Answer:
[tex]a_{n}[/tex] = 5n + 20
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence
30 - 25 = 35 - 30 = 5
this indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 25 and d = 5 , then
[tex]a_{n}[/tex] = 25 + 5(n - 1) = 25 + 5n - 5 = 5n + 20
Find the length of each segment.
Answer:
1. 30; 2. 6.25.
Step-by-step explanation:
1. CE:CF=FD:DG; ⇒ 32/24=40/DG; ⇒ DG=30;
2. PQ:QM=RN:RM; ⇒ 5/8=RN/10; ⇒ RN=6.25.
8) A hexagonal pyramid 10 mi tall with a regular
base measuring 6 mi on each side and an
apothem of length 5.2 mi.
A) 936 mi³
C) 315 mi³
B) 312 mi³
D) 52 mi³
The volume of the pyramid is 936 mi³
What is volume of a pyramid?A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.
The volume of a pyramid is expressed as;
V = 1/3bh
where b is the base area and h is the height of the pyramid.
Area of the hexagon = 1/2 × p × a
perimeter = 6 × 6 = 36 mi
area = 1/2 × p × a
= 1/2 × 36 × 5.2
= 187.2/2
= 93.6 mi²
Volume = 93.6 × 10
= 936 mi³
therefore the volume of the pyramid is 936 mi³
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HELP PLS Triangle D has been dilated to create triangle D′. Use the image to answer the question.
Determine the scale factor used.
Scale factor of one third
Scale factor of 3
Scale factor of 4
Scale factor of one fourth
The scale factor will be one-third which is 1/3. Then the correct option is A.
Given that:
Dimension of a small triangle, 6, 8, and 10
Dimension of a giant triangle, 18, 24, and 30
Dilation is the process of increasing the size of an item without affecting its form. The object's size can be raised or lowered depending on the scale factor. There is no effect of dilation on the angle.
The scale factor is calculated as,
SF = 6 / 18
SF = 1 / 3
The scale factor will be one-third which is 1/3. Then the correct option is A.
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Answer:
1/3
Step-by-step explanation:
I took the test!
A circle has a radius of 9 cm and a sector of the circle has an arc length of 9.7 cm. The angle at the centre of the sector is xº. Calculate the value of x to the nearest degree. 9 cm X 3 9.7 cm
Answer:
62 degrees
Step-by-step explanation:
Hope this helps! If it’s wrong I’m really sorry. I used the formula θ = s/r then converted it from radians to degrees.
Pls give brainliest!
a. Find x. The figure is not drawn to scale. b. Is the triangle equilateral, isosceles, or scalene? Explain.
*
0 points
Captionless Image
Answer: Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,
8x-10 =6x
8x-6x = 10
2x =10
x= 5.
Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.
For many years, businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent survey showed that 52% of employers are likely to require higher employee contributions for health care coverage this year relative to last year. Suppose the survey was based on a sample of 900 companies likely to require higher employee contributions for health care coverage this year relative to last year.
1. At 95% confidence, compute the margin of error for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answer to four decimal places.)
2. Compute a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answers to four decimal places.)
The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage is 0.0344. The 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage is ( 0.4823, 0.5577.).
To compute the margin of error for the proportion, we use the formula:
Margin of error = z*√((P(1-P))/n)
where z is the z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96), P is the sample proportion, and n is the sample size. From the information given, we have
P = 0.52 (sample proportion)
n = 900 (sample size)
z = 1.96 (for 95% confidence level)
Substituting these values into the formula, we get
Margin of error = 1.96√((0.52(1-0.52))/900) ≈ 0.0344
Therefore, the margin of error is approximately 0.0344, or 3.44%.
To compute the confidence interval, we use the formula:
Confidence interval = P ± z*(√((P(1-P))/n))
where P, z, and n are the same as in part 1. Substituting these values into the formula, we get
Confidence interval = 0.52 ± 1.96*(√((0.52*(1-0.52))/900)) ≈ (0.4823, 0.5577)
Therefore, we can say with 95% confidence that the true proportion of companies likely to require higher employee contributions for health care coverage this year relative to last year is between 0.4823 and 0.5577.
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marcus deposits $500 in an account that pays 6.8% simple annual interest. if he keeps the money in the account for 5 years how much interest will he earn
Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.
To calculate the interest Marcus will earn, we can use the formula:
I = P * r * t
where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.
In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.
So we can plug in these values into the formula:
I = 500 * 0.068 * 5
I = $170
This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.
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Identify parallelograms, rectangles and squares
Answer:
figure A = square ( All sides are equal)
figure B = Rectangle (Two sides are equal)
Figure C = parallelogram (is a four-sided polygon (a quadrilateral) in which opposite sides are parallel and equal in length)
Simplify each of the following exponential expressions. a. 7⁴= ? b. (–10)⁴= ? c. 5¹ = ? d. 0⁴= ? e. –6²= ? f. –3⁰= ?
