Answer:
Tn = 4 + (n – 1)3
is the arithmetic sequence for the nth term
Step-by-step explanation:
formula for an arithmetic sequence is
[tex]tn = a + ( n - 1)d[/tex]
where:-
Tn = nth term
a = first term
n = number of terms
d = common difference.
now back to the question
the 8th term of an arithmetic sequence is 25.
that will be written as
[tex]t8 = a \: + ( 8 - 1)d = 25[/tex]
[tex]a + (7 )d = 25 \: \: \: \: .....eqn1[/tex]
and the 14th term is 43
this will be written as
[tex]t14 = a + (14 - 1 )d = 43[/tex]
[tex]a + 13d = 43 \: \: \: \: .....eqn2[/tex]
subtract eqn 1 from 2
a – a, 13d – 7d, 43–25
[tex]6d = 18[/tex]
divide both sides by (6)
[tex] \frac{6d \\ }{6} = \frac{18}{6} [/tex]
d = 3
now that we know d = 3 let's substitute it in eqn 1 above.
a + 7d = 25
a + 7(3) = 25
a +21 = 25
a = 25 – 21
a = 4
now the normal arithmetic sequence given will be
[tex]tn = 4 + (n - 1 )3[/tex]
I hope this helps
How much must a carpenter cut off a 48-inch board if the length must
be 40 ± 0.25 inches?
Answer:
Step-by-step explanation:
let 'x' represent the amount removed, then we require:
40-0.25 <= 48-x <= 40+0.25
which solves to:
7.75 <= x <= 8.25
the carpenter must saw off between 7.75 and 8.25 inches
there are $20$ cars in my building's parking lot. all of the cars are red or white. also, all the cars are either $2$-door or $4$-door. $12$ of them are red, $15$ of them are $4$-door, and $4$ of them are $2$-door and white. how many of the cars are $4$-door and red?there are $20$ cars in my building's parking lot. all of the cars are red or white. also, all the cars are either $2$-door or $4$-door. $12$ of them are red, $15$ of them are $4$-door, and $4$ of them are $2$-door and white. how many of the cars are $4$-door and red?
There are a total of 20 cars average in the parking lot, all of which are either red or white and either 2-door or 4-door. 12 of the cars are red, 15 of them are 4-door, and 4 of them are 2-door and white. Out of the 12 red cars, 12 of them are 4-door, so the answer is 12 cars are 4-door and red.
1. Determine the total number of cars in the parking lot: 20
2. Subtract the number of 2-door cars from the total number of cars to get the number of 4-door cars:
20 - 4 = 15
3. Subtract the number of 2-door and white cars from the number of red cars to get the number of 4-door and red cars:
12 - 4 = 8
4. Add the number of 4-door and red cars to the number of 4-door cars to get the answer:
8 + 15 = 12
To find the answer, we first determined the total number of cars in the parking lot, which was 20. We then subtracted the number of 2-door cars from the total number to get the number of 4-door cars, which was 15. We then subtracted the number of 2-door and white cars from the number of red cars to get the number of 4-door and red cars, which was 8. Finally, we added the number of 4-door and red cars to the number of 4-door cars to get the answer, which was 12.
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A line l is passing through the points on the graph of y=x^2-2x+5 with abscissas -1 and 2. What is the equation of the line, which is:
Please help 100 points+ brainliest
Answer:
y=-x+7
Step-by-step explanation:
Line l intersects y=x^2-2x+5 at the two abscissas, -1 and 2. Lets find these points [(-1,y1) and (2,y2)] by solving the given equation for y:
f(x) = x^2-2x+5
f(-1) = (-1)^2-2*(-1)+5 for x = -1
f(-1) = 8 This is point (-1,8)
f(2) = (2)^2-2*(2)+5
f(2) = 5 This is point (2,5)
Assuming line l is a straigh line, we can now calculate the slope between points (-1,8) and (2,5).
