There are 4845 different ways to select 16 questions out of a total of 20 questions on the exam.
To determine the number of different ways you can select 16 questions out of a total of 20 questions, we can use the concept of combinations.
In this case, we want to select 16 questions from a set of 20 questions, and the order in which we select them doesn't matter. This scenario can be represented by the combination formula.
The formula for combinations is given by:
C(n, k) = n! / (k!(n-k)!)
Where:
n is the total number of items in the set (20 questions)
k is the number of items to be selected (16 questions)
! denotes the factorial operation
Using the combination formula, we can calculate the number of different ways to select the questions:
C(20, 16) = 20! / (16!(20-16)!)
= 20! / (16!4!)
= (20 * 19 * 18 * 17) / (4 * 3 * 2 * 1)
= 4845
Know more about combinations here:
https://brainly.com/question/31586670
#SPJ11
If you can help me I’ll be grateful!!!
Answer:
4044.32
Explanation:
6506.08 (total) - 2461.76 (top)=
4044.32 (lateral+top)
Formulae:
total = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
top= T= πr2
You have a ten-sided die with numbers 0 to 9. if you roll a prime number, you get 1 point; if you roll a composite number, you lose 1 point. find the expected value of the number of points you get. (hint: 0 and 1 are neither prime nor composite)
The expected value of the number of points you get is 0.
To find the expected value of the number of points you get, we need to calculate the probability of getting each outcome (rolling a prime number or rolling a composite number) and multiply it by the corresponding points.
Here's how we can do that:
There are 10 possible outcomes when rolling the ten-sided die, each with an equal probability of 1/10.
Prime numbers on the die: 2, 3, 5, 7 (total 4 numbers)
Composite numbers on the die: 4, 6, 8, 9 (total 4 numbers)
For prime numbers (4 possible outcomes):
Probability of rolling a prime number = Number of prime numbers / Total possible outcomes = 4/10 = 2/5
Points gained for rolling a prime number = 1
For composite numbers (4 possible outcomes):
Probability of rolling a composite number = Number of composite numbers / Total possible outcomes = 4/10 = 2/5
Points lost for rolling a composite number = -1
Expected value = (Probability of prime number [tex]\times[/tex]Points gained) + (Probability of composite number [tex]\times[/tex] Points lost)
Expected value = (2/5 [tex]\times[/tex] 1) + (2/5 [tex]\times[/tex] -1)
Expected value = 2/5 - 2/5
Expected value = 0
For similar question on probability.
https://brainly.com/question/30768613
#SPJ11
PLEASE HELP ASAP
Find the missing side in each triangle using any method. Check your answers using a different method. Round answers to the nearest whole number
AC = ? units
DE = ? units
In triangle ABC, the length of AC is 13 units
In triangle DEF, the length of DE is 24 units
By pythagoras theorem we find the missing length
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
In triangle ABC, we have to find length of AC
AC² = 5² + 12²
=25+144
=169
AC=13 units
In triangle DEF, we have to find length of DE
DF² =DE² + EF²
26²=DE² + 10²
676=DE² + 100
576=DE²
DE=24 units
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ1
Sara sells dolls at her doll store. If she has a doll that she sells for $15.55, what would be the total cost of the doll if the sales tax were 6% of the sale price?
Answer:
$16.48
Step-by-step explanation:
If 6% is sales tax, that means that the total cost of the doll is 106% of the original cost. (basically 100% is the originall doll, and you add 6% of the tax). If you convert 106% from percentage form to decimal form (which you do by dividing by 100), 106% is the same as 1.06 times the original cost of the doll.
Thus you do 1.06 x 15.55 = 16.483 which rounds down to $16.48
100 POINTS NEED HELP ASSAP
A student is using a weak computer to design a logo. If the weak computer is the only constraint, should the student use the online version of
downloaded version of a graphic design software? (1 point)
O The downloaded version, because the online version usually requires better equipment than the downloaded version.
O The online version, because the downloaded version usually requires better equipment than the online version.
O The online version, because the downloaded version may have limited bandwidth that limits how quickly the designer can work.
O The downloaded version, because the online version may have limited bandwidth that limits how quickly the designer can work
The online version, because the downloaded version usually requires better equipment than the online version.
The online version of the graphic design software is likely the better option for the student using a weak computer. This is because the online version typically runs on the software provider's servers, rather than on the user's computer.
Therefore, the online version does not require as much processing power or memory from the user's computer, making it more accessible to those with weaker or older machines.
