Answer:
The rate at which the tank is being emptied is 25 gallons per minute, which means that the change in the amount of oil in the tank per minute is -25. Let's assume that the initial amount of oil in the tank is 2500 gallons and the capacity of the tank is 3000 gallons.
The equation that relates the amount of oil in the tank, V, and time, t, is given by:
V = 2500 - 25t
This equation represents a linear relationship between the amount of oil in the tank and time. As time increases, the amount of oil in the tank decreases linearly at a rate of 25 gallons per minute.
The capacity of the tank, c, is 3000 gallons, which means that the tank will be completely emptied after:
t = (3000 - 2500) / 25 = 20 minutes
After 20 minutes, the amount of oil in the tank will be:
V = 2500 - 25(20) = 2000 gallons
Solve: 2x2 = 98 please help me
Answer:
1=24.5
Step-by-step explanation:
2*2=98
4=98
2= 49
which means
1 is 24.5
how to convert 50cm to in
50cm is equal to 19.685 inches.
Measurement is a crucial aspect of our lives, and it helps us to determine the quantity, size, or amount of things. Different units of measurement are used to measure various objects, and it is essential to know how to convert from one unit to another. In this article, we will discuss how to convert 50cm to inches, which are both commonly used measurements.
To convert 50cm to inches, we need to know the conversion factor between centimeters and inches. One inch is equal to 2.54 centimeters, which means that we can convert centimeters to inches by dividing the measurement by 2.54.
So, to convert 50cm to inches, we need to divide 50 by 2.54. We can do this using a calculator or by long division.
50 / 2.54 = 19.685 inches
In this case, we have learned how to convert 50cm to inches, which involves dividing the measurement by 2.54.
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Dana is preparing cheese plates for her chess club's holiday party. She cuts a block of Colby into 9 equal pieces. Dana serves 6 pieces when the party starts. She saves 3 pieces to serve later.
What fraction of the block of Colby does Dana serve when the party starts?
Dana cuts a block of Colby cheese into 9 equal pieces. She serves 6 pieces when the party starts, which is 2/3 of the block. She saves 3 pieces to serve later, leaving 1/3 of the block remaining.
What are fractions?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. The number below the line is called the denominator.
Dana cuts a block of Colby cheese into 9 equal pieces. This means that each piece is 1/9th of the block of Colby cheese.
Dana serves 6 pieces of the cheese when the party starts. So the total amount of cheese that she serves is 6 times the size of each piece, which is:
6 pieces x (1/9th of the block) = 6/9 or 2/3 of the block.
Therefore, Dana serves 2/3 of the block of Colby cheese when the party starts.
She saves 3 pieces to serve later, which means that there are still 3/9 or 1/3 of the block of Colby cheese left.
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a group of 15 people are ordering pizza each person wants 2 slices and each pizza has 15 sides how many pizzas should they order.
Answer:
The total number of pizzas they will order is 2
Step-by-step explanation:
[tex]15*2=30[/tex]
30 slices total, so they need 2 pizzas for each person to get 2 slices of pizza.
(a) From the 12 albums released by a musician, the recording company wishes to release9 in a boxed set. How many different boxed sets are possible?
(b) There14 are European cities that Rashid would eventually like to visit3. On his next vacation, though, he only has time to visit of the cities: one on Monday, one on Tuesday, and one on Wednesday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)
Answer:
ejekkeifjejejrjjdjejejeiriririrj
For the probability distribution of a discrete random variable x, the sum of the probabilities of all values of x must be:
a. In the range of zero to 1.
b. equal to zero.
c. equal to 1.
d. equal to 0.5.
For the probability distribution of a discrete random variable x, the sum of the probabilities of all values of x must be: equal to 1. The Option C is correct.
Why is sum of probabilities of all values of x equal to 1?The sum of the probabilities of all values of a discrete random variable x must be equal to 1 because, by definition, the probability distribution of a random variable represents the probabilities of all possible outcomes of an experiment, and the sum of the probabilities of all possible outcomes must be equal to 1.
In other words, the probability distribution of a discrete random variable specifies the likelihood of each possible value that the random variable can take on, and the total probability of all possible outcomes must add up to 1, since the outcome of the experiment must be one of the possible values of the random variable.
