Solution:
Given:
Two types of tickets; advanced and same-day tickets.
Let a represent advanced tickets
Let s represent same-day tickets.
Developing the word problem (statements) into mathematical expressions, we have;
[tex]\begin{gathered} \text{Advanced tickets cost \$40. This means;} \\ a=\text{ \$40} \\ \\ \text{Same}-\text{day tickets cost \$25. This means;} \\ s=\text{ \$25} \end{gathered}[/tex][tex]\begin{gathered} \text{Total tickets sold in all is 65. This means;} \\ a+s=65\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ \\ \text{Total amount paid for advanced tickets = \$40a} \\ \text{Total amount paid for same-day tickets = \$25s} \\ \\ \text{Total amount paid for all tickets = \$2225.} \\ \text{Hence,} \\ 40a+25s=2225\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Solving equations (1) and (2) simultaneously to get the values of a and s;
[tex]\begin{gathered} \text{From equation (1)},\text{ } \\ a+s=65 \\ a=65-s\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(3) \\ \\ \text{Substituting equation (3) in equation (2),} \\ 40a+25s=2225 \\ 40(65-s)+25s=2225 \\ 2600-40s+25s=2225 \\ 2600-15s=2225 \\ \text{Collecting the like terms;} \\ 2600-2225=15s \\ 375=15s \\ 15s=375 \\ \text{Dividing both sides by 15 to get s,} \\ s=\frac{375}{15} \\ s=25 \\ \text{Thus, same-day tickets sold were 25 tickets} \end{gathered}[/tex]Substituting the value of s in equation (3) to get the value of a.
[tex]\begin{gathered} a=65-s \\ a=65-25 \\ a=40 \\ \text{Thus, advanced tickets sold were 40 tickets} \end{gathered}[/tex]Therefore, advanced tickets sold were 40 tickets and same-day tickets sold were 25 tickets.
for choose one you have to tell me what kind of angle it is.
Part 1
By angle addition property
m<4+m<5+m<1=180 degrees
m<4=39 degrees
m<5=45 degrees
substitute
39+45+m<1=180
m<1=180-39-45
m<1=96 degreesPart 2
we see that
m<4 and m<3 are alternate interior angles
and since lines, l and k are parallel, <4 and <3 are congruent
so
m<3=39 degreesPart 3
we see that <2 and <5 are alternate interior angles
and since lines, l and k are parallel, < 2 and <5 are congruent
so m<2=45 degrees
Part 4
therefore m<1+m<2+m<3=180 degrees
The relationship between <1, <2 and <3 is an example of the following rule
The sum of the interior angles measures of a triangle is 180 degrees
A club consists of 15 people including Ali, Kendra,
Ted, Alice, Marie, Dan, Linda and Frank. From the 15
members, a president, vice president and treasurer
will be selected at random. An advisory committee
of 5 other individuals will also be selected at
random.
Determine the probability that Ali is selected
president, Kendra is selected vice president, Ted is
named the treasurer and the other 5 individuals
named form the advisory committee.
The required probability of the random event is 0.273.
The probability is estimated by dividing the total number of possible outcomes by the number of possible ways the event could occur.The probability and chances of that happening are two distinct ideas. Odds are calculated by dividing the probability of an event by the likelihood that it won't.Keep in mind that a president, vice president, and treasurer will be chosen at random from the 15 members. The number of options to choose from to fill these spots is thus:
[tex]_{15}P_3=\frac{15!}{(15-3)!} =2730[/tex].
The required probability of the random event is 0.273.
Learn more about probability here:
https://brainly.com/question/24756209
#SPJ1
The following information is from Madison Corporation's accounting records for May. Check No. 3269 was returned as a double payment and voided. Checks that have not cleared the bank include No. 3252, No. 3260, and series No. 3275–3278. Check No. Amount Check No. Amount 3247 $32.64 3263 $24.87 3248 400.00 3264 45.00 3249 309.22 3265 33.78 3250 256.00 3266 756.77 3251 3,212.17 3267 84.34 3252 56.89 3268 789.00 3253 98.02 3269 48.90 3254 47.55 3270 34.41 3255 1,124.77 3271 872.00 3256 250.00 3272 22.00 3257 68.00 3273 562.38 3258 215.56 3274 512.00 3259 38.55 3275 603.50 3260 92.65 3276 67.00 3261 44.61 3277 301.61 3262 72.96 3278 47.88 In addition to the above list of checks, Madison had Check No. 2264 for $32.98 and Check No. 2655 for $45.99 outstanding previously that have not cleared. Question Content Area 1. Create an outstanding checks list for Madison at the end of May. Round your answers to two decimal places.