Additionally, the online version may also have the advantage of automatic updates, so the student can always have the latest version of the software without needing to manually download and install updates.
Learn more about Software's here:
https://brainly.com/question/985406
#SPJ1
What is y=4/5x+2 written in standered form
This graph represents an exponential function.
Complete the sentences.
The function's y-intercept is ___ , and the equation of its asymptote is ___. The graph shows that the function ____ by a factor of ____ each time x increases by 1. This function can be represented by the equation _____ .
The function's y-intercept is 4, and the equation of its asymptote is y = 0. The graph shows that the function increases by a factor of [tex]\frac{3}{2}[/tex] each time x increases by 1. This function can be represented by the equation [tex]y = 4(\frac{3}{2})^x[/tex].
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, base, or constant.Based on the graph, we would calculate the value of a and b as follows;
[tex]f(x) = a(b)^x[/tex]
4 = a(b)⁰
a = 4
Next, we would determine value of b as follows;
6 = 4(b)¹
6 = 4b
b = 6/4
b = 3/2
Therefore, the required exponential function is given by;
[tex]y = 4(\frac{3}{2})^x[/tex]
In conclusion, the graph shows that the exponential function increases by a factor of [tex]\frac{3}{2}[/tex] or 1.5 each time x increases by 1.
Read more on exponential equation here: brainly.com/question/28939171
#SPJ1
installation of some software package requires downloading 90 files. on the average, it takes 18 seconds to download one file, with a standard deviation of 10 seconds. what is the probability that the installation of the software package takes more than 28 minutes? answer the following questions before computing the probability. what is the random variable of interest? is it continuous or discrete?
The final answer is So, to compute the probability, we need to find P(Z > 0.2) and subtract it from 1.
The random variable of interest in this scenario is the total time taken to download all 90 files and complete the installation of the software package.
This random variable is continuous since it represents a time duration, which can take on any value within a range. To compute the probability that the installation takes more than 28 minutes, we first need to calculate the mean and standard deviation of the total download time.
The mean download time for one file is given as 18 seconds, so the mean download time for 90 files is (18 seconds/file) * 90 files = 1620 seconds.
The standard deviation of the download time for one file is 10 seconds. Since the files are downloaded independently, the standard deviation of the total download time for 90 files can be calculated using the formula for the standard deviation of the sum of independent random variables:
Standard deviation of the total download time = square root(90) * 10 seconds =[tex]30 * 10[/tex] seconds = 300 seconds.
Now, to find the probability that the installation takes more than 28 minutes (which is equivalent to 28 minutes * 60 seconds = 1680 seconds), we need to standardize the value using the z-score formula:[tex]z = (x - μ) /[/tex]∅
where x is the desired time (1680 seconds), μ is the mean download time (1620 seconds), and σ is the standard deviation (300 seconds).
z = [tex]\frac{(1680 - 1620) }{300}[/tex]= [tex]\frac{60}{300}[/tex][tex]= 0.2[/tex]
Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of 0.2. The probability that the installation takes more than 28 minutes is equal to 1 minus this probability, as we are interested in the probability of the installation taking more time.
To learn more about Standard Deviation, visit here
https://brainly.com/question/29115611
#SPJ4
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3 ≤ x ≤ 7
The average rate of change of the function over the interval 3 ≤ x ≤ 7 is 3/2 or 1.5.
How to find the average rate of changeTo find the average rate of change of a function over an interval, we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a and
b are the endpoints of the interval and f(x) is the function.
Using the values from the table, we have:
a = 3, b = 7
f(a) = 2, f(b) = 8
Therefore, the average rate of change of the function over the interval 3 ≤ x ≤ 7 is:
average rate of change = (f(b) - f(a)) / (b - a) = (8 - 2) / (7 - 3) = 6/4 = 3/2
So the average rate of change of the function over the interval 3 ≤ x ≤ 7 is 3/2 or 1.5.
Learn more about average rate of change at https://brainly.com/question/8728504
#SPJ1
What is the area of the shape below?
15 m
15 m
17 m
7m
Answer:
(1/2)(15)(7 + 15) = (1/2)(22)(15) = 165 m^2
Answer:
165m²
Step-by-step explanation:
First you make it into a triangle and rectangle. The rectangle would be 15x7. The triangle would be 1/2x15x8.
