The cost of each pen is $25. This can be solved using unitary method.
Unitary method: what is it?In the unitary technique, the value of a single unit is determined first, and then the value of the required number of units is determined.
When employing ratio and proportion to solve a problem, it is essential to comprehend the units and values.
To make things simpler, always place the known facts on the left and the things that need to be calculated on the right. The number of apples in the aforementioned situation is known, but it is unclear how much the fruit is worth on the market.
It should be stressed that the unitary technique applies the notions of ratio and proportion to problems.
Let the cost of each pen be x .
then according to the question, the cost of book will be x-10
now
90 = 3x + x - 10
x = 25
hence the cost of the book is x - 10 = 15
and the cost of each pen is 25
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2. In a books sale, 1461 books were sold on Friday.
On Saturday 2396 books were sold.
a. How many books were sold on both days?
b. How many more books were sold on Saturday than on
Friday?
Answer:
1750 BOOKS
Step-by-step explanation:
Answer:
There were a total of 14 books on Friday and 2396 on Saturday to find the total amount sold on both days you will add the two together.
1,461 + 2,396 = 3,857
A. There were a total of 3, 857 books sold on both days.
To find how many more books were sold on Saturday than Friday, youn will subtract.
2,396 - 1,461 = 935
B. 835 more books were sold on Saturday than Friday.
Step-by-step explanation:
Hope it helps! =D
the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w if it takes 10 hours to paint 400 feet of fence with six workers how long it will take for 10 workers to paint 1000 ft fence
Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
What is proportionality constant?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.
Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.
This is represented as follows:
t = k(l/p)
Where, k is the proportionality constant.
Given that, it takes 10 hours to paint 400 feet of fence with six workers.
Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:
10 = k (400 / 6)
10 = k (66.66)
k = 10 / 66.66
k = 0.15
Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:
t = (0.15) (1000 / 10
t = (0.15) (100)
t = 15
Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
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A certain type of insect has a 0.2 chance of dyingonanyonedayandthisprobability remains relatively constant for a few days.
a. Whatistheprobabilitythataninsectof this type survives its first day?
b. Whatistheprobabilitythataninsectof this type survives its first three days?
c. Whatistheprobabilitythataninsectof this type dies on its fourth day?
d. How many days do you expect an insect of this type to survive?
e. If 200 insects of this type are being studied in a laboratory, how many do you expect to be alive after the third day?
The answer to each question are:
a). probability of an insect of this type surviving its first day is 0.8
b). probability of an insect of this type surviving it's first three days is 0.512.
c). probability of an insect of this type dying on its fourth day is 0.2.
d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.
a). The probability that an insect of this type survives its first day is 1 - 0.2 = 0.8.
b). The probability that an insect of this type survives it's first three days is 0.8 * 0.8 * 0.8 = 0.512.
c). The probability that an insect of this type dies on its fourth day is 0.2.
d). The expected number of days that an insect of this type would survive is not determinable with the information given.
e). If 200 insects of this type are being studied in a laboratory, you would expect approximately 200 * 0.512 = 102.24 to be alive after the third day. Round down to 102 insects.
Hence, The answer to each question is:
a). probability of an insect of this type surviving its first day is 0.8
b). probability of an insect of this type surviving it's first three days is 0.512.
c). probability of an insect of this type dying on its fourth day is 0.2.
d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.
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need the answer asap ! thank you to anyone who helps !
Answer:
Step-by-step explanation:
D
How do I find the median of this trapezoid?