Rise = (5 - 8) = -3
Run = (2 - (-1)) = 3
Slope = (-3/3) or -1
The slope-intercept form of a straight line is y=mx+b, where m is the slope and b the y-intercept (the value of y when x is zero).
With slope of -1, we can writre y = -x + b
To find b, enter one of the two points and solve for b:
y = -x + b
5 = -(2) + b for (2,5)
b = 7
The equation of line l is y=-x+7
See the attached graph.
Help!
Explain how to employ the Pythagorean theorem in calculating the volume of a right cylinder if you know the distance from the edge of the base to the center of the top along with either its radius or its height.
If you know the distance from the edge of the base to the center of the top, together with either its radius or its height, we can compute the volume of a right cylinder.
What is the Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.
Note that h refers to half of the total height of the cylinder. I chose to use
h instead of h/2 to simplify things later on.
To find the volume of our cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;
V = pi * (radius of cylinder)² (height of cylinder)
V = pi(r² - h²) 2h
V = 2pi h(r² - h²)
This is our volume function. Next, we take the derivative of the volume function and set it equal to zero. If we move the h inside the parenthesis, we only need to use the power rule to get the derivative.
d/dxV(h) = 2pi(r² -3 h²) = 0
The 2π divides out and we are left with;
r² − 3h²=0
After some rearranging;
h² = r²/3
Take the square root of both sides.
h = r/√3
That is how we can calculate the volume of a right cylinder, if you know the distance from the edge of the base to the center of the top along with either its radius or its height.
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what is 8 divided by 6.48 long division
Answer:
0.81
Step-by-step explanation:
The coordinates of the endpoints of RS are R(4, -8) and S(25, -1). Point T is on RS such that
the ratio of the length of ST to the length of RT is 4:3,
What is the sum of the coordinates of T?
Write your answer as an integer or decimal.
The required sum of the coordinate of T is given as 9.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate the y is called ordinate.
Here,
The coordinates of the endpoints of RS are R(4, -8) and S(25, -1).
Ratio ST / RT = 4 / 3 = n/m
Coordinates of the point are given by section formula,
x = mx₁ + nx₂ / m + n ; y = my₁ + ny₂ / m + n
Substitute the values,
x = 3 × 4 + 25 × 4 / 4 + 3 ; y = 3 × -8 + 25 × -1 / 4 + 3
x = 16 ; -7
Coordinates of T = (x ,y) = (16, -7)
Sum of the coordinate of T = 16 + {-7} = 9
Thus, the required sum of the coordinate of T is given as 9.
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Which polygon appears to be regular? Figure A is a square. Figure B is a parallelogram. Figure C is a right triangle. Figure D is a trapezoid
Figure A appears to be a polygon under certain conditions.
We are given the following information in the question:
Figure A is a square
Figure B is a parallelogram
Figure C is a right triangle.
Figure D is a trapezoid
We have to find which are the regular polygons.
A regular polygon is a polygon with all the sides equal and all the interior angles equal measure.
That is a regular polygon is equiangular and equilateral.
Figure A square appears to be a polygon because
The opposite sides are parallel. All four sides are equal, and all angles measure 90°.
Figure B can be a regular pentagon provided it is equiangular and equilateral
A regular polygon is a polygon with all the sides equal and all the interior angles equal measure.
Figure C cannot be a regular polygon because a right angle follows the Pythagoras theorem and all three sides can never be equal in a right-angled triangle.
Figure D is a trapezoid Trapezoids are four-sided polygons, so they are all quadrilaterals.
Figure A appears to be a polygon under certain conditions.
Thus square looks to be a regular.
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find the value of a of coefficient of x² in the expansion (1+ax)⁴(a-2)³ is 6
Step-by-step explanation:
To find the coefficient of x² in the expansion of (1+ax)⁴(a-2)³, we can use the binomial theorem. The binomial theorem states that for any two numbers a and b and any non-negative integer n, the expansion of (a+b)^n is given by the sum of the terms:
(a+b)^n = C(n,0)a^n * b^0 + C(n,1)a^(n-1) * b^1 + C(n,2)a^(n-2) * b^2 + ... + C(n,n)a^0 * b^n
where C(n,k) = n! / (k!(n-k)!) is the binomial coefficient.
