The period of simple harmonic motion for this mass-spring system is approximately 1.42 seconds.
To find the period of simple harmonic motion for a mass-spring system, we need to use the following formula:
T = 2π * √(m/k)
where T is the period, m is the mass of the object, and k is the spring constant. First, we need to convert the weight (2 N) to mass using the acceleration due to gravity (g = 9.8 m/s²):
m = W / g = 2 N / 9.8 m/s² ≈ 0.204 kg
Now that we have the mass, we can plug the values into the formula:
T = 2π * √(0.204 kg / 4 N/m)
T = 2π * √(0.051 kg/m)
T ≈ 2π * 0.226 s
T ≈ 1.42 s
So, the period of simple harmonic motion for this mass-spring system is approximately 1.42 seconds.
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A directional test (>) one sample t test was conducted. The results was t (30) = 6.23. You will: A. accept the null. B. reject the null. C. cannot tell with the information provided
Reject the null So the correct option is A . In a directional test, the null hypothesis states that the population mean is either equal to or greater than a specific value, and the alternative hypothesis states that the population mean is less than the specific value.
In this case, since the test is a ">" one sample t-test, the alternative hypothesis is that the population mean is greater than the specific value.
The test statistic t-value of 6.23 indicates that the sample mean is significantly greater than the hypothesized population mean. As the t-value is very large, the p-value would be very small, leading to the rejection of the null hypothesis. Therefore, we can conclude that the population mean is greater than the specific value with a high level of confidence.
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show that each of the following relations ∼ on z is an equivalence relation, and find itsequivalence classes.(a) m ∼n ⇔ |m −3|= |n −3|(b) m ∼n ⇔ m +n is even
We can write the equivalence class of m as [m] = {n ∈ Z : m + n is even}.
(a) To show that ∼ is an Equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.
Reflexivity: For any integer m, we have |m - 3| = |m - 3|, so m ∼ m. Therefore, ∼ is reflexive.
Symmetry: For any integers m and n, if |m - 3| = |n - 3|, then |n - 3| = |m - 3|, so n ∼ m. Therefore, ∼ is symmetric.
Transitivity: For any integers m, n, and p, if |m - 3| = |n - 3| and |n - 3| = |p - 3|, then |m - 3| = |p - 3|, so m ∼ p. Therefore, ∼ is transitive.
To find the equivalence classes of ∼, we need to determine the sets of integers that are related to each other. For any integer m, the equivalence class of m is the set of all integers n such that |m - 3| = |n - 3|. In other words, the equivalence class of m is the set of integers that are the same distance from 3 as m. We can write the equivalence class of m as [m] = {n ∈ Z : |m - 3| = |n - 3|}.
(b) To show that ∼ is an equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.
Reflexivity: For any integer m, we have m + m = 2m, which is even. Therefore, m ∼ m. Therefore, ∼ is reflexive.
Symmetry: For any integers m and n, if m + n is even, then n + m is also even, so n ∼ m. Therefore, ∼ is symmetric.
Transitivity: For any integers m, n, and p, if m + n is even and n + p is even, then m + p is even, so m ∼ p. Therefore, ∼ is transitive.
To find the equivalence classes of ∼, we need to determine the sets of integers that are related to each other. For any integer m, the equivalence class of m is the set of all integers n such that m + n is even.
In other words, the equivalence class of m is the set of integers that differ from m by an even amount. We can write the equivalence class of m as [m] = {n ∈ Z : m + n is even}.
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What is the evidence that the energy of the spring is higher when you stretch or compress it?
Answer: When a spring is compressed or stretched, it will try to restore its equilibrium position by exerting a force equal and opposite to the external force. So the external work done by us in compression as well as stretching will store in the spring as potential energy
Answer: Energy of the spring is equal when compressed as when stretched.
Step-by-step explanation: Potential Energy (PE) of the spring is highest at both compression and when stretched. During this time, the Kinetic Energy (KE) is zero. When the spring is at rest, KE is highest and PE is zero.
recursive function calls are ________ efficient than loops.
Recursive function calls can be less efficient than loops in certain cases because they create additional function calls and memory overhead. However, recursive functions can also be more efficient in some scenarios, particularly when dealing with complex data structures or problems that naturally lend themselves to a recursive approach. Ultimately, the efficiency of a recursive function versus a loop depends on the specific problem and how it is implemented.
