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]Melanie went shopping and spent $18 on scarves. If she spent $77 total, what percentage did she spend on scarves? Round your answer to the nearest percent.
Answer:
23.4%
Step-by-step explanation:
[tex]\frac{18}{77} =\frac{x}{100}[/tex]
$18 divided by $77 is the equivalent of X(% spent on scarves) divided by 100. To find X you cross multiply and divide. [tex](18*100)/77=23.377...[/tex], rounded, X = 23.4
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Given the table in I which represents function I.
x y
0 5
1 10
2 15
3 20
4 25
• Graph II shows Item II which represents the second function.
Let's determine the increasing and decreasing function.
For Item I, we can see that as the values of x increase, the values of y also increase. Since one variable increases as the other increases, the function in item I is increasing.
For the graph which shows item II, as the values of x increase, the values of y decrease, Since one variable decreases as the other variable decreases, the function in item I is decreasing.
Therefore, the function in item I is increasing, and the function in item II is decreasing.
ANSWER:
A. The function in item I is increasing, and the function in item II is decreasing.
In a right triangle, the hypotenuse is the longest side?
Okay, here we have this:
The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.
This mean that the statement is true.
One factor of the polynomial x3 − 7x2 + 13x − 3 is (x − 3). What is the other factor of the polynomial? (Note: Use long or synthetic division.) A. (x2 + 4x − 1) B. (x2 − 4x + 1) C. (x − 4) D. (x + 4)
The other factor of the polynomial from what we have here is given as x² - 4x + 1 option B is correct.
How to solve the polynomialWe are required to divide x³ - 7x² + 13x - 3 by x -3
We have this as
x² - 4x + 1
-----------------
x-3 | x³ - 7x² + 13x - 3
we would have
x³ - 3x²
subtract this value by the one that we have above
then we would have
-4x² + 13x
-4x² + 12x
subtract these values from each other to get the value below.
x - 3
Hence the solution to the polynomial would be x² - 4x + 1.
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(a) The perimeter of a rectangular parking lot is 340 m.If the width of the parking lot is 77 m, what is its length?Length of the parking lot: 0m(b) The area of a rectangular pool is 7410 m².If the length of the pool is 95 m, what is its width?Width of the pool: Im
Part a)
Perimeter = 340 = 2•77 + Length doubled
then
Length x 2 = 340 - 154 = 186
Length= 186/2 = 93
ANSWER IS Length of parking lot is= 93 meters
Part b)
Area = 7410 = Width x Length
. 7410 = Width x 95
. 7410/95 = Width
THEN Width of the pool IS
78 square meters
at what rate is the depth of the pool water increasing?
Given:
Find-:
Rate is the depth of the pool water increasing
Explanation-:
The rate of change is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Choose any two points is:
[tex]\begin{gathered} (x_1,y_1)=(2,1) \\ \\ (x_2,y_2)=(4,2) \end{gathered}[/tex]So, the rate of change is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2-1}{4-2} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]So, 1/2 ft per hour
The GCD of two numbers is 11 and their LMC is 220. One of the numbers is 55. find the other number.
If the GCD of two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
The one number = 55
Consider the second number as x
GCD is the greatest common divisor
LCM is the least common multiple
The greatest common divisor of two numbers = 11
The least common multiple of two numbers = 220
We know
The product of two numbers= The product of GCD and LCM
55 × x = 11 × 220
55x = 2420
x = 44
Hence, If the GCD if two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
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Q.Using triangle congruency theorems, justify why the triangles are similar.
4a)
Looking at the figure,
AD and BE are parallel lines
AE and BD are transversals
Thus,
angle DAE is congruent to angle BEA because they are alternate angles(They lie in similar positions but on alternate sides of the transversal
Also,
angle ADB is congruent to angle EBD because they are alternate angles(They lie in similar positions but on alternate sides of the transversal.
Angle ACD is congruent to angle BCE
Recall, 2 triangles are similar if at least, 2 of their corresponding angles are congruent. In this case, 3 corresponding triangles are congruent. Thus,
triangle ADC is similar to triangle EBC by AA(angle angle) postulate
4b) If 2 triangles are similar, it means that the ratio of their corresponding sides is equal. Thus,
AD/EB = DC/BC = AC/ CE
From the information given,
AD = 2
AC = 4
EB = 5
Thus,
2/5 = 4/CE
By cross multiplying,
2 * CE = 5 * 4
2CE = 20
CE = 20/2
CE = 10
Which relation below is not a function
Answer:
0,0
Step-by-step explanation:
Two numbers can not equal another number
uhh im stuck and im stressed .. and i dont understand area model math..