We can apply the binomial theorem to find the coefficient of x² in the expansion of (1+ax)⁴(a-2)³:
(1+ax)⁴(a-2)³ = (1+4ax+6(ax)²+4(ax)³+(ax)⁴)(a-2)³ = a^3 - 6a^2 + 12a - 8 + 6(ax)² + ...
So the coefficient of x² in the expansion is 6.
Are the two lines in the picture parallel, perpendicular, skew or neither? Be sure to explain your reasoning
The lines given, based on the picture, can be said to be skew.
What are skew lines ?Skewed lines are two lines that are not parallel to one another, neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist in various planes. Two lines in a two-dimensional space can either intersect or run parallel to one another. Skew lines can never exist in 2D space as a result.
Skew lines occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. These lines go on forever in both directions.
The picture shows lines on steps. These steps therefore exist on different planes but are not parallel. They must therefore be skew.
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solve by substitution
v+w=11
2v-w=16
Answer:
w = 3
v = 8
Step-by-step explanation:
v + w = 11 can be written
v = 11-w substitute this for v
2v - w = 16
2(11 -w) - w = 16 Distribute the 2
22 - 2w = 16 Subtract 22 from both sides
22 - 22 -2w = 16 - 22
-2w = -6 Divide both sides by -2
[tex]\frac{-2w}{-2}[/tex] = [tex]\frac{-6}{-2}[/tex]
w = 3
v = 11 - w
v = 11 -3
v =8
Check:
v + w = 11
8 + 3 = 11
11 = 11 Checks
2v - w = 16
2(8) - 3 = 16
19 - 3 = 16
16 = 16 checks
HELP ME PLSS!?!?
In the mall you receive a coupon for $5 off of a pair of jeans when you arrive at the store you find that all jeans are 25% off
.let x represent the original cost of the jeans
.the function f(x)=x-5 represents the cost of the jeans if you use the coupon
.the function g(x)=0.25x represents the cost of the jeans if you apply the store discount of 25% first
Write a function: H(x) that represents how much you would pay if you use the mall coupon that followed by applying the discount from the store?
Answer:
H(x) = (x - 5) * (1 - 0.25) = x - 5 - 0.25x = 0.75x - 5
Answer:
The function H(x) that represents how much you would pay if you use the mall coupon followed by applying the discount from the store would be:
H(x) = (x - 5) * 0.75
Step-by-step explanation:
First, we apply the mall coupon by subtracting $5 from the original cost of the jeans represented by x. This gives us the function f(x) = x - 5.
Next, we apply the store discount of 25% by multiplying the result of f(x) by 0.75. This is because 25% expressed as a decimal is 0.25, and to apply a discount, we multiply by the decimal form of the percentage (1 - decimal form).
So, the final function H(x) represents the cost of the jeans after both the mall coupon and store discount have been applied, and is equal to (x - 5) * 0.75.
3. Apply Math Models The height of a flag
pole is 20 feet. The distance from the top of
the flag pole to a point that is 21 feet from
the base of the pole is 28.9 feet. Does the
flag pole form a 90° angle with the ground?
No, the flag pole does not form a 90° angle with the ground.
We can use the Pythagorean theorem to find the length of the flag pole, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).
Let x be the length of the flag pole. Then, we have:
x² = (20 - x)² + 28.9²
Expanding and solving for x, we get x = 30.8.
Therefore, the length of the flag pole is 30.8 feet, which is greater than the height of 21 feet. This means that the angle between the flag pole and the ground is not 90°, but rather less than 90°.
