You have the following inequality:
x + 19 > 31
subtract 19 both sides and simplify:
x > 31 - 19
x > 12
The graph of the previous inequality is:
18/10 [blank] x/12 x =
18/10 = x/12
(18/10)* 12 = (x/12)* 12
18*12/ 10 = x (12/12)
216/ 10 = x
x= 108/5
x = 21.6
find the area of a regular 18-gon with radius of 14 mmA≈ __ mm squared do not found until the final answer, then round to the nearest tenth as needed.
ANSWER
EXPLANATION:
Given that;
The radius of the 18-gon is 14mm
Follow the steps below
Step 1; Calculate the interior angle by using the below formula
[tex]\text{ }\theta\text{ = }\frac{\text{ 180 \lparen n - 2\rparen}}{n}[/tex]Since the polygon has 18 sides, then n = 8
[tex]\begin{gathered} \text{ }\theta\text{ }=\text{ }\frac{180\text{ \lparen18 - 2\rparen}}{18} \\ \\ \theta\text{ }=\text{ }\frac{180\text{ }\times\text{ 16}}{18} \\ \\ \theta\text{ }=\text{ }\frac{2880}{18} \\ \theta\text{ }=\text{ 160}\degree \end{gathered}[/tex]Step 2; Find the base angle of the triangle
Recall, that all regular polygon can be divided into isosceles triangle by joining the vertices to the center. Hence, the base angle can be calculated below as
[tex]\begin{gathered} \text{ Base angle = }\frac{160}{2} \\ \text{ Base angle = 80}\degree \end{gathered}[/tex]Step 3; Find the height of triangle using trigonometric
[tex]\begin{gathered} \text{ tan }\theta\text{ }=\text{ }\frac{\text{ opposite}}{\text{ adjacent}} \\ \text{ } \end{gathered}[/tex]Since the radius of the polygon is 14mm, therefore, the base length is
[tex]\begin{gathered} \text{ Base length = }\frac{14}{2} \\ \text{ Base length = 7mm} \end{gathered}[/tex][tex]\begin{gathered} \text{ Tan 80 = }\frac{h}{7} \\ \text{ cross multiply} \\ \text{ h = tan 80 }\times\text{ 7} \\ \text{ h = 7tan 80} \\ \text{ tan 80 = 5.671} \\ \text{ h = 7 }\times\text{ 5.671} \\ \text{ h = 39.697 mm} \end{gathered}[/tex]Step 4; Find the area of the triangle
[tex]\begin{gathered} \text{ Area of a triangle = }\frac{1}{2}bh \\ \text{ Area of a trianlge = }\frac{1}{2}\times7\times39.697 \\ \text{ Area of a triangle = }\frac{277.879}{2} \\ \text{ Area of a triangle = 138.94 mm}^2 \end{gathered}[/tex]Step 5; Find the area of the polygon
Since there are 18 triangles in the polygon, then calculate the area of the 18-gon
Area of 18-gon = 18 x 138.94
Area of 18-gon = 2500.9 mm^2
Therefore, the area of the 18-gon is 2500.
50. What is the intersection of plane STUV and plane UYXT?SуUWZA. SVB.YZC. STD. TX
The intersection of plane STUV and plane UYXT will be the line segment TU.
The task is to determine the intersection of the planes UYXT and STUV.
We are aware of;
When two planes overlap, their intersection is a straight line.
The points 'T' and 'U' are shown in the picture to be on both planes UYXT and STUV.
As a result, the line connecting these two points, that is, the line TU likewise lies on both planes.
As a result, the line 'TU' is formed by the intersection of both planes.
Thus, the intersection of plane STUV and plane UYXT will be the line segment TU.
To learn more about the intersection of the planes visit:
https://brainly.com/question/1646172
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which ordered pair below would prevent this table from being a function?
We have the following:
A relation is a correspondence of elements between two sets.
A function is a relation where each element of a set (A) corresponds to one and only one element of another set (B).
Therefore, the only value in x that is repeated is -2, therefore the answer (-2, 0)
Completing the square to find the zeros3. a^2+2a-3=0
Answer:
1 and -3.
Explanation:
Given the quadratic polynomial:
[tex]a^2+2a-3=0[/tex]To use the completing the square method to find the zeros, follow the steps below:
Step 1: Take the constant to the right-hand side.
