dt = (dV/dt) ÷ (2πr²)
Given: Radius of the cylindrical tank, r = 3 m
Rate at which the water is being filled,
dV/dt = 54π cubic meters per minute.
we
Height of the cylindrical tank, h = ?
We need to find out how fast is the height of the water increasing.
This can be calculated using the formula.
dh/dt = (dV/dt) ÷ (2πr²)
Substitute the values of dV/dt and r in the above formula,
we get,
dh/dt = (54π) ÷ (2π x 3²)
dh/dt = 54/18
dh/dt = 3 m/min
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a bond is worth 100$ and grows in value by 4 percent each year. f(x) =
To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).
Help me with the even numbers. 2,4,6,and8
2= 2
4=10
i cant see 6 or 8
PLEASE HELP ASAP!!!!!!!!!!!!!!
Rewrite each of the following expressions without using absolute value
1.|x-1| if x>1
2. |x-y| if x>y
3. |3-[tex]\sqrt{4}[/tex]
4. |4r -12| if r<3
5. |[tex]\sqrt{15} -5+1[/tex]
6. |4-[tex]\sqrt{7}[/tex]
7. |7m-56| if m<8
8. |z-7|-|z-9| if z<7
Answer:
1 4(3-r) or 12-4r
2. 7( 8-m) or 56-7m
3. -2
Step-by-step explanation:
1) |4r−12| , if r<3
|4r-12|
Factor out a 4
4|r-3|
|r-3| will be less than 0 since r is less than 3
So we can rewrite it as 3-r to remove the absolute value signs and make it positive
4 (3-r)
12 -4r
2. |7m–56| , if m<8
Factor out a 7
7| m-8|
|m-8| will be less than 0 since m is less than 8
So we can rewrite it as 8-m to remove the absolute value signs and make it positive
7( 8-m)
56-8m
3) |z−7|−|z−9| , if z<7
|z-7| will be less than 0 since z is less than 7 and |z-9| will be less than 0 since z is less than 7
So we can rewrite it as 7-z and 9-z to remove the absolute value signs and make it positive
7-z - (9-z)
Distribute the minus sign
7-z-9+z
-2
an open rectangular gutter is made by turning up the sides of a piece of metal 20 in wide. the area of the cross section of the gutter is 50 in^2 find the depth of the gutter
Three divided by six hundred twenty two (remainder included
the answer is 207 Remainder 1
he square quilt block shown is made from nine unit squares, some of which have been divided in half to form triangles. what fraction of the square quilt is shaded? express your answer as a common fraction.
To find the fraction of the square quilt block that is shaded, we need to count the number of shaded unit squares and divide it by the total number of unit squares in the quilt block. Let us begin by counting the number of shaded unit squares.
We notice that there are a total of 6 unit squares that are shaded. The unit squares that are shaded are the 2 squares that are completely shaded and the 4 squares that are half shaded due to the presence of triangles.
Next, we need to count the total number of unit squares in the quilt block. We notice that the quilt block is made up of 9 unit squares, each of which can be divided into 4 smaller unit squares. Thus, the total number of unit squares in the quilt block is 9 x 4 = 36.
Therefore, the fraction of the square quilt block that is shaded is 6/36 or 1/6.
To summarize, the shaded portion of the quilt block consists of 6 unit squares out of a total of 36 unit squares. Thus, the fraction of the square quilt block that is shaded is 1/6.
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Find the HEIGHT of a cylinder if the volume is 1607 and the radius is 4.
Answer:
Step-by-step explanation:
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
We are given that V = 1607 and r = 4. We can plug these values into the formula and solve for h:
1607 = π(4^2)h
1607 = 16πh
h = 1607/(16π)
h ≈ 25.5
Therefore, the height of the cylinder is approximately 25.5 units. Note that we rounded the answer to one decimal place since the radius was given to one decimal place.
