Answers
Answer:
D is not a function--an x-value cannot correspond to more than one y-value.
Related Questions
4(3c+3)-3c+1=3(3c+5)-2
Answers
The given equation is,
[tex]4(3c+3)-3c+1=3(3c+5)-2[/tex]The above equation can be simplified as follow,
[tex]undefined[/tex]A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 32o. From a point 2,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 35o. How tall (in feet) is the mountain? Round to two decimal places.
___________
Answers
To calculate the angle of elevation, just measure the angle formed by the line of sight and the level plain. The elevation of the peak is 10406.58 feet at its highest point.
This is further explained below.
What is the height of the mountain?Where
<A=30
AB=2000
<A B C=180-33
<A B C=147
<B C A=180-<A-<A B C
< B C A=180-30-147
<BCA=3
To begin, the side length BC may be calculated by using the following formula:
[tex]\frac{B C}{\sin A}=\frac{A B}{\sin C}[/tex]
So, we have:
B C=sin A *(A B/sin C)
B C=sin (30) *2000/sin (3)
B C=19107.3
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Fred takes out a mortgage for $60,000 at 7% for 20 years. What are his monttpayment, the total amount paid, and the cost of the mortgage?
Answers
We will have the following:
First, we determine the monthly rate:
[tex]r_m=\frac{0.07}{12}=\frac{7}{1200}[/tex]Now, we determine the monthly payment:
[tex]\begin{gathered} A=P\frac{(1+r_m)^n}{(1+r_m)^n-1} \\ \\ \Rightarrow A=60000\frac{(1+(7/1200))^{^{240}}}{(1+(7/1200))^{240}-1}\Rightarrow A\approx465.18 \end{gathered}[/tex]So, the monthly payment will be approximately $465.18.
The total amount paid will be:
[tex]\begin{gathered} X=A\ast n\ast t \\ \\ \Rightarrow X=(465.18)(12)(20)\Rightarrow X\approx111643.2 \end{gathered}[/tex]So, the total payment will be approximately $111 643.2.
The cost of the mortgage is:
[tex]c=111643.2-60000\Rightarrow c\approx51643.2[/tex]So, the cost of the mortgage is approximately $51 643.2.
leon wrote an expression that is equivalent to (30+6)÷12 witch expression could be the one leon wrote
Answers
ANSWER
(3 · 3 · 2 · 2) ÷ (3 · 2 · 2)
EXPLANATION
The given expression is also equivalent to 36 ÷ 12 - because 30 + 6 = 36.
In the equivalent expression we have:
[tex]\begin{gathered} 3\cdot3\cdot2\cdot2=36 \\ 3\cdot2\cdot2=12 \end{gathered}[/tex]Therefore it's 36 ÷ 12 too
Find the due date of a note dated October 24, 2018 for 2 months.
Answers
2 months after october 24th 2018 will be:
24th December 2018 which was a monday.
Add 3 days of grace period will give the due date to be 27th December 2018.
Why is it incorrect to write {∅} to denote a set with no elements?
Answers
Answer:
It's incorrect because {∅} is saying that the set contains empty sets, which is not the same as saying the set is empty (which can be denoted by { } or ∅
Step-by-step explanation: It's all in the answer.
use the quadratic formula to find both solitions to the quadratic equation given below x^2+6×=16
Answers
Answer:
x1=4
x2=-8
Step-by-step explanation:
x^2+6x-16=0
a=1 b=6 c=-16
D=b^2 - 4ab= 36+64=100
D>0, 2 sqrt
x1= -b+sqrt{D} /2= -6+10/2= 4
x2= -b-sqrt{D} /2= -6-10/2= -8
(That's what we were taught!)
Suppose that a regression line for some data transformed with logarithmspredicts that when x equals 4, log(y) will equal 2.671. What does theregression line predict y will equal when x equals 4?
Answers
Explanation:
The information that we have is that when the value of x is 4
[tex]x=4[/tex]The logarithm of y is 2.671
[tex]log(y)=2.671[/tex]The question is:
What does the regression line predict y will equal when x =4?
That means we need to solve for y in
[tex]log(y)=2.671[/tex]To find the predicted y-value.