Mathematically, this can be expressed as:
∑P(x) = 1 where P(x) is the probability of the random variable x taking on a particular value. This equation ensures that the total probability of all possible outcomes is equal to 1, which is a fundamental principle of probability theory.
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The vertex of the parabola below is at the point (2, -5). Which of the equations below could be the one for this parabola?   A. x = -4(y - 2)2  B. y = (x + 2)2 - 5
The equation y = (x - 2)² - 5 below could be the one for this parabola. Option B is the correct answer.
What is parabola?A parabola is formed by cutting a right circular cone in half along a plane perpendicular to the cone's generator. It is a locus of a moving point whose separation from the focus is equal to its separation from a stationary line (directrix)
Focus is a fixed point.
Directrix is the name for fixed line.
The equation of the parabola is given by the formula:
y = a(x - Vₓ)² + Vy
Here, Vx and Vy are the coordinates of the vertex of the parabola.
Substituting the value of coordinates of vertex we have:
y = a(x - 2)² - 5
Hence, the equation y = (x - 2)² - 5 below could be the one for this parabola. Option B is the correct answer.
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Can someone please help me with this question?
A semicircle has radius 5.6cm. Work out the perimeter of the semicircle.
Answer:
28.79 cm.
Step-by-step explanation:
The perimeter of a semicircle is equal to the sum of the diameter (which is twice the radius) and half of the circumference of the circle.
The diameter of the semicircle is 2 × 5.6cm = 11.2cm.
The circumference of a full circle with radius 5.6cm is 2π × 5.6cm = 11.2π cm.
Therefore, the circumference of the semicircle is 1/2 of the circumference of the full circle, which is 1/2 × 11.2π cm = 5.6π cm.
The perimeter of the semicircle is the sum of the diameter and the circumference, which is:
11.2cm + 5.6π cm ≈ 28.79cm (rounded to two decimal places)
Therefore, the perimeter of the semicircle is approximately 28.79 cm.
Answer:
pi ( 5.6 ) + 11.2 or approximately 28.79291 cm
Step-by-step explanation:
The outside of the semicircle or the perimeter is 1/2 of the circumference and the length that closes the circle is the diameter.
Perimeter = 1/2 C + d
= 1/2 *pi*d + d
The diameter is 2 times the radius.
= 1/2 ( pi) * (2r) + 2r
= pi r + 2 r
= pi ( 5.6 ) + 11.2
Approximating pi, we get approximately 28.79291
what is 103 as a decimal?
103 in decimal terms can be denoted by simply dividing the term by 100 so the value will be given as 1.03.
The division method can be used to convert 103/100 to a decimal. Here is a brief recap on fractions before we go to the method: A fraction is a representation of a number that has been divided into two parts: the numerator, which is the number at the top, and the denominator, which is the number at the bottom. Divide the numerator (103 in this case) by the denominator (100 in this case) to produce a decimal using the division method:
100 (denominator) minus 103 (numerator) equals 1.03.
So there you have it! When you convert 103/100 to a decimal, the result is 1.03.
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How Many Cups In A Pounds ?
Answer:
There are 1.91 cups in a pound
what is liters to mi?
A liter is a metric unit of volume, while a milliliter (ml) is a subunit of a liter. There are 1,000 milliliters in one liter.
This means that to convert liters to milliliters, you can multiply the number of liters by 1,000. Conversely, to convert milliliters to liters, you would divide the number of milliliters by 1,000.
For example, if you have 2.5 liters of water, you can convert this to milliliters by multiplying 2.5 by 1,000, which gives you 2,500 milliliters. This conversion is commonly used in fields such as chemistry and medicine, where small amounts of liquids are measured in milliliters.
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A kite flying in the air has an 86-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 53°. Find the height of the kite.
Round your answer to the nearest tenth.
Answer:
≈ 106.5 feet
Step-by-step explanation:
Let's start by drawing a picture of the situation. Imagine a kite flying in the air, with a string attached to it that is pulled taut (pulled tight so there's no slack). The string is 86 feet long. We want to know how high the kite is in the air, and we know that the angle of elevation of the kite is 53 degrees.