The outstanding checks list for Madison at the end of May shows a total of $1,169.53, including the following checks and their amounts:
Check No. Amount
3252 56.89
3260 92.65
3275 603.50
3276 67.00
3277 301.61
3278 47.88.
What are outstanding checks?Outstanding checks are checks issued by Madison to its suppliers of services and goods that have not been cleared at the bank.
Perhaps, the payees have not submitted or presented them for payment.
Issued Checks:Check No. Amount
3247 $32.64
3263 $24.87
3248 400.00
3264 45.00
3249 309.22
3265 33.78
3250 256.00
3266 756.77
3251 3,212.17
3267 84.34
3252 56.89
3268 789.00
3253 98.02
3269 48.90
3254 47.55
3270 34.41
3255 1,124.77
3271 872.00
3256 250.00
3272 22.00
3257 68.00
3273 562.38
3258 215.56
3274 512.00
3259 38.55
3275 603.50
3260 92.65
3276 67.00
3261 44.61
3277 301.61
3262 72.96
3278 47.88
Outstanding Checks:Check No. Amount
3252 56.89
3260 92.65
3275 603.50
3276 67.00
3277 301.61
3278 47.88
Total $1,169.53
Thus, the list of outstanding checks totals $1,169.53.
Learn more about outstanding checks at https://brainly.com/question/1442615
#SPJ1
Identify all the sets to which the number belongs. Choose from rational number, irrational number, whole number, and itenger. 0.62478916532
0.62478916532 is an irrational number
This is because it cannot be expressed as a rational number except in surd form which is also known to be irrational. it is neither a whole number nor an integer too
ANSWER => Option B
what number do I need to add -5 to get -7
- 5 - 2 = - 7
The number that you need to add to - 5 to get - 7 is - 2
This can be ssen on the number line. If you are adding, you move towards the right but since we are adding a negative number, the - sign makes the plus sign to become - sign. So we would subtract by moving 2 points to the left of -5 and that gives - 7
Find the area swept by the door. Note: Enter your answer in terms of \piπpi.
We are asked to determine the area swept by the door. We notice that the area forms a sector of a circle. The area of the sector of a circle is given by:
[tex]A=\frac{1}{2}r^2\theta[/tex]Where:
[tex]\begin{gathered} A=\text{ area} \\ r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}[/tex]To convert the given angle into radians we use the following conversion factor:
[tex]\pi\text{ radians = 180 degr}ees[/tex]Now, we multiply by the conversion factor:
[tex]45\times\frac{\pi}{180}=\frac{\pi}{4}[/tex]Now, we plug in the values in the formula for the area:
[tex]A=\frac{1}{2}(80cm)^2(\frac{\pi}{4})[/tex]Solving the operations:
[tex]A=800\pi cm^2[/tex]Therefore, the area is 800 pi square centimeters.
how do you find slope?1?!
Answer:
Pick two points on the line and determine their coordinates.
Answer:
Step-by-step explanation:
Rise over Run
1. Find 2 points
2. Count the Y distance .then the X distance
3.Y/X
EX. (0,0) and (4,4)
0 to 4 of the y-axis is 4
0 to 4 on the x-axis is 4
4/4= 1 slope 1
Select the correct answer.The Junior and senior classes at Central High School were asked to choose a destination for a field trip. The results are shown in the giventwo-way frequency table.JuniorsSeniorsTotalCentral High School Field Trip DestinationAmusement Park5764121OA 38.55%B. 19.93%OC 47.50%OD. 42.31%ntum. All rights reserved.Museum Broadway Show214465What percentage of surveyed students chose the amusement park?4258100Total120166286
The probability that the subject is physics if an assignment is submitted on time is 89.7%.
Given that,
The table is
Subject: On-time Assignment: On-time Arrival to Class:
PHYSICS 89.7% 82.3%
MATH 88.2% 88.7%
CHEMISTRY 89.4% 83.1%
BIOLOGY 90.1% 82.4%
TOTAL 88.5% 84.7%
What is probability?
The characteristic or state of being probable; the probability that something will occur or be the case:
If an assignment is turned in on time, there is an 89.7% chance that the subject will be physics.
