Answer:
I hope this helps please rate my answer
Step-by-step explanation:
2/5×60
2×12=24
22 The regular selling price is a 22" tube television is $389. The markdown rate is 33%. Use the
percent paid to determine the sale price.
A. $245.34
C. $260.63
B. $267.89
D. $287.56
The Sale price is C. $260.63.
What is selling price?Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.
What is sale price?Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.
In the given question,
To find the sale price, we need to first calculate the amount of the markdown:
Markdown = Regular Price x Markdown Rate
Markdown = $389 x 0.33
Markdown = $128.37
The sale price is then the regular price minus the markdown:
Sale Price = Regular Price - Markdown
Sale Price = $389 - $128.37
Sale Price = $260.63
Therefore, the answer is C. $260.63.
To know more about sale price, visit:
https://brainly.com/question/29363568
#SPJ1
i have an assignment, its 2n + 10 = 90 our teacher is asking whats the n can someone help, with solutions is okay :)
Answer: n=40
Step-by-step explanation:
let me know if i got this right for you broski
now dance
the radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.6 in/s. at what rate is the volume of the cone changing when the radius is 144 in. and the height is 138 in.?
Answer:
Let's use the formula for the volume of a right circular cone to solve this problem:
V = (1/3)πr^2h
We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.
Using the chain rule of differentiation, we can express the rate of change of the volume as follows:
dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)
To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:
dV/dr = (2/3)πrh
dV/dh = (1/3)πr^2
Substituting the given values and their rates of change, we have:
dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)
dV/dt = 55,742.4 - 1,994,598.4
dV/dt = -1,938,856 in^3/s
Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.
Step-by-step explanation:
Given the following key, what polynomial is modeled by the diagram below?
The polynomial function modeled by the given diagram is given as follows:
p(x) = 3x² - 7x - 6.
How to obtain the polynomial function?The polynomial function modeled by the given diagram is obtained considering the keys of the problem, which are the terms represented by each figure.
The polynomial is constructed as follows:
3 large non-shaded squares: 3x².Two non-shaded rectangles: 2x.Nine shaded rectangles: -9x.Six shaded small squares: -6.Then the expression used to construct the polynomial is given as follows:
p(x) = 3x² + 2x - 9x - 6.
Combining the like terms, the polynomial function is defined as follows:
p(x) = 3x² - 7x - 6.
More can be learned about polynomial functions at https://brainly.com/question/7693326
#SPJ1
Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2
No, the given value of h=2 is not a solution of the equation 1/3h=6.
The data in the table below shows the average temperature in Northern Latitudes:
Estimate to the nearest whole number the average temperature for a city with a latitude of 48.
[___________]
Therefore , the solution of the given problem of mean comes out to be 15 is the solution.
What is mean?The sum of all values divided by all of the values constitutes the result from a collection, also referred to as the arithmetic mean. It is often referred to be known as "mean" as well as is one of the most frequency used main trend indicators. To find the answer, multiply the collection's overall amount of numbers by all of its values. Either the original data or data which has been combined into frequency charts can be used for calculations.
Here,
We can use linear interpolation between the two closest latitude numbers in the table, 45 and 50, to determine the typical temperature for a city with a latitude of 48.
Let T(45) and T(50) represent the typical temperatures at respective latitudes of 45 and 50, respectively. The following algorithm can be used to determine the temperature at 48 degrees latitude:
=> T(48) = T(45) + (T(50) - T(45)) * (48 - 45)/(50 - 45)
Using the numbers from the table as inputs, we obtain:
=> T(48) = 14 + (16 - 14) * (48 - 45)/(50 - 45)
=> T(48) = 14 + 2 * 3/5
=> T(48) = 14 + 1.2
=> T(48) = 15.2
The estimated average temperature for a city with a latitude of 48 is 15, rounded to the closest whole number.
Consequently, 15 is the solution.
To know more about mean visit:
https://brainly.com/question/30094057
#SPJ1
The following product can be expanded into a power series with coefficients ak:
expression is given in attach file.
Find the coefficients ak in front of the individual xk terms for all k 2 N
Using coefficients ak, the following product may be extended into a power series: the expression is provided in the attached file. For each of the [tex]k 2 N[/tex]phrases, determine the coefficients ak before them. The formula [tex]ak = (-1)k(k+1)/2[/tex] yields the coefficients ak.
To get the coefficients ak, we may first simplify the above formula by factoring out a -x and rearranging terms. This results in the equation: [tex](1-x)/(1+x)2 = -x/(1+x) - x2/(1+x)2.[/tex]
Now, each term in the statement may be expanded into a power series using the formula for the geometric series. This results in: Both[tex]-x/(1+x) and -x2/(1+x)2[/tex] are equal to[tex]-x + x + x + 2 + x + 3 +...[/tex]
By combining like terms and adding these two power series, we can determine that the coefficient in front of [tex]xk is (-1)k(k+1)/2.[/tex] Hence,[tex]ak = (-1)k(k+1)/2[/tex] is the formula for the coefficients ak.
learn more about power series here:
https://brainly.com/question/29896893
#SPJ4
Find the interest refund on a 35-month loan with interest of $2,802 if the loan is paid in full with 13 months remaining.
