The perimeter for the length L and width W that is 2L will be 2W=L as the definition of perimeter says, "The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges".
What is perimeter?The total length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The perimeter of a shape is the space surrounding its edge. A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. We must add up the lengths of the rectangle's four sides in order to determine its perimeter. Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two. The perimeter formula is defined as perimeter=2(length + width).
Here,
Perimeter=2(length + width)
Length=L
Width=W=2L
2(L+W)=P
In accordance with the definition of perimeter, the perimeter for a length L and a width W that is equal to 2L will be 2W=L "In geometry, a shape's perimeter is referred to as its overall length. The perimeter of a shape is determined by adding all of its sides' and edges' lengths ".
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Find z_1 x z_2 for z_1 = 9(cos225° + isin225°) and z_2 = 3(cos45° + isin45°).The 'z' is all subscript.
Using Euler's Formula:
[tex]re^{i\theta}=r(\cos (\theta)+i\sin (\theta))[/tex]Since:
[tex]\begin{gathered} z1=9(\cos (225)+i\sin (225)) \\ z2=3(\cos (45)+i\sin (45)) \\ \end{gathered}[/tex]We can rewrite them as:
[tex]\begin{gathered} z1=9e^{225i} \\ z2=3e^{45i} \end{gathered}[/tex]So:
[tex]\begin{gathered} z1\times z2=(9e^{225i})(3e^{45i})=27e^{225i+45i}=27e^{270i} \\ so\colon \\ z1\times z2=27(\cos (270)+i\sin (270)) \end{gathered}[/tex][tex]\begin{gathered} a=r\cos (\theta) \\ b=r\sin (\theta) \\ where \\ r=27 \\ \theta=270 \end{gathered}[/tex]So:
[tex]undefined[/tex] 3.152 written as an improper fraction or a mixed number and explained how it was done.
Answer: 3.152 as an improper fraction would be: 394 / 125
Step-by-step explanation: You can take any number, such as 3.152, and write a 1 as the denominator to make it a fraction and keep the same value, like this:
3.152 / 1
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 3.152, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 1000 to get the following fraction:
3152 / 1000
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 3152 and 1000 is 8. When we divide the numerator and denominator by 8, we get the following:
394 / 125
(have a nice day)
12)50 students took a quiz with five questions. The frequency table below shows the results of the quiz. Use the frequency table to answer the following questions. ValueFrequencyRelative FrequencyCumulative Frequency040.084180.1612260.1218320.04204150.3355150.350a)How many students answered exactly 3 questions correctly?Number of students answered exactly three questions = 2b)How many students answered less than 3 questions correctly?c)What proportion (percent) of students answered exactly 4 questions correctly?
From the table, we have:
• The first column (Value),: indicates the # of correct answers,
,• The second column (Frequency),: indicates the # of students that answer the # of correct answers to the left in the table,
,• The third column (Relative Frequency),: indicates the proportion of the # of students to the total,
,• The fourth column (Cumulative Frequency),: gives the sum of the previous frequencies up to that row.
Using these data, we answer the questions:
a) Looking at the column Frequency for Value = 3, we find that 2 students answered exactly 3 answers correct.
b) Looking at the column Cumulative Frequency for Value = 2 (the previous value to 3), we find that 18 students answered less than 3 questions correctly.
c) Looking at the column Relative Frequency for Value = 4, we find that 0.3 = 0.3 * 100% = 30% of the students answered exactly 4 questions correctly.
Answera) 2
b) 18
c) 30%
A pack of cinnamon-scented pencils sells for $8.00. What is the sales tax rate if the total cost of the pencils Is $8.56 The sales tax rate is ___%
To find the tax rate we can use the rule of three.
[tex]\begin{gathered} 8\rightarrow100 \\ 8.56\rightarrow x \end{gathered}[/tex]Then,
[tex]x=\frac{8.56\cdot100}{8}=107[/tex]Now, since 8.56 dollars represents 107% of the prices, this means that the tax rate is 7.
Voters in Arizona in 2020 passed Prop 207, legalizing the sale of recreational marijuana. At the time the industry estimated that the Arizona Department of Revenue would collect $135 million in taxes. In the first year, the state has generated approximately $200 million in tax revenue.State the absolute difference in the estimated amount of tax revenue generated and the actual amount received by the AZ Department of Revenue. Be sure to answer in a complete sentence.
