The store has a surplus of 10000 pencil packs and decided to donate them to area schools. If there are 27 schools and the store wants to donate the same number of packs to each school, each school will receive 370 packs.
To calculate the number of packs each school will receive, we need to divide the total number of packs by the number of schools.
In this case, we have:
Total number of packs = 10000
The number of schools = 27
The number of packs each school will receive = Total number of packs / Number of schools= 10000 / 27= 370
Therefore, each school will receive 370 pencil packs.
To know more about surplus,visit:
https://brainly.com/question/28537213
#SPJ11
An IV blood administration is in place. A bag of 376 ml is hung at
1100hrs. How long will this bag take to infuse at maximum time?
The time it would take for the bag to infuse at the maximum time would be the value of 1. 5 hours.
How to find the time ?The maximum rate of infusion for an IV bag is 250 ml/hour. This means that the maximum time it would take for the bag to infuse is:
= Quantity in bag / Maximum rate of infusion
Therefore, it will take:
= 376 ml / 250 ml/hour
= 1. 5 hours to infuse the entire bag
In conclusion, the time it would take for the bag to infuse at the maximum time is 1. 5 hours.
Find out more on Blood administration at https://brainly.com/question/30748600
#SPJ4
Cinia has made a pyramid model for her history project at school. The pyrarrid model has a square base. Each triangular side of the model has a
base length of 10 centimeess and a slant height of ē. 9 centimeters. Olivia wants to wrap the pyramid in wrapping paper before putting it into her
school bag
How much wrapping paper will Ona need to cover the pyramid?
Olivia will need 280 square centimeters of wrapping paper to cover the pyramid for her history project.
To calculate the amount of wrapping paper Olivia will need to cover the pyramid, we need to find the total surface area of the pyramid, including the base and the triangular sides.
The base of the pyramid is a square, so its area can be found by squaring the length of one side. Given that the base length is 10 centimeters, the area of the base is 10^2 = 100 square centimeters.
The triangular sides of the pyramid are all congruent, so we can calculate the area of one triangular side and multiply it by the number of sides (4 in this case) to get the total area.
To find the area of one triangular side, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the base length is 10 centimeters, and the height is the slant height of 9 centimeters.
Area = (1/2) * 10 * 9 = 45 square centimeters
Since there are four triangular sides, the total area of the triangular sides is 4 * 45 = 180 square centimeters.To calculate the total surface area, we need to add the area of the base and the area of the triangular sides:
Total surface area = base area + triangular side area
Total surface area = 100 + 180 = 280 square centimeters
Therefore, Olivia will need 280 square centimeters of wrapping paper to cover the pyramid for her history project.
Learn more about pyramid here
https://brainly.com/question/30615121
#SPJ11
Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48. 1 ppm and a standard deviation of 6 ppm. The Environmental Protection Agency takes a random sample of 37 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 48. 5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places
To find the probability that the disposal of small capacitors containing PCB will be regulated, we need to calculate the probability that the sample mean amount of PCB is 48.5 ppm or more. The mean amount of PCB in these capacitors is 48.1 ppm, with a standard deviation of 6 ppm.
We can use the Central Limit Theorem and the standard normal distribution to determine the probability. By calculating the z-score and using the z-table or a statistical calculator, we can find the probability.
To calculate the probability, we can use the Central Limit Theorem, which states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the underlying distribution of the population.
First, we calculate the z-score using the formula:
z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
In this case, the sample mean is 48.5 ppm, the population mean is 48.1 ppm, the standard deviation is 6 ppm, and the sample size is 37.
z = (48.5 - 48.1) / (6 / sqrt(37))
Calculating the z-score:
z ≈ 0.1404
Next, we can use the z-table or a statistical calculator to find the probability associated with the z-score. The probability corresponds to the area under the standard normal distribution curve beyond the z-score.
Using the z-table or a calculator, we find that the probability is approximately 0.556.Rounding to three decimal places, the probability that the disposal of these capacitors will be regulated is approximately 0.556.
To learn more about Z-score - brainly.com/question/31871890
#SPJ11
Identify the expression as an equation containing factors, a fractional equation, or a proportion.
2x/x+7 - x/x+3 = 1 + 1/x^2+10+21
A. Proportion
B. Fractional Equation
C. Equation containing fractions
The given expression is an equation containing fractions.