Now, the angle of elevation is the angle between the horizontal (the ground) and the line of sight from the observer (you) to the object (the kite). In this case, you are looking up at the kite, so the line of sight is the string that connects the kite to the ground.
To find the height of the kite, we need to use trigonometry. Specifically, we'll use the tangent function, which relates the opposite side of a right triangle (in this case, the height of the kite) to the adjacent side (in this case, the length of the string) and the angle of elevation.The formula for the tangent function is:
tan(theta) = opposite/adjacent
Where theta is the angle of elevation, opposite is the height of the kite, and adjacent is the length of the string.
We know that the angle of elevation is 53 degrees, and the length of the string is 86 feet. So we can plug those values into the formula and solve for the height of the kite:
tan(53) = opposite/86
opposite = 86 * tan(53)
≈ 106.5
So the height of the kite is approximately 106.5 feet.
Which of the following shows the simplified form of sine of x over the quantity 1 plus cosine of x (end quantity)?
A. sin x − tan x
B. sin x − cot x
C. csc x − cot x
D. 1
The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity) is 1. Option D
How to find the simplified form of the expressionThe question can be interpreted as sin(x) / (1 + cos(x))
sin(x) / (1 + cos(x)) = (sin(x) / cos(x)) / (1/cos(x) + cos(x)/cos(x))
= tan(x) / (1 + sec(x))
= (sin(x)/cos(x)) / (cos(x)/(cos(x)+1))
= (sin(x)/cos(x)) / ((cos(x)+1)/cos(x))
= sin(x) / (cos(x) + 1)
Therefore, the simplified form of sin(x) / (1 + cos(x)) is:
sin(x) / (1 + cos(x)) = sin(x) / (cos(x) + 1) = 1
Hence, The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity) is 1
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What is the 6 times table?
The 6 times table is a multiplication table that shows the results of multiplying any number by 6.
It is a fundamental arithmetic skill that students typically learn in elementary school, and is an important building block for more advanced math concepts.
To generate the 6 times table, you simply multiply 6 by each whole number starting with 1, and continue the pattern up to a desired number. The first few products in the 6 times table are as follows:
1 x 6 = 6
2 x 6 = 12
3 x 6 = 18
4 x 6 = 24
5 x 6 = 30
6 x 6 = 36
7 x 6 = 42
8 x 6 = 48
9 x 6 = 54
10 x 6 = 60
...
and so on.
It is important for students to memorize the 6 times table, as it can be used to solve a variety of math problems involving multiplication, division, fractions, and decimals. Mastery of the 6 times table is also a key step in preparing for more advanced math concepts, such as algebra and calculus.
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Michelle has 18.9 yards of string. She cuts the string into 5 pieces of equal length. How long is each piece? Responses 2.65 yd 2.65 yd 3.27 yd 3.27 yd 3.78 yd 3.78 yd 4.08 yd
Answer:
Michelle has 18.9 yards of string. She cuts the string into 5 pieces of equal length. How long is each piece?
3.78 yd18.9 ÷ 5
Step-by-step explanation:
You're welcome.
PLS SOLVE THIS ASAPP ILL GIVE BRAINLY
Answer:
a
Step-by-step explanation:
Answer:
1. 24, use similar triangles
2. A , C , D
Step-by-step explanation:
What value of x makes this equation true -3x + 1 = 7
Answer:
x = -2
Step-by-step explanation:
-3x + 1 = 7
Subtract 1 from both sides:
-3x = 6
Divide -3 by both sides:
x = -2
What is a factor tree for 78?
The factor tree shows how 78 can be factored into its prime factors.
78 = [tex]2 \times 3 \times 13.[/tex]
The first step in creating a factor tree for the number 78 is to identify two factors of 78 that sum up to 78. One such pair of factors is 6 and 13. After we reach prime numbers, we can carry on breaking down each component.
Prime factorization is the process of converting a composite number into the product of its prime factors. A prime factor is a prime number that divides the original integer by itself with no remainder.
The prime factorization of the number 78 is
78 = 6 x 13
78 = 2 x 3 x 13.
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A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 30 times, and the man is asked to predict the outcome in advance. He gets 22 out of 30 correct. What is the probability that he would have done at least this well if he had no ESP?
the probability that the man would have done at least as well as 22 out of 30 correct predictions by chance alone is approximately 0.149 or 14.9%, which suggests that his ESP claim may not be supported by the coin flip test results alone.