Recursive function calls are generally less efficient than loops. This is because recursion can consume more memory and processing power due to the overhead of maintaining a separate function call stack for each recursive call. Loops, on the other hand, often have lower memory usage and can be more efficient in terms of processing time, especially for simple tasks or iterations. However, there are cases where recursion can provide a more elegant solution, but it's important to consider the trade-offs between readability and efficiency.
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List the five (5) number summary and interquartile range for the following data.
pls don't send a link for me to download
The min is 85, max is 125, median is 110, Q1 is 95 , Q3 is 120 and IQR is 25 from box plot
The minmum from box plot is 85
The maximum from box plot is 125
Median is 110
Q₁ is 95
Q₃ is 120
IQR =Q₃-Q₁
=120-95
=25
Hence, the min is 85, max is 125, median is 110, Q1 is 95 , Q3 is 120 and IQR is 25
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Which equation represents a line which is parallel to the line
y =-4/3x-7?
The equation 4x + 3y = -18 is parallel to the given line since they have the same slope.
Equation of a lineThe equation of a line in slope-intercept form is expressed as y = mx + b
where
m is the slope
b is the y-intercept
Given the equation below
y =-4/3x-7
The slope of the line is -4/3.
In order to determine the equation that represents a line which is parallel to the line, we need to determine the line that has a slope of -4/3
For the equation 4x + 3y = -18:
3y = -4x - 18
Divide through by 3 to have:
3y/3 = -4x/3 - 18/3
y = -4/3 x - 6
Since the slope of the line is -4/3, hence the equation 4x + 3y = -18 is parallel to the given line.
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If m∠FCD = (2x 5)° and m∠FED = (3x − 10)°, what is the value of x? 19 35 37 73
If angle mFCD = (2x + 5)° and m∠FED = (3x − 10)°, the value of x is 1. Option A is the correct answer.
Since FCD and FED are adjacent angles, their sum must be equal to the measure of angle FCE:
m∠FCD + m∠FED = m∠FCE
Substituting the given measures, we get:
(2x+5) + (3x-10) = m∠FCE
Simplifying the left side, we get:
5x-5 = m∠FCE
We know that the sum of the angles in triangle FCE is 180 degrees, so we can use that information to solve for x:
m∠FCE + m∠FEC + m∠CEF = 180
Substituting in the value we found for m∠FCE, and noting that m∠FEC and m∠CEF are each 90 degrees since triangle FCE is a right triangle, we get:
5x-5 + 90 + 90 = 180
Simplifying and solving for x, we get:
5x + 175 = 180
5x = 5
x = 1
Therefore, the value of x is 1.
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If m∠FCD = (2x + 5)° and m∠FED = (3x − 10)°, what is the value of x?
a. 1
b. 3
c. 7
d. 4
Answer:
37
Step-by-step explanation:
5(37)=185
185-5=180
2. Given: Triangle XYZ
Label the coordinates and find the
distances.
Prove: Triangle XYZ is an isosceles
triangle.
PROOF:
Answer:
x=(1,5)
z=(8,-4)
y=(-6,-4)
distance of XZ= 11.4
distance of ZY= 14
distance of YX= 11.4
this is an isosceles triangle because the distance between XZ and YX are the same meaning two legs of the triangle have equal length which defines an isosceles triangle
find the following. f(x) = x2 3, g(x) = 5 − x (a) (f g)(x) = (b) (f − g)(x) = (c) (fg)(x) = (d) (f/g)(x) = what is the domain of f/g? (enter your answer using interval notation.)
The domain is restricted because when x=5, the denominator of f/g becomes zero, which is undefined. Therefore, the domain of f/g is (-∞,5) U (5,∞).
(a) To find (f g)(x), we substitute g(x) into f(x) as follows: (f g)(x) = f(g(x)) = f(5-x) = (5-x)^2/3.
(b) To find (f - g)(x), we subtract g(x) from f(x) as follows: (f - g)(x) = f(x) - g(x) = x^2/3 - (5-x) = x^2/3 - 5 + x.
(c) To find (fg)(x), we multiply f(x) by g(x) as follows: (fg)(x) = f(x)*g(x) = x^2/3 * (5-x).
