Nya's average speed was 10 miles per hour.
What is the speed, distance, and time?
Speed, distance, and time are related concepts in physics that are used to measure and describe motion.
Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit of time, such as miles per hour or kilometers per hour. Speed can be calculated using the formula:
Speed = Distance / Time
To find Nya's average speed in miles per hour, we need to divide the distance she traveled by the time it took her to travel that distance.
Average speed = distance/time
We know that Nya rode her bike 2 ½ miles in ¼ hour. To use these measurements in the formula, we need to convert the units to the same unit of measurement. In this case, we need to convert the distance to miles and the time to hours.
Average speed = (2.5 miles) / (0.25 hour)
To find out the speed in miles per hour, you need to multiply by the conversion factor 1 hour/60 minutes, so
Average speed = (2.5 miles) / (0.25 hour) * (1 hour/60 minutes)
Average speed = (2.5 miles) / (0.25 hour) * (4)
Average speed = 10 miles per hour.
Hence, Nya's average speed was 10 miles per hour.
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find the exact value of cos -pi/3
The exact value of cos (-pi/3) can be found using the unit circle or the angle addition formula.
Using the unit circle, we know that the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is cos(-pi/3) and y-coordinate is sin(-pi/3).
On the unit circle, the angle of -pi/3 is the same as the angle of 2pi/3 (since the unit circle has a period of 2pi), therefore the x-coordinate of the point on the unit circle that corresponds to an angle of -pi/3 is -1/2.
Alternatively, using the angle addition formula:
cos (-pi/3) = cos(pi - pi/3) = cos(pi) * cos (pi/3) - sin(pi) * sin(pi/3) = -1/2
So, the exact value of cos (-pi/3) is -1/2.
The point (-4,5) is rotated 270 degrees counterclockwise
The new point that will be formed when the point (-4,5) is rotated 270 degrees counterclockwise is; (5, 4)
What is the transformation rule?There are different types of transformations namely dilation, rotation, reflection e.t.c
Now, when we rotate a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means that we switch x and y and make x negative.
Now, we are told that the point (-4,5) is rotated 270 degrees counterclockwise. Thus, following the transformation rule as described above gives us;
(-4,5) → (5, 4)
Thus, we conclude that the new coordinate we will obtain in this process is (5, 4)
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Write the fraction as a mixed number 11 over 4
The answer is 2¾. You can also buy calculators that do this for you automatically.
Answer:
Step-by-step explanation:
2 3/4
Use what you know about scientific notation to write the number - 8,000 with a power of 10.
- 8,000
- 8,000 = 0
Therefore , the solution to the given problem of expression comes out to be -8 * 10³.
How do you determine an expression?A number must be substituted for each variable and arithmetic operations must be carried out in order to verify an algebraic expression. The response variable is equivalent to 6 in the illustration above because 6 + 6 equals 12. The variables can be replaced with their values if we know what they are, and the expression can then be evaluated.
Here,
Given : - 8,000
To write -8000 with a power of 10
Thus,
-8000 written into
=> -8 * 10³
So, we get -8 * 10³ as the scientific notation for the given expression
Therefore , the solution to the given problem of expression comes out to be -8 * 10³.
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Did I get this right? (pre calc)
The center of the ellipse is (2, -8), The endpoints of the major axis are 10 units from the center, The endpoints of the minor axis are 9 units from the center, To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with smooth curve.
What is ellipse?An ellipse in mathematics is a plane curve that has two focal points and is such that the sum of the two distances from any point on the curve to the focal points is a constant. It generalizes a circle, a special kind of ellipse in which the two focal points coincide.
Glven:
The equation of ellipse is,
[tex]\frac{(x-2)^2}{81}+\frac{(x+8)^2}{100}=1[/tex]
SInce, the general form of ellipse is,
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
where,
(h, k) is the center of ellipse
a is the minor axis
b is the major axis.
Here
(h, k) = (2, -8) is the center of the ellipse.
9 is the minor axis and 10 is the major axis of the ellipse.
Also the graph of ellipse connects (2, 2), (11, -8), (2, -18) and (-7, -8) with smooth curve.
Hence, the center of the ellipse is (2, -8).
