Answer:
$212
Step-by-step explanation:
Naya had a rectangular carpet, it's too large for her living room.
So she cut off a 1-foot wide strip off each side of the carpet.
As a result, the area of the carpet became 26cubic feet
smaller. What's the original perimeter of this carpet?
Answer: 30 ft
Let's assume the original dimension of the carpet was LxW. Now let's have Lin cut a 1 foot wide strip from the length. That gives her a strip that's L feet long. She then cuts a strip from the other side, giving her another strip that L feet long. She then cuts a strip from the width, giving her a 3rd strip that's (W-2) feet long. And finally, she cuts a 4th strip that's also W-2 feet long. So the total length of all those strips is L + L + W - 2 + W - 2 = 2L + 2W - 4 feet long. And since all the strips are 1 foot wide, they cover 2L + 2W - 4 square feet. So: 2L + 2W - 4 = 26 2L + 2W = 30 Now the original perimeter of the carpet is 2L + 2W, therefore the original perimeter is 30 feet.
Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.)
y = X3 - x / x² – 3x + 2 X = y =
The horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.
What do you mean by curve?A curve is a continuous, smooth, and often repeating shape in the plane or in space. It is a geometric object that can be described mathematically by an equation or a set of points.
In mathematics, curves are used to model real-world phenomena and to study geometric and mathematical properties. For example, curves can be used to describe the shape of objects, the path of moving objects, or the graph of a mathematical function.
There are many types of curves, including lines, circles, ellipses, parabolas, hyperbolas, and spirals, among others. Each type of curve has unique properties and characteristics, and they are studied and used in different ways in different fields of mathematics and science.
The horizontal asymptotes are found by examining the degree of the numerator and denominator when x approaches infinity or negative infinity.
Since the numerator is of degree 3 and the denominator is of degree 2, the horizontal asymptote is y = X3 - x / x² – 3x + 2 = X.
For the vertical asymptotes, we look for the values of x that make the denominator equal to zero and the numerator either equal to zero or undefined.
The denominator x² – 3x + 2 = 0 has roots at x = 1 and x = 2.
At x = 1, the numerator x³ - x = 0, so the function has a hole at x = 1 and y = 0.
At x = 2, the function is undefined, so x = 2 is a vertical asymptote.
Thus, the horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.
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using a formula for the variance of a sample, what is the denominator?
The denominator of the formula for the variance of a sample is given as follows:
N - 1.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:
Fraction = x/y.
The terms are named as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.The formula for the variance of a sample is given as follows:
[tex]s^2 = \frac{sum (X - \overbar{X})^2}{N - 1}[/tex]
Hence the denominator is the bottom term, which is of N - 1.
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Assume that a procedure yields a binomial distribution with a trial repeated
n=5
times. Use some form of technology like Excel or StatDisk to find the probability distribution given the probability
p=0. 649
of success on a single trial.
(Report answers accurate to 4 decimal places. )
k P(X = k)
0
1
2
3
4
5
The discrete probability distribution of the number of successes in a series of n independent experiments is called the binomial distribution with parameters n and p in probability theory and statistics.
What is the binomial distribution?
The binomial distribution formula aids in determining the likelihood that "x" successes will occur in "n" separate trials of a binomial experiment. Recall that there are two possible outcomes for the statistics probability distribution known as the binomial distribution. The binomial distribution in probability theory has two parameters, n and p. When the probability distribution satisfies the following conditions, it becomes a binomial probability distribution. Each experiment may only yield two results, or results that can be reduced to two results. These results could result in success or failure. There must be a specific number of trails. Each trial's results must be distinct from one another.
Additionally, each trial's likelihood success rate must remain constant.
Using binomial probability formula,
k P(X = k)
0 0.0001
1 0.0020
2 0.0236
3 0.1355
4 0.3899
5 0.4489
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solve the system. x1 − 6x3 = 11 2x1 2x2 3x3 = 11 x2 5x3 =
For the above system of equations 2x+4y+3z=11, 2y+5z=-9, x=11+6z,The value of y=-8, z=7/5, x=97/5.
What is equation?An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol.
