An employee at a state park has 84 photos of animals found at the park. She wants to arrange the photos in rows so that every row except the bottom row has the same number of photos. She also wants there to be at least 8 rows. Complete the description of two different ways she can arrange the photos.
Answers
Reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.5 rows of 10 photos and last row with 3 photos,
6 rows of 8 photos and last row with 5 photos,
7 rows of 7 photos and last row with 4 photos,
Hence, reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.
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Related Questions
match the following each letter may be used more than once.a. 12/15b. 15/12c. 9/15d. 9/12e. 12/9f. 15/9
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We have a right triangle and we have to write some of the trigonometric ratios.
A trigonometric ratio relates a trigonometric function of an angle of the tiangle with a quotient of two of the sides of the triangle.
The basic trigonometric ratios are:
[tex]\begin{gathered} \sin (\alpha)=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \cos (\alpha)=\frac{\text{Adyacent}}{\text{Hypotenuse}} \end{gathered}[/tex]We can also write the trigonometric ratio for the tangent:
[tex]\tan (\alpha)=\frac{\sin (\alpha)}{\cos (\alpha)}=\frac{\text{Opposite}}{\text{Adyacent}}[/tex]Now, we can write sin(x):
[tex]\sin (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XZ}=\frac{12}{15}[/tex]The opposite side to X is YZ and the hypotenuse is XZ, so sin(X) = YZ/XZ = 12/15.
In the same way, we can calculate cos(x):
[tex]\cos (X)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{XY}{XZ}=\frac{9}{15}[/tex]The tan(x) can be calculated as:
[tex]\tan (X)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{YZ}{XY}=\frac{12}{9}[/tex]For Z, the opposite and adyacent angles are different than for X, so we can write:
[tex]\tan (Z)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{XY}{YZ}=\frac{9}{12}[/tex]Answer:
sin(X) = 12/15
cos(X) = 9/15
tan(X) = 12/9
tan(Z) = 9/12
write each fraction in simplest form 3/12
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3/12 is 1/4 in its simplest form
What is the new equation 1 when youmultiply by -1?
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the equation will be
-x - y = 7
Select all the lines that are perpendicular to 3x – y = 10. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36)
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The lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
Line equation:
3x - y = 10
y = 3x - 10
here slope m = 3.
perpendicular line slope = -1/m = -1/3
so the perpendicular line must have slope m = -1/3
A.
y = 3x + 5
here slope m = 3
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
B.
y = -13x + 17
here slope m = -13
This line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
C.
x + 3y = 27
3y = -x + 27
y = -1/3(x) + 27/3
y = -1/3(x) + 9
here slope m = -1/3
This line is perpendicular to the 3x - y = 10 because here slope is equal to -1/3.
D.
y - 2 = 13(3x+36)
y = 39x + 468 - 2
y = 39x + 466.
here slope m = 39.
So this line is not the perpendicular to 3x - y = 10 because here slope not equal to -1/3.
Therefore the lines that are perpendicular to 3x – y = 10. is option C (x+3y= 27).
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Solve the system of linear equations.7x + 2y = -88y = 4x
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7x + 2y = -8 Equation 1.
8y = 4x Equation 2.
We solve for y in eq. 2; as follows:
y = 4x/8.
Now we replace y on eq. 1:
7x + 2(4x/8) = -8
7x + x = -8
8x = -8
x = -8/8
x = -1
Finally we replace x on eq 2:
8y = 4(-1)
8y = -4
y = -4/8
y = -1/2
In an arithmetic sequence a18 = -10 and a40= 100 , write the explicit rule, the recursive rule, and find s30
Answers
Answer:
Explicit rule [tex]a_n=5n-100[/tex]Recursive rule [tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms [tex]-675[/tex]
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Let the first term be a and common difference be d.
Use equations for nth term and sum of the first n terms[tex]a_n=a+(n-1)d\\[/tex][tex]S_n=n(a+a_n)/2[/tex]Use the first equation to find the values of a and d[tex]a_{18}=a+17d=-10[/tex][tex]a_{40}=a+39d=100[/tex]Substract the first equation from the second and solve for d39d - 17d = 100 + 1022d = 110d = 110/22d = 5Find aa + 17*5= - 10a + 85 = - 10a = - 95Explicit rule[tex]a_n=-95+5(n-1)=-95+5n-5=5n-100[/tex]Recursive rule[tex]a_1=-95,a_n=a_{n-1}+5[/tex]Sum of the first 30 terms[tex]S_{30}=(-95-95+29*5)*30/2=(-45)*15=-675[/tex]The explicit rule is a(n) = - 95 + 5 · (n - 1), whose recursive rule is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5. The 30th element of the arithmetic sequence is 50.