The endpoints of the major axis are 10 units from the center.
The endpoints of the minor axis are 9 units from the center.
To graph the ellipse, connects (2, 2), (11, -8), (2, -18) and (-7, -8) with smooth curve.
The graph of the ellipse visit.
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use your trapezoid areas to find an estimate for the total area between the curve and the x-axis. show your work. make sure you include the formula you used for area of a trapezoid, and the lengths and heights of all the trapezoids you added.
The formula for the area of a trapezoid is (a+b)*h/2, where a and b are the lengths of the bases and h is the height.
To estimate the total area between the curve and the x-axis using trapezoids, we can divide the region between the curve and the x-axis into a number of trapezoids, and calculate the area of each trapezoid. The sum of the areas of all the trapezoids will estimate the total area.
For example, consider the curve y = x^2 and the x-axis between x = 1 and x = 2. We can divide this region into 3 trapezoids with bases at x = 1, x = 1.5, x = 2, and heights of 0.25, 0.5625, and 1 respectively.
The area of the first trapezoid is (1 + 1.5) * 0.25 / 2 = 0.1875
The area of the second trapezoid is (1.5 + 2) * 0.5625 / 2 = 0.40625
The area of the third trapezoid is (2 + 2) * 1 / 2 = 1
The sum of the areas of all the trapezoids is 0.1875 + 0.40625 + 1 = 1.60625. This estimates the total area between the curve y = x^2 and the x-axis between x = 1 and x = 2.
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what is the quotient of (x^4-6x^3-19x^2+24x) divided by (x+3)?
The quotient of the division is x^3 - 3x^2 - 10x + 64
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
quotient of (x^4-6x^3-19x^2+24x) divided by (x+3)
Using the long division method of quotient, we have
x + 3 | x^4 -6x^3 -19x^2 +24x
The division steps are as follows
x^3 - 3x^2 - 10x + 64
x + 3 | x^4 -6x^3 -19x^2 +24x
x^4 + 3x^3
------------------------------------------------
-3x^3 -19x^2 +24x
-3x^3 - 9x^2
------------------------------------------------
-10x^2 + 24x
-10x^2 - 30x
------------------------------------------------
64x
64x + 192
----------------------------------------------------
-192
Hence, the quotient is x^3 - 3x^2 - 10x + 64
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An IV is infusing at 77 mcgtt/min. What would this rate of flow equal in mL/h?
A. 77 mL/h
B. 12 mL/h
C. 770 mL/h
D. 7.7 mL/h
An IV is infusing at 77mcgtt/min. rate of flow equal in mL/h is 77 mL/h
1gtt/min equals 3.00 mL/h
If you simply need to figure out the infusion rate, or the mL per hour to infuse, take the total volume in mL, divided by the total time in hours that the medication is ordered to be infused over, to equal the rate in mL per hour.
1 drop per minute to milliliters per hour = 3.00 mL/h
2 drops per minute to milliliters per hour = 6.00 mL/h
Change hours to minutes. Change milliliters to drops.
1 ml : 60mcgtt
1hr :60min
77mcgtt/min =77*60/60 ml/h
=77ml/h
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Now solve the equation Bc = proj, d = v by typing in the following: >> C = Blv Check that your answer is correct by entering >> B*C - v Make sure the answer is zero. (Keep in mind that MATLAB may return a very small number instead of zero due to rounding errors.)
A data set consisting of newborn baby weights is normally distributed (bell-shaped) with a mean of 9.5 pounds
and standard deviation of 1.5 pounds.
Use the Empirical Rule to address the following questions.
Hint: sketch the distribution to help visualize the problem.
Approximately 99.7% of the newborn weights lie between
What approximate percentage of the newborn weights lie between 8 and 11 pounds?
and
What approximate percentage of the newborn weights lie between 6.5 and 12.5 pounds?
These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.More can be learned about the Empirical Rule at brainly.com/question/10093236
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Help would be appreciated
The value of [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex] is after simplification is C)-30
What is mixed fraction?
A mixed number combines an integer (whole number) with a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number). When a number contains both an integer (whole number) and a correct fraction, it is known as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).