The estimated amount of tax is 135 million
The actual amount received is 200 million
The difference means subtraction
Taking the absolution value means when we subtract, we find the positive value of the result
| estimated - actual |
| 135 million - 200 million |
| -65 million|
Taking the positive result
65 million
The absolute value of the difference in the estimate amount of the tax revenue generated and the actual amount received by the AZ department of Revenue is 65 million dollars.
-. Write an equation in slope-intercept form that
describes the line through the points (2,7) and
(-1,-5).
The slope-intercept form equation of the line is y=(-2/3)x-(17/3) when the line is passing through the points (2,7) and (-1,-5).
What is meant by slope?Finding the ratio of vertical change to horizontal change between any two distinct points on a line yields the slope. Occasionally, the ratio is written as a quotient, which produces the same number for every two distinct points on the same line. A negative rise refers to a diminishing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.
The absolute value of the slope is used to determine how steep, incline, or grade a line is. The steeper the line, the larger the absolute magnitude of the slope.
The slope-intercept form is y=mx+c
Given points are (2,7) and (-1,-5)
Slope m= (y₂-y₁)/(x₂-x₁)
m=(-5+7)/(-1-2)
m=-2/3
By substituting m value in the above equation we get,
y=(-2/3)x + c
Given that, the above equation is passing through the point (-1,-5)
-5=(-2/3)(-1)+c
c=-5-(2/3)
c=-17/3
y=(-2/3)x-(17/3)
Therefore, the equation of the slope-intercept form is y=(-2/3)x-(17/3)
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The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?A 4B. -2C -1D. 1
You need to know the following:
1. The "difference" is the result of a subtraction.
2. The word "times" indicates a multiplication.
3. The sum is the result of an addition.
Let be "n" the number mentioned in the exercise.
Knowing the explained above, you know that "the difference of a number and 6" can expressed as:
[tex]n-6[/tex]And "5 times the sum of the number and 2" can be expressed as:
[tex]5(n+2)[/tex]Therefore, "the difference of a number and 6 is the same as 5 times the sum of the number and 2" can be written as the following equation:
[tex]n-6=5(n+2)[/tex]Now, in order to find the number, you must solve for "n":
[tex]undefined[/tex]Write an equation in slope-intercept form for the graph shown.
Answer:
y= 2x-3
Step-by-step explanation:
4/2 OR 2 is the slope
-3 is the intercept
84 points + brainliest if well explained and correct:
During a thunderstorm at a sports event, a detector goes off to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table.
Lightning detector activates Lightning detector does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
What is the ratio of false positives to false negatives in this scenario? Round your answer to one decimal place.
0.1
1.5
2.3
3.5
The ratio of false positives to false negatives is (d) 3.5
How to determine the ratio?The table of values is given as
Activates. Does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
The false negative is when there is lighting and it does not activate
So, we have
False negative = 2%
The false positive is when there is no lighting and it activates
So, we have
False positive = 7%
When represented as ratio, we have
Ratio = 7% : 2%
So, we have
Ratio = 7 : 2
This gives
Ratio = 7/2
Evaluate
Ratio = 3.5
Hence, the ratio is (d) 3.5
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Leah is buying titles for her bathroom. Each tile is 3/8 foot wide and covers an area that is 7/3 square feet. The bathroom floor is in the shape of a rectangle. She is putting 8 tiles along the longer wall of the bathroom and 5 tiles along the shorter wall of the bathroom. What is the perimeter of the bathroom? The bathroom and one tile are pictured below.
The perimeter of the rectangular floor is 103 feet.
What are rectangles?With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel.Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's length is its longer side, while its width is its shorter side.So, the perimeter of the bathroom floor will be:
First, let the length of the tiles be 'x'.Now,
7/3 = x × 3/8x = 7/3 ÷ 3/8x = 7/3 × 8/3x = 56/9So, the length of the tile is 56/9.
Now, the l and b of the rectangular floor will be:
56/9 × 8 + 3/8 × 5448/9 + 15/88(448) + 9(15)/723584 + 135/723719/7251.65Formula is: 2(l+b)
Now,
2 × 51.65103.3Rounding off: 103 feet
Therefore, the perimeter of the rectangular floor is 103 feet.
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The measures of two complementary angles are described by the expressions (11x−11)° and (16x−7)°. Find the measures of the angles.I know complementary when their measures add to 90 degrees. but I'm not to sure where to plug the numbers in
Given:
[tex](11x-11)^{\circ}and(16x-7)^{\circ}\text{ forms an complementary angles.}[/tex][tex]\begin{gathered} 11x-11+16x-7=90 \\ 27x-18=90 \\ 27x=90+18 \\ 27x=108 \\ x=\frac{108}{27} \\ x=4 \end{gathered}[/tex]
b. A family of four went to see a live concert in Vancouver. Each family member bought
a commemorative concert T-shirt, which cost 1/5 of the price of a ticket. The total bill
for 4 tickets and 4 T-shirts was $384. How much did each ticket and each T-shirt cost?
