The height of the given trapezoid-shaped tabletop is 75.5 centimeters.
The height of the trapezoid-shaped tabletop. To calculate the height, we can use the formula for the area of a trapezoid: A = (1/2)(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height.
Given the area (A) is 7,701 square centimeters, the longer base (b1) measures 119 centimeters, and the shorter base (b2) is 85 centimeters, we can solve for the height (h) using the following steps:
1. Plug in the given values into the formula: 7,701 = (1/2)(119 + 85)h
2. Simplify the expression inside the parentheses: 7,701 = (1/2)(204)h
3. Multiply the two numbers inside the parentheses: 7,701 = 102h
4. Divide both sides of the equation by 102 to solve for h: h = 7,701 / 102
5. Calculate the value of h: h ≈ 75.5 centimeters
So, the height of the trapezoid-shaped tabletop is approximately 75.5 centimeters.
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Ms. Brock runs a house cleaning business. To save money, she bought a 1-gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1-pint spray bottles as she could. How many spray bottles did she fill?
Ms. Brock can now fill up to 88 spray bottles with her preparation.
How to find the number of spray bottles she fillIt is calculated that:
one gallon of liquid comprises 128 fluid ounces and one pint has a sum of 16 fluid ounces.hence we have that
1 gallon = 128 fluid ounces
1 pint = 16 fluid ounces
cross multiplying
16 fluid ounces x 1 gallon = 128 fluid ounces x 1 pint
1 gallon = (128 fluid ounces x 1 pint) / 16 fluid ounces
1 gallon = 8 pints
Consequently, there are 8 pints in one full gallon.
Ms. Brock blended 1 gallon of cleaner with 10 gallons of water, thus resulting in 11 gallons.
To figure out the total number of pints Ms. Brock has in her solution, we must multiply 11 gallons by 8 pints/gallon:
11 gallons x 8 pints/gallon = 88 pints
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The probability of spinning an odd number , not flipping heads , then not spinning a 6 is _?
The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40
Multiply the three probabilities in order to get the compound probability:
Probability = favorable outcome / total number of outcome
Probability of getting an odd number
favorable outcome = 5
Total number of outcome = 10
P(odd number)= 5/10 = 1/2
Probability of not getting filling head
Favorable outcome = 1
P( not flipping heads)= 1/2
Probability of not getting a 6
favorable outcome = 9
P(not spinning a 6)= 9/10
= 1/2×1/2×9/10
= 9/40
The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40
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In 3 minutes, a conveyor belt moves 200 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area
If both belts are used, it will take 2.25 minutes to move the cans to the storage area
To solve this problem, we need to use the concept of rate of work. We know that the larger belt can move 200 pounds of aluminum in 3 minutes, which means its rate of work is 200/3 = 66.67 pounds per minute. Similarly, the smaller belt can move the same quantity of cans in 9 minutes, which means its rate of work is 200/9 = 22.22 pounds per minute.
When both belts are used together, their rates of work add up, so the total rate of work is 66.67 + 22.22 = 88.89 pounds per minute. We can use this rate of work to find how long it will take to move the cans to the storage area.
Let's assume that it takes x minutes to move the cans using both belts. Then, we can set up the following equation:
88.89x = 200
Solving for x, we get:
x = 2.25 minutes
Therefore, it will take 2.25 minutes to move the cans to the storage area using both belts.
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Find the coordinates of the points on the curve x(????)=3????^2 +1 ????????????y(????)=????^3 −1, for which the tangent linehas a slope of 1/2
The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).
To find the coordinates of the points on the curve x(t) = 3t^2 + 1 and y(t) = t^3 - 1, where the tangent line has a slope of 1/2, follow these steps:
1. Calculate the derivatives of x(t) and y(t) with respect to t:
dx/dt = 6t
dy/dt = 3t^2
2. The slope of the tangent line is given by dy/dx, so calculate dy/dx using the chain rule:
dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2
3. Set the slope equal to 1/2 and solve for t:
t/2 = 1/2
t = 1
4. Plug the value of t back into the original equations for x(t) and y(t) to find the coordinates of the point:
x(1) = 3(1)^2 + 1 = 4
y(1) = (1)^3 - 1 = 0
The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).