Here the given expression is ,
=> [tex]3\frac{3}{5}[/tex] ×[tex](-8\frac{1}{3})[/tex]
Now we need to convert them into improper fraction then,
=> [tex]\frac{15+3}{5}[/tex] × [tex]\frac{-(24+1)}{3}[/tex]
=> [tex]\frac{18}{5}[/tex] × [tex]\frac{-25}{3}[/tex]
=> 6 × -5 = -30
Hence the correct option is C)-30.
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This table shows the amount of commission
earned for a broker receiving 3% commission
on sales. How much would this agent earn in
commission for $680,000 in sales?
Commission Earned
Sales (in thousands of $)
Commission (in thousands of $)
140
4.2
280
8.4
420
12.6
560 680
16.8
?
Answer:
$20,400
Step-by-step explanation:
You just have to multiply 680,000 by 0.03 (since 3% is equivalent to 0.03)
Write 3 numbers that are divisible by
both 2 and 5.
Numbers divisible by 2 and 5:
[tex]10[/tex][tex]20[/tex][tex]30[/tex]Check:
[tex]10\div2=5\\10\div5=2[/tex]
[tex]20\div2=10\\20\div5=4[/tex]
[tex]30\div2=15\\30\div5=6[/tex]
solve for the matrix x if ax(d+bx)−1=c. assume that all matrices are n×n and invertible as needed, you can enter the inverse of a matrix A as A^(-1)
The answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]
Matrix is an arrangement of numbers into rows and columns. A matrix is a rectangular arrangement of numbers into rows and columns.Matrix is a set of numbers arranged in rows and columns so as to create a rectangular array. The numbers are said entries of the matrix. Matrices have huge applications in engineering, physics, economics, and statistics as well as in various branches of mathematics. Matrices have important applications in computer graphics, where they have been used to represent rotations and other transformations of images.According to the question,
AX [tex](D^{-1} + X^{-1} B^{-1} )[/tex] =C
⇒X[tex](D^{-1} + X^{-1} B^{-1} )[/tex]= [tex]A^{-1} C[/tex]
⇒[tex]XD^{-1} + XX^{-1} B^{-1}[/tex] = [tex]A^{-1} C[/tex]
⇒ [tex]XD^{-1} +B^{-1}[/tex] = [tex]A^{-1} C[/tex]
⇒ [tex]XD^{-1} = A^{-1} C -B^{-1}[/tex]
⇒ [tex]X= (A^{-1} C -B^{-1})D[/tex]
So, the answer is : [tex]X= (A^{-1} C -B^{-1})D[/tex]
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calculate the iterated integral. 3 0 1 5xy x2 + y2 dy dx 0
The value of the integral can be calculated by using the simple rules of definite integral and double integral.
The first integral is a bit tricky, as the limits of integration are not in the standard order (with respect to x and y). However, we can change the order of integration by switching the limits of integration, so that we can use Fubini's theorem.
The double integral can be solved by converting the rectangular region R into polar coordinates.
The double integral is ∫∫R 5xsin(x+y)dA, R=[0,pi/3]×[0,pi/6]. This can be further solved as
= ∫(0,pi/3) ∫(0,pi/6) 5rrsin(rcos(θ)+rsin(θ))dθ dr
= ∫(0,pi/3) ∫(0,pi/6) 5r^2sin(r(cos(θ)+sin(θ)))dθ dr
= ∫(0,pi/3) 5r^2(-cos(r*(cos(θ)+sin(θ))) | (0,pi/6))dr
= ∫(0,pi/3) 5r^2(-cos(r*(√(2)/2)))dr
= -5/2∫(0,pi/3) r^2cos(r*(√(2)/2))dr
The integral above is not in a closed form but can be evaluated using numerical integration techniques.
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Complete Question:
Calculate the iterated integral. integral_0^3 integral_0^1 5xy Square root x^2 + y^2 dy dx = Calculate the double integral. double integral R 5x sin (x + y) dA, R = [0, pi/3] times [0, pi/6] The value of integral is
please help me!!! What is the area of the trapezoid?
The area of trapezoid is 16 m².