The exponential expressions when simplified are 2401, 10000, 5, 0, 36 and 1
Simplifying each of the exponential expressionsFrom the question, we have the following parameters that can be used in our computation:
The exponential expressions a to f
The general rule is that
a^b = a * a * a..... in b places
Using the above as a guide, we have the following:
a. 7⁴ = 7 * 7 * 7 * 7 = 2401
b. (–10)⁴ = (–10) * (–10) * (–10) * (–10) = 10000
c. 5¹ = 5
d. 0⁴ = 0 * 0 * 0 * 0
e. –6² = -6 * -6 = 36
f. –3⁰ = 1
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Find the sum of x+9 and 7x^- 2x+1.
The sum of given two expressions x+9 and 7x²-2x+1 results in the expression 7x² - x + 10.
To find the sum of two expressions, we simply add their like terms.
The given expressions are x+9 and 7x²-2x+1.
The first expression has two terms - x and 9.
The second expression has three terms - 7x², -2x, and 1.
We cannot add the terms of the two expressions directly since they are not like terms. However, we can simplify the expressions and then add the like terms.
First, we can simplify the second expression by combining the like terms -2x and 1.
7x² - 2x + 1 = 7x² - (2x - 1)
Now, we can add the like terms from both expressions.
(x + 9) + (7x² - 2x + 1) = x + 7x² - (2x - 1) + 9
= 7x² - x + 10
Note that we could also have added the two expressions without simplifying the second expression first. We would get the same result.
(x + 9) + (7x² - 2x + 1) = x + 7x² - 2x + 9 + 1
= 7x² - x + 10
In either case, the final answer is 7x² - x + 10.
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You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)
Calculating the endpoint of the pointFrom the question, we have the following parameters that can be used in our computation:
Start = (0, -4)
Also, we have
You move left 1 unit and right 4 units
Mathematically, this can be expressed as
(x, y) = (x - 1 + 4, y)
Substitute the known values in the above equation, so, we have the following representation
Endpoint = (0 - 1 + 4, -4)
Evaluate the expression
Endpoint = (3, -4)
Hence, the endpoint is (3, -4)
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1/3 divided by 2/9 simplified?
Answer:3/2
Step-by-step explanation:
1/3 ÷ 2/9=
1/3 ×9/2=3/2
Answer:
3/2 u can also do 1 1/2 their equivalent fractions
Step-by-step explanation:
sorry about the handwriting :) not the best
Ben's Barbershop has a rectangular logo for their business that measures 7(1)/(5) feet long with an area that is exactly the maximum area allowed by the building owner. Create an equation that could be used to determine M, the unknown side length of the logo.
An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M
Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:
A = L x W
where A is the area of the logo, L is the length of the logo, and W is the width of the logo.
Substituting the given values, we get:
A = (7(1)/(5)) x M
or
A = (36/5) x M
Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:
A = X
Combining both equations, we get:
X = (36/5) x M
This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.
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Suppose that the demand of a certain item is x=-0.7p+10.
Evaluate the elasticity at 6.
The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.
What is the item's demand if elasticity is at 6?The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)
The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.
Let say Initial quantity demanded is:
x = -0.7(6) + 10
x = 5.8
Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:
= -0.7(6.01) + 10
= 5.793
The % change in quantity demanded will be:
= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%
= [(5.793 - 5.8) / 5.8] x 100%
= -0.12%
As price has changed from 6 to 6.01, we can calculate the percentage change as follows:
% change in price = [(new price - initial price) / initial price] x 100%
= [(6.01 - 6) / 6] x 100%
= 0.17%
Elasticity of demand = (% change in quantity demanded) / (% change in price)
= (-0.12% / 0.17%)
= -0.71
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1234-4566/45.44+67*755.34
Answer:
To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
The expression is:
1234 - 4566 / 45.44 + 67 * 755.34
First, we need to perform the division operation since it comes before addition and multiplication.
4566 / 45.44 = 100.50
Now, we can substitute that into the expression:
1234 - 100.50 + 67 * 755.34
Next, we need to perform the multiplication operation:
67 * 755.34 = 50,548.78
Now, we can substitute that into the expression:
1234 - 100.50 + 50,548.78
Next, we can perform the addition and subtraction operations:
1234 + 50,448.28 = 51,682.28
Therefore, the result of the expression is 51,682.28.
Which value of y is a solution of this inequality?
