The explicit formula for the given geometric series will be [tex]a_n = -4(3)^{n-1}[/tex].
What is geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.
Given that the geometric series is -4,-12,-36,-108. The formula for the nth term of the geometric progression will be written as:-
[tex]a_n = a_1(r)^{n-1}\\[/tex]
Here, r is the common ratio of the series. The value of the common ratio is r = -12 / -4 = 3.
The formula will be:-
[tex]a_n = a_1(r)^{n-1}\\[/tex]
[tex]a_n = -4(3)^{n-1}\\[/tex]
Therefore, the formula for the nth term will be [tex]a_n = -4(3)^{n-1}\\[/tex].
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Find the value of xx and yy in the parallelogram below.
Answer:
x = 12
y = 11
Step-by-step explanation:
It's a parallelogram, so opposite sides are equal.
4x + 10 = 58
4x = 58 - 10 = 48
x = 48/4 = 12
10y - 6 = 104
10y = 104 + 6 = 110
y = 110/10 = 11
Work out the percentage change to 2 decimal places when a price of £15 is decreased to £14.
give woking out :))
The percent change in the price is -6.67
How to find the precentage change?The percentage change will be given by the formula:
Percent change = 100%*(new price - old price)/old price
We know that:
old price = 15 pounds.
new price = 14 pounds
Replacing that we will get:
percent change = 100%*(14 - 15)/15 = -6.67%
The price is 6.67% smaller.
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Question is in the picture.
The equation is given as y = 4x - 3 , where the slope is m = 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The value of term 1 = 1 square
The value of term 2 = 5 suqres
The value of term 3 = 9 squares
So , the increment in the number of squares is 4
Let the first point be P ( 1 , 1 )
Let the second point be Q ( 2 , 5 )
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 5 - 1 ) / ( 2 - 1 )
Slope m = 4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 1 = 4 ( x - 1 )
On simplifying the equation , we get
y - 1 = 4x - 4
Adding 1 on both sides of the equation , we get
y = 4x - 3
Therefore , the value of y is 4x - 3
when x = 1 . y = 4 - 3 = 1
when x = 2 , y = 4 ( 2 ) - 3 = 8 - 3 = 5
Hence , the equation of line is y = 4x - 3
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800 students attend Ridgewood Junior High School. 25% of students bring their
lunch to school everyday. How many students brought their lunch to school on
Thursday?
200 number of students brought their lunch to school on Thursday.
What do you mean by Percentage?A Percentage is a number or ratio that can be expressed as a fraction of 100.
To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
Percentage formula = (Value/Total Value) × 100
P% of Number = X
where X is the required percentage.
If we remove the % sign, we need to express the above formula
P/100 × Number = X
Given:
Total number of students in school = 800
25% students bring their lunch every day.
25% of 800
= [tex]\frac{25}{100} \times 800[/tex]
= 25 × 8
= 200
200 students bring their lunch to school on Thursday.
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Which of the following are equations for the line shown below? Check all that
apply.
(-3,-5)
(3,-2)
A. Y+2=0.5(x-3)
B. Y-5=0.5(x-3)
C. Y+5=0.5(x+3)
D. Y=0.5x-3.5
Answer:
Both C and D are equations for the two given points.
Step-by-step explanation:
A. Y+2=0.5(x-3) NO
(-3,-5): -5+2 = 0.5(-3-3); -3 = 0.5(-6); -3 = -3 YES
(3,2): 2+2 = 0.5(3-3): 4 = 0.5(0); 4 = 0 NO
B. Y-5=0.5(x-3) NO
(-3,-5): -5-5=0.5(-3-3); -10 = -3 NO
(3,-2): -2-5=0.5(3-3); -7 = 0 NO
C. Y+5=0.5(x+3) YES
(-3,-5): -5+5=0.5(-3+3); 0 = 0 YES
(3,-2): -2+5=0.5(3+3); 3 = 3 YES
D. Y=0.5x-3.5 YES
(-3,-5): -5 = 0.5(-3)-3.5; -5 = -5 YES
(3,-2): -2 = 0.5(3)-3.5; -2 = 1.5 - 3.5 YES
use point slope form to write the equation of a line that passes through the point (17,-7) with slope - 1/2
Answer:
y + 7 = -1/2 ( x - 17)
Step-by-step explanation:
y-y₁=m(x-x₁)
[tex]x_{1\\} = 17[/tex]
[tex]y_{1}[/tex] = -7
y - (-7) = -1/2(x - 17)
y + 7 = -1/2(x -17)
Write an algebraic expression to represent the following situation: "Adele bought a skirt and a blouse. The skirt cost $15 more than the blouse. Let B represent the cost of the blouse. Write an expression for the cost of the skirt."
S=B+15
15 more than blouse (b)
S representing skirts
Which equation represents the line that passes through the point (1,5) and has a slope of -2?
Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1
Graph the Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1.
The preimage's point corresponds to the image's points in the following way:
P(-6, 2) → P'(6, 2)
Q(-2, -1) → Q' (2, -1)
R(-2, -3) → R'(2, -3)
S(-6, -6) → S'(6, -6)
(x,y)→(−x,y)
A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
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Ken is going on a hike with his friends. He brings 8 liters of water for everyone to share. While hiking, they drink 5 of liters.
Answer: If Ken brought 8 liters of water for everyone to share and they drank 5 liters of it, then the remaining amount of water they have is 8 - 5 = 3 liters.
Step-by-step explanation:
prove that if a sequence converges it has exactly one limit point. is the converse true? prove it or give a counterexample.
The counterexample proves that the converse of the theorem is not always true, and we have to be careful when making statements about limit points and convergence of sequences.
A sequence is a set of numbers that are generated one after the other in a specific pattern.
The theorem states that if a sequence converges, it will have exactly one limit point. In other words, if a sequence is getting closer and closer to a certain number, there will be only one number that it approaches. This is a fundamental idea in mathematics, and it is important to understand why it is true.
To prove this theorem, let's consider a sequence (a_n) that converges to a limit L. If there were two different limit points, say L1 and L2, then there would be a contradiction. This is because by definition, the sequence (a_n) would be getting closer and closer to L1 and L2 at the same time, which is not possible. Hence, it must be true that the sequence (a_n) has exactly one limit point, L.
The converse of this theorem is not always true. In other words, just because a sequence has exactly one limit point, it doesn't necessarily mean that it converges to that limit. To see why this is the case, let's consider the following sequence:
(2, 3, 4, 5, 6, ...)
In this sequence, the limit point is 6. However, the sequence does not converge to 6 because it is not getting closer and closer to 6 as it goes on. Instead, it is increasing by 1 with each term, and therefore it does not converge.
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portion of all homes in the city that have a television. which conditions for constructing this confidence interval did the sample meet?
If the sample met these conditions, then it is possible to construct a confidence interval for the proportion of all homes in the city that have a television.
In order to construct a confidence interval, the sample must meet the following conditions:
The sample must be a random sample of the population.The sample must be large enough to ensure a normal distribution.The sample size should be at least 30.The population should be normally distributed.The sample must be randomly selected from the population, large enough to ensure a normal distribution, and the population must be normally distributed. If these conditions are met, then a confidence interval can be constructed to provide an estimate of the proportion of homes that have a television.
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please help ME EMERGENCY~
The amount that the salesperson will earn in commission from selling the couch is $ 27. 23.
The amount the sale of the couch by the store would get it is $ 467. 77.
How to find the commission ?The commission on the couch can be found by the formula :
= Selling price of couch x Commission to salesperson
= 495 x 5 . 5 %
= $ 27. 23
The money the store will get from the sale of the couch to Lin and her dad is:
= Selling price of couch - Commission to salesperson
= 495 - 27. 23
= $ 467 . 77
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The full question is:
Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5 1/2% of the selling price.
A.How much commission will the salesperson earn by selling a couch for $495?
B.How much money will the store get from the sale of the couch?
The shape of Tina's kitchen is a rectangle 925 cm long by 485 cm wide.
a) Work out the area of Tina's kitchen in square meters.
Show how to use estimation to check your answers.
Flooring costs $56 per square meter.
It is only sold in whole numbers of square meters.
B) How much does Tina pay to buy flooring for her kitchen floor?
Show how to use inverse operations to check your answer
a) The area of Tina's kitchen is 44.8625 square meters. b) Tina cost $2520 to buy flooring for her kitchen floor.
a) To work out the area of Tina's kitchen in square meters, we need to divide the area in square centimeters by 10,000, which is the number of square centimeters in a square meter:
Area = length x width = 925 cm x 485 cm = [tex]448,625 cm^2[/tex]
Area in square meters =[tex]448,625 cm^2 / 10,000 cm^2/m^2 = 44.8625 m^2[/tex]
b) To find how many whole square meters of flooring Tina needs, we round the area of the kitchen up to the nearest whole number:
Area in square meters rounded up = ceil(44.8625) = [tex]45 m^2[/tex]
The cost of the flooring is $56 per square meter, so Tina pays:
Total cost = [tex]45 m^2 * $56/m^2 = $2520[/tex]
To use inverse operations to check this answer, we can divide the total cost by the cost per square meter to get the number of square meters, and then multiply by the cost per square meter to check that we get back to the total cost:
Number of square meters =[tex]$2520 / $56/m^2 = 45 m^2[/tex]
Total cost = [tex]45 m^2 x $56/m^2 = $2520[/tex] (same as the original answer)
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Given h(x) = -x+5, solve for x when h(x) =0
The value of h(x) = 0 gives x=5.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the b. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
h(x) = -x + 5
So, for h(x)= 0 we have
-x + 5= 0
now, solving for x
-x = -5
x= 5
Thus, the value of x is 5.