Here,
x-6z=11
2x+4y+3z=11
2y+5z=-9
x=11+6z
substitute and calculate,
y=-8
z=7/5
x=97/5
The value of y=-8, z=7/5, x=97/5 for the given system of equation: 2x+4y+3z=11, 2y+5z=-9, x=11+6z.
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Solve the following equations
9 ^ (x + 10) + 3 = 92
Answer:
We can solve for x by using logarithms.
9^(x + 10) + 3 = 92
9^(x + 10) = 89
Take the log base 9 of both sides:
x + 10 = log9(89)
x = log9(89) - 10
To find the value of log9(89), you can use a logarithm table or calculator.
The solution for x is:
x = log9(89) - 10
describe the similarities and differences between a frequency table and a frequency distribution. be sure to include which requires qualitative data and which requires quantitative data.
A frequency table is a simple tabular representation of the number of times a particular value or range of values appears in a data set.
It lists the values in one column and the corresponding frequencies in another column. For example, if we have data on the heights of a group of people, a frequency table could list the heights (in cm) in one column and the number of people with that height in the other column.
A frequency distribution is a graphical representation of the same information as a frequency table. It shows the number of occurrences of values in a data set by grouping the values into classes or intervals, and then plotting the frequency of each class or interval. For example, a histogram is a type of frequency distribution where the data is divided into equal-width intervals and the height of each bar represents the frequency of the data that falls within that interval.
A frequency table can be used for both qualitative and quantitative data, whereas a frequency distribution can only be used for quantitative data. This is because the classes or intervals used in a frequency distribution require a numerical representation of the data, which is not possible for qualitative data.
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The diameter of a cone's circular base measures 6 inches, and the slant height of the cone is 8 inches
What is the approximate surface area of the cone?
94.2 in²
103.6 in²
131.9 in²
257.5 in²
The surface area of a cone is 103.6 in².
Option B is the correct answer.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
We have,
Cone:
Diamter = 6 in
Radius = 3 in
Slant height.
s = 8 in
Now,
The surface area of a cone.
= πrs + πr²
= πr (s + r)
= 3.14 x 3 (8 + 3)
= 3.14 x 3 x 11
= 103.62 in²
Thus,
103.62 in² is the surface area of a cone.
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Which equation can be used to solve for the measure of
angle ABC?
[Not drawn to scale)
O tan(x) = 36
O tan(x) =
O since) –
sin(x) = 10. 3
Using relations in a right- triangle, the equation can be used to break for the measure of angle ABC is tan x = 2.4/10
The relations in a right triangle are given as follows
The sine of an angle is given by the length of the contrary side to the angle divided by the length of the hypotenuse.
The cosine of an angle is given by the length of the conterminous side to the angle divided by the length of the hypotenuse.
The digression of an angle is given by the length of the contrary side to the angle divided by the length of the conterminous side to the angle.
For angle Alphabet = x, we've that
The length of the contrary side is of2.4 cm.
The length of the conterminous side is of 10 cm.
Hence, the equation is tan x = 2.4/10.
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At Tall Timbers Tree Farm, customers can pay to cut their own fir or pine trees. During the first weekend of December, 43 pine trees were sold. The farm sold 97 trees in all that weekend.
Let f represent how many fir trees the farm sold. Which equation models the problem?
The equation models the problem is 54
How to determine the number?The given parameters that will help us to determine the number are
During the first weekend of December, 43 pine trees were sold. The farm sold 97 trees in all that weekend.
There are two kinds of trees
Tir and Pine. On the farm and in the weekend as 97 trees were sold with 43 pine tress.
Let f represent fir trees
This implies that f+43 = 97
⇒f= 97-43
f=54 tress
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In AJKL, j = 520 inches, k = 730 inches and l=640 inches. Find the measure of ZK to
the nearest degree.
The measure of ∠K is 72°.
To find the measure of ∠K in ΔJKL, we can use the Law of Cosines. The formula is:
cos C = (a^2 + b^2 - c^2) / 2ab where C is the angle opposite the side of length c.
In this case,
a = JK = 720 inchesb = KL = 640 inchesc = LJ = 520 inches.Plugging in the values, we get:
cos C = (720^2 + 640^2 - 520^2) / 2 * 720 * 640
cos C = 0.4756
Finally, to find the measure of ∠K, we use the inverse cosine function:
∠K = cos^-1 (0.4756)
∠K = 72.22°
Rounding to the nearest degree, ∠K = 72°.