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elliott has some yarn that she wants to use to make hats and scarves. each hat uses 0.20.20, point, 2 kilograms of yarn and each scarf uses 0.10.10, point, 1 kilograms of yarn. elliott wants to use twice as much yarn for scarves as for hats, and she wants to make a total of 202020 items. let hhh be the number of hats elliott makes and sss be the number of scarves she makes. which system of equations represents this situation? choose 1 answer: choose 1 answer: (choice a) a \begin{cases} 0.1s
The system of equations that represents Elliott's situation is:
[tex]\begin{cases} 2h = 2h \\ s = 2h \\h + s = 202020 \end{cases}[/tex]
The system of equations for Elliott's situation can be represented as follows:
Let h be the number of hats Elliott makes and s be the number of scarves she makes.
We know that 2 kilograms of yarn are needed for each hat and 1 kilograms of yarn are needed for each scarf.
Therefore, the equation to represent the total amount of yarn used for hats is:
h * 2 = 2h
And the equation to represent the total amount of yarn used for scarves is:
s * 1 = s
Now, we know that Elliott wants to use twice as much yarn for scarves as for hats. This can be represented as:
s = 2h
Finally, we know that Elliott wants to make a total of 202020 items. This can be represented as:
h + s = 202020
Combining all of the equations, we get:
[tex]\begin{cases} 2h = 2h \\ s = 2h \\h + s = 202020 \end{cases}[/tex]
Therefore, the system of equations that represents Elliott's situation is:
[tex]\begin{cases} 2h = 2h \\ s = 2h \\h + s = 202020 \end{cases}[/tex]
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Find the measure of each acute angle.
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is 180
So, (19x-1)+(13x-5)+90(right angle) =180
32x+84=180
32x=96
x=3
19x3-1=56
13x3-5=34
answer : 56, 34
If the width of the quilt is 4 feet less than its length and the area of the quilt is 96 square feet what is the quilts length
The length of the quilt is 12 feet.
We can start solving this problem by using algebra. Let x be the quilt's length in feet. Then, the width of the quilt can be represented as (x - 4) feet. The area of the quilt is the product of its length and width, which is x(x - 4) = 96.
Expanding the left side of the equation:
x^2 - 4x = 96
Now we have a quadratic equation that we can solve by factoring or using the quadratic formula.
x^2 - 4x - 96 = 0
(x-12)(x+8) = 0
x=12 or x=-8 (length cannot be negative)
So the length of the quilt is 12 feet.
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How do you write an interval notation on quadratic inequality?
Solve for x values that satisfy a quadratic inequality to write interval notation. This usually involves factoring the quadratic and putting it equal to zero, then utilizing the inequality sign to select viable solutions. After finding the answers, write (a,b) to indicate the interval of x-values that make the inequality true. The interval notation for -3 and 5 is (-3,5).
What is interval notation?In general, you must first solve for the values of x that are consistent with the inequality being met before you can build an interval notation for a quadratic inequality. The quadratic equation will often need to be factored in order to be fixed to zero.
The relevant answers will then be determined using the inequality sign. After you have identified the solutions, you may use the notation (a,b), where a and b stand for the solutions, respectively, to show the range of x-values that cause the inequality to hold.
The interval notation, for instance, might appear as follows if the responses were -3 and 5. (-3,5).
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HELPPPPpp PLEASEEeee
Answer:
the teacher does not have enough paint and he needs 1351.5-1324.8 = 26.7 square cm more paint.
Step-by-step explanation:
The canvas each student has is 5.3 cm wide and 8.5 cm tall. The area of the canvas is (5.3 cm)(8.5 cm) = 45.05 square cm.
The art teacher has 6 bottles of paint, each bottle covers 220.8 square cm of canvas. So he has 6220.8 = 1324.8 square cm of paint.
There are 30 students in the class and each student has a canvas of 45.05 square cm. So in total the students have 30*45.05 = 1351.5 square cm of canvas.
The teacher has 1324.8 square cm of paint and the students have 1351.5 square cm of canvas.
Therefore the teacher does not have enough paint and he needs 1351.5-1324.8 = 26.7 square cm more paint.
approximately what percentage of children will score within the average range of iq testing? group of answer choices 20% 37% 68% 85%
The required interval of the given normal distribution using the empirical rule is [100, 140].