To solve for y, we make 10 the base of the two sides of the equation as shown in the following expression:
[tex]10^{log(y)}=10^{2.671}[/tex]Due to the properties of logarithms, on the left side, we will be left only with 'y'
[tex]y=10^{2.671}[/tex]And finally, solving the operations on the right-hand side, the result is:
[tex]y=468.813[/tex]Answer:
[tex]y=468.813[/tex]Two right rectangular prisms are shown below. 2 inches 5 Inches 9 inches inches 7 NI inches inches Prism I Prism II If each prism is packed with small cubes of side length 1 inch, how many more cubes are in Prism Il than in Prism I? O 42 cubes О 210 cubes O 510 cubes O 720 cubes
Answers
The number of small cubes in the prism I can be determined as,
[tex]\begin{gathered} N_1=\frac{Volume\text{ of prism I}}{Volume\text{ of one small cube}} \\ =\frac{\frac{7}{4}\text{ in}\times\frac{5}{4}\text{ in}\times\frac{3}{2}\text{ in}}{\frac{1}{4}\text{ in}\times\frac{1}{4}\text{ in}\times\frac{1}{4}\text{ in}} \\ =210 \end{gathered}[/tex]The number of cubes in the prism II can be determined as,
[tex]\begin{gathered} N_2=\frac{2\text{ in}\times\frac{5}{2}\text{ in}\times\frac{9}{4}in}{\frac{1}{4}in\times\frac{1}{4}in\times\frac{1}{4}in} \\ N_2=720 \end{gathered}[/tex]The difference in the number of cubes is,
[tex]\begin{gathered} N_2-N_1=720-210 \\ =510 \end{gathered}[/tex]Thus, Prism II has 510 more cubes than Prism I.
Thus, option (c) is the correct solution.
1. P(video games and kid is 10 to 12 years old)2. P(basketball/kid is 13 to 15 years old)3. P(kid is 13 to 15 years old/basketball)4. P(darts/kid is 10 to 15 years old)5. P(basketball and darts)6. P(basketball and kid is 13 to 18 years old)Answer the following problems about two way frequency tables make sure to reduce your fraction.
Answers
1. P(video games and kid is 10 to 12 years old)
[tex]\begin{gathered} P(video\text{ games and kid i 10 to 12 years old)} \\ =\text{ }\frac{number\text{ of kids 10 - 12 years old playing video games}}{total\text{ number of students}} \\ =\text{ }\frac{17}{143} \end{gathered}[/tex]Therefore,
The P(video games and kid is 10 to 12 years old) = 17/143
2. P(basketball/kid is 13 to 15 years old)
[tex]\begin{gathered} P\mleft(basketball/kid\text{ is 13 to 15 years old}\mright)\text{ } \\ =\text{ }\frac{number\text{ of kids 13 - 15 years old playing basketball}}{number\text{ of kids of age 13 to 15 years old}} \\ =\text{ }\frac{14}{45} \end{gathered}[/tex]P(basketball/kid is 13 to 15 years old) = 14/45
3. P(kid is 13 to 15 years old/basketball)
[tex]\begin{gathered} P(\text{kid is 13 to 15 years old / basket ball)} \\ =\text{ }\frac{number\text{ of kids aged 13 to 15 years old }}{number\text{ of kids playing basketball}} \\ =\text{ }\frac{14}{54} \\ =\text{ }\frac{7}{27} \end{gathered}[/tex]P(kid is 13 to 15 years old/basketball) = 7/27
4. P(darts/kid is 10 to 15 years old)
[tex]\begin{gathered} P(\text{darts / kid is 10 to 15 years old)} \\ =\text{ }\frac{number\text{ of kids age 10 to 15 playing darts}}{\text{number of kids age 10 to 15}} \\ =\text{ }\frac{kids\text{ age 10 to 12 + age 13 to 15 playing darts}}{\text{kids age 10 to 12 + age 13 to 15}} \\ =\text{ }\frac{12\text{ + 15}}{34\text{ + 45}} \\ =\text{ }\frac{27}{79} \end{gathered}[/tex]P(darts/kid is 10 to 15 years old) = 27/79
5. P(basketball and darts)
[tex]\begin{gathered} P(basketball\text{ and darts)} \\ \sin ce\text{ there are no kids playing basketball and darts at the } \\ \text{same time} \\ \text{then,} \\ P(basketball\text{ and darts) = 0} \end{gathered}[/tex]P(basketball and darts) = 0
6. P(basketball and kid is 13 to 18 years old)
[tex]\begin{gathered} P(\text{basketball and kid is 13 to 18 years old)} \\ =\text{ }\frac{number\text{ of kids 13 to 18 years playing basket}}{nu\text{mber of kid 13 to 18 years }} \\ =\text{ }\frac{\text{kids 13 to 15 years + 16 - 18 years playing basketball}}{\text{kids 13 to 15years + 16 to 18 years}} \\ =\text{ }\frac{14\text{ + 18}}{45\text{ + 35}} \\ =\text{ }\frac{32}{80} \\ =\frac{2}{5} \end{gathered}[/tex]P(basketball and kid is 13 to 18 years old) = 2/5
3.
