A rectangular page is to contain 95 square inches of print. the margins on each side are 1 inch. find the dimensions of the page such that the least amount of paper is used.
You have the opportunity to lease space for your business with a fixed-rate lease. The property owner has proposed a five-year lease with a rent of $4,000 per month. How much is the rent per year? How much is the rent over the life of the lease?
QM Q9.) Write the standard form of the equation of the circle with the given center and radius.
What are some uses for the distance formula? Finding the perimeter of polygons. Finding the area of rectangles. Finding the equation of a circle. Finding the midpoint of segments. Finding how much gas you will need on a trip.
The Distance Formula is used widely in mathematics to calculate the distance between two points, which includes finding the perimeter of polygons, the equation of a circle and the midpoint of segments.
Explanation:The Distance Formula is a valuable tool in mathematics that has a wide range of practical uses and applications. It is primarily used to calculate the distance between two specific points on a coordinate plane. Some uses include the following:
Finding the perimeter of polygons: Distance Formula can be used to calculate the length of each side of the polygon, and then by summing these lengths, we get the perimeter. Finding the equation of a circle: By using Distance Formula, we can establish the radius of the circle - the distance from the center of the circle to any point on the circle. Finding the midpoint of segments: Distance Formula helps to identify the exact middle point between two defined points.
However, usage of the Distance Formula to determine the amount of gas needed for a trip would be incorrect as it requires additional factors like the fuel efficiency of your vehicle and the nature of your trip.
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0.88 cm equals how many mm
Given the parent function of y=|x|, state the type of transformation that occured to get the function below. y=1/4|x|
the transformation that occurred to the parent function[tex]\( y = |x| \)[/tex] to get the function[tex]\( y = \frac{1}{4}|x| \)[/tex] is a vertical compression by a factor of 4.
The parent function ( y = |x| ) represents the absolute value function, which takes the absolute value of \( x \) and outputs its positive value.
The function [tex]\( y = \frac{1}{4}|x| \)[/tex] is a transformation of the absolute value function. Specifically, it involves the following transformations:
1. **Vertical Compression:**
The coefficient[tex]\( \frac{1}{4} \)[/tex] before[tex]\( |x| \)[/tex] compresses the graph vertically. It shrinks the height of the graph by a factor of 4 compared to the parent function [tex]\( y = |x| \).[/tex]
So, the transformation that occurred to the parent function[tex]\( y = |x| \)[/tex] to get the function[tex]\( y = \frac{1}{4}|x| \)[/tex] is a vertical compression by a factor of 4.
1. Clyde has the chance to buy a piece of old Pennsylvania Dutch pottery that he thinks he can resell for $500. If Clyde needs a 125% markup on cost, what price should he pay?
2. Orchard Supply sells lawn fertilizer at a price of $12.50 per bag. If the markup is 25% of cost, find the cost.
A rectangle has a width of 8 centimeters and an area of 160 square centimeters a similar rectangle has an area of 250 square centimeters. What are the dimensions of the larger rectangle?
The dimensions of the lager rectangle are;
length = 25cm
width = 10cm
Similar shapes are shapes with equal corresponding angles and equal side ratio. This side ratio is called scale factor.
scale factor = √ area factor
area factor = area of new shape/ area of old shape
area factor = 250/160
= 25/16
scale factor = √25/√16 = 5/4
Therefore the width of the larger rectangle = 8 × 5/4 = 10cm
the length = 250/10 = 25 cm
Therefore the dimensions of the larger rectangle are;
length = 25cm
width = 10cm
What is the value of x in the following equation 1/5x=5^8
A)-8 B) 8 C)40 D)-40
Alex walked 1 mile in 15 minutes. Sally walked 3,520 yards in 24 minutes. In miles per hour, how much faster did Sally walk than Alex? (Note: 1 mile = 1,760 yards)
Is 7+8x=y proportional, if so what is the constant proportionality?
Is y=-2/5x proportional, if so what is the constant proportionality?
Q #14 Solve the equation
The scatter plot shows the relationship between the number of car accidents in a month and the number of drivers attending a program on distracted driving. The equation represents the linear model for this data. y=−0.0067x+17 What does the number -0.0067 in the equation mean in this context? There were 0.67 accidents per month. The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program. The number of accidents was reduced by 0.67 per month for every additional driver in the program. The number of accidents increased by 0.67 per month for every additional 100 drivers in the program. The number of accidents was reduced by 0.67 per month every month.
Answer:
the answer is A
Solve the equation: Sin2x - Sinx = 0
PLZ HELP ASAP INSCRIBED SHAPES
A student conducted a poll of 100 internet users and found the average time spent online per day was 2 hours. The student described 2 hours as a parameter. The student is incorrect because the value is a numerical measurement describing a characteristic of _____.
a ratio
a sample
a population
quantitative data
In statistics A sample is a part of a population .A sample statistic is any quantity we derive from a sample taken from a population . A sample refers to a set of observations drawn from a population.
We are given A student conducted a poll of 100 internet users and found the average time spent online per day was 2 hours .Here 2 hours is an observation derived from the set of observations made .So 2 hours is a characterstic of a sample.