The median of the trapezoids is given by QR = 23.5 and VW = 15.2
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the first trapezoid be represented as A
Let the second trapezoid be represented as B
Now , the median of the trapezoid M = ( 1/2 ) ( sum of longer base and shorter base )
Substituting the values in the equation , we get
a)
The length of longer base = 35.6
The length of shorter base = 11.4
So , the median of A is QR = ( 1/2 ) ( 35.6 + 11.4 )
On simplifying the equation , we get
The median of trapezoid QR = ( 1/2 ) 47
The median of trapezoid QR = 23.5
b)
The length of longer base = 19.1
The length of shorter base = 11.3
So , the median of B is VW = ( 1/2 ) ( 19.1 + 11.3 )
On simplifying the equation , we get
The median of trapezoid VW = ( 1/2 ) 30.4
The median of trapezoid VW = 15.2
Hence , the median of trapezoid is solved
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Question: Graph the inequality on the axes below.
y ≤ x -2.
where would i graph, where would i shade and is the line dotted or not
Answer:
To graph the inequality y ≤ x - 2 on the axes, you would:
Plot the line y = x - 2 on the graph. The line will be a straight line passing through the point (-2,0) and has a slope of 1.
Determine the direction of the inequality symbol. Since it is a less-than-or-equal-to symbol, we will shade the region that is less than or equal to the line.
Shade the region that is less than or equal to the line in the graph. In this case, the region above the line y = x - 2.
The line is solid, it's not dotted.
Note: The graph will be a straight line that is tilted towards the top right of the coordinate axes, the region above the line will be shaded.
Step-by-step explanation:
what is statistical risk? a board game in which you attempt to conquer the world by strategically positioning your armies to destroy your enemies so you can rub it in the face of your brothers or sisters for the rest of the vacation or weekend the long run probability that you will make a particular kind of mistake the prbability that a single flip of a coin will come up 'tails' none of the above
Statistical risk refers to the likelihood of an adverse event occurring, as determined through statistical analysis. This can include events such as financial loss, injury, or death. It is typically measured using probability, which is a value between 0 and 1 that represents the likelihood of an event occurring.
For example, in finance, the risk of an investment is often measured by the standard deviation of the returns over time. In healthcare, the risk of a particular treatment or procedure is often measured by the rate of complications or adverse events.
The board game you described, where the goal is to conquer the world, does not involve statistical risk. It is a game of strategy, and the outcome is determined by the players' decisions and actions, rather than by chance.
The long-run probability of making a particular kind of mistake is an example of statistical risk. For example, if a pilot has a history of making landing errors, we can use statistical analysis to determine the probability that they will make a similar mistake in the future.
The probability that a single flip of a coin will come up 'tails' is also an example of statistical risk. In this case, the probability of the coin landing tails is 0.5 or 50%.
In summary, Statistical risk is the likelihood of an adverse event occurring, as determined through statistical analysis. It is measured using probability, and it is used to understand and manage the risk in various fields such as finance, healthcare, and engineering.
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a smaller square of side length feet is cut out of a square board. what is the approximate area (shaded region) of the remaining board in square feet?
If a smaller square of side length 17 feet is cut out of a square board , then the approximate area of remaining board in square feet is x² - 289 square feet .
le the side length of the big square board be = "x" ft ;
the side length of smaller square is = 17 ft ;
So , the area of the smaller square is = (side length) × (side length)
= 17 × 17
= 289 ft² .
and , the area of the larger square is = (x) × (x) ;
= x² .
So , the approximate area of the remaining board is calculated as :
= x² - 289 ;
Therefore , area of remaining board is "x² - 289" .
The given question is incomplete , the complete question is
A smaller square of side length 17 feet is cut out of a square board. What is the approximate area of the remaining board in square feet ?
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I just don't understand any of this because I'm dyslexic.
Answer:
HI = 9
Step-by-step explanation:
HJ = HI + IJ
2x + 10 = x + 9 + 1
2x - x = 10 - 10
∴ x = 0
∴ HI = x + 9
= 0 + 9
= 9
8x+10y=-30 into slope intercept form, simplifying all fractions
A conversion of this equation in standard form to slope-intercept is y = 4x/5 - 3.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.Based on the information provided about the line, it is represented by this equation;
8x + 10y = -30
Making y the subject of formula in the above equation, we have the following:
10y = 8x - 30
y = 8x/10 - 30/10
y = 4x/5 - 3
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What is the slope of the line shown in the graph?
Someone please help me :/
Answer: It's the third down. (-1/-2) - PLEASE TAKE THIS WITH A GRAIN OF SALT. I'm not very good at this type of math.