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The complete question is:
In ΔJKL, j = 520 inches, k = 730 inches, and l=640 inches. Find the measure of ∠K to the nearest degree.
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A shower used 60 gallons of water in 6 minutes complete the table and the plot the point
The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.
Time (minutes): 0, 2, 4, 6
Gallons of Water Used: 0, 20, 40, 60
Plot: (0, 0), (2, 20), (4, 40), (6, 60)
To complete the table, you need to fill in the time (minutes) and gallons of water used columns.
The time column should have four entries: 0, 2, 4, and 6.
The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.
The point (0, 0) represents 0 minutes and 0 gallons of water used.
The point (2, 20) represents 2 minutes and 20 gallons of water used.
The point (4, 40) represents 4 minutes and 40 gallons of water used.
The point (6, 60) represents 6 minutes and 60 gallons of water used.
The complete question is :
A shower used 60 gallons of water in 6 minutes. Complete the table and plot the point.
Time (minutes): 0, 2, 4, 6
Gallons of Water Used: 0, 20, 40, 60
Plot: (0, 0), (2, 20), (4, 40), (6, 60)
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John, scores 35 more than triple the amount of points and Amy. If Amy, scores 25 point, how many points does Giannis John score?
John scored 110 points in total.
What is an equation?A equation is used to equate two expressions. For example -
4x + 4 = 7
Given is that John, scores 35 more than triple the amount of points than Amy. Amy scores 25 points.
The total points scored by john would be -
{p} = 3{a} + 35 .... Eq { 1 }
{p} = 3 x 25 + 35
{p} = 110 points
Therefore, John scored 110 points in total.
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Find the total when $9500 is invested at 10% simple interest for 5 years.
The total amount when $9500 is invested at 10% simple interest for 5 years is $14, 250
How to determine the total amountIt is important to note that the formula for simple interest is expressed mathematically with the equation;
I = PRT/100
The parameters are given;
I is the simple interest P is the initial amount or the principal amountR is the simple interest rateT is the time takenFrom the information given, we have the values of the principal amount, time and the interest rate
Substitute the values, we get;
Simple interest, I = $9500 × 10×5/100
Multiply the values
Simple interest, I = $475, 000/100
Divide the values
Simple interest, I = $4, 750
Thus, the total amount is $14, 250
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i dont know how to solve it but i got it right
The required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. between the interval of 7 a.m. to 9 a.m.
What is a piecewise function?A piecewise function is one that is constructed from pieces of different functions at different intervals.
Here,
A graph of the piecewise function is shown, from the graph it's clear that systolic pressure is low for the interval 5 < x < 9, such that the patient takes the medication at 7 A. M. So, corresponding to that required systolic pressure will be lower between 7 a.m. to 9 a.m.
Thus, the required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. is 7 a.m. to 9 a.m.
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In two or more complete sentences, describe how to find the interval(s) where the function is increasing and how interval notation is used to express the interval(s). In your final answer, include the interval in which the function is increasing.
The solution is (-5,0), the interval in which the function is increasing.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number
For Decreasing:
(-8,-5)
(4,8)
For Increasing:
(-5,0)
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A parabolic arch similar to the Hiroshima Peace Arch is 14 m high at the centre of the arch and spans a distance of 30 m. Find the height of the arch at a distance of 7. 5 m from the center
The height of the arch at a distance of 7.5 m from the center is 7m
What is parabola's equation?It's important to keep in mind that a parabola has the usual form of y = a(x - h)2 + k, where (h, k) denotes the vertex and a determines the shape and vertical orientation. x and y are (100, 0) in. You are then provided with the parabola's equation.
What height of the arch, as measured from a point on the water 40 meters from the center of the arch, would sustain a bridge over a river?
The arch is 200 meters wide at water level and 80 meters tall at its tallest point
The peak of the arch might serve as the vertex and be located at position y0 on the y-axis if we wish to plot this on a graph or represent it in an equation
The equation of the parabolic arch is
x² = - 4ay
Lets take x and y for first case as (14, 30)
⇒ 14² = - 4a(30)
⇒ a = −49/30
Now we have a so lets put the formula for another variable to find height
Here, y = 7.5
x² = - 4ay
⇒ x² - 4(-49/30)(7.5)
x = 7
Thus, The height of the arch at a distance of 7.5 m from the center is 7m.