Given expression is:
[tex]$$\frac{2x}{x+7} - \frac{x}{x+3} = 1 + \frac{1}{x^2+10x+21}$$[/tex]
We can rewrite the given expression as follows:
[tex]$$\frac{2x(x+3)-x(x+7)}{(x+7)(x+3)}=\frac{x^2+10x+22}{(x+3)(x+7)}$$[/tex]
Simplifying the numerator and denominator of the above expression,
we get:[tex]$$\frac{x^2-4x-21}{(x+7)(x+3)} = \frac{x^2+10x+22}{(x+7)(x+3)}$$[/tex]
On simplifying, we get the following equation:
[tex]$$x^2-4x-21=x^2+10x+22$$[/tex]
Simplifying the above equation, we get:
$$14x=-43$$
On dividing by 14 on both sides,
we get:[tex]$${x=-\frac{43}{14}}$$[/tex]
To know more about denominator visit:
https://brainly.com/question/32621096
#SPJ11
Mark wants to buy a video game for $39.99, he has a 30% discount and then pays 5% sales tax. What is the final cost of the video game?
Given the cost of the video game is $39.99, Mark gets a discount of 30%.Content loaded means there's enough information available to solve the problem. Here's how to find out the final cost of the video game. First, calculate the discount on the cost of the video game:$39.99 × 30/100 = $11.997
This gives us the discount that Mark gets on the video game. So, the cost of the video game after discount will be: Cost of the video game = $39.99 - $11.997 = $27.993Now, let's add the sales tax. The sales tax is 5%. Thus, the sales tax will be: Sales tax = $27.993 × 5/100 = $1.39965So, the final cost of the video game will be :Final cost = $27.993 + $1.39965 = $29.39265Thus, the final cost of the video game after the discount and the sales tax is $29.39.
Learn more about discount here:
https://brainly.com/question/2730006
#SPJ11
¿Qué altura tiene un poste que proyecta una sombra de 16m,al mismo tiempo que un observador de 1.80m de estatura proyecta una sombra de 1.20m?
To determine the height of the pole, we can use the concept of similar triangles. The ratios of corresponding sides of similar triangles are equal.The height of the pole is 24 meters.
By setting up a proportion between the height of the pole and the length of its shadow and the height of the observer and the length of their shadow, we can find the height of the pole.
Let's denote the height of the pole as h. We can set up a proportion between the height of the pole and the length of its shadow and the height of the observer and the length of their shadow:
h / 16 = 1.80 / 1.20
By cross-multiplying and solving for h, we get:
h = (16 * 1.80) / 1.20 = 24
Therefore, the height of the pole is 24 meters.
To learn more about similar triangles click here :
brainly.com/question/29731302
#SPJ11
Which is the correct simplified version of the expression shown below after distributing and combining like terms? 4(9-3/4x)+6x
The correct simplified version of the expression 4(9-3/4x)+6x after distributing and combining like terms is: 33 - 6x. To understand the concept of distributing and combining like terms, let us first take a look at the original expression.
4(9-3/4x)+6xTo simplify this expression, we start by applying the distributive property of multiplication over addition. That is, we multiply the number outside the parentheses (4) by each term inside the parentheses. This gives us:36 - 3x + 6xNext, we combine like terms. Here, the like terms are -3x and 6x since they both have the variable x in them. When we combine them, we get 3x. Hence, we have:36 + 3xFinally, we simplify further by rearranging the terms in descending order of degree. This gives us the final expression:3x + 36However, this is not one of the answer options provided in the question.
Therefore, we need to simplify it further. We can do this by taking out a common factor of 3 from the two terms. This gives us:3(x + 12)We can check that this is the correct answer by distributing the 3 back in and confirming that we get the original expression. Therefore, the correct simplified version of the expression after distributing and combining like terms is: 33 - 6x.
To know more about expression visit:
https://brainly.com/question/28170201
#SPJ11
A vendor has $22.00 and wants to buy bushels of corn. The vendor finds a farmer who sells each bushel of corn for $3.00 and charges a fixed delivery fee of $5.50.
The vendor cannot purchase a fraction of a bushel, the vendor can afford to buy a maximum of 5 bushels of corn with the given amount of money.