3y-4<11
A. y=4
B. y=5
C. y=6
D. y=7
Answer:
B. y=5
Step-by-step explanation:
3y-4<11
3y-4+4<11+4
3y<15
3y/3<15/3
y<5
Lawrence is increasing the rectangular patio in his backyard. His patio is currently 12
feet by 10 feet. He wants to increase the patio by adding a decorative tile the same width (x) all the way around creating a total area of 180 square feet. Select all the quadratic equations that represent Lawrence’s new patio area.
The quadratic equation representing the new patio area after adding a decorative tile of width x all the way around is: 0 = 4x^2 + 44x - 60
Options A and E are correct.
What is a Quadratic Function?In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Since the area of the new patio is given as 180 square feet, we can create a quadratic equation to represent the new patio area:
Area = length × width
180 = (12 + 2x) × (10 + 2x)
After we expand, the answer is given as 0 = 4x^2 + 44x - 60
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Please help!
Whoever answers right gets brainliest!!!!
Answer:
[tex]y - 4 = - 3(x - 2)[/tex]
Given ƒ(x) = −2x² + x − 8, find ƒ (9)
Answer: -161
Step-by-step explanation: you solve by plugging 9 in for x so you get f(9) = -2(9)^2 +9-8 you solve using PEMDAS and you get -161
CAN SOMEONE HELP WITH THIS QUESTION?
The number of cars that pass through the intersection between 6 am and 10 am is 4800.
To find the number of cars that pass through the intersection between 6 am and 10 am, we need to integrate the traffic flow rate function r(t) over the interval [0,4].
Integrating r(t) with respect to t, we get:
∫(400+ 600t - 150t²)dt = 400t + 300t² - 50t³ + C
where C is the constant of integration.
Evaluating this expression between t=0 and t=4 (since we are interested in the interval between 6 am and 10 am), we get:
(400(4) + 300(4)² - 50(4)³) - (400(0) + 300(0)² - 50(0)³) = 4800 cars
In summary, we can find the number of cars that pass through an intersection between two specific times by integrating the traffic flow rate function over that interval.
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Please im begging someone please help me this is so hard. If you help me ill give you 60 points. PLEASE ILL GIVE BRAINLIEST
Answer: B, C, D
Step-by-step explanation:
Looking at the parabola, this is a width vs area graph.
A) Incorrect. the greatest possible area is not 10. Area goes higher
B) True. The highest possible area, highest point for area is 100
C) True. The area is 0 when width is 0
D)True. The area is also 0 when the width is 20
Determine the equation of the circle graphed below.
The equation of the circle graphed is (x + 4)^2 + (y + 5)^2 = 16
Determining the equation of the circle graphedFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (-4, -5)
Radius, r = 4 units
The equation of the circle graphed is represented as
(x - a)^2 + (y - b)^2 = r^2
So, we have
(x + 4)^2 + (y + 5)^2 = 4^2
Evaluate
(x + 4)^2 + (y + 5)^2 = 16
Hence, the equation is (x + 4)^2 + (y + 5)^2 = 16
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The table below shows different possibilities for the number of games a team would
need to win to maintain a certain percentage of wins.
A 18 20
B 30 20
POSSIBLE BASEBALL
GAMES WON
C 18 30
D 50 30
Number of
Games Won
6
24
36
42
Which ratio of the number of games won to the number of games played could also be
included in this table?
Number of
Games Played
10
40
60
70
The ratio that could also be included in this table is (c) 18 : 30
Calculating the ratio that could also be included in this table?From the question, we have the following parameters that can be used in our computation:
Games won Games played
6 10
24 40
36 60
42 70
From the above, we have the ratio of the number of games won to the number of games played to be
Ratio = 6 : 10
Simplify
Ratio = 3 : 5
From the options, we have
(c) 18 : 30
Simplify
Ratio = 3 : 5
Hence, the ratio that could also be included in this table is (c) 18 : 30
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Mathematics
Find the rate
What percent of 200 is 50?
What percent of 50 is 40?
What percent of 10 is 6?
200 is what percent of 200?
What percent of 800 is 200?
Show your solution, HELP PLS ASAP!!!
I'LL GIVE 20 POINTS!!
Answer:
Step-by-step explanation:
25%
80%
60%
100%
25%
A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70 degree?
______m^2
The area of a sector is 8.75 [tex]m^{2}[/tex].
What is a sector?A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
where r is the radius, and θ is the central angle.
Given a circle whose area is 45 sq. m.; then;
area of a circle = π[tex]r^{2}[/tex]
45 = π[tex]r^{2}[/tex]
r = [tex]\sqrt{\frac{45}{\pi } }[/tex]
Then,
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
= ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]
= [tex]\frac{7}{36}[/tex]*π*45/π
= [tex]\frac{7}{36}[/tex]*45
= 8.75 sq. m.
The area of the sector is 8.75 [tex]m^{2}[/tex].
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a⃗ =⟨4, −3⟩ and b⃗ =⟨−1,−2⟩.