How much greater is the surface area of the rectangular prism than the surface area of the cube?
6 cm
(1 point)
3 cm
2 cm
O 36 cm²
O 33 cm²
O 18 cm²
O 45 cm²
3 cm
Answers
The dimensions of the rectangular prism of 6 cm by 3 cm by 2 cm and the dimension of the cube of 3 cm gives the amount the surface area of the prism is greater than the cube as 18 cm²
What is a rectangular prism?A rectangular prism is a six faced solid hexahedron.
The given dimension of the rectangular prism are:
Length = 6 cm
Height = 3 cm
Width = 2 cm
The side length of the cube = 3cm
The surface area of the rectangular prism is therefore:
[tex]A_p[/tex] = 6 × 3 × 2 + 6 × 2 × 2 + 3 × 2 × 2 = 72
The surface area of the rectangular prism is 72 cm²
The surface area of the cube: [tex]A_c[/tex] = 6 × 3² = 54
The surface area of the cube, [tex]A_c[/tex] = 54 cm²
The amount by which area of the rectangular prism is greater than the area of the cube is therefore: [tex]A_p[/tex] - [tex]A_c[/tex] = 72 cm² - 54 cm² = 18 cm²
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y= -2x - 7x - y = -8
Answers
Given the system of equations:
[tex]\begin{gathered} y=-2x-7\rightarrow(1) \\ x-y=-8\rightarrow(2) \end{gathered}[/tex]we will find the solution to the system by graphing
To draw the lines, we need to know two points on each line
so, substitute with two values of x and calculate the corresponding value of y
For line (1): y = -2x - 7
[tex]\begin{gathered} x=0\rightarrow y=-2\cdot0-7=-7 \\ x=1\rightarrow y=-2\cdot1-7=-9 \end{gathered}[/tex]so, line (1) passes through the points ( 0, -7) and ( 1, -9)
For line (2): x - y = -8
y = x + 8
[tex]\begin{gathered} x=0\rightarrow y=8 \\ x=1\rightarrow y=1+8=9 \end{gathered}[/tex]So, line 2 passes through the points ( 0, 8) and ( 1, 9)
The graph of the line will be as shown in the following picture
As shown in the figure:
Line (1) is the blue line
Line (2) is the red line
The point of intersection = ( -5, 3)
So, the solution is point ( -5, 3)
coupon A 45% off of a $73 jacket coupon B $30 rebate on a $73 Jacket
Answers
To be able to determine which among the coupon gives a lower price, let's determine what is 45% of $73 so that we could compare it with the $30 rebate. The highest amount among the two coupons will give you a lower price.
Let's determinte the 45% of 73:
[tex]\text{73 x }\frac{45\text{\%}}{100\text{\%}}\text{ }\rightarrow\text{ 73 x 0.45}[/tex][tex]\text{ = \$32.85}[/tex]Coupon A gives you $32.85 dollar off of a $73 Jacket.
Coupon A will give you a lower price compared to Coupon B. The price of the jacket will be $2.85 lesser than using Coupon B.