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(5x + 6)(2x² + 3x + 8) = ?
Step 02:
Area Model
First, you must multiply the values in the rows by each of the values in the columns.
Then, you must add all the values resulting from the multiplications.
10x³
2x²
+ 12x²
15x²
18x
3x
40x
48
8
--------------------------------------------
10x³ + 29x² + 61x + 56
The answer is:
(5x + 6)(2x² + 3x + 8) = 10x³ + 29x² + 61x + 56
factor the equationx^2-17x+42
To factor an expression of the form:
[tex]x^2+Bx+C[/tex]we need to find two integers a and b that fullfil:
[tex]\begin{gathered} a+b=B \\ ab=C \end{gathered}[/tex]then we write the expression as:
[tex]x^2+ax+bx+C[/tex]and factor by agrupation.
Let's do this with the expression:
[tex]x^2-17x+42[/tex]In this case B=-17 and C=42.
If we take a=-14 and b=-3, then:
[tex]\begin{gathered} (-14)(-3)=42 \\ -14-3=-17 \end{gathered}[/tex]then we write the expression as:
[tex]\begin{gathered} x^2-14x-3x+42=x(x-14)-3(x-14) \\ =(x-3)(x-14) \end{gathered}[/tex]Therefore, the factorize expression is:
[tex](x-3)(x-14)[/tex]Shaq was climbing a cliff. He stopped for a snack. After that, he slipped 20 feet to an earlier foothold and then slipped 4 feet to another foothold. Model the distance Shaq traveled on the cliff after his snack as a sum.
1) Let's make a sketch to better understand this:
Suppose Shaq was on 40 feet after the snack he slipped 20 feet and then 6 feet.
After the snack, He traveled 20 +4 = 24 feet
From the initial point, He went 24 feet down.
You might need:CalculatorHiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 squaremeters left to paint.Let y represent the area (in square meters) left to paint after chours.Which of the following information about the graph of the relationship is given?
The graph is that of area painted against the number of hours. Given that he painted 8 square meters per hour, the slope is 8 square meters per hour because slope is known as unit rate.
After 3 hours of painting, he would have painted 8*3 = 24 square meters.
Since he has 28 meters left to paint, it means that the total rea of the room that
which of these is closest to the unit distance between points M and M' ?
the coordinate of M is (-3, -5)
it is given that M is translated 6 unit right , and 5 unit up.
so the coordinate of M' is (-3+6 , -5 + 5) = (3, 0)
so, the distance between M and M' is,
[tex]d=\sqrt[]{(3-(-3))^2+(0-(-5))^2}[/tex][tex]\begin{gathered} d=\sqrt[]{6^2+5^2} \\ d=\sqrt[]{36+25} \\ d=\sqrt[]{61} \end{gathered}[/tex]d = 7.81
so, the closest to the unit distance is 8
thus, the answer is option D
Write these numbers from least to greatest: 0, -6.1, 4, 10/2
Answer:
10/2, 4, 0, -6.1
Step-by-step explanation:
It is the only answer that makes sense.
pls mark brainliest
Answer: -6.1, 0, 4 , 10/2
Step-by-step explanation:
-6.1 is the only negative number, so it is the least. Zero comes next. 10/2 is 5, so 4 comes before it. Therefore 4 is the 3rd installment in these ordered numbers.
4. If line segment AB has coordinates A(-2,4) and B(2,0) and line segment
CD has coordinates C(3,4)and D(-3,-2), how would you describe these two
line segments?
These 2 lines perpendicular to each other on the graph.
What are perpendicular lines?The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I
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select the ordered pair that represent solutions of the system of inequalities A) (-1,3)B) (0,0)C) (-4,1)D) (0,2)E) (-5,0)F) ( -4,4)G) (-5,3)H) (-6,5)please answer fast
From the graph, the solution of the graph is given by the area of intersection of the two functions. The are under the area of the two functions are (-4, 1), (-5, 0), (-4, 4)
Write the equation of a quadratic in general form, given its solutions.x=4 ; x=-1
The given solutions of the quadratic equation:
x = 4 and x = -1
First we make them factors of the equation:
x= 4 becomes:
[tex]x-4\text{ = 0}[/tex]and x = -1 becomes:
[tex]x\text{ + 1 = 0}[/tex]So (x-4) and (x+1) are the factors.