(d) To find (f/g)(x), we divide f(x) by g(x) as follows: (f/g)(x) = f(x) / g(x) = x^2/3 / (5-x). The domain of f/g is all values of x except x=5.
The domain is restricted because when x=5, the denominator of f/g becomes zero, which is undefined. Therefore, the domain of f/g is (-∞,5) U (5,∞).
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Imprecision is more difficult to determine than bias because we usually know the true value of an observation before we begin to sample.
Is this true or false? Explain Why?
The statement is true because bias can be assessed by comparing the sample estimate to the true value, which is known in some cases.
Why the statement is true?Imprecision refers to the lack of consistency or reproducibility in measurements or observations. It can arise from a variety of sources such as instrument variability, human error, and natural variation in the phenomenon being measured. In contrast, bias refers to a systematic deviation from the true value or a consistent tendency to overestimate or underestimate the true value.
The statement is saying that it is easier to determine bias because we usually know the true value of an observation before we begin to sample. This is because bias can be quantified by comparing the sample mean or estimate to the true value. In other words, if we have a known true value, we can determine if our sample is biased towards overestimating or underestimating that value.
On the other hand, imprecision is more difficult to determine because we do not have a true value to compare our observations to. Instead, we rely on statistical measures of variability such as standard deviation or confidence intervals to assess the precision of our measurements. However, these measures only provide an estimate of the variability and do not give us a definitive answer about the true level of imprecision.
In summary, the statement is true because bias can be determined by comparing the sample estimate to the true value, while imprecision is more difficult to determine without a known true value.
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A water tank in the shape of a right rectangle prism is 11 feet deep the top of the water tank has an area of 220 ft.² what is the volume in cubic feet of the water tank
Answer:
Step-by-step explanation:
Step 1: Recall the formula for the volume of a right rectangular prism: Volume = length x width x height.
Step 2: Note that we are given the height of the water tank (11 feet), but we need to find the length and width.
Step 3: Use the formula for the area of a rectangle to find the length and width of the top of the water tank. The area is given as 220 ft², so:Area = length x width
220 ft² = length x width.
Step 4: Find two numbers that multiply to 220 and also have a sum of 2 times the height (22 feet). One way to do this is to list the factor pairs of 220 and check the sums:1 x 220 = 220 (not a factor pair)2 x 110 = 220 (not a factor pair)4 x 55 = 220 (not a factor pair)5 x 44 = 220 (not a factor pair)10 x 22 = 220 (sum is 32)11 x 20 = 220 (sum is 31)20 x 11 = 220 (sum is 31)22 x 10 = 220 (sum is 32)Therefore, the length and width of the top of the water tank are 11 feet and 20 feet (or 20 feet and 11 feet).
Step 5: Plug in the values for the length, width, and height into the volume formula and solve:Volume = length x width x height
Volume = 11 ft x 20 ft x 11 ft
Volume = 2,420 ft³
the final answer: The volume of the water tank is 2,420 cubic feet.
air pollution in mexico city has been declining over the last several decades. this decline has had positive impacts on human health and mortality. this graph shows the relationship between ozone (o3) concentration in parts per billion (ppb) and the number of infant deaths per 100,000 births.there are two vertical axes. the vertical axis at the left is labeled o 3 in p p b and ranges from 28 to 38 in increments of 2. the vertical axis at the right is labeled deaths per 100,000 births and ranges from 35 to 45 in increments of 5. the horizontal axis shows years from 1997 to 2005 in increments of 2 years. the line for ambient o 3 provides following data. 1997: o 3 in p b b, 37; deaths per 100, 000 births, 45. 1999: o 3 in p b b, 34; deaths per 100, 000 births, 42; 2001: o 3 in p b b, 33.5; deaths per 100, 000 births, 41; 2003: o 3 in p b b, 31.5; deaths per 100, 000 births, 38; 2005: o 3 in p b b, 32; deaths per 100, 000 births, 39. the line for infant mortality provides following data. 1997: o 3 in p b b, 38; deaths per 100, 000 births, 46. 1999: o 3 in p b b, 34; deaths per 100, 000 births, 42; 2001: o 3 in p b b, 31; deaths per 100, 000 births, 37; 2003: o 3 in p b b, 28; deaths per 100, 000 births, 34.5; 2005: o 3 in p b b, 28; deaths per 100, 000 births, 35. all data are approximated. data from arceo, e. et al., 2015. does the effect of pollution on infant mortality differ between developing and developed countries? evidence from mexico city. the economic journal 126: 257-280. doi:10.1111/ecoj.12273from the graph, which of the following statements are true and which are false?drag ''true'' or ''false'' to the end of each statement.
