Answer: 4/15ft2
Step-by-step explanation:
Area of a rectangle is
Length ×breadth
Length is 3/5
Breadth is 4/9
Area = length × breadth
Area= 3/5×4/9
Area=12/45
Divide both the numerator and denominator by 3
We have
Area= 4/15ft2
2000 is placed into a bank account that pays 3% compound interest per year
The compound interest on 2000 is 60.
Step-by-step explanation:
Given,
Principal (P) = 2000
Rate of interest (r) = 3%
Time (T) = 1 years
To find the interest calculated compound in 1 year.
Formula
Amount = P[tex](1+\frac{r}{100} )^{T}[/tex]
Putting the given values we get,
Amount = 2000[tex](1+\frac{3}{100} )^{1}[/tex]
= 2060
So,
The interest = 2060-2000 = 60
solve for x in the diagram in the pic
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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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:
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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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
The two sets of data below show the number of bubbles blown in fifty trials using two different bubble solutions.
A box plot titled Bubbles Created with Solution 1. The number line goes from 80 to 116. The whiskers range from 80 to 114, and the box ranges from 100 to 112. A line divides the box at 110.
Bubbles Created with Solution 1
A box plot titled Bubbles Created with Solution 2. The number line goes from 72 to 110. The whiskers range from 72 to 110, and the box ranges from 74 to 80. A line divides the box at 76.
Bubbles Created with Solution 2
Which best describes the measure of center that can be used to most accurately compare the two data sets?
the mean, because it increases the influence of outliers
Answer:
d
Step-by-step explanation:
i got it right
Answer:
the median, because it decreases the influence of outliers
Step-by-step explanation:
What is the answer 2+495758?
Answer:
495760
Step-by-step explanation:
Answer:
495760
Step-by-step explanation:
add 2 to 8
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:
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] .
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
24+28 applying distr
Answer:
Distributive property does not apply here because there is nothing to distribute nor is there any parenthesis.
2n - 5 = 31
Answer: The value of n is ....
Answer:
n = 18
Step-by-step explanation:
2n - 5 = 31
Add 5 to each side
2n - 5+5 = 31+5
2n = 36
Divide each side by 2
2n/2 = 36/2
n = 18
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
Solve this question
Answer:
∠ RQU = 25°
Step-by-step explanation:
The opposite angles of an inscribed circle are supplementary, thus
∠ URS + ∠ UTS = 180°, that is
∠ URS + 124° = 180° ( subtract 124° from both sides )
∠ URS = 56°
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ URS is an external angle to Δ QUR, that is
∠ RQU + 31° = 56° ( subtract 31° from both sides )
∠ RQU = 25°
The coroner arrives at the scene of a murder at 11 p.m. She takes the temperature of the body and finds it to be 81.7°F. She waits 1 hour, takes the temperature again, and finds it to be 80.2°F. She notes that the room temperature is 67°F. When was the murder committed?
Answer:
11:45 AM
Step-by-step explanation:
We have that in one hour the body temperature decreased
went down in
81.7 - 80.2 = 1.2
i.e. 1.2 degrees.
Normal body temperature is 98.6 degrees.
The difference between normal and 11 pm is 98.6-81.7 = 16.9
i.e. 16.9 degrees
now to know how much it decreases every hour:
16.9/ 1.5 = 11.26, that is 11 hours and 15 minutes (1/4 of an hour)
If that was 11:00 PM - 11:15 minutes, the murder was at 11:45 AM
Final answer:
To determine the time of death using body temperature changes from normal to discovered levels, applying physics principles is essential.
Explanation:
The time of death for the old man can be determined by calculating the rate at which body temperature decreases from the normal level to the discovered level. In this case, we have a normal body temperature of 37°C, a discovered temperature of 28°C, and subsequent temperatures of 24°C and 0°C. Using the information provided, the time of death for the old man was approximately 10:00 PM.