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Among american adults, 42. 5 percent are considered: multiple choice question. Obese. Athletic. Anorexic. Underweight
Answer:
Obese
Step by Step Explanation:
looked it up :)
At the performance of Seussical the Musical at your local high school, there are adult tickets and student/child tickets. You're trying to remember the cost of each to tell your music extended family to come see the musical. Your friend, her mom, and her little sister paid a total of $23 on opening night, and you know that another family paid $39 for two adults and three students. If x is cost of adult tickets and y is cost of student tickets, the two equations for these situations can be written as:
The cost of an adult ticket is $9 and the cost of a student/child ticket is $7. The solution was found by solving a system of two equations, where the variables x and y represent the costs of the two types of tickets.
Let's assign variables for the unknowns
x = cost of adult tickets
y = cost of student/child tickets
From the given information, we can create two equations
Equation 1 Friend, mom, and little sister paid a total of $23
x + 2y = 23
Equation 2 Another family paid $39 for two adults and three students
2x + 3y = 39
We now have two equations with two unknowns, which we can solve using substitution or elimination.
Here, using substitution
Solve for x in Equation 1
x = 23 - 2y
Substitute the value of x into Equation 2
2(23 - 2y) + 3y = 39
Simplify and solve for y
46 - 4y + 3y = 39
-y = -7
y = 7
Substitute the value of y into Equation 1 to solve for x
x + 2(7) = 23
x = 9
Therefore, the cost of adult tickets is $9 and the cost of student/child tickets is $7.
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Please answer the question correctly and neatly. Will upvote if
correct.
Using a Table of Integrals with the appropriate substitution, find e3r + 6e2x + 7e et - 64 peste da Answer: ] +0
The equation provided, "e3r + 6e2x + 7e et - 64 pestle da," is not an integral expression and does not have a variable of integration.
Additionally, the requested answer, "] +0," does not make sense in the context of the question. Please provide a complete and accurate question for me to assist you with. Hi! Based on your terms provided ("Integrals", "substitution", and "find"), I understand that you are looking to solve an integral using substitution. However, the integral you provided appears to have some typographical errors. Please provide the correct integral, and I'll be happy to help you solve it.
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3. la mamá de jordan compró 7 cajas de envases de jugo para después del entrenamiento del equipo. cada caja tenía 8 envases de jugo. después que el equipo bebió todo el jugo que quiso, quedaron 29 envases de jugo. el equipo abrió una nueva caja solo después de beber todo el jugo de la caja anterior. ¿cuántas cajas de jugo abrió el equipo?
Answer:
Step-by-step explanation:
The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.
Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.
To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,
so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.
Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.
Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.
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6. How fast is each train traveling (km/h)? Round to the nearest whole number. a) Train A travels 520.4 km in 4.8 h b) Train B travels 72.1 km in 0.8 h
Answer: a) To find the speed of Train A, we need to divide the distance traveled by the time taken:
Speed = Distance / Time
Speed = 520.4 km / 4.8 h
Speed ≈ 108.42 km/h
Rounding to the nearest whole number, we get:
Train A is traveling at 108 km/h (approximately).
b) To find the speed of Train B, we need to divide the distance traveled by the time taken:
Speed = Distance / Time
Speed = 72.1 km / 0.8 h
Speed ≈ 90.13 km/h
Rounding to the nearest whole number, we get:
Train B is traveling at 90 km/h (approximately).