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GARDEN Camila put a frame around a triangular garden in her yard. The two legs of the triangle are 8 feet long each, and the third side is equal to the length of a leg times 2⎯⎯√ . What is the perimeter of the triangle? Give your answer as a simplified radical expression,
The perimeter of the triangle is 16+8√2 feet.
The perimeter of any two-dimensional figure is defined as the distance around the figure. The formula for a closed shape figure's perimeter is typically equal to the length of the figure's outer line.
The perimeter of a triangle will therefore be equal to the sum of its three sides. Consequently, if a triangle has sides a, b, and c,
Here, a= 8 feet
b= 8 feet
c= 8√2 (length of a leg * √2= 8*√2)
Perimeter= Sum of all three sides of the triangle
Perimeter = a + b + c
Perimeter= 8+ 8 +8√2
Perimeter= 16+8√2 feet.
16+8√2 feet is the perimeter of the triangular garden.
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Consider AGHJ in the figure below.
The perpendicular bisectors of its sides are KN, LN, and MN. They meet at a single point N.
(In other words, N is the circumcenter of AGHJ.)
Suppose LN=22, GJ=92, and GN=122.
Find HN, LJ, and GK.
Note that the figure is not drawn to scale.
Answer:
Step-by-step explanation:
3X2+3Y^2-7X-6Y-3
Find the diameter
The diameter of the circle is 22 / 12 units
What is the diameterTo find the diameter of the figure, we need to rewrite this in standard form of a equation of a circle.
3x² + 3y² - 7x - 6y - 3 ;
This will be written in (h, k) form which is
3x² + 3y² - 7x - 6y - 3
The coordinate of the center is at (7/6, 1)
The radius of the circle is 11/6 and we can find the diameter of the circle by;
diameter of circle = 2 * radius of circle
diameter = 2 * 11 / 6
diameter = 22 / 12
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Which values are solutions to the inequality below? Check all that apply.
√x <10
A. 100
B. 25
C. -100
D. 105
E. 36
F. 9
Answer:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v
Step-by-step explanation:
its E and A
Answer:
The solutions to the inequality are B, E, and F: 25, 36, and 9.
Step-by-step explanation:
The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:
√x < 10
x < 10^2 = 100
So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:
A. 100 (not a solution)
B. 25 (solution)
C. -100 (not a solution)
D. 105 (not a solution)
E. 36 (solution)
F. 9 (solution)
Use this for question 6 to 8:
Four machines A, B, C and D produce respectively 30%, 30%, 15% and 25% of the total number of
items from a factory. The percentage of defective output from these machines are 1%, 1.5%, 3% and
2% respectively. Given that an item is to be selected at random from the total output.
6: Find the probability that the item will be defective.
(a) 0.105
(2 marks)
(b) 0.017
(c) 0.007
(d) 0.170
7: If an item selected at random is found defective, what is the probability that it is produced by
machine A
(2 marks)
(2 marks)
(d) 0.007
(a) 0.018
(b) 0.015
(c) 0.111
8: Find the probability that the item is produce by machine D
(a) 0.294
(b) 0.034
(c) 0.118
(d) 0.253
The probability that the item will be defective is 0.017, the probability that an item selected at random is defective is 0.018 and the probability that an item is produced by machine D is 0.25
What is the probability that the item will be defectiveUsing the formula of probability distribution to solve the given problem;
6: The probability that the item will be defective is the sum of the probabilities of a defective item from each machine:
(1% * 30%) + (1.5% * 30%) + (3% * 15%) + (2% * 25%) = 0.017
So the answer is b
7: If an item is selected at random and found to be defective, the probability that it was produced by machine A is the probability of a defective item from machine A divided by the overall probability of a defective item:
(1% * 30%) / 0.017 = 0.018
The answer is option a
8: The probability that the item was produced by machine D is the probability of a non-defective item from machine D divided by the overall probability of a non-defective item:
(25% * 98%) / (100% - 0.017) = 0.25 * 0.98 / 0.895 = 0.25
So the answer is (d) 0.253
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Russell and Valerie start to walk away from the Cafeteria to their classes.
Russell walks 10 yards due West, then turns 40° toward South and walks 5 yards.
Valerie walks 10 yards due East, then turns 60° toward North and walks 5 yards.
Which student is farther from the cafeteria? Explain how you know using a diagram and words.
Julia downloaded a 22 MB file in 5 seconds on her tablet. Later she downloaded a 30 MB file on her smart phone in 6 seconds. Are these rates equivalent? Explain your reasoning.
