Answer:
15 possible outcomes
Step-by-step explanation:
Given;
A frozen yogurt shop offers scoops in cake cone, waffle cones, or cups.
N1 = 3 possible options
You can get vanilla, chocolate, strawberry, pistachio, or coffee flavored frozen yogurt.
N2 = 5 possible options
The total number of possible outcomes in the sample space when you order a scoop of yogurt is the product of the available options;
N = N1 × N2 = 3 × 5
N = 15 possible outcomes
There are about 208,000,000,000 different 8-letter passwords that can be formed using a 26-letter
alphabet.
Express this number using scientific notation.
0 2.08 x 1011
O 208 10
O 20.8 x 1010
0 0.208 x 1012
Answer:
2.08 x 10^11
Step-by-step explanation:
To put a number into scientific notation you move the decimal to the spot right after the first digit. To figure out what the power is you count how many digits you moved it past in order to get to the spot you want it (right after the first digit; in this case the 2)
So in this case you would move the decimal from the end of the number backwards past 9 zeros, the 8, and another zero, which is a total of 11 digits.
From there you take the number with the new decimal place and multiply by 10 to the power of the number you counted earlier, which for this example is 11
So the final answer is 2.08 x 10^11
4x + 3y - z = -6
6x - y + 3z = 12
8x + 2y + 4z = 6
Answer:
(x, y, z) = (1, -3, 1)
Step-by-step explanation:
Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:
(x, y, z) = (1, -3, 1)
__
Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.
Using the first equation to write an expression for z, we have ...
z = 4x +3y +6
Substituting that into the second and third equations gives ...
6x -y +3(4x +3y +6) = 12 ⇒ 18x +8y = -6
8x +2y +4(4x +3y +6) = 6 ⇒ 24x +14y = -18
Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:
3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)
10y = -30
y = -3
Substituting into the first equation (of the equations in x and y), we have ...
18x +8(-3) = -6
18x = 18
x = 1
Finally, substituting into the equation for z gives ...
z = 4(1) +3(-3) +6 = 1
The solution is (x, y, z) = (1, -3, 1).
___
The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.
The area of the triangle below is 2/5 square foot. What is the length, in feet, of the base of the triangle? Area = bh/2
Answer:
2/3 feet.
Step-by-step explanation:
We have to calculate the length of the base of the triangle, in this case they give us the area of the triangle but still it is necessary to know the height of the triangle to calculate the length of the base, otherwise it would be impossible.
I have found an image where the graph is, which I will attach where you can see that the height is 6/5 ft. The area of the triangle is:
A = b * h / 2
solved for b which is the length of the base of the triangle would be:
b = 2 * A / h
replacing:
b = 2 * (2/5) / (6/5)
b = 20/30
b = 2/3
Which means that the length of the base of that triangle is 2/3 feet.
AnswerSo C:
Step-by-step explanation:
pls halp me TwT im l
confused since quarantine happened reee
lateral area
surface area
volume
Answer:
22 is the answer but which country are you from
Answer:
22
Step-by-step explanation:
A bowl of cold gazpacho soup is warming to room temperature.the temperature difference between the soup and the room decreases by 5% every minute. What will the temperature difference be in 5 minutes if it is currently 16°C
Answer:
The temperature difference in 5 minutes will be 12.38ºC
Step-by-step explanation:
The difference in temperature after t minutes is given by the following equation:
[tex]T(t) = T(0)(1-r)^{t}[/tex]
In which T(0) is the initial temperature and r is the decrease rate, as a decimal.
Decreases by 5% every minute.
This means that [tex]r = 0.05[/tex]
What will the temperature difference be in 5 minutes if it is currently 16°C
This is T(5) when [tex]T(0) = 16[/tex]
So
[tex]T(t) = T(0)(1-r)^{t}[/tex]
[tex]T(t) = 16(1-0.05)^{t}[/tex]
[tex]T(t) = 16*(0.95)^{t}[/tex]
[tex]T(5) = 16*(0.95)^{5} = 12.38[/tex]
The temperature difference in 5 minutes will be 12.38ºC
What’s the correct answer for this?