Step-by-step explanation:
Waterways Corporation is preparing its budget for the coming year, 2022. The first step is to plan for the first quarter of that coming year. The company has gathered information from its managers in preparation of the budgeting process. Sales Unit sales for November 2021 112,000
Unit sales for December 2021 104,000
Expected unit sales for January 2022 113,000
Expected unit sales for February 2022 112,000
Expected unit sales for March 2022 116,000
Expected unit sales for April 2022 125,000
Expected unit sales for May 2022 138,000
Unit selling price $12
Waterways likes to keep 10% of the next month’s unit sales in ending inventory. All sales are on account. 85% of the Accounts Receivable are collected in the month of sale, and 15% of the Accounts Receivable are collected in the month after sale. Accounts receivable on December 31, 2021, totaled $187,200. Direct Materials
Direct materials cost 80 cents per pound. Two pounds of direct materials are required to produce each unit. Waterways likes to keep 5% of the materials needed for the next month in its ending inventory. Raw Materials on December 31, 2021 totaled 11,290 pounds. Payment for materials is made within 15 days. 50% is paid in the month of purchase, and 50% is paid in the month after purchase. Accounts Payable on December 31, 2021, totaled $120,595. Labor requires 12 minutes per unit for completion and is paid at a rate of $9 per hour. Manufacturing Overhead
Indirect materials
30¢ per labor hour
Indirect labor
50¢ per labor hour
Utilities
50¢
per labor hour
Maintenance
20¢
per labor hour
Salaries
$41,000 per month
Depreciation
$18,000 per month
Property taxes
$2,900 per month
Insurance
$1,200 per month
Maintenance
$1,300 per month
Selling and Administrative
Variable selling and administrative cost per unit is $1. 60. Advertising
$15,000 a month
Insurance
$1,400 a month
Salaries
$70,000 a month
Depreciation
$2,800 a month
Other fixed costs
$3,300 a month
Other Information
The Cash balance on December 31, 2021, totaled $99,000, but management has decided it would like to maintain a cash balance of at least $700,000 beginning on January 31, 2022. Dividends are paid each month at the rate of $2. 70 per share for 4,610 shares outstanding. The company has an open line of credit with Romney’s Bank. The terms of the agreement requires borrowing to be in $1,000 increments at 9% interest. Waterways borrows on the first day of the month and repays on the last day of the month. A $480,000 equipment purchase is planned for February
Waterways Corporation's budget for Q1 2022 involves sales, inventory, materials, labor, overhead, expenses, and financing.
How to prepare Waterways Corporation's budget for 2022?Waterways Corporation is preparing its budget for the first quarter of 2022. The company has gathered information from its managers to begin the budgeting process.
The company expects unit sales to be 112,000 in November 2021, 104,000 in December 2021, and 113,000 in January 2022. The company also expects to keep 10% of next month's unit sales in ending inventory. The company collects 85% of Accounts Receivable in the month of sale and 15% in the month after sale.
Raw materials cost 80 cents per pound, and two pounds of direct materials are required to produce each unit. The company likes to keep 5% of the materials needed for the next month in its ending inventory.
Labor requires 12 minutes per unit, paid at a rate of $9 per hour. The company has variable selling and administrative costs of $1.60 per unit, including advertising, insurance, salaries, and depreciation. The company also plans to make a $480,000 equipment purchase in February.
The company's cash balance on December 31, 2021, was $99,000, but the management wants to maintain a cash balance of at least $700,000 starting on January 31, 2022. The company pays dividends each month at the rate of $2.70 per share for 4,610 shares outstanding.
The company has an open line of credit with Romney's Bank with borrowing terms of $1,000 increments at 9% interest. The company borrows on the first day of the month and repays on the last day of the month.
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without the addition of fertiliser, the annual crop from a potato farm would only be 80% of the previous years crop. a farm produced 15 tonnes of potatoes in its first year of production. assume that no fertiliser is used. give answers correct to two decimal places where necessary. list the size of the potato crop for each of the first four years
The crop sizes for first 4 years without using fertilisers are:
15 tonnes12 tonnes9.6 tonnes7.68 tonnes.What is the size each of the first 4 years?The size of the potato crop for each of the first four years is computed as follows:
For Year 1:
= 15 tonnes * 1
= 15 tonnes
For Year 2:
= 15 tonnes x 0.8
= 12 tonnes
For Year 3:
= 12 tonnes x 0.8
= 9.6 tonnes
For Year 4:
= 9.6 tonnes x 0.8
= 7.68 tonnes
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Solve the problem The total cost, in dollars, to produce x DVD players is Cbx) 120 + 3x==2-3. Find the marginal cost when x-3 A) $228 B) $225 C) $105 D) $108
The problem involves finding the marginal cost of producing a certain number of DVD players, given the total cost function. Specifically, we are given the total cost function C(x) = 120 + 3x^2-3, where x is the number of DVD players produced, and we need to find the marginal cost when x = 3.