Given in the figure,
Height of trapezoid = 4 m
Length of 1st parallel base = 2 m
Length of 2nd parallel base = 6 m
We know that,
Area of trapezoid = 1/2 * sum of bases * height
∴
Area of trapezoid = 1/2 * (2+6) * 4
= 8 * 2 = 16 m²
Therefore, the area of trapezoid is 16 m².
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f(x) = 6x + 3, find f(8)
Answer:
f(8) = 51
Step-by-step explanation:
f(x) = 6x + 3
Let x = 8
f(8) = 6(8) + 3
= 48+3
= 51
Answer:
51
Step-by-step explanation:
f ( x ) = 6x + 3
To find the value of f ( 8 ), replace x with 8.
f ( 8 ) = 6 × 8 + 3
f ( 8 ) = 48 + 3
f ( 8 ) = 51
Which if the following is the correct graph of the solution to the inequality-13>-5x+2>-28
The correct graph of the solution to the compound inequality as given in the task content is;
What is the graph of the solution to the given compound inequality?As evident from the task content, it follows that the correct graph of the solution to the compound inequality is to be determined.
Since the given compound inequality is; -13 > -5x + 2 > -28.
To solve the inequality, subtract 2 from all sections of the compound inequality;
-15 > -5x > -30
Divide through the inequality by -5 while flipping the inequality signs so that we have;
3 < x < 6
Therefore, the correct graph for the compound inequality in discuss is as represented in the attached image.
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I NEED HELP PLEASE I WILL GIVE BRAINLYIES
Answer: b
Step-by-step explanation:
Can someone please tell me the answer will mark brainiest
Radius, diameter, center, and circumference--all are parts of a circle .Every point in the plane that is a certain distance away from a certain point forms a circle (center).
what is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
Area of circle =
[tex]\pi r^2\\r = 10\\A = 3.14 X 10 X 10\\A = 314 unit sq\\[/tex]
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On solving the provided question, we can say that area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.
What is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
here,
in the circle
the given radius is as = 3.4
area of circle = [tex]\pi r^2 =[/tex] 3.14*.3.4*3.4 = 1.28112 cm sq.
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HELPPPP
If a fair coin is tossed 9 times, what is the probability, rounded to the nearest
thousandth,
of getting at most 1 heads?
When a fair coin is tossed nine times, there is a 0.090 (rounded off to the nearest thousandth) chance that at most one will land on heads.
what is probability ?The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number between 0 and 1, where about 0 represents how likely the event is to occur and 1 represents certainty. A probability is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the total number of outcomes to the proportion of occurrences in a whole set of equally likely options that lead to a specific occurrence.
given
binomial probability ⁿCₓ[(p)ˣ(q)ⁿ⁻ˣ]
where p= probability of tail = 1/2 (favorable outcome)
q = probability of head = 1/2: (1 - p)
n = total outcome = 9
x = 4
ⁿCₓ[(p)ⁿ(q)ⁿ⁻ˣ] = ⁹C₄[(1/2)⁴(1/2)⁵]
= [1/16 x 1/32]
= (512)
126/512 = 0.24609
≈ 0.090 nearest thousandth rounded off .
When a fair coin is tossed nine times, there is a 0.090 (rounded off to the nearest thousandth) chance that at most one will land on heads.
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PLEASE ANSWER
50 degrees
120 degrees
60 degrees
40 degrees
The angle B in triangle ABC is 60° i.e. C.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now
∠NAB+∠CAB=180° (Supplementary angles)
∠CAB=180-∠NAB
=180-100
∠CAB=80°
As
∠A+∠B+∠C=180° (sum of all angles of a triangle =180°)
∠B=180-80-40
∠B=60°
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Find the domain and the range of the function. (Enter your answers using interval notation.)
h(x) = −√x+6
The domain and the range of this function in interval notation include the following;
Domain = [-6, ∞].
Range = [-∞, 0].
How to identify the domain and range of a function?In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:
Domain = -6 < x < ∞ or [-6, ∞].
Range = -∞ < y < 0 or [-∞, 0].
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Calculate S3, S, and Ss and then find the sum for the telescoping series 3C0 n + 1 n+2 where Sk is the partial sum using the first k values of n. S3 = 1/6 S4 = __
S5 = __
S = __
The solutions are -
S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)
S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)
S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)
The sum of the series is 1/3.