- Air pollution in Mexico City has been declining over the last several decades. (True)
- The decline in air pollution has had positive impacts on human health and mortality. (True)
- The graph shows the relationship between ozone concentration and the number of infant deaths per 100,000 births. (True)
- The vertical axis on the left is labeled deaths per 100,000 births. (False)
- The line for ambient ozone concentration shows a decrease over time. (True)
- The line for infant mortality shows an increase over time. (False)
- The data for both lines are approximated. (True)
Based on the provided data and graph, here are the statements and their truth values:
1. Air pollution, specifically ambient ozone (O3) concentration, in Mexico City has been declining from 1997 to 2005.
- True
2. Infant deaths per 100,000 births have also been decreasing from 1997 to 2005.
- True
3. There is a correlation between decreasing O3 concentration and the decrease in infant deaths per 100,000 births.
- True
4. The vertical axis on the left is labeled deaths per 100,000 births.
-False
5. The line for ambient ozone concentration shows a decrease over time.
-True
6. The line for infant mortality shows an increase over time.
-False
7. The data for both lines are approximated.
-True
Remember that correlation does not imply causation, but the data does show a relationship between the decrease in air pollution and the decrease in infant mortality in Mexico City during the given time period.
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a scale model of a skyscraper was built at a scale of 1 : 250 and is 1.4 meters tall. what is the height of the original skyscraper
The height of the original skyscraper is 350 meters.
To find the height of the original skyscraper, we need to use the scale factor of 250.
First, we need to figure out how many times bigger the original skyscraper is compared to the model. We can do this by dividing 1 by 250:
1 / 250 = 0.004
This means that the original skyscraper is 0.004 times bigger than the model.
To find the height of the original skyscraper, we need to multiply the height of the model (1.4 meters) by the scale factor (250):
1.4 x 250 = 350 meters
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Baseball Basketball Tennis Soccer
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
The correct option to represent the sample data is: option (A) . Since the data is categorical and discrete, a bar graph is the most appropriate way to display the data
How to Identify a bar graph?A bar graph, also known as a bar chart, is a graphical representation of data in which the data is presented using rectangular bars. The length or height of each bar is proportional to the value that it represents.
The correct answer is: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44.
Since the data is categorical and discrete, a bar graph is the most appropriate way to display the data. The bars should be labeled with the sports and their corresponding heights should be the number of students who chose that sport.
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Select the graph that represents h = -16ť²2 +80.
O
Answer:
Alr Look search up desmos press desmos then press graphing calculator input the function and it shows the graph
Step-by-step explanation:
The graph of the given equation is attached.
What is graph?A graph is a diagram or a pictorial representation of data or values that show the relationship between quantities or objects.
A graph is a structure consisting of a set of objects called vertices or nodes, and some pairs of them are connected by lines or curves called edges or links.
A graph can also be a curve or line that shows a mathematical function or equation, usually drawn in a coordinate system.
Given is an equation, h = -16t² + 80, we need to graph it,
So, as we see that the function is a quadratic function, then the graph will be parabolic also the equation has negative sign so the parabola will open downwards,
Finding the coordinates,
Put t = 0,
h = 80
(0, 80)
Put t = 1,
h = 64
(1, 64)
plot these points on the graph and join them, the curve we will get is the graph for the equation.
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PLEASE HELP I NEED THE ANSWER TO BOTH QUESTIONS I GIVE BRAINLIEST
Answers: Angle ABE = 117 And DBE = 27
In △ABC, the angles A and C are equal to 30◦ and 120◦ respectively, and the side AC = 20ft, find the length of the perpendicular from B upon AC produced.
