The 10th term in the geometric sequence can be found by using the common ratio of 1/3 and applying it to the formula T(n) = a1 * r^(n-1). The 10th term is determined to be 1/9.
Calculating the 10th Term of a Geometric Sequence
To find the 10th term in the geometric sequence (2187, 729, 243, 81, 27), we first need to determine the common ratio (r). We can find r by dividing any term by its preceding term. Using the second and first terms, we get:
r = 729 / 2187 = 1/3
With the common ratio identified, we can use the formula for the nth term of a geometric sequence:
T(n) = a1 * r^(n-1)
Where a1 is the first term of the sequence and n is the term number. So, the 10th term (T(10)) is calculated as:
T(10) = 2187 * (1/3)^(10-1) = 2187 * (1/3)^9
To calculate this, we simply apply the exponent to the common ratio:
T(10) = 2187 * 1/19683 = 2187 / 19683 = 1/9
Therefore, the 10th term of the geometric sequence is 1/9.
The table contains data for five students: hours slept, x, and corresponding test scores, y. Use the regression calculator to make a scatterplot with a trend line. A 2-column table with 5 rows. Column 1 is labeled x with entries 4, 6, 6, 8, 10. Column 2 is labeled y with entries 62, 75, 88, 79, 97. Based on the trend line, what score would you expect after sleeping for 5 hours? As the number of hours sleeping increases, the coressponding test score
Answer:
72 & tends to increase
Step-by-step explanation:
just took the test
A student who slept for 5 hours could be expected to score around 68.5,
According to the given information:
The table is,
x y
4 62
6 75
6 88
8 79
10 97
Now create a scatterplot of the data.
Use the trend line equation to make a prediction for what test score you would expect if a student slept for 5 hours.
From the scatterplot,
The trend line equation is y = 4.3x + 52.4.
To find the predicted test score for x = 5, substitute x = 5 into the equation:
y = 4.3(5) + 52.4 y = 75.9
So you would expect a student who slept for 5 hours to have a test score around 75.9.
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Gavin is moving into a new apartment that has a kitchen with an area of 50 square feet. If the area of the kitchen is 10 square feet more than the area of the bedroom, what is the area of the bedroom?
The area of the bedroom is 40 square feet, 10 square feet less than the area of the kitchen.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, Gavin is moving into a new apartment that has a kitchen with an area of 50 square feet.
Also given that the area of the kitchen is 10 square feet more than the area of the bedroom.
Let, The area of the bedroom be 'x' square feet.
Therefore, x + 10 = 50.
x = 50 - 10.
x = 40 square feet.
So, The area of the bedroom is 40 square feet.
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Final answer:
The area of the bedroom is 40 square feet, calculated by subtracting 10 square feet from the kitchen's area of 50 square feet.
Explanation:
To find the area of the bedroom, we start with the area given for the kitchen, which is 50 square feet. The problem states that the kitchen is 10 square feet larger than the bedroom. Therefore, to find the area of the bedroom, we subtract the difference from the kitchen area.
Area of bedroom = Area of kitchen - 10 square feet
Area of bedroom = 50 square feet - 10 square feet
Area of bedroom = 40 square feet
Help! Someone please help me
a) 50 degrees
b) 30 degrees
c) 100 degrees
d) 90 degrees
Answer:
50 degrees
Step-by-step explanation:
It would be 50 degrees because angle CGD is directly across so the angle measures would be the same
The circumference of a circle is 36cm what is the radius?
Answer:
About 5.73 cm
Step-by-step explanation:
C=2πr so
36=2πr (divide by 2)
18=πr (using 3.14 as π)
18=(3.14)r (divide by 3.14)
r=5.732484076 so
R≈5.73 cm
Final answer:
The radius of a circle with a circumference of 36cm is approximately 5.73cm, calculated by dividing the circumference by the product of 2 and Pi (
).
Explanation:
Calculating the Radius from the Circumference
The circumference of a circle is closely related to its radius through the mathematical constant which is approximately 3.14159. The circumference (C) can be expressed using the formula C = 2
r, where r is the radius. Given that the circumference is 36cm, we can rearrange the formula to solve for the radius: r = C / (2
r). Substituting the given circumference into the equation, we get:
r = 36cm / (2
3.14159)
By performing the division, we can find the radius of the circle:
r = 36cm / (2 * 3.14159)
r = 36cm / 6.28318
r ≈ 5.73cm
Therefore, the radius of the circle is approximately 5.73cm.