22 MB in 5 seconds
how many MB per second
divide the 5 out
22/5 = 4.4 MBPS
30 MB in 6 seconds
30/6 = 5 MBPS
5 MBPS > 4.4 MBPS
No, they aren't equivalent because one is greater than the other.
Hope this helps,
- Jeron :- )
I need help on question six, pls help me
Answer:
The surface area of the label is 28 squared inches.
Step-by-step explanation:
The dimensions of juice box are length=2 inches, breadth=1.5 inches and height= 4 inches.
The lateral surface area of a cuboid is given by 2(length+breadth)×height.
Now, lateral surface area of juice box = 2(2+1.5)×4
= 2×3.5×4
= 28 squared inches
Answer:
28 square inches
Step-by-step explanation:
Lateral surface of Cuboid:The label covers the lateral surface area of the box.
l = 2 in ; w = 1.5 in ; h = 4 in
[tex]\boxed{\text{\bf lateral surface area of cuboidal box = 2h*(l +w)}}[/tex]
[tex]\sf = 2*4 *( 2 +1.5)\\\\= 2 * 4 * 3.5\\\\ = 28 \ in^2[/tex]
The surface of the area of a cylinder is 372pi square centimeters the radius is 6 cm what is the height of the cylinder
If the surface of the area of a cylinder is 372π square centimeters. Then the height of the cylinder is 31 centimeters.
What is the surface area of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,
SA = 2πrh square units
The surface of the area of a cylinder is 372π square centimeters the radius is 6 cm. Then the height of the cylinder is given as,
SA = 2πrh
372π = 2π x 6 x h
h = 372 / 12
h = 31 centimeters
The height of the cylinder is 31 centimeters.
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7. Given that 2x² + 4x + 3 = k where k is a constant, find the range of values for k for which the equation has no real roots. (b) The function f is defined on the set R of real numbers by f(x) →kx² + kx + 1, where k is a member of R. Calculate the range of values of k for which the equation f(x) = 0 hasreal roots. Given that k = -2, solve the equation f(x) = 0. 1/2
Answer: (a) The equation 2x^2 + 4x + 3 = k has real roots if and only if its discriminant, which is 4^2 - 4(2)(3), is nonnegative. The discriminant is equal to 0, so the equation has real roots if and only if k = 3.
(b) For the equation f(x) = kx^2 + kx + 1 to have real roots, its discriminant, which is 1 - 4k, must be nonnegative. This gives us k >= 1/4. The range of values of k for which the equation has real roots is k >= 1/4.
(c) When k = -2, the equation f(x) = -2x^2 - 2x + 1 = 0. Solving this equation using the quadratic formula, we get x = (-1 ± √(1 + 8))/4. So, the roots are x = (-1 ± √(9))/4 = (-1 ± 3)/4 = 1/2, -2.
(3+4x-2)4 2/7
please help or my mom said she was going to put me up for adoption which i don't care for i just want to get this work done
The value of x in expression is -1/8.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
(3+4x-2)4 2/7=0
(3+4x-2)16/7=0
48+64x-32=0
x=-1/8
Therefore, the answer of given algebra problem will be -1/8.
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Y=x+3
3x-3y=9
Solved in substitution
The requried, given system of equations y=x+3 and 3x-3y=9 has no common solution.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
From the first equation, we can solve for y:
y = x + 3
Substitute y = x + 3 into the second equation:
3x - 3(x + 3) = 9
Simplify the right side:
3x - 3x - 9 = 9
-9 = 9 (inconsistent)
Since the equation -9 = 9 is inconsistent, the system of equations has no solution, which means that there are no values of x and y that make both equations true at the same time. It implies the system of equations has no solution.
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can someone help me with this
The distances traveled by the car are given as follows:
3 minutes: 3.45 kilometers.5 minutes: 5.75 kilometers.What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
v = 1.15 km/min, t = 1 min.
Hence the equation for the distance in km after t minutes is given as follows:
d = 1.15t.
Then after 3 minutes, the distance is of:
d = 1.15 x 3 = 3.45 km.
After 5 minutes, the distance is of:
d = 1.15 x 5 = 5.75 km.
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1. Andrew lives in Johannesburg. His parents are planning a vacation to Cape Town They decide to fly to Cape Town and then rent a car. The car rental company charge R200 per day (including 200 km free) and R1,80 per km. The insurance be 7,5% of the daily rental amount and the GPS an additional R45 per day a.What will the total cost be for the car rental if they spent 6 days in Cape Town travelled 1650 km in total?
Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era, and find the correct solution
Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era, and find the correct solution
The students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: Given, Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5.
We have to find the error made by the students.
5 less than a number n = n - 5
5 less than a number n divided by 3 = (n - 5)/3
Correct expression = (n - 5)/3
Expression written by student = (n/3) - 5
Therefore, the students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.
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What’s the Error? A Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5. What error did the they make?