Answer:
$205
Step-by-step explanation:
To solve this problem, we need to multiply $2,560 by 8%. Don't forget to change 8% into its decimal form (8% -> .08).
2,560 x .08 = 204.8
Fran budgets $205 dollars for groceries each month.
To make f continuous at x=2 , f(2) should be defined as what value? Justify your answer.
Answer:
To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]
Step-by-step explanation:
A function, let say [tex]f(x)[/tex], is defined at [tex]x = c[/tex] is continuous at [tex]x = c[/tex]
If the limit of [tex]f(x)[/tex] as [tex]x[/tex] approaches [tex]c[/tex] is equal to the value of [tex]f(x)[/tex] at [tex]x = c[/tex].
Mathematically it is written as:
if
[tex]\lim _{x\to c}\:f\left(x\right)=f\left(c\right)[/tex]
then
[tex]f(x)[/tex] is continuous at [tex]x = c[/tex].
So from the above definition, we conclude that:
To make f continuous at [tex]x=2[/tex], [tex]f(2)[/tex] should be defined [tex]x = 2.[/tex]
i.e.
if
[tex]\lim _{x\to 2}\:f\left(x\right)=f\left(2\right)[/tex]
then
[tex]f(x)[/tex] is continuous at [tex]x = 2[/tex].
To make f continuous at x=2, define f(2) to be equal to 4. This makes the left-hand limit, right-hand limit, and function value at x=2 all equal to 4, which satisfies the definition of continuity.
To make a function continuous at a point, the left-hand limit and right-hand limit at that point must be equal to the function's value at that point. In other words, if a function is continuous at x=a, then
[tex]\lim_{x \to a^+} f(x)=f(a)[/tex]
Therefore, to make f continuous at x=2, we must define f(2) to be equal to the limit of f(x) as x approaches 2 from both the left and the right.
We can see that the limit of f(x) as x approaches 2 from the left is 4. This is because f(x) approaches 4 as x approaches 2 from the left, even though f(2) is undefined.
We can also see that the limit of f(x) as x approaches 2 from the right is 4. This is because f(x) approaches 4 as x approaches 2 from the right, even though f(2) is undefined.
Therefore, to make f continuous at x=2, we must define f(2) to be equal to 4.
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Find the infinite geometric sum, if possible: 50 + 150 + 450 + …
Answer:
Find the infinite geometric sum, if possible: 50 150 + 450 +... -75 25 1000000 Does not exist and
Step-by-step explanation:
17. A bottlenose dolphin jumps out of the water. The path the dolphin Travels can be
modeled by h = -0.2d2 + 2d, where h represents the height of the dolphin and d
represents horizontal distance.
a. What is the maximum height the dolphin reaches?
b. How far did the dolphin jump?
The maximum height that the dolphin reaches is 5 units, which occurs at a horizontal distance of 5 units. The dolphin's total horizontal jump distance is 10 units.
Explanation:The maximum height the dolphin reaches (the vertex of the parabola) is found by the formula -b/(2a) for the maximum or minimum of a parabola ax^2 + bx + c. In your equation, a = -0.2 and b = 2. Therefore, the horizontal distance, d, at the maximum height is d = -b/(2a) = -2/(-0.4) = 5 units. Substituting d = 5 into the original equation gives h = -0.2*5^2 + 2*5 = 5 units. Thus, the maximum height the dolphin reaches is 5 units.
The dolphin's horizontal distance (the 'd' value when h = 0) specifies the full length of the jump. Solving the equation -0.2*d^2 + 2*d = 0 gives d = 0 (the start of the jump) and d = 10 (the end of the jump). Thus, the dolphin jumped 10 units horizontally.
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The maximum height reached by the dolphin is 5 meters, and it jumps a horizontal distance of 10 meters. This is determined by analyzing the quadratic equation for maximum height and the point where the dolphin returns to the water surface.
To determine the maximum height (h) the dolphin reaches, we need to analyze the given quadratic equation h = -0.2d² + 2d. Because the coefficient of d² is negative, the parabola opens downward, indicating that the vertex of the parabola will give us the maximum height. The vertex of a parabola in the form of h = ad² + bd + c is given by the formula d = -b/(2a). In this case, a = -0.2 and b = 2, so the horizontal distance (d) at the vertex is d = -2/(2 × (-0.2)) = 5 meters. Plugging this back into the equation, we get h = -0.2(5)² + 2(5) = -0.2(25) + 10 = -5 + 10 = 5 meters.
So, the maximum height reached by the dolphin is 5 meters.
The dolphin jumps until it returns to the water surface, which means the height h becomes 0. We solve the quadratic equation 0 = -0.2d² + 2d by factoring out d: 0 = d(-0.2d + 2). This gives us two solutions: d = 0 (the starting point) and -0.2d + 2 = 0 which leads to d = 10.