Do 9 and 10 keep it 9th grade if you can Question 9-10
Answers
Given the formula for the volume of a cylinder:
[tex]V=\pi r^2h[/tex]You know that "r" is the radius of the cylinder and "h" is the height.
a. In order to solve the formula for "h", you can divide both sides of the formula by:
[tex]\pi r^2[/tex]As follows:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{V}{\pi r^2}[/tex]b. Having a cylindrical swimming pool, you know that:
[tex]\begin{gathered} r=12\text{ }ft \\ V=1810\text{ }ft^3 \end{gathered}[/tex]And, for this case:
[tex]\pi\approx3.14[/tex]Therefore, you can substitute values into the formula for the height of a cylinder found in Part "a" and evaluate:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{(3.14)(12\text{ }ft)^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{452.16\text{ }ft^2}[/tex][tex]h\approx4\text{ }ft[/tex]Hence, the answers are:
a.
[tex]h=\frac{V}{\pi r^2}[/tex]b.
[tex]h\approx4\text{ }ft[/tex]a rectangular Garden has a length of 10 m and a width of 8 meters fill in the Box to show the perimeter and the area of the garden
Answers
Explanation
Step 1
Area,To find the area of a rectangle, multiply its height by its width
then
[tex]\text{Area}_{rec\tan gle}=length\cdot width[/tex]Let
length=10 m
width=8 m
replace,
[tex]\begin{gathered} \text{Area}_{rec\tan gle}=length\cdot width \\ \text{Area}_{rec\tan gle}=10\text{ m }\cdot\text{ 8 m} \\ \text{Area}_{rec\tan gle}=80m^2 \end{gathered}[/tex]Step 2
find the perimeter:
Perimeter is the distance around the outside of a shape,so for the garden the perimeter is
[tex]\text{Perimeter}_{rec\tan gle}=2(length+width)[/tex]replace,
[tex]\begin{gathered} \text{Perimeter}_{\text{garden}}=2(10m+8m) \\ \text{Perimeter}_{\text{garden}}=2(18\text{ m)} \\ \text{Perimeter}_{\text{garden}}=36\text{ m} \end{gathered}[/tex]I hope this helps you
What is period of the function, give the exact value
Answers
Solution
Step 1:
Find the midline
[tex]\begin{gathered} Midline\text{ = }\frac{maximum\text{ + minimum}}{2} \\ Maximum\text{ = 11.4} \\ minimum\text{ = -5.5} \\ midline\text{ = }\frac{11.4\text{ + \lparen-5.5\rparen}}{2} \\ midline\text{ = }\frac{5.9}{2} \\ midline\text{ = 2.95} \end{gathered}[/tex]Step 2:
Find the amplitude
[tex]\begin{gathered} Amplitude\text{ = }\frac{maximum\text{ - minimum}}{2} \\ Amplitude\text{ = }\frac{11.4\text{ - \lparen-5.5\rparen}}{2} \\ Amplitude\text{ = 8.45} \end{gathered}[/tex]Step 3:
Period:
To find the period, use the values of x.
[tex]\begin{gathered} Period\text{ = 2\lparen11.4 + 5.5\rparen} \\ Period\text{ = 2 }\times\text{ 16.9} \\ period\text{ = 33.8} \end{gathered}[/tex]Final answer
Period = 33.8
The same set of data has been fit using two different functions. The following images show the residual plots of each function.
Answers
We have the residuals of each function graphed.
They represent the distance, taking into account the sign, of each data point to the line of best fit.
A good fit will have residuals that are close to the x-axis. Also, the distribution for the residuals should not have too much spread, meaning that all the points should have approximately the same residual in ideal conditions.
In this case, we see that Function A has most residuals around the horizontal axis. Except for one of the points, that may be considered an outliert.
In the case of Function B there is a clear pattern (a quadratic relation between x and the residual) that shows that the degree of the best fit function is not the adequate (maybe two degrees lower than what should be).
This results in residuals that have a wide spread depending on the value of x.
Then, we can conclude that Function A has a better fit because the points are clustered around the x-axis.
Answer: Function A has a better fit because the points are clustered around the x-axis [Third option]
simplify 12 times y to the 6th power times z to the 4th power divided by 6 times y times z to the 6th power
Answers
The simplified expression of the given expression is 2y^5 z^{-2}
What is expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.
