Answers
The height of the square pyramid with the given slant height base base length is found as: 91.17 in.
Explain about the square pyramid?A square pyramid is really a pyramid with only a square base. A pentahedron, that is. With a base and three triangle sides, a pyramid is a 3D shape.
A square base is what a pyramid with a square base is built upon. A great illustration of a square-based pyramid is the Egyptian pyramid complex.
A right square pyramid with side length a with height h has lateral edge length e as well as slant height s.
Given data:
Slant height s = 91.8 in.
Height H = ?
Base length a = 21.4 in.
Slant height s formula is:
s² = H² + 1/4 a²
H² = s² - 1/4 a²
H² = 91.8² - 1/4 *(21.4)²
H = √8312.75
H = 91.17 in.
Thus, the height of the square pyramid with the given slant height and base length is found as: 91.17 in.
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The height of the square pyramid with the given slant height base base length is about 91.2 in. to one decimal place
What is a square pyramid?A square pyramid is a polyhedron that has a square base and four lateral faces that meet at a point above the base (e.g. the apex)
The given parameters to solve the question are given as follows
Slant height s = 91.8 in.
Height H = ?
Base length a = 21.4 in.
Slant height s formula is: s² = H² + 1/4 a²
H² = s² - 1/4 a²
By substitution into the formula we have
H² = 91.8² - 1/4 *(21.4)²
H = √8312.75
H = 91.17 in.
Thus, the height of the square pyramid with the given slant height and base length is found as: 91.2 in.
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Related Questions
Find the missing length.
Answers
The value of the missing side length is 9.
What is the value of the missing length?The figures in the image are two similar triangle.
Side lengths of smaller triangle are:
x and (10-4)
Side lengths of larger triangle are:
(x+6) and 10
Since the triangle are similar, we take the proportion of the side lengths and solve for x.
x/(10-4) = (x+6)/10
x/6 = (x+6)/10
Cross multiply
x × 10 = 6( x + 6 )
Apply distributive property to eliminate the parenthesis.
x × 10 = 6×x + 6×6
10x = 6x + 36
10x - 6x = 36
4x = 36
x = 36/4
x = 9
Therefore, the value of x is 9.
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x = 30° is a zero for y = tan 3(x +30°). True or False with justification
Answers
Answer: true
Step-by-step explanation:
true
which of the following graph/s pass the vertical line test and would it be considered a function
Answers
Applying the concept of vertical line test, only graph 1 is qualified to be a function.
What is vertical line test?An analytical tool for determining if a given relation is a function is the vertical line test. The test is drawing a vertical line somewhere on the relation's graph and determining if it crosses the graph several times.
Every vertical line must cross the graph at exactly one place in order for the relation to be a function. This is due to the fact that there is no ambiguity in the mapping between inputs and outputs, where each input (x-value) corresponds to a certain output (y-value).
On the other hand, the connection is not a function if the vertical line crosses the graph more than once. This is due to the unclear mapping between inputs and outputs and the presence of at least two outputs that correspond to the same input.
Without having to explicitly analyze the relation for all potential inputs, the vertical line test is a helpful technique for rapidly identifying whether a particular relation is a function or not. It is especially beneficial for relational graphs like scatterplots, line graphs, and curves.
Using vertical line test, only graph 1 is a function
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Calculator
3.05 Quiz: Volumes of Cones
What is the approximate volume of a cone with a height of 12 in. and radius of 9 in.?
Use 3.14 to approximate pi, and express your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
in³
Answers
Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.
How do we find volume of cone ?To find the volume of a cone, we use the following formula:
V = 1/3 * π * r² * h
where V is the volume of the cone, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base of the cone, and h is the height of the cone.
To use the formula, we simply substitute the given values for r and h into the formula and simplify. Make sure that the radius and height are measured in the same units. The resulting volume will be in cubic units.
The formula for the volume of a cone is:
V = 1/3 * π * r² * h
where π is pi (approximately 3.14), r is the radius of the base of the cone, and h is the height of the cone.