To determine how many bushels of corn the vendor can afford to buy, we need to consider the cost of each bushel of corn and the fixed delivery fee. Here's how we can calculate it:
Subtract the fixed delivery fee from the total amount of money the vendor has:
$22.00 - $5.50 = $16.50
Divide the remaining amount of money by the cost per bushel of corn to find the maximum number of bushels the vendor can buy:
$16.50 ÷ $3.00 = 5.5 bushels
Since the vendor cannot purchase a fraction of a bushel, the vendor can afford to buy a maximum of 5 bushels of corn with the given amount of money.
Please note that in this calculation, we assumed that the vendor would spend all of the available money on purchasing corn, without considering any additional expenses or constraints.
Learn more about vendor here
https://brainly.com/question/29157067
#SPJ11
Levi has the next 5 hours available to work on a research paper, and he can type 80 words per minute. The function W(t)=80t represents the number of words Levi produces in t minutes of typing. In this context, what is the largest possible domain of W(t)?
The largest possible domain of W(t) is [0, 300].
Levi has 5 hours to work on a research paper and he can type 80 words per minute. The function W(t) = 80t represents the number of words Levi produces in t minutes of typing. We want to find the largest possible domain of W(t). The domain of W(t) is the set of all possible input values of t that make the function W(t) defined. So, we need to find out the maximum number of minutes Levi can work for. We know that he has 5 hours to work, and there are 60 minutes in one hour.
Therefore, he has a total of: 5 hours × 60 minutes/hour = 300 minutes Thus, the domain of W(t) is the set of all real numbers between 0 and 300 inclusive. We include 0 because Levi can type for 0 minutes (i.e. he hasn't started typing yet), and we include 300 because that's the maximum number of minutes he has available to type in. Hence, the largest possible domain of W(t) is [0, 300].
To know more about possible visit:-
https://brainly.com/question/30584221
#SPJ11
A regulation baseball has a diameter of about 3 in. What is the best approximation for the volume of this baseball? 14. 13 in³ 28. 26 in³ 84. 78 in³ 113. 04 in³ baseball with diameter of 3 inches.
The best approximation for the volume of a regulation baseball with a diameter of about 3 inches is 14 in³.
The volume of a sphere is given by the formula V = (4/3)πr³, where V represents the volume and r represents the radius. In this case, we have the diameter, which is 2 times the radius.
The radius of a baseball with a diameter of about 3 inches is approximately 3/2 = 1.5 inches.
Substituting the radius into the volume formula:
V = (4/3)π(1.5)³ = (4/3)(3.14)(1.5)³ = (4/3)(3.14)(3.375) ≈ 14 in³
Therefore, the best approximation for the volume of the baseball is 14 in³.
Learn more about radius here:
https://brainly.com/question/811328
#SPJ11
In order for a ladder to reach a height of 10 feet it needs to be placed at a 75⁰ angle to the ground. The ground already has an elevation of 15⁰.what degree does the ladder need to me set at?
To reach a height of 10 feet while accounting for the ground elevation of 15⁰, the ladder needs to be set at an angle of approximately 80.77⁰.
When placing the ladder on the ground, we need to consider both the desired height and the ground elevation. Let's denote the angle at which the ladder needs to be set as x⁰.
To find the value of x⁰, we can use trigonometry. In this case, we'll use the tangent function. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the opposite side is the height of the ladder (10 feet), and the adjacent side is the horizontal distance the ladder needs to cover on the ground.
The tangent of an angle is given by the formula: tan(x⁰) = opposite/adjacent.
To calculate the adjacent side, we can use the height of the ladder and the ground elevation angle: adjacent = height / tan(ground elevation).
Plugging in the values, we have: adjacent = 10 / tan(15⁰).
Solving this equation gives us the value of the adjacent side. We can then find x⁰ by taking the arctan of the ratio: x⁰ = arctan(adjacent/height).
Calculating this value, we find x⁰ ≈ 80.77⁰.
Therefore, the ladder needs to be set at an angle of approximately 80.77⁰ to reach a height of 10 feet, accounting for the ground elevation of 15⁰.