Therefore, the dolphin jumped a horizontal distance of 10 meters
What is the greatest common factor of the given monomials 5m⁴,50nm and15³n²
Answer:
5m
Step-by-step explanation:
The GCF is 5m assuming that the question was actually:
5m⁴, 50nm, 15m³n²
Final answer:
The greatest common factor of the given monomials 5m⁴, 50nm, and 15³n² is 5m.
Explanation:
To find the greatest common factor of the given monomials 5m⁴, 50nm, and 15³n², we need to factorize each monomial and find the common factors.
The prime factorization of 5m⁴ is 5 * m * m * m * mThe prime factorization of 50nm is 2 * 5 * n * mThe prime factorization of 15³n² is 3 * 5 * 5 * 5 * n * nNow, we can find the common factors by looking at the factors that are present in each monomial.
The common factors are 5 and m.
So, the greatest common factor is 5m.
can you please help with showing all parts please
Answer:
solution is 7. graphing is: open circle on 7 with the arrow pointing right. -->
Step-by-step explanation:
the answer has to be more than 4, so five or more. Then you add 2 to 5 and get 7. 7-2=5 which is greater than 4.
What is d + 11 =26
..............???
Answer:
15
Step-by-step explanation:
subtract 11 from 26 which the opposite operation to get your answer.
Write -7.5 as a common fraction.
Answer:
-15/2 (or -7 1/2)
Step-by-step explanation:
-7.5 is equal to -75/10.
When you simplify it, you get:
-15/2 which simplifies to -7 1/2
Curtis rides his bike 9 miles one way then turns around and rides back. On the return trip, his speed is increased 20% because the wind is at his back. Let s be his speed in miles per hour riding against the wind. What is an expression that represents his total time in hours riding there and back?
Answer:
The expression that represents his total time is given by "t = 7.5/s" where s is his speed against the wind.
Step-by-step explanation:
In order to solve this problem we will assign a variable to Curtis speed on the first leg of the trip, this will be called "s". Since the speed on the first part is "s" and the speed on the second part is 20% higher, then the speed on the second part is "1.2s". Each leg of the course is 9 miles long, therefore the time it took to go each way is given by:
time = distance/speed
First part:
t1 = 9/s
Second part:
t2 = 9/1.2s = 7.5/s
The expression for the whole course is the sum of each, so we have:
t = t1 + t2
t = 9/s + 7.5/s
t = (9 + 7.5)/s = (16.5)/s
Every 60 minutes the world population increases by 100,000 people. How many people will be born in the next 480 minutes?
Look at the figure. How can you prove ∆ABD and ∆ACD are congruent?
Answer:
You can prove it by the SAS postulate.
Step-by-step explanation:
What is the next term of the arithmetic sequence 10,13,16
Answer:
The next term should be 19
Step-by-step explanation:
Each time you add 3, from 10 to 13, and 13 to 16
The next number would be 19 because 16 + 3 = 19
Find all real square roots of 64
Answer:
8 and -8
Step-by-step explanation:
The definition of a square root is 'a number which produces a specified quantity when multiplied by itself.' Though a negative number cannot have a square root or be a perfect square, it can be a square root.
8 is the only positive square root, but every number that has a square root, also has a second one, the negative version.
-8 is also the square root because it can be multiplied by itself to get 64 :D
The real square roots of the integer 64 will have 8 and -8.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Let's say the square root of 64 is x.
x = √64
Square both sides
x² = (√64)² = 64
x² = 64
Now, find two equal number that gives 64 by multiplying.
Consider, 8 and 8 → 8² = 64
Thus, x = 8
Another could be -8 and -8 → (-8)² = 64
Hence "The real square roots of the integer 64 will have 8 and -8".
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Plz help me outt ASAP
Answer:
53
Step-by-step explanation:
tanx=opp/adj
x=tan^-1(72/54)
x=53.130
Suppose the exact weight of a gallon of water is 8.3 pounds. Four students weighed the gallon of water. Which measurement is most accurate? A) 131.84 ounces B) 133 ounces C) 133.44 ounces D) 140 ounces
The 8 students in Mrs. Clark's dass were asked how many minutes it takes them to get to school in the morning. Here is what they answered:
13, 4, 8, 15, 15, 11, 16,3
Find the mean and median travel times for these students.
If necessary, round your answers to the nearest tenth.