Determine whether it is possible to find values of L 0 so that the given boundary-value problem has precisely one nontrivial solution, more than one solution, no solution, and the trivial solution. (Let k represent an arbitrary integer. If an answer does not exist, enter DNE.) y" + 16y=0, y(0)= 1, y(L) = 1 (a) precisely one nontrivial solution (b) more than one solution (c) no solution (d) the trivial solution
There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
We are given the boundary-value problem:
y" + 16y = 0, y(0) = 1, y(L) = 1
The characteristic equation is r^2 + 16 = 0, which has roots r = ±4i.
The general solution to the differential equation is then y(x) = c1cos(4x) + c2sin(4x).
Using the boundary conditions, we get:
y(0) = c1 = 1
y(L) = c1cos(4L) + c2sin(4L) = 1
Substituting c1 = 1 into the second equation, we get:
cos(4L) + c2*sin(4L) = 1
Solving for c2, we get:
c2 = (1 - cos(4L))/sin(4L)
Thus, the general solution to the differential equation that satisfies the given boundary conditions is:
y(x) = cos(4x) + (1 - cos(4L))/sin(4L)*sin(4x)
Now, we can answer the questions:
(a) To have precisely one nontrivial solution, we need the coefficients c1 and c2 to be uniquely determined. From the above expression for c2, we see that this is only possible if sin(4L) is nonzero. Thus, if sin(4L) ≠ 0, there exists precisely one nontrivial solution.
(b) If sin(4L) = 0, then c2 is undefined and we have a family of solutions that differ by a constant multiple of sin(4x). Hence, there are infinitely many solutions.
(c) There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.
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A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation
The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25
Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.
The amount of medicine in the 10 grams of 15% solution is
0.15 × 10 = 1.5 grams
The amount of medicine in the 25 grams of 10% solution is
0.10 × 25 = 2.5 grams
So the total amount of medicine in the original mixture is,
1.5 + 2.5 = 4 grams
Now let x be the amount of pure medicine added.
The total amount of medicine in the final mixture is,
4 + x
The total amount of solution in the final mixture is,
10 + 25 + x
So the concentration of the final mixture is,
(4 + x) / (10 + 25 + x)
We know that this concentration is 25%, so we can write:
(4 + x) / (10 + 25 + x) = 0.25
This is the equation that represents the situation.
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The given question is incomplete, the complete question is:
A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation
What is the value of y in the solution to the system of equations?
²x+y=1
-X
2x - 3y = -30
-8
-3
3
O 8
So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75. As a result, the answer is y = 31/4.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
the system of equations,
[tex]y = 1 - 2x\\2x - 3(1 - 2x) = -30\\2x - 3 + 6x = -30\\8x = -27\\x = -27/8\\2(-27/8) + y = 1\\-27/4 + y = 1\\y = 1 + 27/4\\y = 31/4[/tex]
So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75.
As a result, the answer is y = 31/4.
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The third term of a sequence is 14. Term to term rule is square, then subtract 11. Find the first term of the sequence
The third term of a sequence is 14. Term to term rule is square, then subtract 11. The first term of the sequence is 6.
The given information is about the third term of a sequence which is 14, and the term to term rule is square, then subtract 11.
We have to find the first term of the sequence. The sequence can be calculated using the following formula:
An = A1 + (n-1)d
Where, An is the nth term of the sequence A1 is the first term of the sequence d is the common difference between the terms of the sequence. Let's solve the problem by finding the value of the common difference between the terms of the sequence.
Using the given information, we can write: A3 = 14=> A1 + (3 - 1)d = 14=> A1 + 2d = 14 ----- (i)
Also, the term to term rule is square, then subtract 11.So, we can write, A2 = A1 + d = (A1)² - 11 ---- (ii)
Substituting the value of d from equation (ii) in equation (i),
we get: A1 + 2 [(A1)² - 11] = 14 Simplifying this equation, we get: A1² - 2A1 - 12 = 0 On solving this quadratic equation
we get: A1 = -2 or A1 = 6 Ignoring the negative value of A1, we get the first term of the sequence to be 6.