Learn more about tangent here: https://brainly.com/question/10053881
#SPJ11
A subwoofer box for sound costs $260. 40 after a price increase. The cost before the price increase was $240. 0. What was the approximate percent of the price increase
Will be awarded brainliest :) PLS HELPP
The approximate percent of the price increase is approximately 8.5%. To find the approximate percent of the price increase, we can use the following formula: Percent Increase = ((New Value - Old Value) / Old Value) * 100
To calculate the approximate percent of the price increase, we can follow these steps:
Determine the old value: In this case, the old value is the cost before the price increase, which is given as $240.0.
Determine the new value: The new value is the cost after the price increase, which is given as $260.40. Calculate the difference: Subtract the old value from the new value to find the increase in price. In this case, it is $260.40 - $240.0 = $20.40.
Calculate the percent increase: Divide the difference by the old value, then multiply by 100 to express it as a percentage. In this case, it is (20.40 / 240.0) * 100 ≈ 8.5%.
Therefore, the approximate percent of the price increase is approximately 8.5%. This means that the price increased by around 8.5% from its original value of $240.0 to the new value of $260.40.
learn more about percent here: brainly.com/question/31323953
#SPJ11
D. If y/z = 0. 7, what is the measure of α to the nearest degree?
If y/z = 0.7, then α can be determined using the trigonometric ratio "tan".
Since y/z = 0.7, we can let y = 7x and z = 10x. Thus, y + z = 7x + 10x = 17x.Also, we have tan α = y/x = (7/10)x/x = 7/10.So, we have tan α = 7/10.Thus, α = tan⁻¹(7/10).
Now, we can use a calculator to evaluate the angle to the nearest degree.
Using a scientific calculator, we can compute tan⁻¹(7/10) ≈ 35.54°.
Hence, the measure of α to the nearest degree is 36° (since we round up to the nearest degree).
That α measures 36° to the nearest degree.
To know more about trigonometric ratio visit :-
https://brainly.com/question/23130410
#SPJ11
The area of a triangular garden can be no more than 160 square feet. The base of the triangle is 12 feet. What is the height of the triangle?
The height of the triangle is approximately 26.67 feet. To find the height of a triangle, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, we know that the area of the triangular garden can be no more than 160 square feet, and the base of the triangle is 12 feet. We can substitute these values into the formula and solve for the height.
160 = (1/2) * 12 * height
Multiplying both sides of the equation by 2:
320 = 12 * height
Dividing both sides of the equation by 12:
height = 320 / 12
height ≈ 26.67 feet
Therefore, the height of the triangle is approximately 26.67 feet.
learn more about equation here: brainly.com/question/29657983
#SPJ11
10 year ago, the ratio o fjeremy's age to ranyd's age to Kaden's age was 4:3:1. the sum of thie r presesnt age is 102. Find randy's age now
To find Randy's age now, we need to use the information provided about the ratio of Jeremy's age, Randy's age, and Kaden's age 10 years ago, as well as the sum of their present ages. By setting up equations based on the given information, we can solve for Randy's age now.
Let's assume that Jeremy's age 10 years ago was 4x, Randy's age was 3x, and Kaden's age was x. This satisfies the given ratio of 4:3:1.
Now, 10 years have passed, so we need to consider their present ages. Jeremy's present age would be 4x + 10, Randy's present age would be 3x + 10, and Kaden's present age would be x + 10.
The sum of their present ages is given as 102, so we can set up the equation:
(4x + 10) + (3x + 10) + (x + 10) = 102
Simplifying the equation, we have:
8x + 30 = 102
Subtracting 30 from both sides, we get:
8x = 72
Dividing both sides by 8, we find:
x = 9
Therefore, Randy's age now is 3x + 10, which is equal to 3(9) + 10 = 37 years.
To learn more about ratio: -brainly.com/question/13419413
#SPJ11
The perimeter of a rectangle is 22cm and the length of each side is a natural number. How many different areas in centimeter squared can the rectangle have?
option B is the correct answer.
The perimeter of a rectangle is 22 cmLet the length of the rectangle be 'l' and the breadth be 'b'As per the question, the perimeter of the rectangle is given by;Perimeter = 2(l + b) => 2(l + b) = 22 => l + b = 11.As we know that the area of a rectangle is given by;Area = l × b
Therefore, the different areas of the rectangle are; l × b1 × (11 - 1) = 10 cm²2 × (11 - 2) = 18 cm²3 × (11 - 3) = 24 cm²4 × (11 - 4) = 28 cm²5 × (11 - 5) = 30 cm²6 × (11 - 6) = 30 cm²7 × (11 - 7) = 28 cm²8 × (11 - 8) = 24 cm²9 × (11 - 9) = 18 cm²10 × (11 - 10) = 10 cm²Hence, there are only 8 different areas of the rectangle i.e., 10 cm², 18 cm², 24 cm², 28 cm², 30 cm².