Answer:
mean=10.625=10.6
median=12
Step-by-step explanation:
Mean
The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics. Depending on the context, whether mathematical or statistical, what is meant by the "mean" changes. In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values. The equation for calculating an arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used
Median
The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers. Note that when calculating the median of a finite list of numbers, the order of the data samples is important. Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results. In the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. When the data sample contains an even number of values, the median is the mean of the two middle values. While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample. In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same
plz mark brainliest
What aspect of this graph is likely being emphasized by the choice of graph style, choice of scale, and so on? a. the unrelated nature of the data b. the broad differences over short intervals c. the total values of the data as a whole d. the indirect connection between weight and leaf content
Answer:
D
Step-by-step explanation:
Answer is D.
Answer:
d.
the indirect connection between weight and leaf content
Step-by-step explanation:
Which of the following is a rational number? (1 point)
square root of 79, square root of 80, square root of 81, square root of 82
Answer:
81
Step-by-step explanation:
solve for x in the diagram in the pic
24+28 applying distr
Answer:
Distributive property does not apply here because there is nothing to distribute nor is there any parenthesis.
Which statements about the hyperbola are true? Check all that apply. There is a vertex at (–5, 2). The center of the hyperbola is at (–2, 2). There is a vertex at (–2, 7). The transverse axis is vertical. The directrices are vertical lines.
First , second and last option are relevant to hyperbola . So , they are correct.
Review each statement to determine if it is true for a hyperbola
It is confirm that the first statement is true because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis
It is It is confirm that the second statement is true because the center of a hyperbola is the midpoint of the vertices
It is confirm that the third statement is false because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis
It is confirm that the fourth statement is false because the transverse axis of a hyperbola is the line segment that contains the vertices and the foci
It is confirm that the fifth statement is true because the directrices of a hyperbola are two lines parallel to the conjugate axis and located a distance from the center equal to the distance from the center to the foci.
Therefore, the first, second, and last options are correct.
Question :
Equation of the axes: The equation of the axes of a hyperbola is x = h, where h is the x-coordinate of the center of the hyperbola.
Equation of the asymptotes: The equation of the asymptotes of a hyperbola is y = ±(b/a)x, where a and b are the distances from the center to the vertices along the transverse and conjugate axes.
Equation of the conjugate hyperbola: The equation of the conjugate hyperbola can be found by interchanging a and b in the equation of the original hyperbola.
Review each statement to determine if it is true for a hyperbola
1. "A point on a hyperbola that sits on the transverse axis is called a vertex." - True. That's because the vertices of a hyperbola are indeed points on the hyperbola that line up with the transverse axis.
2. "The center of a hyperbola is right in the middle of its vertices." - True. Think of it like finding the midpoint between two ends. That's where the center of the hyperbola sits.
3. "A hyperbola's vertex is exactly where it meets the transverse axis." - false.
4. "The transverse axis of a hyperbola is the line connecting its vertices and foci." - False. The transverse axis actually links the vertices directly, not the vertices and the foci.
5. "The directrices of a hyperbola are two lines that run parallel to its conjugate axis, and they're positioned at a distance from the center to match the distance from the center to the foci." - True. It's like setting up boundaries at a certain distance from the center to guide the shape of the hyperbola.
So, yes, you're right about the first, second, and last statements being true.
incomplete question
A point at (3, 5) is reflected across the y-axis. What is the distance of this new point y-axis? Explain how you know. axis, NOT the original coordinate pair! 10. Kate plotted a point K in Quadrant I. After she reflected the point across an axis, the reflected point was in Quadrant II. Give a possible ordered pair for point K and its reflection. Describe how the point was reflected. Quadrant IV.) )? (Hint: Look at the across the from the HINT: You MUST count from the x
When a point is reflected across the y-axis, the x-coordinate remains the same, but the sign changes. The distance of the new point from the y-axis is the same as the distance of the original point from the y-axis.
When a point is Reflecting points across the y-axis, the x-coordinate remains the same, but the sign changes.
So, if the original point is (3, 5), the new point will be (-3, 5). The distance of the new point from the y-axis is still 3 units.
This is because the distance between any point and the y-axis is the distance between the x-coordinate of that point and 0 on the number line.
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Mr. Smith wants to rent a car but is not sure how long he is going to need it.The rental car company he finds charges a $50.00 fee and then they also add on a $0.15 per mile charge for driving it. Write an expression to represent the cost of renting a car for any number of weeks.
Answer:
total cost = 50 + 0.15 * x
Step-by-step explanation:
We have a fixed charge and a variable charge, which would be the number of miles you travel with the car. Therefore, the expression that represents this, would be the following:
x = is the number of miles traveled in a given period
total charge = 50 + 0.15 * x
This total charge corresponds to the cost of renting a car in any amount of time (weeks)
On a recent trip to the convenience store, you picked up 4 gallons of milk, 6 bottles of water and 5 snack size bags of chips. You total bill before tax was $ 29.7. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.80 more than a bottle of water, how much does each item cost
Answer:
Milk $3.60
Water $1.80
Chips $0.90.