To get the general quadratic equation, we would expand the factors
[tex]\begin{gathered} (x-4)(x+1)\text{ = 0 } \\ x(x+1)\text{ -4(x+1) = 0} \\ x^2+x\text{ -4x-4 = 0} \end{gathered}[/tex][tex]\begin{gathered} Adding\text{ like terms} \\ x^2-3x-4\text{ = 0} \end{gathered}[/tex]The general quadratic equation:
[tex]x^2\text{ - 3x - 4 = 0}[/tex]PLEASE PLEASE HELP
5. Renae Walters is paid a salary of $15,000 per month.
a. How much has she earned for the year after being paid at the end of January? _______________________________
b. How much is deducted in January for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
c. How much has she earned for the year after being paid at the end of November? ___________________________________
d. How much is deducted in November for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
e. How much has she earned for the year after being paid at the end of December? ___________________________________
f. How much is deducted in December for Social Security? For Medicare?
Social Security _____________________ Medicare _______________________
The amount for social security for all 3 months will $930 and the contribution for Medicare will be $217.5.
How to estimate the amount for social security for all 3 month?Given that the salary exists paid in US dollars, we can consider that Renae Walters falls under the social security and Medicare tax rates for the United States. These rates, as of 2020, fall at 6.2% for social security and 1.45% for Medicare.
Social security contribution = Social security tax rate × Income earned
January for example Social Security = 0.062 × $15,000 = $930
Medicare contribution = Medicare tax rate × Income earned
January for example Medicare = 0.0145 × $15,000= $217.5
The above method will apply through the months without changes.
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H D 2 cm 4 cm The two rectangles below are similar. What is the ratio of the perimeters of rectangle ABCD to rectangle EFGH? B А 4 cm E 8 cm F 2:1 8:1 1:4 1:2 2
In order to determine the ratio of the perimeters for the given rectangles, first calcualte their perimeters. Use the following formula:
P = 2w + 2l
w: width
l: length
For the smaller rectangle you have:
w = 2cm
l = 4 cm
P = 2(2cm) + 2(4cm) = 4cm + 8cm = 12cm
For the bigger triangle you have:
w' = 4cm
l' = 8cm
P' = 2(4cm) + 2(8cm) = 8cm + 16cm = 24cm
Then, you have:
P/P' = 12cm/24cm = 1/2
Hence, the ratio is 1:2
In a certain fraction, the denominator is 3 less than the numerator. If 1 is added to both the numerator and denominator, the resulting fraction is equal to 10/7 Find the original fraction.
The original fraction has a denominator that is 3 less than the numerator. If we define the numerator as x, then the denominator is x-3, and the fraction can be written as x/(x-3).
If 1 is added both to the numerator and denominator, the resulting fraction is equal to 10/7.
Then, we can write:
[tex]\begin{gathered} \frac{x+1}{(x-3)+1}=\frac{10}{7} \\ \frac{x+1}{x-2}=\frac{10}{7} \\ 7(x+1)=10(x-2) \\ 7x+7=10x-20 \\ 7x-10x=-20-7 \\ -3x=-27 \\ x=\frac{-27}{-3} \\ x=9 \end{gathered}[/tex]With the value of x, we can replace it in the fraction and know the value of it:
[tex]\frac{x}{x-3}=\frac{9}{9-3}=\frac{9}{6}=\frac{3}{2}[/tex]Answer: The fraction is 9/6, that can be simplified to 3/2 or 1.5.
What is the explicit formula for the sequence?3,1,-1, -3, -5,...a,= -2n +5a, = 17-5an= 2n-5an= -2n + 3
We need the formula that gives us the values of the sequence
where n is the value of the position
using the formula
[tex]a_n=-2n+5[/tex][tex]\begin{gathered} a_1=-2(1)+5=3 \\ a_2=-2(2)+5=1 \\ a_3=-2(3)+5=-1 \\ a_4=-2(4)+5=-3 \\ a_5=-2(5)+5=-5 \end{gathered}[/tex]as we can see the formula is the correct formula because we obtain the values of the sequence
If tan=21/20,0
a. sin a/2
b. cos a/2
c. tan a/2
Using trigonometry we can conclude that the value is sin a/2=7/58, cos a/2= -3/√58, tan a/2= -7/3.
What is Trigonometry?A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical research led to the development of the field in Hellenistic civilization during the third century BC.We are aware:
x=tan(a/2)And,
tan(a)=2tan(a/2)/1-tan²(a/2)=21/20= 2x/1x2⇒21−21x²=40x⇒21x²+40x−21=0⇒21x²+49x−9x−21=0⇒7x(3x+7)−3(3x+7)=0⇒(3x+7)(7x−3)=0Thus, x=7/3 or x=3/7
It is now given:
180<a<270⇒ 90<a/2<135The a/2 second quadrant.
