A triangular pyramid has a slant height of 13 inches. The triangular base has a perimeter of 23 inches and an area of 15 square inches. Find the surface area
Please show the work so that I understand it. Also please hurry as I need the answer soon.
if 0.75 pounds of chicken cost $2.10, how much does the chicken cost per pound?
The data set below consists of the scores of 15 students on a quiz. for this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? explain your thinking. 90 90 91 91 89 90 89 91 91 90 60 90 89 90 91
In the given data set, the standard deviation is the more appropriate measure of variation as it takes all the scores into account and provides a better insight into the data compared to the range.
Explanation:In the given data set, both range and standard deviation can be used to measure the variation. However, the standard deviation might be a better measure in this instance. The standard deviation provides a numerical measure of the overall amount of variation in the data set. It indicates how far the values are from their average, or mean. In contrast, the range only provides the difference between the highest and lowest values, potentially overlooking the distribution of all the values.
When calculating the standard deviation for your dataset, it becomes evident that most scores are concentrated around the 90s, but there's one score dramatically lower at 60. This single score skews the data set and increases the standard deviation, indicating a larger spread around the mean than what might first be observed. As such, the standard deviation gives us a more detailed understanding of the spread within this set of quiz scores, making it the more useful measure in this case compared to the range.
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factor a^2b^2-7ab+10
The factored form of −7ab+10 is (ab−5)(ab−2).
Explanation:To factor the expression −7ab+10, we look for two binomials whose product gives the original expression. In this case, the factors are
(ab−5)(ab−2).
Expanding
(ab−5)(ab−2) using the distributive property, we get:
(ab−5)(ab−2)=(ab)(ab)−(ab)(2)−(5)(ab)+(5)(2)
Simplifying each term, we get:
−2ab−5ab+10
Combining like terms, we have:
−7ab+10
Therefore, the factored form of −7ab+10 is (ab−5)(ab−2).
Leia cuts congruent triangular patches with an area of 63 square centimeters from a rectangular piece of fabric that is 27 centimeters long and 21 centimeters wide. How many of the patches can Leia cut from 33 pieces of the fabric?
Leia can cut a total of 297 triangular patches from 33 pieces of fabric, with each piece yielding 9 patches.
To calculate how many triangular patches can Leia cut from 33 pieces of fabric, we first need to find out how many patches can be cut from a single piece of fabric. The area of each triangular patch is 63 square centimeters. The area of the fabric is length * width, which is 27 cm * 21 cm = 567 square centimeters.
Now, if we divide the area of the fabric by the area of one triangular patch, we get the number of patches per fabric piece: 567 cm2 / 63 cm2 = 9 patches per fabric piece.
Since Leia has 33 pieces of fabric, the total number of patches she can cut is 9 patches * 33 pieces = 297 patches.
An investigation of the ability of a hybrid tomato plant to produce a certain protein found that the amount x of the protein produced in the plant had a mean of 109.9109.9 micrograms per gram of fresh weight with a standard deviation of 8.18.1. consider a random sample of n equals 60n=60 hybrid tomato plants and let x overbarx represent the sample mean amount of the protein produced. would it be expected to observe a value of x overbarx less than 107107 micrograms per gram of fresh weight? explain. consider an event with a probability less than 0.05 unlikely.
What is the mixed number form for 56.4?
The arithmetic sequence 2, 4, 6, 8, 10, . . . represents the set of even natural numbers. What is the 100th even natural number? a100 =
Answer: The 100th even natural number is 200.
Step-by-step explanation: Given that the following arithmetic sequence represents the set of natural numbers :
2, 4, 6, 8, 10, . . ..
We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.
We know that
the n-th term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
For the given sequence, we have
a = 2 and d = 4 - 2 = 6 - 4 = . . . =2.
Therefore, the 100-th term of the sequence will be
[tex]a_{100}=a+(100-1)d=2+99\times2=2+198=200.[/tex]
Thus, the 100th even natural number is 200.
a new truck that sells for $29000 depreciates 12% each year. Write a function that models the value of the truck
How many sequences of outcomes are possible if one rolls two identical dice 10 successive times?