Step-by-step explanation:
What is the ordered pair that represents the point (−4, −7) after a reflection over the x-axis?
(4, 7)
(−4, 7)
(7, −4)
(−7, −4)
After reflection over the x-axis the ordered pair is at (-4, 7).
What is the reflection?When two different media come together at an interface, a wavefront might change direction so that it returns to the first medium, which is known as reflection.
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
Here,
The reflection of point (-4, 7) across the x-axis is (-4, -7).
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Need help please !!
Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers,and 20% are German shepherds. He designs a simulation.
Let 0,1, and 2 represent retrievers.
Let 3 and 4 represent terriers.
Let 5 and 6 represent German shepherds.
Let 7,8, and 9 represent other dogs.
The table shows the simulation results
The probability that at least one of the next five dogs he sees is a German shepherd is 0.75.
We have from the question.
0,1, and 2: retrievers
3 and 4: terriers
5 and 6: German shepherds
7,8 and 9: other dogs
In these results, 5 and 6 represent a german shepherd "at least one of the next five dogs he sees is a German shepherd." this means that at least one of the five numbers is 5 or 6.
There are a total of 20 results among them; 12 results include at least one 5 or 6.
∴P = 12/20 = 0.75
Hence, the correct option is B.
--The given question is incomplete; the complete question is
"Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers, and 20% are German shepherds. He designs a simulation. Let 0,1 and 2 represent retrievers. Let 3 and 4 represent terriers. Let 5 and 6 represent German shepherds. Let 7,8, and 9 represent other dogs. The table shows the simulation results. According to this simulation, what is the probability that at least one of the next five dogs he sees is a German shepherd?
A. 0.70
B. 0.75
C. 0.65
D. 0.60"--
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Select the correct answer
Consider this absolute value function.
f(x)=[x+3]
if function f is written as piece wise function which piece will include?
Absolute value function f(x) = | x + 3 | written in piece wise function includes the piece given by option B . x + 3, x > -3.
Function f(x) is represented as absolute value function:
f(x) = | x + 3 |
Absolute function is always positive when the included variable is greater than zero.
| x + 3 | > 0
⇒ ( x + 3 ) > 0
Subtract three from both the sides we get,
⇒ x + 3 - 3 > 0 - 3
⇒ x > -3
Here piecewise function incudes the piece :
x + 3, x > -3.
Therefore, the absolute function f(x) = | x + 3 | includes the piece after written in piecewise function form is equal to option B. x + 3, x > -3.
The above question is incomplete , the complete question is:
Select the correct answer.
Consider this absolute value function.
f(x) = | x + 3 |
If function f is written as a piecewise function, which piece will it include?
A. x + 3, x > 3
B. x + 3, x > -3
C. -x + 3, x < -3
D. -x - 3, x < 3
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K travels 1 mile north, then 2 miles east, then 3 miles north again, and then once more east for 4 miles.
How far is she from her starting point when she arrives? Round to the nearest hundredth
The total distance from the starting point is 7.21 miles
Now, According to the question:
The movements are represented as:
[tex]N_1= 1miles\\E_1= 2miles\\\\N_2 =3 miles\\\\E_2 = 4miles[/tex]
To find the distance from the starting point.
First, calculate the total distance towards North.
[tex]N = N_1+N_2[/tex]
N = 1 + 3
N = 4 miles
Next, calculate the total distance towards East
[tex]E = E_1+E_2[/tex]
E = 2 + 4
E = 6 miles
The total distance from the starting point is calculated using Pythagoras theorem.
[tex]D^2=N^2+E^2[/tex]
[tex]D^2[/tex] = [tex]4^2+6^2[/tex]
[tex]D^2[/tex] = 16 + 36
[tex]D^2 =[/tex] 52
[tex]D = \sqrt{52}[/tex]
D = 7.21
Hence, The total distance from the starting point is 7.21 miles
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Factorise the following expression
please
The factorization of the given expression is p(4p-12q+qp).
What is factorization?The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.
The given expression is 4p²-12pq+qp².
Group and factor out the greatest common factor (GCF), then combine.