Represent a⃗ +b⃗ by using the head to tail method.
Use the Vector tool to draw the vectors, complete the head to tail method, and draw a⃗ +b⃗ . Do not draw any unnecessary vectors.
To use the Vector tool, select the initial point and then the terminal point.
The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,
a + b = < 3, -5 >
The graph of the vector sum is given below.
The addition of vectors suggests the addition of the corresponding components of the involving vectors.
Given the vectors are:
a = < 4, - 3 >
b = < - 1, - 2 >
So doing vector addition we get,
a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>
Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.
Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,
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Answer: Look at the image below
Step-by-step explanation: I took the test.
Step 1: Select Vector
Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)
Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)
Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)
Your answer should now look like mine, now go get that A.
Select the correct answer.
What are the zeros of g(x) = x³ + 6x² - 9x-54?
A. 1, 2,27
B.3, -3, -6
C.-6, 3, 6
D. 2, -1, 18
Answer:
The answer is C
Step-by-step explanation:
The zeros of g(x) = x³ + 6x² - 9x-54 are -6, 3, 6. Therefore, the correct answer is C.
Someone help please! I’m taking a test and just need some assistance
Answer: Given b=2√14 and c=9,
a = 5
Step-by-step explanation:
CAN SOMEONE HELP WITH THIS QUESTION?
a) The velocity function is v(t) = -3 cos(t) - 1.
b) The object's displacement is 3sin(3) - K - 3.
c) The total distance traveled by the object from time 0 to time 3 is 3sin(3) + 3 meters.
a) To find the equation for the velocity of the object, we need to integrate the function for acceleration with respect to time. The velocity function v(t) is the antiderivative of a(t). Since a(t) = 3 sin(t), the antiderivative of a(t) is v(t) = -3 cos(t) + C, where C is the constant of integration.
We can find C using the initial velocity given. Since v(0) = -2m/s, we substitute t=0 and v(0) = -2m/s into the velocity function to get:
v(0) = -3 cos(0) + C = -2
Solving for C, we get C = -1. Now we can write the velocity function as:
v(t) = -3 cos(t) - 1
b) To find the displacement of the object from time 0 to time 3, we need to integrate the velocity function with respect to time over the interval [0,3]. The displacement function s(t) is the antiderivative of v(t):
s(t) = ∫v(t) dt = ∫(-3cos(t) - 1) dt = 3sin(t) - t - K
where K is the constant of integration. Since we want to find the displacement from time 0 to time 3, we evaluate s(3) - s(0):
s(3) - s(0) = (3sin(3) - 3) - (0 - K) = 3sin(3) - K - 3
c) To find the total distance traveled by the object from time 0 to time 3, we need to calculate the area under the absolute value of the velocity curve over the interval [0,3]. Since the velocity is negative for some time intervals, we take the absolute value of the velocity function:
|v(t)| = |-3cos(t) - 1| = 3cos(t) + 1
We can integrate this function from 0 to 3 to get the total distance traveled:
∫|v(t)| dt = ∫(3cos(t) + 1) dt = 3sin(t) + t + C
Evaluating this at t=3 and t=0, we get:
∫|v(t)| dt = (3sin(3) + 3) - (0 + 0) = 3sin(3) + 3
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Point A is at 0 radians with coordinates (1,0) on the unit circle. Point B is the result of point A rotating 7 pie/6 radians counterclockwise
around the unit circle. Name two other positive angles of rotation that take A to B.
Answer:
19π/6 radians and 31π/6 radians
Step-by-step explanation:
To rotate point A counterclockwise by 7π/6 radians, we can add this angle to the angle of point A, which is 0 radians, to get the angle of point B:
The angle of point B = angle of point A + 7π/6 radians
= 0 radians + 7π/6 radians
= 7π/6 radians
Angle of point B in degrees = (7π/6) * (180/π) degrees
= 210 degrees
To find two other positive angles of rotation that take A to B, we can add any multiple of 2π radians to the angle of point B. This is because adding 2π radians is equivalent to a full rotation around the unit circle, which brings us back to the same point. Therefore, we have:
angle of rotation 1 = angle of point B + 2π radians
= 7π/6 radians + 2π radians
= 19π/6 radians
angle of rotation 1 in degrees = (19π/6) * (180/π) degrees
= 285 degrees
angle of rotation 2 = angle of point B + 4π radians
= 7π/6 radians + 4π radians
= 31π/6 radians
angle of rotation 2 in degrees = (31π/6) * (180/π) degrees
= 465 degrees
So the two other positive angles of rotation that take A to B are (19π/6 radians and 31π/6 radians) or 285 degrees and 465 degrees respectively.
Note:
To convert the angles from radians to degrees, we can use the conversion factor:
1 radian = 180/π degrees