Answer:
XY = 5268
Step-by-step explanation:
XY = XZ (originating from the same point)
85b+83=91b-283
85b-91b=-283-83
-6b=-366
Dividing both sides by -6
b = 61
Now
XY = 85b+83
= 85(61)+83
= 5268
(Old Final Exam Problem-A2011) A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: S= π r2 + π r r2+h2 Suppose you start out with a cone of height 8 cm and base radius 6 cm, and you want to change the dimensions in such a way that the total surface area remains the same. Suppose you increase the height by 15/100. In this problem, use tangent line approximation to estimate the new value of r so that the new cone has the same total surface area. The estimated value of r =
Answer:
5.972 cm
Step-by-step explanation:
Using implicit differentiation, we have ...
0 = (2πr +π(√(r^2+h^2) +r^2/√(r^2+h^2))·dr/dh +πrh/√(r^2+h^2)
For the given values of r and h, this is ...
0 = (12π +π(10 +36/10))dr/dh +48π/10
dr/dh = -4.8/(12+13.6) = -0.1875
Then the tangent line is ...
r = -0.1875(h -8) +6
__
For a height of 8 +15/100 = 8.15, the estimated value of r is ...
r = -0.1875(8.15 -8) +6 = -0.1875(0.15) +6 = 5.971875
The estimated value of r is 5.972 cm.
How would I find the domain and range of this graph?
Answer:
Domain: [-3, 5]
Range: [-5, 4]
Step-by-step explanation:
The first thing is to define what is the domain and the range. The domain of a function f (x) is the set of all the values for which the function is defined, and the range of the function is the set of all the values that f takes.
In other words, the domain is the value on the "x" axis and the range is the value on the "y" axis.
In this case, both are an interval, the domain would be from -3 to 5 and in the case of the range it would be from -5 to 4.
Domain: [-3, 5]
Range: [-5, 4]
A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette deck)ie one of each. A purchaser is offered a choice ofmanufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
CD Player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette Deck: Onkyo, Sony, Teac, Technics
A switch board display in the store allows a customer to hooktogether any selection of components (consisting of one of eachtype). Use the product rules to answer the following questions.
a. In how many ways can one component of each type beselected?
b. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
c. In how many ways can components be selected if noneis to be sony?
d. In how many ways can a selection be made if at leastone sony component is to be included?
e. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component? Exactly onesony component?
Answer:
Step-by-step explanation:
(a)
The number of receivers is 5.
The number of CD players is 4.
The number of speakers is 3.
The number of cassettes is 4.
Select one receiver out of 5 receivers in [tex]5C_1[/tex] ways.
Select one CD player out of 4 CD players in [tex]4C_1[/tex] ways.
Select one speaker out of 3 speakers in [tex]3C_1[/tex] ways.
Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.
Find the number of ways can one component of each type be selected.
By the multiplication rule, the number of possible ways can one component of each type be selected is,
The number of ways can one component of each type be selected is
[tex]=5C_1*4C_1*3C_1*4C_1\\\\=5*4*3*4\\\\=240[/tex]
Part a
Therefore, the number of possible ways can one component of each type be selected is 240.
(b)
The number of Sony receivers is 1.
The number of Sony CD players is 1.
The number of speakers is 3.
The number of cassettes is 4.
Select one Sony receiver out of 1 Sony receivers in ways.
Select one Sony CD player out of 1 Sony CD players in ways.
Select one speaker out of 3 speakers in ways.
Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.
Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.
By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,
Number of ways can one components of each type be selected
[tex]=1C_1*1C_1*3C_1*4C_1\\\\=1*1*3*4\\\\=12[/tex]
Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.
(c)
The number of receivers without Sony is 4.