What is the Mean in the following number sequence:
6, 14, 8, 15, 16, 13, 19
Look at the attached picture ⤴
Hope it will help u...
Answer: 13
Step-by-step explanation: To get the mean we have to add all the numbers and then divide it by 7 because there are 7 numbers.
6+14+8+15+16+13+19=91
91 divided by 7 = 13
I hope this helps!
Which two numbers doesStartRoot 52 EndRoot lie between on a number line? 7.0 and 7.1 7.1 and 7.2 7.2 and 7.3 7.3 and 7.4
√52 = 7.21110...
7.21 is in between 7.2 and 7.3
Answer:C - 7.2 and 7.3
The two numbers which the square root of 52 lie between are; 7.2 and 7.3.
What numbers does the square root of 52 lie between?From the task content;
It follows that the square root of 52 must be evaluated as follows.√52 = 7.211
On this note, it follows that the number 7.211 lies between 7.2 and 7.3.
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in the figure below AC and BE are diameters of circle P. what is the arc measure of DBE in degrees
The measure of Arc DE is 39 degree.
What are Vertical Angles?The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.
Given:
From figure:
m<APB + m<APE = 180 (Linear pair)
4w+ 8 + 4w + 4= 180
8w + 12= 180
8w = 168
w = 21
Also, <APB = <PED + <DPC (Vertical opposite angle)
4w+ 8 = <PED + 2w+ 11
92 = <PED + 53
<PED = 39
So, the measure of Arc DE is 39 degree.
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Which set of data has the strongest linear association?
Answer:
Top right
Step-by-step explanation:
The one on the top right has the greatest amount of dots on the line.
hope this helps :)
By looking at the given graphs, we conclude that the set of data with the strongest linear association is the one in the top right.
What is the linear association?
Linear association is a measure of "how much" a set of data behaves like a line.
So, we just need to see which of the given sets of data behaves more like a line (we can compare with the shown lines).
As you can see, in the only set where almost all the points lie in the graphed line is in the top right graph. In the other 3, we can see points outside of the line.
So the set of data with the strongest linear association is the one in the top right graph.
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Bobby spent 122 minutes on school work the first week, but only spent 109 minutes on school work the second week.
Answer:
what am I suppose to solve the difference of minutes is 13
evaluate 49 ÷ (5 + 2) − 2 × (1 + 1)
Answer:
3
Step-by-step explanation:
49 divided by (5+2) - 2 x (1+1)
49 divided by 7 - 2 x 2
7-4
3
what is the measure of A?
Answer:
50
Step-by-step explanation:
The inside of a triangle equals 180 and so you subtract the other two values(100 and 30) to 180 and you get 50.
Answer:
50
Step-by-step explanation:
The sum of the angles of a triangle add to 180
A+B+C = 180
A + 100+ 30 = 180
A + 130= 180
Subtract 130 from each side
A+130-130= 180-130
A = 50
jordan purchased 30 bags of candy for $12. At that rate how many bags of candy can he purchase for $8
Answer:
45 bags of candy
Step-by-step explanation:
The first thing is to calculate the money Jordan has, we know that by multiplying the number of bags by their price, that is:
30*12 = 360
I mean, he's got $360, now with this money he wants to buy $8 bags, so it would be
360/8 = 45
That means I could buy 45 bags of candy if they cost $8
Jordan can purchase 20 bags of candy for $8.
Jordan purchased 30 bags of candy for $12. At that rate, to find out how many bags of candy he can purchase for $8, we first calculate the cost per bag of candy by dividing the total cost by the number of bags purchased. This gives us a rate of $0.40 per bag of candy ($12/30 = $0.40). To determine how many bags of candy Jordan can purchase for $8, we then divide $8 by the cost per bag, which is $0.40.
Calculating, $8/$0.40 = 20 bags of candy. Thus, for $8, Jordan can purchase 20 bags of candy at the same rate.
f(x) = 3x^2+12x+5f(x)=3x 2 +12x+5f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 12, x, plus, 5 What is the value of the discriminant of fff? How many distinct real number zeros does f(x)f(x)f, left parenthesis, x, right parenthesis have?