To find the marginal cost, we need to take the derivative of the total cost function with respect to x and evaluate it at x = 3. The marginal cost represents the cost of producing one additional unit of the product, and is an important concept in economics and business.
Understanding the relationship between marginal cost and production volume is crucial for optimizing production and pricing decisions for companies. Marginal cost analysis is used extensively in many fields, including manufacturing, finance, and marketing.
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Marcus is taking part in a charity run. He has received $250 in fixed pledges, and he will receive $25 more in pledges for each mile he runs. Write an equation for the amount of money P Marcus will earn in terms of the distance d he runs, measured in miles
Answer:
250+25d= P
Step-by-step explanation:
How to say it aloud: "$250 plus 25 times miles ran is equal to total amount earned"
250 is a fixed amount that is apart of the equation. In order to get a correct total at the end, $250 must be added to 25d.
25d stands for $25 times the amount of miles ran, which according to the word problem is represented by d. The reason we multiply 25 times d is because Marcus is getting $25 for every mile he runs. At the end of his run, we need to multiply $25 by those miles.
The reason everything equals P is because according to the word problem, P is the amount of money earned.
I hope that makes sense.
Q 28 : A new school has built lockers for its students. All the digits from 0 to 9, together with
the letters A to Y, have been used to identify the lockers. Only 4 digits have been used to
identify the lockers with the letter Z. How many lockers have been built in this school, if each
locker is identified by one letter and one digit?
If each locker is identified by one letter and one digit, the total number of lockers built in the school is 229.
There are 26 letters in the alphabet (A to Z), and if each locker is identified by one letter and one digit, then there are a total of 26 × 10 = 260 possible locker identifications using the letters A to Y and digits 0 to 9.
Out of these, there are 4 digits used to identify the lockers with the letter Z. So, there are 10 − 1 = 9 digits left to use for the remaining lockers, as we cannot use the digit already used for the lockers with the letter Z.
Similarly, there are 25 letters left to use for the remaining lockers, as we cannot use the letter Z.
Therefore, the number of remaining lockers is 9 × 25 = 225. Adding the 4 lockers with the letter Z, the total number of lockers built in the school is 225 + 4 = 229.
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What is the sum of the heights of the two trees?
Round your answer to the nearest whole number
The sum of the heights of the two trees with given volumes and radius is equal to 9 cm (nearest whole number ).
Volumes of the cylindrical trunks of first tree = 904.78 cm³
and Volumes of the cylindrical trunks of first tree =113 cm³.
radius of the first tree = 6cm
Radius of the second tree = 6cm
The formula for the volume of a cylinder is V = πr²h,
where r is the radius of the cylinder,
h is the height of the cylinder,
and π is the constant approximately value equal to 3.14.
For the first tree,
⇒904.78 = π(6)²h
⇒h = 904.78 / (π(6)²)
⇒h ≈ 8.004 cm
For the second tree, we have,
⇒113 = π(6)²h
⇒h = 113 / (π(6)²)
⇒h ≈ 0.9996 cm
This implies,
The sum of the heights of the two trees is equal to,
= 8.004 + 0.9996
= 9.003 cm
= 9 cm ( nearest whole number)
Hence, the sum of the heights of the two trees is approximately 9 cm nearest whole number.
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The given question is incomplete, I answer the question in general according to my knowledge:
The two trees trunk are in cylindrical shape. one with radius 6cm and volume 904.78 cm³ and another one with radius 6cm and volume 113 cm³.