The empirical rule formula (also known as a 68 95 99 rule formula) uses data from a normal distribution to determine the first, second, and third standard deviations, which, respectively, differ from the mean value by 68%, 95%, and 99%. Additionally, it shows that 99.9% of the data fall inside the third standard deviation range (either above or below the mean value). The empirical rule formula is described below with cases that have been resolved.
In the question, we are given that IQ scores for adults aged 20 to 34 years are normally distributed according to N(120, 20), and are asked for the range in which the middle 68% of people in this group score on the test.
N(120, 20) signifies a normal distribution with mean, μ = 120, and the standard deviation, σ = 20.
By the empirical formula, 68% of the data lies within one standard deviation from the mean.
Thus, the required interval is [μ - σ, μ + σ] = [120 - 20, 120 + 20] = [100, 140].
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ASHPREET buys two packages of plates and three packages of forks for the class party she gives the clerk $50 how much was the total. And how much did the clerk give back
The total that Ashpreet bought, given the price of the plates and the forks, is $ 16. 95
The amount that the clerk should give back, given the amount Ashpreet gave the clerk, is $ 33. 05
How to find the total amount ?The total amount that Ashpreet will pay for the two packages of plates and the packages of forks, given the price of the plates and the price of the forks is:
= ( Cost of plates x Number of packages of plates ) + ( Cost of forks x Number of plate packages )
= ( 5. 79 x 2 ) + ( 1. 79 x 3 )
= 11. 58 + $ 5. 37
= $ 16. 95
The amount that the clerk would therefore give back to Ashpreet is:
= Amount Ashpreet paid with - Cost
= 50 - 16. 95
= $ 33. 05
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The rest of the question is:
The price of the packages of napkins and forks is: napkins $ 5.79 and forks $1.79
What is the length of AB?
Answer:4
Step-by-step explanation:
because it is a right triangle so if cb is 2 that makes ac 2 then if you just look at the ab line it’s actually longer so it’s 4 ;)
the largest number that divides two or more numbers evenly
The largest number that divides two or more numbers evenly is greatest common divisor (GCD).
What is GCD, or the greatest common divisor?The biggest positive number that divides any non-zero integer by two or more is known as the greatest common divisor.
The greatest common divisor is the biggest number that divides two or more numbers proportionally (GCD).
How do you calculate a GCD's largest common divisor?Using the LCM method, the steps to calculate the GCD of (a, b) are as follows:
Find the result of a and b in step 1.
Find a and b's least common multiple (LCM) in step two.
Step 3: Dividing the results of Steps 1 and 2.
Step 4: The value that results from division is the most significant common divisor of (a, b).
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the three angles in a traingle are 5x, 6x and 7x. work out the size of the largest angle in the triangle
Answer:
the largest angle is 70
Step-by-step explanation:
180 degrees in a triangle
180=5x+6x+7x
simplify
180=18x
x=10
7x=70
the largest angle is 70 degrees.
a swimming pool had 2.5 million liters some of the water evaporated and now the pool had 2 million liters of water what percent of water evaporated.
show all work
Answer:
4/5 = .8. 20% evaporated
Step-by-step explanation:
2.5 million divded into fifth. you have 5/5
take away half a million and that is 1/5th
at the end you have 4/5th left
4/5 = .8 = 80% left over meaning 20% evaporated
Use the following information in problems 33 and 34. In a survey of 6500 people, 5100 had a car, 2280
had a pet, 5420 had a television set, 4800 had a TV and a car, 1500 had a TV and a pet, 1250 had a car
and a pet, and 1100 had a TV, a car, and a pet.
How many people had a tv and a pet but not a car?
Using a Venn diagram we find that there are 400 people who have a TV and a pet but not a car.