Answer:
Discriminant = 84
The polynomial has two real distinct roots
Step-by-step explanation:
Given: [tex]f(x)=3x^2+12x+5[/tex]
To find: discriminant of the given function and number of distinct real zeros
Solution:
For a polynomial [tex]f(x)=ax^2+bx+c[/tex] , discriminant is given by [tex]D=b^2-4ac[/tex]
If [tex]D>0[/tex], then the polynomial has two real and distinct roots.
If [tex]D=0[/tex] then the polynomial has two real and equal roots.
If D<0 then roots are not real.
Here, in [tex]f(x)=3x^2+12x+5[/tex]
a = 3, b = 12 and c = 5
[tex]D=(12)^2-4(3)(5)=144-60=84[/tex]
As D > 0, the polynomial has two real distinct roots.
Answer:
The discriminant of F is 84
F has 2 distinct real number zeros
Step-by-step explanation:
What is the range and the domain of: F(x)=x2-2x-3
PLS SOMEONE LOOK AT THE PHOTO I POSTED AND ANSWER AS SOON AS POSSIBLE PLS ITS ASKING FOR X= AND Y= NOT AN EQUATION JUST PLS ANSWER IT RIGHT
We can solve it, but we can't actually use the interactive system they want you to use. Let's see if we can guide you through it.
My guess is you can control the lines by dragging the two points on the line.
Let's make the green line y = 2x + 3
When x=0 we get y=3, point (0,3). That's the y intercept, 3 up on the y axis. Drag one green point there.
When x=2 we get y=7, point (2,7), two to the right, seven up. Drag the other green point there. The green line is now y = 2x + 3.
Similarly the red line is made y = -3x + 3. When x=0, y=3, point (0,3). [Surprise!] When x=2, y=-3, point (2,-3). Drag the red points to (0,3) and (2,-3).
We already saw where they meet, at (0,3), x=0, y=3, the y intercept of both lines.
Answer: x=0, y=3
Which point is located at (–1, 3)?
1 A
2
3 C
4 D
Answer:
Point C
Step-by-step explanation:
Answer:
3. C
Step-by-step explanation:
X before Y
A circle is graphed on a coordinate grid and then reflected across the x-axis. If the center of the original circle was located at (x, y), which ordered pair represents the center of the new circle after the transformation? *
(x, y)
(-x, y)
(x, -y)
(-x, -y)
Answer:
C (x,-y)
Step-by-step explanation:
Answer:
x,-y
Step-by-step explanation:
It cannot transform across x axis unless it goes down to negative y.
In a graph we have 4 areas to fit a description of reflect accross an axis.
As this was x axis it can only be reflection negative y or reverse.
We cannot reverse this as the object has the positive y side of x
The image is the reflection or the transformation, and so this image is now negative y.
x-y= x object | y image = positive x = negative y.
a 19%
b 26
c 67%
d 28%
Answer:
d= 28%
Step-by-step explanation:
Mowe Middle School has 564 students, which is 60% of the number of students who
otterd Wison Middle School How many students attend Wison Middle School?
(5k-3)9+k) what is the value of k
Answer:
Set the factors equal to 0.
(5k - 3)(9 + k) = 0
The zero product property states that if two terms being multiplied have a product of zero, then at least one of them must be zero. In our case, this means we can set both (5k - 3) and (9 + k) equal to 0:
5k - 3 = 0
5k = 3
k = 3/5
9 + k = 0
k = -9
The value of k is 3/5 and -9.
Tell the measure of the angle in degrees 1/10
Answer:
360 x 1/10 = 360/10 simplify is 36
36 degrees is 1/10
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
20. BUSINESS The function f(x) = 1000-0.01x² models the manufacturing cost per item when x items are produced,
and g(x) = 150-0.001x² models the service cost per item. Write a function C(x) for the total manufacturing and
service cost per item.