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when we make inferences about one population proportion, what assumptions do we need to make? mark all that apply.
The data should come from a binomial distribution. There should be no non-response or other forms of bias. The sample size should not be more than 10% of the population size, and the sample should be independent of one another.
When making inferences about one population proportion, the following assumptions need to be made:
Option 1: The sample is a simple random sample from the population.
Option 2: The sample size should be large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
Option 3: The data comes from a binomial distribution.
Option 4: There is no non-response or other forms of bias.
Option 5: The sample size is no more than 10% of the population size.
Option 6: The sample is independent of one another.In order to make inferences about one population proportion, the assumptions mentioned above need to be made. It is vital to make sure that the sample is a simple random sample from the population, and that the sample size is large enough so that both np ≥ 10 and n(1 − p) ≥ 10.
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a manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 9 inches and standard deviation of 1 inches. if a sample of 50 items are chosen at random, what is the probability the sample's mean length is greater than 9.1 inches? round answer to
If a sample of 50 items are chosen at random. the probability that the sample mean length is greater than 9.1 inches is 0.0571, or 5.71%.
How to find the probability?The sample mean of the 50 items follows a normal distribution with mean equal to the population mean (μ), and standard deviation equal to σ/√n, where n is the sample size.
Substituting the given values, we have:
= μ = 9 inches
= σ/√n = 1/√50 inches
Now, we need to standardize the sample mean distribution to find the corresponding z-score using the formula:
z = (X- μX) / σX
Substituting the given values, we have:
z = (9.1 - 9) / (1/√50) = 1.58
The probability of getting a z-score of 1.58 or less is 0.9429. Therefore, the probability of getting a z-score of 1.58 or greater is:
P(z > 1.58) = 1 - P(z ≤ 1.58) = 1 - 0.9429 = 0.051
Therefore the probability that the sample mean length is greater than 9.1 inches is 0.0571.
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I'm learning probability in geometry but haven't learned it for percentage. Can someone help me?
Answer:
Step-by-step explanation:
a. 100 divided by 75 = 1.3333333333333333333333333333333
1.3333333333333333333333333333333 times 43 = 57.333333333333333333333333333332
round it to the nearest whole number: ≅ 57%
the shortest side of a triangle with angles 50o, 60o, and 70ohas length of 9 furlongs. what is the approximate length, in furlongs, of the longest side?
The longest side of a triangle with angles of 50°, 60°, and 70° and a length of 9 furlongs on the shortest side is approximately 12.2 furlongs.
What is the Law of Cosines?The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle are known (SAS) or the lengths of the three sides (SSS) are known.
To calculate this, using the Law of Cosines formula,
which is:
[tex]c^2 = a^2 + b^2 - 2abcosC[/tex]
where c is the longest side, a is the shortest side, b is the other side of the triangle, and C is the angle
between a and b.
In this case, c = 12.2 furlongs,
a = 9 furlongs,
b is the side opposite the angle 70°, and C = 70°.
So the formula becomes:
[tex]c^2 = 92 + b^2 - 2(9)(b)cos70^{o}[/tex]
Solving for b gives us b = 12.2 furlongs, which is the length of the longest side.
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16. A savings account was worth $1250 at the end of 2010 and worth $1306 at the end of 2011. The linear model
for the worth of the account is w = 56t+1250, where t is the number of years since the end of 2010.
Find an exponential model, in the form of w= a(b)', for the worth of the savings account. Round b to the
nearest thousandth.
How much greater is the worth predicted by the exponential model than predicted by the linear model at the
end of 2020? Round to the nearest cent.
An exponential model for the worth of the savings account is [tex]W = 1250(1.045)^t[/tex]
The worth predicted by the exponential model is greater than predicted by the linear model at the end of 2020 by $131.2.