If an assignment is turned in on time, there is an 88.2% probability that the subject is math.
If an assignment is turned in on time, there is an 89.4% probability that the subject is chemistry.
If an assignment is turned in on time, the probability that the subject is biology is 90.1%.
Therefore, the chance that the subject is physics if an assignment is submitted on time is 89.7%.
To learn more about time visit: https://brainly.com/question/28050940
#SPJ9
Three people travel by car to San Diego, a distance is 380 miles. Thetrip takes 6 hours. Daily cost for meals is $20 per person and gas costs$3.59 per gallon and their vehicle gets 15 mpg. Calculate the cost perperson for this trip to the nearest dollar.A) $85B) $70C) $50D) $90E) $105
Given:
• Distance = 380 miles
,• Time = 6 hours
,• Daily cost for meals = $20 per person
,• Cost of gas = $3.59 per gallon
,• Vehicle gets 15 miles per gallon.
Let's calculate the cost per person for this trip.
We have the following:
To find the total cost of gas they used for this trip, we have:
[tex]\frac{380}{15}*3.59=90.95[/tex]The total cost of gas for this trip is $90.95
The cost of gas per person will be:
[tex]\frac{90.95}{3}=\text{ \$30.32}[/tex]Cost of gas per person is $30.32
Therefore, the cost per person for this trip will be:
Cost per person = Cost of gas per person + Cost of meal per person
Cost per person = $30.32 + $20 = $50.32 ≈ $50
Therefore, the cost per person for this trip to the nearest dollar is $50
ANSWER:
C) $50
Write this equation in Y=MX+B form: 3x+4y=8
the initial expression is:
[tex]3x+4y=8[/tex]So to write it in the form slope intercept we can rest 3x in bout sides of the equation so:
[tex]\begin{gathered} -3x+3x+4y=-3x+8 \\ 4y=-3x+8 \end{gathered}[/tex]now we divide by 4 so:
[tex]\begin{gathered} \frac{4y}{4}=-\frac{3}{4}x+\frac{8}{4} \\ y=-\frac{3}{4}x+2 \end{gathered}[/tex]No M is equal to -3/4 and B is equal to 2e
Answer:
y = -3/4x + 2
Step-by-step explanation:
Given:
Write this equation in "y=mx+b form"
Equation given: 3x+4y=8
Solve:
3x + 4y = 8
⇒ 3x -3x + 4y = 8 -3x ⊂ Subtract 3x from both side ⊃
⇒ 4y = -3x + 8
⇒ 4y/4 = -3x/4 +8/4 ⊂ Divide all by 4 ⊃
⇒ y = -3/4x + 2
Hence, this equation ( 3x + 4y = 8) in y = mx+b is y = -3/4x + 2
Lenvy~♡
What is the perimeter of STUV?* STUV – XYZW T Z 20
The perimeter of the figure is the addition of the segments so in this case we have to find the sides so:
[tex]\frac{35}{21}=\frac{25}{TU}=\frac{20}{UV}=\frac{20}{SV}[/tex]So:
[tex]\begin{gathered} TU=\frac{25\cdot21}{35}=15 \\ UV=\frac{20\cdot21}{35}=12 \\ SV=\frac{20\cdot21}{35}=12 \end{gathered}[/tex]So the perimeter will be:
[tex]\begin{gathered} P=21+15+12+12 \\ P=60 \end{gathered}[/tex]A fashion photographer needs to hire a stylist to prepare her models. Emmet charges $177 for showing up, plus $75 per hour. Pam charges $187 plus $70 per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her the same amount. What would the duration be? What would the cost be?
Emmet charges $177 for showing up, plus $75 per hour
Total charge = Show up charge + Per hour charges
Pam charges $187 plus $70 per hour
either stylist would cost her the same amount
i.e the total cost of photographer and stylist
Let x be the time taken in shoot
so, the charge of Emmet is 177 + 75x
The charge of palm = 187+70x
Since the charge is equal so,
[tex]\begin{gathered} 177+75x=187+70x_{} \\ 75x-70x=187-177 \\ 5x=10 \\ x=2 \end{gathered}[/tex]we get x= 2
i.e. 2 hours
The duration at which the cost of palm and emmet is equal is 2 hours
for the cost
substitute the value of x in the cost equation :
Emmet = 177 + 75x
Emmet cost=177+75(2)
Emmet cost = 327
Since the cost is same so,
The cost of emmet and palm is $327
Answer: 2 hours & $327
prove that the sum of the lengths of the diagonals of a quadrilateral is less than the perimeter but greater than the half of the perimeter of this quadrilateral
Let us consider a quadrilateral ABCD (as shown in the figure below) such that AC and BD are the two diagonals of ABCD.
