Given that the total money Elise had, was $30.
Since she spent $18 on gifts and the rest on 3 corn dogs.
Let the cost of a corn god be 'x' dollars. Then the cost of 3 corn dogs will be,
[tex]\begin{gathered} \text{Expense on corn dogs}=\text{ No. of corn dogs}\times\text{ Cost of 1 corn dog} \\ \text{Expense on corn dogs}=3\times x \\ \text{Expense on corn dogs}=3x \end{gathered}[/tex]So it is found that Elise spent $(3x) on corn dogs.
Since she had spent all the money in buying these two things, the total exprense must be equal to the total money Elise had in the beginning,
[tex]\begin{gathered} \text{Expense on corn dogs}+\text{ Expense on gifts}=30 \\ 3x+18=30 \end{gathered}[/tex]Thus, the required equation is obtained.
Therefore, option (a) is the correct choice.
fine the value of x in(2x+5)(8x+5)
We are given the value of two angles as functions of "x"
[tex]\begin{gathered} \text{angle 1 = 2x+5;} \\ \text{angle 2 = 8x+5} \end{gathered}[/tex]These are supplentary angles, that is, their sum is 180 degrees
[tex]\text{angle 1 + angle 2 =180}^{\circ}[/tex]Replacing the values for the angles
[tex](2x+5)+(8x+5)=180[/tex]Now we solve the equation, first by adding similar terms
[tex]10x+10=180[/tex]Now we substract 10 on both sides
[tex]10x=170[/tex]Now we divide by 10 on both sides
[tex]x=\frac{170}{10}=17[/tex]The value of x is 17
Please find entire surface are of a stereo receiver (question 17)
We could approach the stereo receiver to a rectangular prism, that has the formula of surface area (A):
[tex]A=2ab+2bc+2ac[/tex]As the dimensions are given: a = 18", b = 16", c = 9"; then we just have to replace these values in the formula:
[tex]A=2(18)(16)+2(16)(9)+2(18)(9)[/tex]Simplifying:
[tex]A=576+288+324[/tex][tex]A=1188[/tex]Answer: 1188 in²
Question 7 of 9Constance has an apple that weighs 85,000 milligrams and a peach that weighs 0.15 kilograms. Which fruit has the greater mass? Choose the words and numbers to complete the statements.Convert the masses of both fruits to the same unit.85,000 milligrams is the same asChoose...grams.0.15 kilograms is the same asChoose...grams.TheChoose...has the greater mass.
The Solution:
Given:
Apple weight = 85,000 milligrams
Peach weight = 0.15 kilograms.
Required:
To determine which fruit has a greater mass.
Converting 0.15 kilogram to milligrams, we get:
[tex]\begin{gathered} 0.15\times1000000=150\text{ milligrams} \\ 85000mg>150mg \end{gathered}[/tex]Clearly, Apple has a greater mass than a peach.
Therefore, the correct answer is Apple fruit.
(c) When the local time in Athens is 09 00, the local time in Berlin is 08 00.
A plane leaves Athens at 13.15
It arrives in Berlin at 1505 local time.
(i) Find the flight time from Athens to Berlin.??
Answer:
l _ to the cinema at least a week
The flight time from Athens to Berlin is 50 minutes as per the given data.
What is local time?Local time refers to the time in a specific location or time zone. It is the time that is used and observed by people in a particular region or city.
To find the flight time from Athens to Berlin, we need to calculate the time difference between the two cities and subtract it from the elapsed time between the departure and arrival times.
Athens is one hour ahead of Berlin when it is 9:00 AM in Athens, it is 8:00 AM in Berlin. This means that when the plane leaves Athens at 13:15 local time, it is 12:15 in Berlin.
The elapsed time between the departure time (13:15) and the arrival time (15:05) is 1 hour and 50 minutes.
However, we need to account for the time difference between the two cities. Since Berlin is one hour behind Athens, we need to subtract one hour from the elapsed time:
1 hour and 50 minutes - 1 hour = 50 minutes
Therefore, the flight time from Athens to Berlin is 50 minutes.
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The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 80?
Answer:
25%
Explanation:
In the given box-and-whisker plot, the third quartile, Q3 = 80.
The percentage of data values that are greater than the third quartile is 25%.
Therefore, the percentage of the data values greater than 80 is 25%.
help me with this question
Answer:
Step-by-step explanation:
just 3,2
Combine like terms to simplify the expression: 1.17 -0.07a + (-3.92a) 1.17 - 3.850 Stuck? Watch a video or use a hint.
The given expression is
[tex]1.17-0.07a+(-3.92a)[/tex]Observe that -0.07a and -3.92a are like terms, let's add them.