To determine the probability that the man would have gotten at least 22 correct coin flip predictions if he had no ESP, we can use a statistical tool called a binomial distribution. Assuming the coin is fair, the probability of getting any single coin flip prediction correct is 0.5, since there are only two possible outcomes (heads or tails) and they are equally likely. We can use this probability to calculate the probability of getting exactly 22 correct predictions out of 30 coin flips, which is:
P(X = 22) = (30 choose 22) {multiply} 0.5^22 {multiply} 0.5{power}8 = 0.099
This means that the probability of getting exactly 22 correct predictions by chance is less than 10%. However, the question asks for the probability of getting at least 22 correct predictions, which includes the probabilities of getting 23, 24, 25, 26, 27, 28, 29, or 30 correct predictions as well.
To calculate this cumulative probability, we can add up the probabilities of getting each of these outcomes separately:
P(X >= 22) = P(X = 22) + P(X = 23) + ... + P(X = 30)
Using a binomial distribution table or calculator, we can find that this cumulative probability is approximately 0.149.
Therefore, the probability that the man would have done at least as well as 22 out of 30 correct predictions by chance alone is approximately 0.149 or 14.9%, which suggests that his ESP claim may not be supported by the coin flip test results alone.
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What is 70 degree C into F?
After converting from Celsius to Fahrenheit 70 degrees Celsius is equivalent to 158 degrees Fahrenheit.
To convert Celsius to Fahrenheit, you can use the following formula:
°F = (°C x 9/5) + 32
In this case, to convert 70 degrees Celsius to Fahrenheit, we can substitute 70 for °C in the formula:
°F = (70 x 9/5) + 32
Simplifying this expression, we can first perform the multiplication and division:
°F = (126) + 32
Then we can add 126 and 32 to get the final answer:
°F = 158
It's worth noting that the Celsius and Fahrenheit scales are both used to measure temperature, but they have different starting points and different degrees of scale. Celsius is based on the freezing and boiling points of water, where 0 degrees Celsius is the freezing point and 100 degrees Celsius is the boiling point at sea level.
Fahrenheit, on the other hand, is based on a system of degrees devised by Gabriel Fahrenheit, with 32 degrees being the freezing point and 212 degrees being the boiling point at sea level.
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2. A certain TV can be purchased from the manufacturer for $220. A certain online retailer has a standard markup of 25%, and a certain superstore has a standard markup of 45%.
(a) What is the price of the TV when purchased online? What is the price of the TV when purchased at the superstore?
(b) What is the difference between the prices in Part (a)? How does this relate to the difference in the markup?
Answer:
(1) As a result, the Monitor costs $275 to buy online. (2) There is a 20% price disparity between the two retailers.
What is a good illustration of purchased?10,000 pairs of shoes are ordered by Shoes Unlimited from an overseas vendor. This entails the business issuing a purchase requisition, which serves as a formal promise to buy the specified kind and number of shoes.
(a) To find the price of the TV when purchased online, we can add 25% markup to the manufacturer's price of $220:
Price online = $220 + (0.25 * $220)
Price online = $220 + $55
Price online = $275
So the price of the TV when purchased online is $275.
To find the price of the TV when purchased at the superstore, we can add 45% markup to the manufacturer's price of $220:
Price at superstore = $220 + (0.45 * $220)
Price at superstore = $220 + $99
Price at superstore = $319
So the price of the TV when purchased at the superstore is $319.
(b) The difference between the prices in part (a) is:
Price at superstore - Price online = $319 - $275 = $44
The difference in markup between the two stores is:
Markup at superstore - Markup online = 45% - 25% = 20%
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Question 3 Benda is taking about buying a house for $249.000 The table below shows the projected value of two different houses for three years Number of years 1 2 3 House 1 (value in dollars) 253.960 259 059 60 264 240 79 House 2 (value in dollars) 256 000 263.000 270.000 Part A: What type of function Inear or exponential can be used to describe the value of each of the houses after a fixed number of years? Explain your (2) Part B: Wibe one function for each house to describe the value of the house fix) in dollars, after x years (4 points) Part C: Belinda wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in t
please I need help I will give alot of points
Answer:
Part A:
To determine whether a linear or exponential function can be used to describe the value of each house after a fixed number of years, we need to examine the change in the value of the houses over time. If the change is constant, a linear function can be used. If the change is proportional to the current value, an exponential function can be used.