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which expression is obtained on subtracting 4x+6 from 7+2x
The expression is obtained on subtracting 4x + 6 from 7 + 2x is -2x + 1
What is the resulting expression of subtracting 4x+6 from 7+2x?Given the two expressions in the question;
( 4x + 6 ) and ( 7 + 2x )
To subtract 4x + 6 from 7 + 2x simply means ( 7 + 2x ) - ( 4x + 6 ).
Now, simplify
( 7 + 2x ) - ( 4x + 6 )
Distribute the negative sign to all the terms in the second expression.
( 7 + 2x ) -4x - 6
Now collect and add like terms
2x - 4x - 6 + 7
Add 2x and -4x
-2x - 6 + 7
Add -6 and 7
-2x + 1
Therefore, the resulting expression is -2x + 1.
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Find the perimeter of the rectangle ABCD whose sides are 6 cm and 5 cm. ?
The perimeter of the rectangle ABCD is 22 cm.
What is the perimeter of a rectangle?
In order to find the perimeter or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length.
Perimeter = (length+width)×2 is the formula for the perimeter.
The perimeter of a rectangle is the sum of the lengths of all four sides.
If the sides of a rectangle have lengths of 6 cm and 5 cm, then the perimeter can be calculated as follows:
6 cm + 6 cm + 5 cm + 5 cm = 22 cm
The perimeter of a rectangle with sides 6 cm and 5 cm is 22 cm (2 * 6 cm + 2 * 5 cm = 22 cm).
Hence, the perimeter of the rectangle ABCD is 22 cm.
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Find the hypotenuse of each isosceles right triangle when the legs are of the given measure.
Given = 3√2
_________ inches
A health club charges a $20 one-time sign-up fee and a monthly membership fee of $54 per month. Find the rate of change.
The rate of change for a health club is, 24.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
A health club charges a $20 one-time sign-up fee and a monthly membership fee of $54 per month.
Hence, The equation to represents that the health club charges,
⇒ y = 24x + 54
Since, The general form of the slope - intercept equation is :
⇒ y = mx + c
Where, m = slope = rate of change in y per change in x
Therefore, By comparing the expressions, the slope of the cost function given is 24.
Hence, The rate of change = 24
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These POINTS are not free please answer each question correctly
Answer:
X=. 1. X=. 2
Step-by-step explanation:
The first story (movie theater) has the equation 6(x+3)= 24. The equation for the juice story is 3(x+6)=24 . The x in the move theater story is the cost of each ticket. The x in the juice story is the amount of juice poured to each friend originally (before the extra 6 ounces). The solution to the movie theater story is 6((1)+3)=24. So x is one is the first story.In the juice story, 3((2)+6)= 24. So x is two. The solution tells me that in the movie theater story that each ticket cost 1 dollar. In the second story, it tells me that 2 ounces of juice where poured to each freind originally. So each freind got a total of 8 ounces of juice.
Step-by-step explanation:
I see only 2 stories and equations.
a.
6(x + 3) = 24
is for the first story (6 show tickets and snacks).
3(x + 6) = 24
is for the second story (juice for 3 friends).
b.
in the first story it is the price of one ticket to the show.
in the second story it is the original amount of juice each friend gets before adding 6 oz.
c. and d.
6(x + 3) = 24
6x + 18 = 24
6x = 6
x = 1
each ticket to the show was $1.
3(x + 6) = 24
3x + 18 = 24
3x = 6
x = 2
each of the 3 friends got first 2 oz of juice, before they each got additional 6 oz. so, ultimately, each friend got 8 oz.
unit 1, lesson 13: congruence
Answer: 1. No, because figure 1 is 5 squares and figure 2 is 6 squares
Step-by-step explanation:
Log2+log3=logx find the value of x
The value of x is 6 using logarithmic properties.
What does it mean to be logarithmic?The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.
Who is the father of the logarithm?The Scottish mathematician John Napier reported his findings on logarithms in 1614. He was there to aid with the multiplication of quantities known as sines at the time.