Substituting the given values, we get:
V = 1/3 * 3.14 * 9² * 12
= 1/3 * 3.14 * 81 * 12
= 3.14 * 324
= 1017.36
Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.
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The exponential function below is used by a biologist and her lab tomorrow the growth of some bacteria. A=2e^0.3t in the function the value of a depends on the value of t what statement describes that relationship 
Answers
The relationship between A and t is exponential, meaning that as time increases, the number of bacteria grows at an accelerating rate.
What is exponential function?An exponential function is a mathematical function of the form:
f(x) = a^x
where "a" is a positive constant called the base, and "x" is the independent variable. The base "a" is usually a number greater than 1, but it can also be a fraction between 0 and 1.
Exponential functions have some key properties that make them useful for modeling many natural phenomena. One of the most important properties is that they exhibit exponential growth or decay, meaning that the rate of change of the function is proportional to the current value of the function.
In the given question,
In the exponential function A=2e^(0.3t), the value of A depends on the value of t. Specifically, A is a function of t, where t is the independent variable and A is the dependent variable. This means that as the value of t changes, the value of A changes as well.
The function describes the growth of some bacteria, where A represents the number of bacteria at time t. The value of t represents the time elapsed since the start of the observation period. The function suggests that the growth rate of the bacteria is proportional to the current number of bacteria, with a growth rate of 0.3 per unit time.
The relationship between A and t is exponential, meaning that as time increases, the number of bacteria grows at an accelerating rate. This relationship can be observed by plotting the function on a graph, where A is plotted on the y-axis and t is plotted on the x-axis. The resulting curve will be a steeply upward-sloping curve that gets steeper and steeper as time goes on.
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Thelma and David built a recycling bin. The area of the base is 72 ft² and it is 14 feet high.
What is the volume of the recycling bin?
Answers
Answer: The volume of the recycling bin can be calculated by multiplying the area of the base by the height of the bin.
Given that the area of the base is 72 ft² and the height is 14 feet, we can use the formula:
Volume = Area of Base × Height
Substituting the given values, we get:
Volume = 72 ft² × 14 feet
Volume = 1008 cubic feet
Therefore, the volume of the recycling bin is 1008 cubic feet.
Step-by-step explanation:
suppose that a friend is helping put on a fundraiser for the local animal shelter. one activity is a game using a bowl that contains six green marbles and eight blue marbles. to play the game, each person draws two marbles without replacement and without looking. if both marbles are green, the player wins $25. if not, the player must donate $10 to the animal shelter. the marbles are then replaced for the next player. calculate the expected value of the game for the player.
Answers
Answer:
To calculate the expected value of the game for the player, we need to find the probability of each possible outcome and the corresponding payoff or cost, and then multiply each probability by its payoff or cost, and sum the results. Let's first find the probability of each possible outcome:
- Probability of drawing two green marbles: (6/14) * (5/13) = 0.164
- Probability of not drawing two green marbles: 1 - 0.164 = 0.836
If both marbles are green, the player wins $25, so the payoff is $25. If not, the player must donate $10 to the animal shelter, so the cost is -$10. Therefore, the expected value of the game for the player is:
Expected value = (Probability of winning * Payoff) + (Probability of losing * Cost)
Expected value = (0.164 * $25) + (0.836 * -$10)
Expected value = $4.10 - $8.36
Expected value = -$4.26
The expected value of the game for the player is -$4.26, which means that on average, the player can expect to lose $4.26 per game. Therefore, playing this game is not a good bet for the player.
You are studying an amoeba through a microscope. The amoeba moves on a grid-indexed microscope slide in a straight line from square B3 to square G7. the side length of each grid square is 2 mm. How far does the amoeba travel? round your answer to the nearest 10th.
Answers
To find the distance traveled by the amoeba, we need to calculate the Euclidean distance between the starting point B3 and the ending point G7.