15x7=105
1/2x15x8=60
105+60=165 meters squared
A train travels at 110 miles per hour. At this rate, how far will the train travel in 2 1/2 hours
Answer:
275 miles
Step-by-step explanation:
110/2=55
(2*110)+55
=275
Answer:
275 miles
Step-by-step explanation:
110×2=220
110÷2=55
220+55=275
a pizza restaurant offers 5 different toppings. how many different combinations of pizzas can be made if each pizza can have any number of toppings, including no toppings, but no two pizzas can have the same set of toppings? also, the same topping cannot be used more than once.
Therefore, there are 16,807,680 different combinations of pizzas that can be made if each pizza can have any number of toppings, including no toppings, but no two pizzas can have the same set of toppings and the same topping cannot be used more than once.
There are 2^5 = 32 possible combinations of toppings for a single pizza, since each topping can either be included or not. However, since no two pizzas can have the same set of toppings, once a combination is used for one pizza, it cannot be used again.
Therefore, for the first pizza, there are 32 possible combinations of toppings. For the second pizza, there are only 31 possible combinations left, since the combination used for the first pizza cannot be used again. For the third pizza, there are 30 possible combinations left, and so on.
So the total number of different combinations of pizzas that can be made is:
32 x 31 x 30 x 29 x 28 = 16,807,680
To know more about combinations,
https://brainly.com/question/29978135
#SPJ11
Please help I also need to round to the nearest tenth is necessary
The volume and the surface area is 85.33π in³ and 16π in² respectively.
Given that a sphere of diameter 8 in, we will find it surface area and volume,
Surface area of a sphere = 4π × radius²
= 4π × (8/2)² [∵ diameter = 2 × radius]
= 16π in²
Volume of a sphere = 4π/3 × radius³
= 4π/3 × 4³
= 256π/3
= 85.33π in³
Hence the volume and the surface area is 85.33π in³ and 16π in² respectively.
Learn more about sphere click;
https://brainly.com/question/12063484
#SPJ1
Evaluate The Integral: 4 4/5 T3 − 3/4 T2 + 2/5 T (Dt) 0
To evaluate the given integral, we need to plug in the limits of integration, which are 0 and 4, into the antiderivative of the integrand.
The antiderivative of 4/5 t^3 - 3/4 t^2 + 2/5 t is:
(4/5) * (t^4/4) - (3/4) * (t^3/3) + (2/5) * (t^2/2) + C
where C is the constant of integration.
Now, plugging in the limits of integration:
[(4/5) * (4^4/4) - (3/4) * (4^3/3) + (2/5) * (4^2/2)] - [(4/5) * (0^4/4) - (3/4) * (0^3/3) + (2/5) * (0^2/2)]
Simplifying this expression, we get:
(256/5 - 64 + 16/5) - (0 - 0 + 0)
= 240/5
= 48
Therefore, the value of the given integral is 48.
To learn more about integration click here : brainly.com/question/31109342
#SPJ11
To evaluate the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt, we can use the power rule of integration.
Applying the power rule, we can integrate each term of the polynomial separately:
∫ (4/5t^3) dt = (4/5) * (1/4) * t^4 + C1 = t^4/5 + C1
∫ (-3/4t^2) dt = (-3/4) * (1/3) * t^3 + C2 = -t^3/4 + C2
∫ (2/5t) dt = (2/5) * (1/2) * t^2 + C3 = t^2/5 + C3
Adding the constants of integration, we can write the complete integral:
∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt = (t^4/5 + C1) - (t^3/4 + C2) + (t^2/5 + C3)
To evaluate the definite integral between the limits 0 and 4, we substitute the upper limit (4) and lower limit (0) into the expression:
[(4^4/5 + C1) - (4^3/4 + C2) + (4^2/5 + C3)] - [(0^4/5 + C1) - (0^3/4 + C2) + (0^2/5 + C3)]
Simplifying the expression further, we get:
[(1024/5 + C1) - (0 + C2) + (16/5 + C3)] - [(0 + C1) - (0 + C2) + (0 + C3)]
Since the constants of integration cancel out, we are left with:
[(1024/5) - (0) + (16/5)] - [(0) - (0) + (0)]
= 1024/5 + 16/5
= 1040/5
= 208
Therefore, the value of the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt is 208.
To learn more about integration : brainly.com/question/31744185
#SPJ11
What is the y-intercept the equation y=(x+4)2? The equation you wrote to answer the last question should help you. (Only enter the y-coordinate.)