Given,
Log2+ log3= logx
To find= We need to find the value of x
The value of log2= 0.301
The value of log 3= 0.477
Now, putting the value in the given expression, we get:
0.301+ 0.477= logx
logx= 0.778
Now, taking the antilog os=f x:
x= antilog(0.778)
x= 5.99=6
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Question 3(Multiple Choice Worth 1 points)
(05. 06 MC)
The scatter plot shows the number of stamps Katie collected in different months:
210
180
150
120
Number of
Stamps 90
60
30
Months
What is the approximate predicted number of sta
mps she collected in the 25th month?
By applying linear equation concept, it can be concluded that the number of stamps in the 25th month is 990 stamps
Linear equation is equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
y = mx + C where
m = Δy / Δx = slope of the line
C = constant
We have the following data:
Month Number of stamps
1 30
2 70
3 110
4 150
5 190
As we look at the attached graph, this data is depicted as a linear graph. Thus we want to find the linear equation.
First, we calculate the m:
m = Δy / Δx
= (70 - 30) / (2 - 1)
= 40 / 1
= 40
To find C, we pick one point, let say point (1,30) and input it into the equation:
y = mx + C
30 = 40*1 + C
30 = 40 + C
C = -10
Now we have the linear equation:
y = mx + C
y = 40x - 10
We want to know the number of stamps in the 25th month, so we input this value into the equation:
y = 40x - 10
= 40*25 - 10
= 1000 - 10
= 990
Thus, the number of stamps in the 25th month is 990 stamps.
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Helppppppppp me FIND C
To find C the Pythagorean formula is used which would be = 7.6
How to calculate the missing side of the triangle?The formula for the Pythagorean theorem is given as follows:
c² = a²+b²
where;
a = 7
b = 3
C = ?
c² = 7²+3²
c² = 49+ 9
c² = 58
C= √ 58
C = 7.6
Therefore, when the Pythagorean formula is being used, the value of the missing side of the triangle = 7.6.
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The hypotenuse of the right triangle is:
C = 7.6
How to find C on the right triangle?On the image we can see a right triangle where C is the hypotenuse of said triangle.
Remember the Pithagorean's theorem, it says that if A and B are the two legs of the right triangle, then C can be written as:
C = √(A² + B²)
Here we can see that:
A = 3
B = 7
Replacing that we will get:
C = √(3² + 7²) =7.6
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Alfred is a real go-getter. He reports that he has raised ninety-eight dollars more than the minimum required. How many total tickets did he sell?.
Alfred sold 98 + the minimum required tickets, so the total number of tickets he sold is 98 + the minimum required.
1. Alfred reported that he raised 98 dollars more than the minimum required.
2. To get the total number of tickets he sold, we will need to add the 98 dollars more than the minimum required to the minimum required amount.
3. Therefore, the total number of tickets Alfred sold is 98 + the minimum required.
Alfred sold 98 + the minimum required tickets, so the total number of tickets he sold is 98 + the minimum required.
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Farah is buying clothes from a website. The website shows this information about a jacket Farah wants to buy. The website claims this is a saving of 46%
The website is advertising a 46% discount on the jacket, meaning that Farah will pay 46% less than the original price if she decides to buy it now.
A discount is a reduction in the original price of an item, allowing the customer to purchase it for less than the original price.
To calculate the discount mathematically, we can use the following formula:
Discounted price = Original price * (1 - discount percentage)
Let's assume the original price of the jacket is P dollars.
The discount percentage is 46%, which can be written as a decimal 0.46. To find the discounted price, we need to multiply the original price by (1 - discount percentage), which is (1 - 0.46) = 0.54.
So, the discounted price after the 46% saving will be P * 0.54 dollars.
In other words, Farah will pay 0.54 times the original price, P, to buy the jacket with the advertised 46% saving.
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please please help me i need it step by step
The lateral Surface Area of a Cylinder is is 345 cm²
What are solids ?
A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.
lateral Surface Area of a Cylinder is :
L= 2 × π × r × h
where, r = base radius,
and h = height of the cylinder
L= 2 × 3.14 × 4.9 × 11.2
=> L= 344.646 cm²
Nearest whole number: 345 cm²
The lateral Surface Area of a Cylinder is is 345 cm²
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