What is the sum of the heights of the two trees? Round your answer to the nearest whole number
B. analyze relationships deloria says she can find the relative
frequency of nuts based on another relative frequency. what might
she be doing
nuts:3/30=15%
Deloria is analyzing the relationships between relative frequencies of nuts.
She has found that the relative frequency of a specific type of nut is 15%, which is calculated by dividing the number of that nut (3) by the total number of nuts (30).
Deloria might be comparing this relative frequency to other types of nuts to determine their prevalence or importance in a given context.
To calculate the relative frequency, we can divide the number of occurrences of the specific nut (3) by the total number of nuts (30):
Relative frequency = (Number of occurrences of specific nut) / (Total number of nuts)
Relative frequency = 3 / 30 = 0.1 = 10%
Therefore, the relative frequency of the specific type of nut is 10%, not 15%. It seems there was an error in the initial statement.
By analyzing relative frequencies, Deloria can compare the prevalence or importance of different types of nuts in a given context.
By calculating and comparing the relative frequencies of different types of nuts, Deloria can gain insights into the distribution and significance of each nut type within the dataset or sample.
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A quadratic expression has x + 4 and 4x + 9 as its linear factors. Between which values of
x can a zero of the associated quadratic function be found?
The range of x values between which a zero can be found is -9/4 < x < -4.
Since x + 4 and 4x + 9 are linear factors of the quadratic expression, the quadratic expression can be written as:
Q(x) = k(x + 4)(4x + 9)
where k is some constant.
To find the values of x for which Q(x) = 0, we can set each factor equal to zero and solve for x:
x + 4 = 0 --> x = -4
4x + 9 = 0 --> x = -9/4
Therefore, the zeros of Q(x) are x = -4 and x = -9/4.
To find the range of x values between which a zero can be found, we need to determine the sign of Q(x) in each of the three intervals:
1. x < -9/4
2. -9/4 < x < -4
3. x > -4
For x < -9/4, both x + 4 and 4x + 9 are negative, so Q(x) = k(negative)(negative) = k(positive), which is positive.
For x > -4, both x + 4 and 4x + 9 are positive, so Q(x) = k(positive)(positive) = k(positive), which is also positive.
For -9/4 < x < -4, x + 4 is positive and 4x + 9 is negative, so Q(x) = k(positive)(negative) = k(negative), which is negative.
Therefore, the range of x values between which a zero can be found is -9/4 < x < -4.
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You must build a ramp with a rise of 15 inches to roll some gym equipment into your school. If you follow the ADA specifications:
To build a ramp with a 15-inch rise for rolling gym equipment into your school, following ADA specifications, we should create a ramp with a run of 180 inches to maintain a 1:12 slope.
For building a ramp with a rise of 15 inches for rolling gym equipment into your school, following ADA specifications. Let's use these terms in our step-by-step explanation:
1. ADA specifications: The Americans with Disabilities Act (ADA) specifies that the slope of a ramp should be no more than 1:12, which means that for every 1 inch of rise, there should be 12 inches of run.
2. Ramp rise: In this case, the rise is 15 inches.
3. Calculate ramp run: To find the ramp run, we can use the ADA specification of 1:12. Multiply the rise (15 inches) by 12.
15 inches x 12 = 180 inches
4. Ramp run: Based on the calculation, the run for the ramp should be 180 inches.
5. Ramp length: To ensure a safe and accessible ramp, follow the ADA specifications and use a ramp length of 180 inches to achieve the 15-inch rise.
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A 13-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 5 feet from the base of the building. How high up the wall does the ladder reach?
The difference of two rational numbers is 17/28,if the small rational number is -9/14 find the other
Step-by-step explanation:
Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:
x - (-9/14) = 17/28
Simplifying the left-hand side:
x + 9/14 = 17/28
Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:
28(x + 9/14) = 28(17/28)
Simplifying:
4(2x + 9) = 17
Expanding:
8x + 36 = 17
Subtracting 36 from both sides:
8x = -19
Dividing by 8:
x = -19/8
Therefore, the other rational number is -19/8.