Using the Pythagorean theorem, we can find the length of the diagonal line connecting these two points:
d = √[(G - B)² + (7 - 3)²] * 2
where G - B represents the horizontal distance between the two points in number of squares.
In this case, G - B = 6 (from B to G there are 6 squares horizontally).
Substituting the values, we get:
d = √[6² + 4²] * 2 = √(36 + 16) * 2 = √52 * 2 ≈ 11.4 mm
Therefore, the amoeba travels approximately 11.4 mm. Rounded to the nearest 10th, the distance is 11.4 ≈ 11.4 mm.
Determine the inverse of the matrix C equals a matrix with 2 rows and 2 columns. Row 1 is 9 comma 7, and row 2 is 8 comma 6..
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is 3 comma negative 3.5, and row 2 is negative 4 comma 4.5.
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is negative 3 comma 3.5, and row 2 is 4 comma negative 4.5.
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is 6 comma 8, and row 2 is 7 comma 9.
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is negative 9 comma 8, and row 2 is 7 comma negative 6.
Answers
Answer: [-4.5 -3.5]
[-4 -3]
Step-by-step explanation:
Music and a matrix calculator online, mwah
The width of a rectangle measures ( 9.5 c + 6.2 d ) (9.5c+6.2d) centimeters, and its length measures ( 5.1 c − 3.4 d ) (5.1c−3.4d) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
The expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.
The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the rectangle has two sides with a length (9.5c+6.2d) and two sides with a length (5.1c−3.4d).
Therefore, the perimeter can be calculated by adding the lengths of all four sides:
Perimeter = (9.5c+6.2d) + (9.5c+6.2d) + (5.1c−3.4d) + (5.1c−3.4d)
Simplifying and combining like terms, we get:
Perimeter = 2(9.5c+6.2d) + 2(5.1c−3.4d)
Perimeter = 19c + 12.4d + 10.2c − 6.8d
Perimeter = 29.2c + 5.6d
Therefore, the expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.
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Please help me I really stuck
Answers
Answer:
We can find the value of Y when k = 5/4 by substituting k = 5/4 in the given expression for Y:
Y = 16 × 10^8 × k
Y = 16 × 10^8 × (5/4)
Y = 20 × 10^8
To express this in standard form, we can convert it to scientific notation:
Y = 2.0 × 10^9
Step-by-step explanation:
y^(5/4) = (16×10^(8k))^(5/4)
remember all the rules of exponents :
an exponent of an exponent : we multiply both exponents.
x^(a/b) =
[tex] \sqrt[b]{ {x}^{a} } = ({ \sqrt[b]{x} })^{a} [/tex]
and
(a×b)^c = a^c × b^c
so, with that we can do the trick here :
y^(5/4) = (16×10^(8k))^(5/4) =
= 16^(5/4) × 10^(8k × 5/4)
16^(5/4) =
[tex] \sqrt[4]{ {16}^{5} } = ( \sqrt[4]{16} )^{5} = ( \sqrt[4]{ {2}^{4} })^{5} = {2}^{5} = 32[/tex]
10^(8k × 5/4) = 10^(40k/4) = 10^(10k)
so, the result is
32 × 10^(10k)
[tex]32 \times {10}^{10k} [/tex]
Mr Khan put $6000 in his bank. He withdraws it all four years later.
How much does he withdraw if the simple interest rate was 4% per year?
Answers
Step-by-step explanation:
If the simple interest rate is 4% per year, then the interest earned each year is calculated by multiplying the principal amount by the interest rate.
The interest earned in one year is:
Interest = Principal x Rate = $6000 x 0.04 = $240
After four years, the total interest earned is:
Total Interest = Interest x Time = $240 x 4 = $960
Therefore, the total amount Mr. Khan can withdraw after four years is:
Withdrawal Amount = Principal + Total Interest = $6000 + $960 = $6960
Answer:
If the simple interest rate was 4% per year, we can use the formula for simple interest to calculate the amount of interest Mr. Khan earned on his $6000 deposit:
Simple interest = P * r * t
Where P is the principal (the initial amount deposited), r is the interest rate (as a decimal), and t is the time (in years).