How to derive an arithmetic sequence
Arithmetic sequences are sets of elements generated by a formula of the form:
a(n) = a + r · (n - 1), for n ≥ 1
Where:
a - First element of the sequence.r - Common raten - Index of the n-th element of the sequence.Please notice that the common rate is the difference between any two consecutive elements of the sequence. The recursive form is described by the following form:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + r
Now we should determine the elements of the explicit rule by solving the following system of linear equations:
n = 18
- 10 = a + r · (18 - 1)
a + 17 · r = - 10
n = 40
100 = a + r · (40 - 1)
a + 39 · r = 100
Then, we solve the system of linear equations by numerical methods:
(a, r) = (- 95, 5)
And the 30th element of the arithmetic series:
a(n) = - 95 + 5 · (n - 1)
a(30) = - 95 + 5 · (30 - 1)
a(30) = 50
And the recursive form is [tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] + 5.
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A billboard has an area of 32 square meters. Express the area in square feet.
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We will use the equivalency:
[tex]\begin{gathered} 1m=3.281ft \\ \frac{3.281ft}{1m}=1 \end{gathered}[/tex]Then, if we have an area of 32 m^2, we can multiply this value by the equivalency factor we wrote (as it is equal to 1) as:
[tex]\begin{gathered} A=32m^2\cdot(\frac{3.281ft}{1m})^2 \\ A=32m^2\cdot\frac{10.765ft^2}{1m^2} \\ A=344.48ft^2 \end{gathered}[/tex]Answer: the area is 344.48 sq ft.
Evaluate log3/8 91 using the change of base formula. Round your answer to one decimal place.
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We have to apply the change of base formula:
[tex]\log _b(a)=\frac{\log _x(a)}{\log _x(b)}[/tex]We can apply this to our expression as:
[tex]\log _{\frac{3}{8}}(91)=\frac{\ln(91)}{\ln(\frac{3}{8})}=\frac{\ln (91)}{\ln (3)-\ln (8)}\approx\frac{4.511}{1.099-2.079}=\frac{4.511}{-0.980}\approx-4.6[/tex]Answer: -4.6
"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
Answers
"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
So, it will mean the lines are parallel
so, the graph which describe the system is pink
The answer is option D
The function g is defined as follows.=gx+5x27If the graph of g is translated vertically upward by 3 units, it becomes the graph of a function f.Find the expression for fx.
Answers
f(x) = 5x²+10
Explanations:
Given the function g(x) expressed as:
[tex]g(x)=5x^2+7[/tex]If the function g(x) is translated vertically upward by 3 units to produce f(x), the resulting translation used will be given as:
[tex]f(x)=g(x)+3[/tex]Substitute the function g(x) into the translation rule to have:
[tex]\begin{gathered} f(x)=5x^2+7+3 \\ f(x)=5x^2+10 \end{gathered}[/tex]Therefore the expression for f(x) is 5x²+10
Ming prepared three chemical solutions with temperatures -5, -4, and -3. what is the correct compares of the three temputures?
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So we will like to compare the three numbers -5, -4 and -3. We will like to compare the three temperatures. To know wich numbers is less than the other we can draw the real line
The more to the left the number are the lesser it is therefore
[tex]-5<-4<-3[/tex]simplifying like terms and distributive property7b + 2(46 - 3)
Answers
We will solve as follows:
[tex]7b+2(46-3)=7b+92-6[/tex][tex]=7b+86[/tex]So, the solution is 7b + 86.
Give the equation of the transformed quadratic toolkit function shown below.()=−(+1)2+2()=−(−1)2+2()=−(+1)2+2()=(−1)2−2
Answers
The Solution:
Given:
Required:
Determine the function of the given graph.
The required equation is:
[tex]y=-\left(x-1\right)^{2}+2[/tex]Answer:
[option 2]
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour, how long will it take them to be 3180 miles apart?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour,
how long will it take them to be 3180 miles apart?