Now, in triangle ABC and triangle ADC, by using the properties of triangle inequality we have-
AB +BC > AC .... (1)
and AD + CD >AC .... (2)
adding equations (1) and (2) we get-
AB+ BC+CD+AD > 2AC .... (3)
Similarly for diagonal BD we get-
AB+BC+CD+AD > 2BD .... (4)
Adding equations (3) and (4) we get-
2(AB+BC+CD+AD) > 2(AC+BD)
⇒ (AB+BC+CD+AD) > AC+BD
here (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence, we have proven that the sum of the length of the diagonals of a quadrilateral is less than the perimeter.
Now the 2 diagonals divide the quadrilateral into 4 quadrilaterals
Therefore, AO+OD > AD
OD+OC > CD
OC+OB > BC
and OA+OB > AB
Adding all these equations-
2(AC+BD)>AB+BC+CD+AD
⇒AC+BD > 1/2(AB+BC+CD+AD)
Hence, we've proven that the sum of the length of the diagonals is greater than the half of the perimeter of this quadrilateral.
Learn more about quadrilaterals here-
https://brainly.com/question/26690979
#SPJ1
Suppose you have an experiment where you toss a fair coin 3 time you didn't count the number of heads observe over those 3 tosses use this experiment to address each of the falling question round solution to 3 destiny places
a) In order to complete the table for the probability distribution for the variable X:
X = the number of heads observed when you flip a coin three times,
b) we create a list of all the possible outcomes. We use the notation: H = heads, T = tails.
The possible outcomes after tossing the coin three times are:
[tex]HHH,HHT,HTH,THH,TTT,TTH,THT,HTT[/tex]From the list above we see that we have 8 equiprobable events. Now, we classify the events according to the number of Heads included.
- Events with x = #H = 0: TTT
- Events with x = #H = 1: HTT, THT, TTH
- Events with x = #H = 2: HHT, HTH, THH
- Events with x = #H = 3: HHH
Using the data above we compute the probabilities for each x, we simply compute the quotient between the number of outcomes of each case by N = 8 (the total number of possible outcomes):
[tex]\begin{gathered} P\mleft(x=0\mright)=\frac{1}{8}=0.125 \\ P(x=1)=\frac{3}{8}=0.375 \\ P(x=2)=\frac{3}{8}=0.375 \\ P(x=3)=\frac{1}{8}=0.125 \end{gathered}[/tex]c) Shape of the probability disribution. The probability distribution of x is: Symmetric.
d) Using the data above, we can compute the mean number of heads for the distribution:
[tex]\begin{gathered} E(x)=\sum ^3_{n=0}x_n\cdot P(x_n_{}) \\ E(x)=0\cdot P(x=0)+1\cdot P(x=1)+2\cdot P(x=2)+3\cdot P(x=3) \\ E(x)=0+1\cdot0.375+2\cdot0.375+3\cdot0.125 \\ E(x)=\frac{3}{2}=1.5 \end{gathered}[/tex]So the mean number of heads for this distribution is 1.5
find an equation of the line described. write the equation in slope intercept form when possible slope 1, through (-9,4) the equation of the line is y= _
The expression for the slope intersept form of a line is,
[tex]y-y_1=m\cdot(x-x_1)[/tex]Put the values implies,
[tex]\begin{gathered} y-4=1(x-(-9)) \\ y-4=x+9 \\ y=x+13 \end{gathered}[/tex]Therefore, the slope intersept form is y=x+13.
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST (also please show how you got answer)
only giving brainlyest for correct answer
The slope of the line is 125.
The slope in the context represent the change in price with respect to the sizes of the houses.
The line won't pass through the point (5, 650)
How to find the slope of a line?The slope of a line is the change in y with respect to change in x.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
using (0, 0)(2, 250)
m = 250 - 0 / 2 - 0
m = 250 / 2
Therefore,
m = 125
The slope simply implies the change in price with respect to the change in sizes of the houses.
Using the slope intercept equation we can know if the line passes through (5, 650).