In this case, P = $6000, r = 0.04, and t = 4. Substituting these values into the formula, we get:
Simple interest = $6000 * 0.04 * 4 = $960
The total amount Mr. Khan can withdraw after four years is the sum of his initial deposit and the interest earned:
Total amount = Principal + Interest
Total amount = $6000 + $960 = $6960
Therefore, Mr. Khan can withdraw $6960 from his bank account after four years if the simple interest rate was 4% per year.
(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)
13. A savings account earns 10% simple
interest. How much interest does an $800
deposit earn in four years?
14. a. Greg deposits $800 into a savings
account that earns 10% interest
compounded
annually. What is Greg's
balance after four years?
b. How much interest did Greg's
account earn?
Answers
Answer:
Greg's account earned 80$ because 0.10×800=80 80+800=880 total
Jeremiah's ice cream was 23.9 ounces when he checked out at the store. He ate 11.38 ounces before leaving, how many ounces did he take home as leftovers?
Answers
Answer:
12.52 ounces
Step-by-step explanation:
Leftovers= 23.9-11.38
=12.52 ounces
What can be submitted for bands in a single -arm row?
Answers
Resistance bands, loop bands, tube bands with handles, and cable machines can be used for single-arm rows
In a single-arm row exercise, a variety of equipment can be used to add resistance and challenge the muscles. Here are some examples of what can be submitted for bands in a single-arm row
Resistance bands: Resistance bands are a popular option for single-arm rows. They come in different colors to indicate the level of resistance and can be easily adjusted to increase or decrease the difficulty. To perform a single-arm row with a resistance band, step on the center of the band with one foot and grasp the other end with one hand
Loop bands: Loop bands are a type of resistance band that is formed into a loop. They can be placed around the wrists or forearms to provide resistance during a single-arm row. To perform a single-arm row with a loop band, loop the band around your hand and hold onto the other end with your other hand.
Tube bands with handles: Tube bands with handles are another option for single-arm rows. These bands have handles on each end, allowing for a more comfortable grip. To perform a single-arm row with a tube band, attach one end of the band to a stationary object and hold onto the other end with one hand.
Cable machines: Cable machines are a piece of gym equipment that can also be used for single-arm rows. To perform a single-arm row on a cable machine, adjust the weight to the desired resistance and attach a handle to the cable.
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for her phone service, jenny pays a monthly fee of $24, and she pays an additional $0.06 per minute of use. the least she has been charged in a month is .what are the possible numbers of minutes she has used her phone in a month?use for the number of minutes, and solve your inequality for $96.36.
Answers
Jenny must have used at least 1600 minutes of her phone service to incur a minimum monthly fee of $96.36. This can be calculated by solving the inequality $24 + 0.06x ≥ $96.36 where x is the number of minutes.
Rearranging this equation to 0.06x ≥ $72.36 and solving for x gives us the result x ≥ 1600.
Given that, For her phone service, Jenny pays a monthly fee of $24, and she pays an additional $0.06 per minute of use. The least she has been charged in a month is $96.36.To find the possible numbers of minutes she has used her phone in a month.
Inequality for $96.36 is(0.06m + 24) ≥ 96.36where m is the number of minutes used. In order to solve the above inequality, we will simplify it first(0.06m + 24) ≥ 96.360.06m + 24 - 24 ≥ 96.36 - 24.060.06m ≥ 72.36m ≥ 72.36/0.06m ≥ 1206So, the possible numbers of minutes she has used her phone in a month is greater than or equal to 1206 minutes. Answer: $\boxed{m≥1206}$
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[tex]306^{2} +270^2[/tex]
Answers
USE PEDMAS PLEASE 30 POINTS
Select the expression that makes the equation true.
one half x (3 x 5 + 1) – 2 = ___
4 x (2 + 3)
(4 x 3) ÷ 2
6 ÷ 3 + 2
6 + 8 ÷ 4
Answers
The expression that makes the equation true= 4 x (2 + 3).