Answer: $1,071.54
Step-by-step explanation:
To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:
Monthly interest = Total interest / Number of months
Monthly interest = $2,802 / 35
Monthly interest = $80.06
Total interest charged on the loan = Monthly interest x Number of months
Total interest charged on the loan = $80.06 x 35
Total interest charged on the loan = $2,802.10
Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:
Interest for remaining 13 months = Monthly interest x Remaining months
Interest for remaining 13 months = $80.06 x 13
Interest for remaining 13 months = $1,040.78
Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:
Interest refund = Total interest charged - Interest for remaining months
Interest refund = $2,802.10 - $1,040.78
Interest refund = $1,074.32
Therefore, the interest refund on the loan is $1,074.30.
I need helppp, I’ll give brainliest
The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].
what is range ?The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].
given
The collection of all x-values for which h(x) is specified is the domain of the function h.
The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.
The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.
The range is therefore [-3, 0].
To know more about range visit:
https://brainly.com/question/28135761
#SPJ1
The complete question is :- The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.
-2
-3-
4-
domain =
range =
There are two coins in a bin. When one of them is flipped it lands on heads with probability 0.6 and when the other is flipped, it lands on heads with probability 0.3. One of these coins is to be chosen at random and then flipped. a) What is the probability that the coin lands on heads? b) The coin lands on heads. What is the probability that the chosen coin was the one that lands on heads with probability 0.6?
The probability that the coin lands on heads if one of them is flipped and lands on heads with probability 0.6 is 0.6 × 1/2 + 0.3 × 1/2 = 0.45. Therefore, the probability that the coin lands on heads is 0.45.
a) Let A be the event that the chosen coin is the one that lands on heads with probability 0.6 and B be the event that the coin lands on heads. Then, the required probability is P(A | B) = P(A and B) / P(B) .
Here, P(A and B) = probability that the chosen coin is the one that lands on heads with probability 0.6 and it actually lands on heads.
Since the probability that the coin lands on heads are 0.45 and the probability that the chosen coin is the one that lands on heads with a probability of 0.6 is 1/2, we have P(A and B) = 0.6 × 1/2 = 0.3. The probability that the coin lands on heads is 0.45.
So, P(B) = probability that the coin lands on heads = 0.45.P(A | B) = P(A and B) / P(B) = 0.3 / 0.45 = 2/3.
Hence, the probability that the chosen coin was the one that lands on heads is 0.6 if the coin lands on heads are 2/3.To learn more about “probability” refer to the: https://brainly.com/question/13604758
#SPJ11
Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z < 0.79) = Х 5 ? (b) P(Z > 0.75) (c) P(-1.06 < Z< 2.17) =
The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).
The probability of Z > 0.75 is 1 - 0.77337 = 0.22663
The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968
Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).
Learn more about Probabilities
brainly.com/question/30034780
#SPJ11
Which exspression is equivalent to 9(4/3m-5-2/3m+2)
By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To simplify the expression,
[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]
Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
To know more about expression visit :-
https://brainly.com/question/14083225
#SPJ1
Using the given variable, write an inequality to model the scenario.
Bowlers that score at least 228 points will make it to the next round.
Let p = the number of points
Answer:
p ≥ 228
Step-by-step explanation:
p ≥ 228
This inequality means the Bowlers have to score at least 228 points to move on.
Hope this helped!
what is the solution to the equality shown?
3m+5>2(m-7)
Hello,
3m + 5 > 2(m - 7) =
3m + 5 > 2m - 14
3m - 2m > - 14 - 15
x > - 29
Step-by-step explanation:
3m±2m>-14-5
5m>-19
m>-19/5
m>3.8
Shade in the regions represented by the inequalities
Answer:
Step-by-step explanation:
see diagram
Use a ruler and pair of compasses to make an accurate drawing of line
AB and its perpendicular bisector, as shown. You must show all of your
construction lines.
Mark point C on your drawing.
Measure the length of AC in your drawing to 1 d.p.