Answer:
x-intercepts: (-4,0)
y-intercepts: (0,16)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
have a great day and thx for your inquiry :)
Choose the representation that is INCORRECT and does NOT match the others.
Answer:
The table is the incorrect representation.
please help my answers are wrong
The proof that shows that sides SP is congruent to side TR is explained below.
How to Prove that Sides SP and TR are Congruent to Each Other?First, using the given information, we have to establish that both triangles are congruent to each other, then state that the two sides are congruent since corresponding parts of congruent triangles are congruent.
Therefore, the correct proof is:
Statement Reason
1. QP ≅ QR; SQ ≅ TQ 1. Given
2. <SQP ≅ <TQR 2. Vertical Angle Theorem
3. ΔSQP ≅ ΔTQR 3. SAS congruence theorem
4. SP ≅ TR 4. Corresponding parts of congruent
triangles are congruent.
Learn more about congruent triangles on:
https://brainly.com/question/1675117
#SPJ1
WILL GIVE BRAINLIST TO BEST ANSWER
Find the value of x that makes lines u and v parallel
If those two angles = 180, then lines u and v are parallel.
90 + (x+102) = 180
192 + x = 180
x = 180-192
x = -12
So if x = -12, then lines u and v are parallel.
Answer:
x = -12
Step-by-step explanation:
We know that the right angle measuring 90° on line u and the (x + 102)° angle are both same side interior angles. When two lines are parallel, the measure of their same interior angles are always equal to 180. Thus, we can solve for x by making the sum of the 90° right angle and the (x + 102)° angle equal to 180:90 + x + 102 = 180
192 + x = 180
x = -12
Therefore, in order for lines u and v to be parallel, the value of x must be -12
Find the values of x and y in the picture
Answer:
x = 56y = 75Step-by-step explanation:
You want the measures of the angles marked x° and y° in the given diagram.
Inscribed angleThe measure of an inscribed angle is half the measure of the arc it intercepts. This means any inscribed angles that intercept the same arc will have the same measure.
The inscribed angles with vertices J and K both intercept arc FH, so both have the marked measure of 56°.
x = 56
Angle at chordsThe angle where the chords cross (y°) will be half the sum of the arcs those chords intercept. Here, those are arcs FH and JK.
Given that half the arc measure is the measure of the intercepting inscribed angle, we can simply sum the inscribed angles to get y°:
y° = 56° +19° = 75°
y = 75
#95141404393
you need to run stats testing on sales data from two different buffalo wild wings stores to see if there's a correlation between number of employees and customer satisfaction. the test you want is a:
If there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis.
To run stats testing on sales data from two different Buffalo Wild Wings stores, we need to use a correlation analysis. Specifically, we need to use Pearson's correlation coefficient to determine if there is a relationship between the number of employees and customer satisfaction. The Pearson's correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation and +1 indicating a perfect positive correlation. If the coefficient is close to zero, it indicates that there is no correlation.
The data we need to collect includes the number of employees in each store and the sales data for a specific period. We also need to gather customer satisfaction data, which can be collected through surveys or other feedback mechanisms. Once we have the data, we can use a statistical software program like SPSS or Excel to perform the correlation analysis.
If the correlation coefficient is positive and statistically significant, it means that there is a relationship between the number of employees and customer satisfaction. This could mean that more employees lead to better customer service, which in turn leads to higher customer satisfaction and sales. However, if the correlation is negative or not statistically significant, it means that there is no relationship between the two variables.
In conclusion, to determine if there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis. Gathering accurate data and using statistical software will allow us to determine if there is a significant relationship between the variables.
To know more about Employees visit:
https://brainly.com/question/29450584
#SPJ11
The range of the data in the 4th of July parade is blank the range of data in the New Year’s Day parade
The range of the data on the 4th of July parade is greater than the range of the data in the New Years's Day parade.
A dataset's range, which reflects the gap among its greatest and lowest values, is measured statistically.
By deducting lowest value from the greatest value, it is computed. If range of total data is wider in Fourth of July parade than it is in the New Year's Day parade, then highest and lowest figures in Fourth of July parade will be further apart than highest and lowest values in New Year's Day parade.
For example, if highest value in 4th of July parade is 100 and lowest value is 10, then total range is 100 - 20 = 80.
If the highest value in the New Year's Day parade is 60 and the lowest value is 20, then the range is 60 - 20 = 40.
Thus, here range of the data in 4th of July parade is greater than range of the data in the New Year's Day parade.