This calculation is based on the rate of body temperature decrease from the point of discovery to the hospital, considering the normal body temperature, room temperature, and the temperatures recorded during the investigation. This scenario demonstrates the application of physics principles in forensic investigations to determine the time of death based on body temperature changes.
a hotel swimming pool is made up of four semicircles and a square. Find the perimeter of the swimming pool. Round your answer to the nearest tenth
Answer:
62.8
Step-by-step explanation:
d=10
10x3.14
31.4
31.4x2
62.8 is the perimeter
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:
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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please help
Jonathan is trying to drain his pool to install a new liner. The graph below represents the amount of water remaining in his pool as he drains it.
A)
Number of Gallons drained per hour; Number of hours (Independent Variables)
Number of Gallons in the pool (Dependent Variable)
B) -25 (It's the negative value of how many gallons are drained in an hour)
C)13000 (It means how many gallons were in the pool to begin with)
D)3000 (It's the corresponding value for 40 as the x-value)
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
The circumference of a circle is 16π cm. What is the area, in square centimeters? Express your answer in terms of \piπ.
Answer:
64 pi
Step-by-step explanation:
lmk if you need an explanation
Answer:
[tex]64\pi[/tex]
Step-by-step explanation:
The area of a circle can be found using:
[tex]a=\pi r^{2}[/tex]
We have the circumference, but we need the radius. Circumference can be found using:
[tex]c=2\pi r[/tex]
We know the circumference is 16[tex]\pi[/tex], so we can substitute that in for c
16[tex]\pi[/tex] =2[tex]\pi[/tex] r
We need to solve for r, or the radius. To do this, divide both sides by 2[tex]\pi[/tex]. This will get r by itself.
16[tex]\pi[/tex] /2[tex]\pi[/tex] =2[tex]\pi[/tex] r/2[tex]\pi[/tex]
8=r
Now we know the radius, and can substitute it into the area formula
[tex]a=\pi r^2[/tex]
Substitute 8 in for r
[tex]a=\pi 8^2[/tex]
[tex]a=64\pi[/tex]
This answer is expressed in terms of pi, since it includes pi in the answer. Therefore, the area, in terms of pi is [tex]64\pi[/tex]
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.
Logan rode his bike 2 1/2 miles in 10 minutes. At this pace, how far can Logan ride his bike in an hour?
a.4 miles
b.25 miles
c.15 miles
d.10 miles
The principal of Brookefield Middle School maintains order by appointing 2 hall monitors for every corridor, and 4 teachers for every 12 hall monitors. If the school has 24 corridors, how many teachers would be required to maintain order in the school?
a.16
b.14
c.12
d.18
The expression 96.8 + (365.21 - 98.76) represents A.
The expression 96.8 + (64.87 - 71.25) represents B.
The numerical value of A - B is)_______
The numerical value of B - A is)_______
Maura works at a car dealership. She earns a base salary plus a commission that is 7% of her total sales.
How much commission does Maura earn from a $30,000 sale?
a.2,100
b.210
c.4,286
d.9,00
Answer:
The first one is c.
The second one is a.
third is 272.83 and -272.83
fourth is a
Step-by-step explanation:
your welcome
50 pts !!! What is the product of x+2 and x-7? Write your answer in standard form.
Please use the foil method. show all work!!!
Answer:
x^2-7x+2x-14 or x squared minus seven x plus two x minus fourteen
Step-by-step explanation:
(x+2)*(x-7)= x^2-7x+2x-14
First: x^2
Outer: -7x
Inner: 2x
Last: -14
Answer:
x²-5x-14
Step-by-step explanation:
Write the equation (x+2)(x-7)
Multiply (F in FOIL)
x*x =x²
Multiply (O in FOIL)
x*-7 = -7x
Multiply (I in FOIL)
2*x = 2x
Multiply (L In FOIL)
2*-7 = -14
Combine like terms
-7x + 2x = -5x
Write the equation
x²-5x-14
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
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.
Every 60 minutes the world population increases by 100,000 people. How many people will be born in the next 480 minutes?
idk what I should do
Answer:
c.
Step-by-step explanation:
All of the things are correct with this one.
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