To find S3, we need to find the sum of the first 3 terms of the series:
S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)
To find S4, we need to find the sum of the first 4 terms of the series:
S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)
To find S5, we need to find the sum of the first 5 terms of the series:
S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)
To find the sum of the telescoping series, we can use the property of the telescoping series where the terms will cancel out. In this case, we can see that the first term of each group of two terms cancels out with the second term of the next group of two terms.
S = (1/3) - (1/8)
The series starts at n=2 and ends at infinity, so the sum of the series is the difference between 1/3 and the limit of 1/n as n approaches infinity, which is zero.
S= (1/3) -0 = 1/3
So the sum of the series is 1/3.
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The complete question is -
Calculate S3, S4, and S5 and then find the sum for the telescoping series: S=∑n=2∞(1/n+1)−(1/n+2). where Sk is the partial sum using the first k values of n.
please help me understand this
The value of a is 3√3/2 and value of b is 3/2. The solution has obtained using the trigonometry formulas.
What is trigonometry?
The study of the right-angle triangle's sides, angles, and connection is the main focus of the field of mathematics known as "trigonometry." Therefore, it helps to find the unknown or missing angles or sides of a right triangle using the trigonometric formulas, functions, or trigonometric identities. The angles in trigonometry can either be expressed in degrees or radians. The most used trigonometric angles for computations include 0, 30, 45, 60, and 90 degrees.
In the figure, we are given that one angle measures 30° and the other measures 90° and the hypotenuse is 3.
So, using trigonometry, we know that
Cos theta = adjacent side/hypotenuse
And, Cos 30° is √3/2
So,
⇒√3/2 = a/3
⇒a= 3√3/2
Sin theta = opposite side/hypotenuse
And, Sin 30° is 1/2
So,
⇒1/2 = b/3
⇒b= 3/2
Hence, the value of a is 3√3/2 and value of b is 3/2.
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PLEASE HELP OR I WILL FAIL 1/7+3/7
Answer: 4/7
Step-by-step explanation:
pretty simple, 1/7 and 3/7 both has a denominator of "7", so the seven stays the same. (While writing this I made a chart to see where I put everything)
Write:
1/7 = (denominator 7)
+ 3/7 = (denominator 7)
Now we start doing the math, what goes into 7? 7x1 so 1 x 3 = 3
know we go up to the numerator, 7x1=7, so 1 x 1 = 1
add 3 + 1 and that adds up to 4
so your answer is 4/7, hope it helps
Determine whether the geometric series is convergent or divergent.
10−8+6.4−5.12+⋯
O Convergent
O divergent
The given series is convergent and the sum(S) is 5.555.
Consider 10 - 8 + 6.4 - 5.12 + ...
A geometric progression will converge if the common ratio of the series is between -1 and 1.
Here is the common ratio,
r = -8/10
⇒ r = -0.8
Which is -1 < -0.8 < 1.
Hence, the given series is convergent.
Sum of series = S = a/(1 - r)
Here, first term(a) = 10,
common ratio(r) = -0.8,
S = a/(1 - r)
⇒ S = 10/(1 - (-0.8))
⇒ S = 10/(1 + 0.8)
⇒ S = 10/1.8
⇒ S = 5.555
Therefore, the given series is convergent and the sum( S)is 5.555.
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If 3x+y+4-(y + 6) = 14 + x, what is the value of x ?
Answer:
x=8
Step-by-step explanation:
Answer:
3x+y+4-(y + 6) = 14 + x
x=8
An image of lines p and q parallel to each other. Lines m and n are not parallel to each other. Line m, p form an angle of one hundred two degrees and an angle marked y. Lines n, q form an angle marked x and an angle of one hundred fifteen degrees.Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure. The value of x is degrees, and the value of y is degrees.
Answer:
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There are 140 students in the seventh grade, and 5% are in the Environmental Club.
How many students are in the Environmental Club?
Answer:
7 students.
Step-by-step explanation:
A trick for this is to find 10% of the students in the Environmental Club and then divide by 2.
10% of 140 is simple; just remove the 0 and you got 14.
Next, divide 14/2 to get 5%
14/2 = 7
7 students are apart of the Environmental Club