Here, the greatest common factor of the terms is p
Now, p(4p-12q+qp)
Therefor, the factorization of the given expression is p(4p-12q+qp).
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What is the sum of the geometric series?
Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 2) (negative 3) Superscript n minus 1
–122
–2
40
54
Step-by-step explanation:
Σ^n=1 -144 (1/2)n-1
This is a finite geometric series with n
=4, a₁-144, and r = 2.
S = a₁ (1-r") / (1 − r)
S-144 (1 - (1/2)) / (1 - 1/2)
S=-270
If you wanted to find the infinite sum (n
= ∞0)
:S = a₁ / (1 − r)
S-144/(1-1/2)
S=-288
Find the perimeter of a rectangle measuring 4.1263cm long and 2.8315cm. Correct the answer to 3d.p and 3s.f
The perimeter of a rectangle measuring 4.1263cm long and 2.8315cm is 13.9 cm
How to determine the perimeter of the rectanglefrom the question, we have the following parameters that can be used in our computation:
Length = 4.1263 cm
Width = 2.8315 cm
The perimeter of a rectangle can be calculated using tge following equation
Perimeter = 2 x (Length + Width)
substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 x (4.1263 + 2.8315)
Evaluate
Perimeter = 13.9156
Approximate
Perimeter = 13.9 to 3 significant figures
Perimeter = 13.916 to 3 decimal places
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Please help me out on my homework
Answer: No Solution is the answer
Step-by-step explanation:
Have a photo attached with the work
What is the product of the polynomials?
Answer:
Multiply all of the terms of each polynomial and then combine like terms. Example: Multiply: ( 2 x 2 + x − 3 ) ( x 2 − 2 x + 5 ) . Solution: Multiply each term of the first trinomial by each term of the second trinomial and then combine like terms.
In the graph, the area above f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.
Graph of two intersecting lines. The line g of x is solid, and goes through the points 0, negative 2 and 1, 0 and is shaded in below the line. The other line f of x is dashed, and goes through the points 0, 3, 3, 0 and is shaded in above the line.
The graph represents which system of inequalities?
Group of answer choices
y > 2x − 3
y > −x − 3
y < 2x − 2
y < −x + 3
y ≤ 2x − 2
y > −x + 3
None of the above
The given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.
What are inequalities?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
If an inequality matching y > -ax + b is solved, area A will be shaded above a dashed line with a negative slope.
Such inequality exists between Options A and C.
The solution of an inequality that fits y ax + b will be below a solid line with a positive slope where region B is shaded (for some positive a).
The only option with the correct inequality symbol is Choice C.
We discover that choice C matches the graph when we closely examine it.
Region A matches y > -x+3 because the line with a negative slope has a slope of -1 and a y-intercept of 3.
Region B corresponds to y 2x -2 because the line with a positive slope has a slope of +2 and a y-intercept of -2.
Therefore, the given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.
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Correct question:
In the graph, the area above f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.
Graph of two intersecting lines. The line g of x is solid, and goes through the points 0, negative 2 and 1, 0 and is shaded in below the line. The other line f of x is dashed, and goes through the points 0, 3, 3, 0 and is shaded in above the line.
The graph represents which system of inequalities?
Group of answer choices
a. y > 2x − 3
y > −x − 3
b. y < 2x − 2
y < −x + 3
c. y ≤ 2x − 2
y > −x + 3
d. None of the above
3. Find the area of the circle below.
Help the circle is 3
Answer:
28.26 [tex]in^{2}[/tex]
Step-by-step explanation:
a = [tex]\pi r^{2}[/tex]
a = 3.14([tex]3^{2}[/tex])
a = 3.14(9)
a = 28.26
How to solve image. (solving rational expressions) and check for extraneous solutions
The evaluation of the equation to find the value of n in the rational function [tex]\frac{1}{n^2} + \frac{1}{n} = \frac{1}{2\cdot n^2}[/tex] is; n = -1/2
What is a rational function?A rational function is a function that contains rational fractions, such that the dividend and the divisor are polynomial expressions.