[tex]\text{1}.17-3.99a[/tex]Hence, the final expression is 1.17 - 3.99a.Persent to a decinal 7%.
To express a percentage as decimal numbers you have to make the following convertion:
Consider that 100% is equal to 1, use cross multiplication to convert 7%:
100%____1
7%____x
[tex]x=\frac{7\cdot1}{100}=\frac{7}{100}=0.07[/tex]So, remember, to transform any percentage in decimal numbers, just divide it by 100.
In simple layman’s English please explain the difference between uniform probability models and non-uniform probability models.
In a uniform probability model, all events have the same chance of occurring. For a non-uniform probability model, all events do not have the same chance of occurring
I need help on in the answer to this question
Using the 2 tangents line formula:
[tex]m\angle Q=\frac{1}{2}((360-mPR)-mPR)[/tex][tex]\begin{gathered} 81x-1=\frac{1}{2}(360-2(100x)) \\ 81x-1=\frac{1}{2}(360-200x) \\ 81x-1=180-100x \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 81x+100x=1+180 \\ 181x=181 \\ x=\frac{181}{181} \\ x=1 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} mPR=100(1)_{} \\ mPR=100 \end{gathered}[/tex]Answer:
A. 100
The triangle is a 45°-45°-90° triangle.x√2 = 66²36X =(√2)²x = 18Did not multiply the numerator by the radicalShould have squared the denominator only.No ErrorShould have squared the numerator onlyJUN1O6V2=82
Answer:
Did not multiply the numerator by the radical
Explanation:
The hypotenuse of a 45-45-90 triangle is equal to the leg times √2.
In this case, the leg is x and the hypotenuse is 6, so we have the following equation
hypotenuse = leg √2
6 = x √2
To solve for x, we get
[tex]\begin{gathered} x\sqrt{2}=6 \\ \\ x=\frac{6}{\sqrt{2}} \end{gathered}[/tex]Then, we need to multiply the numerator and denominator by √2, so
[tex]x=\frac{6}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{6\sqrt{2}}{(\sqrt{2})^2}[/tex]Therefore, the solution is equal to
[tex]x=\frac{6\sqrt{2}}{2}=3\sqrt{2}[/tex]Therefore, the error in the process was that they did not multiply the numerator by the radical
Ignore the second part where it has a question mark that was my attempt the question is on top.
The inverse function is [tex]f^-1(X)=5x+6[/tex],
Given,
[tex]y=\frac{x-6}{5}[/tex]
To find inverse function, first interchange the variables 'x' and 'y'
[tex]x=\frac{y-6}{5}[/tex]
solve for y,
[tex]5x=y-6\\\\5x+6=y\\\\y=5x+6[/tex]
Replace y with [tex]f^-1(x)[/tex]
[tex]f^-1(X)=5x+6[/tex]
Thus, the inverse function is [tex]f^-1(X)=5x+6[/tex]
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if x + 9 equals 13 what is the value of x
X + 9 = 13
To know the value of x you have to subtract 9 from both sides of the equation
x+9-9= 13-9
x= 4
find the slope of the line through the giving points-1 -5 and 1 -1
the given points are
(x1 , y1) = (-1 , -5) and ()x2, y2) = (1 , -1)
the slope of the line is given as follows,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} m=\frac{-1-(-5)}{1-(-1)} \\ m=\frac{-1+5}{1+1}=\frac{4}{2}=2 \end{gathered}[/tex]so the slope is m = 2
You deposit $75 in an account that earns simple interest at an annual rate of 5% . How much money is in the account after 3 years?
The account balance in the account $86.25 after 3 years by using simple interest.
What is the simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The formula of the simple interest is I = PRt.
P = Principal
R = Rate of interest per year
t = time
In the given question Principal = $75, R = 5% = 0.05, t = 3 years.
I = 75 × 0.05 × 3 = 11.25
The account balance after 3 years will be sum of principal and interest.
The account balance after 3 years is = $(75 + 11.25) = $ 86.25.
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Find the compound interest and future value. Round your answers to the nearest cent. Do not round intermediate steps.Principal Rate Compounded Time$580 4.65% Quarterly6 yearsThe future value is $and the compound interest is $ХSCheck
Compound Interest
The Future Value of investment on compound interest can be calculated with the formula:
[tex]FV=PV(1+i)^n[/tex]Where PV is the present value or Principal, i is the adjusted interest rate and n is the number of compounding periods.
The principal is PV=$580.
The APR is 4.65% = 0.0465
The compounding period is quarterly.
Since there are 4 quarters in a year, the adjusted interest rate is:
i = 0.0465 / 4 = 0.011625.