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
Hence, The expression that makes the equation true=
4 x (2 + 3).
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Answer:
a
Step-by-step explanation:
none
A tabletop in the shape of a trapezoid has an area of 6,350 square centimeters. Its longer base measures 115 centimeters, and the shorter base is 85 centimeters. What is the height?
Answers
The height of the trapezoid can be found by dividing the area (6,350 cm2) by the average of the two bases (100 cm). The height is 63.5 cm.
The formula used to find the area of a trapezoid is A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the two bases and h is the height. We are given the area (A) and the lengths of both bases (b1 and b2). All we need to do is solve for h.
To do this, we first need to find the average of the two bases. The average of the two bases is the sum of the two bases divided by two. In this case, the longer base (b1) is 115 cm and the shorter base (b2) is 85 cm, so we can calculate the average as (115 + 85) ÷ 2 = 100 cm.
We can now substitute this value into the area formula and solve for h. A = (1/2)(100)h, so h = A ÷ (1/2)(100). Plugging in the area given (6,350 cm2), we get h = 6,350 ÷ (1/2)(100) = 63.5 cm. The height of the trapezoid is 63.5 cm.
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Work out the value of u in the equation below. Give your answer to 1 d.p.
tan 34° = 9/u
Answers
Answer:
u ≈ 13.3
Step-by-step explanation:
tan34° = [tex]\frac{9}{u}[/tex] ( multiply both sides by u )
u × tan34° = 9 ( divide both sides by tan34° )
u = [tex]\frac{9}{tan34}[/tex] ≈ 13.3 ( to 1 decimal place )
Can someone please help me!!
Answers
Answer: 240°
Step-by-step explanation:
The sum of the angles in a circle adds up to 360°, and the central angles are congruent to its arcs, so what we have is arcGFE + arcGHE = 360°, but we know arcGHE adds up to 120°. This makes our equation arcGFE + 120° = 360°, which means arcGHE = 240°
What is the solution to this equation?
x/5 = 25
A. x=20
B. x=30
C. x=20
D. x=125
Answers
Answer:D. x=125
Step-by-step explanation:
Answer:D
Step-by-step explanation:
125/5= 25
REFLECTION HELP If P= (-2,4), then find: Ry=1 (P)
(?, ?)
Answers
Answer:
P'(-2, -2)
Step-by-step explanation:
You want to know the location of P(-2, 4) after it is reflected in y=1.
ReflectionThe image point will be as far below the line y=1 as point P is above the line. The x-coordinate is unchanged.
P is 4 -1 = 3 units above the line y=1.
P' will be 3 units below the line y=1, so its y-coordinate is 1 -3 = -2.
The image point is P'(-2, -2).
__
Additional comment
Reflection in the line y=k is described by the transformation ...
(x, y) ⇒ (x, 2k-y)
P(-2, 4) ⇒ P'(-2, 2(1) -4) = P'(-2, -2)
if there are 10 students and sum of their age is 150 then find the mean age of students
Answers
[tex]10[/tex] pupils mean in age from sum [tex]150[/tex] to [tex]15[/tex] years.
What does the math mean?The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from the scaling factor) of a dataset. This indicator of central tendency is usually referred to as the "average".
How is the mean determined?Just dividing the total number of values inside a data collection by the sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table may be utilized in the computation. Often, average is referred to as mean or mathematical mean. Mean is only a way of summarizing the sample's average.
Mean age [tex]=[/tex] (sum of ages) / (number of students)
Mean age [tex]= 150 / 10[/tex]
Mean age [tex]= 15[/tex]
Therefore, the mean age of the [tex]10[/tex] students is [tex]15[/tex] years.