Step-by-step explanation:
1. Draw a line of 8cm.
2. Take a compass and keep it in the length of more than 8 cm.
3. Draw an arc from point A and B which will intersect at point between A and B.
4. Draw a straight line from the arc.
5. You will find out that the line will be drawn exactly between A and B at 4cm.
Below is a list of all possible outcomes in the experiment of rolling two die. 1.2 1,3 14 15 1,6 21 22 23 24 25 2,6 34B2 33 3,4 3 5 3.6 41 4 2 43 4,4 4 5 4,6 5 52 33 5 4 5,5 56 6,1 6,2 6.3 6 4 6,5 6.6 Determine the following probabilities. Write your answers as reduced fractions_ P(sum is odd) P(sum is 5) P(sum is 7) = P(sum is 7 and at least one of the die is a 1) = 18 P(sum is 7 or at least one of the die is 1) = 36
Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, 15, 52, 25, 34, and 43Therefore, the probability of the sum being 7 or at least one die being 1 is:P(sum is 7 or at least one die is 1) = 15/36 = 5/12
Hence, P(sum is odd) = 7/36, P(sum is 5) = 1/9, P(sum is 7) = 1/6, P(sum is 7 and at least one die is 1) = 5/18, and P(sum is 7 or at least one die is 1) = 5/12.
In the given experiment of rolling two dice, the following probabilities are to be determined:
P(sum is odd), P(sum is 5), P(sum is 7), P(sum is 7 and at least one of the die is 1), and P(sum is 7 or at least one of the die is 1).The sum of two dice is odd if one die has an odd number and the other has an even number. The possibilities of odd numbers are 1, 3, and 5, while the possibilities of even numbers are 2, 4, and 6. Therefore, the following outcomes satisfy the condition:
1, 22, 24, 36, 42, 44, and 66Thus, the probability of the sum being odd is: P(sum is odd) = 7/36The sum of two dice is 5 if one die has 1 and the other has 4, or one die has 2 and the other has 3. Thus, the following outcomes satisfy the condition:1, 42, 3Therefore, the probability of the sum being 5 is: P(sum is 5) = 4/36 = 1/9The sum of two dice is 7 if the dice show 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.
Thus, the following outcomes satisfy the condition:1, 63, 54, 45, 36, and 2Therefore, the probability of the sum being 7 is: P(sum is 7) = 6/36 = 1/6The sum of two dice is 7 and at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, or 1 and 5. Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, and 15
Therefore, the probability of the sum being 7 and at least one die being 1 is:P(sum is 7 and at least one die is 1) = 10/36 = 5/18The sum of two dice is 7 or at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, 1 and 5, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.
for such more questions on probabilities
https://brainly.com/question/13604758
#SPJ11
Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 +h). s(6 + h) = Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h. 8(6+h) - s(6) h = Rationalize the numerator in the average velocity. (If it applies, simplify again.) $(6 + h) - $(6) h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero. s(6 + h) – $(6) v(6) lim h -0
The instantaneous velocity of the object at t = 6 is 2.
Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56
Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2
Therefore, the instantaneous velocity of the object at t = 6 is 2.
Learn more about Instantaneous velocity
brainly.com/question/28837697
#SPJ11
some rate functions require algebraic manipulation or simplification to set the stage for undoing the chain rule or other antiderivative techniques. find an equivalent closed form for each function.a. S π / π /4 5t+4 / t² + 1 dtHint : begin by writing as a sum of two functions ____ previewb. S π/t 4tan (t) dt Hint : begin by using a trig identity to change the form of the rate function___ preview
the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)
Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt
Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C
a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt
Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.
Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,
we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:
S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)
dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change
for such more questions on function
https://brainly.com/question/11624077
#SPJ11
Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem. (Round your answer to four decimal places.) y' = x^2 + xy y(0) = 4
By using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429.
The Euler's method is used to estimate a numerical solution of a first-order differential equation. The formula of Euler's method is given by:
y_1 = y_0 + hf(x_0, y_0)
Where: y_1 is the next value of y after one iterationy
0 is the initial value of yy' = f(x, y)h is the step size
This method is an iterative procedure that advances the estimate of y by one step by approximating the curve using a tangent line at each point along the curve.
Given that y(0) = 4 and h = 0.2, we can use Euler's method to estimate y(1) where y(x) is the solution of the initial-value problemy' = x2 + xy, y(0) = 4
Using Euler's method with a step size of 0.2, we get:
1) When x = 0, y = 4
y_1 = y_0 + hf(x_0, y_0) = 4 + 0.2(0 + 4(0))= 4.02
When x = 0.2, y = 4.02
y_2 = y1 + hf(x_1, y_1) = 4.02 + 0.2(0.2^2 + 0.2(4.02))= 4.10523
When x = 0.4, y = 4.1052
y_3 = y_2 + hf(x_2, y_2) = 4.1052 + 0.2(0.4^2 + 0.4(4.1052))= 4.1994144
When x = 0.6, y = 4.1994
4 = y_3 + hf(x_3, y_3) = 4.1994 + 0.2(0.6^2 + 0.6(4.1994))= 4.3032545
When x = 0.8, y = 4.3033
y_5 = y_4 + hf(x_4, y_4) = 4.3033 + 0.2(0.8^2 + 0.8(4.3033))= 4.4174496
When x = 1, y = 4.4174
y_6 = y_5 + hf(x_5, y_5) = 4.4174 + 0.2(1^2 + 1(4.4174))= 4.5429404
Therefore, using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429 (rounded to four decimal places).