What is an exponential function?In Mathematics, an exponential function can be modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.Based on the information provided about the savings account, we would determine the growth rate as follows;
[tex]W = P_{0}e^{rt}[/tex]
Growth rate, r = 1/(1 - 0)ln(1250/1306)
Growth rate, r = ln(1250/1306)
Growth rate, r = 0.0438
In the form [tex]W = a(b)^t[/tex], the required exponential function is given by;[tex]W = 1250(1.045)^t[/tex]
Years = 2020 -2010 = 10 years.
From the linear function, we have:
W = 56t + 1250
W = 56(10) + 1250
W = $1,810.
From the exponential function, we have:
[tex]W = 1250(1.045)^t\\\\W = 1250(1.045)^{10}[/tex]
W = $1,941.2
Difference = $1,941.2 - $1,810
Difference = $131.2.
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A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points)
Answer:
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given the diameter of both the cylinder and the cone is 8 inches, the radius is 8/2 = 4 inches.
The volume of the cylinder is Vcyl = π(4)²(3) = 48π cubic inches.
The formula for the volume of a cone is V = (1/3)πr²h.
The volume of the cone is Vcone = (1/3)π(4)²(18) = 96π/3 = 32π cubic inches.
Therefore, the relationship between the volume of the cylinder and the cone is that the volume of the cone is exactly two-thirds of the volume of the cylinder.
We can see this by dividing the volume of the cylinder by the volume of the cone:
Vcyl/Vcone = (48π) / (32π) = 3/2
So, the volume of the cylinder is 1.5 times greater than the volume of the cone.
a local county has an unemployment rate of 4%. a random sample of 19 employable people are picked at random from the county and are asked if they are employed. round answers to 4 decimal places.
The probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
We need to calculate the probability that exactly 8 of the 19 people in the random sample are employed. The probability of a single person being employed is 4%, or 0.04.
To calculate the probability of 8 people being employed out of the 19, we can use the binomial distribution formula:
P(X=8) = nCx * (p^x) * (1-p)^(n-x) Where n = 19, x = 8, p = 0.04, and 1-p = 0.96
So, P(X=8) = 19C8 * (0.04^8) * (0.96^11) = 0.2793 or 27.93%.
Therefore, the probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.
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in a causal study of the effect of shelf placement on sales of a brand of cereal, which is the dependent variable? group of answer choices where the cereal was placed on the shelf sales of the cereal concomitant variation of the cereal none of the above
A causal study is a study that seeks to determine whether one variable causes another variable.
The independent variable is the variable that is believed to cause the change in the dependent variable, while the dependent variable is the variable that is believed to be influenced by the independent variable.
In a causal study of the effect of shelf placement on sales of a brand of cereal, the independent variable is where the cereal was placed on the shelf. The dependent variable is sales of the cereal.
This is because the sales of the cereal are influenced by where it is placed on the shelf.The answer to the question is sales of the cereal.
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Do the Cauchy-Schwarz Inequality and the triangle inequality hold for the given vectors and inner product?u = (5, 3), v = (14, 4), (u, v) = u · v(a) the Cauchy-Schwarz Inequality Yes / No(b) the triangle inequality Yes / No
a) Yes, the Cauchy-Schwarz Inequality holds for the given vectors and inner product. Since 74 ≤ 76.84, the Cauchy-Schwarz Inequality holds.
b) Yes, the triangle inequality holds for the given vectors and inner product. Since 20.25 ≤ 23.21, the triangle inequality holds.
How do we know the Cauchy-Schwarz Inequality and the triangle inequality hold given vectors and inner product?Cauchy-Schwarz Inequality:
Using the given inner product, we have:
|u · v| ≤ ||u|| ||v||where ||u|| and ||v|| denote the norms of the vectors u and v, respectively.