Step 2:
Let the distance of one of the planes flying west at 520 miles per hour be:
[tex]520\text{ x}[/tex]And let the distance of the other plane flying east at 540 miles per hour be:
[tex]540\text{ x}[/tex]where x , represents the time of flight in hours, such that:
[tex]\begin{gathered} 520\text{ x + 540 x = 3180} \\ 1060\text{ x = 3180} \\ \text{Divide both sides by 1060, we have that:} \\ x\text{ = }\frac{3180}{1060} \\ x\text{ = 3} \end{gathered}[/tex]CONCLUSION:
The time it will take them to be 3180 miles apart will be in 3 hours' time.
Find f[2) if f(x) = (x+ 1)^2 O9O6 O5
Answers
You have the following function:
f(x) = (x + 1)²
In order to determine the value of f(2) you replace the value x = 2 in the given function and make the operations, just as follow:
f(2) = (2 + 1)² simplify inside parenthesis
f(2) = (3)² 3² is the same as 3x3=9
f(2) = 9
Hence, the value of the function when x = 2 is f(2) = 9
What volume of ice cream is contained in a 10 cm-high ice cream cone with a base radius of 4 cm?
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We would find the volume of the ice cream contained in the cone by applying the formula for determining the voume of a cone which is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
height = 10
radius = 4
pi is a constant whose value is 3.142
Thus,
Volume = 1/3 x 3.142 x 4^2 x 10
Volume = 167.57
rounding to the nearest whole number,
Volume = 168 cubic cm
can you find the domain of a piecewise functuon
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a piecewise function
x+ 4 , if -4 ≤x <3
. 3 ≤ x < 6
Then ,answer is [ -4,6)
simplify 3y -(2y - 3)/4
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The expression is given
[tex]\frac{3y-(2y-3)}{4}[/tex]Simplify the expression
[tex]\frac{3y-2y+3}{4}=\frac{y+3}{4}[/tex]Hence the answer is
[tex]\frac{y+3}{4}[/tex]the rest of the question say what is the length of the tangent line labeled X
Answers
To solve this problem, consider the following picture
By the tangent secant segment theorem we have the following equation
[tex]a^2=b\cdot(b+c)[/tex]Note that in our case, we have a=x, b=3 and c=9. So if we replace this values in the equation, we have
[tex]x^2=3\cdot(3+9)=3\cdot12=36[/tex]so, applying the square root on both sides, we get
[tex]x=\sqrt[]{36}=\pm6[/tex]Since x is a distance, it should be strictly positive, so we have that
[tex]x=6[/tex]Using the explicit formula, find the 3rd term f(n)=5+4(n-1)
Answers
Answer:
13
Explanation:
The explicit formula of a sequence is given below:
[tex]f\mleft(n\mright)=5+4\mleft(n-1\mright)[/tex]When n=3
[tex]\begin{gathered} f\mleft(3\mright)=5+4\mleft(3-1\mright) \\ =5+4(2) \\ =5+8 \\ =13 \end{gathered}[/tex]The 3rd term of the sequence is 13.
The cost to manufactute a hair clip is $.50. With a markip of 200 percent,what is the selling price of this hair clip?
Answers
The selling price of this hair clip will be $ 1.50.
Cost price of the clip is = $ 0.50
Markup price = 200 percent
Mark up price = 200 % of 0.5
Mark up price = 200 / 100 × 0.50
Mark up price = 2 × 0.50
Mark up price = $ 1
Selling price of the product will be:
SP = $ 0.50 + $ 1
SP = $ 1.50
Therefore, we get that, the selling price of this hair clip will be $ 1.50.
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Your question was incomplete. Please refer the content below:
The cost to manufacture a hair clip is $0.50. With a markup of 200 percent, what is the selling price of this hair clip?
7. Marco was asked to rotate thecoordinate P(3,-4) 180 degrees about theorigin. Then, he decided to perform atranslation of (x, y+2) followed by adilation of 2. Marco was convinced thatP and P'" had the same coordinates. IsMarco correct? Explain your reasoning.
Answers
Let's take this, step by step.
First step:
Rotate the coordinate 180 degrees about the origin.
When a 180 degrees rotation about the origin is performed the coordinates (x, y) changes to (-x, -y)
Thus, P(3, -4) changes to P'(-3, 4)
Second Step:
Perform a translation of (x, y+2)
P'(-3,4) = P''(-3, 4+2) = P''(-3, 6)
Third step:
Perform a dilation of 2.
P''(-3, 6) = P'''(-3*2, 6*2) = P'''(-6, 12)
We can see that,
P(3, -4) while P'''(-6, 12)
Therefore, P and P''' do not have the same coordinates
Hello everybody! Can anyone help me with this? I just need to know if it's a Direct variation, a inverse variation, or neither? (Look at the photo) Thanks!