To know more about Euler's method: https://brainly.com/question/14286413
#SPJ11
if a watch costs $40 and you must pay 6.5% sales tax how much will the tax be ?
Answer:$2.60
Step-by-step explanation:40*0.065
Answer:42.06
Step-by-step explanation:
Which of the expressions below are equal to 8? Select all that apply. A) 2 + 2 + 2 + 2 B) 4 x 2 C) 1 x 8 D) 8 + 8 E) 4 + 4 + 4 + 4
Answer:
A ,B ,C
Step-by-step explanation:
2+2+2+2 equals 8
4x2 equals 8 and
1x8 equals 8
Answer:
A) 2 + 2 + 2 + 2
B) 4 × 2
C) 1 × 8
Hope this helps!
Step-by-step explanation:
A = 4 + 4 = 8
B = 8
C = 8
D = 16
E = 16
Multiply the polynomials.
(2x² + 6x+6)(3x - 2)
_____________
A. 6x³14x²2 + 6x + 12
B. 6x³ + 14x² + 6x + 12
Wan
C. 6x³22x² - 30x - 12
D. 6x³ + 14x² + 6x - 12
how does the graph of the function g(x) = 2x – 3 differ from the graph of f(x) = 2x?
Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)
Find the value of x.
Answer:
x=1.9
Step-by-step explanation:
[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]
[tex]11x=21.16[/tex]
[tex]X=1.9[/tex]
a random sample of 15 recent college graduates found that starting salaries for attorneys in new york city had a mean of $102,342 and a standard deviation of $21,756. there are no outliers in the sample data set. construct a 95% confidence interval for the average starting salary of all attorneys in the city.
The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a p-value of 1-∝.
So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]
Now, find M as such
[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ
In which is the standard deviation of the population and n is the size of the sample.
[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.
The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.
So the correct answer is:
(91331.94, 113352.06)
Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.
Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.
To learn more about Standard deviation visit here:
brainly.com/question/23907081
#SPJ4
Complete Question:
A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices
A). (89869.82, 114814.18)
B). (90292.73, 114391.27)
C). (91331.94, 113352.06)
D). (90371.37, 114312.63)
A surfboard is in the shape of a rectangle and semicircle. The perimeter is to be 4m. Find the maximum area of the surfboard correct to 2 places.
The maximum area of the surfboard correct to 2 places is 0.67 m².
Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.
Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)
Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)
We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)
Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.
To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),
we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.
Area of surfboard =
[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]
[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]
for such more questions on quadratic equations
https://brainly.com/question/30164833
#SPJ11
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the sixth grade?
The number of students that are in the sixth grade is given as follows:
250 students.
How to obtain the number of students?The number of students is obtained applying the proportions in the context of the problem.
We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.
190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:
0.76n = 190
n = 190/0.76
n = 250 students.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
what is the z-score for the 75th percentile of the standard normal distribution is: 0.67 1.645 1.28 -0.67 -1.28
The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.
The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.
I found one that shows the following:
Z value Table entry
0.67 0.7486
0.68 0.7517
As a result, the Z value for 0.75 is between 0.67 and 0.68.
Interpolation yields the z value of 0.6745.
If you have a TI-84 calculator, you may calculate the z value as follows:
VARS - 2nd (this will show the DISTR menu)
To select invNorm, press 3.
Enter the value for the area/table (0.75)
If you press enter, it will return the z value.
Learn more about Normal distribution:
https://brainly.com/question/28000192
#SPJ4
Complete question:
what is the z-score for the 75th percentile of the standard normal distribution is:
0.67 1.645 1.28 -0.67 -1.28Hunters with dogs walked through the forest. If you count their legs, it will be 78, and if their heads, then 24. How many hunters were there and how many dogs did they have?
From the given data of hunters and do we find out there are 9 hunters and 15 dogs.
Let's assume that there were "h" hunters and "d" dogs.
Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:
2h + 4d = 78
We can simplify this equation by dividing both sides by 2:
h + 2d = 39
We also know that there were 24 heads in total, which includes the hunters and the dogs:
h + d = 24
We can now solve these two equations simultaneously to find the values of h and d.
First, we can solve for h in terms of d from the second equation:
h = 24 - d
We can substitute this expression for h in the first equation:
(24 - d) + 2d = 39
Simplifying and solving for d:
d = 15
Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:
h + d = 24
h + 15 = 24
h = 9
Therefore, there were 9 hunters and 15 dogs.
To learn more about equation click here
brainly.com/question/29657983
#SPJ4