Therefore,
y = 125x + 0
625 = 125(5)
Therefore, the line won't pass through the point (5, 650).
learn more on slope here: https://brainly.com/question/12203383
#SPJ1
in the triangles below, m
In the given triangles,
∠B = ∠A
∠T = ∠M
Since, two angles of a triangle are equal, the third angle will also be equal.
Also, ΔLBT is similar to ΔHAM ........(by Angle - Angle similarity)
Now,
⇒ LB/HA = BT/AM = LT/HM ..........(Sides of similar triangles are proportional)
⇒ LB/HA = BT/AM
⇒ 4/HA = 6/10
⇒ 10 x 4 = HA x 6
⇒ HA = 40/6
⇒ HA = 20/3
⇒ HA = 6 2/3
What are Similar Triangles?Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size. Triangle resemblance is shown by the symbol ~ in this case.It is possible to prove that the corresponding sides of two triangles with congruent angles (also known as equiangular triangles) are proportionate. The AAA Similarity Theorem refers to this.Numerous synthetic (coordinate-free) Euclidean geometry proofs are based on similar triangles.The angle bisector theorem, geometric mean theorem, Menelaus' theorem, and Pythagorean theorem are only a few examples of basic conclusions that can be proven in this fashion. The fundamentals of right triangle trigonometry are also provided by similar triangles.
To learn more about Similar triangles, refer to:
https://brainly.com/question/25882965
#SPJ9
Kristen gets a full scoop of frozen yogurt in a cone. The scoop is aperfect sphere with the same radius as the cone. She wonders if theentire volume of the frozen yogurt could fit completely inside thecone. What is the relationship between the volume of the coneand the volume of frozen yogurt? Is the volume of the cone greatenough to fit all of the frozen yogurt? Explain. (Use 3.14 for (pie) andround your answer to the nearest whole number)
The volume of a sphere is calculated as follows:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius of the sphere.
Substituting with r = 5 cm, we get:
[tex]\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot5^3 \\ V=\frac{4}{3}\cdot\pi\cdot125 \\ V=523.3\operatorname{cm}^3 \end{gathered}[/tex]The volume of a right circular cone is calculated as follows:
[tex]V=\pi r^2\frac{h}{3}[/tex]where h is the height of the cone.
Substituting with r = 5 cm, and h = 11 cm, we get:
[tex]\begin{gathered} V=\pi\cdot5^2\cdot\frac{11}{3} \\ V=\pi\cdot25\cdot\frac{11}{3} \\ V=287.8\operatorname{cm}^3 \end{gathered}[/tex]The volume of the cone is less than the volume of the sphere, then the
entire volume of the frozen yogurt cannot fit completely inside the
cone.
Which of the following values are solutions to th I. 2 II. – 6 None O I only Submit Ang O II only O III only I and II I and III O II and III I, II and III
ok, but the inequality is not complete in the picture
[tex]\begin{gathered} \text{ 1 }\leq\text{ 1 - 2x} \\ \text{ 1 - 1 }\leq\text{ -2x} \\ \text{ 0 }\leq\text{ -2x} \\ \text{ 0/-2 }\ge\text{x} \\ \text{ 0 }\ge\text{ x} \end{gathered}[/tex]Determine whether WX and YZ are parallel, perpendicular or neither.W(6.-6), X(7.1). Y(3,-1), Z(2,6)
ANSWER
Neither
EXPLANATION
To determine whether WX and YZ are parallel or perpendicular, wehave to find their slopes and compare them.
Slope is given as:
[tex]\text{slope = }\frac{y_2-y_1}{x_{2_{}}-x_1}[/tex]SLOPE OF WX
For WX,
(x1, y1) = (6, -6)
(x2, y2) =(7, 1)
So:
[tex]\begin{gathered} \text{slope = }\frac{1\text{ - (-6)}}{7\text{ - 6}}\text{ = }\frac{1\text{ + 6}}{1} \\ \text{slope = 7} \end{gathered}[/tex]SLOPE OF YZ
For YZ:
(x1, y1) = (3, -1)
(x2, y2) = (2, 6)
So:
[tex]\begin{gathered} \text{slope = }\frac{6\text{ - (-1)}}{2\text{ - 3}} \\ \text{slope = }\frac{6\text{ + 1}}{-1} \\ \text{slope = -7} \end{gathered}[/tex]For WX and YZ to be parallel, their slope must be the same.