To know more about Perimeter visit:
https://brainly.com/question/7486523
#SPJ11
What x-values are solutions of x3 + 5x2 − x − 7 = x2 + 6x + 3? Simplify the polynomial and find the zeros to find the intersection points. Enter your answers in increasing order.
To find the x-values that are solutions of the equation
[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3)[/tex], we first need to simplify the equation and find the zeros.
By subtracting x^2 + 6x + 3 from both sides of the equation, we get:
[tex]x^3 + 5x^2 - x - 7 - (x^2 + 6x + 3) = 0[/tex]
[tex]x^3 + 5x^2 - x - 7 - x^2 - 6x - 3 = 0\\x^3 + 4x^2 - 7x - 10 = 0[/tex]
Now, to find the zeros of this polynomial, we set it equal to zero and factor it if possible:
[tex]x^3 + 4x^2 - 7x - 10 = 0[/tex]
By trying different values, we can find that x = -2 is a zero of the polynomial. Therefore, (x + 2) is a factor of the polynomial.
Using synthetic division or long division, we can divide the polynomial [tex]x^3 + 4x^2 - 7x - 10 = 0[/tex] by (x + 2):
[tex]| (x^3 + 4x^2 - 7x - 10) ÷ (x + 2) |= x^2 + 2x - 5[/tex]
Now, we can factor the quadratic equation x^2 + 2x - 5:
(x + 2)(x - 1) = 0
Setting each factor equal to zero and solving for x, we get:
x + 2 = 0 --> x = -2
x - 1 = 0 --> x = 1
Therefore, the x-values that are solutions to the equation x^3 + 5x^2 - x - 7 = x^2 + 6x + 3 are x = -2 and x = 1. The intersection points of the two polynomials occur at these x-values.
To know more about equation visit:
https://brainly.com/question/29538993
#SPJ11
Carol had $15,500 in visa sales one month. How much more did she net than if sales had been $14,300?
Carol netted $1,200 more with $15,500 in Visa sales compared to if sales were $14,300.
1. Calculate the difference between the two sales amounts: $15,500 - $14,300 = $1,200.
By subtracting $14,300 from $15,500, we find that Carol's sales were $1,200 higher with $15,500 in Visa sales.
2. The sales amount represents the total revenue generated from Visa transactions, but to determine how much Carol "netted," we need to consider any expenses or costs associated with these sales.
3. Subtract any expenses or costs from the total revenue to calculate the net amount. However, since the question does not provide information about expenses or costs, we'll assume that the sales amount refers to the net amount.
4. Therefore, the difference of $1,200 represents the additional money Carol received with $15,500 in Visa sales compared to if sales were $14,300.
Learn more about costs : brainly.com/question/31517591
#SPJ11
Franklin is purchasing replacement equipment for outdoor recess. Mr. DiCanio
put in a order totaling $97. 23 to purchase 4 playground balls for $17. 25 each, a
package of 10 jump ropes for $18. 75, and 1 Nerf football. How much did the Nerf
football cost?
As Franklin is purchasing replacement, the Nerf football cost an amount of $9.48.
How much did the Nerf football cost?To get the cost of the Nerf football, we will subtract the cost of the playground balls and the package of jump ropes from the total order cost.
The cost of 4 playground balls is:
= 4 * $17.25
= $69.00
The cost of package of 10 jump ropes = $18.75
So, the total cost of playground balls and jump ropes will be:
= $69.00 + $18.75
= $87.75
Cost of Nerf football = Total order cost - Total cost of playground balls and jump ropes
Cost of Nerf football = $97.23 - $87.75
Cost of Nerf football = $9.48
Read more about football cost
brainly.com/question/22184199
#SPJ4
the value of a gift card to a rock climbing gym decreased by 34 after 4 equal charges to the gift card find the quotient -34 * 4
What is the explicit formula for the sequence below?4, – 12, 36, – 108,...A.tn=(−3)n−1B.tn=4(−3)n−1C.tn=4(3)n−1D.tn=4(−3)n
The explicit formula for the given sequence 4, -12, 36, -108,... is D. tn = 4(-3)n. Option D
In the given sequence, each term is obtained by multiplying the previous term by -3. This indicates an exponential decay pattern with a common ratio of -3.