The number of periods is n=6 years * 4 = 24 quarters
Now compute the future value:
[tex]FV=580(1+0.011625)^{24}[/tex]Calculating:
[tex]\begin{gathered} FV=\$580\cdot1.31968 \\ FV=\$765.42 \end{gathered}[/tex]The future value is $765.42 and the present value is $580, so the interest is:
I = $765.42 - $580
I = $185.42
HELP MEEEEisolate the variable to solve 4x + 4 > -20. what number line shows the solution set?
Given,
The expression is,
[tex]4x+4>-20[/tex]Required
The solution of the inequality.
Taking the given expression as,
[tex]\begin{gathered} 4x+4>-20 \\ 4x+4-4>-20-4 \\ 4x>-24 \\ \frac{4x}{4}>-\frac{24}{4} \\ x>-6 \end{gathered}[/tex]So, the solution of the inequality is x > -6.
Hence, option B is correct.
Can you explain to me why I got this wrong? And what are the correct answers
To get the true statements, we will be testing the options one by one in order.
First option
[tex]\begin{gathered} \cos (25)=0.9063 \\ \cos (65)=0.4226 \\ \therefore\cos (25)\ne\cos (65) \end{gathered}[/tex]Second option
[tex]\begin{gathered} \cos (25)=0.9063 \\ \sin (65)=0.9063 \\ \therefore\cos (25)=\sin (65) \end{gathered}[/tex]Third option
[tex]\begin{gathered} \sin (25)=0.4226 \\ \cos (65)=0.4226 \\ \therefore\sin (25)=\cos (65) \end{gathered}[/tex]Fourth option
[tex]\begin{gathered} \tan (45)=1 \\ \tan (45)=1 \\ \therefore\tan (45)=\tan (45) \end{gathered}[/tex]Fifth option
[tex]\begin{gathered} \tan (65)=2.1445 \\ \tan (25)=0.4663 \\ \therefore\tan (65)=\tan (25) \end{gathered}[/tex]Hence, the correct options are Options 2, 3, 4.
Three math classes at Sunview High School collected the most box tops for a school fundraiser, and so they won a $600 prize to share among them. Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr. Canyon’s class collected 1,855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected?
The total amount fundraised is given as follows:
[tex]3760+2301+1855=7916\text{ box tops}[/tex]The proportion of Mr. Aceves' class collected is given as follows:
[tex]\frac{3760}{7916}\text{ box tops}[/tex]The proportion of Mr. Baca's class collected is given as follows:
[tex]\frac{2301}{7916}\text{ box tops}[/tex]The proportion of Mr. Canyon's class is given as follows:
[tex]\frac{1855}{7916}\text{ box tops}[/tex]Now compute the amount for Mr. Aceves' class is given as follows:
[tex]\frac{3760}{7916}\times600\approx284.99[/tex]Again, compute the amount for Mr. Baca's class is given as follows:
[tex]\frac{2301}{7916}\times600\approx174.41[/tex]Again, compute the amount for Mr. Canyon's class is given as follows:
[tex]\frac{1855}{7916}\times600\approx140.60[/tex]As a result, $284.99 will go to Mr. Aceve's class, $174.41 will go to Mr. Baca's class, and $140.60 will go to Mr. Canyon's class.
Is the ordered our (-2,8) a solution to: y-9=3x
It is not a solution
1) To get to know that, we need to plug it in the equation and check whether it is true or false.
2) Picking point (-2,8) and plugging -2 into x and 8 into y, we get:
[tex]\begin{gathered} y-9=3x \\ (8)-9=3(-2) \\ -1=-6\:False \end{gathered}[/tex]2) Hence, we can tell that (-2,8) is not a solution to that equation
which of the following is equivalent to the logarithmic equation below? log4 64=3
If PN = 2x + 5 ON =x + 3 and OS = 3x - 2. Solve for ps
Remember that
In a rectangle
opposite sides are parallel and congruent and the measure of the interior angles are 90 degrees
The diagonals are congruent
so
PS=ON
PO=SN
PN=OS
equate the equations of diagonals
PN=2x+5
OS=3x-2
2x+5=3x-2
solve for x
3x-2x=5+2
x=7
Find out PS
Remember that
PS=ON=x+3
substitute the value of x
PS=7+3
Ps=10 unitsWhich expression is -7 +6 X 5 - 2? O A) 13 X 5 - 2 O B) 7+11 – 2 OC) 13 X 3OD) 37 - 2
Which expression is equal to 7 + 6 x 5 - 2?