Answer:
We can start by drawing a diagram of the triangle ABC:
A
/ \
/ \
/ \
/ \
/ \
B ----------- C
We know that angle A is 30 degrees and angle C is 120 degrees, so angle B must be:
angle B = 180 - angle A - angle C
= 180 - 30 - 120
= 30 degrees
Now we can use the sine function to find the length of the perpendicular from B to AC produced. Let's call this length x:
sin(angle B) = perpendicular / hypotenuse
sin(30) = x / 20
We can solve for x by multiplying both sides by 20 and taking the sine of 30:
x = 20 sin(30)
x = 20 (1/2)
x = 10
Therefore, the length of the perpendicular from B upon AC produced is 10 feet.
Step-by-step explanation:
pls help this is my last try to get it right
The figure ABCD is translated vertically to form the figure A'B'C'D'. Then the correct option is D.
Given that:
Rhombus, ABCD
Image of Rhombus, A'B'C'D'
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
The reflection does not change the shape and size of the geometry. But flipped the image.
The figure ABCD is translated vertically to form the figure A'B'C'D'. Then the correct option is D.
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need help all info is in the picture
The linear equation in the slope intercept form is:
y = (-5/3)*x - 3
How to write the linear equation?We want to find a line perpendicular to:
y = (3/5)*x - 1
Remember that two lines are perpendicular if the product between the slopes is -1, then the slope of our line is:
a*(3/5) = -1
a = -5/3
So our line is:
y = (-5/3)*x +b
And we also want our line to pass through the point (-3, 2), then replacing these values we will get.
2 = (-5/3)*-3 + b
2 = 5 + b
2 - 5 = b
-3 =b
The linear equation is:
y = (-5/3)*x - 3
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A coin is biased so that the probability of a head is 2/3 The coin is tossed repeatedly.
Find the probability that:
a the first tail will occur on the sixth toss
b in the first 8 tosses there will be exactly 2 tails.
a) The probability = (2/3)^5 * (1/3) = 32/243. b) P = C(8,2) * (1/3)^2 * (2/3)^6 = 28 * 4/729 = 112/729
How to find the probability givena) The probability of getting tails on any toss is 1/3, since the coin is biased and the probability of getting a head is 2/3. Therefore, the probability of getting tails on the first five tosses and then getting a tail on the sixth toss is:
P = (2/3)^5 * (1/3) = 32/243
b) We can use the binomial distribution to find the probability of getting exactly 2 tails in the first 8 tosses. The probability of getting 2 tails in 8 tosses is:
P = C(8,2) * (1/3)^2 * (2/3)^6 = 28 * 4/729 = 112/729
where C(8,2) is the number of ways to choose 2 tails out of 8 tosses.
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for the following conjecture, state the null and alternative hypotheses. the average weight loss for a sample of people who exercise 30 minutes per day for 6 weeks is greater than 8.2 pounds.
For the given conjecture, which is "the average weight loss for a sample of people who exercise 30 minutes per day for 6 weeks is greater than 8.2 pounds", the null and alternative hypotheses can be stated as follows:
Null Hypothesis (H0): The average weight loss for the sample is equal to or less than 8.2 pounds (≤ 8.2 lbs).
Alternative Hypothesis (H1): The average weight loss for the sample is greater than 8.2 pounds (> 8.2 lbs).
These hypotheses are formed to test whether there is significant evidence to support the conjecture that exercising 30 minutes per day for 6 weeks leads to an average weight loss of more than 8.2 pounds.
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Can someone help me asap? It’s due today!! I will give brainliest if it’s correct
Answer:
1270 students
Step-by-step explanation:
3020×42/100=1268.4
so approximately 1270
If you have access to a graphing calculator or free graphing web
resource, utilize it for this problem. If not, graph it by hand on a coordinate
plane. Start by graphing the function f(x) = x-4. Now graph a new
function, g(x) = 3x - 12. If f(x) was transformed into g(x) in a single step,
what type of transformation was it? What was the "k" value? What happened
to the slope and y-intercept you see in your graphs? Use 2 complete
sentences.
Answer: By plotting the functions f(x) = x-4 and g(x) = 3x - 12 on a coordinate plane, we can see that the transformation from f(x) to g(x) was a vertical stretch by a factor of three with no translation. This transformation has a "k" value of 3. We can see that the slope of g(x) is three times steeper than that of f(x), and that the y-intercept of g(x) is similarly three times lower than that of f(x), representing the vertical stretch by a factor of three.