The number of CD players without Sony is 3.
The number of speakers without Sony is 3.
The number of cassettes without Sony is 3.
Select one receiver out of 4 receivers in 4C_1 ways.
Select one CD player out of 3 CD players in 3C_1 ways.
Select one speaker out of 3 speakers in 3C_1 ways.
Select one cassette out of 3 cassettes in 3C_1 ways.
Find the number of ways can components be selected if none is to be Sony.
By the multiplication rule, the number of ways can components be selected if none is to be Sony is,
[tex]=4C_1*3C_1*3C_1*3C_1\\\\=108[/tex]
[excluding sony from each of the component]
Therefore, the number of ways can components be selected if none is to be Sony is 108.
(d)
The number of ways can a selection be made if at least one Sony component is to be included is,
= Total possible selections -Total possible selections without Sony
= 240-108
= 132
Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.
(e)
If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,
[tex]= \text {Total possible selections with at least one Sony} /\text {Total possible selections}[/tex]
= 132 / 240
= 0.55
The probability that the system selected contains exactly one Sony component is,
[tex]= \text {Total possible selections with exactly one Sony} /\text {Total possible selections}[/tex][tex]\frac{1C_1*3C_1*3C_1*3C_1+4C_11C_13C_13C_1+4C_13C_13C_13C_1}{240} \\\\=\frac{99}{240} \\\\=0.4125[/tex]
Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.
If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.
Given f(x) = 6x + 2, find f(x-3)
Answer:
6x -16
Step-by-step explanation:
f(x) = 6x + 2
f(x-3) =
Replace x with x-3
f(x) = 6(x-3) + 2
Distribute
= 6x - 18 +2
= 6x -16
The right answer is 6x-16
please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
f(x) = (x - 5)(5x + 2)
lesser x =
greater x =
Answer:
hope
this
is
correct
Solve x-6y=17 for y, please help
Answer:
y = x/6 - 17/6
Step-by-step explanation:
x - 6y = 17
<=>6y = x - 17
<=> y =x/6 - 17/6
Hope this helps!
simplify the expression 2\3(-4)-(1/6-8/6
Answer:
1/8
Step-by-step explanation:
Answer:
When you simplify it, you get the answer of 1.
Step-by-step explanation:
Order of operation rules are required that you multiply and divide before you carrying out addition and/or subtraction.
So, simplify 2/3 / (-4) first, obtaining -1/6.
Now, you have -1/6 - 1/6 + 8/6, which combines to 1 or 6/6.
The graph below represents a recent 10 meter race between two remote control cars.
10 I'm
Remote Control Car Race
Answer:
It's B I think.
Step-by-step explanation: If they the lines intersected then it'd mean they crashed.
The graph below shows a recent 10-meter race between two remote-control automobiles. The racial assertions in A, B, and C are true.
What is a graph?A graph that shows the relationship between two or more variables, each of which is measured along one of two axes that are at right angles to one another.
At 6 meters into the race, the blue car overtook the red car because, at that moment, the blue car had a bigger distance than the red car.
Due to the greater slope of the blue vehicle's path compared to the red car's line, the blue car is faster.
Because the blue car's x-intercept is at (3, 0), where x stands for time and y for distance from the starting line, it began 3 seconds later than the other cars.
Hence Statements B, C, and D about race are true.
Q.The graph below represents a recent 10-meter race between two remote control cars.
A graph titled Remote Control Car Race has seconds after the race starts on the x-axis and distance from the start line (meters) on the y-axis. A line labeled red car goes through (3, 2) and (6, 4). A line labeled blue car goes through (3, 0) and (5, 2).
Which statements about race are true? Check all that apply.
The red car won the race because it started above the blue car.
The cars crashed 9 seconds into the race because that is the point of intersection, and neither car continued on after that point in time.
The blue car passed the red car at 6 m into the race because that is the point of intersection, and the blue car has a greater distance than the red car after that time.