Answer:
Profit is calculated by subtracting the total cost from the total revenue as expressed in the equation given above as,
P(x) = R(x) - C(x)
If we are to substitute the given expression for each of the terms, we have,
P(x) = x(S(x)) - C(x)
Substituting,
P(x) = x(30 - 0.01x) - (0.15x³ + 0.01x² + 2x + 120)
Simplifying,
P(x) = 30x - 0.01x² - 0.15x³ - 0.01x² - 2x - 120
Combining like terms,
P(x) = -0.15x³ - 0.02x² + 28x - 120
The answer to this item is the second among the choice, number 2.
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Step-by-step explanation:
Final answer:
To find the total cost function C(x), you combine the manufacturing cost function f(x) = 1000 - 0.01x² and the service cost function g(x) = 150 - 0.001x², resulting in C(x) = 1150 - 0.011x².
Explanation:
To create a function C(x) for the total manufacturing and service cost per item, you will simply add the manufacturing cost function f(x) and the service cost function g(x) together. The provided functions are f(x) = 1000 - 0.01x² for the manufacturing cost per item and g(x) = 150 - 0.001x² for the service cost per item.
When you add these two functions, you get:
C(x) = f(x) + g(x)
= (1000 - 0.01x²) + (150 - 0.001x²)
= 1150 - 0.011x²
This new function, C(x), represents the total cost per item when x items are produced, encompassing both manufacturing and service costs.
A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?
Answer:
the height of the trapezoid is 4.5 feet.
Step-by-step explanation:
i got it right
The height of the trapezoid cannot be determined from the information given in the problem. The areas and base lengths or the lengths of the diagonals of the trapezoid are required to determine its height.
Explanation:The question seems to be a bit conflicted. First, if we look at the information given, the plot of land with an area of
33.75 square feet
is the space for the trapezoid, not its height. The shed, with its dimensions, will take up 16 square feet. But putting a shed on the trapezoid or relating this to the height of the trapezoid doesn't seem to connect. The
height of the trapezoid
is not something we can determine with the information given. To determine the
height of a trapezoid
, you need either the areas and base lengths or the lengths of the diagonals. Unfortunately, the information about the shed doesn't help in determining the height of the trapezoid.
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Which composition of similarity transformations maps TriangleLMN to TriangleL'M'N'? a dilation with a scale factor less than 1 and then a reflection a dilation with a scale factor less than 1 and then a translation a dilation with a scale factor greater than 1 and then a reflection a dilation with a scale factor greater than 1 and then a translation
Answer:
The answer should be D if you're on edge
Step-by-step explanation:
Triangle LMN is dilated with a scale factor greater than 1 and then translated to form Triangle L'M'N'
What are similar figures?
Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. All the corresponding angles are congruent.
Triangle L'M'N' is larger than LMN. Hence:
Triangle LMN is dilated with a scale factor greater than 1 and then translated to form Triangle L'M'N'
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The manager of a dress shop recorded the number of dresses sold during the week the data is as follows
17 15 16 20 15 19
Find the mean deviation for this data
4.98
1.67
2.21
1.91
The mean deviation for the data (17, 15, 16, 20, 15, 19) is calculated by finding the mean, determining the absolute differences from the mean for each value, summing those differences, and then dividing by the number of values, resulting in a mean deviation of 1.67.
The mean deviation is a measure of the average distance between each data value and the mean of the data set. To calculate the mean deviation of the given data (17, 15, 16, 20, 15, 19), first we find the mean of these values.
Add up all the numbers: 17 + 15 + 16 + 20 + 15 + 19 = 102.Divide the sum by the number of data values: 102 / 6 = 17. This is the mean.Find the absolute difference between each data value and the mean, then sum those differences: |17 - 17| + |15 - 17| + |16 - 17| + |20 - 17| + |15 - 17| + |19 - 17| = 0 + 2 + 1 + 3 + 2 + 2 = 10.Finally, divide the sum of the absolute differences by the number of data values to get the mean deviation: 10 / 6 = 1.67.The calculated mean deviation for the provided data is 1.67.
Which statement is true?
Answer:The mode is equal to the minimum
Step-by-step explanation:
Find out the mean, median, mode and minimum
minimum = 48
mean = 50.4
mode = 48
median = 50
Answer:
The mode is equal to the minimum
Step-by-step explanation:
Find out the mean, median, mode and minimum
minimum = 48
mean = 50.4
mode = 48
median = 50
Laisha drew a model on grid paper of a decorator tile that she wants to buy. Each grid line represents 5 cm. Her drawing has coordinates (3, 4), (5, 10), (7, 4), and (5, 0). Calculate the area of the real tile.