A girl throws a 2 kg rock with a net force of 6 N. What is the acceleration of the rock?
12m/s²
0.33m/s²
8m/s²
3m/s²
A rectangular prism has a length of 114 centimeters, a width of 4 centimeters, and a height of 314 centimeters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
cm³
Please help me with question 22
fractions that name the same number are
These are called "Equivalent Fractions."
Equivalent fractions may look different from each other, but all equivalent fractions have he same value.
what is (½)3. ???????
Omar owns a sandwich shop, and his best selling sandwich is the BLT. When making BLT sandwiches, it takes of a pound of bacon to make 4 sandwiches. He uses pounds of bacon for every 2 tomatoes used and 5 tomatoes for every full head of lettuce used.
If Omar is making enough BLT sandwiches to use 2 full heads of lettuce, then he is going to use pounds of bacon and will make a total of BLT sandwiches.
When making enough BLT sandwiches to use 2 full heads of lettuce, Omar will be using 2.5 pounds of bacon and will end up making a total of 40 BLT sandwiches.
Explanation:The subject of this question is Mathematics, specifically ratios and proportions. Given that Omar uses one full head of lettuce for every 5 tomatoes, for 2 heads of lettuce, he will use 10 tomatoes (2*5). Since he uses 1/2 pound of bacon for every 2 tomatoes, then for 10 tomatoes, he will need 2.5 pounds of bacon (10/2*0.5). Finally, since it takes 1/4 pound of bacon to make 4 sandwiches, with 2.5 pounds of bacon he will make 40 sandwiches (2.5/0.25*4). Therefore, Omar will use 2.5 pounds of bacon and make a total of 40 BLT sandwiches.
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what is 3x5x4x.............. can anyone answer asap pls
a bin size of __ is most appropriate for the data set shown above??
Write the rate using fraction form. Lisa ran 15 laps in 5 mins
It takes 484848 minutes for 777 people to paint 777 walls. How many minutes does it take 202020 people to paint 202020 walls?
Answer:
Approximately 391 minutes taken by 20 people to paint 20 walls.
Step-by-step explanation:
Given : It takes 48 minutes for 7 people to paint 7 walls.
To find : How many minutes does it take 20 people to paint 20 walls?
Solution :
7 people to paint 7 walls in 48 minutes.
So, 1 people to paint 7 walls in [tex]\frac{48}{7}[/tex] minutes.
and 1 people to paint 1 walls in [tex]\frac{48}{7\times 7}[/tex] minutes.
Now, We have to find minutes does it take 20 people to paint 20 walls.
20 walls will be painted in [tex]\frac{48\times 20}{7\times 7}[/tex] minutes.
20 people to paint 20 walls in [tex]\frac{48\times 20\times 20}{7\times 7}[/tex] minutes.
i.e. [tex]\frac{48\times 20\times 20}{7\times 7}=\frac{19200}{49}=391.83[/tex]
Therefore, Approximately 391 minutes taken by 20 people to paint 20 walls.
What is the length of line segment XZ
The line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.
How is a tangent inclined to the circle?A tangent to a circle is always perpendicular to it, that is, the radius drawn from the center of the circle to the tangent, is always perpendicular to it.
What is the Pythagoras Theorem?According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle, is equal to the sum of the squares of the legs, that is, the other two sides.
How to solve the question?In the question, we are asked to find the length of the line segment XZ.
Firstly, we name the center of the circle O.
The diameter of the circle is given to be 12 units.
Thus, its radius = 12/2 = 6 units,
Joining the radius OW, we get a right triangle OWZ, as the radius from the center of the circle to the tangent is always perpendicular.