The blue car is faster because the slope of its line is steeper than the slope of the line representing the red car.
The blue car started 3 seconds late because it has an x-intercept of (3, 0) and x represents the time and y represents the distance from the starting line.
learn more about graphs here :
https://brainly.com/question/10712002
#SPJ6
What is 8 times as many as 3 is
Answer:
24?
Step-by-step explanation:
find the difference
8ab^3 square root ac^2-14ab^3 squareroot ac^2
Answer:
-6ab^3sqrtac^2 option b
Step-by-step explanation:
i just did it
Answer:
Step-by-step explanation:
In the game of roulette, a player can place a $4 bet on the number 10 and have a 1/38 probability of winning. If the metal ball lands on 10, the player gets to keep the $4 paid to play the game and the player is awarded an additional $140. Otherwise, the player is awarded nothing and the casino takes the player’s $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?
this one is kinda Hard ill do sum research and help
Manuel is 6 years older than melissa. In 6 years the sum of their ages will be 52. How old is manuel now?
_______years old
Answer:
58
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
lolololololololol
Please help me figure this one out!
Answer:
7
Step-by-step explanation:
∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹)
This is the sum of the first 3 terms of the sequence.
The first 3 terms are:
4 × (½)¹⁻¹ = 4
4 × (½)²⁻¹ = 2
4 × (½)³⁻¹ = 1
So the sum is:
∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹) = 4 + 2 + 1 = 7
Simplify
sin^2x+tan^2x+cos^2x
Answer:
sec²x
Step-by-step explanation:
sin²x + tan²x + cos²x
sin²x + cos²x + tan²x
1 + tan²x ( sin²x + cos²x = 1 )
sec²x ( 1 + tan²x = sec²x )
Answer:
Step-by-step explanation:
SIN^2x + tan^2 x + cos^2x
= x( sin^2 + tan^2+cos^2)
=x(1+tan^2) since sin^2+cos^2 =1
=xsec^2 ( since sec^2 = 1+tan^2)
=sec^2x
hope it helps
A sample of size =n72 is drawn from a population whose standard deviation is =σ25. Part 1 of 2 (a) Find the margin of error for a 95% confidence interval for μ. Round the answer to at least three decimal places. The margin of error for a 95% confidence interval for μ is . Part 2 of 2 (b) If the sample size were =n89, would the margin of error be larger or smaller?
Answer:
a) margin of error ME = 5.77
b) Margin of error becomes smaller
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-ME
Where margin of error ME = zr/√n
a)
Given that;
Mean = x
Standard deviation r = 25
Number of samples n = 72
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
ME = 1.96(25/√72)
ME = 1.96(2.946278254943)
ME = 5.774705379690
ME = 5.77
b)
For n = 89
ME = 1.96(25/√89)
ME = 1.96(2.649994700015)
ME = 5.193989612031
ME = 5.19
5.19 is smaller than 5.77 in a) above. So,
Margin of error becomes smaller
a bus drives at 66 km at an average speed of 66 km/h. how long does the journey take?
Answer:
1 hour
Step-by-step explanation:
From Distance = speed × time
time = Distance/ speed
=66/66 = 1 hour
I need 6th question in the paper
Answer:
8
Step-by-step explanation:
[tex] a = 1 - \sqrt{2} [/tex]
[tex] (a - \dfrac{1}{a})^3 = [/tex]
[tex] = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 [/tex]
[tex] = (\dfrac{a^2 - 1}{a})^3 [/tex]
[tex] = (\dfrac{(a + 1)(a - 1)}{a})^3 [/tex]
[tex] = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 [/tex]
[tex]= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex] = 2^3 [/tex]
[tex] = 8 [/tex]
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5), as instructed, to ?nd a second solution y2(x)
y"+2y'+y=0; y1=xe^-x.