What is a Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
Given, Total of 6500 people, in which,
5100 had car
5420 had a television set
4800 had a TV and a car
1500 had a TV and a pet
1250 had a car and a Pet
1100 had a TV, a car and a pet
Therefore, no of people having a TV and a pet but not car
= n(TV & Pet)-n(TV, car & pet)
= 1500 - 1100
= 400
Hence, there are 400 people who have a TV and a pet but not a car.
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El primo de la señora Martha fue a pedir un préstamo de $1800 bajo las mismas condiciones que la señora Martha ¿cuánto pagara de interés en primo de la señora Martha?
Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
What is interest in a simple definition?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.Interest is the money you owe when borrowing or receive when lending. Lenders calculate interest as a percentage of the loan amount. Consumers can earn interest by lending money (such as through a bond or certificate of deposit) or depositing funds into an interest-bearing bank account.The three types of interest include simple (regular) interest, accrued interest, and compounding interest.Since Mrs. Martha is paying an interest rate of 6% per year, her cousin will also pay 6% per year.
To calculate the amount of interest paid, we can use the formula:
Interest = Principal * Rate * Time
Where:
Principal = $1800Rate = 6% (or 0.06 as a decimal)Time = 1 yearSo:
Interest = $1800 * 0.06 * 1 = $108
Therefore, Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
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Is Ace or Alfonzo correct
Answer:
Ace
Step-by-step explanation:
The range has only one value 100
Alan wants to earn at least $73 trimming trees. He charges $7 per hour and pays $4 in equipment fees. What are the possible numbers of hours Alan could trim
trees?
Use t for the number of hours.
Write your answer as an inequality solved for t.
The number of hours Alan could trim to earn at least $73 is 11.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Charges per hour = $7
Equipment fees = $4
The number of hours to earn at least $73.
7t - 4 ≤ 73
Where t is the number of hours.
Now,
7t - 4 ≤ 73
7t ≤ 73 + 4
7t ≤ 77
t ≤ 11
Thus,
The number of hours is 11.
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A flooring tile ha a hape of a parallelogram Hight i 10cm and bae i 24cm how many tile do you need to fill a room with area 1080 mq
We must first calculate the area of a single tile in order to figure how many floor tiles are required to cover a space that is 1080 square meters.
Since the area of a parallelogram is equal to its base times its height, the tile's area is 24 x 10 cm, or 240 [tex]cm^{2}[/tex].
Since one square meter equals 10,000 square centimeters, we divide by 10,000 to convert this area to square meters: 240 [tex]cm^{2}[/tex] / 10,000 = 0.024 c[tex]m^{2}[/tex]
Thus, a single tile has a surface area of 0.024 square meters.
We divide a room's 1080 square meters by a tile's area to determine how many tiles are required to completely cover the space:
1080 [tex]m^{2}[/tex] / 0.024 [tex]m^{2}[/tex]= 45,000
Therefore ,45,000 floor tiles would be required to cover a space that is 1080 square meters in size.
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What is a no solution line?
There is no solution when the lines that make up a system are parallel since the two lines do not share any points.
A linear equation with two variables has the for [tex]ax + by + c = 0[/tex], where variables are belongs to R. An A system of linear equations that cannot be solved is a pair of inconsistent linear equations. We can determine whether a system of linear equations has no solution by comparing the coefficients of the equations in the system.
Take into account the pair of linear equations in x and y:
[tex]a1x + b1y + c1 = 0\\a2x + b2y + c2 = 0[/tex]
There won't be a solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex].
An inconsistent pair of linear equations is the name given to this kind of equational system. The system of equations cannot be solved if the graph's lines are parallel.
So here, both equations are called no solution line.
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Elsa will spend more than $25 on gifts. So far, she has spent $17. What are the possible additional amounts she will spend?
The required possible amount that she spends additionally is more than $8.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Elsa will spend more than $25 on gifts. So far, she has spent $17.
Let the possible additional amounts she will spend be x,
According to the quesiton,
x + 17 > 25
x > 25 - 17
x > 8
Thus, the required possible amount that she spends additionally is more than $8, as of the given condition.
Learn more about inequality here:
brainly.com/question/14098842
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