For WX and YZ to be perpendicular, the slope of one must be the negative inverse of the other.
Since their slopes are neither the same or the negative inverse of one another, WX and YX are neither parallel or perpendicular to one another.
A pizza parlor offers a choice of 12 different toppings. How many 2-topping pizzas are possible? (no double-orders of toppings are allowed)
==========================================================
Explanation:
There are 12 choices for the first topping and 11 for the next topping. The decrease is to account for the fact we cannot select a repeat topping.
That gives 12*11 = 132 permutations. If order of toppings mattered, then this would be our final answer.
However, the topping order doesn't matter. So we need to divide by 2 to correct for the double counting.
There are 132/2 = 66 combinations.
------------
Alternative Method:
n = 12 toppings are available and r = 2 selections are allowed
Order doesn't matter so we use the nCr combination formula
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\12 C 2 = \frac{12!}{2!*(12-2)!}\\\\12 C 2 = \frac{12!}{2!*10!}\\\\12 C 2 = \frac{12*11*10!}{2!*10!}\\\\ 12 C 2 = \frac{12*11}{2!}\\\\ 12 C 2 = \frac{12*11}{2*1}\\\\ 12 C 2 = \frac{132}{2}\\\\ 12 C 2 = 66\\\\[/tex]
There are 66 combinations
Notice the 2nd to last step involves 132/2 which was mentioned in the previous section.
TWO tailors, Aisha and Debbie, sit down to do some embroidery. Alsha can embroider 4 shirtsper hour, and Debbie can get through 6 shirts per hour. In addition, the tailors had previouslyfinished some shirts. Aisha has already completed 20 shirts, and Debbie has completed 10shirts. Aisha and Debbie decide to take a break when they have finished the same totalnumber of shirts. How long will that take?Write a system of equations, graph them, and type the solution
For the information given in the statement you have
[tex]\begin{gathered} t=4h+20\Rightarrow\text{ shirts embroidered by Aisha} \\ t=6h+10\Rightarrow\text{ shirts embroidered by Debbie} \end{gathered}[/tex]Angel Sanchez has 6 books on a shelf; 2 mysteries, 3 science fiction books, and 1 biography. Determine the probability of each situationla) Selecting one mystery and then one science fiction, with replacementb) Selecting one mystery and then one science fiction, without replacementa) The probability of selecting one mystery and then one science fiction, with replacement is
It is given that there are 6 books in total, with 2 mysteries, 3 science fiction books, and 1 biography.
Recall that the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
(a) It is required to find the probability of selecting one mystery and then one science fiction, with replacement.
The probability of selecting one mystery is:
[tex]P(M)=\frac{1}{6}[/tex]The probability of selecting one science fiction next with replacement is:
[tex]P(S)=\frac{1}{6}[/tex]The probability of independent events is the product of their respective probabilities.
Hence, the probability of selecting one mystery and then one science fiction, with replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}[/tex]The answer is 1/36.(b) It is required to find the probability of selecting one mystery and then one science fiction, without replacement.
Since there is no replacement, the probability of selecting one science fiction next without replacement is:
[tex]P(S)=\frac{1}{6-1}=\frac{1}{5}[/tex]Hence, the probability of selecting one mystery and then one science fiction, without replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{5}=\frac{1}{30}[/tex]The answer is 1/30.How many years are there in 467 days?
Answer:
there are approximately 1.28 years in 467 days
Step-by-step explanation:
1 yr = 365 days
467/365 = 1.28
Answer: 1 year and 102 days.
Step-by-step explanation:
There are 365 days in a year.
Solve this system of equations byusing the elimination method.3x + 4y = 4-X – 3y = 7=\וז ו7ro
Given:
System of equation is given as
[tex]\begin{gathered} 3x+4y=4 \\ -x-3y=7 \end{gathered}[/tex]Required:
Solve system of equation by using the method elimination.
Explanation:
By using the elimination method
we multiply second equation with 3 and then add in first equation
because by doing this process we eliminate the x
[tex]\begin{gathered} 3x+4y+3(-x-3y)=4+3*7 \\ 3x+4y-3x-9y=4+21 \\ -5y=25 \\ y=-5 \end{gathered}[/tex]now put the value of y in first equation
[tex]\begin{gathered} 3x+4(-5)=4 \\ 3x-20=4 \\ 3x=20+4 \\ 3x=24 \\ x=8 \end{gathered}[/tex]Final answer:
Solution of given system of equation is (8,-5)
In ASTU, SU is extended through point U to point V, m/STU = (3x + 14)°,
m/UST = (2x + 12)°, and m/TUV = (7x+6)°. What is the value of x?