To derive the explicit formula, we start with the initial term 4 and observe that each subsequent term can be obtained by multiplying the previous term by -3:
Term 1: 4
Term 2: -3 × 4 = -12
Term 3: -3 ×(-12) = 36
Term 4: -3 × 36 = -108
We can generalize this pattern by using the formula tn = ar^(n-1), where tn represents the nth term, a is the initial term, and r is the common ratio. In this case, a = 4 and r = -3. Thus, the explicit formula for the sequence is tn = 4(-3)n which matches option D.
learn more about explicit formula here:
https://brainly.com/question/25094536
#SPJ11
−1. 23m=−0. 492 A. M = 0. 738 B. M = 0. 60516 C. M = 0. 4 D. I don't know
The value of 'm' that satisfies the equation -1.23m = -0.492 is m = 0.4, which corresponds to option C.
To solve the equation -1.23m = -0.492, we need to isolate the variable 'm'.
We can do this by dividing both sides of the equation by -1.23:
m = -0.492 / -1.23
Simplifying the right side of the equation:
m = 0.
Therefore, the solution to the equation is m = 0.4.
Based on the options provided, we can see that option C, M = 0.4, matches the solution we obtained.
Therefore, the correct choice would be option C.
For more question on variable
brainly.com/question/28248724
#SPJ8
Elizabeth’s credit card computes her finance charges using the previous balance method and a 30-day billing cycle. The table below shows Elizabeth’s credit card transactions in July. Date Amount ($) Transaction 7/1 969. 26 Beginning balance 7/3 45. 00 Payment 7/10 67. 48 Purchase 7/12 20. 00 Payment 7/28 85. 00 Payment If Elizabeth has an APR of 14. 61%, how much will her July finance charge be? a. $9. 97 b. $12. 62 c. $11. 80 d. $10. 80.
To calculate Elizabeth's finance charge using the previous balance method, we need to determine the average daily balance and then apply the APR (Annual Percentage Rate) to calculate the finance charge.
First, let's calculate the average daily balance:
Beginning Balance: $969.26
Days until payment: 2 (from July 1st to July 3rd)
Payment: $45.00
Days until purchase: 7 (from July 3rd to July 10th)
Purchase: $67.48
Days until payment: 2 (from July 10th to July 12th)
Payment: $20.00
Days until payment: 16 (from July 12th to July 28th)
Payment: $85.00
To calculate the average daily balance, we sum up the balances for each day and divide it by the total number of days in the billing cycle (30 days).
Average Daily Balance = (969.26 × 2 + 0 × 7 + 67.48 × 2 + 0 × 16) / 30 = $85.95
Next, we can calculate the finance charge using the APR:
Finance Charge = Average Daily Balance × (APR / 365) × Number of Days in the Billing Cycle
Finance Charge = 85.95 × (0.1461 / 365) × 30 ≈ $9.97
Therefore, Elizabeth's July finance charge will be approximately $9.97. The correct answer is option a.
Learn more about Annual Percentage Rate here -: brainly.com/question/30774234
#SPJ11
A bedroom wall measures 11 ft x 13 ft, and features a rectangular doorway that measures 6 ft x 3 ft. How many square of paint will be needed to cover the wall only?
The wall area that needs to be painted, excluding the doorway, is 125 square feet.
The total area of the wall is obtained by multiplying its length and width:
Total area = 11 ft * 13 ft = 143 square feet.
The area of the doorway is given by multiplying its length and width:
Doorway area = 6 ft * 3 ft = 18 square feet.
To find the area of the wall that needs to be painted, we subtract the area of the doorway from the total area:
Painting area = Total area - Doorway area = 143 square feet - 18 square feet = 125 square feet.
Therefore, you will need 125 square feet of paint to cover the wall only.