We can calculate:
||u|| = sqrt(5^2 + 3^2) = sqrt(34)||v|| = sqrt(14^2 + 4^2) = sqrt(212)Then, applying the Cauchy-Schwarz Inequality, we have:
|u · v| = |(5)(14) + (3)(4)| = 74||u|| ||v|| = sqrt(34) sqrt(212) ≈ 76.84Triangle Inequality:
The triangle inequality states that for any vectors u, v, and w, we have:
||u + v|| ≤ ||u|| + ||v||Using the given vectors, we can calculate:
||u + v|| = ||(5 + 14, 3 + 4)|| = ||(19, 7)|| = sqrt(19^2 + 7^2) ≈ 20.25||u|| + ||v|| = sqrt(5^2 + 3^2) + sqrt(14^2 + 4^2) ≈ 23.21Learn more about Triangle Inequality
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i dont know how yo do this question
Step-by-step explanation:
2x + 2y = 28 <=====given
x * y = 40 <===given ..... re-arrange to :
y = 40 / x <===substitute this 'y' into the first equation
2x + 2 ( 40/x) = 28 <=====solve for x
2x^2 -28x + 80 = 0
x^2 -14x +40 = 0
(x -10)(x-4) = 0 shows x = 10 or 4 then y = 4 or 10
dimensions 10 and 4 inches
Answer:
4 or 10 inches
Step-by-step explanation:
I added a photo of my solution
The price of a television is dropped by 20% during a sale.After the sale the price is increased by 20%. what is the price of the television after the sale if the original price was 1200
The price of the television after the drop in its sales price would be = 1200
How to calculate the price of the television after deduction of sales discount?The percentage of money that was removed from the cost price for the television = 20%
The original price of the television = 1200
The percentage equivalent of 1200 that is 20 = 20/100×1200/1
= 24000/100
= 240
After the sales 240(20%) is added back to the sale price which show that it remains the same after sales.
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what is the probability of getting all tails? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.
Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.
To calculate the probability of getting all tails in three flips, we need to multiply the probabilities of getting tails on each individual flip. Since the flips are independent events (i.e. the outcome of one flip does not affect the outcome of another flip), we can simply multiply the probabilities together:P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)
= (1/2) x (1/2) x (1/2)
= 1/8
Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.
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How much plastic wrap will be needed to completly cover and ice cream cone with the slant height of 4. 25 inches and a diameter of 2 inches
The amount of plastic wrap required to cover the entire cone will be 16.575 square inches.
To calculate how much plastic wrap is required to completely cover an ice cream cone with a slant height of 4.25 inches and a diameter of 2 inches, we must use the surface area of the cone.
Here, the ice cream cone can be visualized as a cone-shaped object with an added circular base.
We must use the following formula to calculate the surface area:
Surface area = πr2 + πrl
Where r is the radius and l is the slant height of the cone.
As we know the diameter of the ice cream cone is 2 inches, and its radius can be calculated by dividing it by
2.r = d/2 = 2/2 = 1 inch.
Substitute the values of r and l in the formula, and then calculate the surface area of the cone.
π = 3.14r = 1 inchl = 4.25 inches
Surface area = πr2 + πrl
= 3.14 × 1² + 3.14 × 1 × 4.25
= 3.14 + 13.435
= 16.575 square inches
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Four cities recorded the temperature at midnight.
*Delway’s temperature was –8°C.
*Hickory’s temperature was –10°C.
*Midway’s temperature was –2°C.
*Ridgemonte’s temperature was 3°C.
Which list shows the cities in order from warmest to coldest?
A Delway, Hickory, Midway, Ridgemonte
B Hickory, Delway, Midway, Ridgemonte
C Midway, Ridgemonte, Hickory, Delway
D Ridgemonte, Midway, Delway, Hickory
A triangle has an area of 19.68 sqaure millimeteres and a height of 4.8 millimeteres. What is the length of the base?
Answer:
8.2mm
Step-by-step explanation:
Formula for area of triangle is 1/2 base x height
Since we are trying to find base, we must work in reverse.
19.68mm / 4.8 = 4.1mm (1/2 the base)
To find base we must multiply by 2
2 x 4.1mm = 8.2mm
Base = 8.2mm