By applying the exterior angle property, the value of x is equal to 5.
What is the exterior angle property?The exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
How to determine the value of x?In order to determine the value of x in triangle STU (ΔSTU), we would have to apply exterior angle property.
Mathematically, the exterior angle property can be used to model triangle STU (ΔSTU) and this is given by:
m<TUV = m<STU + m<UST
Substituting the given parameters into the formula, we have;
(7x+6)° = (3x + 14)° + (2x + 12)°
7x + 6 = 5x + 16
7x - 5x = 16 - 6
2x = 10
x = 10/2
x = 5.
Read more on exterior angle property here: https://brainly.com/question/28034179
#SPJ1
Calculus early transcendental functions. Solve the equation.. use logs and round to 2 decimal places
This becomes:
[tex]\begin{gathered} \text{Log}_8(7(\frac{2x}{5}+9))=2\text{Log}_88 \\ \text{Log}_8(\frac{14x}{5}+63)=\text{Log}_88^2 \\ \frac{14x}{5}+63=8^2 \end{gathered}[/tex][tex]\begin{gathered} \frac{14x}{5}=8^2-63 \\ \frac{14x}{5}=64-63 \\ \frac{14x}{5}=1 \\ \text{corss}-\text{multiply} \\ 14x=5 \\ x=\frac{5}{14} \end{gathered}[/tex]A company purchased a new truck at a cost of $72,000 on July 1, 2019. The truck is estimated to have a useful life of 5 years and a salvage value of $2,000. The company uses the straight-line method of depreciation. The book value of the truck on December 31, 2019 is:
A company purchased a new truck, then the book value of the truck on December 31, 2019 is $51,000, because the company uses the straight-line method of depreciation.
A company purchased a new truck at a cost = $72,000 on July 1, 2019.
Estimated to have a useful life time = 5 years
A salvage value = $2,000
The formula for depreciation expense, using straight line method is;
What is a depreciation expense :Depreciation expense is the cost of an asset that has been depreciated for a single period, and shows how much of the asset's value has been used up in that year. Accumulated depreciation is the total amount of depreciation expense that has been allocated for an asset since the asset was put into use.
Based on the given conditions, formulate :
= (Cost - Salvage value) / life time (Equation-1)
We consider,
Cost = $72,000
Salvage value = $2,000
Life time = 5 years
We can substitute this values in equation-1,
So,
We can write,
= ($72,000 - $2,000) / 5
= $70,000 / 5
= $14,000.
Therefore,
The book value of the truck on December 31, 2019 would be;
= (cost - book value x (difference of year + difference of months/total months))
= $72,000 - $14,000 × (1 + 6/12)
= $72,000 - $14,000 x (1+1/2)
= $72,000 - $14,000 x (1+0.5)
= $72,000 - $14,000 x 1.5
= $72,000 - $21000
= $51,000
Note that we arrived at the value of 6 because July to December is 6 months.
Therefore,
The book value of the truck on December 31, 2019 is $51,000, because the company uses the straight-line method of depreciation.
To learn more about information visit Depreciation method :
brainly.com/question/19053579
#SPJ1
A pharmaceutical company makes the capsule below. Find the volume of the capsule
Write the transformed equation for f(x) -5, calling it h(x)
The image of the function after the translation is h(x) = 6x - 3
How to determine the equation of h(x)?The given parameters are:
f(x) = 6x + 2
The transformation is given as
f(x) - 5
This implies that we translate the function f(x) 5 units down
Mathematically, this transformation can be represented as
(x, y) = (x, y - 5)
When represented as a function, we have
h(x) = f(x) - 5
Substitute the equation f(x) = 6x + 2 in the equation h(x) = f(x) - 5
So, we have the following equation
h(x) = 6x + 2 - 5
Evaluate the like terms
h(x) = 6x - 3
Hence, the equation of h(x) is h(x) = 6x - 3
Read more about translation at
https://brainly.com/question/7592534
#SPJ1
Possible question
Given that the equation of f(x) is f(x) = 6x + 2
Write the transformed equation for f(x) -5, calling it h(x)