Looking at the data in the table, we can see that the value of House 1 is increasing by a relatively constant amount each year, whereas the value of House 2 is increasing by a proportional amount. Therefore, a linear function can be used to describe the value of House 1, and an exponential function can be used to describe the value of House 2.
Part B:
For House 1, we can use the formula y = mx + b, where y is the value of the house in dollars, x is the number of years, m is the slope or rate of increase, and b is the initial value. Using the data from the table, we can find the slope and initial value:
m = (264240.79 - 253960) / 2 = 5140.395
b = 253960
So the function to describe the value of House 1 after x years is:
y = 5140.395x + 253960
For House 2, we can use the formula y = ab^x, where y is the value of the house in dollars, x is the number of years, a is the initial value, and b is the growth factor. Using the data from the table, we can find the initial value and growth factor:
a = 256000
b = (270000 / 256000)^(1/3) = 1.02905
So the function to describe the value of House 2 after x years is:
y = 256000(1.02905)^x
Part C:
To determine which house will have the greatest value in 45 years, we can plug in x = 45 into the functions we found in Part B and compare the results. Using a calculator, we get:
House 1: y = 5140.395(45) + 253960 = 472 339.25
House 2: y = 256000(1.02905)^45 = 798 825.85
Therefore, House 2 will have a significantly higher value after 45 years.
Step-by-step explanation:
ABCD is a kite, So AC - DB and DE=EB Calculate the length of \overline{AC} AC to the nearest tenth of a centimeter.
Answer:
AC=9CM
Step-by-step explanation:
Since ABCD is a kite, we know that the two diagonals, AC and BD, intersect at right angles and that the two pairs of adjacent sides are congruent. Therefore, we have:
AC = BD and AB = BC = CD = DA
We also know that DE = EB, which means that triangle ADE is congruent to triangle BEC (by the side-side-side congruence rule), so we have:
AD = BC and AE = EC
AD=5cm and DC=4cm
Combining these equations, we have:
AC = AD + DC
AC=5cm+4cm=9cm
Yes or no help now asapppp
The ordered pair (0,1) is not a solution to the inequality, as the line is dashed, meaning that points exactly on the line are not solutions to the inequality.
How to interpret the solution to the inequality?The general format of an ordered pair is given as follows:
(x,y).
For the ordered pair (0,1), we have that the coordinates are given as follows:
x-coordinate of 0.y-coordinate of 1.Hence the point is exactly at y = 1 on the y-axis, where the line crosses the y-axis. However, the line is dashed, meaning that it is not part of the solution.
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The GDP deflator formula can be used in a variety of ways. Use it to answer the questions that follow. Round final answers to two decimal places, as needed
The nominal GDP in 2012 is $3,450.00.
The GDP deflator is a price index that measures the average price level of goods and services produced in an economy. It is calculated as the ratio of nominal GDP to real GDP, multiplied by 100.
Nominal GDP (Gross Domestic Product) is a measure of the total value of all goods and services produced within a country's borders during a given period of time, usually a year, using current market prices
To use the GDP deflator formula to answer the question, we need to rearrange the formula and solve for nominal GDP:
Nominal GDP = Real GDP × (GDP deflator / 100)
Plugging in the given values, we get:
Nominal GDP = $2,300.00 × (150.00 / 100) = $3,450.00
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The given question is incomplete, the complete question is:
: The GDP deflator formula can be used in a variety of ways. Use it to answer the questions that follow. Round final answers to two decimal places, as needed. Real GDP $2300.00 GDP deflator 150.00 .what is the nominal GDP in 2012 ?
Use powers of 16 in the top row. Use radicals or rational numbers in the second row
The table given in the answer is an example of a conversion table that shows the decimal equivalents of powers of 16. The first row contains the values of 16 raised to the powers of 4, 3, 2, 1, and 0, respectively. The second row shows the equivalent decimal values of these powers of 16.
