The explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
The recursive rule is given as:
[tex]a_n=a_{n-1}+7[/tex]
[tex]a_1 = 17[/tex]
The above shows that the sequence is an arithmetic sequence.
Start by calculating a2
We have:
[tex]a_n=a_{n-1}+7[/tex]
Substitute 2 for n
[tex]a_2=a_1+7[/tex]
This gives
[tex]a_2 = 17 + 7[/tex]
[tex]a_2 = 24[/tex]
So, we have:
a1=17
a2 = 24
The common difference (d) is:
d =a2 - a1
d = 24 - 17
d = 7
The explicit rule is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 17 + (n - 1) * 7[/tex]
Expand
[tex]a_n = 17 - 7 + 7n[/tex]
[tex]a_n = 10 + 7n[/tex]
Hence, the explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
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Solve the system of equations and choose the correct answer from the list of options. (4 points) x − y = 7 y = 3x + 12
Simplify the trigonometric expression.
A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?
ANYONE WHO KNOWS SURFACE AREA!!!
I need help urgently!
What is the sum or difference 6x^7+8x^7
The sum of the expressions 6x^7 and 8x^7 is 14x^7. This follows the simple rule of addition with similar terms, where the coefficients are added together while the variable remains the same.
Explanation:The sum of 6x7 and 8x7 follows the usual rules of addition, it treats similar terms in a similar way to ordinary numbers. To combine these expressions, you simply add or subtract the coefficients (the number parts), while keeping the variables (the letter parts) the same. In this case, the variable is x7. Thus, adding the coefficients 6 and 8 gives you 14, and you keep the x7 the same. The sum is therefore 14x7.
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A carpenter earns $18 an hour for a regular work week (40) hours. He earns time and a half for overtime. The weekly wage function is W(h)={ 18h 040} where h is the number of hours worked for the week. Find the wage if the carpenter worked 42.5 hours in the week
Final answer:
To find the carpenter's weekly wage after working 42.5 hours, we calculate the regular pay for 40 hours at $18 per hour, which is $720, and then add the earnings from 2.5 hours of overtime at time and a half ($27 per hour), which is $67.5. The total weekly wage is $787.5.
Explanation:
To calculate the weekly wage of the carpenter who worked 42.5 hours, with $18 per hour for the first 40 hours and time and a half for overtime, we will use the wage function provided: W(h) = 18h for hours up to 40, and for hours above 40, it's (18 × 1.5) × (h - 40). Let's apply this to the 42.5 hours worked.
The carpenter's earnings for the regular 40 hours are $720 (which is 40 hours × $18). For the 2.5 hours of overtime, he earns time and a half, which is $27 per hour (18 × 1.5). The overtime earnings are $67.5 (2.5 hours × $27). So, the total wage is:
$720 + $67.5 = $787.5
Therefore, the carpenter's weekly wage for working 42.5 hours at the given rate is $787.5.
A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?
Please explain “ write the equation of the perpendicular bisector of rs point r is located at (-1,3) and point s is located at (3,1) “
You buy a new yoga ball. The ball has a diameter of 26 inches. What is the volume of the ball? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer:
The volume of the ball is [tex]9,198.11\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere (yoga ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]r=26/2=13\ in[/tex] -----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}(3.14)(13^{3})=9,198.11\ in^{3}[/tex]
What is the y-intercept of the function f(x) = –2/9 + 1/5
Need help to write equations for 5, 6 & 7
What is the standard deviation of the following data set rounded to the nearest tenth? 52.1, 45.5, 51, 48.8, 43.6
Answer:
Standard deviation is 3.2.
Step-by-step explanation:
Given data is,
52.1, 45.5, 51, 48.8, 43.6,
Let x represents the data points,
Now, mean of the data is,
[tex]\mu = \frac{52.1 + 45.5 + 51 + 48.8 + 43.6}{5}=48.2[/tex]
Population size, N = 5,
Hence, the standard deviation of the following data set is,
[tex]\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu )^2[/tex]
[tex]=\sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i-48.2 )^2[/tex]
[tex]=\sqrt{\frac{1}{5} (15.21+7.29+7.84+0.36+21.16)}[/tex]
[tex]=\sqrt{10.372}[/tex]
[tex]=3.2205589577[/tex]
[tex]\approx 3.2[/tex]
O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale.
Assuming that lines that appear to be tangent are tangent, what is the value of x?
Hamilton received a 75 on his algebra exam. The professor is allowing students to take a 7-question bonus quiz to improve their algebra exam score. Each question answered correctly on the bonus quiz will add 3 points to the exam score. Hamilton needs to receive at least a 90 on his exam score in order to make an "A" for the semester. If x represents the number of questions answered correctly on the bonus quiz, which of the following inequalities symbolizes this situation?