Answer:
[/tex]y2=e^(-x)[/tex]
Step-by-step explanation:
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION
There are 4, 6, and 7 points on three lines. How many quadrilaterals is it possible to create with given points as vertices?
Answer:
Step-by-step explanation:If you choose any 3 of the 7 vertices, you can connect them with lines to create a unique triangle.
So, the question becomes "In how many different ways can we select 3 vertices from 7 vertices?"
Since the order in which we select the 3 vertices does not matter, we can use COMBINATIONS.
We can select 3 vertices from 7 vertices in 7C3 ways.
Can someone help me with the answer
Answer:
D. 129°
Step-by-step explanation:
Angles XZY and XZV form a linear pair, so are supplementary.
angle XZV = 180° -51° = 129°
Plz help fast Jack, John, Lily, and Sara want to take a picture together. In how many ways can they are arranged?
Answer:
The best estimate would be around 10-16
Step-by-step explanation:
The think is that they can be in many orders and since there is four of them it would be more orders.
Hope this helps
Flow meters are installed in urban sewer systems to measure the flows through the pipes. In dry weatherconditions (no rain) the flows are generated by waste-water from households and industries, together withsome possible drainage from water stored in the topsoil from previous rainfalls. In a study of an urbansewer system, the following values were obtained for flowrates during dry weather conditions:
423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0
Assume that the flow rates are normally distributed.
a. Construct a 98% two-sided confidence interval for the standard deviation of the flow rate under dry weather conditions.
b. Explain, only using words, the meaning of the CI you determined in (a).
Answer:
a) [tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]
[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]
Now we just take square root on both sides of the interval and we got:
[tex] 19.08 \leq \sigma \leq 66.56[/tex]
b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56
Step-by-step explanation:
423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0
Part a
The confidence interval for the population variance is given by the following formula:
[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]
On this case we need to find the sample standard deviation with the following formula:
[tex]s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}
And in order to find the sample mean we just need to use this formula:
[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}[/tex]
The sample deviation for this case is s=30.23
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
[tex]df=n-1=9-1=8[/tex]
The Confidence interval is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and the critical values are:
[tex]\chi^2_{\alpha/2}=20.09[/tex]
[tex]\chi^2_{1- \alpha/2}=1.65[/tex]
And replacing into the formula for the interval we got:
[tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]
[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]
Now we just take square root on both sides of the interval and we got:
[tex] 19.08 \leq \sigma \leq 66.56[/tex]
Part b
For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56
How many solutions are there to the equation below?
5(x + 10) - 25 = 5x + 25
O A. 1
OB.O
O C. Infinitely many
Answer: Infintely many
Step-by-step explanation:
5(x + 10) - 25 = 5x + 25
5x +50 - 25 = 5x + 25
5x +25 = 5x + 25
Same equation
One study revealed that a child under the age of 10 watches television 4.5 hours per day. A group of families from a certain comunity would like to beleive that their children watch television less than the national average. A random sample of 14 children from the community yielded a mean of 4.1 hours per day with standard deviation of 1.2. Test the appropriate hypothesis at the level of significance 0.01. Assume the viewing time is normally distributed and interpret your results.
Answer:
[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]
The degrees of freedom are given by:
[tex] df=n-1= 14-1=13[/tex]
And the p value would be:
[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.
Step-by-step explanation:
Information given
[tex]\bar X=4.1[/tex] represent the sample mean
[tex]s=1.2[/tex] represent the sample deviation
[tex]n=14[/tex] sample size
[tex]\mu_o =4.5[/tex] represent the value to test
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is less than 4.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 4.5[/tex]
Alternative hypothesis:[tex]\mu < 4.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{4.1-4.5}{\frac{1.2}{\sqrt{14}}}=-1.25[/tex]
The degrees of freedom are given by:
[tex] df=n-1= 14-1=13[/tex]
And the p value would be:
[tex]p_v =P(t_{13}<-1.25)=0.117[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 4.5 minutes.