[tex]a^2+2a=3[/tex]Step 2: Divide the coefficient of a by 2, square it and add it to both sides.
[tex]a^2+2a+(1)^2=3+(1)^2[/tex]Step 3: Write the left-hand side as a perfect square.
[tex](a+1)^2=4[/tex]Step 4: Take the square root of both sides.
[tex]a+1=\pm\sqrt[]{4}[/tex]Step 5: Solve for a.
[tex]\begin{gathered} a=-1\pm\sqrt[]{4} \\ a=-1\pm2 \\ a=-1+2\text{ or }a=-1-2 \\ a=1\text{ or }a=-3 \end{gathered}[/tex]The zeros of the quadratic equation are 1 and -3.
Which expression is undefined? -8÷(-8) -8÷80÷88÷0
The expressions where a number is divided by 0 are undefined, as the result would became indefinitely big (infinity).
The expression -8÷80÷88÷0 has a division by 0, so it is undefined.
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10 Which of the following inequalities is represented by the number line?
Here, we want to select the inequality that is represented by the plot
The first thing we will do here is to get the type of circle given, whether shaded or unshaded
As we can see, the circle on the number -3 is unshaded
What this mean is that the type of inequality we shall be considering is the one without equal to
Hence, option A and C is out of it
To get the correct one between B and D, we have to look at the direction of the black line beside the circle
The direction of the black line as we can see is towards the right hand side
What this mean is that the inequality in question is greater than the value on which we have the circle
Conclusively, this mean that our answer is the second option
To show that you can identify implied mul-tiplication, rewrite this algebraic equationusing the times symbol wherever multipli-cation is implied.
In general, if a and b are two numbers,
[tex]\begin{gathered} ab=a*b \\ and \\ a(b)=a*b \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} bc=b*c \\ \Rightarrow3(bc)=3*(b*c)=3*b*c \\ and \\ 2d=2*d \end{gathered}[/tex]Thus, the answer is[tex]3*b*c=2*d[/tex]3*b*c=2*dWrite an equation for the conic in the xy-plane for
Given:
[tex]\frac{(x^{\prime})^2}{15}-\frac{(y^{\prime})^2}{6}=1\text{ at }\theta=30^o[/tex]To find:
We need to find an equation for the conic in the xy-plane.
Explanation:
We can find the conic equation by using the following equation.
[tex]x^{\prime}=x\cos \theta+y\sin \theta\text{ and }y^{\prime}=y\cos \theta-x\sin \theta[/tex][tex]\text{Substitute }\theta=30^o\text{ in the eqatuions.}[/tex][tex]x^{\prime}=x\cos 30^o+y\sin 30^o\text{ and }y^{\prime}=y\cos 30^o-x\sin 30^o\text{.}[/tex][tex]\text{Use }\cos 30^o=\frac{\sqrt[]{3}}{2}\text{ and }\sin 30^o=\frac{1}{2}\text{.}[/tex][tex]x^{\prime}=x(\frac{\sqrt[]{3}}{2})+y(\frac{1}{2})\text{ and }y^{\prime}=y(\frac{\sqrt[]{3}}{2})-x(\frac{1}{2})[/tex][tex]x^{\prime}=\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y\text{ and }y^{\prime}=\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x[/tex][tex]\text{ Substitute }x^{\prime}=\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y\text{ and }y^{\prime}=\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x\text{ in the given equation.}[/tex][tex]\frac{(\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y)^2}{15}-\frac{(\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x)^2}{6}=1[/tex][tex]\frac{1}{15}(\frac{\sqrt[]{3}}{2}x+\frac{1}{2}y)^2-\frac{1}{6}(\frac{\sqrt[]{3}}{2}y-\frac{1}{2}x)^2=1[/tex][tex]\frac{1}{15}\mleft\lbrace(\frac{\sqrt[]{3}x}{2})^2+(2\times\frac{\sqrt[]{3}x}{2}\times\frac{y}{2})+(\frac{y}{2})^2\mright\rbrace-\frac{1}{6}\mleft\lbrace(\frac{\sqrt[]{3}y}{2})^2-2\times\frac{\sqrt[]{3}y}{2}\times\frac{x}{2}+(\frac{x}{2})^2\mright\rbrace=1[/tex][tex]\frac{1}{15}\mleft\lbrace\frac{3x}{4}^2+\frac{\sqrt[]{3}xy}{2}+\frac{y^2}{4}^{}\mright\rbrace-\frac{1}{6}\mleft\lbrace\frac{3y}{4}^2-\frac{\sqrt[]{3}xy}{2}+\frac{x}{4}^2\mright\rbrace=1[/tex][tex]\frac{3x^2}{15\times4}^{}+\frac{\sqrt[]{3}xy}{15\times2}+\frac{y^2}{15\times4}^{}-\frac{3y^2}{6\times4}^{}+\frac{\sqrt[]{3}xy}{6\times2}-\frac{x}{6\times4}^2=1[/tex][tex]\frac{x^2}{20}^{}+\frac{\sqrt[]{3}xy}{30}+\frac{y^2}{60}^{}-\frac{y^2}{8}^{}+\frac{\sqrt[]{3}xy}{12}-\frac{x^2}{24}^{}=1[/tex]Here LCM is 360, making the denominator 360.