Learn more about rectangles here: brainly.com/question/29123947
#SPJ11
Work out an approximate solution to x3 + 2x – 1 = 0
Use the iteration Xn+ 1 =
1
x + 2
Start with Xy = 1
Give your answer to 2 decimal places.
Answer:
x = 0.45 (2 d.p.)
Step-by-step explanation:
Iteration is a numerical method used to approximate solutions to equations where exact solutions are difficult or impossible to obtain analytically.
It involves putting an approximate value of the solution into an iteration formula to calculate a new value based on the previous one. This process is repeated multiple times, with each iteration generating a more accurate approximation of the solution.
The iteration formula is just a rearrangement of the equation, leaving a single ‘x’ on one side.
For this problem, we have already been given the iteration formula and the starting value of x₁. However, sometimes you will need to determine the iteration formula. For example, to determine the iteration formula for x³ + 2x - 1 = 0, rearrange the equation as follows:
[tex]\begin{aligned}x^3+2x-1&=0\\x^3+2x&=1\\x(x^2+2)&=1\\x&=\dfrac{1}{x^2+2}\end{aligned}[/tex]
Therefore, the iteration formula is:
[tex]\boxed{x_{n+1}=\dfrac{1}{{x_n}^2+2}}[/tex]
To calculate the approximate solution to x³ + 2x - 1 = 0 using the given iteration formula, start by substituting x₁ = 1 into the formula to find x₂:
[tex]x_2=\dfrac{1}{x_{1}{^2}+2}=\dfrac{1}{(1)^2+2}=\dfrac{1}{1+2}=\dfrac{1}{3}=0.3333...[/tex]
Substitute the found value of x₂ into the formula to find the value of x₃:
[tex]x_3=\dfrac{1}{x_{2}{^2}+2}=\dfrac{1}{\left(\frac{1}{3}\right)^2+2}=\dfrac{1}{\frac{1}{9}+2}=\dfrac{1}{\frac{19}{9}}=\dfrac{9}{19}=0.47368...[/tex]
Continue this way until the solutions are the same when rounded to 2 d.p:
[tex]x_4=0.44956...[/tex]
[tex]x_5=0.45411...[/tex]
[tex]x_6=0.45326...[/tex]
[tex]x_7=0.45342...[/tex]
[tex]x_8=0.45339...[/tex]
[tex]x_9=0.45339...[/tex]
Therefore, the approximate solution to x³ + 2x - 1 = 0 is 0.45, rounded to 2 decimal places.
Additional information
The quickest way to compute each solution (each value in the iteration sequence) is to enter the value of x₁ into the calculator and press "=" so that the value of x₁ becomes the "answer". Then type the iteration formula into the calculator, replacing xₙ with "answer":
[tex]\boxed{\dfrac{1}{\text{Ans}^2+2}}[/tex]
Each time you press "=", the next value of xₙ in the sequence is computed.
Una caja contiene lápices azules y rojos. ¿Cómo se interpreta que la razón entre los lápices azules y los rojos en la caja sea 3:1? A. Hay tres lapices rojos y 1 azul B. Hay tres lapices azules y 1 rojo C. Hay el triple de lapices rojos que de lapices azules D. Hay el triple de lapices azules que de lapices rojos AYUDA PLISSSSSS
La opción que interpreta correctamente la razón entre los lápices azules y rojos en la caja de 3:1 es la opción B: "Hay tres lápices azules y 1 rojo".
Cuando se dice que la razón entre los lápices azules y los rojos en la caja es de 3:1, significa que por cada grupo de tres lápices azules, hay un lápiz rojo.
La opción A indica que hay tres lápices rojos y 1 azul, lo cual es incorrecto ya que la razón especifica que hay más lápices azules que rojos. La opción C sugiere que hay el triple de lápices rojos que de lápices azules, lo cual también es incorrecto según la razón proporcionada. La opción D indica que hay el triple de lápices azules que de lápices rojos, lo cual es contrario a la razón establecida de 3:1.
Por lo tanto, la opción que interpreta correctamente la razón 3:1 es la opción B: "Hay tres lápices azules y 1 rojo".
Learn more about interpteta here
https://brainly.com/question/24800958
#SPJ11
An airplane moves velocity of (200 km/Hr) for (45 min) then changes its velocity to (240 km/Hr) for (35 min) calculate the average velocity of the airplane during its journey
The average velocity of an airplane during its journey when it moves at a velocity of 200 km/hour for 45 minutes and changes its velocity to 240 km/hour for 35 minutes can be calculated as follows:The first step is to convert the time from minutes to hours.