Step-by-step explanation:
If w = cost of 1 bottle of water, m = cost of 1 gal of milk and c cost of 1 bag of chips we have.
4m + 6w + 5c = 29.7
Also we have w = 2c and m = 1.8 + w.
From the first equation we have c = w/2.
So substituting for c and m in the initial equation we have:
4(1.8 + w) + 6w + 5(w/2) = 29.7
7.2 + 4w + 6w + 2.5w = 29.7
12.5w = 22.5
w = 1. 80.
So c = w/2 = 1.8/2 = 0.90.
and m = 1.8 + 1.8 = 3.60.
The cost of bag of chips is $5.58 , bottle of water is $ 11.16 and gallon of milk is $12.96.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
It is given that
4 gallons of milk, 6 bottles of water and 5 snack size bags of chips costs $29.7
Let the price of bag of chips is $x
Then
bottle of water , y costs twice as much as a bag of chips
y = 2x
a gallon of milk , z costs $1.80 more than a bottle of water
z = y +1.8
z = 2x +1.8
The equation that will be formed is
x + 2x + 2x +1.8 = 29.7
5x +1.8 = 29.7
5x = 27.9
x = $5.58
y = $11.16
z = $12.96
Therefore the cost of bag of chips is $5.58 , bottle of water is $ 11.16 and gallon of milk is $12.96.
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An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet long and has a base with a circumference of 21.980 feet, what is the volume of the sculpture? Use 3.14 for piπ HELP Me PLZ
the volume of the sculpture is [tex]Volume = 64.11ft^3[/tex] .
Step-by-step explanation:
Here we have , An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet long and has a base with a circumference of 21.980 feet, We need to find the volume of the sculpture . Let's find out:
We know that
⇒ [tex]Circumference = 2\pi r[/tex]
According to question ,
⇒ [tex]21.980 = 2\pi r[/tex]
⇒ [tex]\frac{21.980}{2\pi} = r[/tex]
⇒ [tex]r=3.5[/tex]
Now , We know that Volume of cone :
⇒[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
⇒[tex]Volume = \frac{1}{3}(3.14) (3.5)^25[/tex]
⇒[tex]Volume = 64.11ft^3[/tex]
Therefore , the volume of the sculpture is [tex]Volume = 64.11ft^3[/tex] .
Help me serious answers please
Mags and Vector are playing a board game. They use a spinner to determine if they should move forward or backward. They roll a number cube with the numbers 1-6 on it to determine how many spaces to move. What is the probability of moving backward an even number of spaces?
Answer:
1/4
Step-by-step explanation:
What is this data an example of?
*serious answers only*
Each time x goes up by 2, y decreases by 4
This indicates we have a linear function. The slope in this case would be
m = rise/run = (change in y)/(change in x) = -4/2 = -2
The y intercept can be found by following these steps
y = mx+b
0 = -2(5)+b
0 = -10+b
10 = b
b = 10
Therefore, the equation of this line is y = -2x+10. Plug in something like x = 1 and it should lead to y = 8. The same applies for any other column of x,y values.
The rectangle below has an area of x^2-6x-7 square meters and a width of x-7 meters
Complete Question:
The rectangle below has an area of x^2-6x-7 square meters and a width of x-7 meters. What expression represents the length of the rectangle?
Answer:
The expression represents the length of the rectangle is (x + 1) meterSolution:
Given that,
[tex]\text{Area of rectangle} = x^2 - 6x - 7 \\\\Width = x - 7[/tex]
TO FIND: LENGTH = ?
We know that,
[tex]Area\ of\ rectangle = length \times width \\\\Therefore\\\\x^2 - 6x - 7 = length \times x - 7\\\\length = \frac{x^2 - 6x - 7 }{x - 7 }\\\\length = \frac{(x-7)(x + 1)}{x - 7}\\\\\text{cancel out x-7 from numerator and denominator} \\\\length = x + 1[/tex]
Thus expression represents the length of the rectangle is (x + 1) meter
What is the property of equation for -1/3+1/3=0
Answer:
Additive inverse property
Step-by-step explanation:
-1/3 + 1/3 =0
We are adding opposites to get to zero
a+ -a =0
which equation represents a line parallel to 3x-8y=12?
Answer:
B. y = -3/8x - 4
Step-by-step explanation:
Given equation: 3x - 8y = 12
Find a parallel line that matches one of the equations shown.
First, find the slope by solving for y:
3x - 8y = 12
8y = -3x + 12
y = -3/8x + 12/8
y = -3/8x + 3/2
Slope m = -3/8
Since the slope of a line parallel is the same slope, the only equation that fits the conditions is B because in the form y = mx + b, m = -3/8