Answers
Remember that
A relationship between two variables, x, and y, represent a proportional variation (direct variation) if it can be expressed in the form y=Kx
An equation of the line that passes through the origin
A relationship between two variables, x, and y, represents an inverse variation if it can be expressed in the form y=1/x
There is a vertical asymptote at x=0
therefore
Looking at the graph
we have an inverse variationanswer is I6) Identifyas amonomial, binomial, or trinomial.4x2 – y + 0z4 binomial monomial Trinomial
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For this problem we have the following expression given:
[tex]4x^2-y+0z^4[/tex]Since any number multiplied by 0 is 0 then our expression becomes:
[tex]4x^2-y[/tex]And since we have two terms we can categorize the expression as a binomial.
I need help with this math problem. It’s homework and I have been sitting here for 3 hours. Please please help me.
Answers
Given:
Coordinates (-3 , 2), (6 , 2), (6 , -4), (-3 , -4)
Required:
Area and Parameter
Explanation:
Formula to find the distance between two points
Distance between (-3 , 2), (6 , 2) and (6 , 2), (6 , -4)
[tex]\begin{gathered} d=\sqrt{(6-(-3))\placeholder{⬚}^2+(2-2)\placeholder{⬚}^2} \\ d=9 \end{gathered}[/tex]Final Answer:
Volunteer drivers are needed to bring a students to the championship baseball game. Drivers either have cars, which can eat 4 students, or vans which can seat 6 students. The equation 4c +60 80 describes the relationship between the number of carse and number of vans v that can transport exactly so students 3 Explain how you know that this graph represents this equation number of vans 2 4 6 8 10 12 14 16 18 20 22 24 number of cars
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One featue of the equation is that when c = 0
[tex]\begin{gathered} 4(0)+6v=80 \\ \therefore v=13.33 \end{gathered}[/tex]The other feature is that when v = 0
[tex]\begin{gathered} 4c+6(0)=80 \\ \therefore c=20 \end{gathered}[/tex]Therefore, our graph must contain the points (0, 13.33) and (20, 0), and looking at the graph given we see that it has exactly those points; hence, the graph represents the equation given
A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds the amplitude has decreased to 13 cm. The spring oscillates 14 times each second. Find a function that models the distance, D the end of the spring is below equilibrium in terms of seconds, t, since the spring was released.
Answers
The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
What is equilibrium?A state of balance between opposing forces or actions that is either static (as in a body acted on by forces whose resultant is zero) or dynamic (as in a reversible chemical reaction when the rates of reaction in both directions are equal).
Given that, a spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second.
Amplitude begins at 17 cm, [tex]A_{0}[/tex] = 17 cm
The amplitude decreases by 13/3 = 4.33 per second = 0.043%
The amplitude function can be then modelled as =
A(t) = [tex]A_{0}[/tex][tex](1-0.043)^{t}[/tex]
A(t) = [tex]A_{0}[/tex][tex]0.957^{t}[/tex]
The spring oscillates 14 times each second, therefore,
T = 1/14
2π/B = 1/14
B = 28π
The graphical equation is;
D(t) = [tex]A_{cos}[/tex](Bt-C)+D
Horizontal shift = 0
Vertical shift = 0
Hence, The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
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It costs mrs. barazal $245 for her and 6 people to take a day-long guided tour of the Everglades how much does the guided tour cost per person?
Answers
For Barazal and 6 persons the cost is $245
So, the number of persons = 7
so, the cost per person = 245/7 = $35
So
the guided tour cost per person = $35
Question 5 of 10 Which function is increasing? O A 19-(0) OB. Rx) = 5* O C. f( 10w -() OD. (X) = (0.5)
Answers
Increasin function:
f(x) = a^x
Where a must be greater than 1:
A. 1/15 = 0.06 NO
B. 5 YES
C. 1/5 NO
D. 0.5 NO
Correct option B.5
5>1
Hi, I'm having a really hard time doing Multi Step Equations in Math, please help me.
Answers
You have the following equation:
4x - 3 = 2x + 5
In order to solve the previous equation, proceed as follow:
4x - 3 = 2x + 5 subtract 2x both sides
4x - 2x - 3 = 5 add 3 both sides
4x - 2x = 5 + 3 simplify like terms
2x = 8 divide by 2 both sides
x = 8/2
x = 4
Hence, the solution to the given equation is x = 4