16⁴ 16³ 16² 16 1
256 64 16 4 1
These values could also be expressed using radicals or rational numbers, but in this case, the decimal form is simpler and more commonly used.
This can be calculated as 16 x 16 x 16 x 16, which equals 65,536. Similarly, the second entry in the first row is 16³, which means 16 raised to the third power.
To understand why this is the case, we need to convert 16⁴ to decimal form. This can be done by multiplying each digit in the binary representation of 16⁴ by the corresponding power of 2 and adding up the results.
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A country's population in 1993 was 105 million.
In 1997 it was 110 million. Estimate
the population in 2006 using the exponential
growth formula. Round your answer to the
nearest million.
P = Aekt
Enter the correct answer.
Answer:We use the formula for exponential growth:P = Po exp(kt)Using the population data from 1993 to 1996, we can solve for the growth rate k76 = 72 exp(k(3))76/72 = exp(3k)ln (76/72) = 3kk = ln(76/72) / 3 = 0.0180In 10 years (2003), the population will be:P = Po exp(0.0180t)P = 72 exp(0.0180(10))P = 86.22 million
Step-by-step explanation:
Renaldo has a budget of $500 to buy gift boxes for a party. Large boxes cost $65 and small boxes cost $35. Write and graph an inequality that represents the number of each type of gift box that Renaldo can buy. If Renaldo buys 6 small gift boxes, how many large gift boxes can he afford to buy?
Answer:
Here is how to write and graph an inequality for the budget problem:
Let x be the number of large boxes and y be the number of small boxes. The total cost of the boxes must be less than or equal to the budget of $500. So, we can write the inequality as:
65x + 35y ≤ 500
To graph this inequality, we need to find the boundary line and the shaded region. The boundary line is the equation that we get when we replace the inequality sign with an equal sign, which is:
65x + 35y = 500
To graph this line, we need to find two points on it. We can do this by plugging in some values for x or y and solving for the other variable. For example, if x = 0, then y = 500/35 = 14.29. If y = 0, then x = 500/65 = 7.69. So, two points on the line are (0, 14.29) and (7.69, 0). We can plot these points on a coordinate plane and draw a solid line through them, since the inequality includes the equal sign.
To find the shaded region, we need to test a point that is not on the line and see if it satisfies the inequality. For example, we can test the point (0, 0), which is the origin. Plugging in x = 0 and y = 0 into the inequality, we get:
65(0) + 35(0) ≤ 500
0 ≤ 500
This is true, so the point (0, 0) is a solution to the inequality. This means that the shaded region is the area that includes the point (0, 0) and is below the line.
If Renaldo buys 6 small gift boxes, then y = 6. To find how many large gift boxes he can afford, we need to plug in y = 6 into the inequality and solve for x. We get:
65x + 35(6) ≤ 500
65x + 210 ≤ 500
65x ≤ 290
x ≤ 290/65
x ≤ 4.46
This means that Renaldo can buy at most 4 large gift boxes if he buys 6 small gift boxes. However, since x has to be a whole number, the largest possible value for x is 4. So, Renaldo can buy 4 large gift boxes and 6 small gift boxes and still stay within his budget.
I hope this helps!
Step-by-step explanation:
write 5 x 5 x 5 x 5 using exponets
Answer:5 and a tiny 4 in the corner of that 5
Step-by-step explanation:
there are four 5s so u do 5 with little 4
4. f(x) = 3x
y-intercept
Domain
Range
End Behavior:
As x → ∞o, f(x) →
As x→→∞, f(x) →
Domain (-2,-1,0, 1, 2}
The given function is f(x) = 3x.
To find the y-intercept, we plug in x = 0:
f(0) = 3(0) = 0
So the y-intercept is 0.
The domain of the function is given as (-2, -1, 0, 1, 2}. This means that the function is defined only for these values of x.
The range of the function is all real numbers, since for any real number y, we can find an x such that f(x) = y. We can see this from the fact that the function is a linear function with a non-zero slope.
The end behavior of the function as x approaches infinity depends on the sign of the coefficient of x, which is positive in this case. Therefore, as x → ∞, f(x) → ∞. Similarly, as x → -∞, f(x) → -∞.
Note that the given domain is a finite set of values, and does not affect the end behavior of the function as x approaches infinity or negative infinity...