In the right triangle OWZ, by Pythagoras Theorem, we can write:
OZ² = OW² + WZ² {Since, OZ is the hypotenuse},
or, (k + 6)² = 6² + (k + 4)² {Since, OZ = OY + YZ = Radius + k = 6 + k, and OW = Radius = 6},
or, k² + 12k + 36 = 36 + k² + 8k + 16 {Using the formula (a + b)² = a² + 2ab + b²},
or, k² + 12k - k² - 8k = 36 + 16 - 36 {Rearranging},
or, 4k = 16 {Simplifying},
or, k = 4 {Simplifying}.
Now, XZ = XY + YZ = Diameter + k = 12 + 4 = 16 units.
Thus, line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.
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the system of equations n= 2p+3 and n= 5+p is graphed what is the solution to the system of equations
Step-by-step explanation:
Graph is not given.
We have
n= 2 p+3
and
n= 5+p
That is
2 p+3 = 5 + p
p = 5 - 3
p = 2
Substituting in n= 5+p
n = 5 + 2 = 7
So the solution is n = 7 and p = 2
what is -20 divide it by -2
A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent? An image shows the tent, the staked rope, and the measurements as a right triangle. The height of the triangle is unknown. The base of the triangle is 6 feet. The hypotenuse is 8 feet.
The support given to the tent forms a right triangle.
The height of the tent is 5.3 ft
The given parameters are:
[tex]\mathbf{Base = 6}[/tex]
[tex]\mathbf{Hypotenuse= 8}[/tex]
The height is calculated as follows:
[tex]\mathbf{Hypotenuse^2 = Base^2 + Height^2}[/tex]
Substitute known values
[tex]\mathbf{8^2 = 6^2 + Height^2}[/tex]
This gives
[tex]\mathbf{64 = 36 + Height^2}[/tex]
Collect like terms
[tex]\mathbf{Height^2 = 64 - 36 }[/tex]
[tex]\mathbf{Height^2 = 28 }[/tex]
Take square roots
[tex]\mathbf{Height = 5.3 }[/tex]
Hence, the height of the tent is 5.3 ft
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find the domain of the following function below. f(x)=3x-5/2
ratio as a fraction 8 to 14
The function ƒ(x) is modified as follows: It is multiplied by –3. x is replaced by x + 3. The new function is graphed. Which of the following effects on the graph of ƒ(x) are needed to produce the new graph? Choose all that apply.
horizontal translation
vertical translation
dilation
reflection over the x-axis
reflection over the y-axis
Answer:
Horizontal Translation, Dilation and Reflection along y-axis
Step-by-step explanation:
A massless beam supports two weights as shown. 685 n w l 4 l 4 l 2 l a b find w such that the supporting force at a is zero. answer in units of n.
Final answer:
To find the weight W such that the support force at A is zero, the principle of static equilibrium is used. By taking moments about point B and setting the sum of moments to zero, W is found to be 342.5 N.
Explanation:
The question requires the application of the principles of static equilibrium to find the unknown weight W that would set the supporting force at point A to zero. In static equilibrium, the sum of all forces and the sum of all torques (moments) about any point must be zero.
We can analyze the forces acting on the beam by taking moments about point B to find the value of W. Because the support at A is required to exert no force, we only consider the gravitational force due to the beam's weight and the weight applied at point B. By setting the sum of moments about B to zero, we can solve for W.
Using the conditions for static equilibrium:
Sum of vertical forces = 0
Sum of moments (torques) = 0
The moment leverage for the 685 N weight is at L/4, and for the unknown weight W, it is at L/2. Assuming the beam is massless the equation for the sum of moments around point B is:
(685 N) * (L/4) - (W) * (L/2) = 0
Solving for W:
W = (685 N) / 2
Thus, W is equal to 342.5 N.
caculate the distances tarryn if she drives 7/8 mile each way to and from work, 5 days a week
She will cover 35/8 miles.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
total distance in miles = 7/8 miles per day
So, in 5 days in a week.
She will cover
=5*7/8
=35/8 miles.
Hence, She will cover 35/8 miles.
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A central angle measuring 150° intercepts an arc in a circle whose radius is 6. What is the area of the sector of the circle formed by this central angle? 15π 24π 30π 36π
Answer: 15
Step-by-step explanation: its 15