The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
In the question ,
it is given that ,
a family of four people went to see a live concert in Vancouver ,
and the price of T-shirt is 1/5 of the price of the ticket .
let the price of 1 ticket be = x ,
so , the price of 1 T-Shirt be = x/5 .
also given that the bill for 4 tickets and 4 T-Shirts was $384 ,
that means
4x + 4x/5 = 384
taking LCM as 20 and solving further ,
we get,
20x/5 + 4x/5 = 384
24x/5 = 384
24x = 384*5
24x = 1920
x = 1920/24
x = 80
the cost for T-Shirt = 80/5 = 16
Therefore , The cost of 1 ticket is $80 and the cost of 1 T-Shirt is $16 .
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3. The equation 11a +8s = 4752 represents the ticket sales at last night's football game for a
adult tickets and s student tickets.
a. How much money was collected in total from all ticket sales?
b. What is the price of an adult ticket? What is the price of a student ticket?
c. If the ticket booth sold only adult tickets, how many would they have sold?
d. If the ticket booth sold only student tickets, how many would they have sold?
Step-by-step explanation:
The equation 11a +8s = 4752 represents the ticket sales at last night's football game for a adult tickets and s student tickets.
a. How much money was collected in total from all ticket sales? $4,752
________________________
b. What is the price of an adult ticket? $11 What is the price of a student ticket? $8
________________________
c. If the ticket booth sold only adult tickets, how many would they have sold?
if only adults:
11a = 4752
a = 432 tickets
________________________
d. If the ticket booth sold only student tickets, how many would they have sold?
if only students:
8a = 4752
a = 594 tickets
What is the value of x?
Answer:
75 degree
Step-by-step explanation:
We know that a straight angle is 180 degree
and in the picture we can see an angle of 105 degree
so we get 180-105= 75 degree
Which situation could be represented by the graph
Answer:
what graph
Step-by-step explanation:
What is the solution to the missing side of the figure, rounded to the nearest tenths place?A) 16.2.B.) √261C) 16.1D.) 261
The figure appears to be a triangle with the following measures:
Opposite Side = a = 6
Adjacent Side = b = 15
Hypotenuse = c = unknown
To be able to find the measure of the unknown side, since it appears to be a right triangle, we will be using the Pythagorean Formula:
[tex]\text{ c}^2=a^2+b^2[/tex][tex]\text{ c = }\sqrt[]{a^2+b^2}[/tex][tex]\begin{gathered} \text{ c = }\sqrt[]{(6)^2_{}+(15)^2} \\ \end{gathered}[/tex][tex]\text{ = }\sqrt[]{36\text{ + 225}}[/tex][tex]\text{ = }\sqrt[]{261}[/tex][tex]\text{ c = }\sqrt[]{261}\text{ = 16.1554944214}[/tex]14. You buy a package that contains 10 1/2 cups of fruit and nut mix. How many snack bags each with 3/4 cup of fruit and nut mix can you fill from the package?
Given:
The package contains 10 1/2 cups of fruit and nut mix
When need to snack bags, each bag contain 3/4 cup
So, to find the number of bags, divide 10 1/2 by 3/4
so, the number of bags =
[tex]10\frac{1}{2}\div\frac{3}{4}=\frac{21}{2}\div\frac{3}{4}=\frac{21}{2}\cdot\frac{4}{3}=7\cdot2=14[/tex]So, the answer is: the number of bags = 14
Can someone please explain to me why -4² = -16?
Answer:
-4 x -4 = -16
4 x 4 = 16
^2 or to the power of 2 basely means 4 times itself, because 2.
For the point P(-24,-24) and Q(-19,-19), find the distance d(P,Q) and theof the midpoint M of the segment PQ,coordinates
Solution:
Given;
[tex]P(-24,-24),Q(-19,-19)[/tex]The distance d(P,Q) is;
[tex]\begin{gathered} d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \\ x_1=-24,y_1=-24,x_2=-19,y_2=-19 \\ \\ d=\sqrt{(-19-(-24))^2+(-19-(-24))^2} \\ \\ d=\sqrt{50} \\ \\ d=5\sqrt{2} \end{gathered}[/tex]Also, the midpoint, M, is;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \\ M=(\frac{-24+(-19)}{2},\frac{-24+(-19)}{2}) \\ \\ M=(-\frac{43}{2},-\frac{43}{2}) \end{gathered}[/tex]The number of infected
zombies triples every
hour. How many
zombies are there after 6
hours if one zombie was
initially infected?