We can do this by dividing the number of minutes by 60 (since there are 60 minutes in an hour).So, time taken to move at a velocity of 200 km/hr for 45 minutes = 45/60 = 0.75 hoursTime taken to move at a velocity of 240 km/hr for 35 minutes = 35/60 = 0.583 hoursNow we can find the total distance traveled by the airplane. We can do this by multiplying the velocity of the airplane with the time it traveled at that velocity.Distance traveled at 200 km/hr = 200 x 0.75 = 150 kmDistance traveled at 240 km/hr = 240 x 0.583 = 139.92 kmTotal distance traveled by the airplane = 150 + 139.92 = 289.92 km.
The average velocity of the airplane during its journey can now be found by dividing the total distance traveled by the total time taken to travel that distance. Total time taken = 0.75 + 0.583 = 1.333 hours Average velocity of the airplane = Total distance traveled.
To know more about velocity visit :
https://brainly.com/question/30559316
#SPJ11
Consider right triangle \triangle MNO△MNOtriangle, M, N, O below. Which expressions are equivalent to \cos(\angle M)cos(∠M)cosine, left parenthesis, angle, M, right parenthesis?
The expressions equivalent to cos(angle M) are cos(angle N) and cos(angle O).
In a right triangle, the cosine of one angle is equal to the cosine of the other acute angle. In triangle MNO, angle M is one of the acute angles. The other two angles are N and O. The cosine function is defined as the ratio of the adjacent side to the hypotenuse.
Since the cosine function depends only on the ratio of sides, and not on the specific angle, the cosine of angle M is equivalent to the cosine of angle N, and the cosine of angle O
Therefore, the expressions equivalent to cos(angle M) in triangle MNO are cos(angle N) and cos(angle O).
Learn more about hypotenuse here :
https://brainly.com/question/16893462
#SPJ11
Find the measure of each angle to the nearest tenth of a degree.
tan X=0. 2962
Now we know that;tan x = Opposite/Adjacent side of the angle x tan x = Opposite/Adjacent sideTherefore, the Opposite side = tan x * Adjacent sideHere, we have only the value of tan x.
Thus, we need the value of any one side to find the other side value. But, we don't have the value of any of the sides. So, we will take an arbitrary value of one of the sides, suppose 1.We know that tan x = Opposite/Adjacent sideNow, we have Adjacent side = 1Therefore, tan x = Opposite/1Opposite side = tan xNow, Opposite side = 0.2962 (from the given equation)
Therefore, the measure of the angle can be found using the tangent ratio formula.tan x = Opposite/Adjacenttan x = 0.2962/1tan x = 16.92°Thus, the measure of the angle x to the nearest tenth of a degree is 16.9°.Therefore, the answer is, the measure of angle x is 16.9° to the nearest tenth of a degree.
To Know more about arbitrary visit:
brainly.com/question/1468627
#SPJ11
1. Use each of the Numbers once, In any order. To form at least TWO number sentences that equal the target number
TARGET NUMBER: 2
17, 5, 8, 2, 9
2. Let A=3 B=28 C=50
D=12 E=2 F=18
Write a minimum of 5 different
relationship statements for the
variables.
Ex. DE=B-2E
Using 17 + 5 - 8 + 9 - 2 = 21 and 2 + 9 - 8 + 17 - 5 = 15 as two number sentences, we can form the target number of 2.
1) 2C = BF
2) B - 3E = A
3) C - A = 2D
4) F - A + B = 47
5) 3E - B + 2A = 8
In the first statement, the variable C is multiplied by 2, and the result is equal to the product of variables B and F. In the second statement, the product of variables E and 3 is subtracted from B, and the result is equal to A.
In the third statement, the difference between variables C and A is equal to twice the value of variable D. In the fourth statement, the sum of variables F and B is subtracted from A, and the result is equal to 47.
In the fifth statement, twice the value of variable A is added to 3 times the value of variable E, and this sum is subtracted from the value of variable B, which gives 8.
Learn more about variable here:
https://brainly.com/question/29696241
#SPJ11