Given expression, [tex]\frac{12y^6 z^4}{6 yz^6}[/tex]
Simplifying and we get
[tex]\frac{12y^6 z^4}{6 yz^6}\\=2y^{6-1} z^{4-6}\\=2y^5 z^{-2}[/tex]
Therefore, the simplified expression of the given expression is 2y^5 z^{-2}
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While waiting for the school bus, Michiko records the colors, of all cars passing through an intersection. Thetable shows the results, Estimate the probability that the next car through the intersection will be red. Exgressyour answer as a percent. If necessary, round your anewer to the nearest tenth
Answers
Given the following question:
Estimate the probability that the next car will be red.
11, 24, 16, 9
[tex]\begin{gathered} 11\text{ + 24}=35 \\ 35\text{ + 16 = 51} \\ 51\text{ + 9 = }60 \\ 60=100\text{per} \end{gathered}[/tex][tex]p=\frac{11}{60}[/tex][tex]\frac{11}{60}\times100=18.333333[/tex][tex]\begin{gathered} 18.333333 \\ 3\text{ < 5} \\ 18.3 \end{gathered}[/tex]18.3% or the first option.
what is the slope of a line parallel to the line whose equation is 18 x - 3 y equals -45
Answers
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
Let's solve for "y" from the equation of the line given in the exercise, in order to express it in Slope-Intercept form:
[tex]\begin{gathered} 18x-3y=-45 \\ -3y=-18x-45 \\ y=\frac{-18x-45}{-3} \\ y=6x+15 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m=6 \\ b=15 \end{gathered}[/tex]By definition, the slopes of parallel lines are equal. Therefore, the slope of the line parallel to line given in the exercise, is:
[tex]m=6[/tex]I don't understand this. Proving and applying ASA and Salad congruence
Answers
Given two triangles, we can say that they are congruent by the SAS postulate (Side Angle Side) if both triangles have two congruent sides and the angle that they form is also congruent
In this case, we have that triangle IHG and DFE have already two congruent sides, then, to make them congruent, the angle that they each form (angle IHG and angle DEF) must be congruent so we can use the SAS postulate
Solve the problems. Simon is organizing his 36 toy cars into equal-sized piles. Which list shows all of the possible numbers of cars that could be in each pile? A 2. 3,4,6 B 1, 2, 3, 4,6 C 2, 3, 4, 6, 9, 12, 18 D 1, 2, 3, 4, 6, 9, 12, 18, 36
Answers
Consider that the total available toy cars is 36.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
So Simon can make 1 pile of 36 toy cars, 2 piles of 18 cars each, 3 piles of 12 cars each, 4 piles of 9 cars each, 6 piles of 6 cars each, 9 piles of 4 cars each, 12 piles of 3 cars each, 18 piles of 2 cars each, and 36 piles of 1 car each.
Thus, the possible number of cars that could be in each pile are 1,2, 3, 4, 6, 9, 12, 18, 36.
Therefore, option D is the correct choice.
Cut a 10-foot (ft.) long piece of wood into two pieces so that one piece is 2 ft longer than the other. Which of the following equations depicts the given situation?A. x/2 = 10B. x + 2 = 10C. 2x + 2 = 10D. None of the choices
Answers
Given:
Cut a 10-foot (ft.) long piece of wood into two pieces so that one piece is 2 ft longer than the other.
Required:
Which of the following equations depicts the given situation?
Explanation:
Let 10 feet long piece of wood cut into two pieces of length x(smaller piece) and
x+2 larger piece.
So, the equation will be
x + x + 2 =10
2x + 2=10
Answer:
Option C is correct.
The state of California charges homeowners approximately $1,200 per year in property taxes for every $100,000 a person's home is worth. If Mr. Cohen's home in Studio City, CA is worth $1,600,000, how much does he have to pay in property taxes per year? Set up a pair of equivalent ratios and then use your knowledge of cross products to solve. You may use calculator.
Answers
We have the next information
1,200 ----- 100,000
x ----- 1,600,000
x is the missing quantity
x can be calculated in this way
[tex]x=\frac{1,600,000\cdot1200}{100,000}=19200[/tex]Mr. Cohen has to pay per year $19,200 taxes per year
In the diagram below, if the measure of < C = 45 °, and side AB = 6.8, then side BC = _____.