Step-by-step explanation:
a rectangle is inscribed with its base on the x-axis and its upper corners on the parabola 6-x^2 . what are the dimensions of such a rectangle with the greatest possible area?
The dimensions of the rectangle with the greatest possible area are 2[tex]\sqrt{(2)}[/tex] by 4.
Let's denote the dimensions of the rectangle as length (L) and width (W). Since the base of the rectangle is on the x-axis, the width of the rectangle is equal to the x-coordinate of the upper corners of the rectangle.
Let's assume that the x-coordinate of the upper corners of the rectangle is x. Then, the width of the rectangle is W = 2x, and the length of the rectangle is L = 6 -[tex]x^2[/tex].
The area of the rectangle is A = LW = [tex]2x(6 - x^2) = 12x - 2x^3.[/tex]
To find the maximum area, we need to take the derivative of A with respect to x and set it equal to zero:
[tex]dA/dx = 12 - 6x^2 = 0[/tex]
Solving for x, we get:
x = ±sqrt(2)
Since we are interested in the dimensions of the rectangle on the parabola, we take the positive value of x.
Therefore, the width of the rectangle is:
W = 2x = 2sqrt(2)
And the length of the rectangle is:
L = 6 - [tex]x^2[/tex]= 6 - 2 = 4
So the dimensions of the rectangle with the greatest possible area are 2sqrt(2) by 4.
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need help I don't get it
Answer: scalene.
Step-by-step explanation: Based on the given measurements of the sides and angles of the triangle, we can classify each triangle by its sides as follows:
9.8, 4.8, and 6.8: These three sides have different lengths, so the triangle is scalene.
Therefore, the triangle is scalene.
Note that the angles given in the problem are not necessary to classify the triangle by its sides, as the sides uniquely determine the type of triangle.
if p > 5 is prime and p is divided by 10, show that the remainder is 1, 3, 7, or 9
If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9
The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.
However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).
Therefore, p must end in 5. This means that p can be written in the form:
p = 10n + 5
where n is some integer. Now, let's consider what happens when we divide p by 10:
p/10 = (10n + 5)/10 = n + 0.5
Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.
To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).
Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.
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a square pyramid has a base measuring 10 inches on each side. the height of the pyramid is 5 inches. a similar square pyramid has a base measuring 2 inches on each side. how do the surface areas of these pyramids compare? drag a value to the box to correctly complete the statement.
Answer:
It's 25
Step-by-step explanation:
I took the quiz.
a rectangle having integer length and width has a perimeter of 100 units. what is the number of square units in the least possible area?
the least possible area of the rectangle with integer length and width and a perimeter of 100 units is 625 square units.
Let's start by using the formula for the perimeter of a rectangle, which is:
perimeter = 2(length + width)
We know that the perimeter is 100 units, so we can substitute that in:
100 = 2(length + width)
Simplifying this equation, we get:
50 = length + width
We also know that the length and width are both integers. Since we want to find the least possible area, we want the rectangle to be as close to a square as possible. This means that the length and width should be as close to each other as possible. The two integers that are closest to each other and add up to 50 are 25 and 25.
So the dimensions of the rectangle are length = 25 units and width = 25 units. Now we can use the formula for the area of a rectangle, which is:
area = length x width
Substituting the values we found, we get:
area = 25 x 25 = 625 square units
Therefore, the least possible area of the rectangle with integer length and width and a perimeter of 100 units is 625 square units.
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30 points if someone gets it right
Find the volume of the cube shown, in cubic yards. Your answer may be exact or accurate to the nearest hundredth.
Volume of solid is 8000 cubic yards.
We know that,
Volume is defined as the amount of space occupied by an object within the boundaries in the three dimensional space.
A base of a solid whose height is 20 yards is shown.
Let us consider the solid as cube.
Volume of cube = a^3 cubic units.
Here side, a =20 yards.
Volume ,V= 20^3
= 8000 cubic yards.
Hence, Volume of solid is 8000 cubic yards.
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What is 52 percent of 25?
Answer:
13
Step-by-step explanation:
Write 52% as 52/ 100
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
52/ 100 of 25 = 52/ 100 × 25
Therefore, the answer is 13