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Which of the following equations will produce the graph shown below?
A. X^2- y^2/4= 1
B. Y^2/9 - x^2/4=1
C. Y^2- x^2/9= 1
D. Y^2/2 - x^2/4= 1
Answers
From following equations option B will produce the hyperbola graph shown in the figure
what is hyperbola ?
A hyperbola is a type of conic section, which is a curve that is formed by the intersection of a plane and a double cone. A hyperbola can also be defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is a constant.
In the given question,
Based on the shape of the hyperbola shown on the y-axis graph, we can tell that the hyperbola has a vertical transverse axis, which means that its equation must have the form:
(y - k)² / a² - (x - h)² / b² = 1
where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.
Option A is not correct because it produces a hyperbola with a horizontal transverse axis, whereas the given graph has a hyperbola with a vertical transverse axis.
We can eliminate option D since its equation has a transverse axis that is not vertical.
Next, we can eliminate option A since the coefficient of x² is positive, which means that the transverse axis is horizontal.
Option C has a transverse axis that is also horizontal, so we can eliminate it as well.
That leaves us with option B, which has a vertical transverse axis and its equation fits the form we determined earlier. Therefore, the equation Y²/9 - x²/4=1 will produce the hyperbola shown on the y-axis graph
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What is the similarity between these numbers: 7, 21, 69, 71?
A They are all multiples of 7
B They are all factors of 71
C They are all prime numbers
D They have a pattern of + 14
Answers
Answer:
A
Step-by-step explanation:
The answer is A because the numbers only go under category A
make a cylinder and find
CSA
TSA
Volume
Answers
Answer:
This means that a cylinder has two kinds of surface areas -Total Surface Area (TSA) and Curved Surface Area (CSA). For a cylinder whose base radius is 'r' and height is 'h': TSA of cylinder = 2πr2 + 2πrh (or) 2πr (r + h) CSA of cylinder = 2πrh.
Help me find area
9th grade
Answers
Answer:
Step-by-step explanation: add all of them together
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5 5 5
2 0 0 0 0 3 6
3 0 1 4 9 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5 5 5
2 0 0 0 0 3 6
3 1 4 9 9
Key 1|1 = 11
Answers
Not answer but helpful:
The required stem-and-leaf plot shown below that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s.
What is stem-and-leaf plots?
A stem-and-leaf plot is a type of data display that helps to show the distribution of a set of numerical data.
here,
For the given data set:
Stem Leaf
0 4
1 1, 3, 3
2 0, 0, 0, 6, 7
3 0, 0, 0, 7
The stem-and-leaf plot shows that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s. The plot makes it easier to see the distribution of the data, rather than just looking at the raw values.
a sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. the total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. which system of equations can be used to find s, the number of pages in each issue of the sports magazine, and t, the number of pages in each issue of the technology magazine?
Answers
The number of pages in each issue of the technology magazine is 74 pages.
The number of pages in each issue of the sports magazine is s and the number of pages in each issue of the technology magazine is t.
To solve this problem, we have to write a system of equations using the given information. We have to find s and t.
System of equations can be used to find s and t; 12s = 10t + 32 and t = s + 18
The given sports magazine prints 12 issues per year and the technology magazine prints 10 issues per year.
The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. That means we can write an equation based on the information given for the number of pages in all the issues of the sports magazine and the technology magazine.
12s = 10t + 32
We also know that each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. That means we can write another equation based on the information given for the number of pages in each issue of the sports magazine and the technology magazine.
t = s + 18
Now, we can solve for s and t by substituting t = s + 18 in the first equation: 12s = 10(s + 18) + 32
12s = 10s + 180 + 32
12s - 10s = 180 + 32s = 56
So, the number of pages in each issue of the sports magazine is 56 pages. And, the number of pages in each issue of the technology magazine is: t = s + 18t = 56 + 18t = 74 pages.
So, each issue of the technology magazine contains 74 pages.
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