The second option a Sample is the right answer.
One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. let p represent the number of female insects in a population and s the number of sterile males introduced each generation. let r be the per capita rate of production of females by females, provided their chosen mate is not sterile. then the female population is related to time t by t = p + s p[(r − 1)p − s] dp. suppose an insect population with 10,000 females grows at a rate of r = 1.2 and 400 sterile males are added. evaluate the integral to give an equation relating the female population to time. (note that the resulting equation can't be solved explicitly for p. remember to use absolute values where appropriate.)
To be clear, the given relation between
time and female population is an integral:
[tex]t = \int { \frac{P+S}{P[(r - 1)P - S]} } \,
dP [/tex]
if AB if the midsegment find x SHOW WORK
Trevor just received a jar of mixed nuts containing 325 almonds, 250 pistachios, 75 cashews, and 350 pecans for his birthday. He's going to start randomly choosing some nuts from the jar, and he's not going to do anything that would favor him choosing any particular type of nut over another. Let's use this information to calculate some probabilities. (4 points: Part I - 1 point; Part II - 1 point; Part III - 1 point; Part IV - 1 point)
What is the probability that the first nut Trevor chooses is a pecan?
Part II: What is the probability that the first nut Trevor chooses is an almond or a cashew?
Final answer:
The probability of choosing a pecan first is 35%, and choosing either an almond or a cashew first is 40%.
Explanation:
Probability Calculation in Combinatorics
The student's question involves calculating the probability of certain outcomes when choosing nuts from a jar. To answer Part I: the probability that the first nut Trevor chooses is a pecan, we'll need to divide the number of pecans (350) by the total number of nuts in the jar (1000). Therefore, the probability of choosing a pecan first is 350/1000 or 0.35 (35%).
For Part II, we calculate the probability of choosing either an almond or a cashew. The total of almonds and cashews is 325 almonds + 75 cashews = 400. So, the probability is 400/1000, which simplifies to 0.4 (40%).
An airliner travels 45 miles in 5 minutes. What is it’s speed in miles?
Help with this one please
The Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic Mean Inequality (RMS-AM-GM-HM), is an inequality of the root-mean square, arithmetic mean, geometric mean, and harmonic mean of a set of positive real numbers that says:
with equality if and only if . This inequality can be expanded to the power mean inequality.
As a consequence we can have the following inequality: If are positive reals, then with equality if and only if ; which follows directly by cross multiplication from the AM-HM inequality.This is extremely useful in problem solving.
Please Help!
Khalid has a game board as shown below, which is a square with 20-cm sides. The area of the largest circle is 320 square centimeters.
What is the probability of scoring 1, 3, or 5 points with one randomly thrown dart?
A. 1/2
B. 5/8
C. 3/4
D. 4/5
Answer:
Option D. 4/5
Step-by-step explanation:
we know that
The probability of scoring 1, 3, or 5 points with one randomly thrown dart is equal to divide the area of the largest circle by the area of the square game board
step 1
Find the area of the square game board
[tex]A=b^{2}[/tex]
we have
[tex]b=20\ cm[/tex]
substitute
[tex]A=20^{2}[/tex]
[tex]A=400\ cm^{2}[/tex]
step 2
Find the probability
[tex]P=320/400[/tex]
[tex]P=0.8=8/10=4/5[/tex]
For the particular problem raised in the introduction, assume that the total bill is $44. to answer the question "how should the bill be split?" we will create a linear equation. the unknown is how much money a single person (besides anika) must pay, so call that x. although four people (you plus three friends) went to dinner, only three are paying the unknown amount x for a total of 3x. since anika is paying $2, the total amount paid is 3x+2 dollars, which must equal the amount of the bill, $44. thus, the equation to find x is 3x+2=44. the steps for solving a linear equation are as follows: move all of the constants to the right side. move all of the variable terms (terms containing x) to the left side. divide both sides by the coefficient of the variable to isolate the variable. you will go through these steps one at a time to solve the equation and determine how much each person should pay.
Dustin is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. if the angle of elevation from dustin's mom to Dustin is 73 degrees, how far off the ground is nick?
A. 118.2 ft
B. 120.9 ft
C. 124.3 ft
D. 126.5 ft
E. 128.1 ft
The correct option is A. [tex]118.2\ ft[/tex]. Dustin is approximately [tex]118.2\ ft[/tex] off the ground.
To find how far Dustin is off the ground, we can use trigonometry, specifically the tangent function.
Let [tex]\( h \)[/tex] denote the height of Dustin above the ground.
Given:
Angle of elevation [tex]\( \theta = 73^\circ \)[/tex]
Distance from Dustin's mother to the base of the ferris wheel [tex]\( d = 38 \)[/tex]feet
We can set up the tangent function:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d} \][/tex]
Substitute the given values:
[tex]\[ \tan(73^\circ) = \frac{h}{38} \][/tex]
Now, solve for [tex]\( h \)[/tex]
[tex]\[ h = 38 \times \tan(73^\circ) \][/tex]
Use a calculator to find [tex]\( \tan(73^\circ) \)[/tex]
[tex]\[ \tan(73^\circ) = 3.0985 \][/tex]
Therefore,
[tex]\[ h = 38 \times 3.0985 \][/tex]
[tex]\[ h = 117.839 \][/tex]
Rounding to the nearest tenth, Dustin is approximately [tex]\( 117.8 \) feet[/tex] off the ground.