As a result:
x = tan(a/2)negativeTherefore,
x = tan(a/2)= -7/3sin(a/2) => +veThis means that:
sin(a/2) = 1/cos(a/2) = 1/(1+cot²(a/2))= 1/(1+1/tan(a/2))=1/√(1+9/49)=7/√58The formula is now:
cos(a/2)=sin(a/2)/tan(a/2)=7/√58/ -7/3cos(a/2) = -3/√58Therefore, using trigonometry we can conclude that the value is sin a/2=7/58, cos a/2= -3/√58, tan a/2= -7/3.
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a group orders three large veggie pizzas each slice represents eighth of an entire Pizza the group eats 3/4 of a piece of how many slices of pizza are left
1 pizza contain 8 slices, so we can state a rule of three as:
[tex]\begin{gathered} 1\text{ Pizza ------ 8 slices} \\ \frac{3}{4}\text{ pizza ------ x} \end{gathered}[/tex]then, x is given by
[tex]x=\frac{(\frac{3}{4})(8)}{1}\text{ slices}[/tex]which gives
[tex]\begin{gathered} x=\frac{3}{4}\times8 \\ x=\frac{3\times8}{4} \\ x=3\times2 \\ x=6\text{ slices} \end{gathered}[/tex]that is, 3/4 of pizza is equivalent to 6 slices. So, there are 8 - 6 = 2 slices left of one pizza.
However, they bought 3 large pizzas and ate almost one of them. So, there are 2x8 = 16slices plus 2 slices, that is, 18 slices are left.
a plant is already 44 cm tall, and will grow one cm every month. let H be height in cm and M months. write and equation relating H to M . then use equation to find plants height after 32 months
H = height in cm
M = months
The plant is already 44 cm tall
GRowth every month = 1 cm
Equation:
H (m) = 44 + m
The height after m months, will be equal to the initial height (44) plus the number of months.
For 32 months, replace m by 32 and solve:
H (32) = 44+32
H (32) = 76 cm
After 32 months, the plant will be 76 cm tall
See attached for the problem
The areas and volumes are given as follows:
a) Area of the four sides to be painted: 2448 m².
b) Area to be covered with shingles: 1140 m².
c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.
d) Total surface area: 5878.4 m².
Area -> Four sides paintedThe sides painted are divided as follows:
Two rectangles of dimensions 26 m and 18 m.Two rectangles of dimensions 42 m and 18 m.Hence the total area to be painted is found as follows:
Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².
(Area rectangle = base x height)
Area to be covered with shinglesThis part of the problem seems incomplete, however the answer is correct.
Volume of concreteThe volume is given by:
Volume = base area x height.
Hence:
The base area is a rectangle of dimensions 26 m and 42 m.The height is of 16 cm = 0.16 m.Hence the volume is given by:
V = 26 x 42 x 0.16 = 174.72 m³.
Surface areaThe base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:
Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².
The top is composed by:
Two rectangles of dimensions 13.6 m and 42 m.Two triangles of base 26 m and height 4 m.Hence:
Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².
Then the total surface area is:
Total surface area = 4632 + 1246.4 = 5878.4 m².
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and In an experiment, the probability that event A occurs is 3/5 the probability that event B occurs is 3/4 and the probability that events A and B occur is 3/7what is the probability that A occurs given that B occurs
a janitor had 2/3 of a cleaning solution. he used 1/4 of the solution in an day. how much of the bottle did he use?
Answer:
5/12 of the cleaning solution.
Step-by-step explanation:
2/3 – 1/4
------------------------------------------
2 × 4
= 8/12
3 × 4
------------------------------------------
1 x 3
= 3/12
4 x 3
------------------------------------------
8 – 3
12
= 5/12
------------------------------------------
Hopefully this makes sense!
the diagonal of a rectangular swimming pool measures 19 yd if the length of the pool is 15 yd which measurement is closest to the width of the pool?
Answer:
11.67 yards
Explanation:
From the above figure, we can use the Pythagorean theorem to find the width of the pool as shown below;
[tex]\begin{gathered} 19^2=15^2+w^2 \\ 361=225+w^2 \\ 361-225=w^2 \\ 136=w^2 \\ \sqrt[]{136}=w \\ \therefore w=11.67\text{ yards} \end{gathered}[/tex](b) The area of a rectangular painting is 5568 cm².If the width of the painting is 58 cm, what is its length?Length of the painting:
Step 1: Problem
The area of a rectangular painting is 5568 cm².
If the width of the painting is 58 cm, what is its length?
Length of the painting:
Step 2: Concept
Area of a rectangle = Length x Width
Step 3: Method
Given data
Area = 5568 cm square
Width = 58 cm
Length = ?
Area of a rectangle = Length x Width
5568 = 58L
L = 5568/58
L = 96cm
Step 4: Final answer
Length of the painting = 96cm