Suppose that you are gambling at a casino. Every day you play at a slot machine, and your goal is to minimize your losses. We model this as the experts problem. Every day you must take the advice of one of n experts (i. E. A slot machine). At the end of each day t, if you take advice from expert i, the advice costs you some c t i in [0, 1]. You want to minimize the regret R, defined as:
This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices
In this scenario, we can think of the slot machines as experts providing us with advice on which machine to play each day. The cost of taking advice from each expert, represented by cti, is the amount we lose by playing that particular machine.
To minimize our losses and regret, we want to choose the expert (i.e., slot machine) with the lowest cost each day. However, it's important to note that the cost of taking advice from each expert may change each day, so we need to constantly evaluate and adjust our choices.
To formalize this problem as an optimization task, we can use the concept of regret. Regret measures how much worse off we are by not knowing the best expert in advance. In other words, it's the difference between our cumulative losses if we always chose the best expert versus the losses we actually incur by following different experts each day.
To minimize our regret R, we need to choose the best expert as often as possible. One way to achieve this is by using an online learning algorithm that updates our choice based on the outcomes of each day's play. By continuously monitoring the performance of each slot machine, we can adjust our strategy and minimize our losses over time.
In summary, to minimize our losses while gambling at a casino, we need to treat each slot machine as an expert providing us with advice. We must choose the expert with the lowest cost each day and constantly update our strategy to minimize regret.
This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices.
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The temperature on skylar’s thermometer last night was −3°f. this morning it was colder. what could be the temperature on her thermometer this morning?−5°f−1°f0°f2°f
The only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.
The temperature on Skylar's thermometer is measured using a scale that indicates the degree of hotness or coldness of the atmosphere. In this case, we know that the temperature on her thermometer last night was −3°F. The negative sign indicates that the temperature was below the freezing point of water.
We are asked to determine what the temperature could be on her thermometer this morning. Since we are told that the temperature is colder than −3°F, we can eliminate 0°F and 2°F as possible options, as they are warmer than −3°F.
Similarly, −1°F is only slightly colder than −3°F, so it is unlikely to be the temperature on Skylar's thermometer this morning. Therefore, the only option left is −5°F, which is colder than −3°F and thus could be the temperature on her thermometer this morning.
It is important to note that temperature can have a significant impact on our daily lives. Extreme cold temperatures can cause frostbite, hypothermia, and other health hazards, while hot temperatures can lead to dehydration, heat exhaustion, and heat stroke. It is important to dress appropriately and take necessary precautions when the temperature is too low or too high.
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Frank wants to find the area enclosed by the figure at the right the figure on each side has semicircles of a 40 meter by 40 meter square. Find the area by the figure use 3. 14 for pi
The area enclosed by the figure at the right is 2856 square meters.
To find the area enclosed by the figure at the right, we first need to find the area of the square and the two semicircles on each side. The square has sides of 40 meters, so its area is 40 x 40 = 1600 square meters. Each semicircle has a radius of 20 meters (half the side length of the square), so its area is 1/2 x pi x r^2 = 1/2 x 3.14 x 20^2 = 628 square meters. Since there are two semicircles on each side, the total area of all four semicircles is 2 x 628 = 1256 square meters.
To find the total area enclosed by the figure, we add the area of the square and the area of the four semicircles:
1600 + 1256 = 2856 square meters
Therefore, the area enclosed by the figure at the right is 2856 square meters.
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Find the prime factorization of each number. Record without and then with exponents. 75
Answer:
5*5*3
5²*3
Step-by-step explanation:
Assuming that we have to find prime factorization of 75:
75 = 25 * 3
75 = 5*5*3
A rectangular box will have a square cross section and a volume of 500 cubic centimeters. A. Sketch the box and sketch a net for the box. Assume the box will have an open top. Label the dimensions. B. Using w for the width and h for the height, find an expression in h and w for w the surface area of the box. C. Find the width and height that will make the surface area as small as possible
The expression for the surface area of the box is if w is A = x² + 2(xh) + 2(h²) the width of the box and h is the height. The dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.