The first step is to use the PEMDAS, and this rule ensures that certain rules are followed in number operations. It simply means some mathematical signs would be given preference over the others. The acronym PEMDAS ensures that Exponents comes first, followed by Multiplication, Addition an then Subtraction. In this question, the Multiplication sign would be considered first and so we now have;
7 + [6 x 5] - 2
7 + 30 - 2
Then the addition sign would take prefernce now, and you have
[7 + 30] - 2
And that results in option D
D) 37 - 2
a building has 63 apartments in 70 bathrooms what is the ratio Apartments to bathrooms in the building simplest form
ANSWER:
The ratio is 0.9 or 9:10
STEP-BY-STEP EXPLANATION:
We can calculate the ratio, calculating the quotient between the number of apartments and the number of bathrooms, just like this:
[tex]\begin{gathered} \frac{63}{70}=\frac{7\cdot9}{7\cdot10}=\frac{9}{10}=0.9 \\ 9\colon10 \end{gathered}[/tex]convert 2.5 years into hours
We are asked to convert 2.5 years into hours.
Step 1:
There are 365 days in a year so 2.5 years will have
[tex]2.5\cdot365=912.5\text{ days}[/tex]Step 2:
There are 24 hours in a day so 912.5 days will have
[tex]912.5\cdot24=21900\text{ hours}[/tex]Therefore, 2.5 years will have 21900 hours.
Which of the following pairs of points define a line segment parallel to the x-axis?A. (4,3)(-4,3)B. (4,3)(4,-3)C. (-4,-3)(4,-3)D. (3,4)(-3,-4)
EXPLANATION:
1.We must first locate the pairs of points.
-Points A:
Evaluate the expression −2ln(e^2 −12)+8
Solve
[tex]\begin{gathered} -2\ln (e^2-12)+18 \\ -2\ln (7.389-12)+18 \\ -2\ln (-4.611)+18 \end{gathered}[/tex]Answer: Undefined solution
y=4x+6slope: 4y-int: (0,6)why after graphing y-int, is the second point on the line given a slope of 4/1? shouldn't it be 4,0?
The given line is,
[tex]y=4x+6[/tex]Here, the slope is, 4 and y intecept is 6.
For x = 4, we have,
[tex]y=4\times4+6=16+6=22[/tex]Therefore, the two points on the graph is, (0, 6) and (4, 22).
Now, for y = 1, we have,
[tex]\begin{gathered} 1=4x+6 \\ 4x=-5 \\ x=-\frac{5}{4} \end{gathered}[/tex]How many triangles exist that fit the following criteria?B = 30°, a = 4, b = 3
Given:
B = 30°, a = 4, b = 3
We will solve the triangle to find how many triangles exist that fit the given data
We will use the sine rule to find the angle A as follows:
[tex]\begin{gathered} \frac{a}{sin(A)}=\frac{b}{sin(B)} \\ \\ \frac{4}{sin(A)}=\frac{3}{sin(30)} \\ \\ sin(A)=\frac{4}{3}sin(30)=\frac{2}{3} \\ \end{gathered}[/tex]So, the measure of angle A will be as follows:
[tex]A=sin^{-1}(\frac{2}{3})=41.81\degree,or,138.19\degree[/tex]Now, we will find the measure of angle C using the fact that the sum of the angles = 180
[tex]\begin{gathered} C=180-(A+B) \\ A=41.81\degree\rightarrow C=180-(30+41.81)=108.19\operatorname{\degree} \\ A=138.19\operatorname{\degree}\rightarrow C=180-(30+138.19)=11.81\operatorname{\degree} \end{gathered}[/tex]So, there are two triangles that can fit the given data
So, the answer will be Two
A market analyst has projected that the cost of producing d dog leashes will be given by the polynomial10,500 + 3,9d, The revenue generated from the sale of d dog leashes will be given by the polynomial.d14,5 - 0,000030), Find a polynomial expression for the profit earned from producing and selling d dogleashes, Evaluate the expression for da 30,000.© $514,500© $295,650© $280,500© $535,500
Note that Profit = Revenue - Cost
From the problem, we have :
Revenue = d(14.5 - 0.00003d)
and
Cost = 10,500 + 3.9d
The profit function will be :
[tex]\begin{gathered} \text{Profit}=\text{Revenue}-\text{Cost} \\ \text{Profit}=d(14.5-0.00003d)-(10500+3.9d) \\ \text{Profit}=14.5d-0.00003d^2-10500-3.9d \\ \text{Profit}=-10500+10.6d-0.00003d^2 \end{gathered}[/tex]Substitute d = 30,000
[tex]\begin{gathered} \text{Profit}=-10500+10.6d-0.00003d^2 \\ \Rightarrow-10500+10.6(30000)-0.00003(30000)^2 \\ \Rightarrow280500 \end{gathered}[/tex]Answer :
C. $280,500