[tex]18x^2+12\sqrt[]{3}xy+6y^2-45y^2+30\sqrt[]{3}xy-15x^2=360[/tex][tex]3x^2+42\sqrt[]{3}xy-39y^2-360=0[/tex]Final answer:
The equation for the conic in the xy-plane is
[tex]3x^2+42\sqrt[]{3}xy-39y^2-360=0[/tex]If a set of grades for a class has a large range and a small standard deviation,what can you say about the class? Include an interpretation that is specific togrades in a class.
A large ranges indicates that there is a large difference between the highest and lowest grade scores. A smaller deviation indicates that the grades scores are less varied amom themselves.
An example is when the highest grade is 100 and the lowest grade is 5. In this case the range is larger than the case when the highest is 100 and the lowest 60.
A smaller standard deviation means that the data set of grades are close to the mean of the data set. The behavior is the following
Use the drop-down menus to identify the values of theparabola.Vertex=Domain=Range=
Given:
We get the point (0,4) from the graph.
Recall that the vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.
[tex]\text{Vertax =(0,4)}[/tex]Every single number on the x-axis results in a valid output for the function.
The domain of the parabola is real values.
[tex]\text{Domain}=(-\infty,\infty)[/tex]
The maximum value of y is 4 and the parabola is open down.
[tex]Range=(-\infty,4\rbrack[/tex]Final answer:
[tex]\text{Vertax =(0,4)}[/tex][tex]\text{Domain}=(-\infty,\infty)[/tex][tex]Range=(-\infty,4\rbrack[/tex]Circle C and circle J are congruent, what is NM?
Ok, so
We know that two circles are congruent. This makes that the triangles there, are cogruent.
Let me draw the situation here below:
If both triangles are congruent, that means that their sides and angles are equal.
Now if we notice, we realize that side DG and side NM will be equal.
So, DG = NM
Which is the same that
14t - 26 = 5t + 1
If we solve the equation for t:
14t - 5t = 26 + 1
9t = 27
And t = 3
Now, we want to find NM measure.
And we just have to replace t=3 in the expression 5t+1
This will be 5(3) + 1, which is 16.
Therefore, NM measures 16.
Ashton, Anywhere had a population of 294876 in 2007. The population is inci upon this data, predict the population for in 9 years.
Answer:
378,075
Explanation:
The population of Ashton in 2007 = 294876
The population increases at a constant rate of 2.8%.
Therefore, the population at any time, t after 2007 is:
[tex]\begin{gathered} P(t)=294876(1+2.8\%)^t \\ P(t)=294876(1+0.028)^t \\ P(t)=294876(1.028)^t \end{gathered}[/tex]Therefore, the population in 9 years time will be:
[tex]\begin{gathered} P(9)=294876(1.028)^9 \\ =378074.6 \\ \approx378,075 \end{gathered}[/tex]The predicted population in 9 years will be 378,075.
what is the answer to the equation-2n+3=8
-2n + 3 = 8
-2n = 8 - 3
-2n = 5
n = -5/2
Find the surface area of the isosceles trapezoid prism , Do not round answer
From the question;
The Area formula for a trapezoid is;
[tex]\begin{gathered} B=\frac{1}{2}h(b_1+b_2) \\ Where\text{ B=Area} \\ h=\text{height of the trapezoid} \\ b_1,b_2=bases_{} \end{gathered}[/tex][tex]\begin{gathered} B=\frac{1}{2}(3)(4+8) \\ B=18\operatorname{cm} \end{gathered}[/tex]So, we have the surface area as;
[tex]\begin{gathered} SA=ph+2B \\ \text{Where SA= surface area} \\ p=\text{perimeter of the trapezoid} \\ h=\text{height of the prism} \end{gathered}[/tex]But the perimeter p of the trapezoid is;
[tex]\begin{gathered} p=3.7\operatorname{cm}+4\operatorname{cm}+8\operatorname{cm}+3.7\operatorname{cm} \\ p=19.4\operatorname{cm} \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} SA=19.4(9)+2(18) \\ SA=174.6+36 \\ SA=210.6\operatorname{cm} \end{gathered}[/tex]264 milligrams is how many grams
SOLUTION
Milligrams is a unit of measurement for mass in which a unit is a thousandth gram.
Hence
[tex]1000mg=1g[/tex]Then
[tex]264mg=xg[/tex]Therefore
[tex]x=\frac{264}{1000}=0.264g[/tex]Hence
[tex]264mg=0.264g[/tex]Therefore we conclude that
264 milligrams is 0.264g
need help- don’t mind the writing in pencil I forgot to erase it
We will deteremine the length of segment TV as follows:
[tex]A=\frac{WU\cdot TV}{2}\Rightarrow200=\frac{16\cdot TV}{2}[/tex][tex]\Rightarrow400=16\cdot TV\Rightarrow TV=25[/tex]So, the lenght of segment TV is 25 centimeters.
slove two-step liner equations 19=s/2+15
s = 8
Explanation:
19=s/2+15
collect like terms:
19 - 15 = s/2
4 = s/2
[tex]\begin{gathered} 4\text{ =}\frac{s}{2} \\ \text{cross multiply} \\ s\text{ = 4}\times2 \\ s\text{ = 8} \end{gathered}[/tex]help me out please thanks
Answer:
1/10
Step-by-step explanation:
=a+4/5=3/2
=a=4/5-3/2
=a=1/10
Answer: a = 7/10
Step-by-step explanation:
Convert and mix 1 and 1/2 to get 3/2
Next move 4/5 to the right side
Then multiply 4/5 by 3/2 to get the answer 7/10
>>Хx = [?](Enter the number that belongs in the green box.
Answer: x = 90 degrees
Explanation:
In the given figure, the opposite sides are parallel. This means that the vertices are right angles. A right angle is 90 degrees. Thus,
x = 90 degrees
33. A coin is tossed and a die with numbers 1-6 is rolled. What is P(head and 3)a. 1/12b. 1/4C.1/3d. 2/334. Two cards are selected from a deck of cards numbered 1 - 10. Once a card isselected, it is replaced. What is P(two even numbers)?a. 1/4b. 2/9c. 1/2d. 135. Which of the following in NOT an example of independent events?a. rolling a die and spinning a spinnerb. tossing a coin two timesc. picking two cards from a deck with replacement of first cardd. selecting two marbles one at a time without replacement36. A club has 25 members, 20 boys and 5 girls. Two members are selected atrandom to serve as president and vice president. What is the probability that bothwill be girls?b. 1/25c. 1/30d. *a. 1/537. One marble is randomly drawn and then replaced from a jar containing twowhite marbles and one black marble. A second marble is drawn. What is theprobability of drawing a white and then a black?b. 2/9c. 3/8a. 1/3d. 1/638. Maria rolls a pair of dice. What is the probability that she obtains a sum that iseither a multiple of 3 OR a multiple of 4?a. 5/9b. 7/12c. 1/36d. 7/3639. Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What isP(A and B)?c. 4/15d. 2/15b. 1/5a. 2/5
SOLUTION
(33) The question says a coin is tossed and a die with 6 faces is rolled, what is the probability of getting a head and a 3.
Probability is given as
[tex]Probability=\frac{expected\text{ outcome}}{total\text{ outcome }}[/tex]Now, a coin has two faces, a head and a tail. So, total outcome is 2 faces.
We want to get the probability of getting a head. This becomes
[tex]\begin{gathered} Probability\text{ of head = }\frac{expected\text{ outcome}}{total\text{ outcome}}=\frac{1\text{ head}}{2\text{ faces}} \\ =\frac{1}{2} \\ P(head)=\frac{1}{2} \end{gathered}[/tex]So, probability of getting a head is 1/2
A die has 6 faces labelled 1, 2, 3, 4, 5 and 6
Probability of getting a 3 should be
[tex]\begin{gathered} Probability\text{ of getting 3 = }\frac{one\text{ face showing 3}}{6\text{ faces}} \\ that\text{ is }\frac{1}{6} \end{gathered}[/tex]So, probability of getting a 3 is 1/6
Now probability of getting a head and a 3, that is P(head and 3), means we multiply both probabilities, we have
[tex]\begin{gathered} P(head\text{ and 3\rparen = }\frac{1}{2}\times\frac{1}{6} \\ =\frac{1}{12} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{12}[/tex]Can you please show me how to do this so I can teach it to my boys? They need to Express percents as fractions or mixed numbers, and to express each percent as a decimal.
A. Let's convert the following percents into a fraction or a mixed number in the simplest form.
1.) 24%
4.) 150%
To be able to convert percentage into a fraction, we just apply the following formula:
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex]We get,
1.) 24%
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex][tex]\text{ = }\frac{24}{100}[/tex][tex]\text{ = }\frac{\frac{24}{4}}{\frac{100}{4}}\text{ = }\frac{6}{25}[/tex]Therefore, the fractional form of 24% is 6/25.
4.) 150%
[tex]\text{ Fractional Equivalent = }\frac{\text{Percentage}}{100}[/tex][tex]\text{ = }\frac{150}{100}[/tex][tex]\text{ = 1 }\frac{50}{100}\text{ = 1}\frac{1}{2}[/tex]Therefore, the fractional form of 150% is 1 1/2.
B. Express each percent as a decimal.
9.) 8%
14.) 568%
To be able to convert a percentage to a decimal, we just divide all percentages by 100.
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex]9.) 8%
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex][tex]\text{ = 8 }\div\text{ 100}[/tex][tex]\text{ Decimal Equivalent = 0.08}[/tex]14.) 568%
[tex]\text{Decimal Equivalent = Percentage }\div\text{ 100}[/tex][tex]\text{ = 568 }\div\text{ 100}[/tex][tex]\text{ Decimal Equivalent = 5.68}[/tex]Therefore, the decimal equivalent of 568% is 5.68.
how much higher is 1,774 than -118(adding and subtracting integers)
To find the difference between two numbers, we substract the smaller one from the bigger one. In this case, the smaller one is -118 and the bigger one is 1,774. Then:
[tex]1774-(-118)=1774+118=1892[/tex]Then 1774 is higher than -118 by 1892
What is the simplified value of 3/4 5/12 fraction
Thus, the final value is 5/16.
I have a practice question that I need explained and answered. Thank you - Rose
To determine the x - coordinate of the distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The distance between the two points is estimated using the above formular
[tex]\begin{gathered} x_2=4 \\ x_1=?_{} \\ y_1=-1 \\ y_2=9 \\ d=6\sqrt[]{6} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ 6\sqrt[]{6}=\sqrt[]{(x-4)^2+(9--1)^2} \\ \text{square both side } \\ (6\sqrt[]{6)^2}=(\sqrt[]{(x-4)^2+10^2})^2 \\ 216=(x-4)^2+100 \\ 216-100=(x-4)^2 \end{gathered}[/tex][tex]\begin{gathered} 116=(x-4)(x-4) \\ 116=x^2-8x+16 \\ 100=x^2-8x \\ x^2-8x-100=0 \end{gathered}[/tex]Solve using quadratic formular
[tex]\frac{-b\pm\sqrt[]{b^2}-4ac}{2a}[/tex][tex]\begin{gathered} \frac{-b\pm\sqrt[]{b^2}-4ac}{2a}\ldots..\text{ a= 1 , b = -8 , c = -100} \\ \frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-100)}}{2(1)} \\ \frac{8\pm\sqrt[]{64+400}}{2} \\ \frac{8\pm\sqrt[]{464}}{2}=\frac{8\pm4\sqrt[]{29}}{2} \\ \frac{2(4\pm2\sqrt[]{29)}}{2}=4\pm2\sqrt[]{29} \end{gathered}[/tex]Therefore the correct answer for the x - coordinates are:
[tex]\begin{gathered} x=4+2\sqrt[]{29}\text{ and } \\ x_{}=4-2\sqrt[]{29} \end{gathered}[/tex]How do you solve literal equation:u=x-k, solve for x12am=4, solve for aa-c=d-r, solve for a
In order to solve a literal equation, we just need to isolate the chosen variable in one side of the equation. So we have:
[tex]\begin{gathered} u=x-k \\ u+k=x \\ x=u+k \\ \\ 12am=4 \\ a=\frac{4}{12m} \\ a=\frac{1}{3m} \\ \\ a-c=d-r \\ a=d-r+c \end{gathered}[/tex]I need help to find X for my warm up paper. I'll include the photo as it doesnt fit:) 2 brainly tutors tried to help but they just told me they couldnt and I really need help:/
The inscribed angle SKQ intercepts the arc SQ. The next equation relates their measures:
[tex]\begin{gathered} \angle SKQ=\frac{1}{2}\hat{SQ} \\ 75=\frac{1}{2}\hat{SQ} \\ 75\cdot2=\hat{SQ} \\ 150\text{ \degree}=\hat{SQ} \end{gathered}[/tex]Arc SQ can be expressed as the addition of arcs SR and RQ.
[tex]\begin{gathered} \hat{SQ}=\hat{SR}+\hat{RQ} \\ 150=\hat{SR}+60 \\ 150-60=\hat{SR} \\ 90\text{ \degree}=\hat{SR} \end{gathered}[/tex]The inscribed angle KQR intercepts the arc KR. The next equation relates their measures:
[tex]\begin{gathered} \angle KQR=\frac{1}{2}\hat{KR} \\ 78=\frac{1}{2}\hat{KR} \\ 78\cdot2=\hat{KR} \\ 156\text{ \degree}=\hat{KR} \end{gathered}[/tex]Arc KR can be expressed as the addition of arcs KS and SR.
[tex]\begin{gathered} \hat{KR}=\hat{KS}+\hat{SR} \\ 156=\hat{KS}+90 \\ 156-90=\hat{KS} \\ 66\text{ \degree}=\hat{KS} \end{gathered}[/tex]Finally,
[tex]\begin{gathered} \hat{KS}=11x \\ 66=11x \\ \frac{66}{11}=x \\ 6=x \end{gathered}[/tex]7 thirds x 3 eighths
Answer: 0.875
Step-by-step explanation:
7/3 x 3/8 -> 21/24 -> 7/8
7/8 converted to decimal: 0.875
Justin’s shop sells 6 1/2 quarts of ice cream each day. How much is this in pints? Write your answer as a whole number or a mixed number in simplest form.Include the correct unit in your answer.
1) In this question we need to remind ourselves that there is one equivalence between quarts and pints, namely:
[tex]1\:quart--->2\:pint[/tex]2) Based on that, we can write out the following set of ratios:
[tex]\begin{gathered} \frac{1}{6\frac{1}{2}}=\frac{2}{x} \\ \\ x=2\times6\frac{1}{2} \\ \\ x=13 \end{gathered}[/tex]Note that there is a proportional relationship between them.
3) Thus, this is the answer.
Chase rode a Ferris wheel 93 timesaround, one lap after the other. If eachlap of the Ferris wheel took 20 seconds,how long was Chase's ride?minute
If Chase rode 93 times around, and each lap takes 20 seconds, to find out how long was Chase's ride we must multiply the time for each lap, and how many laps she did, then, the calculus will be
[tex]time=93\cdot20[/tex]The result will be in seconds!
[tex]\begin{gathered} time=93\cdot20 \\ \\ \text{time}=1860\text{ seconds} \end{gathered}[/tex]Then Chase's ride was 1860 seconds long! We can covert it in minutes by doing the division by 60
The time in minutes will be
[tex]\begin{gathered} \text{time}=\frac{1860}{60}\text{ minutes} \\ \\ \text{time}=31\text{ minutes} \\ \end{gathered}[/tex]Therefore, Chase's ride took 31 minutes