Read more about range on:
brainly.com/question/30339388
#SPJ1
when we draw small and large samples from the same population, small samples group of answer choices produce a more peaked and narrower distribution. vary more from the population mean result in more degrees of freedom
When we draw small and large samples from the same population, small samples produce a more peaked and narrower distribution.
This phenomenon is due to the presence of fewer degrees of freedom associated with the small samples. Variations between sample and population mean result in fewer degrees of freedom, which results in a greater variation between samples and the population mean.
Degrees of freedom (df) is a statistical measure that quantifies the number of values in the final calculation of a statistic that are free to vary. When we sample data from a population, we calculate the sample mean, standard deviation, and other statistics
Learn more about sample distribution at:
https://brainly.com/question/31483266
#SPJ11
ASAP HELPPP!
Write an equation for the parabola graphed below.
The equation of the parabola graphed below is given as follows:
x = -1/49(y - 2)² - 1.
How to obtain the equation of the parabola?The parabola in the context of this problem is in horizontal form, hence the equation is given as follows:
x = a(y - k)² + h.
In which the parameters are given as follows:
a is the leading coefficient.(h,k) are the coordinates of the vertex.The coordinates of the vertex are given as follows:
(-1, 2).
Hence:
x = a(y - 2)² - 1.
When x = -2, y = -5, hence the leading coefficient a is obtained as follows:
-2 = a(49) - 1
a = -1/49.
Hence the equation is:
x = -1/49(y - 2)² - 1.
More can be learned about the equation of a parabola at https://brainly.com/question/4061870
#SPJ1
whats is 8000 lb =
to
8000 pounds is equal to 4 tons.
A pound is a unit of weight that is approximately equal to 16 ounces, while a ton is a unit of weight equal to 2000 pounds.
Therefore, to convert pounds to tons, you divide the weight in pounds by 2000.
8000 pounds is the weight that we want to convert to tons.
Dividing 8000 by 2000 gives us 4
which means that 8000 pounds is equal to 4 tons.
To learn more on Unit of Measurement click:
https://brainly.com/question/12629581
#SPJ1
How does y=5x and y=5x-4 are related
These two equations have the same slope, slope = 5.
They have different intercepts (the origin (0,0) and (0, -4)).
These lines are parallel.
prove that lim xâ0 x^4 cos(2/x)=0
To prove that lim x → 0 x^4 cos(2/x)=0, we need to show that for any ε > 0, there exists a δ > 0 such that |x^4 cos(2/x)| < ε whenever 0 < |x| < δ.
First, we note that -1 <= cos(2/x) <= 1 for all x. Therefore, we have:
x^4 <= x^4 cos(2/x) <= x^4 for all x
Taking the limit as x approaches 0 of both sides, we get:
lim x â 0 x^4 <= lim x â 0 x^4 cos(2/x) <= lim x â 0 x^4
Using the fact that lim x â 0 x^4 = 0, we can conclude that:
0 <= lim x â 0 x^4 cos(2/x) <= 0
Thus, by the squeeze theorem, we have:
lim x â 0 x^4 cos(2/x) = 0
Therefore, we have shown that lim x â 0 x^4 cos(2/x) = 0.
To learn more about limit : brainly.com/question/12207539
#SPJ11
Solve for a? Please help
we can answer it as follow
The red one show the GCF factor form it is -7 then you you ommit negative of numinator by negative of denominator . then you multiply both side by 4/7
the you simplify and solve a .
Johnny have 5 Apples in 6 rows how much apples will he have left
It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.
If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.
In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.
Learn more about interpretations here: brainly.com/question/26104458
#SPJ11
solve for x show steps
Answer:
x ≈ 50.7
Step-by-step explanation:
x/sin 90 = 23/sin(180-90-63) = 23/sin 27
x = (23 X sin 90) / sin 27
≈ 50.7
In the diagram below, AABC= ADEF. Complete the statement ZA =
C
A
B
F
D
In the diagram, if ΔABC= ΔDEF, then angle A is congruent to angle D.
Option C.
What are similar triangles?Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional in length.
Two triangles are considered similar if they satisfy one of the following conditions:
AA SimilaritySSS SimilaritySAS SimilarityABC ≅ DEF
∠A ≅ ∠ D
Thus, two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion, so angle A of triangle ABC is congruent to angle D of triangle DEF.
Learn more about similar triangles here: https://brainly.com/question/14285697
#SPJ1