2) The specified rational equation or function can be presented as follows;
1/(n²) + 1/n = 1/(2·n²)The above equation consists of rational expressions. The expressions can be resolved by collecting like terms as follows;
The like terms are terms that can be resolved by simple addition or subtraction.
1/n = 1/(2·n²) - 1/(n²) = (1 - 2)/(2·n²) = -1/(2·n²)
1/n = -1/(2·n²)
Multiplying both sides by n, we get;
(1/n) × n = (-1/(2·n²)) × n
(1/n) × n = 1 = (-1/(2·n))
1 = (-1/(2·n))
Multiplying both sides by n, we get;
1 × n = (-1/(2·n)) × n
n = -1/2
The value of n in the equation, 1/(n²) + 1/n = 1/(2·n²), is -1/2Learn more on rational functions here: https://brainly.com/question/29185109
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Ella went on a walk that was 12/5 miles long. She
stopped to have lunch when she had walked 15/16 of
the way.
How far, in miles, did Ella walk before lunch?
Give your answer as a fraction in its simplest form.
Answer:
12/5 = 2.4 miles
2.4 x (15/16) = 2.25 miles.
2.25, or 9/4 miles
A student is standing, with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kg m2.
What is her final moment of inertia (If)?
The student's final moment of inertia is 18.18 kgm².
What is moment of inertia?The moment of inertia of an objecr is the property of an object which shows its ability to rotate.
How to find the final moment of inertia?Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.
What is the law of conservation of angular momentum?The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.
So, Iω = constant where
I = moment of inertia and ω = angular speed.So, Iω = I'ω' where
I = initial moment of inertia of student = 25kgm²ω = initial angular speed of student = 1.6 rev/s I' = final moment of inertia of student ω' = final angular speed of student = 2.2 rev/sMaking I' subject of the formula, we have that
I' = Iω/ω'
So, substituting the values of the variables into the equation, we have that
I' = Iω/ω'
I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s
= 40 kgm²rev/s ÷ 2.2 rev/s
= 18.18 kgm²
So, the final moment of inertia is 18.18 kgm².
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Create a proportion for each set of similar triangles, that can be used to find the missing side lengths indicated. Then solve the proportion.
Using the created proportion for each set of similar triangles, the missing side lengths are 3√29 units and 24 units respectively
How to create a proportion for a set of similar triangles?Similar triangles are triangles that have the same shape, but not necessarily the same size. Two triangles are similar if and only if they have the same shape, meaning they have the same angle measures.
For the 1st triangles, we can write the proportion as follows:
proportion = (√29)/5
(√29)/5 = x/15
x = 15 × (√29)/5
x = 3√29 units
Thus, the missing side length is 3√29 units
For the 2nd triangles, we can write the proportion as follows:
proportion = 12/13
12/13 = x/26
x = 26 × (12/13)
x = 24 units
Thus, the missing side length is 24units
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i need help please i have been stuck on this problem for 2 months
Answer:
$8
Step-by-step explanation:
Which are solutions for the inequality k≤12
? (Select all that apply)
The negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
We need to find the solutions for the inequality k≤12
k lesser than or equal to twelve.
Which means the solution of the inequality are the values which are lesser than or equal to 12.
The solution of the inequality k≤12 is (-∞, 12]
All the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.
Hence, the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.
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Does someone mind helping me with problem? Thank you!
The number of people that attended the school play is given as follows:
Adults: 325.Students: 612.How to model the situation?The situation is modeled by a system of equations, for which the variables are given as follows:
Variable a: number of adults.Variable s: number of students.There was a total of 937 people, hence:
a + s = 937.
s = 937 - a.
The total sales were of $1,109, hence:
2a + 0.75s = 1109.
Replacing s = 937 - a in the second equation, the number of adults is obtained as follows:
2a + 0.75(937 - a) = 1109
1.25a = 406.25
a = 406.25/1.25
a = 325.
Then the number of students is obtained as follows:
s = 937 - a
s = 937 - 325
s = 612.
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−n + (−3) + 3n + 5
please help its due tmrw