A. 3x + 75 < 90
B. 7x + 75 > 90
C. 3x + 75 > 90
D. 7x + 75 < 90
Final answer:
The correct inequality should be 3x + 75 ≥ 90 to indicate Hamilton needs at least 90 on his exam. The closest option given, which is not entirely accurate, is C. 3x + 75 > 90.
Explanation:
To determine the inequality that represents Hamilton’s situation, we need to calculate how many points he requires to reach a score of at least an “A”, which is 90. Each correct bonus question adds 3 points to his exam score of 75. We need to find the number of questions, x, Hamilton must answer correctly to achieve a total score of 90 or more. Therefore, the inequality that encompasses this scenario is 3x + 75 ≥ 90 because each correct answer contributes 3 points towards closing the 15-point gap between his current score and the desired score of 90.
However, the options given do not include the correct representation which would be 3x + 75 ≥ 90. Instead, the closest option is C. 3x + 75 > 90, which would imply that Hamilton must score more than 90, which is not a requirement for making an “A” (as “A” can include exactly 90).
Need this geometry answer quick!
1/2g^2 + 7/2 + 3g^2- 4/5g + 1/4
The expression [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4[/tex]5/4 by combining like terms, which include the [tex]g^2[/tex]s and the constants.
Explanation:The student's question involves combining like terms and simplifying a polynomial expression in mathematics. The expression provided is [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4.[/tex]ed to combine like terms, which involves adding or subtracting the coefficients of terms with the same degree.
First, combine the g2 terms (1/2g2 + 3g2) to get 7/2g2. Next, the constant terms (7/2 + 1/4) are combined to yield 15/4. The term with g, which is -4/5g, does not have a like term, so it remains as it is. After combining like terms, the simplified expression is 7/2g2 - 4/5g + 15/4.
A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. you choose one marble from the jar at random. what is the theoretical probability of choosing a white marble?
The function f(x) = 12x + 50 gives the amount of money a worker earns for working x hours per week. What is the inverse function?
PLEASE HELP AS SOON AS POSSIBLE!!!!!!!!!!!!!!!!!! |r+3| ≥7 solve the inequality (please show work and steps )
Quadrilateral ABCD has the following vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6). Quadrilateral ABCD is a
A. trapezoid
B. parallelogram
C. square
D. rectangle
the answer is TRAPEZOID
An investment of $450 increases at a rate of 6.5% per year. What is the growth factor, b?
From a point on a circle, two perpendicular chords are drawn. One is 6 cm from the center and the other one is 3 cm from the center. Find the lengths of these chords.
2=sqrt P solve for P
The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area?
what is the volume , in cubic units , of a pyramid of height 8 and a square base of length 15?
Students washed cars to raise funds for their school. they collected $291 by charging $3.00 per car. how many cars did they wash?
Find the surface area of the equilateral triangular pyramid.
In a certain population, 95% of the people have rh-positive blood. suppose that two people from this population get married. what is the probability that they are both rh-negative, thus making it inevitable that their children will be rh-negative? web assign answer
Final answer:
The probability that both partners in a marriage are Rh-negative in a predominantly Rh-positive population is 0.25% or 1 in 400, critical for understanding the risk of hemolytic disease of the newborn in subsequent pregnancies.
Explanation:
The probability that both people in a marriage are Rh-negative in a population where 95% of the people are Rh-positive is calculated using the complement. Assuming that 5% of the population is Rh-negative, we would calculate the probability that both parents are Rh-negative by multiplying the individual probabilities:
P(both Rh-negative) = P(one Rh-negative) × P(other Rh-negative) = 0.05 × 0.05 = 0.0025
Therefore, the probability that both people are Rh-negative, and thus all of their children would also be Rh-negative, is 0.25% or 1 in 400.
Rh factor and blood type compatibility are crucial in reproduction and transfusion medicine. Understanding these concepts can help prevent complications such as hemolytic disease of the newborn, which occurs during second or subsequent pregnancies due to sensitization of the Rh-negative mother's immune system to Rh-positive fetal cells from a previous pregnancy.
Need help to write equations for 5, 6 & 7
What is cos 45? Please HELP !!!
Answer:
A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Step-by-step explanation:
Given : Triangle 90 -45 -45 .
To find : What is cos 45.
Solution : We have given
Triangle 90 -45 -45
Hypotenuse = √2 ,
Adjacent side to 45 degree = 1 .
By the trigonometric ratio : cosine is the ratio of the adjacent side to angle to the hypotenuse .
Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].
Plug the values Hypotenuse = √2 , Adjacent side to 45 degree = 1 .
Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
The cosine of 45° is √2 / 2.
In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.
In this case, we want to find the cosine of 45°.
The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.
Using the formula for cosine, we have:
cos 45° = adjacent side / hypotenuse
Substituting the values, we get:
cos 45° = 1 / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
cos 45° = (1 / √2) * (√2 / √2) = √2 / 2
Therefore, the cosine of 45° is √2 / 2.
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