The sketch of the box and the sketch of the net of the box is attached below. The box has a square base of side length x, and height h. The volume of the box is given as 500 cubic centimeters, therefore
x × x × h = 500
The surface area of the box can be found by summing the areas of each of the six faces. The top face is a square of side length x, so its area is x². The other five faces are all rectangles. The area of each of these rectangles is given by its length times its width. Therefore, the surface area of the box is
A = x² + 2(xh) + 2(h²)
To find the dimensions that minimize the surface area, we can use calculus. We can first solve the equation for x in terms of h
x² = 500/h
x = √(500/h)
Substituting this expression for x into the equation for the surface area, we get
A = 500/h + 2h×√(500/h) + 2h²
We can find the derivative of this expression with respect to h
dA/dh = -500/h² + sqrt(500/h) - 4h
Setting this derivative equal to zero and solving for h, we get
-500/h² + sqrt(500/h) - 4h = 0
Using a calculator or computer, we can find that this value is approximately 6.19. Substituting this value back into the equation for x, we get
x = √(500/6.19) ≈ 11.68
Therefore, the dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.
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Jordan buys candy at a store that costs $1.25 per candy bar. Create a table that could represent Jordan's cost depending on the number of candy bars purchased. Create a rule that represents the relationship.
Answer:
1 candy bar is $1.25
2 candy bars is $2.50
3 candy bars is $3.75
4 candy bars is $5
Equation:
y = 1.25x
y being the cost and x being number of candy bars
Graph the image of △WXY after the following sequence of transformations: Reflection across the y-axis Rotation 180° counterclockwise around the origin
The old coordinates are;
W (3, 14)
Y (12, 14)
X (6, 11)
While the new coordinates for the reflected triangle are:
W'' (3, -14)
X'' (6, -11)
Y'' (12, -14).
See the attached image.
What is reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.
A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.
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Rewrite each expression using a single, positive exponent.
The given expression, 14⁻³ · 14¹², written as a single, positive exponent is 14⁹
Rewriting an expression using a single exponentFrom the question, we are to write the given expression using a single, positive exponent
From the given information,
The given expression is
14⁻³ · 14¹²
This means
14⁻³ × 14¹²
To solve this, let us revise some of the laws of indices
mᵃ × mᵇ = mᵃ ⁺ ᵇmᵃ × mᵇ = mᵃ ⁻ ᵇm⁰ = 1Thus,
The expression
14⁻³ × 14¹²
can be written as
14⁻³ ⁺ ¹²
14⁹
Hence, the expression written as a single exponent is 14⁹
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or
Hazel bought 4 souvenirs during 2 days of vacation. How many days will Hazel have to spend on vacation before she will have bought a total of 8 souvenirs? Assume the relationship is directly proportional.
I NEED HELP ON THIS ASAP!!! IT'S DUE TONIGHT
Answer:
First Problem:
Transformation: Reflection across the x-axis, shift 2 units rightward
Equation: g(x)=-5^(x-2)
Second Problem:
Transformation: Reflection across the y-axis, shift 4 units upward
Equation: 10^-x+4
Step-by-step explanation:
Imagine folding a piece of paper and using the x or y axis as the crease marks. By folding them and comparing them, we can find out whether it is either the x-axis, y-axis, or both-axis. Then, we move the graph, to match the position in the second picture.
As for equations, exponential functions have the parent function of y=b^(x+c)+h. By plugging in any points given, let's say (1,5), we can see that 5=b^1 and simplifying shows 5=b. Therefore, the function is y=5^x. Using that first equation, we transform it. If over the x-axis, convert y=b^x to y=-b^x. If over the y-axis, convert y=b^x to y=b^-x. For horizontal shift, if going rightward, it is x-c. If going leftward, it is x+c. For vertical shift, if going up, b^x+h. If going down, b^x-h.
If unsure, plug-in points to see if your answer checks out with the equation :)