Twelve people are entered in a race. If there are no ties, in how many ways can the first three places come out?
[tex] 12\cdot11\cdot10=1320 [/tex]
The number of ways the first three places in a race with twelve competitors can be filled is 1320, calculated by the permutations formula which multiplies the choice for each of the three places -- 12 for first, 11 for second, and 10 for third.
The student's question asks for the number of different ways the first three places in a race can be filled when there are twelve competitors. This is a problem of permutations where we do not consider the remaining positions after the third place. To solve this, we calculate the number of permutations for the first three places, which is a sequence of choices. We have 12 choices for the first place, 11 choices for the second place after the first place has been filled, and 10 choices for the third place after the first two places have been filled.
The total number of permutations can be calculated as:
First place: 12 possibilitiesSecond place: 11 possibilities (since one person is already in the first place)Third place: 10 possibilities (as two contestants are in the first and second place)By the counting principle, we multiply these choices together to find the total number of permutations for the first three places, which is 12 x 11 x 10.
Therefore, the total number of ways the first three places can be awarded is 12 x 11 x 10 = 1320 different permutations.
Two students, Ann and Max, factored the trinomial 4x2 − 6x − 4. Ann factored it as 2(x − 2)(2x + 1) and Max factored it as (x − 2)(4x + 2). Indicate which student factored the trinomial completely and which student did not, and explain why.
For the data set below, calculate the standard deviation to the nearest hundredth decimal place. 27 38 47 42 33 56 37 57 38 52
Final answer:
The standard deviation of the given data set is 10.03, and the value that is one standard deviation below the mean is 32.67. Calculations involve finding the mean, computing squared deviations, calculating the sum of squared deviations, finding the variance, and taking the square root of the variance.
Explanation:
The mean is calculated as: (27 + 38 + 47 + 42 + 33 + 56 + 37 + 57 + 38 + 52) ÷ 10 = 427 ÷ 10 = 42.7.
Now we calculate each deviation from the mean, square it, and sum them:
(27 - 42.7)² = 246.49
(38 - 42.7)² = 22.09
(47 - 42.7)² = 18.49
(42 - 42.7)² = 0.49
(33 - 42.7)² = 94.09
(56 - 42.7)² = 176.89
(37 - 42.7)² = 32.49
(57 - 42.7)² = 204.49
(38 - 42.7)² = 22.09
(52 - 42.7)² = 86.49
A sum of squared deviations = 904.61.
The variance is 904.61 ÷ (10-1) = 100.51.
The standard deviation is the square root of the variance,
which is √100.51 equal to approximately 10.03.
To find the value that is one standard deviation below the mean, we subtract one standard deviation from the mean: 42.7 - 10.03 = 32.67.
Therefore, the standard deviation to the nearest hundredth is 10.03, and the value that is one standard deviation below the mean is approximately 32.67.
The "Let's Roll" game uses a number cube with the numbers 2,4,6,8,10, and 12. There are prizes for rolling any number less than 6. How likely is it to roll a number less than 6?
The probability of rolling a number less than 6 in the 'Let's Roll' game is 1/3.
Explanation:To find the probability of rolling a number less than 6 in the 'Let's Roll' game, we need to count the number of favorable outcomes (numbers less than 6) and divide it by the total number of possible outcomes (numbers on the number cube). In this case, the favorable outcomes are 2, 4, and the total number of outcomes is 6.
Therefore, the probability of rolling a number less than 6 is 2/6 or 1/3.
Therefore the probability of getting a number less than 6 will be 33.3%
Probability is defined as the ratio of the
number of favorable outcomes to the total
number of outcomes in other words the
probability is the number that shows the
happening of the event.
Sample space we have = [ 2,4,6,8,10,12 ] = 6
Desirable outcome will be = [2,4] = 2
Probability = 2 / 6
Probability = 1/3
Probability = 0.33 = 33%
Therefore the probability of getting a number less than 6 will be 33.3%
Find the 15th term of the arithmetic sequence.
a+1, 2a+1, 3a+1
a. a+15
b. 15a+15
c. 15a + 1
d. 14a+14
The surface inside the circles will be painted green. The surface outside the circles will be painted white. What is the ratio of green paint to white paint you will need to paint these tiles? π : (π – 4) (π – 4): π π2 : (π2 – 4) (π2 – 4): π2
Answer:
π : (π – 4)
Step-by-step explanation:
Consider the floor tile below.
The surface inside the circles will be painted green. The surface outside the circles will be painted white. What is the ratio of green paint to white paint you will need to paint these tiles?
π : (π – 4)
(π – 4): π
π2 : (π2 – 4)
(π2 – 4): π2
Odyssey