Answer:
The area of the real tile is 20 cm².
Step-by-step explanation:
Plot the points provided on a graph using grid line representing 5 cm each as follows.
The diagram below shows that the model of the tile is in the shape of a kite.
The area of a kite is:
[tex]\text{Area of a Kite}=\frac{p\times q}{2}[/tex]
Here, p and q are the two diagonals.
The measure of diagonals p and q are:
p = 10 cm
q = 4 cm
Compute the area of the kite as follows:
[tex]\text{Area of a Kite}=\frac{p\times q}{2}[/tex]
[tex]=\frac{10\times 4}{2}\\\\=10\times 2\\\\=20[/tex]
Thus, the area of the real tile is 20 cm².
Laisha's tile, represented by a rhombus with coordinates (3, 4), (5, 10), (7, 4), (5, 0) on a grid where each line is 5 cm, has a real area of 250 square centimeters, calculated using the formula for the area of a rhombus.
The student is asking about calculating the area of a geometric shape based on its coordinates on a grid. To find the real area of Laisha's tile, we need to determine the shape represented by the given coordinates (3, 4), (5, 10), (7, 4), and (5, 0). Noting that each grid line represents 5 cm, it appears that the shape is a diamond or a rhombus, and we can calculate the area by finding the product of the lengths of the diagonals (the distance between (3, 4) and (7, 4) and the distance between (5, 10) and (5, 0)) divided by two.
The length of one diagonal is simply the distance between (3, 4) and (7, 4), which is 4 grid units, or 4 x 5 cm = 20 cm. The length of the other diagonal is the distance between (5, 10) and (5, 0), which is 10 grid units, or 10 x 5 cm = 50 cm. The formula for the area of a rhombus is (d1 x d2) / 2, where d1 and d2 are the lengths of the diagonals. Plugging in our values, we get (20 cm x 50 cm) / 2 = 500 [tex]cm^2[/tex] / 2 = 250 [tex]cm^2[/tex].
The real area of the tile is thus 250 square centimeters.
Which equation represents the graph? (y-1)^2/49-x^2/81=1 (y-1)^2/7-x^2/9=1
Answer: A, (y-1)^2/49-x^2/81=1
The given equations are both hyperbola equations with the center shifted to (0,1). They represent different graphs due to differences in their denominators. Hyperbola equations result in a graph of two separate curves, each one a mirror image of the other.
Explanation:The equations (y-1)^2/49-x^2/81=1 and (y-1)^2/7-x^2/9=1 are both in the form of the hyperbola equation. This type of equation represents a graph that consists of two separate curves, each one a mirror image of the other, positioned about a central point called the center of the hyperbola. In these particular equations, the center of the hyperbola is shifted from the origin to the point (0,1).
Hyperbola equations are generally in the form (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/a^2 - (x-h)^2/b^2 = 1
However, even though these equations are in the form of hyperbolas, they do not represent identical graphs. In the first equation, the y term is divided by 49 and the x term by 81, whereas in the second, these denominators are 7 and 9. These denominator values affect the shape and orientation of the hyperbolae, leading to different graphical representations for each equation.
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Can someone help me find the area and perimeter of the composite figure?
Answer:
Semicircle radius is 4.5
Radius x radius x 3.14 = area of circle but you divide by 2
4.5 x 4.5 = 20.25 x 3.14 = 63.585/2=31.7925 for semicircle
To find the line for the triangle subtract 16 from the other side which is 8 so the triangle is 8 by 3.
8 x 3 = 24/2=12 for triangle
6 + 3 = 9 the missing side.
9 x 8 = 72 so the rectangle is 72
72 + 12 = 84 + 31.7925 = 115.7925 so that is the area
Circumference is the perimeter for the circle. 9 x 3.14 = 28.26
Perimeter of triangle is 19.544
8 + 9 = 17 x 2 = 34
28.26 + 34 = 62.26 + 19.544 = 81.804
Area is 115.7925 and perimeter is 81.804
Step-by-step explanation: