Probability that a person will retake their selfie 3 times = 7/50
Explanations:The total number of times the groupof people take selfies = 27+29+18+14+12
The total number of times the groupof people take selfies = 100
The number of times the selfie was taken thrice = 14
Probability that a person will retake their selfie 3 times = 14/100 = 7/50
A number squared subtracted from 3 times the number is equal to negative 70. Set up and solve a quadratic equation, then solve by factoring.
We will have the following:
From the problem we construct the expression:
[tex]3x-x^2=-70[/tex]Now, we solve for x:
[tex]\begin{gathered} \Rightarrow-x^2+3x+70=0\Rightarrow-(x^2-3x-70)=0 \\ \\ \Rightarrow-(x+7)(x-10)=0 \\ \\ x=-7 \\ x=10 \end{gathered}[/tex]The number can be either -7 or 10.
The playing surfaces of two foosball tables are similar. The ratio of the corresponding sidelengths is 10:7. If the perimeter of the smaller is 42, what is the perimeter of the larger table?
Given:
Ratio of corresponding sides = 10 : 7
Perimeter of smaller table = 42
Total ratio = 10 + 7 = 17
Let's find the perimeter of the larger table.
Given that both tables are similar, it means the corresponding sides are proportional.
To find the ratio of the larger table, let's first find the total perimeter of the both tables:
[tex]\frac{\text{smaller ratio}}{total\text{ ratio}}\times T=perimeter\text{ of smaller table}[/tex]Where T represents the total ratio.
Thus, we have:
[tex]\begin{gathered} \frac{7}{17}\times T=42 \\ \\ \text{Multiply both sides by 17:} \\ \frac{7}{17}\times17\times T=42\times17 \\ \\ 7T=714 \end{gathered}[/tex]Divide both sides by 7:
[tex]\begin{gathered} \frac{7T}{7}=\frac{714}{7} \\ \\ T=102 \end{gathered}[/tex]The total perimeter is 102.
To find the permeter of the larger table, we have:
Perimeter of larger table = Total perimeter - perimeter of smaller table.
Perimeter of larger table = 102 - 42
Perimeter of larger table = 60
Therefore, the perimeter of the larger table is 60.
ANSWER:
60
Lasso SelectInsert SpaceEditUnit 1 - Part 1 - Test ReviewWriting and Modeling with Equations1) A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50cents per ounce of toppings.a) Write an equation the represent the total cost (C) of an ice cream base on the ounce oftoppings (t).......b) Use the equation to determine how much Evan's ice cream would cost with 3 ouncesof toppings.
1
(a) The total cost, C, is given by:
[tex]C(t)=3+0.5t[/tex]b) With 3 ounces of toppings, we have
[tex]t=3[/tex][tex]C(3)=3+0.5(3)=3+1.5=4.5[/tex]Hence Evan's ice cream would cost $4.50
why does a point of intersection of the graphs of the equations represent the solution of the system formed by two equations. do you think this is true for any two types of equations
This is true for any pair of equations, the intersection represents a point where both coordinates x and y, coincide for both functions, it means that they satisfy both equations, and that's why intersection is the solution.
Devon is trying to find the unit price of a6-drink package on sale for $ 2.99. His sister saysthat at that price, each drink would cost just over $ 2.00.Is he right and how do you know? If not, how would Devon's sister find the right price?
Devon is trying to find the unit price of a
6-drink package on sale for $ 2.99. His sister says
that at that price, each drink would cost just over $ 2.00.
Is he right and how do you know? If not, how would Devon's sister find the right price?
To find the unit price, divide the total cost by the number of drinks
so
2.99/6=$0.50 per drink
therefore
He is not right
Simplify the expression. Write your answer as a power. 1 5 T 1 3 The expression is
Convert 3 1/3 miles to feet?
1 mile = 5280 ft
So:
3 1/3 x 5280 = 17,600 ft
The equation y=x relates proportional quantities x and y. What is the value of y when x is 36? Enter your answer in the box.
Direct variation:
We are given that x and y are directly proportional.
[tex]y=x[/tex]Recall that the standard form of the directly proportional relationship is given by
[tex]y=kx[/tex]Where k is the constant of proportionality.
Comparing the standard form with the given equation we see that k is equal to 1.
[tex]y=1\cdot x[/tex]Let us substitute the value of x into the above equation
[tex]y=1\cdot36=36[/tex]Therefore, the value of y is 36.
(when the constant of proportionality (k) is 1 then the x and y values are equal)
explain how you can use proportional reasoning to determine the whole if you know what 21 is 60% of the whole
The whole of the number is 35.
It is given in the question that 21 is 60 % of the whole of the number.
We have to find the whole of the number.
Let the whole of the number be x.
Hence, according to the data given in the question, we can write,
60 % of x = 21
Here, we can use the unitary method to find the whole of the number.
(60/100)*x = 21
(3/5)*x = 21
Dividing the equation by (3/5), we get,
x = 21/(3/5)
x = 21*(5/3)
x = 105/3
x = 35.
Hence, the whole of the number is 35.
To learn more about unitary method, here:-
https://brainly.com/question/22056199
#SPJ1
The graph of the function f is shown above.What is lim f(x)?
Given:
Find-:
[tex]\lim_{x\to2}f(x)[/tex]Explanation:-
[tex]\lim_{x\to2}f(x)[/tex][tex]\begin{gathered} \lim_{x\to2}f(x) \\ \\ =f(2) \end{gathered}[/tex]At x= 2 function value is 1
[tex]\lim_{x\to2}f(x)=1[/tex]Find a,b, c, and d.
According to the given diagram, d and 46° are vertical angles, which means d = 46°.
Then, using the supplementary angles theorem, we have
[tex]\begin{gathered} d+82+b=180 \\ 46+b+82=180 \\ b=180-46-82 \\ b=52 \end{gathered}[/tex]On the other hand, a and 134 are vertical angles, so a = 134°.
Then, using the exterior angle theorem, we have
[tex]\begin{gathered} a=b+c \\ 134=52+c \\ c=134-52 \\ c=82 \end{gathered}[/tex]Hence, a = 134°, b = 52°, c = 82°, and d = 46°.Use properties to evaluate ( = })(-8). O A. 5 OB. 2 O C. -2 O D. -5
How do I write 679,400 in scientific notation?
Given:
679,400
To write this in scientific notation, we have to turn the number to a decimal and multiply by a power of 10.
therefore, we have:
[tex]679,400\Longrightarrow\text{ 6.79400 }\ast10^5[/tex]ANSWER:
[tex]6.794\text{ }\ast10^5[/tex]I need help solving this math problem Find the equation of the line in its form y = mx + b
ANSWER:
[tex]y=2[/tex]STEP-BY-STEP EXPLANATION:
The equation must be in its slope-intercept form, which is as follows:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]We calculate the slope as follows:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{ Replacing the points:} \\ m=\frac{2-2}{7-(-1)}=\frac{0}{7+1}=\frac{0}{8}=0 \end{gathered}[/tex]Now, we calculate the value of b, like this:
[tex]\begin{gathered} 2=0\cdot7+b \\ b=2 \end{gathered}[/tex]Therefore, the equation is the following:
[tex]\begin{gathered} y=0x+2 \\ y=2 \end{gathered}[/tex]Evaluate 6 1/5 - 2 4/5 + 4
Given data;
The given expression is 6 1/5 - 2 4/5 + 4.
The given expression can be written as,
[tex]\begin{gathered} 6\frac{1}{5}-2\frac{4}{5}+4=\frac{31}{5}-\frac{14}{5}+4 \\ =\frac{31-14+20}{5} \\ =\frac{37}{5} \\ =7\frac{2}{5} \end{gathered}[/tex]Thus, the given expression can be written as 7 2/5.
Which of the following statements must be true based on the diagram below?(Diagram is not to scale.)FDEO EF is a segment bisector.EF is an angle bisector.E is the vertex of a right angle.OF is the vertex of a right angle.o F is the midpoint of a segment in the diagram.None of the above.Submit Answer
From the diagram given;
ABCD is a quadrilateral;
Line |EF| bisects the line |AD| and line |CD|,
Thus, from the given options;
LINE |EF| is a segment bisector is the only correct option.
D and E are sets of real numbers defined as follows.D={v | v>4}E = {v | v<)Write Dn E and DU E using interval notation.If the set is empty, write Ø.D n E=D u E=
The first step we have to follow is to write the sets in interval notation.
D contains all the numbers that are greater than 4.
E contains all the number that are less than or equal to 9.
In interval notation, they are written this way:
[tex]\begin{gathered} D=(4,\infty) \\ E=(-\infty,9\rbrack \end{gathered}[/tex]Now, to find D∩E, we have to find the set of values that both sets have in common. That set is compound of the number that are greater than 4 and less than or equal to 9. It means that this set is:
[tex]D\cap E=(4,9\rbrack[/tex]To find D∪E, we have to find the set of values that is formed when these sets are put together. That set is compound of all the real numbers. It means that this set is:
[tex]D\cup E=(-\infty,\infty)[/tex]which method should I use to find the missing angle in the triangle? the following methods to choose from can include Law of Sines, Law of Cosine, SOH-COH-TOA, and inverse tangent. after picking a method that applicable to solving the missing angle round to the nearest whole degree!
From the given figure
The opposite side to x is AB
The adjacent side to x is BC
To find x we will use TOA
[tex]\tan x=\frac{AB}{BC}[/tex]AB = 3 cm
BC = 4 cm
[tex]\tan x=\frac{3}{4}[/tex]To find x we will use the inverse of tan
[tex]x=\tan ^{-1}(\frac{3}{4})[/tex]By using the calculator
x = 36.86989765
Round it to the nearest degree
x = 37 degrees
I inserted a picture of the question can you please hurry or you can just put the answer
Answer:
Explanation:
Given the equation:
[tex]y=3x[/tex]We evaluate two points on the line below:
[tex]\begin{gathered} \text{When }x=0,y=3\times0=0\implies(0,0) \\ \text{When }x=1,y=3\times1=3\implies(1,3) \end{gathered}[/tex]From the given options, the graph that contains the points (0,0) and (1,3) is Graph D.
The correct answer is Graph D.
I need some help solving this practice problem from my trigonometry prep guideI will send you another image with the rest of the answer options ( total of four answer options)
Answer
The graph of f(x) =-3 sec(x/2) + 1 as graphed on the desmos app is shown below;
Hence, the correct option that shows the graph of the given function is
find the real and or complex solutionsx^3-3x^2+2x=0
Given:
[tex]x^3-3x^2+2x=0[/tex]To determine the solutions, we find the factors of the given function. So,
[tex]\begin{gathered} x^3-3x^2+2x=0 \\ \text{Simplify} \\ x(x^2-3x+2)=0 \\ \end{gathered}[/tex]Next, we factor x^2-3x+2=0:
[tex]\begin{gathered} x(x^2-3x+2)=0 \\ x(x-2)(x-1)=0 \end{gathered}[/tex]Then,we find the values of x:
x=0
x-2=0
x=2
x-1=0
x=1
Therefore, the solutions are:
x=0, x=1, x=2
Your answers are X=0,1,2
Find a real number, k, such that the line 12x + ky + 20 = 0 has y-intercept -9. K = ______
Okay, here we have this:
Considering the provided information, we are going to find the requested number "k", so we obtain the following:
Since the y-intercept is the value of y when x equals zero then we get:
12x + ky + 20 = 0
12(0)+k(-9)+20=0
-9k+20=0
-9k=-20
k=-20/-9
k=20/9
Finally we obtain that k is equal to 20/9.
Kinsey has a plan to save $60 a month for 16 months so that she can purchase a new television. After 11 monthsKinsey has saved $600. If the most that Kinsey can possibly save is $80 per month, which of the following statementsis true?a Kinsey will meet her goal and does not need to adjust her planb. Kinsey must save $72 per month to achieve her goalKinsey must save $75 per month to achieve her goalKinsey will not be able to achieve her goal.cd
The total amount she has to save can be calculated as:
[tex]60\frac{\$}{\text{month}}\cdot16\text{ months}=\$960[/tex]After 11 months, she has saved $600.
So she has 16-11=5 months to save and needs to save 960-600=$ 360 to achieve her goal.
Then, we know that she has to save an average of 360/5=72 dollars
Han has a budget of $25 to buy grapes. Write inequalities to represent the number of pounds of grapes that Han could buy in each situation: Grapes cost $2.49 per pound.
Budget: $25
Price per pound: $2.49
We know that the total price can not exceed the budget. Then:
Total_cost ≤ Budget
If Han buys x pounds of grapes, the total cost is:
Total_cost = (Price per pound)*(Number of pounds) = ($2.49)*(x)
Finally, the inequality of the situation is:
[tex]\begin{gathered} 2.49x\leq25 \\ x\leq\frac{2500}{249} \end{gathered}[/tex]in her apartment O'Neal places a rug on the floor that cover 2/3 of her living room. her couch covers 2/3 of the roug how much of the whole living room does the couch cover?
Let:
x = space covered by the couch
y = space covered by the rug
T = total space
so:
[tex]T=\frac{2}{3}\times\frac{2}{3}=\frac{2\times2}{3\times3}=\frac{4}{9}\approx0.444[/tex]How many solutions does the equation 2(2x – 10) - 8 = -2014 - 3x) have?
Given the equation :
[tex]undefined[/tex]I need this problem from my prep guide answered, it has four answer options and I will provide another picture with the rest of the answer optionsThe subject is pre-Calc
Given,
The equation of circle is,
[tex](x+1)^2+(y+3)^2=16[/tex]The standard equation of cicle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where, (h,k) is the center of the circle and r is the radius of the circle.
On compring the standard equation of circle with given equation then,
[tex](h,k)=(-1,-3)[/tex]Both the coordinates of the center of the circle is negative. Thus, lies in the third quadrant.
Here, the circle of option A has its center at third quadrant.
Hence, option A is correct.
How do I divide complex numbers?[tex] \frac{(6 - i)}{(5 + 4i)} [/tex]
Values for relation g are given in the table. Which ordered pair is in g inverse?
A scalar function is defined as:
'A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.'
Therefore, if we have the following function
[tex]f(x)=y[/tex]Given the x, y is unique.
The inverse function, takes the function value to its corresponding x value.
[tex]f^{-1}(f(x))=f^{-1}(y)=x[/tex]In our problem, we have the following function values
[tex]\begin{gathered} g(5)=-3 \\ g(4)=1 \\ g(3)=-2 \\ g(2)=0 \end{gathered}[/tex]If we apply the inverse function on all of those values, we should get the argument of the function back.
[tex]\begin{gathered} g^{-1}(g(5))=g^{-1}(-3)=5 \\ g^{-1}(g(4))=g^{-1}(1)=4 \\ g^{-1}(g(3))=g^{-1}(-2)=3 \\ g^{-1}(2)=g^{-1}(0)=2 \end{gathered}[/tex]Therefore, from the possible answers, only (1, 4) belongs to the inverse.
Use the information given to find the equation of the line using the point-slope formula (y-y_1)=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).Parallel to y=2x+5 and passes through the point (4,3)The point slope form is (y-Answer)=Answer(x-Answer)Converting it to slope intercept form gives us: y=Answerx+Answer
point-slopeWe are required to get the equation of the line in the point-slope and slope-intercept forms.
A line given in the form: y = mx + b is given in the slope-intercept form where m and b are the slope and intercept on the vertical axis respectively.
A pair of parallel lines have the same gradient and we will leverage this fact to get the equation of the line that passes through the point (4,3).
The point-slope slope form of a line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where:} \\ x_1,y_1\text{ are the coordinates of the point} \end{gathered}[/tex]We therefore have:
[tex]\begin{gathered} y-3=2(x-4) \\ as\text{ our }point\text{ slope form} \end{gathered}[/tex]Converting to slope-intercept form:
[tex]\begin{gathered} y-3=2(x-4) \\ \text{Add 3 to both sides to get:} \\ y=2(x-4)+3 \\ y=2x-8+3 \\ y=2x-5 \end{gathered}[/tex]