Answers
Solution
Since
[tex]\begin{gathered} \tan45=\frac{6.8}{BC} \\ \\ \Rightarrow BC=\frac{6.8}{\tan45}=6.8\text{ since}\tan45=1 \end{gathered}[/tex]The correct option is A.
oblem 9If 8 x 17 = 136, then 17 isI % of 136if 44 x 8 = 352, then 44 is% of 352
Answers
Let 'x' represents the missing number
a) x % of 136 = 17
[tex]\begin{gathered} \text{where, }x\text{ \% =}\frac{\text{x}}{100} \\ \frac{x}{100}of136=17 \\ \frac{x}{100}\times136=17 \\ \frac{136x}{100}=17 \\ 1.36x=17 \end{gathered}[/tex]Divide both sides by 1.36
[tex]\begin{gathered} \frac{1.36x}{1.36}=\frac{17}{1.36} \\ x=\frac{25}{2}=12.5 \\ \therefore x=12.5 \end{gathered}[/tex]Hence, 17 is 12.5% of 136.
b) x% of 352 = 44
[tex]\begin{gathered} \text{where, x\%=}\frac{\text{x}}{100} \\ \frac{x}{100}\times352=44 \\ \frac{352x}{100}=44 \\ 3.52x=44 \end{gathered}[/tex]Divide both sides by 3.52
[tex]\begin{gathered} \frac{3.52x}{3.52}=\frac{44}{3.52} \\ x=12.5 \\ \therefore x=12.5 \end{gathered}[/tex]Hence, 44 is 12.5% of 352.
What is the solution to the equation?
-6 = x/8
Enter your answer in the box.
X =
Answers
Answer:
-48
Step-by-step explanation:
First, you multiple the fraction by the denominator, which is 8. You multiple both sides of the equation by 8. -6*8=-48. x/8 * 8 = x. In conclusion, -48 = x or x = -48.
What is the value of the expression below when w = 3?5W^2 – 5W – 8
Answers
According to the given data we have the following expression:
5W^2 – 5W – 8
In order to calculate the value of the expression above when w=3 we would need to substitute the w with 3 and then calculate the expression.
So, if w=3 then:
5(3)^2 -5(3) -8
=45 - 15 -8
=22
The value of 5W^2 – 5W – 8 when w = 3 would be 22
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
The transformation of the map is given as; translation of 1 unit to the right and rotated 180 degree counterclockwise about origin.
What is termed as the translation?In geometry, translation refers to a function which moves an object a specified distance. The element is not otherwise altered. It is not rotated, mirrored, or resized.Each point of the element must be relocated within the same direction and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and the element after the translation is referred to as the image.For the given question;
The graph of the triangle is given,
The triangle is first translated to the 1 unit to its right such that vertex of the triangles lies on the y -axis.
Now, the triangle is rotated about origin in counter clock wise direction about 180 degrees.
Thus, the final image is shown by red triangle.
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The Neckware association of America reported that 3% of ties sold in the United States are bow ties. If 4 customers who purchased a tie randomly selected,find the probability that at least 1 purchased a bow tie
Answers
Pr (people with bow ties) = 3% = 0.03
p = 0.03
Pr (people without bow tie) = 1 - 0.03 = 0.97
q = 0.97
n = 4 customers
[tex]Pr(at\text{ least 1 purchased a bow tie) = 1 - Pr(none purchased a bow tie)}[/tex]To find the probability that at least 1 purchased a bow tie, we will use a binomial probability formula:
[tex]p(x=^{}X)=^nC_xp^xq^{n\text{ - x}}[/tex][tex]\begin{gathered} \text{Pr(none purchased a bow tie) = p(x = 0)} \\ \text{p(x = 0) = }^4C_0\times p^0\times q^{4\text{ - }0} \\ \text{p(x = 0) = 1 }\times\text{ 1}\times q^4=(0.97)^4 \\ \text{p(x = 0) = }0.8853 \\ \\ \text{Pr(none purchased a bow tie) = }0.8853 \end{gathered}[/tex][tex]\begin{gathered} Pr(at\text{ least 1 purchased a bow tie) = 1 - 0.8853} \\ Pr(at\text{ least 1 purchased a bow tie) = 0.1147} \end{gathered}[/tex]