Answer:
f(x) = 4(1.15)6.
Step-by-step explanation:
can someone help me with this assignment pls
The order pair (3, 14) is from the given scatter plot.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
• A scatter plot with increasing values of both variables can be said to have a positive correlation.
• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.
In the given scatter plot, the order pair with x-coordinate 3 is 14
So, the order pair is (3, 14)
Therefore, the order pair (3, 14) is from the given scatter plot.
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The aspect ratio for a computer screenis 118. If the width of the computer screen is 13.5inches. What is the begi of the mean?Answer question 1 photo attached
The aspect ratio for a computer screen is
if the width equals 13.5, then the height is:
[tex]h=\frac{13.5}{1.8}=7.5[/tex]Write the equation of the line in fully simplified slope-intercept form.
pls helpp me
Answer:
y= 1/5x -7
Step-by-step explanation:
1/5 is the slope
-7 is the y-intercept
1. If Rocco makes 18 out of 25 free throws and Graham makes 14 out of 20 free throws, who has the better free
throw record? Show why using comparable rates.
-2/3 (x-7) = 1/6 (x+1) -3
Answer: x = 9
Step-by-step explanation:
We will isolate the variable x to solve this equation.
Given:
-2/3 (x-7) = 1/6 (x+1) -3
Distribute:
-2/3x + 14/3 = 1/6 (x+1) -3
-2/3x + 14/3 = 1/6x + 1/6 -3
Combine like terms on the right side using subtraction:
-2/3x + 14/3 = 1/6x - 17/6
Subtract 1/6x from both sides of the equation:
-5/6x + 14/3 = - 17/6
Subtract 14/3 from both sides of the equation:
-5/6x = -15/2
Divide both sides of the equation by -5/6:
x = 9
octavia simplified the expression as shown explain octavia’s error and correct her work
To simplify
[tex](3x^9)^2(3x^2)^4[/tex]First of all, Octavia error can be spotted from the correct steps below
Step1: Expand the expression
[tex]3^2\times x^{9\times2}\times3^4\times x^{2\times4}=3^2\times x^{18}\times3^4\times x^8[/tex]Step2: Collect like terms
[tex]3^2\times3^4\times x^{18}\times x^8[/tex]Step 3: Simplify by using exponents laws
[tex]3^{2+4}\times x^{18+8}=3^6\times x^{26}[/tex]Step 4: Combine the terms.
The value is
[tex]729x^{26}[/tex]Her error was that she didn't apply the exponents' law properly.
One of the laws she violated was
[tex](a^b)^c=a^{b\times c}[/tex]Her mistake was that she did
[tex](a^b)^c=a^{b+c}\text{ which is wrong}[/tex]So she missed it from our step 1 above
Which of the following terms is defined as a set of all points in a planethat are a given distance from a point?O CircleO Line segmentO RayO Parallel line
Given:
A set of all points in a plane that are a given distance from a point.
Required:
To choose the correct option for the given definition.
Explanation:
A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
Final Answer:
A set of all points in a plane that are a given distance from a point is called circle.
I NEED HELP! ASAP! WILL GIVE 50 POINTS!
Answer:
Of 20,000 people that apply, 6300 actually enroll.
Step-by-step explanation:
70% of 20,000 is 14,000
45% of 14,000 is 6,300
Geometry! Just the first question:)
Hi your answers would be
a) 30 degrees
b) 65 degrees
c) 115 degrees
d) 85 degrees
e) 150 degrees
f) 30 degrees
Hope these answers help.
Answer:
5 round table pizza and amen and amen and amen and amen
Step-by-step explanation:
the program I think the banner side effects
119° 100° 88° 116° 11. Determine the value of x. A. 117° B. 59° C. 63° D. 90°
We have that the shape is a pentagon of sorts, and we will have that the sum of the internal angles of a pentagon equals 540°.
Knowing this, we will find the missing interior angle in the shape:
100° + 119° + 88° + 116° + a = 540°
Then, we will have that the missing side we named a, will have a measure of 117°.
Now, by supplementary angles, we will have the following:
117° + x = 180°
When we solve for x, we will have that is has a measure of 63°
***
You can determine the total sum of interior angles by the function:
[tex](n-2)\cdot180[/tex]Where n is the number of sides the shape has.